Evolution in predator-prey systems
Durrett, Rick
2009-01-01
We study the adaptive dynamics of predator prey systems modeled by a dynamical system in which the characteristics are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the mutational change tends to 0, the system does not exhibit long term prey coexistence and the parameters of the resident prey type converges to the solution of an ODE. When only the predators are allowed to evolve, coexistence of predators occurs. In this case, depending on the parameters being varied we see (i) the number of coexisting predators remains tight and the differences of the parameters from a reference species converge in distribution to a limit, or (ii) the number of coexisting predators tends to infinity, and we conjecture that the differences converge to a deterministic limit.
Predator-prey systems depend on a prey refuge.
Chivers, W J; Gladstone, W; Herbert, R D; Fuller, M M
2014-11-07
Models of near-exclusive predator-prey systems such as that of the Canadian lynx and snowshoe hare have included factors such as a second prey species, a Holling Type II predator response and climatic or seasonal effects to reproduce sub-sets of six signature patterns in the empirical data. We present an agent-based model which does not require the factors or constraints of previous models to reproduce all six patterns in persistent populations. Our parsimonious model represents a generalised predator and prey species with a small prey refuge. The lack of the constraints of previous models, considered to be important for those models, casts doubt on the current hypothesised mechanisms of exclusive predator-prey systems. The implication for management of the lynx, a protected species, is that maintenance of an heterogeneous environment offering natural refuge areas for the hare is the most important factor for the conservation of this species.
Xuming Huang
2009-01-01
Full Text Available We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.
Global stability of predator-prey system with alternative prey.
Sahoo, Banshidhar
2013-01-01
A predator-prey model in presence of alternative prey is proposed. Existence and local stability conditions for interior equilibrium points are derived. Global stability conditions for interior equilibrium points are also found. Bifurcation analysis is done with respect to predator's searching rate and handling time. Bifurcation analysis confirms the existence of global stability in presence of alternative prey.
Harvesting and Conversation in a Predator-Prey System
Hoekstra, Jeljer; Bergh, van den Jeroen C.J.M.
2001-01-01
Optimal harvesting of prey in a predator-prey ecosystem is studiedunder the condition that the existence of the predator has value. Predators (birds) and humans (fishers) compete for prey (shellfish). The behavior of the system is studied and conditions for optimal control are deduced. Various optim
Effects of uniform rotational flow on predator-prey system
Lee, Sang-Hee
2012-12-01
Rotational flow is often observed in lotic ecosystems, such as streams and rivers. For example, when an obstacle interrupts water flowing in a stream, energy dissipation and momentum transfer can result in the formation of rotational flow, or a vortex. In this study, I examined how rotational flow affects a predator-prey system by constructing a spatially explicit lattice model consisting of predators, prey, and plants. A predation relationship existed between the species. The species densities in the model were given as S (for predator), P (for prey), and G (for plant). A predator (prey) had a probability of giving birth to an offspring when it ate prey (plant). When a predator or prey was first introduced, or born, its health state was assigned an initial value of 20 that subsequently decreased by one with every time step. The predator (prey) was removed from the system when the health state decreased to less than zero. The degree of flow rotation was characterized by the variable, R. A higher R indicates a higher tendency that predators and prey move along circular paths. Plants were not affected by the flow because they were assumed to be attached to the streambed. Results showed that R positively affected both predator and prey survival, while its effect on plants was negligible. Flow rotation facilitated disturbances in individuals’ movements, which consequently strengthens the predator and prey relationship and prevents death from starvation. An increase in S accelerated the extinction of predators and prey.
Lijuan Chen; Junyan Xu
2009-01-01
In this paper,a set of sufficient conditions which ensure the permanence of a nonlinear periodic predator-prey system with prey dispersal and predator density-independence are obtained,where the prey species can disperse among n patches,while the density-independent predator is confined to one of the patches and cannot disperse. Our results generalize some known results.
无
2009-01-01
In this paper,a set of suffcient conditions which ensure the permanence of a nonlinear periodic predator-prey system with prey dispersal and predator density-independence are obtained,where the prey species can disperse among n patches,while the density-independent predator is confined to one of the patches and cannot disperse. Our results generalize some known results.
Wave propagation in predator-prey systems
Fu, Sheng-Chen; Tsai, Je-Chiang
2015-12-01
In this paper, we study a class of predator-prey systems of reaction-diffusion type. Specifically, we are interested in the dynamical behaviour for the solution with the initial distribution where the prey species is at the level of the carrying capacity, and the density of the predator species has compact support, or exponentially small tails near x=+/- ∞ . Numerical evidence suggests that this will lead to the formation of a pair of diverging waves propagating outwards from the initial zone. Motivated by this phenomenon, we establish the existence of a family of travelling waves with the minimum speed. Unlike the previous studies, we do not use the shooting argument to show this. Instead, we apply an iteration process based on Berestycki et al 2005 (Math Comput. Modelling 50 1385-93) to construct a set of super/sub-solutions. Since the underlying system does not enjoy the comparison principle, such a set of super/sub-solutions is not based on travelling waves, and in fact the super/sub-solutions depend on each other. With the aid of the set of super/sub-solutions, we can construct the solution of the truncated problem on the finite interval, which, via the limiting argument, can in turn generate the wave solution. There are several advantages to this approach. First, it can remove the technical assumptions on the diffusivities of the species in the existing literature. Second, this approach is of PDE type, and hence it can shed some light on the spreading phenomenon indicated by numerical simulation. In fact, we can compute the spreading speed of the predator species for a class of biologically acceptable initial distributions. Third, this approach might be applied to the study of waves in non-cooperative systems (i.e. a system without a comparison principle).
Influence of stochastic perturbation on prey-predator systems.
Rudnicki, Ryszard; Pichór, Katarzyna
2007-03-01
We analyse the influence of various stochastic perturbations on prey-predator systems. The prey-predator model is described by stochastic versions of a deterministic Lotka-Volterra system. We study long-time behaviour of both trajectories and distributions of the solutions. We indicate the differences between the deterministic and stochastic models.
Predator-prey system with strong Allee effect in prey.
Wang, Jinfeng; Shi, Junping; Wei, Junjie
2011-03-01
Global bifurcation analysis of a class of general predator-prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.
Dynamics of a Delayed Predator-prey System with Stage Structure for Predator and Prey
Liu Juan; Zhang Zi-zhen
2015-01-01
In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical be-haviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally, numerical simulations are presented to support the theoretical analysis.
Periodic Solutions of a Discrete Time Predator-Prey System
Yong-li Song; Mao-an Han
2006-01-01
In this paper, we discuss a discrete predator-prey system with a non-monotonic functional response,which models the dynamics of the prey and the predator having non-overlapping generations. By using the coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions.
Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System
Hui Zhang
2014-01-01
Full Text Available A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations.
Landscape heterogeneity shapes predation in a newly restored predator-prey system.
Kauffman, Matthew J; Varley, Nathan; Smith, Douglas W; Stahler, Daniel R; MacNulty, Daniel R; Boyce, Mark S
2007-08-01
Because some native ungulates have lived without top predators for generations, it has been uncertain whether runaway predation would occur when predators are newly restored to these systems. We show that landscape features and vegetation, which influence predator detection and capture of prey, shape large-scale patterns of predation in a newly restored predator-prey system. We analysed the spatial distribution of wolf (Canis lupus) predation on elk (Cervus elaphus) on the Northern Range of Yellowstone National Park over 10 consecutive winters. The influence of wolf distribution on kill sites diminished over the course of this study, a result that was likely caused by territorial constraints on wolf distribution. In contrast, landscape factors strongly influenced kill sites, creating distinct hunting grounds and prey refugia. Elk in this newly restored predator-prey system should be able to mediate their risk of predation by movement and habitat selection across a heterogeneous risk landscape.
The effect of prey refuge in a patchy predator-prey system.
Ma, Zhihui; Wang, Shufan; Li, Weide; Li, Zizhen
2013-05-01
In this work, we proposed a patchy predator-prey model with one patch as refuge and the other as open habitat, and incorporated prey refuge in the considered model explicitly. We applied an analytical approach to study the dynamic consequences of the simplest forms of refuge used by prey and the migration efficiency. The results have shown that the refuge used by prey and the migration efficiency play an important role in the dynamic consequences of the interacting populations and the equilibrium density of two interacting populations. This work also proposed a new approach which can incorporate prey refuge in predator-prey system explicitly.
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Chakraborty, Subhendu; Kooi, B.W.; Biswas, B.
2015-01-01
on infected populations can have both positive and negative influences on disease in prey populations. Here, we present a predator-prey system where the prey population is subjected to an infectious disease to explore the impact of predator on disease dynamics. Specifically, we investigate how...... the interference among predators affects the dynamics and structure of the predator-prey community. We perform a detailed numerical bifurcation analysis and find an unusually large variety of complex dynamics, such as, bistability, torus and chaos, in the presence of predators. We show that, depending...... on the strength of interference among predators, predators enhance or control disease outbreaks and population persistence. Moreover, the presence of multistable regimes makes the system very sensitive to perturbations and facilitates a number of regime shifts. Since, the habitat structure and the choice...
Red queen dynamics in specific predator-prey systems.
Harris, Terence; Cai, Anna Q
2015-10-01
The dynamics of a predator-prey system are studied, with a comparison of discrete and continuous strategy spaces. For a [Formula: see text] system, the average strategies used in the discrete and continuous case are shown to be the same. It is further shown that the inclusion of constant prey switching in the discrete case can have a stabilising effect and reduce the number of available predator types through extinction.
Deterministic and Stochastic Analysis of a Prey-Dependent Predator-Prey System
Maiti, Alakes; Samanta, G. P.
2005-01-01
This paper reports on studies of the deterministic and stochastic behaviours of a predator-prey system with prey-dependent response function. The first part of the paper deals with the deterministic analysis of uniform boundedness, permanence, stability and bifurcation. In the second part the reproductive and mortality factors of the prey and…
Coexistence of Predator and Prey in Intraguild Predation systems with Ontogenetic Niche Shifts
Hin, V.; Schellekens, T.; Persson, L.; Roos, A.M.
2011-01-01
In basic intraguild predation (IGP) systems, predators and prey also compete for a shared resource. Theory predicts that persistence of these systems is possible when intraguild prey is superior in competition and productivity is not too high. IGP often results from ontogenetic niche shifts, in
Cannibalism in discrete-time predator-prey systems.
Chow, Yunshyong; Jang, Sophia R-J
2012-01-01
In this study, we propose and investigate a two-stage population model with cannibalism. It is shown that cannibalism can destabilize and lower the magnitude of the interior steady state. However, it is proved that cannibalism has no effect on the persistence of the population. Based on this model, we study two systems of predator-prey interactions where the prey population is cannibalistic. A sufficient condition based on the nontrivial boundary steady state for which both populations can coexist is derived. It is found via numerical simulations that introduction of the predator population may either stabilize or destabilize the prey dynamics, depending on cannibalism coefficients and other vital parameters.
On predator-prey systems and small-gain theorems.
Leenheer, Patrick De; Angeli, David; Sontag, Eduardo D
2005-01-01
This paper deals with an almost global convergence result for Lotka-Volterra systems with predator-prey interactions. These systems can be written as (negative) feedback systems. The subsystems of the feedback loop are monotone control systems, possessing particular input-output properties. We use a small-gain theorem, adapted to a context of systems with multiple equilibrium points to obtain the desired almost global convergence result, which provides sufficient conditions to rule out oscillatory or more complicated behavior that is often observed in predator-prey systems.
Effects of a disease affecting a predator on the dynamics of a predator-prey system.
Auger, Pierre; McHich, Rachid; Chowdhury, Tanmay; Sallet, Gauthier; Tchuente, Maurice; Chattopadhyay, Joydev
2009-06-07
We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. We use the classical "aggregation method" in order to obtain a reduced equivalent model. We show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. In this latter case, the predator population tends either to a "disease-free" or to a "disease-endemic" state. Moreover, the total predator density in the disease-endemic state is greater than the predator density in the "disease-free" equilibrium (DFE).
The influence of generalist predators in spatially extended predator-prey systems
Chakraborty, Subhendu
2015-01-01
dynamics of a predator-prey system is investigated by considering two different types of generalist predators. In one case, it is considered that the predator population has an additional food source and can survive in the absence of the prey population. In the other case, the predator population...... the cases. In the presence of generalist predators, the system shows different pattern formations and spatiotemporal chaos which has important implications for ecosystem functioning not only in terms of their predictability, but also in influencing species persistence and ecosystem stability in response...
Vucetich, John A; Hebblewhite, Mark; Smith, Douglas W; Peterson, Rolf O
2011-11-01
1. Predation rate (PR) and kill rate are both fundamental statistics for understanding predation. However, relatively little is known about how these statistics relate to one another and how they relate to prey population dynamics. We assess these relationships across three systems where wolf-prey dynamics have been observed for 41 years (Isle Royale), 19 years (Banff) and 12 years (Yellowstone). 2. To provide context for this empirical assessment, we developed theoretical predictions of the relationship between kill rate and PR under a broad range of predator-prey models including predator-dependent, ratio-dependent and Lotka-Volterra dynamics. 3. The theoretical predictions indicate that kill rate can be related to PR in a variety of diverse ways (e.g. positive, negative, unrelated) that depend on the nature of predator-prey dynamics (e.g. structure of the functional response). These simulations also suggested that the ratio of predator-to-prey is a good predictor of prey growth rate. That result motivated us to assess the empirical relationship between the ratio and prey growth rate for each of the three study sites. 4. The empirical relationships indicate that PR is not well predicted by kill rate, but is better predicted by the ratio of predator-to-prey. Kill rate is also a poor predictor of prey growth rate. However, PR and ratio of predator-to-prey each explained significant portions of variation in prey growth rate for two of the three study sites. 5. Our analyses offer two general insights. First, Isle Royale, Banff and Yellowstone are similar insomuch as they all include wolves preying on large ungulates. However, they also differ in species diversity of predator and prey communities, exploitation by humans and the role of dispersal. Even with the benefit of our analysis, it remains difficult to judge whether to be more impressed by the similarities or differences. This difficulty nicely illustrates a fundamental property of ecological
Global analysis of Ivlev's type predator-prey dynamic systems
XIAO Hai-bin
2007-01-01
Consider a class of Ivlev's type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE,the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.
Stochastic Lattice Gas Model for a Predator-Prey System
Satulovsky, J E; Satulovsky, Javier; Tome, Tania
1994-01-01
We propose a stochastic lattice gas model to describe the dynamics of two animal species population, one being a predator and the other a prey. This model comprehends the mechanisms of the Lotka-Volterra model. Our analysis was performed by using a dynamical mean-field approximation and computer simulations. Our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators. For the sets of parameters used in our computer simulations, these oscillations occur at a local level. Mean-field results predict synchronized collective oscillations.
Chaotic behaviour of a predator-prey system
Kooi, B.W.; Boer, M.P.
2003-01-01
Generally a predator-prey system is modelled by two ordinary differential equations which describe the rate of changes of the biomasses. Since such a system is two-dimensional no chaotic behaviour can occur. In the popular Rosenzweig-MacArthur model, which replaced the Lotka-Volterra model, a stable
Stabilization for a Periodic Predator-Prey System
Carmen Oana Tarniceriu; Sebastian Aniţa
2007-01-01
Ã¯Â»Â¿A reaction-diffusion system modelling a predator-prey system in a periodic environment is considered. We are concerned in stabilization to zero of one of the components of the solution, via an internal control acting on a small subdomain, and in the preservation of the nonnegativity of both components.
Chaotic behaviour of a predator-prey system
Kooi, B.W.; Boer, M.P.
2003-01-01
Generally a predator-prey system is modelled by two ordinary differential equations which describe the rate of changes of the biomasses. Since such a system is two-dimensional no chaotic behaviour can occur. In the popular Rosenzweig-MacArthur model, which replaced the Lotka-Volterra model, a stable
Coexistence of predator and prey in intraguild predation systems with ontogenetic niche shifts.
Hin, Vincent; Schellekens, Tim; Persson, Lennart; de Roos, André M
2011-12-01
In basic intraguild predation (IGP) systems, predators and prey also compete for a shared resource. Theory predicts that persistence of these systems is possible when intraguild prey is superior in competition and productivity is not too high. IGP often results from ontogenetic niche shifts, in which the diet of intraguild predators changes as a result of growth in body size (life-history omnivory). As a juvenile, a life-history omnivore competes with the species that becomes its prey later in life. Competition can hence limit growth of young predators, while adult predators can suppress consumers and therewith neutralize negative effects of competition. We formulate and analyze a stage-structured model that captures both basic IGP and life-history omnivory. The model predicts increasing coexistence of predators and consumers when resource use of stage-structured predators becomes more stage specific. This coexistence depends on adult predators requiring consumer biomass for reproduction and is less likely when consumers outcompete juvenile predators, in contrast to basic IGP. Therefore, coexistence occurs when predation structures the community and competition is negligible. Consequently, equilibrium patterns over productivity resemble those of three-species food chains. Life-history omnivory thus provides a mechanism that allows intraguild predators and prey to coexist over a wide range of resource productivity.
Effects of the prey refuge distribution on a predator-prey system
Lee, Sang-Hee; Kwon, Ohsung; Song, Hark-Soo
2016-03-01
The existence of prey refuges in a predator-prey system is known to be strongly related to the ecosystem's stability. In this study, we explored how the prey refuge distribution affects the predator-prey system. To do so, we constructed a spatial lattice model to simulate an integrative predator (wolf) - prey (rabbit) - plant (grass) relationship. When a wolf (rabbit) encountered a rabbit (grass), the wolf (rabbit) tended to move to the rabbit (grass) for foraging while the rabbit tended to escape from the wolf. These behaviors were mathematically described by the degrees of willingness for hunting ( H) and escaping ( E). Initially, n refuges for prey were heterogeneously distributed in the lattice space. The heterogeneity was characterized as variable A. Higher values of A equate to higher aggregation in the refuge. We investigated the mean population density for different values of H, E, and A. To simply characterize the refuge distribution effect, we built an H-E grid map containing the population density for each species. Then, we counted the number of grids, N, with a population density ≥ 0.25. Simulation results showed that an appropriate value of A positively affected prey survival while values of A were too high had a negative effect on prey survival. The results were explained by using the trade-off between the staying time of the prey in the refuge and the cluster size of the refuge.
PERMANENCE OF A NONLINEAR DISCRETE PREDATOR-PREY SYSTEM
无
2009-01-01
In this paper,we study a nonlinear discrete predator-prey model. We obtain a set of suffcient conditions which guarantee the permanence of the system. And an example together with its numeric simulation is presented to show the feasibility of our result.
Numerical Solutions of a Fractional Predator-Prey System
Xin Baogui; Liu Yanqin
2011-01-01
We implement relatively new analytical technique, the Homotopy perturbation method, for solving nonlinear fractional partial differential equations arising in predator-prey biological population dynamics system. Numerical solutions are given, and some properties exhibit biologically reasonable dependence on the parameter values. And the fractional derivatives are described in the Caputo sense.
PERMANENCE OF A NONLINEAR DISCRETE PREDATOR-PREY SYSTEM
Yaoping Chen; Fengde Chen
2009-01-01
In this paper,we study a nonlinear discrete predator-prey model. We obtain a set of sufficient conditions which guarantee the permanence of the system. And an example together with its numeric simulation is presented to show the feasibility of our result.
Global Stability of a Predator-Prey System with Stage Structure for the Predator
Yan Ni XIAO; Lan Sun CHEN
2004-01-01
In this paper, some feasibly sufficient conditions are obtained for the global asymptotic stability of a positive steady state of a predator-prey system with stage structure for the predator by using the theory of competitive systems, compound matrices and stability of periodic orbits, and then the work of Wang [4] is improved.
Dynamics of additional food provided predator-prey system with mutually interfering predators.
Prasad, B S R V; Banerjee, Malay; Srinivasu, P D N
2013-11-01
Use of additional/alternative food source to predators is one of the widely recognised practices in the field of biological control. Both theoretical and experimental works point out that quality and quantity of additional food play a vital role in the controllability of the pest. Theoretical studies carried out previously in this direction indicate that incorporating mutual interference between predators can stabilise the system. Experimental evidence also point out that mutual interference between predators can affect the outcome of the biological control programs. In this article dynamics of additional food provided predator-prey system in the presence of mutual interference between predators has been studied. The mutual interference between predators is modelled using Beddington-DeAngelis type functional response. The system analysis highlights the role of mutual interference on the success of biological control programs when predators are provided with additional food. The model results indicate the possibility of stable coexistence of predators with low prey population levels. This is in contrast to classical predator-prey models wherein this stable co-existence at low prey population levels is not possible. This study classifies the characteristics of biological control agents and additional food (of suitable quality and quantity), permitting the eco-managers to enhance the success rate of biological control programs.
A predator-2 prey fast-slow dynamical system for rapid predator evolution
Piltz, Sofia Helena; Veerman, Frits; Maini, Philip K.
2017-01-01
We consider adaptive change of diet of a predator population that switches its feeding between two prey populations. We develop a novel 1 fast-3 slow dynamical system to describe the dynamics of the three populations amidst continuous but rapid evolution of the predator's diet choice. The two ext...
Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey
Lianwen Wang
2013-01-01
Full Text Available We investigate a periodic predator-prey system subject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanence, global attractivity, and partial extinction of system are established, respectively. It is shown that impulsive perturbations contribute to the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.
Seasonally perturbed prey-predator system with predator-dependent functional response
Gakkhar, Sunita E-mail: sungkfma@iitr.ernet.in; Naji, Raid Kamel E-mail: naj66dma@iitr.ernet.in
2003-12-01
The effect of seasonality on the prey-predator model with predator-dependent trophic function is investigated analytically as well as numerically. The effect of periodic variations is considered on two different parameters of the system: the growth rate of prey and the death rate of the predators. The two parameters may not be in the same phase. The behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that seasonality in two different parameters with or without phase difference can give rise to multiple attractors, including chaos, with variations in critical parameters.
Chakraborty, Kunal; Das, Sankha Subhra
2014-06-01
We describe a prey-predator system incorporating constant prey refuge through provision of alternative food to predators. The proposed model deals with a problem of non-selective harvesting of a prey-predator system in which both the prey and the predator species obey logistic law of growth. The long-run sustainability of an exploited system is discussed through provision of alternative food to predators. We have analyzed the variability of the system in presence of constant prey refuge and examined the stabilizing effect on predator-prey system. The steady states of the system are derived and dynamical behavior of the system is extensively analyzed around steady states. The optimal harvesting policy is formulated and solved with the help of Pontryagin's maximal principle. Our objective is to maximize the monetary social benefit through protecting the predator species from extinction, keeping the ecological balance. Results finally illustrated with the help of numerical examples.
The global stability of a delayed predator-prey system with two stage-structure
Wang Fengyan [College of Science, Jimei University, Xiamen Fujian 361021 (China)], E-mail: wangfy68@163.com; Pang Guoping [Department of Mathematics and Computer Science, Yulin Normal University, Yulin Guangxi 537000 (China)
2009-04-30
Based on the classical delayed stage-structured model and Lotka-Volterra predator-prey model, we introduce and study a delayed predator-prey system, where prey and predator have two stages, an immature stage and a mature stage. The time delays are the time lengths between the immature's birth and maturity of prey and predator species. Results on global asymptotic stability of nonnegative equilibria of the delay system are given, which generalize and suggest that good continuity exists between the predator-prey system and its corresponding stage-structured system.
A STAGE-STRUCTURED AND HARVESTING PREDATOR-PREY SYSTEM
无
2011-01-01
A predator-prey system with independent harvesting in either species and BeddingtonDeAngelis functional response is investigated. By analyzing characteristic equations and using an iterative technique,we obtain a set of easily verifiable sufficient conditions,which ensure the local and global stability of the nonnegative equilibria of the system. It is also shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Numerical simulations are carried out t...
EXTINCTION OF A DISCRETE NONLINEAR PREDATOR-PREY SYSTEM
无
2010-01-01
In this paper, we consider a discrete nonlinear predator-prey model with nonnegative coefficients bounded above and below by positive constants. We show that under some suitable assumptions the predator species is driven to extinction and the prey species x is globally attractive with any positive solution to a discrete Logistic equation.
A self-organized system of smart preys and predators
Rozenfeld, Alejandro F. [Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, UNLP, CONICET, Suc. 4, C.C. 16 (1900) La Plata (Argentina); Albano, Ezequiel V. [Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, UNLP, CONICET, Suc. 4, C.C. 16 (1900) La Plata (Argentina)]. E-mail: ealbano@inifta.unlp.edu.ar
2004-11-22
Based on the fact that, a standard prey-predator model (SPPM), exhibits irreversible phase transitions, belonging to the universality class of directed percolation (DP), between prey-predator coexistence and predator extinction [Phys. Lett. A 280 (2001) 45], a self-organized prey-predator model (SOPPM) is formulated and studied by means of extensive Monte Carlo simulations. The SOPPM is achieved defining the parameters of the SPPM as functions of the density of species. It is shown that the SOPPM self-organizes into an active state close the absorbing phase of the SPPM, and consequently their avalanche exponents also belong to the universality class of DP.
Chakraborty, Subhendu; Tiwari, P. K.; Sasmal, S.K.
2017-01-01
Additional food for predators has been considered as one of the best established techniques in integrated pest management and biological conservation programs. In natural systems, there are several other factors, e.g., prey refuge, affect the success of pest control. In this paper, we analyze a p...
Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator
Xiao Zhang
2009-01-01
Full Text Available A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.
Unique coevolutionary dynamics in a predator-prey system.
Mougi, Akihiko; Iwasa, Yoh
2011-05-21
In this paper, we study the predator-prey coevolutionary dynamics when a prey's defense and a predator's offense change in an adaptive manner, either by genetic evolution or phenotypic plasticity, or by behavioral choice. Results are: (1) The coevolutionary dynamics are more likely to be stable if the predator adapts faster than the prey. (2) The prey population size can be nearly constant but the predator population can show very large amplitude fluctuations. (3) Both populations may oscillate in antiphase. All of these are not observed when the handling time is short and the prey's density dependence is weak. (4) The population dynamics and the trait dynamics show resonance: the amplitude of the population fluctuation is the largest when the speed of adaptation is intermediate. These results may explain experimental studies with microorganisms.
An exploitation-competition system with negative effect of prey on its predator.
Wang, Yuanshi
2015-05-01
This paper considers an exploitation-competition system in which exploitation is the dominant interaction when the prey is at low density, while competition is dominant when the prey is at high density due to its negative effect on the predator. The two-species system is characterized by differential equations, which are the combination of Lotka-Volterra competitive and predator-prey models. Global dynamics of the model demonstrate some basic properties of exploitation-competition systems: (i) When the growth rate of prey is extremely small, the prey cannot promote the growth of predator. (ii) When the growth rate is small, an obligate predator can survive by preying on the prey, while a facultative predator can approach a high density by the predation. (iii) When the growth rate is intermediate, the predator can approach the maximal density by an intermediate predation. (iv) When the growth rate is large, the predator can persist only if it has a large density and its predation on the prey is big. (v) Intermediate predation is beneficial to the predator under certain parameter range, while over- or under-predation is not good. Extremely big/small predation would lead to extinction of species. Numerical simulations confirm and extend our results. Copyright © 2015 Elsevier Inc. All rights reserved.
Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting
Biwen Li; Zhenwei Li; Boshan Chen; Gan Wang
2015-01-01
A modified predator-prey biological economic system with nonselective harvesting is investigated. An important mathematical feature of the system is that the economic profit on the predator-prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. In addition, the modified model enriches the database for the predator-prey biological economic system. Finally, numeric...
Sufficient and necessary condition for the permanence of periodic predator-prey system
Jingan Cui
2004-01-01
Full Text Available We consider the permanence of a periodic predator-prey system, where the prey disperse in a two-patch environment. We assume the Volterra within-patch dynamics and provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent by using the techniques of inequality analysis. Our work improves previous relevant results.
Bifurcation and Limit Cycle of a Ratio-dependent Predator-prey System with Refuge on Prey
LIU Yan-wei; LIU Xia
2013-01-01
Influences of prey refuge on the dynamics of a predator-prey model with ratiodependent functional response are investigated.The local and global stability of positive equilibrium of the system are considered.Theoretical analysis indicates that constant refuge leads to the system undergo supercritical Hopf bifurcation twice with the birth rate of prey species changing continuously.
Nonlocal Generalized Models of Predator-Prey Systems
Kuehn, Christian
2011-01-01
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many dynamical systems in mathematical biology exhibit steady-state behaviour one also wants to understand nonlocal dynamics beyond equilibrium points. In this paper we analyze predator-prey dynamical systems and extend the method of generalized models to periodic solutions. First, we adapt the equilibrium generalized modeling approach and compute the unique Floquet multiplier of the periodic solution which depends upon so-called generalized elasticity and scale functions. We prove that these functions also have to satisfy a flow on parameter (or moduli) space. Then we use Fourier analysis to provide computable conditions for stability and the moduli space flow. The final stability analysis reduces to two discrete convolutions which can be interpreted to understand when the predator...
A predator-prey system with stage-structure for predator and nonlocal delay
Lin, Z.G.; Pedersen, Michael; Zhang, Lai
2010-01-01
This paper deals with the behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition, which describes a prey-predator model with nonlocal delay. Sufficient conditions for the global stability of each equilibrium are derived by the Lyapunov functional...
Antagonistic evolution in an aposematic predator-prey signaling system.
Speed, Michael P; Franks, Daniel W
2014-10-01
Warning signals within species, such as the bright colors of chemically defended animals, are usually considered mutualistic, monomorphic traits. Such a view is however increasingly at odds with the growing empirical literature, showing nontrivial levels of signal variation within prey populations. Key to understanding this variation, we argue, could be a recognition that toxicity levels frequently vary within populations because of environmental heterogeneity. Inequalities in defense may undermine mutualistic monomorphic signaling, causing evolutionary antagonism between loci that determine appearance of less well-defended and better defended prey forms within species. In this article, we apply a stochastic model of evolved phenotypic plasticity to the evolution of prey signals. We show that when toxicity levels vary, then antagonistic interactions can lead to evolutionary conflict between alleles at different signaling loci, causing signal evolution, "red queen-like" evolutionary chase, and one or more forms of signaling equilibria. A key prediction is that variation in the way that predators use information about toxicity levels in their attack behaviors profoundly affects the evolutionary characteristics of the prey signaling systems. Environmental variation is known to cause variation in many qualities that organisms signal; our approach may therefore have application to other signaling systems.
Evolution of Lotka-Volterra predator-prey systems under telegraph noise.
Auger, P; Du, N H; Hieu, N T
2009-10-01
In this paper we study a Lotka-Volterra predator-prey system with prey logistic growth under the telegraph noise. The telegraph noise switches at random two prey-predator models. The aim of this work is to determine the subset of omega-limit set of the system and show out the existence of a stationary distribution. We also focus on persistence of the predator and thus we look for conditions that allow persistence of the predator and prey community. We show that the asymptotic behaviour highly depends on the value of some constant lambda which is useful to make suitable predictions about the persistence of the system.
Stability Analysis of Predator-Prey System with Fuzzy Impulsive Control
Yuangan Wang
2012-01-01
Full Text Available Having attracted much attention in the past few years, predator-prey system provides a good mathematical model to present the correlation between predators and preys. This paper focuses on the robust stability of Lotka-Volterra predator-prey system with the fuzzy impulsive control model, and Takagi-Sugeno (T-S fuzzy impulsive control model as well. Via the T-S model and the Lyapunov method, the controlling conditions of the asymptotical stability and exponential stability are established. Furthermore, the numerical simulation for the Lotka-Volterra predator-prey system with impulsive effects verifies the effectiveness of the proposed methods.
Moleón, Marcos; Sánchez-Zapata, José A; Gil-Sánchez, José M; Ballesteros-Duperón, Elena; Barea-Azcón, José M; Virgós, Emilio
2012-03-01
How predators impact on prey population dynamics is still an unsolved issue for most wild predator-prey communities. When considering vertebrates, important concerns constrain a comprehensive understanding of the functioning of predator-prey relationships worldwide; e.g. studies simultaneously quantifying 'functional' and 'numerical responses' (i.e., the 'total response') are rare. The functional, the numerical, and the resulting total response (i.e., how the predator per capita intake, the population of predators and the total of prey eaten by the total predators vary with prey densities) are fundamental as they reveal the predator's ability to regulate prey population dynamics. Here, we used a multi-spatio-temporal scale approach to simultaneously explore the functional and numerical responses of a territorial predator (Bonelli's eagle Hieraaetus fasciatus) to its two main prey species (the rabbit Oryctolagus cuniculus and the red-legged partridge Alectoris rufa) during the breeding period in a Mediterranean system of south Spain. Bonelli's eagle responded functionally, but not numerically, to rabbit/partridge density changes. Type II, non-regulatory, functional responses (typical of specialist predators) offered the best fitting models for both prey. In the absence of a numerical response, Bonelli's eagle role as a regulating factor of rabbit and partridge populations seems to be weak in our study area. Simple (prey density-dependent) functional response models may well describe the short-term variation in a territorial predator's consumption rate in complex ecosystems.
Internally driven alternation of functional traits in a multispecies predator-prey system.
Tirok, Katrin; Gaedke, Ursula
2010-06-01
The individual functional traits of different species play a key role for ecosystem function in aquatic and terrestrial systems. We modeled a multispecies predator-prey system with functionally different predator and prey species based on observations of the community dynamics of ciliates and their algal prey in Lake Constance. The model accounted for differences in predator feeding preferences and prey susceptibility to predation, and for the respective trade-offs. A low food demand of the predator was connected to a high food selectivity, and a high growth rate of the prey was connected to a high vulnerability to grazing. The data and the model did not show standard uniform predator-prey cycles, but revealed both complex dynamics and a coexistence of predator and prey at high biomass levels. These dynamics resulted from internally driven alternations in species densities and involved compensatory dynamics between functionally different species. Functional diversity allowed for ongoing adaptation of the predator and prey communities to changing environmental conditions such as food composition and grazing pressure. The trade-offs determined whether compensatory or synchronous dynamics occurred which influence the variability at the community level. Compensatory dynamics were promoted by a joint carrying capacity linking the different prey species which is particularly relevant at high prey biomasses, i.e., when grazers are less efficient. In contrast, synchronization was enhanced by the coupling of the different predator and prey species via common feeding links, e.g., by a high grazing pressure of a nonselective predator. The communities had to be functionally diverse in terms of their trade-offs and their traits to yield compensatory dynamics. Rather similar predator species tended to cycle synchronously, whereas profoundly different species did not coexist. Compensatory dynamics at the community level thus required intermediately strong tradeoffs for functional
Dynamics of a Predator-Prey System with Mixed Functional Responses
Hunki Baek
2014-01-01
Full Text Available A predator-prey system with two preys and one predator is considered. Especially, two different types of functional responses, Holling type and Beddington-DeAngelis type, are adopted. First, the boundedness of system is showed. Stabilities analysis of system is investigated via some properties about equilibrium points and stabilities of two subsystems without one of the preys of system. Also, persistence conditions of system are found out and some numerical examples are illustrated to substantiate our theoretical results.
Coexistence in a One-Predator, Two-Prey System with Indirect Effects
Renato Colucci
2013-01-01
Full Text Available We study the dynamics of a one-predator, two-prey system in which the predator has an indirect effect on the preys. We show that, in presence of the indirect effect term, the system admits coexistence of the three populations while, if we disregard it, at least one of the populations goes to extinction.
Jiwei He
2007-07-01
Full Text Available In this paper, we consider a nonautonomous multispecies competition predator-prey system with Holling's type III functional response and prey supplement. It is proved that the system is uniformly persistent under some conditions. Furthermore, we show that the system has a unique positive periodic solution which is globally asymptotically stable.
Yumin Wu
2012-01-01
Full Text Available A nonautonomous discrete predator-prey system incorporating a prey refuge and Holling type II functional response is studied in this paper. A set of sufficient conditions which guarantee the persistence and global stability of the system are obtained, respectively. Our results show that if refuge is large enough then predator species will be driven to extinction due to the lack of enough food. Two examples together with their numerical simulations show the feasibility of the main results.
Permanence in Nonautonomous Predator-prey Lotka-Volterra Systems
Wu-jun Sun; Zhi-dong Teng; Yuan-hong Yu
2002-01-01
In this paper some easily verifiable sufficient conditions on the permanence of solutions for general nonautonomous two-species predator-prey model are established. These new criteria improve and extend the results given by Ma, Wang[3], Teng[4] and Teng, Yu[6].
On a predator-prey system of Gause type.
Hasík, Karel
2010-01-01
In this paper a Gause type model of interactions between predator and prey population is considered. We deal with the sufficient condition due to Kuang and Freedman in the generalized form including a kind of weight function. In a previous paper we proved that the existence of such weight function implies the uniqueness of limit cycle. In the present paper we give a new condition equivalent to the existence of a weight function (Theorem 4.4). As a consequence of our result, it is shown that some simple qualitative properties of the trophic function and the prey isocline ensure the uniqueness of limit cycle.
Zhang Long [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)], E-mail: longzhang_xj@sohu.com; Teng Zhidong [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)], E-mail: zhidong@xju.edu.cn
2008-05-15
In this paper, we study two species predator-prey Lotka-Volterra type dispersal system with periodic coefficients, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of the patches and cannot disperse. Sufficient conditions on the boundedness, permanence and existence of positive periodic solution for this system are established. The theoretical results are confirmed by a special example and numerical simulations.
A single predator multiple prey model with prey mutation
Mullan, Rory; Abernethy, Gavin M.; Glass, David H.; McCartney, Mark
2016-11-01
A multiple species predator-prey model is expanded with the introduction of a coupled map lattice for the prey, allowing the prey to mutate discretely into other prey species. The model is examined in its single predator, multiple mutating prey form. Two unimodal maps are used for the underlying dynamics of the prey species, with different predation strategies being used. Conclusions are drawn on how varying the control parameters of the model governs the overall behaviour and survival of the species. It is observed that in such a complex system, with multiple mutating prey, a large range of non-linear dynamics is possible.
Ecological conditions affect evolutionary trajectory in a predator-prey system.
Gallet, Romain; Tully, Thomas; Evans, Margaret E K
2009-03-01
The arms race of adaptation and counter adaptation in predator-prey interactions is a fascinating evolutionary dynamic with many consequences, including local adaptation and the promotion or maintenance of diversity. Although such antagonistic coevolution is suspected to be widespread in nature, experimental documentation of the process remains scant, and we have little understanding of the impact of ecological conditions. Here, we present evidence of predator-prey coevolution in a long-term experiment involving the predatory bacterium Bdellovibrio bacteriovorus and the prey Pseudomonas fluorescens, which has three morphs (SM, FS, and WS). Depending on experimentally applied disturbance regimes, the predator-prey system followed two distinct evolutionary trajectories, where the prey evolved to be either super-resistant to predation (SM morph) without counter-adaptation by the predator, or moderately resistant (FS morph), specialized to and coevolving with the predator. Although predation-resistant FS morphs suffer a cost of resistance, the evolution of extreme resistance to predation by the SM morph was apparently unconstrained by other traits (carrying capacity, growth rate). Thus we demonstrate empirically that ecological conditions can shape the evolutionary trajectory of a predator-prey system.
Zuo, Wenjie; Jiang, Daqing
2016-07-01
In this paper, we investigate the dynamics of the stochastic autonomous and non-autonomous predator-prey systems with nonlinear predator harvesting respectively. For the autonomous system, we first give the existence of the global positive solution. Then, in the case of persistence, we prove that there exists a unique stationary distribution and it has ergodicity by constructing a suitable Lyapunov function. The result shows that, the relatively weaker white noise will strengthen the stability of the system, but the stronger white noise will result in the extinction of one or two species. Particularly, for the non-autonomous periodic system, we show that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, numerical simulations illustrate our theoretical results.
A fluid mechanical model for mixing in a plankton predator-prey system
Peng, J.; Dabiri, J. O.
2009-04-01
A Lagrangian method is developed to study mixing of small particles in open flows. Particle Lagrangian Coherent Structures (pLCS) are identified as transport barriers in the dynamical systems of particles. We apply this method to a planktonic predator-prey system in which moon jellyfish Aurelia aurita uses its body motion to generate fluid currents which carry their prey to the vicinity of their capture appendages. With the flow generated by the jellyfish experimentally measured and the dynamics of prey particles in the flow described by a modified Maxey-Riley equation, we use pLCS to identify the capture region in which prey can be captured. The properties of the capture region enable analysis of the effects of several physiological and mechanical parameters on the predator-prey interaction, such as prey size, escape force, predator perception, etc. The method provides a new methodology to study dynamics and mixing of small organisms in general.
THE LIMIT CYCLES OF A KIND OF EXPLOITED PREDATOR-PREY SYSTEM
无
2006-01-01
In this paper, a kind of exploited predator-prey system is studied. By using the qualitative theory, we obtain some sufficient conditions for the existence and nonexistence of limit cycles of the system.
Kar, T K; Ghosh, Bapan
2012-08-01
In the present paper, we develop a simple two species prey-predator model in which the predator is partially coupled with alternative prey. The aim is to study the consequences of providing additional food to the predator as well as the effects of harvesting efforts applied to both the species. It is observed that the provision of alternative food to predator is not always beneficial to the system. A complete picture of the long run dynamics of the system is discussed based on the effort pair as control parameters. Optimal augmentations of prey and predator biomass at final time have been investigated by optimal control theory. Also the short and large time effects of the application of optimal control have been discussed. Finally, some numerical illustrations are given to verify our analytical results with the help of different sets of parameters.
Pattern formation induced by cross-diffusion in a predator-prey system
Sun Gui-Quan; Jin Zhen; Liu Quan-Xing; Li Li
2008-01-01
This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion.From the Turing theory,it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients.However,combined with cross-diffusion,it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations.Furthermore,nsynchrony of the predator and the prey in the space.The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator-prey system.
Zhang, Huayong; Huang, Tousheng; Dai, Liming
2015-05-01
Predator-prey interaction widely exists in nature and the research on predator-prey systems is an important field in ecology. The nonlinear dynamic characteristics of a seasonally perturbed predator-prey system are studied in this research. To study the nonlinear characteristics affected by a wide variety of system parameters, the PR approach is employed and periodic, quasiperiodic, chaotic behaviors and the behaviors between period and quasiperiod are found in the system. Periodic-quasiperiodic-chaotic region diagrams are generated for analyzing the global characteristics of the predator-prey system with desired ranges of system parameters. The ecological significances of the dynamical characteristics are discussed and compared with the theoretical research results existing in the literature. The approach of this research demonstrates effectiveness and efficiency of PR method in analyzing the complex dynamical characteristics of nonlinear ecological systems.
Optimal Harvesting and Stability for a Predator-prey System with Stage Structure
Xin-yu Song; Lan-sun Chen
2002-01-01
The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.
Existence of chaos in two-prey, one-predator system
Gakkhar, S
2003-01-01
A two-prey, one-predator model incorporating nonlinear functional response is investigated analytically as well as numerically. The system appears to exhibit chaos for a range of parametric values when long time behavior studied.
Existence of chaos in two-prey, one-predator system
Gakkhar, Sunita E-mail: sungkfma@isc.iitr.ernet.in; Naji, Ra' id Kamel E-mail: naj66dma@isc.iitr.ernet.in
2003-08-01
A two-prey, one-predator model incorporating nonlinear functional response is investigated analytically as well as numerically. The system appears to exhibit chaos for a range of parametric values when long time behavior studied.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
无
2008-01-01
In this paper, a set of sufficient conditions which ensure the permanence of a periodic predator-prey system with dispersal and general Holling type functional response are obtained. Our results generalize some known results.
POSITIVE PERIODIC SOLUTIONS TO NEUTRAL RATIO-DEPENDENT PREDATOR-PREY SYSTEM
无
2012-01-01
Using Mawhin's continuation theorem of coincidence degree theory,the existenceof periodic solutions to a neutral ratio-dependent predator-prey system is considered.The results in this paper generalize the corresponding results of the known literature.
Periodic Solutions of Periodic Delay Predator-Prey System with Nonmonotonic Functional Response
宋永利; 韩茂安
2003-01-01
By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for theexistence of positive periodic solutions of a delayed predator-prey system with nonmonotonic functional response ina periodic environment.
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge.
Chang, Xiaoyuan; Wei, Junjie
2013-08-01
A diffusive predator-prey model with Holling type II functional response and the no-flux boundary condition incorporating a constant prey refuge is considered. Globally asymptotically stability of the positive equilibrium is obtained. Regarding the constant number of prey refuge m as a bifurcation parameter, by analyzing the distribution of the eigenvalues, the existence of Hopf bifurcation is given. Employing the center manifold theory and normal form method, an algorithm for determining the properties of the Hopf bifurcation is derived. Some numerical simulations for illustrating the analysis results are carried out.
PERMANENCE OF ASYMPTOTICALLY PERIODIC MULTISPECIES LOTKA-VOLTERRA COMPETITION PREDATOR-PREY SYSTEM
无
2006-01-01
In this paper, we consider the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding results given by Peng and Chen [1], Teng and Li [2], Zhao and Chen [3]. Also, we obtain the conditions which ensure the permanence and global attractivity of asymptotically periodic multispecies competition predator-prey system.
Permanence of a stage-structured predator-prey system with a class of functional responses.
Ma, Zhihui; Wang, Shufan; Wang, Wenting; Li, Zizhen
2011-12-01
A stage-structured predator-prey system incorporating a class of functional responses is presented in this article. By analyzing the system and using the standard comparison theorem, the sufficient conditions are derived for permanence of the system and non-permanence of predators.
STABILITY OF A PREDATOR-PREY SYSTEM WITH PREY TAXIS IN A GENERAL CLASS OF FUNCTIONAL RESPONSES
M.YOUSEFNEZHAD; S.A. MOHAMMADI
2016-01-01
In this paper, a diffusive predator-prey system with general functional responses and prey-tactic sensitivities is studied. Providing such generality, we construct a Lyapunov function and we show that the positive constant steady state is locally and globally asymp-totically stable. With an eye on the biological interpretations, a numerical simulation is performed to illustrate the feasibility of the analytical findings.
A Time Delay Predator-Prey System with Three-Stage-Structure
Gao, Qiaoqin; Jin, Zhen
2014-01-01
A predator-prey system was studied that has a discrete delay, stage-structure, and Beddington-DeAngelis functional response, where predator species has three stages, immature, mature, and old age stages. By using of Mawhin's continuous theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution. PMID:25143982
A time delay predator-prey system with three-stage-structure.
Gao, Qiaoqin; Jin, Zhen
2014-01-01
A predator-prey system was studied that has a discrete delay, stage-structure, and Beddington-DeAngelis functional response, where predator species has three stages, immature, mature, and old age stages. By using of Mawhin's continuous theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution.
Coevolution can reverse predator-prey cycles.
Cortez, Michael H; Weitz, Joshua S
2014-05-20
A hallmark of Lotka-Volterra models, and other ecological models of predator-prey interactions, is that in predator-prey cycles, peaks in prey abundance precede peaks in predator abundance. Such models typically assume that species life history traits are fixed over ecologically relevant time scales. However, the coevolution of predator and prey traits has been shown to alter the community dynamics of natural systems, leading to novel dynamics including antiphase and cryptic cycles. Here, using an eco-coevolutionary model, we show that predator-prey coevolution can also drive population cycles where the opposite of canonical Lotka-Volterra oscillations occurs: predator peaks precede prey peaks. These reversed cycles arise when selection favors extreme phenotypes, predator offense is costly, and prey defense is effective against low-offense predators. We present multiple datasets from phage-cholera, mink-muskrat, and gyrfalcon-rock ptarmigan systems that exhibit reversed-peak ordering. Our results suggest that such cycles are a potential signature of predator-prey coevolution and reveal unique ways in which predator-prey coevolution can shape, and possibly reverse, community dynamics.
Emergent impacts of cannibalism and size refuges in prey on intraguild predation systems.
Rudolf, Volker H W; Armstrong, Joanna
2008-10-01
Many organisms undergo ontogenetic niche shifts due to considerable changes in size during their development. These ontogenetic shifts can alter the trophic position of individuals, the type and strength of ecological interactions across species, and allow for cannibalism within species. In this study we ask if and how the interaction of a size refuge and cannibalism in the prey alters the dynamics of intraguild predation (IGP) systems. By manipulating the composition of large cannibalistic (Aeshna umbrosa) and predatory (Anax junius) dragonfly larvae in mesocosms we show that the interaction of cannibals and predators was non-linear and increased the survival of prey. The structure of the final resource community shared by prey and predator differed between small and large dragonfly treatments but not within size classes across species. In general, the small prey stage showed similar shifts in microhabitat use and refuge use when exposed to either conspecific cannibals or predators, while large cannibals showed no clear anti-predator response. However, further behavioral experiments revealed that specific behavioral components, such as distances between individuals or number of movements, differed when individuals were exposed to either cannibals or predators. This indicates that individuals discriminated between conspecific or heterospecific predators. Furthermore, in similar experiments large cannibals and predators showed different behaviors when exposed to conspecifics rather than to each other. These changes in behavior are consistent with the observed increase in prey survival. In general, the results indicate that cannibalism and ontogenetic niche shifts can result in behavior-mediated indirect interactions that reduce the impact of the predator on the mortality of its prey and alter the interactions of IGP systems. However, they also indicate that size is not the sole determinant and that we also need to account for the species identity when predicting the
Dynamic Behaviors of a Discrete Periodic Predator-Prey-Mutualist System
Liya Yang
2015-01-01
Full Text Available A nonautonomous discrete predator-prey-mutualist system is proposed and studied in this paper. Sufficient conditions which ensure the permanence and existence of a unique globally stable periodic solution are obtained. We also investigate the extinction property of the predator species; our results indicate that if the cooperative effect between the prey and mutualist species is large enough, then the predator species will be driven to extinction due to the lack of enough food. Two examples together with numerical simulations show the feasibility of the main results.
Spatiotemporal complexity of a predator-prey system with the effect of noise and external forcing
Rao Feng [Institute of Nonlinear Analysis, College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035 (China); Wang Weiming [Institute of Nonlinear Analysis, College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035 (China)], E-mail: weimingwang2003@163.com; Li Zhenqing [Laboratory of Quantitative Vegetation Ecology, Institute of Botany, Chinese Academy of Sciences, Beijing 100093 (China)
2009-08-30
In this paper, we present a spatial version of the Ivlev-type predator-prey model which contains some important factors, such as noise on predator, external periodic forcing and diffusion processes on both predator and prey. From the numerical results, we know that noise or external periodic forcing can induce instability and enhance the oscillation of the species density, and the cooperation between noise and external periodic forcing inherent to the deterministic dynamics of periodically driven models gives rise to the appearance of a rich transport phenomenology. Furthermore, we demonstrate that the spatially extended system exhibits a resonant patterns and frequency-locking phenomena. Our results show that noise and external periodic forcing play a prominent role in the predator-prey model.
Predator interference and stability of predator-prey dynamics.
Přibylová, Lenka; Berec, Luděk
2015-08-01
Predator interference, that is, a decline in the per predator consumption rate as predator density increases, is generally thought to promote predator-prey stability. Indeed, this has been demonstrated in many theoretical studies on predator-prey dynamics. In virtually all of these studies, the stabilization role is demonstrated as a weakening of the paradox of enrichment. With predator interference, stable limit cycles that appear as a result of environmental enrichment occur for higher values of the environmental carrying capacity of prey, and even a complete absence of the limit cycles can happen. Here we study predator-prey dynamics using the Rosenzweig-MacArthur-like model in which the Holling type II functional response has been replaced by a predator-dependent family which generalizes many of the commonly used descriptions of predator interference. By means of a bifurcation analysis we show that sufficiently strong predator interference may bring about another stabilizing mechanism. In particular, hysteresis combined with (dis)appearance of stable limit cycles imply abrupt increases in both the prey and predator densities and enhanced persistence and resilience of the predator-prey system. We encourage refitting the previously collected data on predator consumption rates as well as for conducting further predation experiments to see what functional response from the explored family is the most appropriate.
Aerosol-cloud-precipitation system as a predator-prey problem.
Koren, Ilan; Feingold, Graham
2011-07-26
We show that the aerosol-cloud-precipitation system exhibits characteristics of the predator-prey problem in the field of population dynamics. Both a detailed large eddy simulation of the dynamics and microphysics of a precipitating shallow boundary layer cloud system and a simpler model built upon basic physical principles, reproduce predator-prey behavior with rain acting as the predator and cloud as the prey. The aerosol is shown to modulate the predator-prey response. Steady-state solution to the proposed model shows the known existence of bistability in cloudiness. Three regimes are identified in the time-dependent solutions: (i) the weakly precipitating regime where cloud and rain coexist in a quasi steady state; (ii) the moderately drizzling regime where limit-cycle behavior in the cloud and rain fields is produced; and (iii) the heavily precipitating clouds where collapse of the boundary layer is predicted. The manifestation of predator-prey behavior in the aerosol-cloud-precipitation system is a further example of the self-organizing properties of the system and suggests that exploiting principles of population dynamics may help reduce complex aerosol-cloud-rain interactions to a more tractable problem.
Revisiting the Stability of Spatially Heterogeneous Predator-Prey Systems Under Eutrophication.
Farkas, J Z; Morozov, A Yu; Arashkevich, E G; Nikishina, A
2015-10-01
We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than on the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator-prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to 'infinity'. We investigate two main scenarios: (1) the spatial gradient of the growth rate is due to abiotic factors only, and (2) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator-prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an 'unlimited' carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism. These results highlight the generality of the stabilization mechanisms we find in spatially structured predator-prey ecological systems in a heterogeneous environment.
Rank One Strange Attractors in Periodically Kicked Predator-Prey System with Time-Delay
Yang, Wenjie; Lin, Yiping; Dai, Yunxian; Zhao, Huitao
2016-06-01
This paper is devoted to the study of the problem of rank one strange attractor in a periodically kicked predator-prey system with time-delay. Our discussion is based on the theory of rank one maps formulated by Wang and Young. Firstly, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when the delayed system undergoes a Hopf bifurcation and encounters an external periodic force. Then we use the theory to the periodically kicked predator-prey system with delay, deriving the conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations.
Turing Patterns in a Predator-Prey System with Self-Diffusion
Hongwei Yin
2013-01-01
Full Text Available For a predator-prey system, cross-diffusion has been confirmed to emerge Turing patterns. However, in the real world, the tendency for prey and predators moving along the direction of lower density of their own species, called self-diffusion, should be considered. For this, we investigate Turing instability for a predator-prey system with nonlinear diffusion terms including the normal diffusion, cross-diffusion, and self-diffusion. A sufficient condition of Turing instability for this system is obtained by analyzing the linear stability of spatial homogeneous equilibrium state of this model. A series of numerical simulations reveal Turing parameter regions of the interaction of diffusion parameters. According to these regions, we further demonstrate dispersion relations and spatial patterns. Our results indicate that self-diffusion plays an important role in the spatial patterns.
Hopf bifurcation of a ratio-dependent predator-prey system with time delay
Celik, Canan [TOBB Economics and Technology University, Faculty of Arts and Sciences, Department of Mathematics, Soeguetoezue 06560, Ankara (Turkey)], E-mail: canan.celik@etu.tr
2009-11-15
In this paper, we consider a ratio dependent predator-prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.
The dynamical complexity of a Ivlev-type prey-predator system with impulsive effect
Wang Hailing [Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China)], E-mail: wanglingdang@163.com; Wang Weiming [School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035 (China)], E-mail: weimingwang2003@163.com
2008-11-15
Based on the classical predator-prey system with Ivlev-type functional response, an impulsive differential equations to model the process of periodic perturbations on the predator at different fixed time is established. It proves that there exists a locally asymptotically stable prey-eradication periodic solution when the impulse period is less than some critical value, and otherwise, the system can be permanent. Numerical results show that the system considered has more complicated dynamics. such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, symmetry-breaking pitchfork bifurcation and crises, etc.
Bayesian inference for functional response in a stochastic predator-prey system.
Gilioli, Gianni; Pasquali, Sara; Ruggeri, Fabrizio
2008-02-01
We present a Bayesian method for functional response parameter estimation starting from time series of field data on predator-prey dynamics. Population dynamics is described by a system of stochastic differential equations in which behavioral stochasticities are represented by noise terms affecting each population as well as their interaction. We focus on the estimation of a behavioral parameter appearing in the functional response of predator to prey abundance when a small number of observations is available. To deal with small sample sizes, latent data are introduced between each pair of field observations and are considered as missing data. The method is applied to both simulated and observational data. The results obtained using different numbers of latent data are compared with those achieved following a frequentist approach. As a case study, we consider an acarine predator-prey system relevant to biological control problems.
Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations
Xianning Liu
2012-01-01
Full Text Available A general predator-prey system is studied in a scheme where there is periodic impulsive perturbations. This scheme has the potential to protect the predator from extinction but under some conditions may also serve to lead to extinction of the prey. Conditions for extinction and permanence are obtained via the comparison methods involving monotone theory of impulsive systems and multiple Liapunov functions, which establish explicit bounds on solutions. The existence of a positive periodic solution is also studied by the bifurcation theory. Application is given to a Lotka-Volterra predator-prey system with periodic impulsive immigration of the predator. It is shown that the results are quite different from the corresponding system without impulsive immigration, where extinction of the prey can never be achieved. The prey will be extinct or permanent independent of whether the system without impulsive effect immigration is permanent or not. The model and its results suggest an approach of pest control which proves more effective than the classical one.
Spatial Patterns of a Predator-Prey System of Leslie Type with Time Delay
Wang, Caiyun; Chang, Lili; Liu, Huifeng
2016-01-01
Time delay due to maturation time, capturing time or other reasons widely exists in biological systems. In this paper, a predator-prey system of Leslie type with diffusion and time delay is studied based on mathematical analysis and numerical simulations. Conditions for both delay induced and diffusion induced Turing instability are obtained by using bifurcation theory. Furthermore, a series of numerical simulations are performed to illustrate the spatial patterns, which reveal the information of density changes of both prey and predator populations. The obtained results show that the interaction between diffusion and time delay may give rise to rich dynamics in ecosystems. PMID:26930573
Spatial Patterns of a Predator-Prey System of Leslie Type with Time Delay.
Wang, Caiyun; Chang, Lili; Liu, Huifeng
2016-01-01
Time delay due to maturation time, capturing time or other reasons widely exists in biological systems. In this paper, a predator-prey system of Leslie type with diffusion and time delay is studied based on mathematical analysis and numerical simulations. Conditions for both delay induced and diffusion induced Turing instability are obtained by using bifurcation theory. Furthermore, a series of numerical simulations are performed to illustrate the spatial patterns, which reveal the information of density changes of both prey and predator populations. The obtained results show that the interaction between diffusion and time delay may give rise to rich dynamics in ecosystems.
Spatial Patterns of a Predator-Prey System of Leslie Type with Time Delay.
Caiyun Wang
Full Text Available Time delay due to maturation time, capturing time or other reasons widely exists in biological systems. In this paper, a predator-prey system of Leslie type with diffusion and time delay is studied based on mathematical analysis and numerical simulations. Conditions for both delay induced and diffusion induced Turing instability are obtained by using bifurcation theory. Furthermore, a series of numerical simulations are performed to illustrate the spatial patterns, which reveal the information of density changes of both prey and predator populations. The obtained results show that the interaction between diffusion and time delay may give rise to rich dynamics in ecosystems.
Shuang Li
2015-06-01
Full Text Available This article concerns the existence of traveling wavefronts for a nonlocal diffusive predator-prey system with functional response of Holling type II. We first establish the existence principle for the system with a general functional response by using a fixed point theorem and upper-lower solution technique. We apply this result to a predator-prey model with Holling type II functional response. We deduce the existence of traveling wavefronts that connect the zero equilibrium and the positive equilibrium.
Abdoul R. Ghotbi
2008-01-01
Full Text Available Due to wide range of interest in use of bioeconomic models to gain insight into the scientific management of renewable resources like fisheries and forestry, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting. The results are compared with the results obtained by Adomian decomposition method. The results show that, in new model, there are less computations needed in comparison to Adomian decomposition method.
Zheyan Zhou
2011-01-01
Full Text Available We propose a discrete multispecies cooperation and competition predator-prey systems. For general nonautonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained; for periodic case, sufficient conditions which ensure the existence of a globally stable positive periodic solution of the system are obtained.
Lili Liu
2011-01-01
Full Text Available Based on a predator-prey differential system with continuously distributed delays, we derive a corresponding difference version by using the method of a discretization technique. A good understanding of permanence of system and global attractivity of positive solutions of system is gained. An example and its numerical simulations are presented to substantiate our theoretical results.
Simulation and analysis of a model dinoflagellate predator-prey system
Mazzoleni, M. J.; Antonelli, T.; Coyne, K. J.; Rossi, L. F.
2015-12-01
This paper analyzes the dynamics of a model dinoflagellate predator-prey system and uses simulations to validate theoretical and experimental studies. A simple model for predator-prey interactions is derived by drawing upon analogies from chemical kinetics. This model is then modified to account for inefficiencies in predation. Simulation results are shown to closely match the model predictions. Additional simulations are then run which are based on experimental observations of predatory dinoflagellate behavior, and this study specifically investigates how the predatory dinoflagellate Karlodinium veneficum uses toxins to immobilize its prey and increase its feeding rate. These simulations account for complex dynamics that were not included in the basic models, and the results from these computational simulations closely match the experimentally observed predatory behavior of K. veneficum and reinforce the notion that predatory dinoflagellates utilize toxins to increase their feeding rate.
PERIODIC SOLUTION TO A DELAYED PREDATOR-PREY SYSTEM WITH STAGE STRUCTURE AND DISPERSION
无
2011-01-01
In this paper,a delayed two-species predator-prey system with stage structure and diffiusion is investigated. Based on the continuation theorem of coincidence degree theory,the suficient conditions for the existence of positive ω-periodic solution to the system are derived. The numerical simulation of an example verifies our main result.
Hopf bifurcation in a predator-prey system with discrete and distributed delays
Yang Yu [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)], E-mail: yuy1981@126.com; Ye Jin [School of Computer Science and Technology, Donghua University, Shanghai 200051 (China)], E-mail: miniyejin@yahoo.com.cn
2009-10-15
In this paper, a predator-prey system with discrete and distributed delays is considered. By regarding the delay as the bifurcation parameter and analyzing the associated characteristic equation of the original system at the positive equilibrium, it is found that Hopf bifurcations occur when the delay passes through a certain critical value. Finally, numerical simulations are given to support our theoretical results.
Kar, T K; Chattopadhyay, S K
2010-01-01
Within the framework of a general equilibrium model we study the long-run dynamics of a prey-predator model in the presence of an alternative prey. Our results show that sustainability, i.e. a positive value of the population in the long run, essentially depends on individual harvesting efforts and digesting factors relative to alternative prey. A detailed bifurcation analysis evidences the richness of possible long-run dynamics. Our model clearly shows that the role of an alternative prey must be taken into consideration when studying prey-predator dynamics.
Kaihong Zhao
2011-04-01
Full Text Available Using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of $2^{n+m}$ positive periodic solutions for a non-autonomous Lotka-Volterra network-like predator-prey system with harvesting terms. Here n and m denote the number of prey and predator species respectively. An example is given to illustrate our results.
Zhang, X; Wu, Z; Zhou, T
2016-01-01
A predator-prey discrete-time model with Holling-IV functional response and distributed delays is investigated in this paper. By using the comparison theorem of the difference equation and some analysis technique, some sufficient conditions are obtained for the permanence of the discrete predator-prey system. Two examples are given to illustrate the feasibility of the obtained result.
STATIONARY STRUCTURES FOR A WEAKLY COUPLED ELLIPTIC SYSTEM ARISING IN TWO-PREDATOR, TWO-PREY MODELS
严平; 林支桂
2001-01-01
Weakly-coupled elliptic system arising in the two-predator, two-prey model is discussed. It is proved that there is no non-constant solution if diffusions or inter-specific competitions are strong, or if the intrinsic growths of the prey are slow and the intrinsic drop rates of predator are fast.
Global bifurcation analysis and pattern formation in homogeneous diffusive predator-prey systems
Wang, Jinfeng; Wei, Junjie; Shi, Junping
2016-02-01
The dynamics of a general diffusive predator-prey system is considered. Existence and nonexistence of non-constant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as non-constant steady state solutions are studied.
Bifurcation Analysis for a Delayed Predator-Prey System with Stage Structure
Jiang Zhichao
2010-01-01
Full Text Available Abstract A delayed predator-prey system with stage structure is investigated. The existence and stability of equilibria are obtained. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the normal form and the center manifold theory. Finally, a numerical example supporting the theoretical analysis is given.
LOCAL AND GLOBAL HOPF BIFURCATIONS FOR A PREDATOR-PREY SYSTEM WITH TWO DELAYS
无
2006-01-01
In this paper, the Leslie predator-prey system with two delays is studied. The stability of the positive equilibrium is discussed by analyzing the associated characteristic transcendental equation. The direction and stability of the bifurcating periodic solutions are determined by applying the center manifold theorem and normal form theory. The conditions to guarantee the global existence of periodic solutions are given.
Global stability analysis of a ratio-dependent predator-prey system
Lu Tie-jun; WANG Mei-juan; LIU Yan
2008-01-01
A ratio dependent predator-prey system with Holling type III functional response is considered.A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymptotic stability of the positive equilibrium.The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.
PERIODICITY IN A DELAYED SEMI-RATIO-DEPENDENT PREDATOR-PREY SYSTEM
DingXiaoquan
2005-01-01
A delayed semi-ratio-dependent predator-prey system in a periodic environment is investigated in this paper. By using a continuation theorem based on Gaines and Mawhin's coincidence degree,the global existence of positive periodic solution is studied. A set of easily verifiable sufficient conditions are obtained.
Bionomic Exploitation of a Ratio-Dependent Predator-Prey System
Maiti, Alakes; Patra, Bibek; Samanta, G. P.
2008-01-01
The present article deals with the problem of combined harvesting of a Michaelis-Menten-type ratio-dependent predator-prey system. The problem of determining the optimal harvest policy is solved by invoking Pontryagin's Maximum Principle. Dynamic optimization of the harvest policy is studied by taking the combined harvest effort as a dynamic…
PERIODIC SOLUTIONS FOR A DISCRETE TIME RATIO-DEPENDENT TWO PREDATOR-ONE PREY SYSTEM
柏灵; 范猛; 王克
2004-01-01
In this paper, we consider a three-species ratio-dependent predator-prey model governed by difference equations with periodic coefficients. By using the method of coincidence degree, we discuss the existence of positive periodic solutions of this system, a set of easily verifiable sufficient conditions are derived.
Stability and Hopf bifurcation in a ratio-dependent predator-prey system with stage structure
Xu Rui [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang 050003, Hebei Province (China); Department of Applied Mathematics, School of Science, Xi' an Jiaotong University, Xi' an 710049 (China)], E-mail: rxu88@yahoo.com.cn; Ma Zhien [Department of Applied Mathematics, School of Science, Xi' an Jiaotong University, Xi' an 710049 (China)
2008-11-15
A ratio-dependent predator-prey model with stage structure for the predator and time delay due to the gestation of the predator is investigated. By analyzing the characteristic equations, the local stability of a positive equilibrium and a boundary equilibrium is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium when {tau} = {tau}{sub 0}. By using an iteration technique, sufficient conditions are derived for the global attractivity of the positive equilibrium. By comparison arguments, sufficient conditions are obtained for the global stability of the boundary equilibrium. Numerical simulations are carried out to illustrate the main results.
Spatiotemporal dynamics of the epidemic transmission in a predator-prey system.
Su, Min; Hui, Cang; Zhang, Yanyu; Li, Zizhen
2008-11-01
Epidemic transmission is one of the critical density-dependent mechanisms that affect species viability and dynamics. In a predator-prey system, epidemic transmission can strongly affect the success probability of hunting, especially for social animals. Predators, therefore, will suffer from the positive density-dependence, i.e., Allee effect, due to epidemic transmission in the population. The rate of species contacting the epidemic, especially for those endangered or invasive, has largely increased due to the habitat destruction caused by anthropogenic disturbance. Using ordinary differential equations and cellular automata, we here explored the epidemic transmission in a predator-prey system. Results show that a moderate Allee effect will destabilize the dynamics, but it is not true for the extreme Allee effect (weak or strong). The predator-prey dynamics amazingly stabilize by the extreme Allee effect. Predators suffer the most from the epidemic disease at moderate transmission probability. Counter-intuitively, habitat destruction will benefit the control of the epidemic disease. The demographic stochasticity dramatically influences the spatial distribution of the system. The spatial distribution changes from oil-bubble-like (due to local interaction) to aggregated spatially scattered points (due to local interaction and demographic stochasticity). It indicates the possibility of using human disturbance in habitat as a potential epidemic-control method in conservation.
Lehmann, Kenna D S; Goldman, Brian W; Dworkin, Ian; Bryson, David M; Wagner, Aaron P
2014-01-01
Current theory suggests that many signaling systems evolved from preexisting cues. In aposematic systems, prey warning signals benefit both predator and prey. When the signal is highly beneficial, a third species often evolves to mimic the toxic species, exploiting the signaling system for its own protection. We investigated the evolutionary dynamics of predator cue utilization and prey signaling in a digital predator-prey system in which prey could evolve to alter their appearance to mimic poison-free or poisonous prey. In predators, we observed rapid evolution of cue recognition (i.e. active behavioral responses) when presented with sufficiently poisonous prey. In addition, active signaling (i.e. mimicry) evolved in prey under all conditions that led to cue utilization. Thus we show that despite imperfect and dishonest signaling, given a high cost of consuming poisonous prey, complex systems of interspecific communication can evolve via predator cue recognition and prey signal manipulation. This provides evidence supporting hypotheses that cues may serve as stepping-stones in the evolution of more advanced communication and signaling systems that incorporate information about the environment.
Kenna D S Lehmann
Full Text Available Current theory suggests that many signaling systems evolved from preexisting cues. In aposematic systems, prey warning signals benefit both predator and prey. When the signal is highly beneficial, a third species often evolves to mimic the toxic species, exploiting the signaling system for its own protection. We investigated the evolutionary dynamics of predator cue utilization and prey signaling in a digital predator-prey system in which prey could evolve to alter their appearance to mimic poison-free or poisonous prey. In predators, we observed rapid evolution of cue recognition (i.e. active behavioral responses when presented with sufficiently poisonous prey. In addition, active signaling (i.e. mimicry evolved in prey under all conditions that led to cue utilization. Thus we show that despite imperfect and dishonest signaling, given a high cost of consuming poisonous prey, complex systems of interspecific communication can evolve via predator cue recognition and prey signal manipulation. This provides evidence supporting hypotheses that cues may serve as stepping-stones in the evolution of more advanced communication and signaling systems that incorporate information about the environment.
Critical and oscillatory behavior of a system of smart preys and predators
Rozenfeld, Alejandro F.; Albano, Ezequiel V.
2001-06-01
It is shown that a system of smart preys and predators exhibits irreversible phase transitions between a regime of prey-predator coexistence and an state where predator extinction is observed. Within the coexistence regime, the system exhibits a transition between a regime where the densities of species remain constant and another with self-sustained oscillations, respectively. This transition is located by means of a combined treatment involving finite-size scaling and Fourier transforms. Furthermore, it is shown that the transition can be rationalized in terms of the standard percolation theory. The existence of an oscillatory regime in the thermodynamic limit, which is in contrast to previous findings of Boccara [Phys. Rev. E >50, 4531 (1994)], may be due to subtle differences between the studied models.
Allee effect in a discrete-time predator-prey system
Celik, Canan [TOBB Economics and Technology University, Faculty of Arts and Sciences, Department of Mathematics, Soeguetoezue 06530, Ankara (Turkey)], E-mail: canan.celik@etu.edu.tr; Duman, Oktay [TOBB Economics and Technology University, Faculty of Arts and Sciences, Department of Mathematics, Soeguetoezue 06530, Ankara (Turkey)], E-mail: oduman@etu.edu.tr
2009-05-30
In this paper, we study the stability of a discrete-time predator-prey system with and without Allee effect. By analyzing both systems, we first obtain local stability conditions of the equilibrium points without the Allee effect and then exhibit the impact of the Allee effect on stability when it is imposed on prey population. We also show the stabilizing effect of Allee effect by numerical simulations and verify that when the prey population is subject to an Allee effect, the trajectory of the solutions approximates to the corresponding equilibrium point much faster. Furthermore, for some fixed parameter values satisfying necessary conditions, we show that the corresponding equilibrium point moves from instability to stability under the Allee effect on prey population.
Stochastic Predator-Prey System Subject to Lévy Jumps
Xinzhu Meng
2016-01-01
Full Text Available This paper investigates a new nonautonomous impulsive stochastic predator-prey system with the omnivorous predator. First, we show that the system has a unique global positive solution for any given initial positive value. Second, the extinction of the system under some appropriate conditions is explored. In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. Simulations are also carried out to illustrate our theoretical analysis conclusions.
A non-autonomous stochastic predator-prey model.
Buonocore, Aniello; Caputo, Luigia; Pirozzi, Enrica; Nobile, Amelia G
2014-04-01
The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey. By introducing random variations in both prey birth and predator death rates, a stochastic model for the predator-prey-like system in a random environment is proposed and investigated. The corresponding Fokker-Planck equation is solved to obtain the joint probability density for the prey and predator populations and the marginal probability densities. The asymptotic behavior of the predator-prey stochastic model is also analyzed.
Dynamics of a periodic Watt-type predator-prey system with impulsive effect
Wang Xiaoqin [Faculty of Science, Shaanxi University of Science and Technology, Xianyang, Shaanxi 712081 (China)], E-mail: wangxiaoqin@sust.edu.cn; Wang Weiming [School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035 (China)], E-mail: weimingwang2003@163.com; Lin Xiaolin [Faculty of Science, Shaanxi University of Science and Technology, Xianyang, Shaanxi 712081 (China)
2009-02-15
In this paper, an impulsive periodic predator-prey system with Watt-type functional response is investigated. By using the Floquet theory of linear periodic impulsive equation, the stability conditions for the prey-eradication positive periodic solution are given, and the boundedness of the system is proved. By the method of coincidence degree, the sufficient conditions for the existence of at least one strictly positive periodic solution are obtained. Furthermore, we give numerical analysis to confirm our theoretical results. It will be useful for ecosystem control.
Stability and Hopf bifurcation in a symmetric Lotka-Volterra predator-prey system with delays
Jing Xia
2013-01-01
Full Text Available This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the Hopf bifurcation. Numerical simulations suggest an existence of Hopf bifurcation near a critical value of time delay.
REGION QUALITATIVE ANALYSIS OF PREDATOR-PREY SYSTEMS ON TIME SCALES
无
2008-01-01
We first investigate some basic properties of dynamic equations on time scales,and propose contained curves to describe the jump direction of the discrete points.Then we perform qualitative analysis regarding the planar predator-prey systems on time scales,thereby obtain two theorems of this system.At last,we emulate application examples to discuss the parameters of the system.
Control problems of an age-dependent predator-prey system
HE Ze-rong; WANG Hai-tao
2009-01-01
This paper is concerned with optimal harvesting problems for a system consisting of two populations with age-structure and interaction of predator-prey. Existence and uniqueness of non-negative solutions to the system and the continuous dependence of solutions on control variables are investigated. Existence of optimal policy is discussed, optimality conditions are derived by means of normal cone and adjoint system techniques.
食饵具有阶段结构的捕食-食饵系统的动力学行为%Dynamic Behavior of a Predator-prey System with Stage-structure for Prey
张嘉防; 张志平
2007-01-01
In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed, and then uniformly persistent sufficient conditions of populations were found.
Nonlinearities lead to qualitative differences in population dynamics of predator-prey systems.
Olga M C C Ameixa
Full Text Available Since typically there are many predators feeding on most herbivores in natural communities, understanding multiple predator effects is critical for both community and applied ecology. Experiments of multiple predator effects on prey populations are extremely demanding, as the number of treatments and the amount of labour associated with these experiments increases exponentially with the number of species in question. Therefore, researchers tend to vary only presence/absence of the species and use only one (supposedly realistic combination of their numbers in experiments. However, nonlinearities in density dependence, functional responses, interactions between natural enemies etc. are typical for such systems, and nonlinear models of population dynamics generally predict qualitatively different results, if initial absolute densities of the species studied differ, even if their relative densities are maintained. Therefore, testing combinations of natural enemies without varying their densities may not be sufficient. Here we test this prediction experimentally. We show that the population dynamics of a system consisting of 2 natural enemies (aphid predator Adalia bipunctata (L., and aphid parasitoid, Aphidius colemani Viereck and their shared prey (peach aphid, Myzus persicae Sulzer are strongly affected by the absolute initial densities of the species in question. Even if their relative densities are kept constant, the natural enemy species or combination thereof that most effectively suppresses the prey may depend on the absolute initial densities used in the experiment. Future empirical studies of multiple predator - one prey interactions should therefore use a two-dimensional array of initial densities of the studied species. Varying only combinations of natural enemies without varying their densities is not sufficient and can lead to misleading results.
Existence, uniqueness and stability of positive steady states to a prey-predator diffusion system
WANG MingXin; WANG XuBo
2009-01-01
In the paper, we study the positive solutions of an elliptic system coming from a prey-predator model with modified Leslie-Gower and Holling-Type Ⅱ schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semi-trivial solution to the unique positive solution of the limiting system.
Dynamic analysis of a fractional order delayed predator-prey system with harvesting.
Song, Ping; Zhao, Hongyong; Zhang, Xuebing
2016-06-01
In the study, we consider a fractional order delayed predator-prey system with harvesting terms. Our discussion is divided into two cases. Without harvesting, we investigate the stability of the model, as well as deriving some criteria by analyzing the associated characteristic equation. With harvesting, we investigate the dynamics of the system from the aspect of local stability and analyze the influence of harvesting to prey and predator. Finally, numerical simulations are presented to verify our theoretical results. In addition, using numerical simulations, we investigate the effects of fractional order and harvesting terms on dynamic behavior. Our numerical results show that fractional order can affect not only the stability of the system without harvesting terms, but also the switching times from stability to instability and to stability. The harvesting can convert the equilibrium point, the stability and the stability switching times.
ISHIKAWA, M.
2008-04-01
Full Text Available We often observe some kind or another of random fluctuations in physical, chemical and social phenomena to a greater or lesser extent. The analysis of influence of such fluctuations on phenomena is very important as a basic problem in various fields including design and planning of controlled systems in control engineering and analysis of option pricing in economics. In this paper, focusing on biological communities, we study the influence of the random fluctuations on predator-prey systems with diffusion. Noting that interaction of phytoplankton and zooplankton is the basis of a food chain in the lake and the ocean, we consider the two-species predator-prey systems consists of phytoplankton and zooplankton. We analyze the influence of the random fluctuations on the spatio-temporal patterns generated by phytoplankton and zooplankton by the numerical simulations.
Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge
Qingsong Liu
2014-01-01
Full Text Available A modified Leslie-Gower predator-prey system with two delays is investigated. By choosing τ1 and τ2 as bifurcation parameters, we show that the Hopf bifurcations occur when time delay crosses some critical values. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and chaotic behaviors are observed. Finally, using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of the periodic solutions.
Global hopf bifurcation on two-delays leslie-gower predator-prey system with a prey refuge.
Liu, Qingsong; Lin, Yiping; Cao, Jingnan
2014-01-01
A modified Leslie-Gower predator-prey system with two delays is investigated. By choosing τ 1 and τ 2 as bifurcation parameters, we show that the Hopf bifurcations occur when time delay crosses some critical values. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and chaotic behaviors are observed. Finally, using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of the periodic solutions.
Inducible defenses in prey intensify predator cannibalism.
Kishida, Osamu; Trussell, Geoffrey C; Nishimura, Kinya; Ohgushi, Takayuki
2009-11-01
Trophic cascades are often a potent force in ecological communities, but abiotic and biotic heterogeneity can diffuse their influence. For example, inducible defenses in many species create variation in prey edibility, and size-structured interactions, such as cannibalism, can shift predator diets away from heterospecific prey. Although both factors diffuse cascade strength by adding heterogeneity to trophic interactions, the consequences of their interactioh remain poorly understood. We show that inducible defenses in tadpole prey greatly intensify cannibalism in predatory larval salamanders. The likelihood of cannibalism was also strongly influenced by asymmetries in salamander size that appear to be most important in the presence of defended prey. Hence, variation in prey edibility and the size structure of the predator may synergistically affect predator-prey population dynamics by reducing prey mortality and increasing predator mortality via cannibalism. We also suggest that the indirect effects of prey defenses may shape the evolution of predator traits that determine diet breadth and how trophic dynamics unfold in natural systems.
Chen Lansun
2010-01-01
Full Text Available We consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly, we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly, the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally, the permanence of the investigated system is also obtained. Our results provide reliable tactic basis for the practical biological economics management.
Predator-prey interactions mediated by prey personality and predator hunting mode.
Belgrad, Benjamin A; Griffen, Blaine D
2016-04-13
Predator-prey interactions are important drivers in structuring ecological communities. However, despite widespread acknowledgement that individual behaviours and predator species regulate ecological processes, studies have yet to incorporate individual behavioural variations in a multipredator system. We quantified a prevalent predator avoidance behaviour to examine the simultaneous roles of prey personality and predator hunting mode in governing predator-prey interactions. Mud crabs, Panopeus herbstii, reduce their activity levels and increase their refuge use in the presence of predator cues. We measured mud crab mortality and consistent individual variations in the strength of this predator avoidance behaviour in the presence of predatory blue crabs, Callinectes sapidus, and toadfish, Opsanus tau We found that prey personality and predator species significantly interacted to affect mortality with blue crabs primarily consuming bold mud crabs and toadfish preferentially selecting shy crabs. Additionally, the strength of the predator avoidance behaviour depended upon the predation risk from the predator species. Consequently, the personality composition of populations and predator hunting mode may be valuable predictors of both direct and indirect predator-prey interaction strength. These findings support theories postulating mechanisms for maintaining intraspecies diversity and have broad implications for community dynamics.
The diffusive Lotka-Volterra predator-prey system with delay.
Al Noufaey, K S; Marchant, T R; Edwards, M P
2015-12-01
Semi-analytical solutions for the diffusive Lotka-Volterra predator-prey system with delay are considered in one and two-dimensional domains. The Galerkin method is applied, which approximates the spatial structure of both the predator and prey populations. This approach is used to obtain a lower-order, ordinary differential delay equation model for the system of governing delay partial differential equations. Steady-state and transient solutions and the region of parameter space, in which Hopf bifurcations occur, are all found. In some cases simple linear expressions are found as approximations, to describe steady-state solutions and the Hopf parameter regions. An asymptotic analysis for the periodic solution near the Hopf bifurcation point is performed for the one-dimensional domain. An excellent agreement is shown in comparisons between semi-analytical and numerical solutions of the governing equations.
Spatiotemporal complexity of a ratio-dependent predator-prey system
Wang, Weiming; Liu, Quan-Xing; Jin, Zhen
2007-01-01
In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain. Furthermore, we present a theoretical analysis of evolutionary processes that involves organisms distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that the typical dynam...
Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting
Fengying Wei
2014-01-01
Full Text Available A kind of delayed predator-prey system with harvesting is considered in this paper. The influence of harvesting and delay is investigated. Our results show that Hopf bifurcations occur as the delay τ passes through critical values. By using of normal form theory and center manifold theorem, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are obtained. Finally, numerical simulations are given to support our theoretical predictions.
Yan Lv; Wei Lv; Jian-hua Sun
2007-01-01
By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.
无
2012-01-01
In this paper,the existence of eight periodic solutions to a Michaelis-Menten-type predator-prey system with delay and harvesting in patch environment is established using the analytical techniques and Mawhin's coincidence degree theory.
Liu Xianning; Chen Lansun
2003-03-01
This paper develops the Holling type II Lotka-Volterra predator-prey system, which may inherently oscillate, by introducing periodic constant impulsive immigration of predator. Condition for the system to be extinct is given and permanence condition is established via the method of comparison involving multiple Liapunov functions. Further influences of the impulsive perturbations on the inherent oscillation are studied numerically, which shows that with the increasing of the amount of the immigration, the system experiences process of quasi-periodic oscillating{yields}cycles{yields}periodic doubling cascade{yields}chaos{yields}periodic halfing cascade{yields}cycles, which is characterized by (1) quasi-periodic oscillating, (2) period doubling, (3) period halfing, (4) non-unique dynamics, meaning that several attractors coexist.
Population-level consequences of heterospecific density-dependent movements in predator-prey systems
2013-01-01
In this paper we elucidate how small-scale movements, such as those associated with searching for food and avoiding predators, affect the stability of predator-prey dynamics. We investigate an individual-based Lotka-Volterra model with density dependent movement, in which the predator and prey populations live in a very large number of coupled patches. The rates at which individuals leave patches depend on the local densities of heterospecifics, giving rise to one reaction norm for each of th...
Extinction and permanence in delayed stage-structure predator-prey system with impulsive effects
Pang Guoping [Department of Mathematics and Computer Science, Yulin Normal University, Yulin, Guangxi 537000 (China) and Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024 (China)], E-mail: g.p.pang@163.com; Wang Fengyan [Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang 325000 (China); College of Science, Jimei University, Xiamen, Fujian 361021 (China); Chen Lansun [Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024 (China)
2009-03-15
Based on the classical stage-structured model and Lotka-Volterra predator-prey model, an impulsive delayed differential equation to model the process of periodically releasing natural enemies at fixed times for pest control is proposed and investigated. We show that the conditions for global attractivity of the 'pest-extinction' ('prey-eradication') periodic solution and permanence of the population of the model depend on time delay. We also show that constant maturation time delay and impulsive releasing for the predator can bring great effects on the dynamics of system by numerical analysis. As a result, the pest maturation time delay is considered to establish a procedure to maintain the pests at an acceptably low level in the long term. In this paper, the main feature is that we introduce time delay and pulse into the predator-prey (natural enemy-pest) model with age structure, exhibit a new modelling method which is applied to investigate impulsive delay differential equations, and give some reasonable suggestions for pest management.
Zhang Long [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)], E-mail: longzhang_xj@sohu.com; Teng Zhidong [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)], E-mail: zhidong@xju.edu.cn
2008-12-15
In this paper, we study two species predator-prey Lotka-Volterra type dispersal system with periodic coefficients in two patches, in which both the prey and predator species can disperse between two patches. By utilizing analytic method, sufficient and realistic conditions on permanence and the existence of periodic solution are established. The theoretical results are confirmed by a special example and numerical simulations.
Stationary distribution and periodic solutions for stochastic Holling-Leslie predator-prey systems
Jiang, Daqing; Zuo, Wenjie; Hayat, Tasawar; Alsaedi, Ahmed
2016-10-01
The stochastic autonomous and periodic predator-prey systems with Holling and Leslie type functional response are investigated. For the autonomous system, we prove that there exists a unique stationary distribution, which is ergodic by constructing a suitable Lyapunov function under relatively small white noise. The result shows that, stationary distribution doesn't rely on the existence and the stability of the positive equilibrium in the undisturbed system. Furthermore, for the corresponding non-autonomous system, we show that there exists a positive periodic Markov process under relatively weaker condition. Finally, numerical simulations illustrate our theoretical results.
Stability, delay, and chaotic behavior in a lotka-volterra predator-prey system.
Nakaoka, S; Saito, Y; Takeuchi, Y
2006-01-01
We consider the following Lotka-Volterra predator-prey system with two delays: x '( t ) = x ( t ) [ r(1) - ax ( t - tau(1) ) - by( t ) ] y '( t ) = y ( t ) [ - r(1) + cx ( t ) - dy( t - tau(2) ) ] ( E ) We show that a positive equilibrium of system ( E ) is globally asymptotically stable for small delays. Critical values of time delay through which system ( E ) undergoes a Hopf bifurcation are analytically determined. Some numerical simulations suggest an existence of subcritical Hopf bifurcation near the critical values of time delay. Further system (E) exhibits some chaotic behavior when tau(2) becomes large.
Predator-prey dynamics in P systems ruled by metabolic algorithm.
Fontana, F; Manca, V
2008-03-01
P systems are used to compute predator-prey dynamics expressed in the traditional formulation by Lotka and Volterra. By governing the action of the transition rules in such systems using the regulatory features of the metabolic algorithm we come up with simulations of the Lotka-Volterra equations, whose robustness is comparable to that obtained using Runge-Kutta schemes and Gillespie's Stochastic Simulation Algorithm. Besides their reliability, the results obtained using the metabolic algorithm on top of P systems have a clear biochemical interpretation concerning the role, of reactants or promoters, of the species involved.
Modelling the Dynamics of the Work-Employment System by Predator-Prey Interactions
Serpa, Nilo
2011-01-01
The broad application range of the predator-prey modelling enabled us to apply it to represent the dynamics of the work-employment system. For the adopted period, we conclude that this dynamics is chaotic in the beginning of the time series and tends to less perturbed states, as time goes by, due to public policies and hidden intrinsic system features. Basic Lotka-Volterra approach was revised and adapted to the reality of the study. The final aim is to provide managers with generalized theoretical elements that allow to a more accurate understanding of the behavior of the work-employment system.
Sjödin, Henrik; Brännström, Ke; Söderquist, Mårten; Englund, Göran
2014-02-07
In this paper we elucidate how small-scale movements, such as those associated with searching for food and avoiding predators, affect the stability of predator-prey dynamics. We investigate an individual-based Lotka-Volterra model with density-dependent movement, in which the predator and prey populations live in a very large number of coupled patches. The rates at which individuals leave patches depend on the local densities of heterospecifics, giving rise to one reaction norm for each of the two species. Movement rates are assumed to be much faster than demographics rates. A spatial structure of predators and prey emerges which affects the global population dynamics. We derive a criterion which reveals how demographic stability depends on the relationships between the per capita covariance and densities of predators and prey. Specifically, we establish that a positive relationship with prey density and a negative relationship with predator density tend to be stabilizing. On a more mechanistic level we show how these relationships are linked to the movement reaction norms of predators and prey. Numerical results show that these findings hold both for local and global movements, i.e., both when migration is biased towards neighbouring patches and when all patches are reached with equal probability. © 2013 Published by Elsevier Ltd. All rights reserved.
Mathematical Modeling and Stability of Predator-Prey Systems
Sobrinho, Altair Santos de Oliveira; Kita, Carolina Massae; Natti, Érica Regina Takano; Natti, Paulo Laerte
2015-01-01
This work investigated the stability of some Lotka-Volterra type models. We used the Liapunov method, which consists in analyzing the stability of systems of ordinary differential equations (ODE's), around the equilibrium, when submitted to perturbations in the initial conditions.
Wang Fengyan [College of Science, Jimei University, Xiamen Fujian 361021 (China)]. E-mail: wangfy68@163.com; Zeng Guangzhao [Department of Mathematics, ShaoGuan University, ShaoGuan, GuangDong 512005 (China)]. E-mail: guangzhaoz@sgu.edu.cn
2007-05-15
In this paper, we introduce and study a Lotka-Volterra predator-prey system with impulsive ratio-harvesting the prey and time delays. By using Floquet theory and small amplitude perturbation skills, we discuss the boundary periodic solutions for predator-prey system under periodic pulsed conditions. The stability analysis of the boundary periodic solution yields an invasion threshold of the predator. Further, by use of the coincidence degree theorem and its related continuous theorem we prove the existence of the positive periodic solutions of the system when the value of the coefficient is large than the threshold. Finally, by comparing bifurcation diagrams with different bifurcation parameters, we show that the impulsive effect and the time delays bring to the system to be more complex, which experiences a complex process of cycles {sup {yields}} quasi-periodic oscillation {sup {yields}} periodic doubling cascade {sup {yields}} chaos.
Jing HUI; Lan Sun CHEN
2004-01-01
The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifurcation theory, it is known that this system has a positive periodic solution provided the time average of the predator's net uninhibited death rate is in a suitable range.The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of predator).
Stability and delay in a three species predator-prey system
Kundu, Soumen; Maitra, Sarit
2016-06-01
In this article a multi-team delayed predator-prey model has been considered. There are two preys and one predator species in this model and the time delay appears for gestation of the predator. The essential mathematical features of the proposed model around the interior equilibrium point are studied in terms of local asymptotic stability by constructing a suitable Lyapunov functional and the condition for existence of Hopf-bifurcation is derived. By the assumption that the prey teams may help each other the effect of the rate of cooperation on the stability of the predator-prey model has been observed. Numerically a critical value for the delay parameter is obtained as a condition for Hopf-bifurcation.
Positive Periodic Solution of a Discrete Predator-prey Patch-system
Shu-yuan Shen; Pei-xuan Weng
2008-01-01
A periodic difference predator-prey model with Holling-(m+1)(m>2) type functional response and impulses is established. Sufficient conditions are derived for the existence of periodic solutions by using a continuation theorem in coincidence degree.
Xuepeng Li
2009-01-01
Full Text Available Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay ̇1(=1([1(−11(1(−(−12(2(/(2+21(], ̇2(=2([2(−21(2(/1(], are obtained, where 1( and 2( stand for the density of the prey and the predator, respectively, and ≠0 is a constant. (≥0 stands for the time delays due to negative feedback of the prey population.
Martín-Fernández, Laura; Gilioli, Gianni; Lanzarone, Ettore; Miguez, Joaquin; Pasquali, Sara; Ruggeri, Fabrizio; Ruiz, Diego P
2014-06-01
Functional response estimation and population tracking in predator-prey systems are critical problems in ecology. In this paper we consider a stochastic predator-prey system with a Lotka-Volterra functional response and propose a particle filtering method for: (a) estimating the behavioral parameter representing the rate of effective search per predator in the functional response and (b) forecasting the population biomass using field data. In particular, the proposed technique combines a sequential Monte Carlo sampling scheme for tracking the time-varying biomass with the analytical integration of the unknown behavioral parameter. In order to assess the performance of the method, we show results for both synthetic and observed data collected in an acarine predator-prey system, namely the pest mite Tetranychus urticae and the predatory mite Phytoseiulus persimilis.
Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses
Hongli Li
2014-01-01
Full Text Available A class of Holling type II predator-prey systems with mutual interference and impulses is presented. Sufficient conditions for the permanence, extinction, and global attractivity of system are obtained. The existence and uniqueness of positive periodic solution are also established. Numerical simulations are carried out to illustrate the theoretical results. Meanwhile, they indicate that dynamics of species are very sensitive with the period matching between species’ intrinsic disciplinarians and the perturbations from the variable environment. If the periods between individual growth and impulse perturbations match well, then the dynamics of species periodically change. If they mismatch each other, the dynamics differ from period to period until there is chaos.
Dynamics of the stochastic Leslie-Gower predator-prey system with randomized intrinsic growth rate
Zhao, Dianli; Yuan, Sanling
2016-11-01
This paper investigates the stochastic Leslie-Gower predator-prey system with randomized intrinsic growth rate. Existence of a unique global positive solution is proved firstly. Then we obtain the sufficient conditions for permanence in mean and almost sure extinction of the system. Furthermore, the stationary distribution is derived based on the positive equilibrium of the deterministic model, which shows the population is not only persistent but also convergent by time average under some assumptions. Finally, we illustrate our conclusions through two examples.
Dynamics of a Ivlev-type predator-prey system with constant rate harvesting
Ling Li [Institute of Nonlinear Analysis, College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035 (China); Wang Weiming [Institute of Nonlinear Analysis, College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035 (China)], E-mail: weimingwang2003@163.com
2009-08-30
In this paper, by using the analysis of qualitative method and bifurcation theory, we investigate the dynamical properties of the Ivlev-type predator-prey model with nonzero constant prey harvesting and with or without time delay, respectively. It is shown that the system we considered can exhibit the subcritical and supercritical Hopf bifurcation. We also study the effect of the time delay on the dynamics of the system. By choosing the delay {tau} as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay {tau} crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhaes. Finally, numerical simulations are performed to illustrate the obtained results.
Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system
Wan-Yong Wang; Li-Jun Pei
2011-01-01
Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria,and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluctuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratiodependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover
Coexistence Steady States in a Predator-Prey Model
Walker, Christoph
2010-01-01
An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence steady states bifurcates from the marginal steady state with no prey. A similar result is obtained when the fertility of the prey varies.
Toscano, Benjamin J; Rombado, Bianca R; Rudolf, Volker H W
2016-08-31
Predators often undergo complete ontogenetic diet shifts, engaging in resource competition with species that become their prey during later developmental stages. Theory posits that this mix of stage-specific competition and predation, termed life-history intraguild predation (LHIGP), can lead to alternative stable states. In one state, prey exclude predators through competition (i.e. juvenile competitive bottleneck), while in the alternative, adult predators control prey density to limit competition and foster coexistence. Nevertheless, the interactions leading to these states have not been demonstrated in an empirical LHIGP system. To address this gap, we manipulated densities of cannibalistic adult cyclopoid copepods (Mesocyclops edax) and their cladoceran prey (Daphnia pulex) in a response-surface design and measured the maturation and survival of juvenile copepods (nauplii). We found that Daphnia reduced and even precluded both nauplii maturation and survival through depletion of a shared food resource. As predicted, adult copepods enhanced nauplii maturation and survival through Daphnia consumption, yet this positive effect was dependent on the relative abundance of Daphnia as well as the absolute density of adult copepods. Adult copepods reduced nauplii survival through cannibalism at low Daphnia densities and at the highest copepod density. This work demonstrates that predation can relax a strong juvenile competitive bottleneck in freshwater zooplankton, though cannibalism can reduce predator recruitment. Thus, our results highlight a key role for cannibalism in LHIGP dynamics and provide evidence for the interactions that drive alternative stable states in such systems.
Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System
Yanuo Zhu
2012-01-01
Full Text Available This work deals with the analysis of a delayed diffusive predator-prey system under Neumann boundary conditions. The dynamics are investigated in terms of the stability of the nonnegative equilibria and the existence of Hopf bifurcation by analyzing the characteristic equations. The direction of Hopf bifurcation and the stability of bifurcating periodic solution are also discussed by employing the normal form theory and the center manifold reduction. Furthermore, we prove that the positive equilibrium is asymptotically stable when the delay is less than a certain critical value and unstable when the delay is greater than the critical value.
Bifurcation and chaos in a ratio-dependent predator-prey system with time delay
Gan Qintao [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China)], E-mail: ganqintao@sina.com; Xu Rui [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China); Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China); Yang Pinghua [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China)
2009-02-28
In this paper, a ratio-dependent predator-prey model with time delay is investigated. We first consider the local stability of a positive equilibrium and the existence of Hopf bifurcations. By using the normal form theory and center manifold reduction, we derive explicit formulae which determine the stability, direction and other properties of bifurcating periodic solutions. Finally, we consider the effect of impulses on the dynamics of the above time-delayed population model. Numerical simulations show that the system with constant periodic impulsive perturbations admits rich complex dynamic, such as periodic doubling cascade and chaos.
Bifurcation and Feedback Control of an Exploited Prey-Predator System
Uttam Das
2014-01-01
Full Text Available This paper makes an attempt to highlight a differential algebraic model in order to investigate the dynamical behavior of a prey-predator system due to the variation of economic interest of harvesting. In this regard, it is observed that the model exhibits a singularity induced bifurcation when economic profit is zero. For the purpose of stabilizing the proposed model at the positive equilibrium, a state feedback controller is therefore designed. Finally, some numerical simulations are carried out to show the consistency with theoretical analysis and to illustrate the effectiveness of the proposed controller.
Asymptotic behavior of a delay predator-prey system with stage structure and variable coefficients
Javier A. Hernandez-Pinzon
2008-10-01
Full Text Available In this paper, we establish a global attractor for a Lotka-Volterra type reaction-diffusion predator-prey model with stage structure for the predator, delay due to maturity and variable coefficients. This attractor is found by the method of upper and lower solutions and is given in terms of bounds for the coefficients.
Bifurcation and chaos in a discrete-time predator-prey system of Holling and Leslie type
Hu, Dongpo; Cao, Hongjun
2015-05-01
A discrete-time predator-prey system of Holling and Leslie type with a constant-yield prey harvesting obtained by the forward Euler scheme is studied in detail. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory. Numerical simulations including bifurcation diagrams, maximum Lyapunov exponents, phase portraits display new and rich nonlinear dynamical behaviors. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period- 1, 2, 11, 17, 19, 22 orbits, attracting invariant cycles, and chaotic attractors of the discrete-time predator-prey system of Holling and Leslie type with a constant-yield prey harvesting. These results demonstrate that the integral step size plays a vital role to the local and global stability of the discrete-time predator-prey system with the Holling and Leslie type after the original continuous-time predator-prey system is discretized.
Bifurcation and complex dynamics of a discrete-time predator-prey system
S. M. Sohel Rana
2015-06-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system of Holling-I type in the closed first quadrant R+2. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. It has been found that the dynamical behavior of the model is very sensitive to the parameter values and the initial conditions. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamic behaviors, including phase portraits, period-9, 10, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. In particular, we observe that when the prey is in chaotic dynamic, the predator can tend to extinction or to a stable equilibrium. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors. The analysis and results in this paper are interesting in mathematics and biology.
Shengmao Fu
2010-01-01
Full Text Available We study a cubic predator-prey system with stage structure for the prey. This system is a generalization of the two-species Lotka-Volterra predator-prey model. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the global existence of solutions and the stability of equilibrium points to the system of weakly coupled reaction-diffusion type are discussed. Finally, the existence of nonnegative classical global solutions to the system of strongly coupled reaction-diffusion type is investigated when the space dimension is less than 6, and the global asymptotic stability of unique positive equilibrium point of the system is proved by constructing Lyapunov functions.
Kooi, Bob W; Venturino, Ezio
2016-04-01
In this paper we analyse a predator-prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the Rosenzweig-MacArthur predator-prey type with an SI (susceptible-infected) disease in the prey. Modeling prey group defense leads to a square root dependence in the Holling type II functional for the predator-prey interaction term. The system dynamics is investigated using simulations, classical existence and asymptotic stability analysis and numerical bifurcation analysis. A number of bifurcations, such as transcritical and Hopf bifurcations which occur commonly in predator-prey systems will be found. Because of the square root interaction term there is non-uniqueness of the solution and a singularity where the prey population goes extinct in a finite time. This results in a collapse initiated by extinction of the healthy or susceptible prey and thereafter the other population(s). When also a positive attractor exists this leads to bistability similar to what is found in predator-prey models with a strong Allee effect. For the two-dimensional disease-free (i.e. the purely demographic) system the region in the parameter space where bistability occurs is marked by a global bifurcation. At this bifurcation a heteroclinic connection exists between saddle prey-only equilibrium points where a stable limit cycle together with its basin of attraction, are destructed. In a companion paper (Gimmelli et al., 2015) the same model was formulated and analysed in which the disease was not in the prey but in the predator. There we also observed this phenomenon. Here we extend its analysis using a phase portrait analysis. For the three-dimensional ecoepidemic predator-prey system where the prey is affected by the disease, also tangent bifurcations including a cusp bifurcation and a torus bifurcation of limit cycles occur. This leads to new complex dynamics. Continuation by varying one parameter
Li, Yuanyuan; Wang, Jinfeng
A diffusive Gause type predator-prey system with Allee effect in prey growth and Holling type III response subject to Neumann boundary conditions is investigated. Existence of nonconstant positive steady state solutions is proved by Leray-Schauder degree theory and bifurcation theory. Global stability of the positive equilibrium of the system is also investigated. Moreover, bifurcations of spatially homogeneous and nonhomogeneous periodic solutions are analyzed. Our rigorous results justify some recent ecological observations.
Limit cycles in a generalized Gause-type predator-prey system
无
2001-01-01
The qualitative behavior of solutions for a generalized Game-type predator-prey system was studied.A large number of biologcal and bioeconomic models are special cases of this system. The system was investigated in the region D = { ( x, y) | x > 0, y > 0} because of the biological meaning of the system. The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system, which ensure that the system has at least one limit cycle. The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare-Bendixson are efficiently employed in the research. The main results and their consequences presented not only generalize some known results, but also improve some corresponding results of other authors.
Characterization of multiple spiral wave dynamics as a stochastic predator-prey system
Otani, Niels F.; Mo, Alisa; Mannava, Sandeep; Fenton, Flavio H.; Cherry, Elizabeth M.; Luther, Stefan; Gilmour, Robert F., Jr.
2008-08-01
A perspective on systems containing many action potential waves that, individually, are prone to spiral wave breakup is proposed. The perspective is based on two quantities, “predator” and “prey,” which we define as the fraction of the system in the excited state and in the excitable but unexcited state, respectively. These quantities exhibited a number of properties in both simulations and fibrillating canine cardiac tissue that were found to be consistent with a proposed theory that assumes the existence of regions we call “domains of influence,” each of which is associated with the activity of one action potential wave. The properties include (i) a propensity to rotate in phase space in the same sense as would be predicted by the standard Volterra-Lotka predator-prey equations, (ii) temporal behavior ranging from near periodic oscillation at a frequency close to the spiral wave rotation frequency (“type-1” behavior) to more complex oscillatory behavior whose power spectrum is composed of a range of frequencies both above and, especially, below the spiral wave rotation frequency (“type-2” behavior), and (iii) a strong positive correlation between the periods and amplitudes of the oscillations of these quantities. In particular, a rapid measure of the amplitude was found to scale consistently as the square root of the period in data taken from both simulations and optical mapping experiments. Global quantities such as predator and prey thus appear to be useful in the study of multiple spiral wave systems, facilitating the posing of new questions, which in turn may help to provide greater understanding of clinically important phenomena such as ventricular fibrillation.
Absence of frequent herpesvirus transmission in a nonhuman primate predator-prey system in the wild.
Murthy, Sripriya; Couacy-Hymann, Emmanuel; Metzger, Sonja; Nowak, Kathrin; De Nys, Helene; Boesch, Christophe; Wittig, Roman; Jarvis, Michael A; Leendertz, Fabian H; Ehlers, Bernhard
2013-10-01
Emergence of viruses into the human population by transmission from nonhuman primates (NHPs) represents a serious potential threat to human health that is primarily associated with the increased bushmeat trade. Transmission of RNA viruses across primate species appears to be relatively frequent. In contrast, DNA viruses appear to be largely host specific, suggesting low transmission potential. Herein, we use a primate predator-prey system to study the risk of herpesvirus transmission between different primate species in the wild. The system was comprised of western chimpanzees (Pan troglodytes verus) and their primary (western red colobus, Piliocolobus badius badius) and secondary (black-and-white colobus, Colobus polykomos) prey monkey species. NHP species were frequently observed to be coinfected with multiple beta- and gammaherpesviruses (including new cytomegalo- and rhadinoviruses). However, despite frequent exposure of chimpanzees to blood, organs, and bones of their herpesvirus-infected monkey prey, there was no evidence for cross-species herpesvirus transmission. These findings suggest that interspecies transmission of NHP beta- and gammaherpesviruses is, at most, a rare event in the wild.
Dynamics in a Discrete-time Predator-prey System with Allee Effect
Xian-wei Chen; Xiang-ling Fu; Zhu-jun Jing
2013-01-01
In this paper,dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail.Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory,and then further illustrated by numerical simulations.Chaos in the sense of Marotto is proved by both analytical and numerical methods.Numerical simulations included bifurcation diagrams,Lyapunov exponents,phase portraits,fractal dimensions display new and rich dynamical behavior.More specifically,apart from stable dynamics,this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it.The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior.The dynamical behavior can move from complex instable states to stable states as the Allee constant increases (within a limited value).Combining the existing results in the current literature with the new results reported in this paper,a more complete understanding of the discrete-time predator-prey with Allee effect is given.
Sparse identification of a predator-prey system from simulation data of a convection model
Dam, Magnus; Brøns, Morten; Rasmussen, Jens Juul
2017-01-01
of the pressure profile, the turbulent flow, and the zonal flow capture the fundamental dynamic behavior of the full system. By applying the sparse identification of nonlinear dynamics (SINDy) method, we identify a predator-prey type dynamical system that approximates the underlying dynamics of the three energy......The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We utilize a data-driven modeling approach to identify a reduced model from simulation data...... state variables. A bifurcation analysis of the system reveals consistency between the bifurcation structures, observed for the simulation data, and the identified underlying system....
Existence of traveling wave solutions for diffusive predator-prey type systems
Hsu, Cheng-Hsiung; Yang, Chi-Ru; Yang, Ting-Hui; Yang, Tzi-Sheng
In this work we investigate the existence of traveling wave solutions for a class of diffusive predator-prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions. The profile equations for the above system can be reduced as a four-dimensional ODE system, and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system. Applying the methods of Wazewski Theorem, LaSalle's Invariance Principle and Hopf bifurcation theory, we obtain the existence results. Our results can apply to various kinds of ecological models.
Responses of many-species predator-prey systems to perturbations
Esmaily, Shadi; Pleimling, Michel
2015-03-01
We study the responses of many-species predator-prey systems, both in the well-mixed case as well as on a two-dimensional lattice, to permanent and transient perturbations. In the case of a weak transient perturbation the system returns to the original steady state, whereas a permanent perturbation pushes the system into a new steady state. Using Monte Carlo simulations, we monitor the approach to stationarity after a perturbation through a variety of quantities, as for example time-dependent particle densities and correlation functions. Different types of perturbations are studied, ranging from a change in reaction rates to the injection of additional individuals into the system, the latter perturbation mimicking immigration. This work is supported by the US National Science Foundation through Grant DMR-1205309.
Predator-prey molecular ecosystems.
Fujii, Teruo; Rondelez, Yannick
2013-01-22
Biological organisms use intricate networks of chemical reactions to control molecular processes and spatiotemporal organization. In turn, these living systems are embedded in self-organized structures of larger scales, for example, ecosystems. Synthetic in vitro efforts have reproduced the architectures and behaviors of simple cellular circuits. However, because all these systems share the same dynamic foundations, a generalized molecular programming strategy should also support complex collective behaviors, as seen, for example, in animal populations. We report here the bottom-up assembly of chemical systems that reproduce in vitro the specific dynamics of ecological communities. We experimentally observed unprecedented molecular behaviors, including predator-prey oscillations, competition-induced chaos, and symbiotic synchronization. These synthetic systems are tailored through a novel, compact, and versatile design strategy, leveraging the programmability of DNA interactions under the precise control of enzymatic catalysis. Such self-organizing assemblies will foster a better appreciation of the molecular origins of biological complexity and may also serve to orchestrate complex collective operations of molecular agents in technological applications.
A derivation of Holling's type I, II and III functional responses in predator-prey systems.
Dawes, J H P; Souza, M O
2013-06-21
Predator-prey dynamics is most simply and commonly described by Lotka-Volterra-type ordinary differential equations (ODEs) for continuous population density variables in the limit of large population sizes. One popular extension of these ODEs is the so-called Rosenzweig-MacArthur model in which various interaction rates between the populations have a nonlinear dependence on the prey concentration. Nonlinear 'functional responses' of this type were originally proposed by Holling on the basis of a general argument concerning the allocation of a predator's time between two activities: 'prey searching' and 'prey handling'. Although these functional responses are constructed in terms of the behaviour of an individual predator, they are routinely incorporated at the population level in models that include reproduction and death. In this paper we derive a novel three variable model for the simplest possible mathematical formulation of predator-prey dynamics that allows the interplay between these various processes to take place, on their different characteristic timescales. We study its properties in detail and show how it reduces to Holling's functional responses in special limits. As a result we are able to establish direct links between individual-level and population-level behaviour in the context of these well-known functional responses. Copyright © 2013 Elsevier Ltd. All rights reserved.
陈凤德; 史金麟; 陈晓星
2004-01-01
In this paper, a non-autonomous predator-prey model with diffusion and continuous time delay is studied, where the prey can diffuse between two patches of a heterogeneous environment with barriers between patches, but for the predator, the diffusion does not involve a barrier between patches, further it is assumed that all the parameters are time-dependent. It is shown that the system can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solution which is globallv asvmptotic stable are derived.
Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense
S. M. Sohel Rana
2015-09-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system involving group defense. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors.
Zhixiang Ju
2015-01-01
Full Text Available Based on the biological resource management of natural resources, a stage-structured predator-prey model with Holling type III functional response, birth pulse, and impulsive harvesting at different moments is proposed in this paper. By applying comparison theorem and some analysis techniques, the global attractivity of predator-extinction periodic solution and the permanence of this system are studied. At last, examples and numerical simulations are given to verify the validity of the main results.
Rui Xu; Lan-sun Chen; M.A.J. Chaplain
2003-01-01
A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are derived for the global attractivity of the positive equilibrium of the system.
LiuQiming; XuRui
2005-01-01
A delayed one-predator and two-prey system with Holling type-Ⅱ functional response is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence and global attractivity of positive periodic solutions to the system.
Smolinský, Radovan; Gvoždík, Lumír
2012-09-01
The ability to modify phenotypes in response to heterogeneity of the thermal environment represents an important component of an ectotherm's non-genetic adaptive capacity. Despite considerable attention being dedicated to the study of thermally-induced developmental plasticity, whether or not interspecific interactions shape the plastic response in both a predator and its prey remains unknown. We tested several predictions about the joint influence of predator/prey scents and thermal conditions on the plasticity of preferred body temperatures (T (p)) in both actors of this interaction, using a dragonfly nymphs-newt larvae system. Dragonfly nymphs (Aeshna cyanea) and newt eggs (Ichthyosaura alpestris) were subjected to fluctuating cold and warm thermal regimes (7-12 and 12-22°C, respectively) and the presence/absence of a predator or prey chemical cues. Preferred body temperatures were measured in an aquatic thermal gradient (5-33°C) over a 24-h period. Newt T (p) increased with developmental temperature irrespective of the presence/absence of predator cues. In dragonflies, thermal reaction norms for T (p) were affected by the interaction between temperature and prey cues. Specifically, the presence of newt scents in cold regime lowered dragonfly T (p). We concluded that predator-prey interactions influenced thermally-induced plasticity of T (p) but not in a reciprocal fashion. The occurrence of frequency-dependent thermal plasticity may have broad implications for predator-prey population dynamics, the evolution of thermal biology traits, and the consequences of sustaining climate change within ecological communities.
Does sex-selective predation stabilize or destabilize predator-prey dynamics?
David S Boukal
Full Text Available BACKGROUND: Little is known about the impact of prey sexual dimorphism on predator-prey dynamics and the impact of sex-selective harvesting and trophy hunting on long-term stability of exploited populations. METHODOLOGY AND PRINCIPAL FINDINGS: We review the quantitative evidence for sex-selective predation and study its long-term consequences using several simple predator-prey models. These models can be also interpreted in terms of feedback between harvesting effort and population size of the harvested species under open-access exploitation. Among the 81 predator-prey pairs found in the literature, male bias in predation is 2.3 times as common as female bias. We show that long-term effects of sex-selective predation depend on the interplay of predation bias and prey mating system. Predation on the 'less limiting' prey sex can yield a stable predator-prey equilibrium, while predation on the other sex usually destabilizes the dynamics and promotes population collapses. For prey mating systems that we consider, males are less limiting except for polyandry and polyandrogyny, and male-biased predation alone on such prey can stabilize otherwise unstable dynamics. On the contrary, our results suggest that female-biased predation on polygynous, polygynandrous or monogamous prey requires other stabilizing mechanisms to persist. CONCLUSIONS AND SIGNIFICANCE: Our modelling results suggest that the observed skew towards male-biased predation might reflect, in addition to sexual selection, the evolutionary history of predator-prey interactions. More focus on these phenomena can yield additional and interesting insights as to which mechanisms maintain the persistence of predator-prey pairs over ecological and evolutionary timescales. Our results can also have implications for long-term sustainability of harvesting and trophy hunting of sexually dimorphic species.
Monitoring in a predator-prey systems via a class of high order observer design.
Mata-Machuca, Juan Luis; Martínez-Guerra, Rafael; Aguilar-López, Ricardo
2010-04-01
The goal of this work is the monitoring of the corresponding species in a class of predator-prey systems, this issue is important from the ecology point of view to analyze the population dynamics. The above is done via a nonlinear observer design which contains on its structure a high order polynomial form of the estimation error. A theoretical frame is provided in order to show the convergence characteristics of the proposed observer, where it can be concluded that the performance of the observer is improved as the order of the polynomial is high. The proposed methodology is applied to a class of Lotka-Volterra systems with two and three species. Finally, numerical simulations present the performance of the proposed observer. Copyright (c) 2010 Elsevier Ireland Ltd. All rights reserved.
Moore, Talia Y; Biewener, Andrew A
2015-12-01
Behavioral studies performed in natural habitats provide a context for the development of hypotheses and the design of experiments relevant both to biomechanics and to evolution. In particular, predator-prey interactions are a model system for integrative study because success or failure of predation has a direct effect on fitness and drives the evolution of specialized performance in both predator and prey. Although all predators share the goal of capturing prey, and all prey share the goal of survival, the behavior of predators and prey are diverse in nature. This article presents studies of some predator-prey interactions sharing common predation strategies that reveal general principles governing the behaviors of predator and prey, even in distantly related taxa. Studies of predator-prey interactions also reveal that maximal performance observed in a laboratory setting is not necessarily the performance that determines fitness. Thus, considering locomotion in the context of predation ecology can aid in evolutionarily relevant experimental design. Classification by strategy reveals that displaying unpredictable trajectories is a relevant anti-predator behavior in response to multiple predation strategies. A predator's perception and pursuit of prey can be affected indirectly by divergent locomotion of similar animals that share an ecosystem. Variation in speed and direction of locomotion that directly increases the unpredictability of a prey's trajectory can be increased through genetic mutation that affects locomotor patterns, musculoskeletal changes that affect maneuverability, and physical interactions between an animal and the environment. By considering the interconnectedness of ecology, physical constraints, and the evolutionary history of behavior, studies in biomechanics can be designed to inform each of these fields.
Spatiotemporal complexity of a ratio-dependent predator-prey system
Wang, Weiming; Liu, Quan-Xing; Jin, Zhen
2007-05-01
In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction diffusion. We obtain the conditions of Hopf, Turing, and wave bifurcation in a spatial domain. Furthermore, we present a theoretical analysis of evolutionary processes that involves organisms distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripelike or spotted or coexistence of both. Our study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves. It may help us better understand the dynamics of an aquatic community in a real marine environment.
Periodicity in a Nonlinear Predator-prey System with State Dependent Delays
Feng-de Chen; Jin-lin Shi
2005-01-01
With the help of a continuation theorem based on Gainesand Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear state dependent delays predator-prey system{dN1(t)/dt=N1(t)[b1(t)-n∑i=1 ai(t)(N1(t-Ti(t,N1(t), N2(t))))ai-m∑cj(t)(N2(t-σj(t,Ni(t),N2(t))))βj],dN2(t)/dt=N2(t)[b2(t)-n∑i=1 di(t)(N1(t-Pi(t,N1(t), N2(t))))γi],where ai (t), cj (t), di(t) are continuous positive periodic functions with periodic ω＞ 0, b1 (t), b2 (t) are continuousare positive constants.
Hopf bifurcations in a predator-prey system with multiple delays
Hu Guangping [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China); School of Mathematics and Physics, Nanjing University of Information and Technology, Nanjing 210044 (China); Li Wantong [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China)], E-mail: wtli@lzu.edu.cn; Yan Xiangping [Department of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070 (China)
2009-10-30
This paper is concerned with a two species Lotka-Volterra predator-prey system with three discrete delays. By regarding the gestation period of two species as the bifurcation parameter, the stability of positive equilibrium and Hopf bifurcations of nonconstant periodic solutions are investigated. Furthermore, the direction of Hopf bifurcations and the stability of bifurcated periodic solutions are determined by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs). In addition, the global existence of bifurcated periodic solutions are also established by employing the topological global Hopf bifurcation theorem, which shows that the local Hopf bifurcations imply the global ones after the second critical value of parameter. Finally, to verify our theoretical predictions, some numerical simulations are also included.
The Dynamics of a Predator-Prey System with State-Dependent Feedback Control
Hunki Baek
2012-01-01
Full Text Available A Lotka-Volterra-type predator-prey system with state-dependent feedback control is investigated in both theoretical and numerical ways. Using the Poincaré map and the analogue of the Poincaré criterion, the sufficient conditions for the existence and stability of semitrivial periodic solutions and positive periodic solutions are obtained. In addition, we show that there is no positive periodic solution with period greater than and equal to three under some conditions. The qualitative analysis shows that the positive period-one solution bifurcates from the semitrivial solution through a fold bifurcation. Numerical simulations to substantiate our theoretical results are provided. Also, the bifurcation diagrams of solutions are illustrated by using the Poincaré map, and it is shown that the chaotic solutions take place via a cascade of period-doubling bifurcations.
Hopf bifurcation in a partial dependent predator-prey system with delay
Zhao Huitao [Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093 (China); Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001 (China)], E-mail: taohuiz@sohu.com; Lin Yiping [Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093 (China)], E-mail: linyiping689@sohu.com
2009-10-30
In this paper, a partial dependent predator-prey model with time delay is studied by using the theory of functional differential equation and Hassard's method, the condition on which positive equilibrium exists and Hopf bifurcation occurs are given. Finally, numerical simulations are performed to support the analytical results, and the chaotic behaviors are observed.
The hunt for canards in population dynamics : A predator-prey system
Verhulst, Ferdinand
2014-01-01
Equations with periodic coefficients for singularly perturbed growth can be analysed by using fast and slow timescales which involves slow manifolds, canards and the dynamical exchanges between several slow manifolds. We extend the time-periodic P.F. Verhulst-model to predator-prey interaction where
Yuanfu Shao
2014-01-01
Full Text Available By constructing a suitable Lyapunov functional, the global attractivity of positive periodic solutions for a delayed predator-prey system with diffusion and impulses is studied in this paper. Finally, an example and numerical analysis are given to show the effectiveness of the main results.
The Global Stability of Predator-Prey System of Gause-Type with Holling Ⅲ Functional Response
无
2000-01-01
This paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator-prey system of Gause-type with Holling Ⅲ functional response. The Dulac's criterion is applied and liapunov functions are constructed to establish the global stability.
无
2008-01-01
By using Gaines and Mawhin's continuation theorem of coincidence degree theory and constructing Lyapunov functionals,a set of easily verifiable sufficient conditions are derived for the existence and global attractivity of a positive periodic solution to a predator-prey system with delays and impulses.
Cuimei ZHANG; Wencheng CHEN; Yu YANG
2006-01-01
In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Holling Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.
无
2008-01-01
In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient conditions are obtained for the existence of periodic solution.
On the dynamics of a generalized predator-prey system with Z-type control.
Lacitignola, Deborah; Diele, Fasma; Marangi, Carmela; Provenzale, Antonello
2016-10-01
We apply the Z-control approach to a generalized predator-prey system and consider the specific case of indirect control of the prey population. We derive the associated Z-controlled model and investigate its properties from the point of view of the dynamical systems theory. The key role of the design parameter λ for the successful application of the method is stressed and related to specific dynamical properties of the Z-controlled model. Critical values of the design parameter are also found, delimiting the λ-range for the effectiveness of the Z-method. Analytical results are then numerically validated by the means of two ecological models: the classical Lotka-Volterra model and a model related to a case study of the wolf-wild boar dynamics in the Alta Murgia National Park. Investigations on these models also highlight how the Z-control method acts in respect to different dynamical regimes of the uncontrolled model. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.
Predator-Prey Interactions in Communities with prey dispersal and Allee effects
Berezovskaya, F; Castillo-Chavez, C
2009-01-01
The population dynamics of predator-prey systems in the presence of patch-specific predators are explored in a setting where the prey population has access to both habitats. The emphasis is in situations where patch-prey abundance drives prey-dispersal between patches, with the fragile prey populations, that is, populations subject to the Allee effect. The resulting four-dimensional model's mathematical analysis is carried out via sub-models that focus in lower dimensional settings. The outcomes depend on, and in fact they are quite sensitive to, the structure of the system, the range of parameter values, and initial conditions. We show that the system can support multi-stability and a diverse set of predator-prey life-history dynamics that includes rather complex dynamical system outcomes. It is argued that in general evolution should favor heterogeneous settings including Allee effects, prey-refuges, and patch-specific predators.
Dynamics of a prey-predator system under Poisson white noise excitation
Pan, Shan-Shan; Zhu, Wei-Qiu
2014-10-01
The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ɛ2 s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.
Form of an evolutionary tradeoff affects eco-evolutionary dynamics in a predator-prey system.
Kasada, Minoru; Yamamichi, Masato; Yoshida, Takehito
2014-11-11
Evolution on a time scale similar to ecological dynamics has been increasingly recognized for the last three decades. Selection mediated by ecological interactions can change heritable phenotypic variation (i.e., evolution), and evolution of traits, in turn, can affect ecological interactions. Hence, ecological and evolutionary dynamics can be tightly linked and important to predict future dynamics, but our understanding of eco-evolutionary dynamics is still in its infancy and there is a significant gap between theoretical predictions and empirical tests. Empirical studies have demonstrated that the presence of genetic variation can dramatically change ecological dynamics, whereas theoretical studies predict that eco-evolutionary dynamics depend on the details of the genetic variation, such as the form of a tradeoff among genotypes, which can be more important than the presence or absence of the genetic variation. Using a predator-prey (rotifer-algal) experimental system in laboratory microcosms, we studied how different forms of a tradeoff between prey defense and growth affect eco-evolutionary dynamics. Our experimental results show for the first time to our knowledge that different forms of the tradeoff produce remarkably divergent eco-evolutionary dynamics, including near fixation, near extinction, and coexistence of algal genotypes, with quantitatively different population dynamics. A mathematical model, parameterized from completely independent experiments, explains the observed dynamics. The results suggest that knowing the details of heritable trait variation and covariation within a population is essential for understanding how evolution and ecology will interact and what form of eco-evolutionary dynamics will result.
Prey-Predator Model with Two-Stage Infection in Prey: Concerning Pest Control
Swapan Kumar Nandi
2015-01-01
Full Text Available A prey-predator model system is developed; specifically the disease is considered into the prey population. Here the prey population is taken as pest and the predators consume the selected pest. Moreover, we assume that the prey species is infected with a viral disease forming into susceptible and two-stage infected classes, and the early stage of infected prey is more vulnerable to predation by the predator. Also, it is assumed that the later stage of infected pests is not eaten by the predator. Different equilibria of the system are investigated and their stability analysis and Hopf bifurcation of the system around the interior equilibriums are discussed. A modified model has been constructed by considering some alternative source of food for the predator population and the dynamical behavior of the modified model has been investigated. We have demonstrated the analytical results by numerical analysis by taking some simulated set of parameter values.
Transmission dynamics of resistant bacteria in a predator-prey system.
Gao, Xubin; Pan, Qiuhui; He, Mingfeng
2015-01-01
This paper discusses the impact on human health caused by the addition of antibiotics in the feed of food animals. We use the established transmission rule of resistant bacteria and combine it with a predator-prey system to determine a differential equations model. The equations have three steady equilibrium points corresponding to three population dynamics states under the influence of resistant bacteria. In order to quantitatively analyze the stability of the equilibrium points, we focused on the basic reproduction numbers. Then, both the local and global stability of the equilibrium points were quantitatively analyzed by using essential mathematical methods. Numerical results are provided to relate our model properties to some interesting biological cases. Finally, we discuss the effect of the two main parameters of the model, the proportion of antibiotics added to feed and the predation rate, and estimate the human health impacts related to the amount of feed antibiotics used. We further propose an approach for the prevention of the large-scale spread of resistant bacteria and illustrate the necessity of controlling the amount of in-feed antibiotics used.
The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs.
Krivan, Vlastimil
2007-11-01
This article studies the effects of adaptive changes in predator and/or prey activities on the Lotka-Volterra predator-prey population dynamics. The model assumes the classical foraging-predation risk trade-offs: increased activity increases population growth rate, but it also increases mortality rate. The model considers three scenarios: prey only are adaptive, predators only are adaptive, and both species are adaptive. Under all these scenarios, the neutral stability of the classical Lotka-Volterra model is partially lost because the amplitude of maximum oscillation in species numbers is bounded, and the bound is independent of the initial population numbers. Moreover, if both prey and predators behave adaptively, the neutral stability can be completely lost, and a globally stable equilibrium would appear. This is because prey and/or predator switching leads to a piecewise constant prey (predator) isocline with a vertical (horizontal) part that limits the amplitude of oscillations in prey and predator numbers, exactly as suggested by Rosenzweig and MacArthur in their seminal work on graphical stability analysis of predator-prey systems. Prey and predator activities in a long-term run are calculated explicitly. This article shows that predictions based on short-term behavioral experiments may not correspond to long-term predictions when population dynamics are considered.
The influence of intraguild predation on prey suppression and prey release: a meta-analysis.
Vance-Chalcraft, Heather D; Rosenheim, Jay A; Vonesh, James R; Osenberg, Craig W; Sih, Andrew
2007-11-01
Intraguild predation (IGP) occurs when one predator species consumes another predator species with whom it also competes for shared prey. One question of interest to ecologists is whether multiple predator species suppress prey populations more than a single predator species, and whether this result varies with the presence of IGP. We conducted a meta-analysis to examine this question, and others, regarding the effects of IGP on prey suppression. When predators can potentially consume one another (mutual IGP), prey suppression is greater in the presence of one predator species than in the presence of multiple predator species; however, this result was not found for assemblages with unidirectional or no IGP. With unidirectional IGP, intermediate predators were generally more effective than the top predator at suppressing the shared prey, in agreement with IGP theory. Adding a top predator to an assemblage generally caused prey to be released from predation, while adding an intermediate predator caused prey populations to be suppressed. However, the effects of adding a top or intermediate predator depended on the effectiveness of these predators when they were alone. Effects of IGP varied across different ecosystems (e.g., lentic, lotic, marine, terrestrial invertebrate, and terrestrial vertebrate), with the strongest patterns being driven by terrestrial invertebrates. Finally, although IGP theory is based on equilibrium conditions, data from short-term experiments can inform us about systems that are dominated by transient dynamics. Moreover, short-term experiments may be connected in some way to equilibrium models if the predator and prey densities used in experiments approximate the equilibrium densities in nature.
Srinivasu, P D N; Prasad, B S R V
2010-04-01
Use of additional food has been widely recognized by experimental scientists as one of the important tools for biological control such as species conservation and pest management. The quality and quantity of additional food supplied to the predators is known to play a vital role in the controllability of the system. The present study is continuation of a previous work that highlights the importance of quality and quantity of the additional food in the dynamics of a predator-prey system in the context of biological control. In this article the controllability of the predator-prey system is analyzed by considering inverse of quality of the additional food as the control variable. Control strategies are offered to steer the system from a given initial state to a required terminal state in a minimum time by formulating Mayer problem of optimal control. It is observed that an optimal strategy is a combination of bang-bang controls and could involve multiple switches. Properties of optimal paths are derived using necessary conditions for Mayer problem. In the light of the results evolved in this work it is possible to eradicate the prey from the eco-system in the minimum time by providing the predator with high quality additional food, which is relevant in the pest management. In the perspective of biological conservation this study highlights the possibilities to drive the state to an admissible interior equilibrium (irrespective of its stability nature) of the system in a minimum time.
Modelling the fear effect in predator-prey interactions.
Wang, Xiaoying; Zanette, Liana; Zou, Xingfu
2016-11-01
A recent field manipulation on a terrestrial vertebrate showed that the fear of predators alone altered anti-predator defences to such an extent that it greatly reduced the reproduction of prey. Because fear can evidently affect the populations of terrestrial vertebrates, we proposed a predator-prey model incorporating the cost of fear into prey reproduction. Our mathematical analyses show that high levels of fear (or equivalently strong anti-predator responses) can stabilize the predator-prey system by excluding the existence of periodic solutions. However, relatively low levels of fear can induce multiple limit cycles via subcritical Hopf bifurcations, leading to a bi-stability phenomenon. Compared to classic predator-prey models which ignore the cost of fear where Hopf bifurcations are typically supercritical, Hopf bifurcations in our model can be both supercritical and subcritical by choosing different sets of parameters. We conducted numerical simulations to explore the relationships between fear effects and other biologically related parameters (e.g. birth/death rate of adult prey), which further demonstrate the impact that fear can have in predator-prey interactions. For example, we found that under the conditions of a Hopf bifurcation, an increase in the level of fear may alter the direction of Hopf bifurcation from supercritical to subcritical when the birth rate of prey increases accordingly. Our simulations also show that the prey is less sensitive in perceiving predation risk with increasing birth rate of prey or increasing death rate of predators, but demonstrate that animals will mount stronger anti-predator defences as the attack rate of predators increases.
Xiangmin Ma
2015-01-01
Full Text Available An impulsive one-predator and two-prey system with stage-structure and generalized functional response is proposed and analyzed. By reasonable assumption and theoretical analysis, we obtain conditions for the existence and global attractivity of the predator-extinction periodic solution. Sufficient conditions for the permanence of this system are established via impulsive differential comparison theorem. Furthermore, abundant results of numerical simulations are given by choosing two different and concrete functional responses, which indicate that impulsive effects, stage-structure, and functional responses are vital to the dynamical properties of this system. Finally, the biological meanings of the main results and some control strategies are given.
Stability and Bifurcation in a State-Dependent Delayed Predator-Prey System
Hou, Aiyu; Guo, Shangjiang
In this paper, we consider a class of predator-prey equations with state-dependent delayed feedback. Firstly, we investigate the local stability of the positive equilibrium and the existence of the Hopf bifurcation. Then we use perturbation methods to determine the sub/supercriticality of Hopf bifurcation and hence the stability of Hopf bifurcating periodic solutions. Finally, numerical simulations supporting our theoretical results are also provided.
Cai Liming [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China); Beijing Institute of Information Control, Beijing 100037 (China)], E-mail: lmcai06@yahoo.com.cn; Li Xuezhi [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China); Yu Jingyuan [Beijing Institute of Information Control, Beijing 100037 (China); Zhu Guangtian [Academy of Mathematics and System Science, C.A.S., Beijing 100080 (China)
2009-05-30
A nonautonomous predator-prey dispersion-delay model with Beddington-DeAngelis functional response is investigated. It is proved that the general nonautonomous system is permanent and globally asymptotically stable under appropriate conditions. Furthermore, if the system is a(n) (almost) periodic one, a set of easily verifiable sufficient conditions are established, which guarantee the existence, uniqueness and global asymptotic stability of a positive (almost) periodic solution of the system.
Environmental fluctuations restrict eco-evolutionary dynamics in predator-prey system.
Hiltunen, Teppo; Ayan, Gökçe B; Becks, Lutz
2015-06-01
Environmental fluctuations, species interactions and rapid evolution are all predicted to affect community structure and their temporal dynamics. Although the effects of the abiotic environment and prey evolution on ecological community dynamics have been studied separately, these factors can also have interactive effects. Here we used bacteria-ciliate microcosm experiments to test for eco-evolutionary dynamics in fluctuating environments. Specifically, we followed population dynamics and a prey defence trait over time when populations were exposed to regular changes of bottom-up or top-down stressors, or combinations of these. We found that the rate of evolution of a defence trait was significantly lower in fluctuating compared with stable environments, and that the defence trait evolved to lower levels when two environmental stressors changed recurrently. The latter suggests that top-down and bottom-up changes can have additive effects constraining evolutionary response within populations. The differences in evolutionary trajectories are explained by fluctuations in population sizes of the prey and the predator, which continuously alter the supply of mutations in the prey and strength of selection through predation. Thus, it may be necessary to adopt an eco-evolutionary perspective on studies concerning the evolution of traits mediating species interactions.
Srinivasu, P D N; Prasad, B S R V
2011-10-01
Necessity to understand the role of additional food as a tool in biological control programs is being increasingly felt, particularly due to its eco-friendly nature. A thorough mathematical analysis in this direction revealed the vital role of quality and quantity of the additional food in the controllability of the predator-prey systems. In this article controllability of the additional food--provided predator-prey system is studied from perspectives of pest eradication and biological conservation. Time optimal paths have been constructed to drive the state of the system to a desired terminal state by choosing quantity of the additional food as control variable. The theory developed in this article has been illustrated by solving problems related to pest eradication and biological conservation.
Disentangling mite predator-prey relationships by multiplex PCR.
Pérez-Sayas, Consuelo; Pina, Tatiana; Gómez-Martínez, María A; Camañes, Gemma; Ibáñez-Gual, María V; Jaques, Josep A; Hurtado, Mónica A
2015-11-01
Gut content analysis using molecular techniques can help elucidate predator-prey relationships in situations in which other methodologies are not feasible, such as in the case of trophic interactions between minute species such as mites. We designed species-specific primers for a mite community occurring in Spanish citrus orchards comprising two herbivores, the Tetranychidae Tetranychus urticae and Panonychus citri, and six predatory mites belonging to the Phytoseiidae family; these predatory mites are considered to be these herbivores' main biological control agents. These primers were successfully multiplexed in a single PCR to test the range of predators feeding on each of the two prey species. We estimated prey DNA detectability success over time (DS50), which depended on the predator-prey combination and ranged from 0.2 to 18 h. These values were further used to weight prey detection in field samples to disentangle the predatory role played by the most abundant predators (i.e. Euseius stipulatus and Phytoseiulus persimilis). The corrected predation value for E. stipulatus was significantly higher than for P. persimilis. However, because this 1.5-fold difference was less than that observed regarding their sevenfold difference in abundance, we conclude that P. persimilis is the most effective predator in the system; it preyed on tetranychids almost five times more frequently than E. stipulatus did. The present results demonstrate that molecular tools are appropriate to unravel predator-prey interactions in tiny species such as mites, which include important agricultural pests and their predators.
Suzuki, Kenta; Yoshida, Takehito
2012-05-07
The metacommunity perspective has attracted much attention recently, but the understanding of how dispersal between local communities alters their ecological dynamics is still limited, especially regarding the effect of non-random, unequal dispersal of organisms. This is a study of a three-trophic-level (predator-prey-resource) system that is connected by different manners of dispersal. The model is based on a well-studied experimental system cultured in chemostats (continuous flow-through culture), which consists of rotifer predator, algal prey and nutrient. In the model, nutrient dispersal can give rise to multistability when the two systems are connected by nutrient dispersal, whereas three-trophic-level systems tend to show a rich dynamical behavior, e.g. antisynchronous or asynchronous oscillations including chaos. Although the existence of multistability was already known in two-trophic-level (predator-prey) systems, it was confined to a small range of dispersal rate. In contrast, the multistability in the three-trophic-level system is found in a broader range of dispersal rate. The results suggest that, in three-trophic-level systems, the dispersal of nutrient not only alters population dynamics of local systems but can also cause regime shifts such as a transition to different oscillation phases.
Xia Liu
2015-01-01
Full Text Available A prey-predator system with the strong Allee effect and generalized Holling type III functional response is presented and discretized. It is shown that the combined influences of Allee effect and step size have an important effect on the dynamics of the system. The existences of Flip and Neimark-Sacker bifurcations and strange attractors and chaotic bands are investigated by using the center manifold theorem and bifurcation theory and some numerical methods.
Zhang, Cong; Huang, Nan-jing; Deng, Chuan-xian
2014-01-01
We consider a Leslie predator-prey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee the existence, uniqueness, and stability of a positive periodic solution.
UNIFORM BOUNDEDNESS AND STABILITY OF SOLUTIONS TO A CUBIC PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION
Huaihuo Cao; Shengmao Fu
2009-01-01
Using the energy estimate and Gagliardo-Nirenberg-typo inequalities,the exi-tence and uniform boundedness of the global solutions to a strongly coupled reaction-zdiffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with serf and cross-diffusion. Sufficient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function.
UNIFORM BOUNDEDNESS AND STABILITY OF SOLUTIONS TO A CUBIC PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION
无
2009-01-01
Using the energy estimate and Gagliardo-Nirenberg-type inequalities,the existence and uniform boundedness of the global solutions to a strongly coupled reaction-diffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with self and cross-diffusion. Suffcient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function.
Yongzhi Liao
2012-01-01
Full Text Available By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.
Shunyi Li
2013-01-01
Full Text Available A predator-prey system with generalized group defense and impulsive control strategy is investigated. By using Floquet theorem and small amplitude perturbation skills, a local asymptotically stable prey-eradication periodic solution is obtained when the impulsive period is less than some critical value. Otherwise, the system is permanent if the impulsive period is larger than the critical value. By using bifurcation theory, we show the existence and stability of positive periodic solution when the pest eradication lost its stability. Numerical examples show that the system considered has more complicated dynamics, including (1 high-order quasiperiodic and periodic oscillation, (2 period-doubling and halving bifurcation, (3 nonunique dynamics (meaning that several attractors coexist, and (4 chaos and attractor crisis. Further, the importance of the impulsive period, the released amount of mature predators and the degree of group defense effect are discussed. Finally, the biological implications of the results and the impulsive control strategy are discussed.
POSITIVE PERIODIC SOLUTION OF ANINTEGRO-DIFFERENTIAL PREDATOR-PREY SYSTEM WITH INFINITE DELAYS
孙德献; 陈凤德
2004-01-01
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a differential-integral predator-prey system with infinite delay dN1(t)/dt=N1(t)[b1(t)-a1(t)∫(-∞,t)K1(t-u)N1(u)du-α(t)∫(-∞,t)K2(t-u)N2(u)/(1+mN1(u))du,dN2(t)/dt=N2(t)[-b2(t)+a2(t)∫(-∞,t)K3(t-u)N1(u)/(1+mN1(u))du] where N1(t),N2(t)satisfy N1(t)=Ф1(t),N2(t)=Ф2(t),Фi∈BC((-∞,0],R+),Фi(0)>0,i=1,2∫(0,+∞)Ki(s)ds=1,i=1,2,3.
PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION
李必文
2004-01-01
A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion system x'1 (t) = x1 (t)g1 (t, x1 (t) ) - a1 (t)y(t)p1 (x1 (t) ) + D1 (t)(x2(t) - x1 (t) ),x'2 (t) = x2 (t)g2 (t, x2 (t) ) - a2 (t)y(t)p2 (x2 (t) ) + D2(t)(x1 (t) - x2 (t)),y' (t) = y(t) {-h(t, y(t) ) + b1 (t)p1 (x1 (t - τ1 ) ) + b2(t)p2(x2(t - τ2))],where ai(t), bi(t) and Di(t)(i = 1, 2) are positive continuous T-periodic functions, gi(t, xi)(i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) ＞ 0 for y ＞ 0, t, y ∈ R, pi(x)(i = 1, 2) are continuous and monotonously increasing functions, and pi(xi) ＞ 0 for xi ＞ 0.
L-shaped prey isocline in the Gause predator-prey experiments with a prey refuge.
Křivan, Vlastimil; Priyadarshi, Anupam
2015-04-01
Predator and prey isoclines are estimated from data on yeast-protist population dynamics (Gause et al., 1936). Regression analysis shows that the prey isocline is best fitted by an L-shaped function that has a vertical and a horizontal part. The predator isocline is vertical. This shape of isoclines corresponds with the Lotka-Volterra and the Rosenzweig-MacArthur predator-prey models that assume a prey refuge. These results further support the idea that a prey refuge changes the prey isocline of predator-prey models from a horizontal to an L-shaped curve. Such a shape of the prey isocline effectively bounds amplitude of predator-prey oscillations, thus promotes species coexistence.
Influence of predator mutual interference and prey refuge on Lotka-Volterra predator-prey dynamics
Chen, Liujuan; Chen, Fengde; Wang, Yiqin
2013-11-01
A Lotka-Volterra predator-prey model incorporating a constant number of prey using refuges and mutual interference for predator species is presented. By applying the divergency criterion and theories on exceptional directions and normal sectors, we show that the interior equilibrium is always globally asymptotically stable and two boundary equilibria are both saddle points. Our results indicate that prey refuge has no influence on the coexistence of predator and prey species of the considered model under the effects of mutual interference for predator species, which differently from the conclusion without predator mutual interference, thus improving some known ones. Numerical simulations are performed to illustrate the validity of our results.
Wang, Wenting; Li, Wenlong; Li, Zizhen; Zhang, Hui
2011-04-01
Spatiotemporal dynamics of a predator-prey system is considered under the assumption that the predator is sensitive to colored noise. Mathematically, the model consists of two coupled diffusion-reactions. By means of extensive numerical simulations, the complex invasion pattern formations of the system are identified. The results show that a geographical invasion emerges without regional persistence when the intensity of colored noise is small. Remarkably, as the noise intensity increases, the species spreads via a patchy invasion only when the system is affected by red noise. Meanwhile, the relationship between local stability and global invasion is also considered. The predator, which becomes extinct in the system without diffusion, could invade locally when the system is affected by white noise. However, the local invasion is not followed by geographical spread.
Zizhen Zhang
2012-01-01
Full Text Available A modified Holling-Tanner predator-prey system with multiple delays is investigated. By analyzing the associated characteristic equation, the local stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays are established. Direction and stability of the periodic solutions are obtained by using normal form and center manifold theory. Finally, numerical simulations are carried out to substantiate the analytical results.
Hengguo Yu
2013-06-01
Full Text Available In this paper, the spatiotemporal dynamics of a diffusive Leslie-Gower predator-prey model with prey refuge are investigated analytically and numerically. Mathematical theoretical works have considered the existence of global solutions, population permanence and the stability of equilibrium points, which depict the threshold expressions of some critical parameters. Numerical simulations are performed to explore the pattern formation of species. These results show that the prey refuge has a profound effect on predator-prey interactions and they have the potential to be useful for the study of the entropy theory of bioinformatics.
Prey-predator model with a nonlocal consumption of prey.
Banerjee, M; Volpert, V
2016-08-01
The prey-predator model with nonlocal consumption of prey introduced in this work extends previous studies of local reaction-diffusion models. Linear stability analysis of the homogeneous in space stationary solution and numerical simulations of nonhomogeneous solutions allow us to analyze bifurcations and dynamics of stationary solutions and of travelling waves. These solutions present some new properties in comparison with the local models. They correspond to different feeding strategies of predators observed in ecology.
Prey-predator model with a nonlocal consumption of prey
Banerjee, M.; Volpert, V.
2016-08-01
The prey-predator model with nonlocal consumption of prey introduced in this work extends previous studies of local reaction-diffusion models. Linear stability analysis of the homogeneous in space stationary solution and numerical simulations of nonhomogeneous solutions allow us to analyze bifurcations and dynamics of stationary solutions and of travelling waves. These solutions present some new properties in comparison with the local models. They correspond to different feeding strategies of predators observed in ecology.
JIAO Jian-jun; CHEN Lan-sun; Juan J. Nieto; Torres Angela
2008-01-01
We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.
Li, Jiqiu; Montagnes, David J S
2015-05-01
Incorporating protozoa into population models (from simple predator-prey explorations to complex food web simulations) is of conceptual, ecological, and economic importance. From theoretical and empirical perspectives, we expose unappreciated complexity in the traditional predator-prey model structure and provide a parsimonious solution, especially for protistologists. We focus on how prey abundance alters two key components of models: predator conversion efficiency (e, the proportion of prey converted to predator, before mortality loss) and predator mortality (δ, the portion of the population lost though death). Using a well-established model system (Paramecium and Didinium), we collect data to parameterize a range of existing and novel population models that differ in the functional forms of e and δ. We then compare model simulations to an empirically obtained time-series of predator-prey population dynamics. The analysis indicates that prey-dependent e and δ should be considered when structuring population models and that both prey and predator biomass also vary with prey abundance. Both of these impact the ability of the model to predict population dynamics and, therefore, should be included in theoretical model evaluations and assessment of ecosystem dynamics associated with biomass flux.
Nonselective Harvesting of a Prey-Predator Fishery with Gompertz Law of Growth
Purohit, D.; Chaudhuri, K. S.
2002-01-01
This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of…
Unusual predator-prey dynamics under reciprocal phenotypic plasticity.
Mougi, Akihiko
2012-07-21
Recent theories and experiments have shown that plasticity, such as an inducible defense or an inducible offense in predator-prey interactions, strongly influences the stability of the population dynamics. However, such plastic adaptation has not been expected to cause unusual dynamics such as antiphase cycles, which occur in experimental predator-prey systems with evolutionary adaptation in the defensive trait of prey. Here I show that antiphase cycles and cryptic cycles (a large population fluctuation in one species with almost no change in the population of the other species) can occur in a predator-prey system when both member species can change their phenotypes through adaptive plasticity (inducible defenses and offenses). I consider a familiar type of predator-prey system in which both species can change their morphology or behavior through phenotypic plasticity. The plasticity, that is, the ability to change between distinct phenotypes, is assumed to occur so as to maximize their fitness. I examined how the reciprocal adaptive plasticity influences the population dynamics. The results show that unusual dynamics such as antiphase population cycles and cryptic cycles can occur when both species show inducible plasticity. The unusual dynamics are particularly likely to occur when the carrying capacity of the prey is small (the density dependence of the prey's growth is strong). The unusual predator-prey dynamics may be induced by phenotypic plasticity as long as the phenotypic change occurs to maximize fitness.
Coupled predator-prey oscillations in a chaotic food web
Beninca, E.; Jöhnk, K.; Heerkloss, R.; Huisman, J.
2009-01-01
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles
Coupled predator-prey oscillations in a chaotic food web
Benincà, E.; Johnk, K.D.; Heerkloss, R.; Huisman, J.
2009-01-01
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles
无
2007-01-01
We consider a delayed stage-structured pest management predator-prey system with impulsive transmitting on predator and chemical control on prey. Sufficient conditions of the global attractiveness of the pest-extinction boundary periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for practical pest management.
An impulsive predator-prey model with disease in the prey for integrated pest management
Shi, Ruiqing; Chen, Lansun
2010-02-01
In this paper, an impulsive predator-prey model with disease in the prey is investigated for the purpose of integrated pest management. In the first part of the main results, we get the sufficient condition for the global stability of the susceptible pest-eradication periodic solution. This means if the release amount of infective prey and predator satisfy the condition, then the pest will be doomed. In the second part of the main results, we also get the sufficient condition for the permanence of the system. This means if the release amount of infective prey and predator satisfy the condition, then the prey and the predator will coexist. In the last section, we interpret our mathematical results. We also point out some possible future work.
张少林; 韦明俊
2006-01-01
研究了一类时滞Predator-Prey系统,其中Prey种群是具有两个生命阶段的种群,即幼年阶段和成年阶段.Predator种群只能捕食Prey幼年种群.通过应用Gaines和Mawhin重合度理论的连续函数定理,给出了系统正周期解存在的充分条件.%A Predator-Prey system with time delay is considered. There are, immature and mature, two stage for prey species in the system. By using the continuation theorem of Gaines and Mawhin's coincidence degree theory, a sufficient condition is derived for the existence periodic positive solution.
Rudolf, Volker H W
2008-06-01
Direct and indirect interactions between two prey species can strongly alter the dynamics of predator-prey systems. Most predators are cannibalistic, and as a consequence, even systems with only one predator and one prey include two prey types: conspecifics and heterospecifics. The effects of the complex direct and indirect interactions that emerge in such cannibalistic systems are still poorly understood. This study examined how the indirect interaction between conspecific and heterospecific prey affects cannibalism and predation rates and how the direct interactions between both species indirectly alter the effect of the cannibalistic predator. I tested for these effects using larvae of the stream salamanders Eurycea cirrigera (prey) and Pseudotriton ruber (cannibalistic predator) by manipulating the relative densities of the conspecific and heterospecific prey in the presence and absence of the predator in experimental streams. The rates of cannibalism and heterospecific predation were proportional to the respective densities and negatively correlated, indicating a positive indirect interaction between conspecific and heterospecific prey, similar to "apparent mutualism." Direct interactions between prey species did not alter the effect of the predator. Although both types of prey showed a similar 30% reduction in night activity and switch in microhabitat use in response to the presence of the predator, cannibalism rates were three times higher than heterospecific predation rates irrespective of the relative densities of the two types of prey. Cumulative predation risks differed even more due to the 48% lower growth rate of conspecific prey. Detailed laboratory experiments suggest that the 3:1 difference in cannibalism and predation rate was due to the higher efficiency of heterospecific prey in escaping immediate attacks. However, no difference was observed when the predator was a closely related salamander species, Gyrinophilus porphyriticus, indicating that
Stationary Patterns in One-Predator Two-Prey Models
Pedersen, Michael; Zhigui, Lin
1999-01-01
Weakly-coupled elliptic system decribing models of simple three-species food webs such as the one-predator, two-prey modelis discussed. We show thatthere is no non-constant solution if diffusions or inter-specific competitions are strong, or if the intrinsic growths of the prey are slow...
Stationary Patterns in One-Predator Two-Prey Models
Pedersen, Michael; Zhigui, Lin
1999-01-01
Weakly-coupled elliptic system decribing models of simple three-species food webs such as the one-predator, two-prey model is discussed. We show that there is no non-constant solution if diffusions or inter-specific competitions are strong, or if the intrinsic growths of the prey are slow...
Lu Hongying
2011-01-01
Full Text Available Abstract A discrete semi-ratio-dependent predator-prey system with Holling type IV functional response and time delay is investigated. It is proved the general nonautonomous system is permanent and globally attractive under some appropriate conditions. Furthermore, if the system is periodic one, some sufficient conditions are established, which guarantee the existence and global attractivity of positive periodic solutions. We show that the conditions for the permanence of the system and the global attractivity of positive periodic solutions depend on the delay, so, we call it profitless.
Mingzhan Huang
2014-01-01
Full Text Available Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the periodic solution and analyse the dynamic phenomenon of homoclinic bifurcation of the first system by choosing the harvesting rate β as control parameter. Besides, we also study the homoclinic bifurcation of the second system about parameter δ on the basis of the theory of rotated vector field. Finally, numerical simulations are presented to illustrate the results.
Ginovart, Marta
2014-08-01
The general aim is to promote the use of individual-based models (biological agent-based models) in teaching and learning contexts in life sciences and to make their progressive incorporation into academic curricula easier, complementing other existing modelling strategies more frequently used in the classroom. Modelling activities for the study of a predator-prey system for a mathematics classroom in the first year of an undergraduate program in biosystems engineering have been designed and implemented. These activities were designed to put two modelling approaches side by side, an individual-based model and a set of ordinary differential equations. In order to organize and display this, a system with wolves and sheep in a confined domain was considered and studied. With the teaching material elaborated and a computer to perform the numerical resolutions involved and the corresponding individual-based simulations, the students answered questions and completed exercises to achieve the learning goals set. Students' responses regarding the modelling of biological systems and these two distinct methodologies applied to the study of a predator-prey system were collected via questionnaires, open-ended queries and face-to-face dialogues. Taking into account the positive responses of the students when they were doing these activities, it was clear that using a discrete individual-based model to deal with a predator-prey system jointly with a set of ordinary differential equations enriches the understanding of the modelling process, adds new insights and opens novel perspectives of what can be done with computational models versus other models. The complementary views given by the two modelling approaches were very well assessed by students.
Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales
Xiaoquan Ding
2012-01-01
Full Text Available This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin, and the Smith growth, and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one periodic solution. Some known results are shown to be special cases of the present paper.
Integrated Pest Management in a Predator-Prey System with Allee Effects.
Costa, M I S; dos Anjos, L
2015-08-01
A commonly used biocontrol strategy to control invasive pests with Allee effects consists of the deliberate introduction of natural enemies. To enhance the effectiveness of this strategy, several tactics of control of invasive species (e.g., mass-trapping, manual removal of individuals, and pesticide spraying) are combined so as to impair pest outbreaks. This combination of strategies to control pest species dynamics are usually named integrated pest management (IPM). In this work, we devise a predator-prey dynamical model in order to assess the influence of the intensity of chemical killing on the success of an IPM. The biological and mathematical framework presented in this study can also be analyzed in the light of species conservation and food web dynamics theory.
Emily W Grason
Full Text Available Top-down effects of predators in systems depend on the rate at which predators consume prey, and on predator preferences among available prey. In invaded communities, these parameters might be difficult to predict because ecological relationships are typically evolutionarily novel. We examined feeding rates and preferences of a crab native to the Pacific Northwest, Cancer productus, among four prey items: two invasive species of oyster drill (the marine whelks Urosalpinx cinerea and Ocenebra inornata and two species of oyster (Crassostrea gigas and Ostrea lurida that are also consumed by U. cinerea and O. inornata. This system is also characterized by intraguild predation because crabs are predators of drills and compete with them for prey (oysters. When only the oysters were offered, crabs did not express a preference and consumed approximately 9 juvenile oysters crab(-1 day(-1. We then tested whether crabs preferred adult drills of either U. cinerea or O. inornata, or juvenile oysters (C. gigas. While crabs consumed drills and oysters at approximately the same rate when only one type of prey was offered, they expressed a strong preference for juvenile oysters over drills when they were allowed to choose among the three prey items. This preference for oysters might negate the positive indirect effects that crabs have on oysters by crabs consuming drills (trophic cascade because crabs have a large negative direct effect on oysters when crabs, oysters, and drills co-occur.
Meng, Xinzhu; Chen, Lansun
2006-12-21
This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.
How the Magnitude of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics.
Cortez, Michael H
2016-09-01
Evolution can alter the stability and dynamics of ecological communities; for example, prey evolution can drive cyclic dynamics in predator-prey systems that are not possible in the absence of evolution. However, it is unclear how the magnitude of additive genetic variation in the evolving species mediates those effects. In this study, I explore how the magnitude of prey additive genetic variation determines what effects prey evolution has on the dynamics and stability of predator-prey systems. I use linear stability analysis to decompose the stability of a general eco-evolutionary predator-prey model into components representing the stabilities of the ecological and evolutionary subsystems as well as the interactions between those subsystems. My results show that with low genetic variation, the cyclic dynamics and stability of the system are determined by the ecological subsystem. With increased genetic variation, disruptive selection always destabilizes stable communities, stabilizing selection can stabilize or destabilize communities, and prey evolution can alter predator-prey phase lags. Stability changes occur approximately when the magnitude of genetic variation balances the (in)stabilities of the ecological and evolutionary subsystems. I discuss the connections between my stability results and prior results from the theory of adaptive dynamics.
The stabilizing effects of genetic diversity on predator-prey dynamics.
Steiner, Christopher F; Masse, Jordan
2013-01-01
Heterogeneity among prey in their susceptibility to predation is a potentially important stabilizer of predator-prey interactions, reducing the magnitude of population oscillations and enhancing total prey population abundance. When microevolutionary responses of prey populations occur at time scales comparable to population dynamics, adaptive responses in prey defense can, in theory, stabilize predator-prey dynamics and reduce top-down effects on prey abundance. While experiments have tested these predictions, less explored are the consequences of the evolution of prey phenotypes that can persist in both vulnerable and invulnerable classes. We tested this experimentally using a laboratory aquatic system composed of the rotifer Brachionus calyciflorus as a predator and the prey Synura petersenii, a colony-forming alga that exhibits genetic variation in its propensity to form colonies and colony size (larger colonies are a defense against predators). Prey populations of either low initial genetic diversity and low adaptive capacity or high initial genetic diversity and high adaptive capacity were crossed with predator presence and absence. Dynamics measured over the last 127 days of the 167-day experiment revealed no effects of initial prey genetic diversity on the average abundance or temporal variability of predator populations. However, genetic diversity and predator presence/absence interactively affected prey population abundance and stability; diversity of prey had no effects in the absence of predators but stabilized dynamics and increased total prey abundance in the presence of predators. The size structure of the genetically diverse prey populations diverged from single strain populations in the presence of predators, showing increases in colony size and in the relative abundance of cells found in colonies. Our work sheds light on the adaptive value of colony formation and supports the general view that genetic diversity and intraspecific trait variation of
张少林; 章迪平
2009-01-01
A Beddington-DeAngelis functional response predator-prey system, which may inherently oscillate, is considered by introducing periodic constant impulsive immigration of predator. The Local stability of the prey extinction periodic solution, as well as the permanence conditions of the system, are established via the method of comparison involving Liapunov functions.%讨论了带有Beddington-DeAngelis功能响应函数的脉冲predator-prey系统,运用比较定理和Liapunov函数,给出了Predator常数周期脉冲迁移环境下系统持久和prey灭绝的条件.
Predator-prey interactions and changing environments: who benefits?
Abrahams, Mark V; Mangel, Marc; Hedges, Kevin
2007-11-29
While aquatic environments have long been thought to be more moderate environments than their terrestrial cousins, environmental data demonstrate that for some systems this is not so. Numerous important environmental parameters can fluctuate dramatically, notably dissolved oxygen, turbidity and temperature. The roles of dissolved oxygen and turbidity on predator-prey interactions have been discussed in detail elsewhere within this issue and will be considered only briefly here. Here, we will focus primarily on the role of temperature and its potential impact upon predator-prey interactions. Two key properties are of particular note. For temperate aquatic ecosystems, all piscine and invertebrate piscivores and their prey are ectothermic. They will therefore be subject to energetic demands that are significantly affected by environmental temperature. Furthermore, the physical properties of water, particularly its high thermal conductivity, mean that thermal microenvironments will not exist so that fine-scale habitat movements will not be an option for dealing with changing water temperature in lentic environments. Unfortunately, there has been little experimental analysis of the role of temperature on such predator-prey interactions, so we will instead focus on theoretical work, indicating that potential implications associated with thermal change are unlikely to be straightforward and may present a greater threat to predators than to their prey. Specifically, we demonstrate that changes in the thermal environment can result in a net benefit to cold-adapted species through the mechanism of predator-prey interactions.
Predator-prey encounters in turbulent waters
Mann, J.; Ott, Søren; Pécseli, H.L.;
2002-01-01
With reference to studies of predator-prey encounters in turbulent waters, we demonstrate the feasibility of an experimental method for investigations of particle fluxes to an absorbing surface in turbulent flows. A laboratory experiment is carried out, where an approximately homogeneous and isot......With reference to studies of predator-prey encounters in turbulent waters, we demonstrate the feasibility of an experimental method for investigations of particle fluxes to an absorbing surface in turbulent flows. A laboratory experiment is carried out, where an approximately homogeneous...
Jiao Jiang
2013-01-01
Full Text Available A delayed Leslie-Gower predator-prey model with nonmonotonic functional response is studied. The existence and local stability of the positive equilibrium of the system with or without delay are completely determined in the parameter plane. Using the method of upper and lower solutions and monotone iterative scheme, a sufficient condition independent of delay for the global stability of the positive equilibrium is obtained. Hopf bifurcations induced by the ratio of the intrinsic growth rates of the predator and prey and by delay, respectively, are found. Employing the normal form theory, the direction and stability of Hopf bifurcations can be explicitly determined by the parameters of the system. Some numerical simulations are given to support and extend our theoretical results. Two limit cycles enclosing an equilibrium, one limit cycle enclosing three equilibria and different types of heteroclinic orbits such as connecting two equilibria and connecting a limit cycle and an equilibrium are also found by using analytic and numerical methods.
Barbara A Han
Full Text Available The effects of parasites and pathogens on host behaviors may be particularly important in predator-prey contexts, since few animal behaviors are more crucial for ensuring immediate survival than the avoidance of lethal predators in nature. We examined the effects of an emerging fungal pathogen of amphibians, Batrachochytrium dendrobatidis, on anti-predator behaviors of tadpoles of four frog species. We also investigated whether amphibian predators consumed infected prey, and whether B. dendrobatidis caused differences in predation rates among prey in laboratory feeding trials. We found differences in anti-predator behaviors among larvae of four amphibian species, and show that infected tadpoles of one species (Anaxyrus boreas were more active and sought refuge more frequently when exposed to predator chemical cues. Salamander predators consumed infected and uninfected tadpoles of three other prey species at similar rates in feeding trials, and predation risk among prey was unaffected by B. dendrobatidis. Collectively, our results show that even sub-lethal exposure to B. dendrobatidis can alter fundamental anti-predator behaviors in some amphibian prey species, and suggest the unexplored possibility that indiscriminate predation between infected and uninfected prey (i.e., non-selective predation could increase the prevalence of this widely distributed pathogen in amphibian populations. Because one of the most prominent types of predators in many amphibian systems is salamanders, and because salamanders are susceptible to B. dendrobatidis, our work suggests the importance of considering host susceptibility and behavioral changes that could arise from infection in both predators and prey.
Predators, prey, and natural disasters attract ecologists.
Mlot, C
1993-08-27
Some 2200 ecologists turned out for the 78th annual meeting of the Ecological Society of America (ESA), held in Madison, Wisconsin, 31 July to 4 August. Among the offerings: reports on the effect of dams and levees on large river ecology, predator-prey interactions, how parasites might control evolution, and the impact of clearcutting on soil organisms.
韩江晶
2013-01-01
By using a shooting method, we show the existence of the traveling wave solutions for a class of diffusive predator-prey systems. Our method is a significant improvement of techniques used by Dunbar, which is mainly to construct an unbounded Wazeeski set. This method provides a more sufficient way to study the existence of the traveling wave solutions for predator-prey system.
Predator-prey oscillations can shift when diseases become endemic.
Bate, Andrew M; Hilker, Frank M
2013-01-07
In epidemiology, knowing when a disease is endemic is important. This is usually done by finding the basic reproductive number, R(0), using equilibrium-based calculations. However, oscillatory dynamics are common in nature. Here, we model a disease with density dependent transmission in an oscillating predator-prey system. The condition for disease persistence in predator-prey cycles is based on the time-average density of the host and not the equilibrium density. Consequently, the time-averaged basic reproductive number R(0)¯ is what determines whether a disease is endemic, and not on the equilibrium-based basic reproductive number R(0)(*). These findings undermine any R(0) analysis based solely on steady states when predator-prey oscillations exist for density dependent diseases.
无
2011-01-01
A non-autonomous predator-prey delay system with Beddington-DeAngelis functional response and impulsive controls is established. A set of sufficient conditions which guarantee the prey and the predator to be permanent are obtained.
Predator personality and prey behavioural predictability jointly determine foraging performance
Chang, Chia-chen; Teo, Huey Yee; Norma-Rashid, Y.; Li, Daiqin
2017-01-01
Predator-prey interactions play important roles in ecological communities. Personality, consistent inter-individual differences in behaviour, of predators, prey or both are known to influence inter-specific interactions. An individual may also behave differently under the same situation and the level of such variability may differ between individuals. Such intra-individual variability (IIV) or predictability may be a trait on which selection can also act. A few studies have revealed the joint effect of personality types of both predators and prey on predator foraging performance. However, how personality type and IIV of both predators and prey jointly influence predator foraging performance remains untested empirically. Here, we addressed this using a specialized spider-eating jumping spider, Portia labiata (Salticidae), as the predator, and a jumping spider, Cosmophasis umbratica, as the prey. We examined personality types and IIVs of both P. labiata and C. umbratica and used their inter- and intra-individual behavioural variation as predictors of foraging performance (i.e., number of attempts to capture prey). Personality type and predictability had a joint effect on predator foraging performance. Aggressive predators performed better in capturing unpredictable (high IIV) prey than predictable (low IIV) prey, while docile predators demonstrated better performance when encountering predictable prey. This study highlights the importance of the joint effect of both predator and prey personality types and IIVs on predator-prey interactions. PMID:28094288
徐瑞; 陈兰荪
2002-01-01
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.
Ji-cai Huang; Dong-mei Xiao
2004-01-01
In this paper the dynamical behaviors of a predator-prey system with Holling Type-IV functional response are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numerical simulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stable limit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddlenode bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibrium and the existence of homoclinic orbit by using numerical simulation.
Bogdanov-Takens bifurcation in a predator-prey model
Liu, Zhihua; Magal, Pierre; Xiao, Dongmei
2016-12-01
In this paper, we investigate a class of predator-prey model with age structure and discuss whether the model can undergo Bogdanov-Takens bifurcation. The analysis is based on the normal form theory and the center manifold theory for semilinear equations with non-dense domain combined with integrated semigroup theory. Qualitative analysis indicates that there exist some parameter values such that this predator-prey model has an unique positive equilibrium which is Bogdanov-Takens singularity. Moreover, it is shown that under suitable small perturbation, the system undergoes the Bogdanov-Takens bifurcation in a small neighborhood of this positive equilibrium.
Goldberg, Joshua F; Hebblewhite, Mark; Bardsley, John
2014-01-01
Refugia can affect predator-prey dynamics via movements between refuge and non-refuge areas. We examine the influence of a refuge on population dynamics in a large mammal predator-prey system. Wolves (Canis lupus) have recolonized much of their former range in North America, and as a result, ungulate prey have exploited refugia to reduce predation risk with unknown impacts on wolf-prey dynamics. We examined the influence of a refuge on elk (Cervus elaphus) and wolf population dynamics in Banff National Park. Elk occupy the Banff townsite with little predation, whereas elk in the adjoining Bow Valley experience higher wolf predation. The Banff refuge may influence Bow Valley predator-prey dynamics through source-sink movements. To test this hypothesis, we used 26 years of wolf and elk population counts and the Delayed Rejection Adaptive Metropolis Markov chain Monte Carlo method to fit five predator-prey models: 1) with no source-sink movements, 2) with elk density-dependent dispersal from the refuge to the non-refuge, 3) with elk predation risk avoidance movements from the non-refuge to the refuge, 4) with differential movement rates between refuge and non-refuge, and 5) with short-term, source-sink wolf movements. Model 1 provided the best fit of the data, as measured by Akaike Information Criterion (AIC). In the top model, Banff and Bow Valley elk had median growth rates of 0.08 and 0.03 (95% credibility intervals [CIs]: 0.027-0.186 and 0.001-0.143), respectively, Banff had a median carrying capacity of 630 elk (95% CI: 471.9-2676.9), Bow Valley elk had a median wolf encounter rate of 0.02 (95% CI: 0.013-0.030), and wolves had a median death rate of 0.23 (95% CI: 0.146-0.335) and a median conversion efficiency of 0.07 (95% CI: 0.031-0.124). We found little evidence for potential source-sink movements influencing the predator-prey dynamics of this system. This result suggests that the refuge was isolated from the non-refuge.
Joshua F Goldberg
Full Text Available Refugia can affect predator-prey dynamics via movements between refuge and non-refuge areas. We examine the influence of a refuge on population dynamics in a large mammal predator-prey system. Wolves (Canis lupus have recolonized much of their former range in North America, and as a result, ungulate prey have exploited refugia to reduce predation risk with unknown impacts on wolf-prey dynamics. We examined the influence of a refuge on elk (Cervus elaphus and wolf population dynamics in Banff National Park. Elk occupy the Banff townsite with little predation, whereas elk in the adjoining Bow Valley experience higher wolf predation. The Banff refuge may influence Bow Valley predator-prey dynamics through source-sink movements. To test this hypothesis, we used 26 years of wolf and elk population counts and the Delayed Rejection Adaptive Metropolis Markov chain Monte Carlo method to fit five predator-prey models: 1 with no source-sink movements, 2 with elk density-dependent dispersal from the refuge to the non-refuge, 3 with elk predation risk avoidance movements from the non-refuge to the refuge, 4 with differential movement rates between refuge and non-refuge, and 5 with short-term, source-sink wolf movements. Model 1 provided the best fit of the data, as measured by Akaike Information Criterion (AIC. In the top model, Banff and Bow Valley elk had median growth rates of 0.08 and 0.03 (95% credibility intervals [CIs]: 0.027-0.186 and 0.001-0.143, respectively, Banff had a median carrying capacity of 630 elk (95% CI: 471.9-2676.9, Bow Valley elk had a median wolf encounter rate of 0.02 (95% CI: 0.013-0.030, and wolves had a median death rate of 0.23 (95% CI: 0.146-0.335 and a median conversion efficiency of 0.07 (95% CI: 0.031-0.124. We found little evidence for potential source-sink movements influencing the predator-prey dynamics of this system. This result suggests that the refuge was isolated from the non-refuge.
A modified predator-prey model for the interaction of police and gangs.
Sooknanan, J; Bhatt, B; Comissiong, D M G
2016-09-01
A modified predator-prey model with transmissible disease in both the predator and prey species is proposed and analysed, with infected prey being more vulnerable to predation and infected predators hunting at a reduced rate. Here, the predators are the police and the prey the gang members. In this system, we examine whether police control of gangs is possible. The system is analysed with the help of stability analyses and numerical simulations. The system has five steady states-four of which involve no core gang members and one in which all the populations coexist. Thresholds are identified which determine when the predator and prey populations survive and when the disease remains endemic. For parameter values where the spread of disease among the police officers is greater than the death of the police officers, the diseased predator population survives, when it would otherwise become extinct.
Angular velocity variations and stability of spatially explicit prey-predator systems.
Abta, Refael; Shnerb, Nadav M
2007-05-01
The linear instability of Lotka-Volterra orbits in the homogenous manifold of a two-patch system is analyzed. The origin of these orbits instability in the absence of prey migration is revealed to be the dependence of the angular velocity on the azimuthal angle; in particular, the system desynchronizes at the exit from the slow part of the trajectory. Using this insight, an analogous model of a two coupled oscillator is presented and shown to yield the same type of linear instability. This enables one to incorporate the linear instability within a recently presented general framework that allows for comparison of all known stabilization mechanisms and for simple classification of observed oscillations.
ZHANG Zi-Zhen; YANG Hui-Zhong
2013-01-01
In this paper,we consider a predator-prey system with modified Leslie-Gower and Holling type III schemes.By regarding the time delay as the bifurcation parameter,the local asymptotic stability of the positive equilibrium is investigated.And we find that Hopf bifurcations can occur as the time delay crosses some critical values.In particular,special attention is paid to the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions.In addition,the global existence of periodic solutions bifurcating from the Hopf bifurcation are considered by applying a global Hopf bifurcation result.Finally,numerical simulations are carried out to illustrate the main theoretical results.
Zhang, Li; Zhang, Fan; Ruan, Shigui
2017-03-01
We study a diffusive predator-prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a reaction-diffusion system with Beddington-DeAngelis functional response. Uniform bound, local and global asymptotic stability of the steady state of the PDE model under the no-flux boundary conditions are discussed in details. Sufficient conditions on the Turing (diffusion-driven) instability which induces spatial patterns in the model are derived via linear analysis. Existence of one-dimensional and two-dimensional spatial Turing patterns, including rhombic and hexagonal patterns, are established by weakly nonlinear analyses. These results provide theoretical explanations and numerical simulations of spatial dynamical behaviors of the wetland ecosystems of the Florida Everglades.
Bifurcations and Chaos in a Discrete Predator-prey System with Holling Type-Ⅳ Functional Response
Ji-cai Huang
2005-01-01
A discrete predator-prey system with Holling type-Ⅳ functional response obtained by the Euler method is first investigated. The conditions of existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory. Furthermore, we give the condition for the occurrence of codimension-two bifurcation called the Bogdanov-Takens bifurcation for fixed points and present approximate expressions for saddle-node, Hopf and homoclinic bifurcation sets near the Bogdanov-Takens bifurcation point. We also show, the existence of degenerated fixed point with codimension three at least. The numerical simulations, including bifurcation diagrams, phase portraits, and computation of maximum Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors such as the attracting invariant circle, period-doubling bifurcation from period-2,3,4 orbits,interior crisis, intermittency mechanic, and sudden disappearance of chaotic dynamic.
Ruiqing Shi
2013-01-01
Full Text Available Stage-structured predator-prey models with disease in the prey are constructed. For the purpose of integrated pest management, two types of impulsive control strategies (impulsive release of infective prey and impulsive release of predator are used. For Case 1, infective prey applications are more frequent than releases of predator (natural enemies. For Case 2, predator (natural enemies releases are more frequent than infective prey applications. In both cases, we get the sufficient conditions for the global attractivity of the susceptible prey-eradication periodic solution. In addition, the persistence of the systems is also discussed. At last, the results are discussed and some possible future work is put forward.
From complex spatial dynamics to simple Markov chain models: do predators and prey leave footprints?
Nachman, Gøsta Støger; Borregaard, Michael Krabbe
2010-01-01
In this paper we present a concept for using presence-absence data to recover information on the population dynamics of predator-prey systems. We use a highly complex and spatially explicit simulation model of a predator-prey mite system to generate simple presence-absence data: the number...... of patches with both prey and predators, with prey only, with predators only, and with neither species, along with the number of patches that change from one state to another in each time step. The average number of patches in the four states, as well as the average transition probabilities from one state...
Role of seasonality on predator-prey-subsidy population dynamics.
Levy, Dorian; Harrington, Heather A; Van Gorder, Robert A
2016-05-07
The role of seasonality on predator-prey interactions in the presence of a resource subsidy is examined using a system of non-autonomous ordinary differential equations (ODEs). The problem is motivated by the Arctic, inhabited by the ecological system of arctic foxes (predator), lemmings (prey), and seal carrion (subsidy). We construct two nonlinear, nonautonomous systems of ODEs named the Primary Model, and the n-Patch Model. The Primary Model considers spatial factors implicitly, and the n-Patch Model considers space explicitly as a "Stepping Stone" system. We establish the boundedness of the dynamics, as well as the necessity of sufficiently nutritional food for the survival of the predator. We investigate the importance of including the resource subsidy explicitly in the model, and the importance of accounting for predator mortality during migration. We find a variety of non-equilibrium dynamics for both systems, obtaining both limit cycles and chaotic oscillations. We were then able to discuss relevant implications for biologically interesting predator-prey systems including subsidy under seasonal effects. Notably, we can observe the extinction or persistence of a species when the corresponding autonomous system might predict the opposite.
Non-algebraic oscillations for predator-prey models
Ferragut, Antoni
2014-01-01
The authors are partially supported by grants MTM2008-03437 and 2009SGR-410. The first author is additionally partially supported by grants Juan de la Cierva and MTM2009-14163-C02-02. We prove that the limit cycle oscillations of the celebrated Rosenzweig-MacArthur differential system and other predator-prey models are non-algebraic.
Simkovsky, Ryan; Daniels, Emy F; Tang, Karen; Huynh, Stacey C; Golden, Susan S; Brahamsha, Bianca
2012-10-09
The grazing activity of predators on photosynthetic organisms is a major mechanism of mortality and population restructuring in natural environments. Grazing is also one of the primary difficulties in growing cyanobacteria and other microalgae in large, open ponds for the production of biofuels, as contaminants destroy valuable biomass and prevent stable, continuous production of biofuel crops. To address this problem, we have isolated a heterolobosean amoeba, HGG1, that grazes upon unicellular and filamentous freshwater cyanobacterial species. We have established a model predator-prey system using this amoeba and Synechococcus elongatus PCC 7942. Application of amoebae to a library of mutants of S. elongatus led to the identification of a grazer-resistant knockout mutant of the wzm ABC O-antigen transporter gene, SynPCC7942_1126. Mutations in three other genes involved in O-antigen synthesis and transport also prevented the expression of O-antigen and conferred resistance to HGG1. Complementation of these rough mutants returned O-antigen expression and susceptibility to amoebae. Rough mutants are easily identifiable by appearance, are capable of autoflocculation, and do not display growth defects under standard laboratory growth conditions, all of which are desired traits for a biofuel production strain. Thus, preventing the production of O-antigen is a pathway for producing resistance to grazing by certain amoebae.
肖海滨
2006-01-01
A class of Beddington-DeAngelis' type predator-prey dynamic system with prey and predator both having linear density restriction is considered. By using the qualitative methods of ODE, the existence and uniqueness of positive equilibrium and its global asymptotic stability are analyzed. The direct criterions for local stability of positive equilibrium and existence of limit cycle are also established when inference parameter of predator is small.
Kaiyuan Liu
2007-01-01
Full Text Available We investigate a delayed stage-structured Ivlev's functional response predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for the biological resource management and enrich the theory of impulsive delay differential equations.
Evolutionary dynamics of prey exploitation in a metapopulation of predators
Pels, S.H.; de Roos, A.M.; Sabelis, M.W.
2002-01-01
In well-mixed populations of predators and prey, natural selection favors predators with high rates of prey consumption and population growth. When spatial structure prevents the populations from being well mixed, such predators may have a selective disadvantage because they do not make full use of
Stochastic population oscillations in spatial predator-prey models
Taeuber, Uwe C, E-mail: tauber@vt.edu [Department of Physics, Virginia Tech, Blacksburg, VA 24061-0435 (United States)
2011-09-15
It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase.
Stability and Hopf Bifurcation of a Predator-Prey Model with Distributed Delays and Competition Term
Lv-Zhou Zheng
2014-01-01
Full Text Available A class of predator-prey system with distributed delays and competition term is considered. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the predator-prey system. According to the theorem of Hopf bifurcation, some sufficient conditions are obtained for the local stability of the positive equilibrium point.
无
2010-01-01
In this paper, a class of simplified Type-IV predator-prey system with linear state feedback is investigated. We prove the boundedness of the positive solutions to this system, and analyze the quality of the equilibria and the existence of limit cycles of the system surrounding the positive equilibra. By Hopf bifurcation theory, the result of having two limit cycles to the system is obtained.
Stochastic eco-evolutionary model of a prey-predator community.
Costa, Manon; Hauzy, Céline; Loeuille, Nicolas; Méléard, Sylvie
2016-02-01
We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic coevolution of prey and predators. The community evolves as a multi-type birth and death process with mutations. We first consider the infinite particle approximation of the process without mutation. In this limit, the process can be approximated by a system of differential equations. We prove the existence of a unique globally asymptotically stable equilibrium under specific conditions on the interaction among prey individuals. When mutations are rare, the community evolves on the mutational scale according to a Markovian jump process. This process describes the successive equilibria of the prey-predator community and extends the polymorphic evolutionary sequence to a coevolutionary framework. We then assume that mutations have a small impact on phenotypes and consider the evolution of monomorphic prey and predator populations. The limit of small mutation steps leads to a system of two differential equations which is a version of the canonical equation of adaptive dynamics for the prey-predator coevolution. We illustrate these different limits with an example of prey-predator community that takes into account different prey defense mechanisms. We observe through simulations how these various prey strategies impact the community.
Inferring predator behavior from attack rates on prey-replicas that differ in conspicuousness.
Yoel E Stuart
Full Text Available Behavioral ecologists and evolutionary biologists have long studied how predators respond to prey items novel in color and pattern. Because a predatory response is influenced by both the predator's ability to detect the prey and a post-detection behavioral response, variation among prey types in conspicuousness may confound inference about post-prey-detection predator behavior. That is, a relatively high attack rate on a given prey type may result primarily from enhanced conspicuousness and not predators' direct preference for that prey. Few studies, however, account for such variation in conspicuousness. In a field experiment, we measured predation rates on clay replicas of two aposematic forms of the poison dart frog Dendrobates pumilio, one novel and one familiar, and two cryptic controls. To ask whether predators prefer or avoid a novel aposematic prey form independently of conspicuousness differences among replicas, we first modeled the visual system of a typical avian predator. Then, we used this model to estimate replica contrast against a leaf litter background to test whether variation in contrast alone could explain variation in predator attack rate. We found that absolute predation rates did not differ among color forms. Predation rates relative to conspicuousness did, however, deviate significantly from expectation, suggesting that predators do make post-detection decisions to avoid or attack a given prey type. The direction of this deviation from expectation, though, depended on assumptions we made about how avian predators discriminate objects from the visual background. Our results show that it is important to account for prey conspicuousness when investigating predator behavior and also that existing models of predator visual systems need to be refined.
Li, Yongkun; Ye, Yuan
2013-11-01
In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we study an impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive almost periodic solutions for the system under consideration. Our results of this paper are completely new and our method used in this paper can be used to study the existence of multiple positive almost periodic solutions to other types of population systems.
Tyson, Rebecca; Lutscher, Frithjof
2016-11-01
The functional response of some predator species changes from a pattern characteristic for a generalist to that for a specialist according to seasonally varying prey availability. Current theory does not address the dynamic consequences of this phenomenon. Since season length correlates strongly with altitude and latitude and is predicted to change under future climate scenarios, including this phenomenon in theoretical models seems essential for correct prediction of future ecosystem dynamics. We develop and analyze a two-season model for the great horned owl (Bubo virginialis) and snowshoe hare (Lepus americanus). These species form a predator-prey system in which the generalist to specialist shift in predation pattern has been documented empirically. We study the qualitative behavior of this predator-prey model community as summer season length changes. We find that relatively small changes in summer season length can have a profound impact on the system. In particular, when the predator has sufficient alternative resources available during the summer season, it can drive the prey to extinction, there can be coexisting stable states, and there can be stable large-amplitude limit cycles coexisting with a stable steady state. Our results illustrate that the impacts of global change on local ecosystems can be driven by internal system dynamics and can potentially have catastrophic consequences.
A Predator-Prey Model with Non-Monotonic Response Function
Broer, H.W.; Naudot, V.; Roussarie, R.; Saleh, K.
2006-01-01
We study the dynamics of a family of planar vector fields that models certain populations of predators and their prey. This model is adapted from the standard Volterra-Lotka system by taking into account group defense, competition between prey and competition between predators. Also we initiate comp
van Maanen, R.; Broufas, G.; de Jong, P.; Aguilar-Fenollosa, E.; Revynthi, A.; Sabelis, M.W.; Janssen, A.
2015-01-01
1. To reduce the risk of being eaten by predators, prey alter their morphology or behaviour. This response can be tuned to the current danger if chemical or other cues associated with predators inform the prey about the risks involved. 2. It is well known that various prey species discriminate
Predator-prey interactions between shell-boring beetle larvae and rock-dwelling land snails.
Baalbergen, Els; Helwerda, Renate; Schelfhorst, Rense; Castillo Cajas, Ruth F; van Moorsel, Coline H M; Kundrata, Robin; Welter-Schultes, Francisco W; Giokas, Sinos; Schilthuizen, Menno
2014-01-01
Drilus beetle larvae (Coleoptera: Elateridae) are specialized predators of land snails. Here, we describe various aspects of the predator-prey interactions between multiple Drilus species attacking multiple Albinaria (Gastropoda: Clausiliidae) species in Greece. We observe that Drilus species may be facultative or obligate Albinaria-specialists. We map geographically varying predation rates in Crete, where on average 24% of empty shells carry fatal Drilus bore holes. We also provide first-hand observations and video-footage of prey entry and exit strategies of the Drilus larvae, and evaluate the potential mutual evolutionary impacts. We find limited evidence for an effect of shell features and snail behavioral traits on inter- and intra-specifically differing predation rates. We also find that Drilus predators adjust their predation behavior based on specific shell traits of the prey. In conclusion, we suggest that, with these baseline data, this interesting predator-prey system will be available for further, detailed more evolutionary ecology studies.
Global stability of prey-taxis systems
Jin, Hai-Yang; Wang, Zhi-An
2017-02-01
In this paper, we prove the global boundedness and stability of the predator-prey system with prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions. By deriving an entropy-like equality and a boundedness criterion, we show that the intrinsic interaction between predators and preys is sufficient to prevent the population overcrowding even the prey-taxis is included and strong. Furthermore, by constructing appropriate Lyapunov functionals, we show that prey-only steady state is globally asymptotically stable if the predation is weak, and the co-existence steady state is globally asymptotically stable under some conditions (like the prey-taxis is weak or the prey diffuses fast) if the predation is strong. The convergence rates of solutions to the steady states are derived in the paper.
Invasive prey indirectly increase predation on their native competitors.
Castorani, Max C N; Hovel, Kevin A
2015-07-01
Ecological theory predicts that invasive prey can interact with native prey directly by competing for shared resources or indirectly by changing the abundance or behavior of shared native predators. However, both the study and management of invasive prey have historically overlooked indirect effects. In southern California estuaries, introduction of the Asian nest mussel Arcuatula senhousia has been linked to profound changes in native bivalve assemblages, but the mechanisms of these interactions remain unclear. We performed three field experiments to assess the mechanisms of competition between Arcuatula and native bivalves, and evaluated the potential for Arcuatula to indirectly mediate native predator-prey dynamics. We found that Arcuatula reduces the diversity, abundance, and size of native bivalve recruits by preemptively exploiting space in surface sediments. When paired with native shallow-dwelling clams (Chione undatella and Laevicardium substriatum), Arcuatula reduces adult survival through overgrowth competition. However, Arcuatula also attracts native predators, causing apparent competition by indirectly increasing predation of native clams, especially for poorly defended species. Therefore, invasive prey can indirectly increase predation rates on native competitors by changing the behavior of shared native predators, but the magnitude of apparent competition strongly depends on the vulnerability of natives to predation. Interestingly, our results indicate that the vulnerability of invasive prey to predation can greatly exacerbate impacts on their native competitors. Our findings suggest that consideration of both direct and indirect effects of invasive prey, as well as native predator-prey relationships, should lead to more effective invasive species management.
Top predators negate the effect of mesopredators on prey physiology.
Palacios, Maria M; Killen, Shaun S; Nadler, Lauren E; White, James R; McCormick, Mark I
2016-07-01
Predation theory and empirical evidence suggest that top predators benefit the survival of resource prey through the suppression of mesopredators. However, whether such behavioural suppression can also affect the physiology of resource prey has yet to be examined. Using a three-tier reef fish food web and intermittent-flow respirometry, our study examined changes in the metabolic rate of resource prey exposed to combinations of mesopredator and top predator cues. Under experimental conditions, the mesopredator (dottyback, Pseudochromis fuscus) continuously foraged and attacked resource prey (juveniles of the damselfish Pomacentrus amboinensis) triggering an increase in prey O2 uptake by 38 ± 12·9% (mean ± SE). The visual stimulus of a top predator (coral trout, Plectropomus leopardus) restricted the foraging activity of the mesopredator, indirectly allowing resource prey to minimize stress and maintain routine O2 uptake. Although not as strong as the effect of the top predator, the sight of a large non-predator species (thicklip wrasse, Hemigymnus melapterus) also reduced the impact of the mesopredator on prey metabolic rate. We conclude that lower trophic-level species can benefit physiologically from the presence of top predators through the behavioural suppression that top predators impose on mesopredators. By minimizing the energy spent on mesopredator avoidance and the associated stress response to mesopredator attacks, prey may be able to invest more energy in foraging and growth, highlighting the importance of the indirect, non-consumptive effects of top predators in marine food webs.
Li, Haiyin; Meng, Gang; She, Zhikun
In this paper, we investigate the stability and Hopf bifurcation of a delayed density-dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered such that the studied predator-prey system conforms to the realistically biological environment. We start with the geometric criterion introduced by Beretta and Kuang [2002] and then investigate the stability of the positive equilibrium and the stability switches of the system with respect to the delay parameter τ. Especially, we generalize the geometric criterion in [Beretta & Kuang, 2002] by introducing the condition (i‧) which can be assured by the condition (H2‧), and adopting the technique of lifting to define the function S˜n(τ) for alternatively determining stability switches at the zeroes of S˜n(τ)s. Afterwards, by the Poincaré normal form for Hopf bifurcation in [Kuznetsov, 1998] and the bifurcation formulae in [Hassard et al., 1981], we qualitatively analyze the properties for the occurring Hopf bifurcations of the system (3). Finally, an example with numerical simulations is given to illustrate the obtained results.
Predator cannibalism can intensify negative impacts on heterospecific prey.
Takatsu, Kunio; Kishida, Osamu
2015-07-01
Although natural populations consist of individuals with different traits, and the degree of phenotypic variation varies among populations, the impact of phenotypic variation on ecological interactions has received little attention, because traditional approaches to community ecology assume homogeneity of individuals within a population. Stage structure, which is a common way of generating size and developmental variation within predator populations, can drive cannibalistic interactions, which can affect the strength of predatory effects on the predator's heterospecific prey. Studies have shown that predator cannibalism weakens predatory effects on heterospecific prey by reducing the size of the predator population and by inducing less feeding activity of noncannibal predators. We predict, however, that predator cannibalism, by promoting rapid growth of the cannibals, can also intensify predation pressure on heterospecific prey, because large predators have large resource requirements and may utilize a wider variety of prey species. To test this hypothesis, we conducted an experiment in which we created carnivorous salamander (Hynobius retardatus) populations with different stage structures by manipulating the salamander's hatch timing (i.e., populations with large or small variation in the timing of hatching), and explored the resultant impacts on the abundance, behavior, morphology, and life history of the salamander's large heterospecific prey, Rana pirica frog tadpoles. Cannibalism was rare in salamander populations having small hatch-timing variation, but was frequent in those having large hatch-timing variation. Thus, giant salamander cannibals occurred only in the latter. We clearly showed that salamander giants exerted strong predation pressure on frog tadpoles, which induced large behavioral and morphological defenses in the tadpoles and caused them to metamorphose late at large size. Hence, predator cannibalism arising from large variation in the timing
Wu, Sainan; Shi, Junping; Wu, Boying
2016-04-01
This paper proves the global existence and boundedness of solutions to a general reaction-diffusion predator-prey system with prey-taxis defined on a smooth bounded domain with no-flux boundary condition. The result holds for domains in arbitrary spatial dimension and small prey-taxis sensitivity coefficient. This paper also proves the existence of a global attractor and the uniform persistence of the system under some additional conditions. Applications to models from ecology and chemotaxis are discussed.
Potential landscape and probabilistic flux of a predator prey network.
Li, Chunhe; Wang, Erkang; Wang, Jin
2011-03-15
Predator-prey system, as an essential element of ecological dynamics, has been recently studied experimentally with synthetic biology. We developed a global probabilistic landscape and flux framework to explore a synthetic predator-prey network constructed with two Escherichia coli populations. We developed a self consistent mean field method to solve multidimensional problem and uncovered the potential landscape with Mexican hat ring valley shape for predator-prey oscillations. The landscape attracts the system down to the closed oscillation ring. The probability flux drives the coherent oscillations on the ring. Both the landscape and flux are essential for the stable and coherent oscillations. The landscape topography characterized by the barrier height from the top of Mexican hat to the closed ring valley provides a quantitative measure of global stability of system. The entropy production rate for the energy dissipation is less for smaller environmental fluctuations or perturbations. The global sensitivity analysis based on the landscape topography gives specific predictions for the effects of parameters on the stability and function of the system. This may provide some clues for the global stability, robustness, function and synthetic network design.
Effects of seasonal growth on delayed prey-predator model
Gakkhar, Sunita [Department of Mathematics, IIT Roorkee, Roorkee 247667 (India)], E-mail: sungkfma@iitr.ernet.in; Sahani, Saroj Kumar [Department of Mathematics, IIT Roorkee, Roorkee 247667 (India)], E-mail: sarojdma@iitr.ernet.in; Negi, Kuldeep [Department of Mathematics, IIT Roorkee, Roorkee 247667 (India)], E-mail: negikdma@iitr.ernet.in
2009-01-15
The dynamic behavior of a delayed predator-prey system with Holling II functional response is investigated. The stability analysis has been carried out and existence of Hopf bifurcation has been established. The complex dynamic behavior due to time delay has been explored. The effects of seasonal growth on the complex dynamics have been simulated. The model shows a rich variety of behavior, including period doubling, quasi-periodicity, chaos, transient chaos, and windows of periodicity.
Global Existence of Classical Solutions to a Three-Species Predator-Prey Model with Two Prey-Taxes
Chenglin Li
2012-01-01
Full Text Available We are concerned with three-species predator-prey model including two prey-taxes and Holling type II functional response under no flux boundary condition. By applying the contraction mapping principle, the parabolic Schauder estimates, and parabolic Lp estimates, we prove that there exists a unique global classical solution of this system.
Mainul Haque; Joydev Chattopadhyay
2007-01-01
The present paper deals with the parametric analysis of ratio-dependent predator-prey system in which a disease is spreading among the prey species only. We have analyzed the behavior of the system around each equilibrium. Threshold Ro is identified which determine when the disease dies out and when it is endemic. Our final conclusion is that introduction of infected prey species in the ratio-dependent predator-prey model may act as a biological control to prevent the population from extinction.%对疾病仅在食饵种群传播的有比例依赖的捕食-被捕食系统的动力学进行了分析,给出了每个平衡点附近系统的性态,定义了决定疾病灭绝和成为地方病的闲值Ro.得出的结论是:在比例依赖的捕食-被捕食系统中,染病食饵种群可以充当一个生物控制量,以抑制种群的绝灭.
Jiao Jianjun [School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004 (China)], E-mail: jiaojianjun05@126.com; Chen Lansun [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)], E-mail: lschen@amss.ac.cn; Cai Shaohong [Guizhou College of Finance and Economics, Guiyang 550004 (China)], E-mail: caish@mail.gzife.edu.cn
2009-05-30
In this work, we investigate a delayed stage-structured Holling II predator-prey model with mutual interference and impulsive perturbations on predator. Sufficient conditions of the global attractivity of prey-extinction periodic solution and the permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for the practical pest management.
非自治脉冲 HollingⅡ捕食系统的研究%Study of a Nonautonomous HollingⅡ Predator-Prey System with Impulses
燕聪妮; 董玲珍; 刘明
2015-01-01
研究了 HollingⅡ捕食系统在受其他因素干扰、系数变化和脉冲扰动时的动力学行为。首先对单种群脉冲非自治系统的动力学行为进行了讨论，分析了单种群系统持续生存和灭绝的条件。进一步，应用这些结论和微分方程比较定理，分别对系统食饵灭绝和食饵捕食者都灭绝的情况进行了研究，并讨论了系统的持久生存性，得到了带脉冲的 HollingⅡ非自治捕食系统灭绝和持久生存的条件。%The dynamical behaviors of Holling II predator-prey system which were disturbed by some effects,coefficients varied and impulses perturbed were studied.Firstly,the dynamical behaviors of sin-gle-species impulses nonautonomous system were discussed,and the permanence and extinction condi-tions of single-species system were analyzed.Further,based on these results and impulsive differential comparison theorem,the system prey extinction and both prey and predator extinction were studied re-spectively,and the permanence of system was discussed,the extinction and permanence conditions of Holling II nonautonomous predator-prey system with impulses were obtained.
A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey
Jianwen Jia
2009-01-01
Full Text Available We introduce and study a Gompertz model with time delay and impulsive perturbations on the prey. By using the discrete dynamical system determined by the stroboscopic map, we obtain the sufficient conditions for the existence and global attractivity of the “predator-extinction” periodic solution. With the theory on the delay functional and impulsive differential equation, we obtain the appropriate condition for the permanence of the system.
Prey patch patterns predict habitat use by top marine predators with diverse foraging strategies.
Kelly J Benoit-Bird
Full Text Available Spatial coherence between predators and prey has rarely been observed in pelagic marine ecosystems. We used measures of the environment, prey abundance, prey quality, and prey distribution to explain the observed distributions of three co-occurring predator species breeding on islands in the southeastern Bering Sea: black-legged kittiwakes (Rissa tridactyla, thick-billed murres (Uria lomvia, and northern fur seals (Callorhinus ursinus. Predictions of statistical models were tested using movement patterns obtained from satellite-tracked individual animals. With the most commonly used measures to quantify prey distributions--areal biomass, density, and numerical abundance--we were unable to find a spatial relationship between predators and their prey. We instead found that habitat use by all three predators was predicted most strongly by prey patch characteristics such as depth and local density within spatial aggregations. Additional prey patch characteristics and physical habitat also contributed significantly to characterizing predator patterns. Our results indicate that the small-scale prey patch characteristics are critical to how predators perceive the quality of their food supply and the mechanisms they use to exploit it, regardless of time of day, sampling year, or source colony. The three focal predator species had different constraints and employed different foraging strategies--a shallow diver that makes trips of moderate distance (kittiwakes, a deep diver that makes trip of short distances (murres, and a deep diver that makes extensive trips (fur seals. However, all three were similarly linked by patchiness of prey rather than by the distribution of overall biomass. This supports the hypothesis that patchiness may be critical for understanding predator-prey relationships in pelagic marine systems more generally.
De Block, Marjan; Pauwels, Kevin; Van Den Broeck, Maarten; De Meester, Luc; Stoks, Robby
2013-03-01
Temperature effects on predator-prey interactions are fundamental to better understand the effects of global warming. Previous studies never considered local adaptation of both predators and prey at different latitudes, and ignored the novel population combinations of the same predator-prey species system that may arise because of northward dispersal. We set up a common garden warming experiment to study predator-prey interactions between Ischnura elegans damselfly predators and Daphnia magna zooplankton prey from three source latitudes spanning >1500 km. Damselfly foraging rates showed thermal plasticity and strong latitudinal differences consistent with adaptation to local time constraints. Relative survival was higher at 24 °C than at 20 °C in southern Daphnia and higher at 20 °C than at 24 °C, in northern Daphnia indicating local thermal adaptation of the Daphnia prey. Yet, this thermal advantage disappeared when they were confronted with the damselfly predators of the same latitude, reflecting also a signal of local thermal adaptation in the damselfly predators. Our results further suggest the invasion success of northward moving predators as well as prey to be latitude-specific. We advocate the novel common garden experimental approach using predators and prey obtained from natural temperature gradients spanning the predicted temperature increase in the northern populations as a powerful approach to gain mechanistic insights into how community modules will be affected by global warming. It can be used as a space-for-time substitution to inform how predator-prey interaction may gradually evolve to long-term warming.
Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation
Haihong Li
2014-01-01
show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results.
Periodic Solutions of a Delayed Predator-Prey Model with Stage Structure for Prey
Rui Xu; Lan-sun Chen; Fei-long Hao
2004-01-01
A periodic predator-prey model with stage structure for prey and time delays due to negative feedbackand gestation of predator is proposed. By using Gaines and Mawhin's continuation theorem of coincidencedegree theory, su.cient conditions are derived for the existence of positive periodic solutions to the proposedmodel. Numerical simulations are presented to illustrate the feasibility of our main result.
A single predator charging a herd of prey: effects of self volume and predator-prey decision-making
Schwarzl, M; Oshanin, G; Metzler, R
2016-01-01
We study the degree of success of a single predator hunting a herd of prey on a two dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into direct escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics ...
Prey-Predator Three Species Model Using Predator Harvesting Holling Type II Functional
Vijaya, S.; Rekha, E.
2016-07-01
This paper presents three species harvesting model in which there is one predator species and two others are prey species. We derive boundedness and equilibrium point for this system. Also we derive the stability of this system analytically. We find bifurcation for this system. We have derived the binomic equilibrium point by using Pontryagin’s maximum principle (PMP). Presented are various suitable analytical and numerical examples with Maple 18 programming.
Existence, uniqueness and stability of positive steady states to a prey-predator diffusion system
2009-01-01
In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.
Dynamics of prey moving through a predator field: a model of migrating juvenile salmon
Petersen, J.H.; DeAngelis, D.L.
2000-01-01
The migration of a patch of prey through a field of relatively stationary predators is a situation that occurs frequently in nature. Making quantitative predictions concerning such phenomena may be difficult, however, because factors such as the number of the prey in the patch, the spatial length and velocity of the patch, and the feeding rate and satiation of the predators all interact in a complex way. However, such problems are of great practical importance in many management situations; e.g., calculating the mortality of juvenile salmon (smolts) swimming down a river or reservoir containing many predators. Salmon smolts often move downstream in patches short compared with the length of the reservoir. To take into account the spatial dependence of the interaction, we used a spatially-explicit, individual-based modeling approach. We found that the mortality of prey depends strongly on the number of prey in the patch, the downstream velocity of prey in the patch, and the dispersion or spread of the patch in size through time. Some counterintuitive phenomena are predicted, such as predators downstrean capturing more prey per predator than those upstream, even though the number of prey may be greatly depleted by the time the prey patch reaches the downstream predators. Individual-based models may be necessary for complex spatial situations, such as salmonid migration, where processes such as schooling occur at fine scales and affect system predictions. We compare some results to predictions from other salmonid models. (C) 2000 Elsevier Science Inc.
谭杨; 郭子君
2014-01-01
A stochastic model of a predator-prey system with disease in the prey population is proposed and analyzed. The solution of the model will be stochastically ultimate boundedness without any additional condition. The infected prey and predator tend to extinct exponentially. The asymptotic behavior around the other equilibrium of the deterministic system is examined that is not the equilibrium of the stochastic system.%研究了一类食饵带有疾病的食饵-捕食者随机模型，分析了模型的有界性，在没有附加条件下证明了模型的解是随机最终有界的和随机系统中染病食饵种群与捕食者种群均几乎处处依指数趋于灭绝，最后研究了随机系统围绕确定性系统的地方病平衡点的渐近性质，得到了随机模型的解存在稳定分布的充分条件。
The influence of dispersal on a predator-prey system with two habitats
Gramlich, Philipp; Rudolf, Lars; Drossel, Barbara; Gross, Thilo
2015-01-01
Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and comprehensive study of the simplest possible system that includes dispersal and local interactions, namely a 2-patch 2-species system. We evaluate the impact of dispersal on stability and on the occurrence of bifurcations, including pattern forming bifurcations that lead to spatial heterogeneity, in 19 different classes of models with the help of the generalized modelling approach. We find that dispersal often destabilizes equilibria, but it can stabilize them if it increases population losses. If dispersal is nonrandom, i.e. if emigration or immigration rates depend on population densities, the correlation of stability with migration rates is positive in part of the models. We also find that many systems show all four types of bifurcations and that antisynchronous oscillations occu...
The influence of dispersal on a predator-prey system with two habitats.
Gramlich, P; Plitzko, S J; Rudolf, L; Drossel, B; Gross, T
2016-06-07
Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and comprehensive study of the simplest possible system that includes dispersal and local interactions, namely a 2-patch 2-species system. We evaluate the impact of dispersal on stability and on the occurrence of bifurcations, including pattern forming bifurcations that lead to spatial heterogeneity, in 19 different classes of models with the help of the generalized modelling approach. We find that dispersal often destabilizes equilibria, but it can stabilize them if it increases population losses. If dispersal is nonrandom, i.e. if emigration or immigration rates depend on population densities, the correlation of stability with dispersal rates is positive in part of the models. We also find that many systems show all four types of bifurcations and that antisynchronous oscillations occur mostly with nonrandom dispersal.
三次Kolmogorov捕食系统的多个稳定极限环%Multiple Stable Limit Cycles for a Cubic Kolmogorov Prey-Predator System
陆征一; 何碧
2001-01-01
构造具有三个极限环(其中两个稳定)的三次Kolmogorov系统.这个例子肯定地回答了Coleman(1982)提出的一个问题.在多项式处理中,利用了计算机代数系统Maple.%A cubic Kolmogorov prey-predator system is constructed and is shown to have three small amplitude limit cycles, among which two are stable. This can serve as an affirmative answer to a question proposed by Coleman(1982). The computer algebraic system, Maple, is applied to manipulate polynomials in dealing with the system.
On the Predator-Prey System with Holling-(n + 1) Functional Response
Wei WANG; Jian Hua SUN
2007-01-01
The qualitative properties of a predatorprey system with Holling-(n + 1) functional response and a fairly general growth rate are completely investigated. The necessary and sufficient condition to guarantee the uniqueness of limit cycles is given. Our work extends the previous relevant results in the reference.
Liu, Yingyuan; Zhang, Xiaolan; Zhou, Tiejun
2014-01-01
The paper studies a periodic and delayed predator-prey system with non-monotonic functional responses and stage structure. In the system, both the predator and prey are divided into immature individuals and mature individuals by two fixed ages. It is assumed that the immature predators cannot attack preys, and the case of the mature predators attacking the immature preys is also ignored. Based on Mawhin's coincidence degree, sufficient conditions are obtained for the existence of two positive periodic solutions of the system. An example is presented to illustrate the feasibility of the main results.
Liu Zhenjie
2009-01-01
Full Text Available This paper investigates the existence of periodic solutions of a ratio-dependent predator-prey diffusion system with Michaelis-Menten functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain suffcient criteria for the existence of periodic solutions for the system. Moreover, when the time scale is chosen as or , the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.
Spatiotemporal dynamics of two generic predator-prey models.
Garvie, Marcus R; Trenchea, C
2010-11-01
We present the analysis of two reaction-diffusion systems modelling predator-prey interactions, where the predator displays the Holling type II functional response, and in the absence of predators, the prey growth is logistic. The local analysis is based on the application of qualitative theory for ordinary differential equations and dynamical systems, while the global well-posedness depends on invariant sets and differential inequalities. The key result is an L(∞)-stability estimate, which depends on a polynomial growth condition for the kinetics. The existence of an a priori L(p)-estimate, uniform in time, for all p ≥ 1, implies L(∞)-uniform bounds, given any nonnegative L(∞)-initial data. The applicability of the L(∞)-estimate to general reaction-diffusion systems is discussed, and how the continuous results can be mimicked in the discrete case, leading to stability estimates for a Galerkin finite-element method with piecewise linear continuous basis functions. In order to verify the biological wave phenomena of solutions, numerical results are presented in two-space dimensions, which have interesting ecological implications as they demonstrate that solutions can be 'trapped' in an invariant region of phase space.
Predator-Prey-Subsidy Population Dynamics on Stepping-Stone Domains.
Shen, Lulan; Van Gorder, Robert A
2017-03-16
Predator-prey-subsidy dynamics on stepping-stone domains are examined using a variety of network configurations. Our problem is motivated by the interactions between arctic foxes (predator) and lemmings (prey) in the presence of seal carrion (subsidy) provided by polar bears. We use the n-Patch Model, which considers space explicitly as a "Stepping Stone" system. We consider the role that the carrying capacity, predator migration rate, input subsidy rate, predator mortality rate, and proportion of predators surviving migration play in the predator-prey-subsidy population dynamics. We find that for certain types of networks, added mobility will help predator populations, allowing them to survive or coexist when they would otherwise go extinct if confined to one location, while in other situations (such as when sparsely distributed nodes in the network have few resources available) the added mobility will hurt the predator population. We also find that a combination of favorable conditions for the prey and subsidy can lead to the formation of limit cycles (boom and bust dynamic) from stable equilibrium states. These modifications to the dynamics vary depending on the specific network structure employed, highlighting the fact that network structure can strongly influence the predator-prey-subsidy dynamics in stepping-stone domains.
Nonlinear functional response parameter estimation in a stochastic predator-prey model.
Gilioli, Gianni; Pasquali, Sara; Ruggeri, Fabrizio
2012-01-01
Parameter estimation for the functional response of predator-prey systems is a critical methodological problem in population ecology. In this paper we consider a stochastic predator-prey system with non-linear Ivlev functional response and propose a method for model parameter estimation based on time series of field data. We tackle the problem of parameter estimation using a Bayesian approach relying on a Markov Chain Monte Carlo algorithm. The efficiency of the method is tested on a set of simulated data. Then, the method is applied to a predator-prey system of importance for Integrated Pest Management and biological control, the pest mite Tetranychus urticae and the predatory mite Phytoseiulus persimilis. The model is estimated on a dataset obtained from a field survey. Finally, the estimated model is used to forecast predator-prey dynamics in similar fields, with slightly different initial conditions.
Human activity helps prey win the predator-prey space race.
Muhly, Tyler B; Semeniuk, Christina; Massolo, Alessandro; Hickman, Laura; Musiani, Marco
2011-03-02
Predator-prey interactions, including between large mammalian wildlife species, can be represented as a "space race", where prey try to minimize and predators maximize spatial overlap. Human activity can also influence the distribution of wildlife species. In particular, high-human disturbance can displace large carnivore predators, a trait-mediated direct effect. Predator displacement by humans could then indirectly benefit prey species by reducing predation risk, a trait-mediated indirect effect of humans that spatially decouples predators from prey. The purpose of this research was to test the hypothesis that high-human activity was displacing predators and thus indirectly creating spatial refuge for prey species, helping prey win the "space race". We measured the occurrence of eleven large mammal species (including humans and cattle) at 43 camera traps deployed on roads and trails in southwest Alberta, Canada. We tested species co-occurrence at camera sites using hierarchical cluster and nonmetric multidimensional scaling (NMS) analyses; and tested whether human activity, food and/or habitat influenced predator and prey species counts at camera sites using regression tree analysis. Cluster and NMS analysis indicated that at camera sites humans co-occurred with prey species more than predator species and predator species had relatively low co-occurrence with prey species. Regression tree analysis indicated that prey species were three times more abundant on roads and trails with >32 humans/day. However, predators were less abundant on roads and trails that exceeded 18 humans/day. Our results support the hypothesis that high-human activity displaced predators but not prey species, creating spatial refuge from predation. High-human activity on roads and trails (i.e., >18 humans/day) has the potential to interfere with predator-prey interactions via trait-mediated direct and indirect effects. We urge scientist and managers to carefully consider and quantify the
Human activity helps prey win the predator-prey space race.
Tyler B Muhly
Full Text Available Predator-prey interactions, including between large mammalian wildlife species, can be represented as a "space race", where prey try to minimize and predators maximize spatial overlap. Human activity can also influence the distribution of wildlife species. In particular, high-human disturbance can displace large carnivore predators, a trait-mediated direct effect. Predator displacement by humans could then indirectly benefit prey species by reducing predation risk, a trait-mediated indirect effect of humans that spatially decouples predators from prey. The purpose of this research was to test the hypothesis that high-human activity was displacing predators and thus indirectly creating spatial refuge for prey species, helping prey win the "space race". We measured the occurrence of eleven large mammal species (including humans and cattle at 43 camera traps deployed on roads and trails in southwest Alberta, Canada. We tested species co-occurrence at camera sites using hierarchical cluster and nonmetric multidimensional scaling (NMS analyses; and tested whether human activity, food and/or habitat influenced predator and prey species counts at camera sites using regression tree analysis. Cluster and NMS analysis indicated that at camera sites humans co-occurred with prey species more than predator species and predator species had relatively low co-occurrence with prey species. Regression tree analysis indicated that prey species were three times more abundant on roads and trails with >32 humans/day. However, predators were less abundant on roads and trails that exceeded 18 humans/day. Our results support the hypothesis that high-human activity displaced predators but not prey species, creating spatial refuge from predation. High-human activity on roads and trails (i.e., >18 humans/day has the potential to interfere with predator-prey interactions via trait-mediated direct and indirect effects. We urge scientist and managers to carefully consider and
Das, Krishna Pada; Bairagi, Nandadulal; Sen, Prabir
It is generally, but not always, accepted that alternative food plays a stabilizing role in predator-prey interaction. Parasites, on the other hand, have the ability to change both the qualitative and quantitative dynamics of its host population. In recent times, researchers are showing growing interest in formulating models that integrate both the ecological and epidemiological aspects. The present paper deals with the effect of alternative food on a predator-prey system with disease in the predator population. We show that the system, in the absence of alternative food, exhibits different dynamics viz. stable coexistence, limit cycle oscillations, period-doubling bifurcation and chaos when infection rate is gradually increased. However, when predator consumes alternative food coupled with its focal prey, the system returns to regular oscillatory state from chaotic state through period-halving bifurcations. Our study shows that alternative food may have larger impact on the community structure and may increase population persistence.
Creel, Scott; Dröge, Egil; M'soka, Jassiel; Smit, Daan; Becker, Matt; Christianson, Dave; Schuette, Paul
2017-08-01
Most species adjust their behavior to reduce the likelihood of predation. Many experiments have shown that antipredator responses carry energetic costs that can affect growth, survival, and reproduction, so that the total cost of predation depends on a trade-off between direct predation and risk effects. Despite these patterns, few field studies have examined the relationship between direct predation and the strength of antipredator responses, particularly for complete guilds of predators and prey. We used scan sampling in 344 observation periods over a four-year field study to examine behavioral responses to the immediate presence of predators for a complete antelope guild (dominated by wildebeest, zebra, and oribi) in Liuwa Plains National Park, Zambia, testing for differences in response to all large carnivores in the ecosystem (lions, spotted hyenas, cheetahs, and African wild dogs). We quantified the proportion that each prey species contributed to the kills made by each predator (516 total kills), used distance sampling on systematic line transects to determine the abundance of each prey species, and combined these data to quantify the per-capita risk of direct predation for each predator-prey pair. On average, antelopes increased their vigilance by a factor of 2.4 when predators were present. Vigilance varied strongly among prey species, but weakly in response to different predators. Increased vigilance was correlated with reduced foraging in a similar manner for all prey species. The strength of antipredator response was not detectably related to patterns of direct predation (n = 15 predator-prey combinations with sufficient data). This lack of correlation has implications for our understanding of the role of risk effects as part of the limiting effect of predators on prey. © 2017 by the Ecological Society of America.
Predation and prey selectivity by Argyrosomus h%/epidotus ...
ly show that larger prey are preferred by larger predators. S. Afr. J. Zoot. 1985 ... found in estuaries in Natal and the Cape (Wallace & van der. Elst 1975 .... Trawling depths and times ...... plankton picker, A. hololepidotus is probably an active.
Olfactory response of the predator Zetzellia mali to a prey patch occupied by a conspecific predator
Zahedi-Golpayegani, A.; Saboori, A.; Sabelis, M.W.
2007-01-01
While searching for food, predators may use volatiles associated with their prey, but also with their competitors for prey. This was tested for the case of Zetzellia mali (Ewing) (Acari: Stigmaeidae), an important predator of the hawthorn spider mite, Amphitetranychus viennensis (Zacher) (Acari: Tet
Yunxian Dai; Yiping Lin; Huitao Zhao
2014-01-01
We consider a predator-prey system with Michaelis-Menten type functional response and two delays. We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delay...
ON A PERIODIC PREY-PREDATOR SYSTEM WITH INFINITE DELAYS%一个具无穷时滞的周期捕食-食饵系统
李永昆; 徐贵桐
2000-01-01
Based on the theory of coincidence degree ,the existence of positive periodic solutions is established for a periodic prey-predator system with infinite delays where α, γ,β,μ are positive continuous ω-periodic functions ,Ki ∈ C(R × [0 ,∞), (0, ∞ ) ) (i = 1,2) are ω-periodic with respect to their first arguments,. respectively,R,∈ C(R × [0, ∞)× [0,∞), (0 ,∞ ))(i= 1,2) are ω-periodic with respect to their first arguments ,respectively.
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2008-01-01
A ratio-dependent predator-prey system with stage structure and time delays for both prey and predator is considered in this paper. Both the predator and prey have two stages,immature stage and mature stage,and the growth of them is of Lotka-Volterra nature. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age,and that mature predators attack immature prey only. The global stability of three nonnegative equilibria and permanence are presented.
Rodrigues, Luiz Alberto Díaz; Mistro, Diomar Cristina; Petrovskii, Sergei
2011-08-01
Understanding of population dynamics in a fragmented habitat is an issue of considerable importance. A natural modelling framework for these systems is spatially discrete. In this paper, we consider a predator-prey system that is discrete both in space and time, and is described by a Coupled Map Lattice (CML). The prey growth is assumed to be affected by a weak Allee effect and the predator dynamics includes intra-specific competition. We first reveal the bifurcation structure of the corresponding non-spatial system. We then obtain the conditions of diffusive instability on the lattice. In order to reveal the properties of the emerging patterns, we perform extensive numerical simulations. We pay a special attention to the system properties in a vicinity of the Turing-Hopf bifurcation, which is widely regarded as a mechanism of pattern formation and spatiotemporal chaos in space-continuous systems. Counter-intuitively, we obtain that the spatial patterns arising in the CML are more typically stationary, even when the local dynamics is oscillatory. We also obtain that, for some parameter values, the system's dynamics is dominated by long-term transients, so that the asymptotical stationary pattern arises as a sudden transition between two different patterns. Finally, we argue that our findings may have important ecological implications.
Indirect evolutionary rescue: prey adapts, predator avoids extinction.
Yamamichi, Masato; Miner, Brooks E
2015-09-01
Recent studies have increasingly recognized evolutionary rescue (adaptive evolution that prevents extinction following environmental change) as an important process in evolutionary biology and conservation science. Researchers have concentrated on single species living in isolation, but populations in nature exist within communities of interacting species, so evolutionary rescue should also be investigated in a multispecies context. We argue that the persistence or extinction of a focal species can be determined solely by evolutionary change in an interacting species. We demonstrate that prey adaptive evolution can prevent predator extinction in two-species predator-prey models, and we derive the conditions under which this indirect evolutionary interaction is essential to prevent extinction following environmental change. A nonevolving predator can be rescued from extinction by adaptive evolution of its prey due to a trade-off for the prey between defense against predation and population growth rate. As prey typically have larger populations and shorter generations than their predators, prey evolution can be rapid and have profound effects on predator population dynamics. We suggest that this process, which we term 'indirect evolutionary rescue', has the potential to be critically important to the ecological and evolutionary responses of populations and communities to dramatic environmental change.
Global Dynamics of a Predator-Prey Model with Stage Structure and Delayed Predator Response
Lili Wang
2013-01-01
Full Text Available A Holling type II predator-prey model with time delay and stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. The existence of Hopf bifurcations at the coexistence equilibrium is established. By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and the sufficient conditions are obtained for the global stability of the coexistence equilibrium.
Dynamics of a predator-prey model with non-monotonic response function
Broer, H.W.; Saleh, K.; Naudot, V.; Roussarie, R.
2007-01-01
A five-parameter family of planar vector fields, which models the dynamics of certain populations of predators and their prey, is discussed. The family is a variation of the classical Volterra-Lotka system by taking into account group defense strategy, competition between prey and competition betwee
Predator-prey interactions, flight initiation distance and brain size.
Møller, A P; Erritzøe, J
2014-01-01
Prey avoid being eaten by assessing the risk posed by approaching predators and responding accordingly. Such an assessment may result in prey-predator communication and signalling, which entail further monitoring of the predator by prey. An early antipredator response may provide potential prey with a selective advantage, although this benefit comes at the cost of disturbance in terms of lost foraging opportunities and increased energy expenditure. Therefore, it may pay prey to assess approaching predators and determine the likelihood of attack before fleeing. Given that many approaching potential predators are detected visually, we hypothesized that species with relatively large eyes would be able to detect an approaching predator from afar. Furthermore, we hypothesized that monitoring of predators by potential prey relies on evaluation through information processing by the brain. Therefore, species with relatively larger brains for their body size should be better able to monitor the intentions of a predator, delay flight for longer and hence have shorter flight initiation distances than species with smaller brains. Indeed, flight initiation distances increased with relative eye size and decreased with relative brain size in a comparative study of 107 species of birds. In addition, flight initiation distance increased independently with size of the cerebellum, which plays a key role in motor control. These results are consistent with cognitive monitoring as an antipredator behaviour that does not result in the fastest possible, but rather the least expensive escape flights. Therefore, antipredator behaviour may have coevolved with the size of sense organs, brains and compartments of the brain involved in responses to risk of predation.
Modelling landscape-level numerical responses of predators to prey: the case of cats and rabbits.
Jennyffer Cruz
Full Text Available Predator-prey systems can extend over large geographical areas but empirical modelling of predator-prey dynamics has been largely limited to localised scales. This is due partly to difficulties in estimating predator and prey abundances over large areas. Collection of data at suitably large scales has been a major problem in previous studies of European rabbits (Oryctolagus cuniculus and their predators. This applies in Western Europe, where conserving rabbits and predators such as Iberian lynx (Lynx pardinus is important, and in other parts of the world where rabbits are an invasive species supporting populations of introduced, and sometimes native, predators. In pastoral regions of New Zealand, rabbits are the primary prey of feral cats (Felis catus that threaten native fauna. We estimate the seasonal numerical response of cats to fluctuations in rabbit numbers in grassland-shrubland habitat across the Otago and Mackenzie regions of the South Island of New Zealand. We use spotlight counts over 1645 km of transects to estimate rabbit and cat abundances with a novel modelling approach that accounts simultaneously for environmental stochasticity, density dependence and varying detection probability. Our model suggests that cat abundance is related consistently to rabbit abundance in spring and summer, possibly through increased rabbit numbers improving the fecundity and juvenile survival of cats. Maintaining rabbits at low abundance should therefore suppress cat numbers, relieving predation pressure on native prey. Our approach provided estimates of the abundance of cats and rabbits over a large geographical area. This was made possible by repeated sampling within each season, which allows estimation of detection probabilities. A similar approach could be applied to predator-prey systems elsewhere, and could be adapted to any method of direct observation in which there is no double-counting of individuals. Reliable estimates of numerical
Prey-mediated avoidance of an intraguild predator by its intraguild prey.
Wilson, Ryan R; Blankenship, Terry L; Hooten, Mevin B; Shivik, John A
2010-12-01
Intraguild (IG) predation is an important factor influencing community structure, yet factors allowing coexistence of IG predator and IG prey are not well understood. The existence of spatial refuges for IG prey has recently been noted for their importance in allowing coexistence. However, reduction in basal prey availability might lead IG prey to leave spatial refuges for greater access to prey, leading to increased IG predation and fewer opportunities for coexistence. We determined how the availability of prey affected space-use patterns of bobcats (Lynx rufus, IG prey) in relation to coyote space-use patterns (Canis latrans, IG predators). We located animals from fall 2007 to spring 2009 and estimated bobcat home ranges and core areas seasonally. For each bobcat relocation, we determined intensity of coyote use, distance to water, small mammal biomass, and mean small mammal biomass of the home range during the season the location was collected. We built generalized linear mixed models and used Akaike Information Criteria to determine which factors best predicted bobcat space use. Coyote intensity was a primary determinant of bobcat core area location. In bobcat home ranges with abundant prey, core areas occurred where coyote use was low, but shifted to areas intensively used by coyotes when prey declined. High spatial variability in basal prey abundance allowed some bobcats to avoid coyotes while at the same time others were forced into more risky areas. Our results suggest that multiple behavioral strategies associated with spatial variation in basal prey abundance likely allow IG prey and IG predators to coexist.
Ni, Wenjie; Wang, Mingxin
2016-10-01
This paper is devoted to study the dynamical properties and stationary patterns of a diffusive Leslie-Gower prey-predator model with strong Allee effect in the prey population. We first analyze the nonnegative constant equilibrium solutions and their stabilities, and then study the dynamical properties of time-dependent solutions. Moreover, we investigate the stationary patterns induced by diffusions (Turing pattern). Our results show that the impact of the strong Allee effect essentially increases the system spatiotemporal complexity.
Adaptive behaviour and multiple equilibrium states in a predator-prey model.
Pimenov, Alexander; Kelly, Thomas C; Korobeinikov, Andrei; O'Callaghan, Michael J A; Rachinskii, Dmitrii
2015-05-01
There is evidence that multiple stable equilibrium states are possible in real-life ecological systems. Phenomenological mathematical models which exhibit such properties can be constructed rather straightforwardly. For instance, for a predator-prey system this result can be achieved through the use of non-monotonic functional response for the predator. However, while formal formulation of such a model is not a problem, the biological justification for such functional responses and models is usually inconclusive. In this note, we explore a conjecture that a multitude of equilibrium states can be caused by an adaptation of animal behaviour to changes of environmental conditions. In order to verify this hypothesis, we consider a simple predator-prey model, which is a straightforward extension of the classic Lotka-Volterra predator-prey model. In this model, we made an intuitively transparent assumption that the prey can change a mode of behaviour in response to the pressure of predation, choosing either "safe" of "risky" (or "business as usual") behaviour. In order to avoid a situation where one of the modes gives an absolute advantage, we introduce the concept of the "cost of a policy" into the model. A simple conceptual two-dimensional predator-prey model, which is minimal with this property, and is not relying on odd functional responses, higher dimensionality or behaviour change for the predator, exhibits two stable co-existing equilibrium states with basins of attraction separated by a separatrix of a saddle point.
Perceptual advertisement by the prey of stalking or ambushing predators.
Broom, Mark; Ruxton, Graeme D
2012-12-21
There has been previous theoretical explorations of the stability of signals by prey that they have detected a stalking or ambush predator, where such perceptual advertisement dissuades the predator from attacking. Here we use a game theoretical model to extend the theory to consider some empirically-motivated complexities: (i) many perceptual advertisement signals appear to have the potential to vary in intensity, (ii) higher intensity signals are likely to be most costly to produce, and (iii) some high-cost signals (such as staring directly at the predator) can only be utilised if the prey is very confident of the existence of a nearby predator (that is, there are reserved or unfakable signals). We demonstrate that these complexities still allow for stable signalling. However, we do not find solutions where prey use a range of signal intensities to signal different degrees of confidence in the proximity of a predator; with prey simply adopting a binary response of not signalling or always signalling at the same fixed level. However this fixed level will not always be the cheapest possible signal, and we predict that prey that require more certainty about proximity of a predator will use higher-cost signals. The availability of reserved signals does not prohibit the stability of signalling based on lower-cost signals, but we also find circumstances where only the reserved signal is used. We discuss the potential to empirically test our model predictions, and to develop theory further to allow perceptual advertisement to be combined with other signalling functions.
Simonis, Joseph L
2012-07-01
Dispersal may affect predator-prey metapopulations by rescuing local sink populations from extinction or by synchronizing population dynamics across the metapopulation, increasing the risk of regional extinction. Dispersal is likely influenced by demographic stochasticity, however, particularly because dispersal rates are often very low in metapopulations. Yet the effects of demographic stochasticity on predator-prey metapopulations are not well known. To that end, I constructed three models of a two-patch predator-prey system. The models constitute a hierarchy of complexity, allowing direct comparisons. Two models included demographic stochasticity (pure jump process [PJP] and stochastic differential equations [SDE]), and the third was deterministic (ordinary differential equations [ODE]). One stochastic model (PJP) treated population sizes as discrete, while the other (SDE) allowed population sizes to change continuously. Both stochastic models only produced synchronized predator-prey dynamics when dispersal was high for both trophic levels. Frequent dispersal by only predators or prey in the PJP and SDE spatially decoupled the trophic interaction, reducing synchrony of the non-dispersive species. Conversely, the ODE generated synchronized predator-prey dynamics across all dispersal rates, except when initial conditions produced anti-phase transients. These results indicate that demographic stochasticity strongly reduces the synchronizing effect of dispersal, which is ironic because demographic stochasticity is often invoked post hoc as a driver of extinctions in synchronized metapopulations.
The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population
Raid Kamel Naji
2016-01-01
Full Text Available We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.
Huang, Jicai; Xia, Xiaojing; Zhang, Xinan; Ruan, Shigui
It was shown in [Li & Xiao, 2007] that in a predator-prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov-Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov-Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov-Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop enclosing an unstable limit cycle, or a stable limit cycle enclosing three unstable hyperbolic positive equilibria for various parameter values, confirm the theoretical results.
Tankam, Israel; Tchinda Mouofo, Plaire; Mendy, Abdoulaye; Lam, Mountaga; Tewa, Jean Jules; Bowong, Samuel
2015-06-01
We investigate the effects of time delay and piecewise-linear threshold policy harvesting for a delayed predator-prey model. It is the first time that Holling response function of type III and the present threshold policy harvesting are associated with time delay. The trajectories of our delayed system are bounded; the stability of each equilibrium is analyzed with and without delay; there are local bifurcations as saddle-node bifurcation and Hopf bifurcation; optimal harvesting is also investigated. Numerical simulations are provided in order to illustrate each result.
Environmental versus demographic variability in stochastic predator-prey models
Dobramysl, U.; Täuber, U. C.
2013-10-01
In contrast to the neutral population cycles of the deterministic mean-field Lotka-Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures associated with long-lived erratic population oscillations. Environmental variability in the form of quenched spatial randomness in the predation rates results in more localized activity patches. Our previous study showed that population fluctuations in rare favorable regions in turn cause a remarkable increase in the asymptotic densities of both predators and prey. Very intriguing features are found when variable interaction rates are affixed to individual particles rather than lattice sites. Stochastic dynamics with demographic variability in conjunction with inheritable predation efficiencies generate non-trivial time evolution for the predation rate distributions, yet with overall essentially neutral optimization.
Using process algebra to develop predator-prey models of within-host parasite dynamics.
McCaig, Chris; Fenton, Andy; Graham, Andrea; Shankland, Carron; Norman, Rachel
2013-07-21
As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used prey-dependent functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in the previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system. Copyright © 2013 Elsevier Ltd. All rights reserved.
Christopher F Steiner
2013-02-01
Full Text Available Heterogeneity among prey in their susceptibility to predation is a potentially important stabilizer of predator-prey interactions, reducing the magnitude of population oscillations and enhancing total prey population abundance. When microevolutionary responses of prey populations occur at time scales comparable to population dynamics, adaptive responses in prey defense can, in theory, stabilize predator-prey dynamics and reduce top-down effects on prey abundance. While experiments have tested these predictions, less explored are the consequences of the evolution of prey phenotypes that can persist in both vulnerable and invulnerable classes. We tested this experimentally using a laboratory aquatic system composed of the rotifer Brachionus calyciflorus as a predator and the prey Synura petersenii, a colony-forming alga that exhibits genetic variation in its propensity to form colonies and colony size (larger colonies are a defense against predators. Prey populations of either low initial genetic diversity and low adaptive capacity or high initial genetic diversity and high adaptive capacity were crossed with predator presence and absence. Dynamics measured over the last 127 days of the 167-day experiment revealed no effects of initial prey genetic diversity on the average abundance or temporal variability of predator populations. However, genetic diversity and predator presence/absence interactively affected prey population abundance and stability; diversity of prey had no effects in the absence of predators but stabilized dynamics and increased total prey abundance in the presence of predators. The size structure of the genetically diverse prey populations diverged from single strain populations in the presence of predators, showing increases in colony size and in the relative abundance of cells found in colonies. Our work sheds light on the adaptive value of colony formation and supports the general view that genetic diversity and intraspecific
2012-01-01
There are concerns that anthropogenic harvesting may cause phenotypic adaptive changes in exploited wild populations, in particular maturation at smaller size and younger age. In this paper, we study the evolutionarily stable size-at- maturation of prey subjected to size-selective harvesting in a simple predator-prey model, taking into account three recognized life-history costs of early maturation, namely reduced fecundity, reduced growth, and increased mortality. Our analysis sh...
Convergence between a mosquito-eating predator's natural diet and its prey-choice behaviour
Jackson, Robert R.; Deng, Chan
2016-01-01
On the basis of 1115 records of Evarcha culicivora feeding in the field, we can characterize this East African jumping spider (Salticidae) as being distinctively stenophagic. We can also, on the basis of laboratory prey-choice experiments, characterize E. culicivora as having a specialized prey-classification system and a hierarchy of innate preferences for various categories of mosquitoes and other arthropods. Prey from the field belonged to 10 arthropod orders, but 94.5% of the prey records were dipterans. Mosquitoes were the dominant prey (80.2% of the records), with the majority (82.9%) of the mosquitoes being females, and thereafter midges were the most common prey (9.2% of the records). Preference profiles that were determined from experiments showed strong convergence with natural diet in some, but not all, instances. In experiments, E. culicivora adults appeared to distinguish between six prey categories and juveniles between seven, with blood-carrying anopheline female mosquitoes being ranked highest in preference. For adults, this was followed by blood-carrying culicine female mosquitoes and then anopheline female mosquitoes not carrying blood, but these two preferences were reversed for juveniles. Moreover, for juveniles, but not for adults, anopheline male mosquitoes seem to be a distinct prey category ranked in preference after blood-carrying culicine females and, for both adults and juveniles, preference for midges is evident when the alternatives are not mosquitoes. These findings illustrate the importance of going beyond simply specifying preferred prey categories when characterizing predators as ‘specialized’ and a need to make clear conceptual distinctions between a predator's natural diet, the prey categories that are relevant to the predator, and the predator's prey-choicebehaviour. PMID:28083103
Predator-induced flow disturbances alert prey, from the onset of an attack.
Casas, Jérôme; Steinmann, Thomas
2014-09-07
Many prey species, from soil arthropods to fish, perceive the approach of predators, allowing them to escape just in time. Thus, prey capture is as important to predators as prey finding. We extend an existing framework for understanding the conjoint trajectories of predator and prey after encounters, by estimating the ratio of predator attack and prey danger perception distances, and apply it to wolf spiders attacking wood crickets. Disturbances to air flow upstream from running spiders, which are sensed by crickets, were assessed by computational fluid dynamics with the finite-elements method for a much simplified spider model: body size, speed and ground effect were all required to obtain a faithful representation of the aerodynamic signature of the spider, with the legs making only a minor contribution. The relationship between attack speed and the maximal distance at which the cricket can perceive the danger is parabolic; it splits the space defined by these two variables into regions differing in their values for this ratio. For this biological interaction, the ratio is no greater than one, implying immediate perception of the danger, from the onset of attack. Particular attention should be paid to the ecomechanical aspects of interactions with such small ratio, because of the high degree of bidirectional coupling of the behaviour of the two protagonists. This conclusion applies to several other predator-prey systems with sensory ecologies based on flow sensing, in air and water.
Stewart, Julia S; Hazen, Elliott L; Bograd, Steven J; Byrnes, Jarrett E K; Foley, David G; Gilly, William F; Robison, Bruce H; Field, John C
2014-06-01
Climate-driven range shifts are ongoing in pelagic marine environments, and ecosystems must respond to combined effects of altered species distributions and environmental drivers. Hypoxic oxygen minimum zones (OMZs) in midwater environments are shoaling globally; this can affect distributions of species both geographically and vertically along with predator-prey dynamics. Humboldt (jumbo) squid (Dosidicus gigas) are highly migratory predators adapted to hypoxic conditions that may be deleterious to their competitors and predators. Consequently, OMZ shoaling may preferentially facilitate foraging opportunities for Humboldt squid. With two separate modeling approaches using unique, long-term data based on in situ observations of predator, prey, and environmental variables, our analyses suggest that Humboldt squid are indirectly affected by OMZ shoaling through effects on a primary food source, myctophid fishes. Our results suggest that this indirect linkage between hypoxia and foraging is an important driver of the ongoing range expansion of Humboldt squid in the northeastern Pacific Ocean.
冯春华
2000-01-01
The almost periodic Volterra predator-prey system was considered, and it was proved that the system can have a unique almost positive periodic solution by using Liapunov functional.%结合运用Liapunov泛函数,研究二维Lotka-Volterra捕食系统概周期正解的存在唯一性.
Seo, G.; DeAngelis, D.L.
2011-01-01
The most widely used functional response in describing predator-prey relationships is the Holling type II functional response, where per capita predation is a smooth, increasing, and saturating function of prey density. Beddington and DeAngelis modified the Holling type II response to include interference of predators that increases with predator density. Here we introduce a predator-interference term into a Holling type I functional response. We explain the ecological rationale for the response and note that the phase plane configuration of the predator and prey isoclines differs greatly from that of the Beddington-DeAngelis response; for example, in having three possible interior equilibria rather than one. In fact, this new functional response seems to be quite unique. We used analytical and numerical methods to show that the resulting system shows a much richer dynamical behavior than the Beddington-DeAngelis response, or other typically used functional responses. For example, cyclic-fold, saddle-fold, homoclinic saddle connection, and multiple crossing bifurcations can all occur. We then use a smooth approximation to the Holling type I functional response with predator mutual interference to show that these dynamical properties do not result from the lack of smoothness, but rather from subtle differences in the functional responses. ?? 2011 Springer Science+Business Media, LLC.
Seo, Gunog; Deangelis, Donald L.
2011-12-01
The most widely used functional response in describing predator-prey relationships is the Holling type II functional response, where per capita predation is a smooth, increasing, and saturating function of prey density. Beddington and DeAngelis modified the Holling type II response to include interference of predators that increases with predator density. Here we introduce a predator-interference term into a Holling type I functional response. We explain the ecological rationale for the response and note that the phase plane configuration of the predator and prey isoclines differs greatly from that of the Beddington-DeAngelis response; for example, in having three possible interior equilibria rather than one. In fact, this new functional response seems to be quite unique. We used analytical and numerical methods to show that the resulting system shows a much richer dynamical behavior than the Beddington-DeAngelis response, or other typically used functional responses. For example, cyclic-fold, saddle-fold, homoclinic saddle connection, and multiple crossing bifurcations can all occur. We then use a smooth approximation to the Holling type I functional response with predator mutual interference to show that these dynamical properties do not result from the lack of smoothness, but rather from subtle differences in the functional responses.
Tripathi, Jai Prakash; Abbas, Syed; Thakur, Manoj
2015-05-01
This paper describes a predator-prey model incorporating a prey refuge. The feeding rate of consumers (predators) per consumer (i.e. functional response) is considered to be of Beddington-DeAngelis type. The Beddington-DeAngelis functional response is similar to the Holling-type II functional response but contains an extra term describing mutual interference by predators. We investigate the role of prey refuge and degree of mutual interference among predators in the dynamics of system. The dynamics of the system is discussed mainly from the point of view of permanence and stability. We obtain conditions that affect the persistence of the system. Local and global asymptotic stability of various equilibrium solutions is explored to understand the dynamics of the model system. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional. The dynamical behaviour of the delayed system is further analyzed through incorporating discrete type gestation delay of predator. It is found that Hopf bifurcation occurs when the delay parameter τ crosses some critical value. The analytical results found in the paper are illustrated with the help of numerical examples.
Zhenjie Liu
2009-01-01
Full Text Available This paper investigates the existence of periodic solutions of a ratio-dependent predator-prey diffusion system with Michaelis-Menten functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain suffcient criteria for the existence of periodic solutions for the system. Moreover, when the time scale 𝕋 is chosen as ℝ or ℤ, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.
Effects of generalized and specialized adaptive defense by shared prey on intra-guild predation.
Ikegawa, Yusuke; Ezoe, Hideo; Namba, Toshiyuki
2015-01-07
Intra-guild predation (IGP), predation on consumers which share common prey with the predators, is an important community module to understand a mechanism for persistence of complex food webs. However, classical theory suggests that persistence of an IGP system is unlikely particularly at high productivity, while empirical data do not support the prediction. Recently, adaptive defense by shared prey has been recognized to enhance coexistence of species and stability of the system. Some organisms having multiple predators in IGP systems employ two types of defenses; generalized defense that is effective against multiple predators and specialized one that is effective against only a specific predator species. We consider an IGP model including shared prey that can use the two types of defenses in combination against the consumer or omnivore. Assuming that the shared prey can change the allocation of defensive effort to increase its fitness, we show that the joint use of two types of adaptive defenses promotes three species coexistence and enhances stability of the IGP system when the specialized defense is more effective than the generalized one. When the system is unstable, a variety of oscillations appear and both the population densities and defensive efforts or only the population densities oscillate. Joint use of defenses against the consumer tends to increase the equilibrium population density of the shared prey with the defense efficiencies. In contrast, efficient generalized and specialized defenses against the omnivore often decrease the prey population. Consequently, adaptive defense by shared prey may not necessarily heighten the population size of the defender but sometimes increases densities of both the attackers and defender in IGP systems. Copyright © 2014 Elsevier Ltd. All rights reserved.
Kooi, B.W.; Venturino, E.
2016-01-01
In this paper we analyse a predator–prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the Rosenzweig–MacArthur predator–prey type with an SI (susceptible-infected) disease in the prey. Modeling prey gr
Kooi, B.W.; Venturino, E.
2016-01-01
In this paper we analyse a predator–prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the Rosenzweig–MacArthur predator–prey type with an SI (susceptible-infected) disease in the prey. Modeling prey
Temperature and prey capture: opposite relationships in two predator taxa
Kruse, Peter Dalgas; Toft, Søren; Sunderland, Keith
2008-01-01
on the predation rate of two carabid beetles (Pterostichus versicolor and Calathus fuscipes) and two spiders (Clubiona phragmitis and Pardosa prativaga) using fruit flies (Drosophila melanogaster) as prey. 3. All four predators and the fruit fly increased their locomotory activity at higher temperatures. Activity...... moulded by light conditions depending on whether the predator is diurnally or nocturnally active. It was hypothesised that flying Diptera are vulnerable to carabid beetles only at low temperatures and over the full temperature range for spiders because carabids, in contrast to spiders, are not built...... to catch swiftly moving prey. 2. The first experiment examined the spontaneous locomotor activity of the predators and of fruit flies at different temperatures (5, 10, 15, 20, 25, and 30 °C) and light conditions (light, dark). A second experiment examined the effect of temperature and light...
Predator-prey interactions between shell-boring beetle larvae and rock-dwelling land snails.
Els Baalbergen
Full Text Available Drilus beetle larvae (Coleoptera: Elateridae are specialized predators of land snails. Here, we describe various aspects of the predator-prey interactions between multiple Drilus species attacking multiple Albinaria (Gastropoda: Clausiliidae species in Greece. We observe that Drilus species may be facultative or obligate Albinaria-specialists. We map geographically varying predation rates in Crete, where on average 24% of empty shells carry fatal Drilus bore holes. We also provide first-hand observations and video-footage of prey entry and exit strategies of the Drilus larvae, and evaluate the potential mutual evolutionary impacts. We find limited evidence for an effect of shell features and snail behavioral traits on inter- and intra-specifically differing predation rates. We also find that Drilus predators adjust their predation behavior based on specific shell traits of the prey. In conclusion, we suggest that, with these baseline data, this interesting predator-prey system will be available for further, detailed more evolutionary ecology studies.
A detailed study of the Beddington-DeAngelis predator-prey model.
Haque, Mainul
2011-11-01
The present investigation accounts for the influence of intra-specific competition among predators in the original Beddington-DeAngelis predator-prey model. We offer a detailed mathematical analysis of the model to describe some of the significant results that may be expected to arise from the interplay of deterministic and stochastic biological phenomena and processes. In particular, stability (local and global) and bifurcation (Saddle-node, Transcritical, Hopf-Andronov, Bogdanov-Takens) analysis of this model are conducted. Corresponding results from previous well known predator-prey models are compared with the current findings. Nevertheless, we also allow this model in stochastic environment with the influences of both, uncorrelated "white" noise and correlated "coloured" noise. This showing that competition among the predator population is beneficial for a number of predator-prey models by keeping them stable around its positive interior equilibrium (i.e. when both populations co-exist), under environmental stochasticity. Comparisons of these findings with the results of some earlier related investigations allow the general conclusion that predator intra-species competition benefits the predator-prey system under both deterministic and stochastic environments. Finally, an extended discussion of the ecological implications of the analytical and numerical results concludes the paper.
Predator-prey relationships among larval dragonflies, salamanders, and frogs.
Caldwell, J P; Thorp, J H; Jervey, T O
1980-09-01
Tadpoles of the barking tree frog, Hyla gratiosa, are abundant in spring and summer in some ponds and Carolina bays on the Savannah River Plant near Aiken, South Carolina. To determine how these tadpoles survive in the presence of predaceous salamander larvae, Ambystoma talpoideum, and larvae of an aeshnid dragonfly, Anax junius, we determined fields densities and sizes of the predators and the prey and conducted predation experiments in the laboratory. Tadpoles rapidly grow to a size not captured by Ambystoma, although Anax larvae can capture slightly larger tadpoles. Differing habitat preferences among the tadpoles and the two predator species probably aid in reducing predation pressure. Preliminary work indicates that the tadpoles may have an immobility response to an attack by a predator. In addition, the smallest, most vulnerable tadpoles have a distinctive color pattern which may function to disrupt the body outline and make them indiscernable to predators.
Role reversal in a predator-prey interaction.
Sánchez-Garduño, Faustino; Miramontes, Pedro; Marquez-Lago, Tatiana T
2014-10-01
Predator-prey relationships are one of the most studied interactions in population ecology. However, little attention has been paid to the possibility of role exchange between species, despite firm field evidence of such phenomena in nature. In this paper, we build a mathematical model capable of reproducing the main phenomenological features of role reversal in a classical system and present results for both the temporal and spatio-temporal cases. We show that, depending on the choice of parameters, our role-reversal dynamical system exhibits excitable-like behaviour, generating waves of species' concentrations that propagate through space. Our findings fill a long-standing gap in modelling ecological interactions and can be applicable to better understanding ecological niche shifts and planning of sustainable ecosystems.
Variable prey development time suppresses predator-prey cycles and enhances stability.
Cronin, James T; Reeve, John D; Xu, Dashun; Xiao, Mingqing; Stevens, Heidi N
2016-03-01
Although theoretical models have demonstrated that predator-prey population dynamics can depend critically on age (stage) structure and the duration and variability in development times of different life stages, experimental support for this theory is non-existent. We conducted an experiment with a host-parasitoid system to test the prediction that increased variability in the development time of the vulnerable host stage can promote interaction stability. Host-parasitoid microcosms were subjected to two treatments: Normal and High variance in the duration of the vulnerable host stage. In control and Normal-variance microcosms, hosts and parasitoids exhibited distinct population cycles. In contrast, insect abundances were 18-24% less variable in High- than Normal-variance microcosms. More significantly, periodicity in host-parasitoid population dynamics disappeared in the High-variance microcosms. Simulation models confirmed that stability in High-variance microcosms was sufficient to prevent extinction. We conclude that developmental variability is critical to predator-prey population dynamics and could be exploited in pest-management programs.
PERIODICITY IN A DELAYED SEMI-RATIO-DEPENDENT PREDATOR-PREY SYSTEM%具有时滞的半比率依赖型捕食者-食饵系统的周期性
丁孝全
2005-01-01
A delayed semi-ratio-dependent predator-prey system in a periodic environment is investigated in this paper.By using a continuation theorem based on Gaines and Mawhins coincidence degree,the global existence of positive periodic solution is studied.A set of easily verifiable sufficient conditions are obtained.
Prey-predator dynamics driven by the solar radiation - Part 1.
Sertorio, L. [Turin Univ., Turin (Italy). Dipt. di Fisica Teorica; Tinetti, G. [Istituto Nazionale di Fisica Nucleare, Turin (Italy)
2000-12-01
In this paper is studied a model ecosystem represented by two components: prey and predator. The predator feeds only on the prey, the prey, in turn, feeds on the solar radiation. In this scheme the two-species dynamics is no longer independent of the external physical conditions. Such independence was instead postulated in the Lotka-Volterra scheme. In this paper is considered the growth of the prey not unbounded (exponential), but logistic, where the saturation factor is governed by the available solar flux, more precisely by the percent of the solar flux that contains the photon frequencies which can drive the photosynthesis. In this way the solar flux represents the driving term of the dynamics, as it is expected in general for a realistic ecosystem. The system is asymptotically stable. The equilibrium values of the prey and predator numbers depend on several parameters. The system contains two nonlinear coupling terms and two coupling parameters. The dependence of the equilibrium point on the coupling parameters is studied in detail. According to this model, it can be defined a predator efficiency and a global solar efficiency. It is discussed the relationship between these two functions of the coupling parameters and the maximum value that the predator population can reach.
一类具有脉冲效应的捕食系统分析%ANALYSIS OF A CLASS OF PREDATOR-PREY SYSTEM WITH IMPULSIVE EFFECT
卢琨
2011-01-01
研究了捕食者具有非单调功能反应函数f(x)=sx(t)y(t)exp(-kx(t))的捕食系统,通过对捕食者进行周期投放,利用脉冲微分方程F1oquet乘子理论和比较定理,得到了食饵根除周期解局部渐近稳定与系统持续生存的条件,即当系统满足如果脉冲周期T＞sq/rd时是持续生存的.%The predator-prey system with non-monotonic functional response that is f(x) = 5x(t)exp(-kx(t)) and periodic impulsive perturbations on the predator are discussed by using the Floquet theory of impulsive equation and comparison theorem, draw the conclusion of the sufficient conditions for the system to be extinct and permanence, that is when the system is satisfied if T>sq/rd the pulse cycle persistence.
Gluttonous predators: how to estimate prey size when there are too many prey
MS. Araújo
Full Text Available Prey size is an important factor in food consumption. In studies of feeding ecology, prey items are usually measured individually using calipers or ocular micrometers. Among amphibians and reptiles, there are species that feed on large numbers of small prey items (e.g. ants, termites. This high intake makes it difficult to estimate prey size consumed by these animals. We addressed this problem by developing and evaluating a procedure for subsampling the stomach contents of such predators in order to estimate prey size. Specifically, we developed a protocol based on a bootstrap procedure to obtain a subsample with a precision error of at the most 5%, with a confidence level of at least 95%. This guideline should reduce the sampling effort and facilitate future studies on the feeding habits of amphibians and reptiles, and also provide a means of obtaining precise estimates of prey size.
The Dynamics of a Nonautonomous Predator-Prey Model with Infertility Control in the Prey
Xiaomei Feng
2014-01-01
Full Text Available A nonautonomous predator-prey model with infertility control in the prey is formulated and investigated. Threshold conditions for the permanence and extinction of fertility prey and infertility prey are established. Some new threshold values of integral form are obtained. For the periodic cases, these threshold conditions act as sharp threshold values for the permanence and extinction of fertility prey and infertility prey. There are also mounting concerns that the quantity of biological sterile drug is obtained in the process of the prevention and control of pest in the grasslands and farmland. Finally, two examples are given to illustrate the main results of this paper. The numerical simulations shown that, when the pest population is permanet, different dynamic behaviors may be found in this model, such as the global attractivity and the chaotic attractor.
Phase transition in predator-prey ecosystems and a connection to transitional turbulence
Shih, Hong-Yan; Goldenfeld, Nigel
2015-03-01
We suggest how the transition from laminar fluid flow to turbulence can be connected to the extinction phase transition in spatially-extended predator-prey systems. By measuring the statistics of spontaneous relaminarization, spatiotemporal intermittency and expanding turbulent puffs in hydrodynamics equations and mapping them to the corresponding states in the predator-prey model, the extinction event and the formation and propagation of spatial patterns in ecology can be interpreted as the instabilities in fluid systems. We also summarize the general phenomena of such predator-prey dynamics in a wide class of transitional turbulence systems such as magnetohydrodynamics. This work was partially supported by the National Science Foundation through Grant NSF-DMR-1044901.
Predator-prey dynamics driven by feedback between functionally diverse trophic levels.
Katrin Tirok
Full Text Available Neglecting the naturally existing functional diversity of communities and the resulting potential to respond to altered conditions may strongly reduce the realism and predictive power of ecological models. We therefore propose and study a predator-prey model that describes mutual feedback via species shifts in both predator and prey, using a dynamic trait approach. Species compositions of the two trophic levels were described by mean functional traits--prey edibility and predator food-selectivity--and functional diversities by the variances. Altered edibility triggered shifts in food-selectivity so that consumers continuously respond to the present prey composition, and vice versa. This trait-mediated feedback mechanism resulted in a complex dynamic behavior with ongoing oscillations in the mean trait values, reflecting continuous reorganization of the trophic levels. The feedback was only possible if sufficient functional diversity was present in both trophic levels. Functional diversity was internally maintained on the prey level as no niche existed in our system, which was ideal under any composition of the predator level due to the trade-offs between edibility, growth and carrying capacity. The predators were only subject to one trade-off between food-selectivity and grazing ability and in the absence of immigration, one predator type became abundant, i.e., functional diversity declined to zero. In the lack of functional diversity the system showed the same dynamics as conventional models of predator-prey interactions ignoring the potential for shifts in species composition. This way, our study identified the crucial role of trade-offs and their shape in physiological and ecological traits for preserving diversity.
Predator-prey dynamics driven by feedback between functionally diverse trophic levels.
Tirok, Katrin; Bauer, Barbara; Wirtz, Kai; Gaedke, Ursula
2011-01-01
Neglecting the naturally existing functional diversity of communities and the resulting potential to respond to altered conditions may strongly reduce the realism and predictive power of ecological models. We therefore propose and study a predator-prey model that describes mutual feedback via species shifts in both predator and prey, using a dynamic trait approach. Species compositions of the two trophic levels were described by mean functional traits--prey edibility and predator food-selectivity--and functional diversities by the variances. Altered edibility triggered shifts in food-selectivity so that consumers continuously respond to the present prey composition, and vice versa. This trait-mediated feedback mechanism resulted in a complex dynamic behavior with ongoing oscillations in the mean trait values, reflecting continuous reorganization of the trophic levels. The feedback was only possible if sufficient functional diversity was present in both trophic levels. Functional diversity was internally maintained on the prey level as no niche existed in our system, which was ideal under any composition of the predator level due to the trade-offs between edibility, growth and carrying capacity. The predators were only subject to one trade-off between food-selectivity and grazing ability and in the absence of immigration, one predator type became abundant, i.e., functional diversity declined to zero. In the lack of functional diversity the system showed the same dynamics as conventional models of predator-prey interactions ignoring the potential for shifts in species composition. This way, our study identified the crucial role of trade-offs and their shape in physiological and ecological traits for preserving diversity.
Debaldev Jana
2014-01-01
Full Text Available In the present paper, I study a prey-predator model with multiple time delays where the predator population is regarded as generalist. For this regard, I consider a Holling-Tanner prey-predator system where a constant time delay is incorporated in the logistic growth of the prey to represent a delayed density dependent feedback mechanism and the second time delay is considered to account for the length of the gestation period of the predator. Predator’s interference in predator-prey relationship provides better descriptions of predator's feeding over a range of prey-predator abundances, so the predator's functional response here is considered to be Type II ratio-dependent. In accordance with previous studies, it is observed that delay destabilizes the system, in general, and stability loss occurs via Hopf bifurcation. There exist critical values of delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Hopf bifurcation occurs when delay parameters cross their critical values. When delay parameters are large enough than their critical values, the system exhibits chaotic behavior and this abnormal behavior may be controlled by refuge. Numerical computation is also performed to validate different theoretical results. Lyapunov exponent, recurrence plot, and power spectral density confirm the chaotic dynamical behaviors.
Global Dynamics of a Predator-prey Mo del
Huang Rui; Pan Qiang-you; Bao Lian-zhang; Wang Chun-peng
2015-01-01
In this paper, we consider a predator-prey model. A suﬃcient condition is presented for the stability of the equilibrium, which is different from the one for the model with Hassell-Varley type functional response. Furthermore, by constructing a Lyapunov function, we prove that the positive equilibrium is asymptotically stable.
Direct identification of predator-prey dynamics in gyrokinetic simulations
Kobayashi, Sumire; Gürcan, Özgür D.; Diamond, Patrick H.
2015-09-01
The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.
Direct identification of predator-prey dynamics in gyrokinetic simulations
Kobayashi, Sumire, E-mail: sumire.kobayashi@lpp.polytechnique.fr; Gürcan, Özgür D [Laboratoire de Physique des Plasmas, CNRS, Paris-Sud, Ecole Polytechnique, UMR7648, F-91128 Palaiseau (France); Diamond, Patrick H. [University of California, San Diego, La Jolla, California 92093-0319 (United States)
2015-09-15
The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.
Along Came a Spider: Using Live Arthropods in a Predator-Prey Activity
Richardson, Matthew L.; Hari, Janice
2011-01-01
We developed a predator-prey activity with eighth-grade students in which they used wolf spiders ("Lycosa carolinensis"), house crickets ("Acheta domestica"), and abiotic factors to address how (1) adaptations in predators and prey shape their interaction and (2) abiotic factors modify the interaction between predators and prey. We tested student…
BIFURCATION AND COMPLEXITY IN A RATIO-DEPENDENT PREDATOR-PREY CHEMOSTAT WITH PULSED INPUT
无
2007-01-01
In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution (xs(t), 0, zs(t)) is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period τ, the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.
Protection zone in a diffusive predator-prey model with Beddington-DeAngelis functional response.
He, Xiao; Zheng, Sining
2016-12-03
In any reaction-diffusion system of predator-prey models, the population densities of species are determined by the interactions between them, together with the influences from the spatial environments surrounding them. Generally, the prey species would die out when their birth rate is too low, the habitat size is too small, the predator grows too fast, or the predation pressure is too high. To save the endangered prey species, some human interference is useful, such as creating a protection zone where the prey could cross the boundary freely but the predator is prohibited from entering. This paper studies the existence of positive steady states to a predator-prey model with reaction-diffusion terms, Beddington-DeAngelis type functional response and non-flux boundary conditions. It is shown that there is a threshold value [Formula: see text] which characterizes the refuge ability of prey such that the positivity of prey population can be ensured if either the prey's birth rate satisfies [Formula: see text] (no matter how large the predator's growth rate is) or the predator's growth rate satisfies [Formula: see text], while a protection zone [Formula: see text] is necessary for such positive solutions if [Formula: see text] with [Formula: see text] properly large. The more interesting finding is that there is another threshold value [Formula: see text], such that the positive solutions do exist for all [Formula: see text]. Letting [Formula: see text], we get the third threshold value [Formula: see text] such that if [Formula: see text], prey species could survive no matter how large the predator's growth rate is. In addition, we get the fourth threshold value [Formula: see text] for negative [Formula: see text] such that the system admits positive steady states if and only if [Formula: see text]. All these results match well with the mechanistic derivation for the B-D type functional response recently given by Geritz and Gyllenberg (J Theoret Biol 314:106-108, 2012
Prey to predator size ratio influences foraging efficiency of larval Aeshna juncea dragonflies.
Hirvonen, Heikki; Ranta, Esa
1996-05-01
We investigated foraging behaviour of larval dragonflies Aeshna juncea in order to examine the significance of prey density and body size in predator-prey dynamics. A. juncea were offered separately three size-classes of Daphnia magna at low and high densities. The data were collected with direct observations of the foraging individuals. We found that large A. juncea larvae could better enhance their intake of prey biomass as prey size and prey density increased than their smaller conspecifics. However, increasing feeding efficiency of both larval instars was constrained by declining attack success and search rate with increasing prey size and density. With small D. magna, in contrast to large A. juncea, small A. juncea increased their searching efficiency as prey density increased keeping D. magna mortality rate at a constant level. In a predator-prey relationship this indicates stabilizing potential and feeding thresholds set by both prey density and prey-predator size ratio. Attack success dropped with prey size and density, but did not change in the course of the foraging bout. For both A. juncea sizes prey handling times increased as more medium and large prey were eaten. The slope of the increase became steeper with increasing prey-predator size ratio. These observations indicate that components of the predator-prey relationship vary with prey density, contrary to the basic assumptions of functional response equations. Moreover, the results suggest that the effects of prey density change during the ontogeny of predators and prey.
Almost Periodic Solutions of Prey-Predator Discrete Models with Delay
Itokazu Tomomi
2009-01-01
Full Text Available Abstract The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system and a competitive system , by using certain stability properties, which are referred to as -weakly uniformly asymptotic stable in hull and -totally stable.
Predation on exotic zebra mussels by native fishes: Effects on predator and prey
Magoulick, D.D.; Lewis, L.C.
2002-01-01
1. Exotic zebra mussels, Dreissena polymorpha, occur in southern U.S. waterways in high densities, but little is known about the interaction between native fish predators and zebra mussels. Previous studies have suggested that exotic zebra mussels are low profitability prey items and native vertebrate predators are unlikely to reduce zebra mussel densities. We tested these hypotheses by observing prey use of fishes, determining energy content of primary prey species of fishes, and conducting predator exclusion experiments in Lake Dardanelle, Arkansas. 2. Zebra mussels were the primary prey eaten by 52.9% of blue catfish, Ictalurus furcatus; 48.2% of freshwater drum, Aplodinotus grunniens; and 100% of adult redear sunfish, Lepomis microlophus. Blue catfish showed distinct seasonal prey shifts, feeding on zebra mussels in summer and shad, Dorosoma spp., during winter. Energy content (joules g-1) of blue catfish prey (threadfin shad, Dorosoma petenense; gizzard shad, D. cepedianum; zebra mussels; and asiatic clams, Corbicula fluminea) showed a significant species by season interaction, but shad were always significantly greater in energy content than bivalves examined as either ash-free dry mass or whole organism dry mass. Fish predators significantly reduced densities of large zebra mussels (>5 mm length) colonising clay tiles in the summers of 1997 and 1998, but predation effects on small zebra mussels (???5 mm length) were less clear. 3. Freshwater drum and redear sunfish process bivalve prey by crushing shells and obtain low amounts of higher-energy food (only the flesh), whereas blue catfish lack a shell-crushing apparatus and ingest large amounts of low-energy food per unit time (bivalves with their shells). Blue catfish appeared to select the abundant zebra mussel over the more energetically rich shad during summer, then shifted to shad during winter when shad experienced temperature-dependent stress and mortality. Native fish predators can suppress adult zebra
Ultrasonic predator-prey interactions in water– convergent evolution with insects and bats in air?
Maria eWilson
2013-06-01
Full Text Available Toothed whales and bats have independently evolved biosonar systems to navigate and locate and catch prey. Such active sensing allows them to operate in darkness, but with the potential cost of warning prey by the emission of intense ultrasonic signals. At least six orders of nocturnal insects have independently evolved ears sensitive to ultrasound and exhibit evasive maneuvers when exposed to bat calls. Among aquatic prey on the other hand, the ability to detect and avoid ultrasound emitting predators seems to be limited to only one subfamily of Clupeidae: the Alosinae (shad and menhaden. These differences are likely rooted in the different physical properties of air and water where cuticular mechanoreceptors have been adapted to serve as ultrasound sensitive ears, whereas ultrasound detection in water have called for sensory cells mechanically connected to highly specialized gas volumes that can oscillate at high frequencies. In addition, there are most likely differences in the risk of predation between insects and fish from echolocating predators. The selection pressure among insects for evolving ultrasound sensitive ears is high, because essentially all nocturnal predation on flying insects stems from echolocating bats. In the interaction between toothed whales and their prey the selection pressure seems weaker, because toothed whales are by no means the only marine predators placing a selection pressure on their prey to evolve specific means to detect and avoid them.Toothed whales can generate extremely intense sound pressure levels, and it has been suggested that they may use these to debilitate prey. Recent experiments however, show that neither fish with swim bladder, nor squid are debilitated by such signals. This strongly suggests that the production of high amplitude ultrasonic clicks serve the function of improving the detection range of the toothed whale biosonar system rather than debilitation of prey.
Bifurcations of a singular prey-predator economic model with time delay and stage structure
Zhang Xue [Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110004 (China); Key Laboratory of Integrated Automation of Process Industry (Northeastern Univ.), Ministry of Education, Shenyang, Liaoning 110004 (China)], E-mail: zhangxueer@gmail.com; Zhang Qingling [Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110004 (China); Key Laboratory of Integrated Automation of Process Industry (Northeastern Univ.), Ministry of Education, Shenyang, Liaoning 110004 (China)], E-mail: qlzhang@mail.neu.edu.cn; Liu Chao [Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110004 (China); Key Laboratory of Integrated Automation of Process Industry (Northeastern Univ.), Ministry of Education, Shenyang, Liaoning 110004 (China); Xiang Zhongyi [Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000 (China)
2009-11-15
This paper studies a singular prey-predator economic model with time delay and stage structure. Compared with other researches on dynamics of prey-predator population, this model is described by differential-algebraic equations due to economic factor. For zero economic profit, this model exhibits three bifurcational phenomena: transcritical bifurcation, Hopf bifurcation and singular induced bifurcation. For positive economic profit, the model undergoes a saddle-node bifurcation at critical value of positive economic profit, and the increase of delay destabilizes the positive equilibrium point of the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results.
Mougi, Akihiko
2012-03-01
Population dynamics and evolutionary dynamics can occur on similar time scales, and a coupling of these two processes can lead to novel population dynamics. Recent theoretical studies of coevolving predator-prey systems have concentrated more on the stability of such systems than on the characteristics of cycles when they are unstable. Here I explore the characteristics of the cycles that arise due to coevolution in a system in which prey can increase their ability to escape from predators by becoming either significantly larger or significantly smaller in trait value (i.e., a bidirectional trait axis). This is a reasonable model of body size evolution in some systems. The results show that antiphase population cycles and cryptic cycles (large population fluctuation in one species but almost no change in another species) can occur in the coevolutionary system but not systems where only a single species evolves. Previously, those dynamical patterns have only been theoretically shown to occur in single species evolutionary models and the coevolutionary model which do not involve a bi-directional axis of adaptation. These unusual dynamics may be observed in predator-prey interactions when the density dependence in the prey species is strong.
Combes, S A; Rundle, D E; Iwasaki, J M; Crall, J D
2012-03-15
Aerial predation is a highly complex, three-dimensional flight behavior that affects the individual fitness and population dynamics of both predator and prey. Most studies of predation adopt either an ecological approach in which capture or survival rates are quantified, or a biomechanical approach in which the physical interaction is studied in detail. In the present study, we show that combining these two approaches provides insight into the interaction between hunting dragonflies (Libellula cyanea) and their prey (Drosophila melanogaster) that neither type of study can provide on its own. We performed >2500 predation trials on nine dragonflies housed in an outdoor artificial habitat to identify sources of variability in capture success, and analyzed simultaneous predator-prey flight kinematics from 50 high-speed videos. The ecological approach revealed that capture success is affected by light intensity in some individuals but that prey density explains most of the variability in success rate. The biomechanical approach revealed that fruit flies rarely respond to approaching dragonflies with evasive maneuvers, and are rarely successful when they do. However, flies perform random turns during flight, whose characteristics differ between individuals, and these routine, erratic turns are responsible for more failed predation attempts than evasive maneuvers. By combining the two approaches, we were able to determine that the flies pursued by dragonflies when prey density is low fly more erratically, and that dragonflies are less successful at capturing them. This highlights the importance of considering the behavior of both participants, as well as their biomechanics and ecology, in developing a more integrative understanding of organismal interactions.
Impacts of biotic resource enrichment on a predator-prey population.
Safuan, H M; Sidhu, H S; Jovanoski, Z; Towers, I N
2013-10-01
The environmental carrying capacity is usually assumed to be fixed quantity in the classical predator-prey population growth models. However, this assumption is not realistic as the environment generally varies with time. In a bid for greater realism, functional forms of carrying capacities have been widely applied to describe varying environments. Modelling carrying capacity as a state variable serves as another approach to capture the dynamical behavior between population and its environment. The proposed modified predator-prey model is based on the ratio-dependent models that have been utilized in the study of food chains. Using a simple non-linear system, the proposed model can be linked to an intra-guild predation model in which predator and prey share the same resource. Distinct from other models, we formulate the carrying capacity proportional to a biotic resource and both predator and prey species can directly alter the amount of resource available by interacting with it. Bifurcation and numerical analyses are presented to illustrate the system's dynamical behavior. Taking the enrichment parameter of the resource as the bifurcation parameter, a Hopf bifurcation is found for some parameter ranges, which generate solutions that posses limit cycle behavior.
Structure of the Bifurcation Solutions for a Predator-Prey Model
WANG Yi-fu; MENG Yi-jie
2006-01-01
A system of reaction diffusion equations modeling the predator-prey interaction in an unstirred chemostat is considered. After transforming the model, the global bifurcation theorem is used to investigate the global structure of solutions of the system with b as the bifurcation parameter.
Stability of the Bifurcation Solutions for a Predator-Prey Model
孟义杰; 王一夫
2003-01-01
The bifurcation solution of the nonnegative steady-state of a reaction-diffusion system was investigated. The combination of the sturm-type eigenvalue and the theorem of bifurcation was used to study the local coexistence solutions, and obtain the stability of bifurcation solutions. The system model describes predator-prey interaction in an unstirred chemostat.
Density-dependent prey mortality is determined by the spatial scale of predator foraging.
McCarthy, Erin K; White, J Wilson
2016-02-01
Foraging theory predicts which prey patches predators should target. However, in most habitats, what constitutes a 'patch' and how prey density is calculated are subjective concepts and depend on the spatial scale at which the predator (or scientist) is observing. Moreover, the predator's 'foraging scale' affects prey population dynamics: predators should produce directly density-dependent (DDD) prey mortality at the foraging scale, but inversely density-dependent (IDD) mortality (safety-in-numbers) at smaller scales. We performed the first experimental test of these predictions using behavioral assays with guppies (Poecilia reticulata) feeding on bloodworm 'prey' patches. The guppy's foraging scale had already been estimated in a prior study. Our experimental results confirmed theoretical predictions: predation was IDD when prey were aggregated at a scale smaller than the foraging scale, but not when prey were aggregated at larger scales. These results could be used to predict outcomes of predator-prey interactions in continuous, non-discrete habitats in the field.
Marine predators and persistent prey in the southeast Bering Sea
Sigler, Michael F.; Kuletz, Kathy J.; Ressler, Patrick H.; Friday, Nancy A.; Wilson, Christopher D.; Zerbini, Alexandre N.
2012-06-01
Predictable prey locations reduce search time and energetic costs of foraging; thus marine predators often exploit locations where prey concentrations persist. In our study, we examined whether this association is influenced by differences among predator species in foraging modes (travel cost, surface feeder or diver) or whether the predator species is a central place forager or not. We examined distributions of two seabird species during their nesting period, the surface-feeding black-legged kittiwake (Rissa tridactyla) and the pursuit-diving thick-billed murre (Uria lomvia), and two baleen whale species, the humpback whale (Megaptera novaeangliae) and the fin whale (Balaenoptera physalus), in relation to two key prey, age-1 walleye pollock (Theragra chalcogramma) and euphausiids (Euphausiidae). Prey surveys were conducted once each year during 2004 and 2006-2010. Concurrent predator surveys were conducted in 2006-2010 (seabirds) and 2008 and 2010 (whales). We compared the seabird and whale foraging locations to where age-1 pollock and euphausiids were concentrated and considered the persistence of these concentrations, where the time-scale of persistence is year (i.e., a comparison among surveys that are conducted once each year). Euphausiids were widespread and concentrations often were reliably found within specific 37 km×37 km blocks ('persistent hot spots of prey'). In contrast, age-1 pollock were more concentrated and their hot spots were persistent only on coarser scales (>37 km). Both seabird species, regardless of foraging mode, were associated with age-1 pollock but not with euphausiids, even though age-1 pollock were less persistent than euphausiids. The higher travel cost central place foragers, thick-billed murres, foraged at prey concentrations nearer their island colonies than black-legged kittiwakes, which were more widespread foragers. Humpback whales were not tied to a central place and mostly were located only where euphausiids were
Land cover diversity increases predator aggregation and consumption of prey.
Penn, Hannah J; Athey, Kacie J; Lee, Brian D
2017-05-01
A lower diversity of land cover types is purported to decrease arthropod diversity in agroecosystems and is dependent on patterns of land use and fragmentation. Ants, important providers of ecosystem services such as biological control, are susceptible to landscape-level changes. We determined the relationships between land cover diversity and fragmentation on the within-field spatial associations of ants to pests and resulting predation events by combining mapping and molecular tools. Increased land cover diversity and decreased fragmentation increased ant abundance, spatial association to pests and predation. Land cover diversity and fragmentation were more explanatory than land cover types. Even so, specific land cover types, such as deciduous forest, influenced ant and pest diversity more so than abundance. These results indicate that geospatial techniques and molecular gut content analysis can be combined to determine the role of land use in influencing predator-prey interactions and resulting predation events in agroecosystems. © 2017 John Wiley & Sons Ltd/CNRS.
Predator and prey space use: dragonflies and tadpoles in an interactive game.
Hammond, John I; Luttbeg, Barney; Sih, Andrew
2007-06-01
Predator and prey spatial distributions have important population and community level consequences. However, little is known either theoretically or empirically about behavioral mechanisms that underlie the spatial patterns that emerge when predators and prey freely interact. We examined the joint space use and behavioral rules governing movement of freely interacting groups of odonate (dragonfly) predators and two size classes of anuran (tadpole) prey in arenas containing two patches with different levels of the prey's resource. Predator and prey movement and space use was quantified both when they were apart and together. When apart from predators, large tadpoles strongly preferred the high resource patch. When apart from prey, dragonflies weakly preferred the high resource patch. When together, large prey shifted to a uniform distribution, while predators strongly preferred the high resource patch. These patterns qualitatively fit the predictions of several three trophic level, ideal free distribution models. In contrast, the space use of small prey and predators did not deviate from uniform. Three measures of joint space use (spatial correlations, overlap, and co-occurrence) concurred in suggesting that prey avoidance of predators was more important than predator attraction to prey in determining overall spatial patterns. To gain additional insight into behavioral mechanisms, we used a model selection approach to identify behavioral movement rules that can potentially explain the observed, emergent patterns of space use. Prey were more likely to leave patches with more predators and more conspecific competitors; resources had relatively weak effects on prey movements. In contrast, predators were more likely to leave patches with low resources (that they do not consume) and more competing predators; prey had relatively little effect on predator movements. These results highlight the importance of investigating freely interacting predators and prey, the potential
Tabiś, Bolesław; Skoneczny, Szymon
2013-07-20
Nonlinear properties of a bioreactor with a developed microbiological predator-prey food chain are discussed. The presence of the predator microorganism completely changes the position and stability of the stationary states. A wide range of unstable steady states appears, associated with high amplitude oscillations of the state variables. Without automatic control such a system can only operate in transient states, with the yield undergoing periodic changes following the dynamics of the stable limit cycle. Technologically, this is undesirable. It has been shown that the oscillations can be removed by employing continuous P or PI controllers. Moreover, with a PI-controller, the predator can be eliminated from the system.
Interactive effects of predation risk and conspecific density on the nutrient stoichiometry of prey.
Guariento, Rafael D; Carneiro, Luciana S; Jorge, Jaqueiuto S; Borges, Angélica N; Esteves, Francisco A; Caliman, Adriano
2015-11-01
The mere presence of predators (i.e., predation risk) can alter consumer physiology by restricting food intake and inducing stress, which can ultimately affect prey-mediated ecosystem processes such as nutrient cycling. However, many environmental factors, including conspecific density, can mediate the perception of risk by prey. Prey conspecific density has been defined as a fundamental feature that modulates perceived risk. In this study, we tested the effects of predation risk on prey nutrient stoichiometry (body and excretion). Using a constant predation risk, we also tested the effects of varying conspecific densities on prey responses to predation risk. To answer these questions, we conducted a mesocosm experiment using caged predators (Belostoma sp.), and small bullfrog tadpoles (Lithobates catesbeianus) as prey. We found that L. catesbeianus tadpoles adjust their body nutrient stoichiometry in response to predation risk, which is affected by conspecific density. We also found that the prey exhibited strong morphological responses to predation risk (i.e., an increase in tail muscle mass), which were positively correlated to body nitrogen content. Thus, we pose the notion that in risky situations, adaptive phenotypic responses rather than behavioral ones might partially explain why prey might have a higher nitrogen content under predation risk. In addition, the interactive roles of conspecific density and predation risk, which might result in reduced perceived risk and physiological restrictions in prey, also affected how prey stoichiometry responded to the fear of predation.
Bifurcations of a predator-prey model with non-monotonic response function
Broer, H.W.; Naudot, Vincent; Roussarie, Robert; Saleh, Khairul
2005-01-01
A 2-dimensional predator-prey model with five parameters is investigated, adapted from the Volterra-Lotka system by a non-monotonic response function. A description of the various domains of structural stability and their bifurcations is given. The bifurcation structure is reduced to four organising
Dynamics in a Lotka-Volterra Predator-Prey Model with Time-Varying Delays
Changjin Xu
2013-01-01
Full Text Available A Lotka-Volterra predator-prey model with time-varying delays is investigated. By using the differential inequality theory, some sufficient conditions which ensure the permanence and global asymptotic stability of the system are established. The paper ends with some interesting numerical simulations that illustrate our analytical predictions.
OPTIMAL CONTROL PROBLEM FOR A PERIODIC PREDATOR-PREY MODEL WITH AGE-DEPENDENCE
无
2012-01-01
In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur's theorem and optimality condition is derived by means of normal cone.
Valerie Allain
Full Text Available The Western and Central Pacific Ocean sustains the highest tuna production in the world. This province is also characterized by many islands and a complex bathymetry that induces specific current circulation patterns with the potential to create a high degree of interaction between coastal and oceanic ecosystems. Based on a large dataset of oceanic predator stomach contents, our study used generalized linear models to explore the coastal-oceanic system interaction by analyzing predator-prey relationship. We show that reef organisms are a frequent prey of oceanic predators. Predator species such as albacore (Thunnus alalunga and yellowfin tuna (Thunnus albacares frequently consume reef prey with higher probability of consumption closer to land and in the western part of the Pacific Ocean. For surface-caught-predators consuming reef prey, this prey type represents about one third of the diet of predators smaller than 50 cm. The proportion decreases with increasing fish size. For predators caught at depth and consuming reef prey, the proportion varies with predator species but generally represents less than 10%. The annual consumption of reef prey by the yellowfin tuna population was estimated at 0.8 ± 0.40 CV million tonnes or 2.17 × 10(12± 0.40 CV individuals. This represents 6.1% ± 0.17 CV in weight of their diet. Our analyses identify some of the patterns of coastal-oceanic ecosystem interactions at a large scale and provides an estimate of annual consumption of reef prey by oceanic predators.
Influence of local carrying capacity restrictions on stochastic predator-prey models
Washenberger, Mark J [Department of Physics and Center for Stochastic Processes in Science and Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435 (United States); Mobilia, Mauro [Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universitaet Muenchen, D-80333 Munich (Germany); Taeuber, Uwe C [Department of Physics and Center for Stochastic Processes in Science and Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435 (United States)
2007-02-14
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained for site-restricted model variants. In accord with the classic Lotka-Volterra mean-field description, both species always coexist in two dimensions. Yet competing activity fronts generate complex, correlated spatio-temporal structures. As a consequence, finite systems display transient erratic population oscillations with characteristic frequencies that are renormalized by fluctuations. For large reaction rates, when the processes are rendered more local, these oscillations are suppressed. In contrast with the site-restricted predator-prey model, we also observe species coexistence in one dimension. In addition, we report results on the steady-state prey age distribution.
Elizabeth M P Madin
Full Text Available Efforts to restore top predators in human-altered systems raise the question of whether rebounds in predator populations are sufficient to restore pristine foodweb dynamics. Ocean ecosystems provide an ideal system to test this question. Removal of fishing in marine reserves often reverses declines in predator densities and size. However, whether this leads to restoration of key functional characteristics of foodwebs, especially prey foraging behavior, is unclear. The question of whether restored and pristine foodwebs function similarly is nonetheless critically important for management and restoration efforts. We explored this question in light of one important determinant of ecosystem function and structure--herbivorous prey foraging behavior. We compared these responses for two functionally distinct herbivorous prey fishes (the damselfish Plectroglyphidodon dickii and the parrotfish Chlorurus sordidus within pairs of coral reefs in pristine and restored ecosystems in two regions of these species' biogeographic ranges, allowing us to quantify the magnitude and temporal scale of this key ecosystem variable's recovery. We demonstrate that restoration of top predator abundances also restored prey foraging excursion behaviors to a condition closely resembling those of a pristine ecosystem. Increased understanding of behavioral aspects of ecosystem change will greatly improve our ability to predict the cascading consequences of conservation tools aimed at ecological restoration, such as marine reserves.
Existence of complex patterns in the Beddington-DeAngelis predator-prey model.
Haque, Mainul
2012-10-01
The study of reaction-diffusion system constitutes some of the most fascinating developments of late twentieth century mathematics and biology. This article investigates complexity and chaos in the complex patterns dynamics of the original Beddington-DeAngelis predator-prey model which concerns the influence of intra species competition among predators. We investigate the emergence of complex patterns through reaction-diffusion equations in this system. We derive the conditions for the codimension-2 Turing-Hopf, Turing-Saddle-node, and Turing-Transcritical bifurcation, and the codimension-3 Turing-Takens-Bogdanov bifurcation. These bifurcations give rise to very complex patterns that have not been observed in previous predator-prey models. A large variety of different types of long-term behavior, including homogenous distributions and stationary spatial patterns are observed through extensive numerical simulations with experimentally-based parameter values. Finally, a discussion of the ecological implications of the analytical and numerical results concludes the paper.
Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model
Chandrima Banerjee
2016-01-01
Full Text Available We investigate the dynamical behaviors of two-prey one-predator model with general Holling type functional responses. The effect of seasonal perturbation on the model has been discussed analytically as well as numerically. The periodic fluctuation is considered in prey growth rate and the predator mortality rate of the model. The impulsive effects involving biological and chemical control strategy, periodic releasing of natural enemies, and spraying pesticide at different fixed times are introduced in the model with seasonal perturbation. We derive the conditions of stability for impulsive system using Floquet theory, small amplitude perturbation skills. A local asymptotically stable prey (pest eradicated periodic solution is obtained when the impulsive period is less than some critical value. Numerical simulations of the model with and without seasonal disturbances exhibit different dynamics. Also we simulate numerically the model involving seasonal perturbations without impulse and with impulse. Finally, concluding remarks are given.
Intermediate fragmentation per se provides stable predator-prey metapopulation dynamics.
Cooper, Jennifer K; Li, Jiqiu; Montagnes, David J S
2012-08-01
The extent to which a landscape is fragmented affects persistence of predator-prey dynamics. Increasing fragmentation concomitantly imposes conditions that stabilise and destabilise metapopulations. For the first time, we explicitly assessed the hypothesis that intermediate levels provide optimal conditions for stability. We examine four structural changes arising from increased fragmentation: increased fragment number; decreased fragment size; increased connectedness (corridors scaled to fragment); increased fragment heterogeneity (based on connectedness). Using the model predator-prey system (Didinium-Paramecium) we support our hypothesis, by examining replicated metapopulations dynamics at five fragmentation levels. Although both species became extinct without fragmentation, prey survived at low and high levels, and both survived at intermediate levels. By examining time to extinction, maximum abundances, and population asynchrony we conclude that fragmentation produces structural heterogeneity (independent of environmental heterogeneity), which influences stability. Our analysis suggests why some theoretical, field and microcosm studies present conflicting views of fragmentation effects on population persistence.
于丽颖
2012-01-01
By means of the continuation theorem based on coincidence degree theory and homotopy mapping, the existence of positive periodic solution of a predator-prey system with stage-structured and cannibalism for prey is obtained. The phenomenon is revealed that when the cannibalism rate of adult prey species and the arrest rate of adult prey species are enough small, the system will bring periodic oscillation of biological nature.%利用重合度理论中的延拓定理和同伦映射，得到了一类食饵具有阶段结构和自食的捕食系统正周期解存在的充分条件，揭示了当成年食饵种群自食率和被捕获率均足够小时，系统将产生生物性周期振荡现象．
Preference and Prey Switching in a Generalist Predator Attacking Local and Invasive Alien Pests
Jaworski, Coline C.; Bompard, Anaïs; Genies, Laure; Amiens-Desneux, Edwige; Desneux, Nicolas
2013-01-01
Invasive pest species may strongly affect biotic interactions in agro-ecosystems. The ability of generalist predators to prey on new invasive pests may result in drastic changes in the population dynamics of local pest species owing to predator-mediated indirect interactions among prey. On a short time scale, the nature and strength of such indirect interactions depend largely on preferences between prey and on predator behavior patterns. Under laboratory conditions we evaluated the prey preference of the generalist predator Macrolophus pygmaeus Rambur (Heteroptera: Miridae) when it encounters simultaneously the local tomato pest Bemisia tabaci (Gennadius) (Hemiptera: Aleyrodidae) and the invasive alien pest Tuta absoluta (Meyrick) (Lepidoptera: Gelechiidae). We tested various ratios of local vs. alien prey numbers, measuring switching by the predator from one prey to the other, and assessing what conditions (e.g. prey species abundance and prey development stage) may favor such prey switching. The total predation activity of M. pygmaeus was affected by the presence of T. absoluta in the prey complex with an opposite effect when comparing adult and juvenile predators. The predator showed similar preference toward T. absoluta eggs and B. tabaci nymphs, but T. absoluta larvae were clearly less attacked. However, prey preference strongly depended on prey relative abundance with a disproportionately high predation on the most abundant prey and disproportionately low predation on the rarest prey. Together with the findings of a recent companion study (Bompard et al. 2013, Population Ecology), the insight obtained on M. pygmaeus prey switching may be useful for Integrated Pest Management in tomato crops, notably for optimal simultaneous management of B. tabaci and T. absoluta, which very frequently co-occur on tomato. PMID:24312646
Patterns formations in a diffusive ratio-dependent predator-prey model of interacting populations
Camara, B. I.; Haque, M.; Mokrani, H.
2016-11-01
The present investigation deals with the analysis of the spatial pattern formation of a diffusive predator-prey system with ratio-dependent functional response involving the influence of intra-species competition among predators within two-dimensional space. The appropriate condition of Turing instability around the interior equilibrium point of the present model has been determined. The emergence of complex patterns in the diffusive predator-prey model is illustrated through numerical simulations. These results are based on the existence of bifurcations of higher codimension such as Turing-Hopf, Turing-Saddle-node, Turing-Transcritical bifurcation, and the codimension- 3 Turing-Takens-Bogdanov bifurcation. The paper concludes with discussions of our results in ecology.
Competition and Facilitation between a Disease and a Predator in a Stunted Prey Population.
Maarten C Boerlijst
Full Text Available The role of diseases and parasites has received relatively little attention in modelling ecological dynamics despite mounting evidence of their importance in structuring communities. In contrast to predators, parasites do not necessarily kill their host but instead they may change host life history. Here, we study the impact of a parasite that selectively infects juvenile prey individuals and prevents them from maturing into adults. The model is inspired by the Ligula intestinalis tape worm and its cyprinid fish host Rutilis rutilis. We demonstrate that the parasite can promote as well as demote the so-called stunting in its host population, that is, the accumulation of juvenile prey, which leads to strong exploitation competition and consequently to a bottleneck in maturation. If competition between infected and uninfected individuals is strong, stunting will be enhanced and bistability between a stunted and non-stunted prey population occurs. In this case, the disease competes with the predator of its host species, possibly leading to predator extinction. In contrast, if the competition between infected and uninfected individuals is weak, the stunting is relieved, and epi-zoonotic cycles will occur, with recurrent epidemic outbreaks. Here, the disease facilitates the predator, and predator density will be substantially increased. We discuss the implications of our results for the dynamics and structure of the natural Ligula-Roach system.
Dubey, B; Zhao, T G; Jonsson, M; Rahmanov, H
2010-05-07
In this study, an analytical method is introduced for the identification of predator-prey populations time-dependent evolution in a Lotka-Volterra predator-prey model which takes into account the concept of accelerated-predator-satiety. Oppositely to most of the predator-prey problem models, the actual model does not suppose that the predation is strictly proportional to the prey density. In reference to some recent experimental results and particularly to the conclusions of May (1973) about predators which are 'never not hungry', an accelerated satiety function is matched with the initial conventional equations. Solutions are plotted and compared to some relevant ones. The obtained trends are in good agreement with many standard Lotka-Volterra solutions except for the asymptotic behaviour. Copyright (c) 2010 Elsevier Ltd. All rights reserved.
Grof-Tisza, Patrick; LoPresti, Eric; Heath, Sacha K; Karban, Richard
2017-03-01
Habitat-forming species provide refuges for a variety of associating species; these refuges may mediate interactions between species differently depending on the functional traits of the habitat-forming species. We investigated refuge provisioning by plants with different functional traits for dragonfly and damselfly (Odonata: Anisoptera and Zygoptera) nymphs emerging from water bodies to molt into their adult stage. During this period, nymphs experience high levels of predation by birds. On the shores of a small pond, plants with mechanical defenses (e.g., thorns and prickles) and high structural complexity had higher abundances of odonate exuviae than nearby plants which lacked mechanical defenses and exhibited low structural complexity. To disentangle the relative effects of these two potentially important functional traits on nymph emergence-site preference and survival, we conducted two fully crossed factorial field experiments using artificial plants. Nymphs showed a strong preference for artificial plants with high structural complexity and to a lesser extent, mechanical defenses. Both functional traits increased nymph survival but through different mechanisms. We suggest that future investigations attempt to experimentally separate the elements contributing to structural complexity to elucidate the mechanistic underpinnings of refuge provisioning.
STABILIZATION OF A KIND OF PREY-PREDATOR MODEL WITH HOLLING FUNCTIONAL RESPONSE
Xi LIU; Qingling ZHANG; Lichun ZHAO
2006-01-01
The stabilization problem of a kind of prey-predator model with Holling functional response is investigated. By approximate linearization approach, a feedback control law stabilizing the closedloop system is obtained. On the other hand, by exact linearization approach, a suitable change of coordinates in the state space and a feedback control law render the complex nonlinear system to be a linear controllable one such that the positive equilibrium point of the closed-loop system is globally asymptotically stable.
Indirect effects of prey swamping: differential seed predation during a bamboo masting event.
Kitzberger, Thomas; Chaneton, Enrique J; Caccia, Fernando
2007-10-01
Resource pulses often involve extraordinary increases in prey availability that "swamp" consumers and reverberate through indirect interactions affecting other community members. We developed a model that predicts predator-mediated indirect effects induced by an epidemic prey on co-occurring prey types differing in relative profitability/preference and validated our model by examining current-season and delayed effects of a bamboo mass seeding event on seed survival of canopy tree species in mixed Patagonian forests. The model shows that predator foraging behavior, prey profitability, and the scale of prey swamping influence the character and strength of short-term indirect effects on various alternative prey. When in large prey-swamped patches, nonselective predators decrease predation on all prey types. Selective predators, instead, only benefit prey of similar quality to the swamping species, while very low or high preference prey remain unaffected. Negative indirect effects (apparent competition) may override such positive effects (apparent mutualism), especially for highly preferred prey, when prey-swamped patches are small enough to allow predator aggregation and/or predators show a reproductive numerical response to elevated food supply. Seed predation patterns during bamboo (Chusquea culeou) masting were consistent with predicted short-term indirect effects mediated by a selective predator foraging in large prey-swamped patches. Bamboo seeds and similarly-sized Austrocedrus chilensis (ciprés) and Nothofagus obliqua (roble) seeds suffered lower predation in bamboo flowered than nonflowered patches. Predation rates on the small-seeded Nothofagus dombeyi (coihue) and the large-seeded Nothofagus alpina (rauli) were independent of bamboo flowering. Indirect positive effects were transient; three months after bamboo seeding, granivores preyed heavily upon all seed types, irrespective of patch flowering condition. Moreover, one year after bamboo seeding
Austin T Humphries
Full Text Available Interactions between predators and their prey are influenced by the habitat they occupy. Using created oyster (Crassostrea virginica reef mesocosms, we conducted a series of laboratory experiments that created structure and manipulated complexity as well as prey density and "predator-free space" to examine the relationship between structural complexity and prey survivorship. Specifically, volume and spatial arrangement of oysters as well as prey density were manipulated, and the survivorship of prey (grass shrimp, Palaemonetes pugio in the presence of a predator (wild red drum, Sciaenops ocellatus was quantified. We found that the presence of structure increased prey survivorship, and that increasing complexity of this structure further increased survivorship, but only to a point. This agrees with the theory that structural complexity may influence predator-prey dynamics, but that a threshold exists with diminishing returns. These results held true even when prey density was scaled to structural complexity, or the amount of "predator-free space" was manipulated within our created reef mesocosms. The presence of structure and its complexity (oyster shell volume were more important in facilitating prey survivorship than perceived refugia or density-dependent prey effects. A more accurate indicator of refugia might require "predator-free space" measures that also account for the available area within the structure itself (i.e., volume and not just on the surface of a structure. Creating experiments that better mimic natural conditions and test a wider range of "predator-free space" are suggested to better understand the role of structural complexity in oyster reefs and other complex habitats.
Humphries, Austin T.; La Peyre, Megan K.; Decossas, Gary A.
2011-01-01
Interactions between predators and their prey are influenced by the habitat they occupy. Using created oyster (Crassostrea virginica) reef mesocosms, we conducted a series of laboratory experiments that created structure and manipulated complexity as well as prey density and “predator-free space” to examine the relationship between structural complexity and prey survivorship. Specifically, volume and spatial arrangement of oysters as well as prey density were manipulated, and the survivorship of prey (grass shrimp, Palaemonetes pugio) in the presence of a predator (wild red drum, Sciaenops ocellatus) was quantified. We found that the presence of structure increased prey survivorship, and that increasing complexity of this structure further increased survivorship, but only to a point. This agrees with the theory that structural complexity may influence predator-prey dynamics, but that a threshold exists with diminishing returns. These results held true even when prey density was scaled to structural complexity, or the amount of “predator-free space” was manipulated within our created reef mesocosms. The presence of structure and its complexity (oyster shell volume) were more important in facilitating prey survivorship than perceived refugia or density-dependent prey effects. A more accurate indicator of refugia might require “predator-free space” measures that also account for the available area within the structure itself (i.e., volume) and not just on the surface of a structure. Creating experiments that better mimic natural conditions and test a wider range of “predator-free space” are suggested to better understand the role of structural complexity in oyster reefs and other complex habitats.
Thomsen, Sarah K; Green, David J
2016-12-01
Apex predators can suppress the foraging activity of mesopredators, which may then result in cascading benefits for the prey of those mesopredators. We studied the interactions between a top predator, the Barn Owl (Tyto alba), and their primary prey, an island endemic deer mouse (Peromyscus maniculatus elusus), which in turn consumes the eggs of seabirds nesting on Santa Barbara Island in California. Scripps's Murrelets (Synthliboramphus scrippsi), a threatened nocturnal seabird, arrive annually to breed on this island, and whose first egg is particularly vulnerable to predation by mice. We took advantage of naturally occurring extreme variations in the density of mice and owls on the island over 3 years and predicted that (1) mouse foraging would decrease with increasing predation risk from owls and moonlight and (2) these decreases in foraging would reduce predation on murrelet eggs. We measured the giving up densities of mice with experimental foraging stations and found that mice were sensitive to predation risk and foraged less when owls were more abundant and less during the full moon compared to the new moon. We also monitored the fates of 151 murrelet eggs, and found that murrelet egg predation declined as owl abundance increased, and was lower during the full moon compared to the new moon. Moreover, high owl abundance suppressed egg predation even when mice were extremely abundant. We conclude that there is a behaviorally mediated cascade such that owls on the island had a positive indirect effect on murrelet egg survival. Our study adds to the wider recognition of the strength of risk effects to structure food webs, as well as highlighting the complex ways that marine and terrestrial food webs can intersect. © 2016 by the Ecological Society of America.
Huang, Tousheng; Zhang, Huayong; Yang, Hongju; Wang, Ning; Zhang, Feifan
2017-02-01
The spatial pattern formation of predator-prey systems is an important issue widely concerned. In this research, we address this issue by developing a new space- and time-discrete predator-prey model, with predation relationship described by Beddington-DeAngelis functional response. The discrete model is given by a coupled map lattice, taking a nonlinear relationship between predator-prey "reaction" stage and dispersal stage. Through analysis of Turing instability and Hopf instability for the discrete model, the parametric conditions for pattern formation are determined. Numerical simulations reveal a surprising variety of spatiotemporal patterns, including regular and irregular patterns of spots, stripes, labyrinth, gaps, mosaics, spirals, circles, and many intermediate patterns in-between. These patterns cover a majority of predator-prey pattern types recorded in literature. Besides, the discrete model predicts the occurrence of spatiotemporal chaos, which is responsible for the formation of irregular patterns. This research demonstrates that the nonlinear mechanisms of the discrete model better capture the complexity of pattern formation of predator-prey systems.
The benefits of being toxic to deter predators depends on prey body size
Smith, Karen E.; Halpin, Christina G.
2016-01-01
Many prey have evolved toxins as a defense against predation. Those species that advertise their toxicity to would-be predators with conspicuous warning signals are known as “aposematic.” Investment in toxicity by aposematically signaling prey is thought to underpin how aversive prey are to predators; increasing toxicity means that predators learn to avoid prey faster and attack them at lower rates. However, predators’ foraging decisions on aposematic prey are determined not only by their toxicity, but also by their nutrient content: predators can trade-off the costs of ingesting toxin with the benefits of acquiring nutrients. Prey body size is a cue that positively correlates with nutrient content, and that varies within and between aposematic species. We predicted that a dose of quinine (known to be toxic to birds) would be a more effective deterrent to avian predators when prey were small compared with when they were large, and that the benefits of possessing toxin would be greater for small-bodied prey. Using an established laboratory protocol of European starlings (Sturnus vulgaris) foraging on mealworms (Tenebrio molitor), we found evidence for increased protection from a dose of quinine for small-bodied compared with large-bodied prey. This shows that larger prey need more toxin to attain the same level of defense as smaller prey, which has implications for the evolution of aposematism and mimicry. PMID:28028378
Chuanjun Dai
2012-01-01
Full Text Available The dynamic complexities of a prey-predator system in the presence of alternative prey with impulsive state feedback control are studied analytically and numerically. By using the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions can be obtained. Furthermore, the corresponding bifurcation diagrams and phase diagrams are investigated by means of numerical simulations which illustrate the feasibility of the main results.
Frequency-Locking in a Spatially Extended Predator-Prey Model
YU Cun-Juan; TAN Ying-Xin
2011-01-01
The study is concerned with the effect of variable dispersal rates on Turing instability of a spatial Holling-Tanner system. A series of numerical simulations show that the oscillatory Turing pattern can emerge due to period diffusion coefficient. Moreover, we find that when the amplitude is above a threshold, 1 : 1 frequency-locking oscillation can be obtained. The results show that period diffusion coefficient plays an important role on the pattern formation in the predator-prey system.
Marc Weissburg
2015-11-01
Full Text Available We examined whether chemically mediated risk perception by prey and the effects of changes in prey behavior on basal resources vary as a function of the amount of prey biomass consumed by the predator. We studied these issues using a tritrophic system composed of blue crabs, Callinectes sapidus (top predator, mud crabs Panopeus herbstii (intermediate prey, and oysters Crassostrea virginica (basal resource. Working in a well characterized field environment where experiments preserve natural patterns of water flow, we found that biomass consumed by a predator determines the range, intensity and nature of prey aversive responses. Predators that consume large amounts of prey flesh more strongly diminish consumption of basal resources by prey and exert effects over a larger range (in space and time compared to predators that have eaten less. Less well-fed predators produce weaker effects, with the consequence that behaviorally mediated cascades preferentially occur in refuge habitats. Well-fed predators affected prey behavior and increased basal resources up to distances of 1–1.5 m, whereas predators fed restricted diet evoked changes in prey only when they were extremely close, typically 50 cm or less. Thus, consumptive and non-consumptive effects may be coupled; predators that have a greater degree of predatory success will affect prey traits more strongly and non-consumptive and consumptive effects may fluctuate in tandem, with some lag. Moreover, differences among predators in their degree of prey capture will create spatial and temporal variance in risk cue availability in the absence of underlying environmental effects.
Upadhyay, Ranjit Kumar [Department of Applied Mathematics, Indian School of Mines University, Dhanbad, Jharkhand 826 004 (India)], E-mail: ranjit_ism@yahoo.com; Kumari, Nitu [Department of Applied Mathematics, Indian School of Mines University, Dhanbad, Jharkhand 826 004 (India)], E-mail: nituism@gmail.com; Rai, Vikas [Department of Applied Mathematics, HMR Institute of Technology and Management, GT Karnal Road, Hamidpur, Delhi 110 036 (India)
2009-10-15
In this paper, dynamical complexities in two reaction-diffusion (RD) model systems are explored. A spatial heterogeneity in the form of linear spatial gradient in the reproductive growth rate of the phytoplankton is incorporated in both the model systems. Extra mortality of the zooplankton due to toxin production by the phytoplankton is included in the second reaction diffusion model system. Effect of toxin production and spatial heterogeneity in the model systems are studied. Toxin production does not seem to have an appreciable effect on the asymptotic dynamics of the model systems. On the other hand, spatial heterogeneity does influence the dynamics. In particular, it increases the frequency of occurrence of chaos as evident from two dimensional parameter scans. Both these model systems display short term recurrent chaos [Rai V. Chaos in natural populations: edge or wedge? Ecol Complex 2004;1: 127-38] as they reside on 'edges of chaos' (EOC) [Rai V, Upadhyay RK. Evolving to the edge of chaos: chance or necessity? Chaos, Solitons and Fractals 2006;30:1074-87]. This suggests that the ecological systems have a tendency to evolve to EOC. The study corroborates the inferences drawn from an earlier study by Rai and Upadhyay [Rai V, Upadhyay RK. Evolving to the edge of chaos: chance or necessity? Chaos, Solitons and Fractals 2006;30:1074-87]. The system's dynamics is largely unpredictable and admits bursts of short-term predictability.
Effects of additional food in a delayed predator-prey model.
Sahoo, Banshidhar; Poria, Swarup
2015-03-01
We examine the effects of supplying additional food to predator in a gestation delay induced predator-prey system with habitat complexity. Additional food works in favor of predator growth in our model. Presence of additional food reduces the predatory attack rate to prey in the model. Supplying additional food we can control predator population. Taking time delay as bifurcation parameter the stability of the coexisting equilibrium point is analyzed. Hopf bifurcation analysis is done with respect to time delay in presence of additional food. The direction of Hopf bifurcations and the stability of bifurcated periodic solutions are determined by applying the normal form theory and the center manifold theorem. The qualitative dynamical behavior of the model is simulated using experimental parameter values. It is observed that fluctuations of the population size can be controlled either by supplying additional food suitably or by increasing the degree of habitat complexity. It is pointed out that Hopf bifurcation occurs in the system when the delay crosses some critical value. This critical value of delay strongly depends on quality and quantity of supplied additional food. Therefore, the variation of predator population significantly effects the dynamics of the model. Model results are compared with experimental results and biological implications of the analytical findings are discussed in the conclusion section.
Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay
Boli Xie
2014-01-01
Full Text Available A predator-prey model with both cross diffusion and time delay is considered. We give the conditions for emerging Turing instability in detail. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dynamics exhibits a delay and diffusion controlled formation growth not only of spots and stripe-like patterns, but also of the two coexist. The obtained results show that this system has rich dynamics; these patterns show that it is useful for the diffusive predation model with a delay effect to reveal the spatial dynamics in the real model.
Predator-prey model for the self-organisation of stochastic oscillators in dual populations
Moradi, Sara; Gürcan, Özgür
2015-01-01
A predator-prey model of dual populations with stochastic oscillators is presented. A linear cross-coupling between the two populations is introduced following the coupling between the motions of a Wilberforce pendulum in two dimensions: one in the longitudinal and the other in torsional plain. Within each population a Kuramoto type competition between the phases is assumed. Thus, the synchronisation state of the whole system is controlled by these two types of competitions. The results of the numerical simulations show that by adding the linear cross-coupling interactions predator-prey oscillations between the two populations appear which results in self-regulation of the system by a transfer of synchrony between the two populations. The model represents several important features of the dynamical interplay between the drift wave and zonal flow turbulence in magnetically confined plasmas, and a novel interpretation of the coupled dynamics of drift wave-zonal flow turbulence using synchronisation of stochasti...
Linfei Nie
2013-04-01
Full Text Available In this article, a singular perturbation is introduced to analyze the global asymptotic stability of positive equilibria of ratio-dependent predator-prey models with stage structure for the prey. We prove theoretical results and show numerically that the proposed approach is feasible and efficient.
Curtis, Rachel; Klemens, Jeffrey A.; Agosta, Salvatore J.; Bartlow, Andrew W.; Wood, Steve; Carlson, Jason A.; Stratford, Jeffrey A.; Steele, Michael A.
2013-01-01
Predator-prey dynamics are an important concept in ecology, often serving as an introduction to the field of community ecology. However, these dynamics are difficult for students to observe directly. We describe a methodology that employs model caterpillars made of clay to estimate rates of predator attack on a prey species. This approach can be…
Horst R. Thieme
2000-10-01
Full Text Available Complex formation is used as a unified approach to derive representations and approximations of the functional response in predator prey relations, mating, and sexual disease transmission. Applications are given to the impact of a generalist predator on a prey population and the spread of a sexually transmitted disease in a multi-group heterosexual population.
Joint evolution of predator body size and prey-size preference
Troost, Tineke; Kooi, Bob; Dieckmann, Ulf
2007-01-01
We studied the joint evolution of predator body size and prey-size preference based on dynamic energy budget theory. The predators’ demography and their functional response are based on general eco-physiological principles involving the size of both predator and prey. While our model can account
Qualitative Analysis on a Reaction-Diffusion Prey Predator Model and the Corresponding Steady-States
Qunyi BIE; Rui PENG
2009-01-01
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem.The local and global stability of the positive constant steady-state are discussed,and then some results for nonexistence of positive non-constant steady-states are derived.
Caparroy, P.; Thygesen, Uffe Høgsbro; Visser, Andre
2000-01-01
A mathematical model of the attack success of planktonic predators (fish larvae and carnivorous copepods) is proposed. Based on a geometric representation of attack events, the model considers how the escape reaction characteristics (speed and direction) of copepod prey affect their probability...... of being captured. By combining the attack success model with previously published hydrodynamic models of predator and prey perception, we examine how predator foraging behaviour and prey perceptive ability affect the size spectra of encountered and captured copepod prey. We examine food size spectra of (i...... also acts in modifying the prey escape direction. The model demonstrates that the reorientation of the prey escape path towards the centre of the feeding current's flow field results in increased attack success of the predator. Finally, the model examines how variability in the kinetics of approach...
Turing patterns and apparent competition in predator-prey food webs on networks
Fernandes, Lucas D
2012-01-01
Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles in many fields of biology, such as ecology and morphogenesis. In the present study we focus on the role of Turing patterns in describing the abundance distribution of predator and prey species distributed in patches in a scale free network structure. We extend the original model proposed by Nakao and Mikhailov by considering food chains with several interacting pairs of preys and predators. We identify patterns of species distribution displaying high degrees of apparent competition driven by Turing instabilities. Our results provide further indication that differences in abundance distribution among patches may be, at least in part, due to self organized Turing patterns, and not necessarily to intrinsic environmental heterogeneity.
Spatial organization, grouping strategies and cyclic dominance in asymmetric predator-prey games
Cazaubiel, Annette; Arenzon, Jeferson J
2016-01-01
Predators may attack isolated or grouped preys in a cooperative, collective way. Whether a gregarious behavior is advantageous to each species depends on several conditions and game theory is a useful tool to deal with such a problem. We here extend the Lett-Auger-Gaillard model [Theor. Pop. Biol. {\\bf 65}, 263 (2004)] to spatially distributed groups and compare the resulting behavior with their mean field predictions for the coevolving densities of predator and prey strategies. We show that the coexistence phase in which both strategies for each group are present is stable because of an effective, cyclic dominance behavior similar to a well studied generalizations of the Rock-Paper-Scissors game with four species (without neutral pairs), a further example of how ubiquitous this mechanism is. In addition, inside the coexistence phase (but interestingly, only for finite size systems) there is a realization of the survival of the weakest effect that is triggered by a percolation crossover.
Stability of a Beddington-DeAngelis type predator-prey model with trichotomous noises
Jin, Yanfei; Niu, Siyong
2016-06-01
The stability analysis of a Beddington-DeAngelis (B-D) type predator-prey model driven by symmetric trichotomous noises is presented in this paper. Using the Shapiro-Loginov formula, the first-order and second-order solution moments of the system are obtained. The moment stability conditions of the B-D predator-prey model are given by using Routh-Hurwitz criterion. It is found that the stabilities of the first-order and second-order solution moments depend on the noise intensities and correlation time of noise. The first-order and second-order moments are stable when the correlation time of noise is increased. That is, the trichotomous noise plays a constructive role in stabilizing the solution moment with regard to Gaussian white noise. Finally, some numerical results are performed to support the theoretical analyses.
Is there universal predator-prey dynamics at the laminar-turbulent phase transition?
Shih, Hong-Yan; Goldenfeld, Nigel
2016-11-01
Direct numerical simulation of pipe flow shows that transitional turbulence is dominated by two collective modes: a longitudinal mode for small-scale turbulent fluctuations whose anisotropy induces an emergent large-scale azimuthal mode (so-called zonal flow) that inhibits anisotropic Reynolds stress. This activation-inhibition interaction leads to stochastic predator-prey-like dynamics, from which it follows that the transition to turbulence belongs to the directed percolation universality class. Here we show how predator-prey dynamics arises by deriving phenomenologically an effective field theory of the transition from a coarse-graining of the Reynolds equation. The rigorous mapping between the conserved currents in Rayleigh-Benard convection (RBC), Taylor-Couette and pipe flows suggests that the zonal flow-turbulence scenario might occur in these systems, consistent with observations of zonal flows in two-dimensional RBC, and bursts of transitional turbulence in Couette flow that follow the critical scalings of directed percolation.
Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure
Lingshu Wang
2014-01-01
Full Text Available A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results.
Sea urchins, their predators and prey in SW Portugal
Nuno Mamede
2014-06-01
Full Text Available Sea urchins play a key role structuring benthic communities of rocky shores through an intense herbivory. The most abundant sea urchin species on shallow rocky subtidal habitats of the SW coast of Portugal is Paracentrotus lividus (Echinodermata: Echinoidea. It is considered a key species in various locations throughout its geographical distribution by affecting the structure of macroalgae communities and may cause the abrupt transformation of habitats dominated by foliose algae to habitats dominated by encrusting algae - the urchin barrens. The removal of P. lividus predators by recreational and commercial fishing is considered a major cause of this phenomenon by affecting the trophic relationships between predators, sea urchins and algae communities. Marine protected areas (MPAs usually lead to the recovery of important predator species that control sea urchin populations and restore habitats dominated by foliose macroalgae. Therefore, MPAs provide a good opportunity to test cascading effects and indirect impacts of fishing at the ecosystem level. The ecological role of P. lividus was studied on rocky subtidal habitats of the SW coast of Portugal (Alentejo considering three trophic levels: population of P. lividus, their predators (fish and shellfish and their prey (macroalgae communities. Several studies were conducted: (1 a non-destructive observational study on the abundance and distribution patterns of P. lividus, their predators and preys, comparing areas with different protection; (2 a manipulative in situ study with cages to assess the role of P. lividus as an herbivore and the influence of predation; (3 a descriptive study of P. lividus predators based on underwater filming; (4 and a study of human perception on these trophic relationships and other issues on sea urchin ecology and fishery, based on surveys made to fishermen and divers. Subtidal studies were performed with SCUBA diving at 3-12 m deep. Results indicate that in the
Fluctuation-induced patterns and rapid evolution in predator-prey ecosystems
Goldenfeld, Nigel
2014-03-01
Predator-prey ecosystems exhibit noisy, persistent cycles that cannot be described by intuitive population-level differential equations such as the Lotka-Volterra equations. Traditionally this paradox has been met by including additional nonlinearities such as predator satiation to force limit cycle behavior. Over the last few years, it has been realized that individual-level descriptions, combined with systematic perturbation techniques can reproduce the key features of such systems in a minimal way, without requiring many additional assumptions or fine tunings. Here I review work in this area that uses these techniques to treat spatial patterns and the phenomenon of rapidly evolving prey sub-populations. In the latter case, I show how stochastic individual-level models reproduce the key features observed in chemostats and in the wild, including anomalous phase shifts between predator and prey species, evolutionary cycles and cryptic cycles. This work shows that stochastic individual-level models naturally describe systems where evolutionary time scales surprisingly match ecosystem time scales.
Stress triangle: do introduced predators exert indirect costs on native predators and prey?
Jennifer R Anson
Full Text Available Non-consumptive effects of predators on each other and on prey populations often exceed the effects of direct predation. These effects can arise from fear responses elevating glucocorticoid (GC hormone levels (predator stress hypothesis or from increased vigilance that reduces foraging efficiency and body condition (predator sensitive foraging hypothesis; both responses can lead to immunosuppression and increased parasite loads. Non-consumptive effects of invasive predators have been little studied, even though their direct impacts on local species are usually greater than those of their native counterparts. To address this issue, we explored the non-consumptive effects of the invasive red fox Vulpes vulpes on two native species in eastern Australia: a reptilian predator, the lace monitor Varanus varius and a marsupial, the ringtail possum Pseudocheirus peregrinus. In particular, we tested predictions derived from the above two hypotheses by comparing the basal glucocorticoid levels, foraging behaviour, body condition and haemoparasite loads of both native species in areas with and without fox suppression. Lace monitors showed no GC response or differences in haemoparasite loads but were more likely to trade safety for higher food rewards, and had higher body condition, in areas of fox suppression than in areas where foxes remained abundant. In contrast, ringtails showed no physiological or behavioural differences between fox-suppressed and control areas. Predator sensitive foraging is a non-consumptive cost for lace monitors in the presence of the fox and most likely represents a response to competition. The ringtail's lack of response to the fox potentially represents complete naiveté or strong and rapid selection to the invasive predator. We suggest evolutionary responses are often overlooked in interactions between native and introduced species, but must be incorporated if we are to understand the suite of forces that shape community
Facilitation of intraguild prey by its intraguild predator in a three-species Lotka-Volterra model.
Shchekinova, Elena Y; Löder, Martin G J; Boersma, Maarten; Wiltshire, Karen H
2014-03-01
Explaining the coexistence of multiple species in the competition and predation theatre has proven a great challenge. Traditional intraguild predation (IGP) models have only relatively small regions of stable coexistence of all species. Here, we investigate potential additional mechanisms that extend these regions of stable coexistence. We used a 3-species Lotka-Volterra system to which we added an interaction term to model a unidirectional facilitative relationship between the two predators in the IGP. In this modelling study the IG predator was able to precondition a part of the common resource by an instantaneous manipulation, which resulted in the immobilization of the resource species. This mechanism of immobilization facilitated the resource uptake by the IG prey and thus increased its growth rates even in the presence of the common predator. The facilitative relationship of the IG prey by the IG predator produced a stable coexistence of both predators even though the IG prey was an inferior competitor for a common resource, which cannot be attained with the traditional IGP models. Furthermore, our model predicted a 3-species stable coexistence even at high enrichment where no coexistence was found in the basic IGP model. Thus, we showed that diversity of resource traits could significantly alter emergent community patterns via shifts in exploitative competition of IGP-related predators. The described mechanism could potentially lead to a higher efficiency in exploitation of common resources and thus promote higher diversity in a real community. Copyright © 2013 Elsevier Inc. All rights reserved.
Do predator-prey relationships on the river bed affect fine sediment ingress?
Mathers, Kate; Rice, Stephen; Wood, Paul
2016-04-01
Ecosystem engineers are organisms that alter their physical environment and thereby influence the flow of resources through ecosystems. In rivers, several ecosystem engineers are also important geomorphological agents that modify fluvial sediment dynamics. By altering channel morphology and bed material characteristics, such modifications can affect the availability of habitats for other organisms, with implications for ecosystem health and wider community composition. In this way geomorphological and ecological systems are intimately interconnected. This paper focuses on one element of this intricate abiotic-biotic coupling: the interaction between fine sediment ingress into the river bed and the predator-prey relationships of aquatic organisms living on and in the river bed. Signal crayfish (Pacifastacus leniusculus) have been shown to modify fine sediment fluxes in rivers, but their effect on fine sediment ingress into riverbeds remains unclear. Many macroinvertebrate taxa have adapted avoidance strategies to avoid predation by crayfish, with one example being the freshwater shrimp (Gammarus pulex) which relies on open interstitial spaces within subsurface sediments as a refuge from crayfish predation. Fine sedimentation that fills gravelly frameworks may preclude access to those spaces, therefore leaving freshwater shrimp susceptible to predation. Ex-situ experiments were conducted which sought to examine: i) if freshwater shrimps and signal crayfish, alone and in combination, influenced fine sediment infiltration rates; and ii) whether modifications to substratum composition, specifically the introduction of fine sediment, modified predator-prey interactions. The results demonstrate that crayfish are significant geomorphic agents and that fine sediment ingress rates were significantly enhanced in their presence compared to control conditions or the presence of only freshwater shrimps. The combination of both organisms (i.e. allowing the interaction between
DYNAMICS OF A NONLINEAR NON-AUTONOMOUS n-PATCHES PREDATOR-PREY DISPERSION-DELAY MODEL
无
2007-01-01
In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved that the system is uniformly persistent under any dispersion rate effect. Furthermore, some sufficient conditions are established for the existence of a unique almost periodic solution of the system. The example shows that the criteria in the paper are new, general and easily verifiable.
Relative Preference and Localized Food Affect Predator Space Use and Consumption of Incidental Prey.
Schartel, Tyler E; Schauber, Eric M
2016-01-01
Abundant, localized foods can concentrate predators and their foraging efforts, thus altering both the spatial distribution of predation risk and predator preferences for prey that are encountered incidentally. However, few investigations have quantified the spatial scale over which localized foods affect predator foraging behavior and consumption of incidental prey. In spring 2010, we experimentally tested how point-source foods altered how generalist predators (white-footed mice, Peromyscus leucopus) utilized space and depredated two incidental prey items: almonds (Prunus dulcis; highly profitable) and maple seeds (Acer saccharum; less profitable). We estimated mouse population densities with trapping webs, quantified mouse consumption rates of these incidental prey items, and measured local mouse activity with track plates. We predicted that 1) mouse activity would be elevated near full feeders, but depressed at intermediate distances from the feeder, 2) consumption of both incidental prey would be high near feeders providing less-preferred food and, 3) consumption of incidental prey would be contingent on predator preference for prey relative to feeders providing more-preferred food. Mouse densities increased significantly from pre- to post-experiment. Mean mouse activity was unexpectedly greatest in control treatments, particularly preferred food (sunflower seeds) created localized refuges for incidental prey at intermediate distances (15 to 25m) from the feeder. Feeders with less-preferred food (corn) generated localized high risk for highly preferred almonds food on risk experienced by incidental prey, which can be positive or negative depending on both spatial proximity and relative preference.
Plant defences limit herbivore population growth by changing predator-prey interactions.
Kersch-Becker, Mônica F; Kessler, André; Thaler, Jennifer S
2017-09-13
Plant quality and predators are important factors affecting herbivore population growth, but how they interact to regulate herbivore populations is not well understood. We manipulated jasmonate-induced plant resistance, exposure to the natural predator community and herbivore density to test how these factors jointly and independently affect herbivore population growth. On low-resistance plants, the predator community was diverse and abundant, promoting high predator consumption rates. On high-resistance plants, the predator community was less diverse and abundant, resulting in low predator consumption rate. Plant resistance only directly regulated aphid population growth on predator-excluded plants. When predators were present, plant resistance indirectly regulated herbivore population growth by changing the impact of predators on the herbivorous prey. A possible mechanism for the interaction between plant resistance and predation is that methyl salicylate, a herbivore-induced plant volatile attractive to predators, was more strongly induced in low-resistance plants. Increased plant resistance reduced predator attractant lures, preventing predators from locating their prey. Low-resistance plants may regulate herbivore populations via predators by providing reliable information on prey availability and increasing the effectiveness of predators. © 2017 The Author(s).
Hagler, James R.; Charles G. Jackson; Rufus Isaacs; Machtley, Scott A.
2004-01-01
The sweetpotato whitefly, Bemisia tabaci (Gennadius) is fed on by a wide variety of generalist predators, but there is little information on these predator-prey interactions. A laboratory investigation was conducted to quantify the foraging behavior of the adults of five common whitefly predators presented with a surfeit of whitefly eggs, nymphs, and adults. The beetles, Hippodamia convergens Guérin-Méneville and Collops vittatus (Say) fed mostly on whitefly eggs, but readily and rapidly prey...
Post-attack aposematic display in prey facilitates predator avoidance learning
Changku eKang
2016-04-01
Full Text Available Warning signals protect unpalatable prey from predation because predators who learn the association between the warning signal and prey unprofitability decrease attacks on the prey. Most of the research have focused on visual aposematic signals that are constantly presented and visible to the predators. But a variety of chemically defended insects are rather cryptic when resting, and only in response to predator attacks (post-attack they perform displays of conspicuous abdomens or hindwings normally hidden under forewings. The function of those displays in unpalatable insects is not well understood. We examined two adaptive hypotheses on this facultative aposematic display using wild-caught oriental tits (Parus minor as predators. First, we tested whether the display increases the rejection of the prey by predators upon seeing the display (i.e. at the moment of attack through learning trials (aposematic signaling hypothesis. Second, we tested whether the display facilitates the memory formation between cryptic visible form of the prey and prey defense so that it prevents the predators initiate an attack upon seeing the cryptic form (facilitation hypothesis. We found that predators learned to avoid attacking the prey which supports the facilitation hypothesis. However, the support for the aposematic signaling hypothesis was equivocal. Our results open new directions of research by highlighting the possibility that similar facilitation effects may contribute to the evolution of various forms of post-attack visual displays in chemically, or otherwise, defended animals.
Predator-prey interactions shape thermal patch use in a newt larvae-dragonfly nymph model.
Lumír Gvoždík
Full Text Available Thermal quality and predation risk are considered important factors influencing habitat patch use in ectothermic prey. However, how the predator's food requirement and the prey's necessity to avoid predation interact with their respective thermoregulatory strategies remains poorly understood. The recently developed 'thermal game model' predicts that in the face of imminent predation, prey should divide their time equally among a range of thermal patches. In contrast, predators should concentrate their hunting activities towards warmer patches. In this study, we test these predictions in a laboratory setup and an artificial environment that mimics more natural conditions. In both cases, we scored thermal patch use of newt larvae (prey and free-ranging dragonfly nymphs (predators. Similar effects were seen in both settings. The newt larvae spent less time in the warm patch if dragonfly nymphs were present. The patch use of the dragonfly nymphs did not change as a function of prey availability, even when the nymphs were starved prior to the experiment. Our behavioral observations partially corroborate predictions of the thermal game model. In line with asymmetric fitness pay-offs in predator-prey interactions (the 'life-dinner' principle, the prey's thermal strategy is more sensitive to the presence of predators than vice versa.
Predator-prey interactions shape thermal patch use in a newt larvae-dragonfly nymph model.
Gvoždík, Lumír; Černická, Eva; Van Damme, Raoul
2014-01-01
Thermal quality and predation risk are considered important factors influencing habitat patch use in ectothermic prey. However, how the predator's food requirement and the prey's necessity to avoid predation interact with their respective thermoregulatory strategies remains poorly understood. The recently developed 'thermal game model' predicts that in the face of imminent predation, prey should divide their time equally among a range of thermal patches. In contrast, predators should concentrate their hunting activities towards warmer patches. In this study, we test these predictions in a laboratory setup and an artificial environment that mimics more natural conditions. In both cases, we scored thermal patch use of newt larvae (prey) and free-ranging dragonfly nymphs (predators). Similar effects were seen in both settings. The newt larvae spent less time in the warm patch if dragonfly nymphs were present. The patch use of the dragonfly nymphs did not change as a function of prey availability, even when the nymphs were starved prior to the experiment. Our behavioral observations partially corroborate predictions of the thermal game model. In line with asymmetric fitness pay-offs in predator-prey interactions (the 'life-dinner' principle), the prey's thermal strategy is more sensitive to the presence of predators than vice versa.
Subsidies to predators, apparent competition and the phylogenetic structure of prey communities.
Helmus, Matthew R; Mercado-Silva, Norman; Vander Zanden, M Jake
2013-11-01
Ecosystems are fragmented by natural and anthropogenic processes that affect organism movement and ecosystem dynamics. When a fragmentation restricts predator but not prey movement, then the prey produced on one side of an ecosystem edge can subsidize predators on the other side. When prey flux is high, predator density on the receiving side increases above that possible by in situ prey productivity, and when low, the formerly subsidized predators can impose strong top-down control of in situ prey--in situ prey experience apparent competition from the subsidy. If predators feed on some evolutionary clades of in situ prey over others, then subsidy-derived apparent competition will induce phylogenetic structure in prey composition. Dams fragment the serial nature of river ecosystems by prohibiting movement of organisms and restricting flowing water. In the river tailwater just below a large central Mexican dam, fish density was high and fish gorged on reservoir-derived zooplankton. When the dam was closed, water flow and the zooplankton subsidy ceased, densely packed pools of fish formed, fish switched to feed on in situ prey, and the tailwater macroinvertebrate community was phylogenetic structured. We derived expectations of structure from trait-based community assembly models based on macroinvertebrate body size, tolerance to anthropogenic disturbance, and fish-diet selectivity. The diet-selectivity model best fit the observed tailwater phylogenetic structure. Thus, apparent competition from subsidies phylogenetically structures prey communities, and serial variation in phylogenetic community structure can be indicative of fragmentation in formerly continuous ecosystems.
Pokhrel, Lok R; Dubey, Brajesh
2012-07-17
This study investigated the potential impacts of low-concentration citrate-coated silver nanoparticles (citrate-nAg; 2 μg L(-1) as total Ag) on the interactions of Daphnia magna Straus (as a prey) with the predatory dragonfly ( Anax junius : Odonata) nymph using the behavioral, survival, and reproductive end points. Four different toxicity bioassays were evaluated: (i) horizontal migration; (ii) vertical migration; (iii) 48 h survival; and (iv) 21 day reproduction; using four different treatment combinations: (i) Daphnia + citrate-nAg; (ii) Daphnia + predator; (iii) Daphnia + citrate-nAg + predator; and (iv) Daphnia only (control). Daphnia avoided the predators using the horizontal and vertical movements, indicating that Daphnia might have perceived a significant risk of predation. However, with citrate-nAg + predator treatment, Daphnia response did not differ from control in the vertical migration test, suggesting that Daphnia were unable to detect the presence of predator with citrate-nAg treatment and this may have potential implication on daphnids population structure owing to predation risk. The 48 h survival test showed a significant mortality of Daphnia individuals in the presence of predators, with or without citrate-nAg, in the test environment. Average reproduction of daphnids increased by 185% with low-concentration citrate-nAg treatment alone but was severely compromised in the presence of predators (decreased by 91.3%). Daphnia reproduction was slightly enhanced by approximately 128% with citrate-nAg + predator treatment. Potential mechanisms of these differential effects of low-concentration citrate-nAg, with or without predators, are discussed. Because silver dissolution was minimal, the observed toxicity could not be explained by dissolved Ag alone. These findings offer novel insights into how exposure to low-concentration silver nanoparticles could influence predator-prey interactions in the fresh water systems.
Generalized Predator-Prey Oscillations in Ecological and Economic Equilibrium
Samuelson, Paul A.
1971-01-01
The standard predator-prey model is generalized beyond the Volterra linear-log form. Conservative oscillations are deduced and also conversion to a variational Hamiltonian form. Generalization to more than two species is also castable into Hamiltonian form, with small vibrations around equilibrium being of undamped sinusoidal type by virtue of associated characteristic exponents all being pure imaginaries. However, introduction into ecological equilibrium of a recognition of limited space and inorganic matter destroys the autonomous periodicity of the motions and makes inapplicable the elegant formalisms of classical statistical mechanics. Introduction of simple diminishing returns leads to damped motions that are kept cyclically alive by shocks of the weather and other exogenous stochastic elements. Introduction of increasing returns solely in an interval near equilibrium leads to autonomous self-exciting oscillations near a stable limit cycle; under stochastic forcing functions, a long-run ergodic state becomes predictable. PMID:5280532
Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach
Tome, Tania; Carvalho, Kelly C de [Instituto de FIsica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970 Sao Paulo (Brazil)
2007-10-26
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model.
Prey, predators, parasites: intraguild predation or simpler community modules in disguise?
Sieber, Michael; Hilker, Frank M
2011-03-01
1. Competition and predation are at the heart of community ecology. The theoretical concept of intraguild predation (IGP) combines these key interactions in a single community module. Because IGP is believed to be ubiquitous in nature, it has been subject to extensive research, and there exists a well-developed theoretical framework. 2. We show that a general class of IGP models can be transformed to simpler, but equivalent community structures. This rather unexpected simplification depends critically on the property of 'indiscriminate predation', which we define broadly as the top-predator not distinguishing between its two different prey species. 3. In a broader context, the great importance of IGP and of the simplifying transformation we report here is enhanced by the recent insight that the basic IGP structure extends naturally to host-parasitoid and host-pathogen communities. We show that parasites infecting prey (predators) tend to render IGP effectively into exploitative competition (tritrophic food chain, respectively). 4. The equivalence between the original and simplified community module makes it possible to take advantage from already existing insights. We illustrate this by means of an eco-epidemiological IGP model that is strikingly similar to a classical exploitative competition model. 5. The change of perspective on certain community modules may contribute to a better understanding of food web dynamics. In particular, it may help explain the interactions in food webs that include parasites. Given the ubiquity of parasitism, food webs may appear in a different light when they are transformed to their simplified analogue. © 2010 The Authors. Journal of Animal Ecology © 2010 British Ecological Society.
Turbulence, Temperature, and Turbidity: The Ecomechanics of Predator-Prey Interactions in Fishes.
Higham, Timothy E; Stewart, William J; Wainwright, Peter C
2015-07-01
Successful feeding and escape behaviors in fishes emerge from precise integration of locomotion and feeding movements. Fishes inhabit a wide range of habitats, including still ponds, turbulent rivers, and wave-pounded shorelines, and these habitats vary in several physical variables that can strongly impact both predator and prey. Temperature, the conditions of ambient flow, and light regimes all have the potential to affect predator-prey encounters, yet the integration of these factors into our understanding of fish biomechanics is presently limited. We explore existing knowledge of kinematics, muscle function, hydrodynamics, and evolutionary morphology in order to generate a framework for understanding the ecomechanics of predator-prey encounters in fishes. We expect that, in the absence of behavioral compensation, a decrease in temperature below the optimum value will reduce the muscle power available both to predator and prey, thus compromising locomotor performance, suction-feeding mechanics of predators, and the escape responses of prey. Ambient flow, particularly turbulent flow, will also challenge predator and prey, perhaps resulting in faster attacks by predators to minimize mechanical instability, and a reduced responsiveness of prey to predator-generated flow. Reductions in visibility, caused by depth, turbidity, or diel fluctuations in light, will decrease distances at which either predator or prey detect each other, and generally place a greater emphasis on the role of mechanoreception both for predator and prey. We expect attack distances to be shortened when visibility is low. Ultimately, the variation in abiotic features of a fish's environment will affect locomotion and feeding performance of predators, and the ability of the prey to escape. The nature of these effects and how they impact predator-prey encounters stands as a major challenge for future students of the biomechanics of fish during feeding. Just as fishes show adaptations for capturing
Predator-Prey Model for Haloes in Saturn's Rings
Esposito, Larry W.; Colwell, Joshua; Sremcevic, Miodrag; Madhusudhanan, Prasanna
Particles in Saturn’s rings have a tripartite nature: (1) a broad distribution of fragments from the disruption of a previous moon that accrete into (2) transient aggregates, resembling piles of rubble, covered by a (3) regolith of smaller grains that result from collisions and meteoritic grinding. Evidence for this triple architecture of ring particles comes from a multitude of Cassini observations. In a number of ring locations (including Saturn’s F ring, the shepherded outer edges of rings A and B and at the locations of the strongest density waves) aggregation and dis-aggregation are operating now. ISS, VIMS, UVIS spectroscopy and occultations show haloes around the strongest density waves. Based on a predator-prey model for ring dynamics, we offer the following explanation: •Cyclic velocity changes cause the perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; •This forms a bright halo around the ILR, if the forcing is strong enough; •Surrounding particles diffuse back too slowly to erase the effect; they diffuse away to form the halo. The most rapid time scale is for forcing/aggregate growth/disaggregation; then irreversible regolith erosion; diffusion and/or ballistic transport; and slowest, meteoritic pollution/darkening. We observe both smaller and larger particles at perturbed regions. Straw, UVIS power spectral analysis, kittens and equinox objects show the prey (mass aggregates); while the haloes’ VIMS spectral signature, correlation length and excess variance are created by the predators (velocity dispersion) in regions stirred in the rings. Moon forcing triggers aggregation to create longer-lived aggregates that protect their interiors from meteoritic darkening and recycle the ring material to maintain the current purity of the rings. It also provides a mechanism for creation of new moons at resonance locations in the Roche zone, as proposed by Charnoz etal and
Spatiotemporal patterns provoked by environmental variability in a predator-prey model.
Fras, Maja; Gosak, Marko
2013-12-01
The emergence of spatiotemporal patterns in the distribution of species is one of the most striking phenomena in ecology and nonlinear science. Since it is known that spatial inhomogeneities can significantly affect the dynamics of ecological populations, in the present paper we investigate the impact of environmental variability on the formation of patterns in a spatially extended predator-prey model. In particular, we utilize a predator-prey system with a Holling III functional response and introduce random spatial variations of the kinetic parameter signifying the intrinsic growth rate of the prey, reflecting the impact of a heterogeneous environment. Our results reveal that in the proximity of the Hopf bifurcation environmental variability is able to provoke pattern formation, whereby the coherence of the patterns exhibits a resonance-like dependence on the variability strength. Furthermore, we show that the phenomenon can only be observed if the spatial heterogeneities exhibit large enough regions with high growth rates of the prey. Our findings thus indicate that variability could be an essential pattern formation mechanism of the populations.
Stability of an intraguild predation system with mutual predation
Wang, Yuanshi; DeAngelis, Donald L.
2016-04-01
We examine intraguild predation (IGP), in which species both compete for resources or space and prey on each other. The IGP system is modeled here by a lattice gas model of the mean-field theory. First, we consider the IGP system of one species in which individuals of the same species cannibalize each other. The dynamical behavior of the model demonstrates a mechanism by which the intraspecific predation promotes persistence of the species. Then we consider the IGP system of two species with mutual predation. Global dynamics of the model exhibit basic properties of IGP: (i) When both species' efficiencies in converting the consumptions into fitness are large, the outcome of their interaction is mutualistic in form and the IGP promotes persistence of both species. (ii) When one species' efficiency is large but the other's is small, the interaction outcomes become parasitic in nature, in which an obligate species can survive through the mutual predation with a facultative one. (iii) When both species' efficiencies are small, the interaction outcomes are competitive in nature and the IGP leads to extinction of one of the species. A novel result of this work is that varying one parameter or population density of the species can lead to transition of interaction outcomes between mutualism, parasitism and competition. On the other hand, dynamics of the models demonstrate that over-predation or under-predation will result in extinction of one/both species, while intermediate predation is favorable under certain parameter ranges.
Taylor, E.J.; Blockwell, S.J.; Pascoe, D. [Univ. of Wales Coll. of Cardiff (United Kingdom)
1994-12-31
Simple multi-species toxicity tests based on the predation of Daphnia magna Straus by Hydra oligactis (Pallas) and competition between Gammarus pulex (L.) and Asellus aquaticus (L.) were used to determine the effects of three reference chemicals. Criteria examined included functional responses; time to first captures; handling times (predator/prey systems) and co-existence and growth. The tests which proved most practicable and sensitive (lowest observed effects 0.1, 21, and 80 {micro}g/l for lindane, copper and 3,4 dichloroaniline, respectively) were: (1) predator-prey tests: determining changes in the size-structure of predated D. magna populations and (2) competition tests: measuring the feeding rate of G. pulex competing with A. aquaticus, using a bioassay based on the time-response analysis of the consumption of Artemia salina eggs. The concentration of a chemical which affected particular response criteria was fond to depend on the test system employed. Results of the tests indicated that effects were often not dose-related and that a given criterion could be variously affected by different test concentrations. The complex pattern of responses may be explained in terms of the differential sensitivity of the interacting species and perhaps subtle alteration in strategies. The sensitivity of the bioassay endpoints is compared to those of a range of single species tests, and their value for predicting the impact pollutants may have upon natural freshwater ecosystems is discussed.
Peacor, Scott D; Peckarsky, Barbara L; Trussell, Geoffrey C; Vonesh, James R
2013-01-01
Defensive modifications in prey traits that reduce predation risk can also have negative effects on prey fitness. Such nonconsumptive effects (NCEs) of predators are common, often quite strong, and can even dominate the net effect of predators. We develop an intuitive graphical model to identify and explore the conditions promoting strong NCEs. The model illustrates two conditions necessary and sufficient for large NCEs: (1) trait change has a large cost, and (2) the benefit of reduced predation outweighs the costs, such as reduced growth rate. A corollary condition is that potential predation in the absence of trait change must be large. In fact, the sum total of the consumptive effects (CEs) and NCEs may be any value bounded by the magnitude of the predation rate in the absence of the trait change. The model further illustrates how, depending on the effect of increased trait change on resulting costs and benefits, any combination of strong and weak NCEs and CEs is possible. The model can also be used to examine how changes in environmental factors (e.g., refuge safety) or variation among predator-prey systems (e.g., different benefits of a prey trait change) affect NCEs. Results indicate that simple rules of thumb may not apply; factors that increase the cost of trait change or that increase the degree to which an animal changes a trait, can actually cause smaller (rather than larger) NCEs. We provide examples of how this graphical model can provide important insights for empirical studies from two natural systems. Implementation of this approach will improve our understanding of how and when NCEs are expected to dominate the total effect of predators. Further, application of the models will likely promote a better linkage between experimental and theoretical studies of NCEs, and foster synthesis across systems.
Coexistence of steady state for a diffusive prey-predator model with harvesting
Yan Li
2016-07-01
Full Text Available In this article, we study a diffusive prey-predator model with modified Leslie-Gower term and Michaelis-Menten type prey harvesting, subject to homogeneous Dirichlet boundary conditions. Treating the prey harvesting parameter as a bifurcation parameter, we obtain the existence, bifurcation and stability of coexistence steady state solutions. We use the method of upper and lower solutions, degree theory in cones, and bifurcation theory. The conclusions show the importance of prey harvesting in the model.
Effects of Endosulfan on Predator-Prey Interactions Between Catfish and Schistosoma Host Snails.
Monde, Concillia; Syampungani, Stephen; Van den Brink, Paul J
2016-08-01
The effect of the pesticide endosulfan on predator-prey interactions between catfish and Schistosoma host snails was assessed in static tank experiments. Hybrid catfish (Clarias gariepinus × C. ngamensis) and Bulinus globosus were subjected to various endosulfan concentrations including an untreated control. The 48- and 96-h LC50 values for catfish were 1.0 and snails were 1137 and 810 µg/L. To assess sublethal effects on the feeding of the catfish on B. globosus, endosulfan concentrations between 0.03 and 1.0 µg/L were used. Predation was significantly greater (p snails using fish may be affected in endosulfan-polluted aquatic systems of Southern Africa because it has been found present at concentrations that are indicated to cause lethal effects on the evaluated hybrid catfish and to inhibit the predation of snails by this hybrid catfish.
Faria, Claudia; Boaventura, Diana; Galvao, Cecilia; Chagas, Isabel
2011-01-01
In this article we propose a hands-on experimental activity about predator-prey interactions that can be performed both in a research laboratory and in the classroom. The activity, which engages students in a real scientific experiment, can be explored not only to improve students' understanding about the diversity of anti-predator behaviors but…
Faria, Claudia; Boaventura, Diana; Galvao, Cecilia; Chagas, Isabel
2011-01-01
In this article we propose a hands-on experimental activity about predator-prey interactions that can be performed both in a research laboratory and in the classroom. The activity, which engages students in a real scientific experiment, can be explored not only to improve students' understanding about the diversity of anti-predator behaviors but…
Birds as predators in tropical agroforestry systems.
Van Bael, Sunshine A; Philpott, Stacy M; Greenberg, Russell; Bichier, Peter; Barber, Nicholas A; Mooney, Kailen A; Gruner, Daniel S
2008-04-01
Insectivorous birds reduce arthropod abundances and their damage to plants in some, but not all, studies where predation by birds has been assessed. The variation in bird effects may be due to characteristics such as plant productivity or quality, habitat complexity, and/or species diversity of predator and prey assemblages. Since agroforestry systems vary in such characteristics, these systems provide a good starting point for understanding when and where we can expect predation by birds to be important. We analyze data from bird exclosure studies in forests and agroforestry systems to ask whether birds consistently reduce their arthropod prey base and whether bird predation differs between forests and agroforestry systems. Further, we focus on agroforestry systems to ask whether the magnitude of bird predation (1) differs between canopy trees and understory plants, (2) differs when migratory birds are present or absent, and (3) correlates with bird abundance and diversity. We found that, across all studies, birds reduce all arthropods, herbivores, carnivores, and plant damage. We observed no difference in the magnitude of bird effects between agroforestry systems and forests despite simplified habitat structure and plant diversity in agroforests. Within agroforestry systems, bird reduction of arthropods was greater in the canopy than the crop layer. Top-down effects of bird predation were especially strong during censuses when migratory birds were present in agroforestry systems. Importantly, the diversity of the predator assemblage correlated with the magnitude of predator effects; where the diversity of birds, especially migratory birds, was greater, birds reduced arthropod densities to a greater extent. We outline potential mechanisms for relationships between bird predator, insect prey, and habitat characteristics, and we suggest future studies using tropical agroforests as a model system to further test these areas of ecological theory.
Rob Williams
Full Text Available Ecosystem-based management (EBM of marine resources attempts to conserve interacting species. In contrast to single-species fisheries management, EBM aims to identify and resolve conflicting objectives for different species. Such a conflict may be emerging in the northeastern Pacific for southern resident killer whales (Orcinus orca and their primary prey, Chinook salmon (Oncorhynchus tshawytscha. Both species have at-risk conservation status and transboundary (Canada-US ranges. We modeled individual killer whale prey requirements from feeding and growth records of captive killer whales and morphometric data from historic live-capture fishery and whaling records worldwide. The models, combined with caloric value of salmon, and demographic and diet data for wild killer whales, allow us to predict salmon quantities needed to maintain and recover this killer whale population, which numbered 87 individuals in 2009. Our analyses provide new information on cost of lactation and new parameter estimates for other killer whale populations globally. Prey requirements of southern resident killer whales are difficult to reconcile with fisheries and conservation objectives for Chinook salmon, because the number of fish required is large relative to annual returns and fishery catches. For instance, a U.S. recovery goal (2.3% annual population growth of killer whales over 28 years implies a 75% increase in energetic requirements. Reducing salmon fisheries may serve as a temporary mitigation measure to allow time for management actions to improve salmon productivity to take effect. As ecosystem-based fishery management becomes more prevalent, trade-offs between conservation objectives for predators and prey will become increasingly necessary. Our approach offers scenarios to compare relative influence of various sources of uncertainty on the resulting consumption estimates to prioritise future research efforts, and a general approach for assessing the extent of
Sloggett, J J; Davis, A J
2010-01-15
By comparison with studies of herbivore physiological adaptation to plant allelochemicals, work on predator physiological adaptation to potentially toxic prey has been very limited. Such studies are important in understanding how evolution could shape predator diets. An interesting question is the specificity of predator adaptation to prey allelochemicals, given that many predators consume diverse prey with different chemical defences. The ladybird Harmonia axyridis, an invasive species in America, Europe and Africa, is considered a significant predatory threat to native invertebrates, particularly other aphid-eating ladybirds of which it is a strong intraguild predator. Although ladybirds possess species-specific alkaloid defences, H. axyridis exhibits high tolerance for allospecific ladybird prey alkaloids. Nonetheless, it performs poorly on species with novel alkaloids not commonly occurring within its natural range. We examined alkaloid fate in H. axyridis larvae after consumption of two other ladybird species, one containing an alkaloid historically occurring within the predator's native range (isopropyleine) and one containing a novel alkaloid that does not (adaline). Our results indicate that H. axyridis rapidly chemically modifies the alkaloid to which it has been historically exposed to render it less harmful: this probably occurs outside of the gut. The novel, more toxic alkaloid persists in the body unchanged for longer. Our results suggest metabolic alkaloid specialisation, in spite of the diversity of chemically defended prey that the predator consumes. Physiological adaptations appear to have made H. axyridis a successful predator of other ladybirds; however, limitations are imposed by its physiology when it eats prey with novel alkaloids.
Plastic responses of a sessile prey to multiple predators: a field and experimental study.
Philipp Emanuel Hirsch
Full Text Available Theory predicts that prey facing a combination of predators with different feeding modes have two options: to express a response against the feeding mode of the most dangerous predator, or to express an intermediate response. Intermediate phenotypes protect equally well against several feeding modes, rather than providing specific protection against a single predator. Anti-predator traits that protect against a common feeding mode displayed by all predators should be expressed regardless of predator combination, as there is no need for trade-offs.We studied phenotypic anti-predator responses of zebra mussels to predation threat from a handling-time-limited (crayfish and a gape-size-limited (roach predator. Both predators dislodge mussels from the substrate but diverge in their further feeding modes. Mussels increased expression of a non-specific defense trait (attachment strength against all combinations of predators relative to a control. In response to roach alone, mussels showed a tendency to develop a weaker and more elongated shell. In response to crayfish, mussels developed a harder and rounder shell. When exposed to either a combination of predators or no predator, mussels developed an intermediate phenotype. Mussel growth rate was positively correlated with an elongated weaker shell and negatively correlated with a round strong shell, indicating a trade-off between anti-predator responses. Field observations of prey phenotypes revealed the presence of both anti-predator phenotypes and the trade-off with growth, but intra-specific population density and bottom substrate had a greater influence than predator density.Our results show that two different predators can exert both functionally equivalent and inverse selection pressures on a single prey. Our field study suggests that abiotic factors and prey population density should be considered when attempting to explain phenotypic diversity in the wild.
González-Olivares, Eduardo; González-Yañez, Betsabé; Mena-Lorca, Jaime; Flores, Jose D
2013-04-01
The main purpose of this work is to analyze a Gause type predator-prey model in which two ecological phenomena are considered: the Allee effect affecting the prey growth function and the formation of group defence by prey in order to avoid the predation. We prove the existence of a separatrix curves in the phase plane, determined by the stable manifold of the equilibrium point associated to the Allee effect, implying that the solutions are highly sensitive to the initial conditions. Trajectories starting at one side of this separatrix curve have the equilibrium point (0,0) as their ω-limit, while trajectories starting at the other side will approach to one of the following three attractors: a stable limit cycle, a stable coexistence point or the stable equilibrium point (K,0) in which the predators disappear and prey attains their carrying capacity. We obtain conditions on the parameter values for the existence of one or two positive hyperbolic equilibrium points and the existence of a limit cycle surrounding one of them. Both ecological processes under study, namely the nonmonotonic functional response and the Allee effect on prey, exert a strong influence on the system dynamics, resulting in multiple domains of attraction. Using Liapunov quantities we demonstrate the uniqueness of limit cycle, which constitutes one of the main differences with the model where the Allee effect is not considered. Computer simulations are also given in support of the conclusions.
Thieltges, David W.; Amundsen, Per-Arne; Hechinger, Ryan F.; Johnson, Pieter T.J.; Lafferty, Levin D.; Mouritsen, Kim N.; Preston, Daniel L.; Reise, Karsten; Zander, C. Dieter; Poulin, Robert
2013-01-01
While the recent inclusion of parasites into food-web studies has highlighted the role of parasites as consumers, there is accumulating evidence that parasites can also serve as prey for predators. Here we investigated empirical patterns of predation on parasites and their relationships with parasite transmission in eight topological food webs representing marine and freshwater ecosystems. Within each food web, we examined links in the typical predator–prey sub web as well as the predator–parasite sub web, i.e. the quadrant of the food web indicating which predators eat parasites. Most predator– parasite links represented ‘concomitant predation’ (consumption and death of a parasite along with the prey/host; 58–72%), followed by ‘trophic transmission’ (predator feeds on infected prey and becomes infected; 8–32%) and predation on free-living parasite life-cycle stages (4–30%). Parasite life-cycle stages had, on average, between 4.2 and 14.2 predators. Among the food webs, as predator richness increased, the number of links exploited by trophically transmitted parasites increased at about the same rate as did the number of links where these stages serve as prey. On the whole, our analyses suggest that predation on parasites has important consequences for both predators and parasites, and food web structure. Because our analysis is solely based on topological webs, determining the strength of these interactions is a promising avenue for future research.
Nonlinear effect of dispersal rate on spatial synchrony of predator-prey cycles.
Fox, Jeremy W; Legault, Geoffrey; Legault, Geoff; Vasseur, David A; Einarson, Jodie A
2013-01-01
Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous.
Global behaviour of a predator-prey like model with piecewise constant arguments.
Kartal, Senol; Gurcan, Fuat
2015-01-01
The present study deals with the analysis of a predator-prey like model consisting of system of differential equations with piecewise constant arguments. A solution of the system with piecewise constant arguments leads to a system of difference equations which is examined to study boundedness, local and global asymptotic behaviour of the positive solutions. Using Schur-Cohn criterion and a Lyapunov function, we derive sufficient conditions under which the positive equilibrium point is local and global asymptotically stable. Moreover, we show numerically that periodic solutions arise as a consequence of Neimark-Sacker bifurcation of a limit cycle.
Wang, Xiaohong; Jia, Jianwen
2015-03-01
In this paper, we propose a delayed predator-prey model with birth pulse and impulsive harvesting in a polluted environment. Existence conditions of the predator-extinction periodic solution are derived by developing the discrete dynamical system, which is determined by the stroboscopic map. Further, we discuss the global attractivity of predator-extinction periodic solution and permanence of the system, and obtain the threshold conditions. The results provide a dependable theoretical strategies to protect population from extinction in a polluted environment. Finally, the numerical simulations are presented for verifying the theoretical conclusions.
Gupta, Govind Sharan; Kumar, Ashutosh; Shanker, Rishi; Dhawan, Alok
2016-08-01
Nano titanium dioxide (nTiO2) is the most abundantly released engineered nanomaterial (ENM) in aquatic environments. Therefore, it is prudent to assess its fate and its effects on lower trophic-level organisms in the aquatic food chain. A predator-and-prey-based laboratory microcosm was established using Paramecium caudatum and Escherichia coli to evaluate the effects of nTiO2. The surface interaction of nTiO2 with E. coli significantly increased after the addition of Paramecium into the microcosm. This interaction favoured the hetero-agglomeration and co-sedimentation of nTiO2. The extent of nTiO2 agglomeration under experimental conditions was as follows: combined E. coli and Paramecium > Paramecium only > E. coli only > without E. coli or Paramecium. An increase in nTiO2 internalisation in Paramecium cells was also observed in the presence or absence of E. coli cells. These interactions and nTiO2 internalisation in Paramecium cells induced statistically significant (p < 0.05) effects on growth and the bacterial ingestion rate at 24 h. These findings provide new insights into the fate of nTiO2 in the presence of bacterial-ciliate interactions in the aquatic environment.
Predation rates and prey selectivity in two predacious estuarine nematode species
Moens, T.; Herman, P.M.J.; Verbeeck, L.; Steyaert, M.; Vincx, M.
2000-01-01
Enoploides longispiculosus and Adoncholaimus fuscus are representatives of nematode genera prominent in sediments of the North Sea and adjacent estuaries. Both are predatory nematodes, although predation is facultative in the latter. The present study investigates functional responses and prey
[Book review] Skua and penguin: Predator and prey, by Euan Young
Pietz, P.J.
1995-01-01
Review of: Skua and Penguin: Predator and Prey. Euan Young. 1994. Cambridge University Press, Cambridge, United Kingdom. xvi + 452 pp., 53 line diagrams, 44 half-tones. ISBN 0-521-32251-0. $99.95 cloth
Predator-prey interactions as macro-scale drivers of species diversity in mammals
Sandom, Christopher James; Sandel, Brody Steven; Dalby, Lars
mechanistic drivers of mammal species richness at macro-scales for two trophic levels: predators and prey. To disentangle biotic (i.e. functional predator-prey interactions) from abiotic (i.e. environmental) and bottom-up from top-down determinants we considered three hypotheses: 1) environmental factors......-down). We gathered distributional range, mass and diet data for 4,091 terrestrial mammal species, excluding bats. Species richness maps were created for predators and prey and structural equation modelling was used to test the three hypotheses at continental and global scales. We also explored...... the importance of functional trait composition by analyzing richness of large and small mass categories for prey (division at 10 kg) and predators (division at 21.5 kg). Results/Conclusions Mammal species richness increased from the poles to the equator, supporting the classic latitudinal richness gradient...
Benefits of Group Foraging Depend on Prey Type in a Small Marine Predator, the Little Penguin.
Sutton, Grace J; Hoskins, Andrew J; Arnould, John P Y
2015-01-01
Group foraging provides predators with advantages in over-powering prey larger than themselves or in aggregating small prey for efficient exploitation. For group-living predatory species, cooperative hunting strategies provide inclusive fitness benefits. However, for colonial-breeding predators, the benefit pay-offs of group foraging are less clear due to the potential for intra-specific competition. We used animal-borne cameras to determine the prey types, hunting strategies, and success of little penguins (Eudyptula minor), a small, colonial breeding air-breathing marine predator that has recently been shown to display extensive at-sea foraging associations with conspecifics. Regardless of prey type, little penguins had a higher probability of associating with conspecifics when hunting prey that were aggregated than when prey were solitary. In addition, success was greater when individuals hunted schooling rather than solitary prey. Surprisingly, however, success on schooling prey was similar or greater when individuals hunted on their own than when with conspecifics. These findings suggest individuals may be trading-off the energetic gains of solitary hunting for an increased probability of detecting prey within a spatially and temporally variable prey field by associating with conspecifics.
Benefits of Group Foraging Depend on Prey Type in a Small Marine Predator, the Little Penguin.
Grace J Sutton
Full Text Available Group foraging provides predators with advantages in over-powering prey larger than themselves or in aggregating small prey for efficient exploitation. For group-living predatory species, cooperative hunting strategies provide inclusive fitness benefits. However, for colonial-breeding predators, the benefit pay-offs of group foraging are less clear due to the potential for intra-specific competition. We used animal-borne cameras to determine the prey types, hunting strategies, and success of little penguins (Eudyptula minor, a small, colonial breeding air-breathing marine predator that has recently been shown to display extensive at-sea foraging associations with conspecifics. Regardless of prey type, little penguins had a higher probability of associating with conspecifics when hunting prey that were aggregated than when prey were solitary. In addition, success was greater when individuals hunted schooling rather than solitary prey. Surprisingly, however, success on schooling prey was similar or greater when individuals hunted on their own than when with conspecifics. These findings suggest individuals may be trading-off the energetic gains of solitary hunting for an increased probability of detecting prey within a spatially and temporally variable prey field by associating with conspecifics.
Benefits of Group Foraging Depend on Prey Type in a Small Marine Predator, the Little Penguin
Sutton, Grace J.; Hoskins, Andrew J.; Arnould, John P. Y.
2015-01-01
Group foraging provides predators with advantages in over-powering prey larger than themselves or in aggregating small prey for efficient exploitation. For group-living predatory species, cooperative hunting strategies provide inclusive fitness benefits. However, for colonial-breeding predators, the benefit pay-offs of group foraging are less clear due to the potential for intra-specific competition. We used animal-borne cameras to determine the prey types, hunting strategies, and success of little penguins (Eudyptula minor), a small, colonial breeding air-breathing marine predator that has recently been shown to display extensive at-sea foraging associations with conspecifics. Regardless of prey type, little penguins had a higher probability of associating with conspecifics when hunting prey that were aggregated than when prey were solitary. In addition, success was greater when individuals hunted schooling rather than solitary prey. Surprisingly, however, success on schooling prey was similar or greater when individuals hunted on their own than when with conspecifics. These findings suggest individuals may be trading-off the energetic gains of solitary hunting for an increased probability of detecting prey within a spatially and temporally variable prey field by associating with conspecifics. PMID:26674073
A stage-structured predator-prey model with distributed maturation delay and harvesting.
Al-Omari, J F M
2015-01-01
A stage-structured predator-prey system with distributed maturation delay and harvesting is investigated. General birth and death functions are used. The local stability of each feasible equilibria is discussed. By using the persistence theory, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functional and LaSalle invariant principle, it is shown that the trivial equilibrium is globally stable when the other equilibria are not feasible, and that the boundary equilibrium is globally stable if the coexistence equilibrium does not exist. Finally, sufficient conditions are derived for the global stability of the coexistence equilibrium.
Qualitative analysis on a diffusive prey-predator model with ratio-dependent functional response
2008-01-01
In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.
Global Stability of a Predator-prey Model with Stage Structure
WANG Li-li; XU Rui
2015-01-01
A Holling type III predator-prey model with stage structure for prey is investi-gated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. By using the uniformly persistence theory, the system is proven to be permanent if the coexistence equilibrium exists. By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that the two boundary equilibria is globally asymptotically stable when the coexistence equilibrium is not feasible. By using compound matrix theory, the sucient conditions are obtained for the global stability of the coexistence equilibrium. At last, numerical simulations are carried out to illustrate the main results.
The role of internal waves in larval fish interactions with potential predators and prey
Greer, Adam T.; Cowen, Robert K.; Guigand, Cedric M.; Hare, Jonathan A.; Tang, Dorothy
2014-09-01
Tidally driven internal wave packets in coastal environments have the potential to influence patchiness of larval fishes, prey, and gelatinous predators. We used the In Situ Ichthyoplankton Imaging System (ISIIS) to synoptically sample larval fishes, copepods, and planktonic predators (ctenophores, hydromedusae, chaetognaths, and polychaetes) across these predictable features in the summer near Stellwagen Bank, Massachusetts, USA. Full water column profiles and fixed depth transects (∼10 m depth) were used to quantify vertical and horizontal components of the fish and invertebrate distributions during stable and vertically mixed conditions associated with tidally generated internal waves. Larval fishes, consisting mostly of Urophycis spp., Merluccius bilinearis, and Labridae, were concentrated near the surface, with larger sizes generally occupying greater depths. During stable water column conditions, copepods formed a near surface thin layer several meters above the chlorophyll-a maximum that was absent when internal waves were propagating. In contrast, ctenophores and other predators were much more abundant at depth, but concentrations near 10 m increased immediately after the internal hydraulic jump mixed the water column. During the propagation of internal waves, the fine-scale abundance of larval fishes was more correlated with the abundance of gelatinous predators and less correlated with copepods compared to the stable conditions. Vertical oscillations caused by the internal hydraulic jump can disperse patches of zooplankton and force surface dwelling larval fishes into deeper water where probability of predator contact is increased, creating conditions potentially less favorable for larval fish growth and survival on short time scales.
刘艳伟; 陆楷章
2009-01-01
two-prey one-predator system with a special Holling-Ⅱ functional response is dis-cussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, by the comparison theorem of impulsive dif-ferential equation, the sufficient conditions are derived for the permanence and the existence of periodic solution of the system.
Non-pest prey do not disrupt aphid predation by a web-building spider.
Welch, K D; Whitney, T D; Harwood, J D
2016-02-01
A generalist predator's ability to contribute to biological control is influenced by the decisions it makes during foraging. Predators often use flexible foraging tactics, which allows them to pursue specific types of prey at the cost of reducing the likelihood of capturing other types of prey. When a pest insect has low nutritional quality or palatability for a predator, the predator is likely to reject that prey in favour of pursuing alternative, non-pest prey. This is often thought to limit the effectiveness of generalist predators in consuming aphids, which are of low nutritional quality for many generalist predators. Here, we report behavioural assays that test the hypothesis that the generalist predator, Grammonota inornata (Araneae: Linyphiidae), preferentially forages for a non-pest prey with high nutritional quality (springtails), and rejects a pest prey with low nutritional quality (aphids). In no-choice assays, molecular gut-content analysis revealed that spiders continued to feed on the low-quality aphids at high rates, even when high-quality springtails were readily available. When provided a choice between aphids and springtails in two-way choice tests, spiders did not show the expected preference for springtails. Decision-making by spiders during foraging therefore appears to be sub-optimal, possibly because of attraction to the less frequently encountered of two preys as part of a dietary diversification strategy. These results indicate that behavioural preferences alone do not necessarily compromise the pest-suppression capacity of natural enemies: even nutritionally sub-optimal pest prey can potentially be subject to predation and suppression by natural enemies.
Spreading and vanishing in the diffusive prey-predator model with a free boundary
Wang, Mingxin
2015-06-01
This paper deals with the diffusive Lotka-Volterra type prey-predator model with a free boundary over a one dimensional habitat. This problem may be used to describe the interaction between indigenous species and invasive species and the spreading of such two species, with the free boundary representing the expanding front. Our main purpose is to study the spreading and vanishing phenomena and long time behaviors of prey and predator.
Toju, Hirokazu; Sota, Teiji
2006-01-01
The escalation of defensive/offensive arms is ubiquitous in prey-predator evolutionary interactions. However, there may be a geographically varying imbalance in the armaments of participating species that affects the outcome of local interactions. In a system involving the Japanese camellia (Camellia japonica) and its obligate seed predator, the camellia weevil (Curculio camelliae), we investigated the geographic variation in physical defensive/offensive traits and that in natural selection on the plant's defense among 17 populations over a 700-km-wide area in Japan. The sizes of the plant defensive apparatus (pericarp thickness) and the weevil offensive apparatus (rostrum length) clearly correlated with each other across populations. Nevertheless, the balance in armaments between the two species was geographically structured. In the populations for which the balance was relatively advantageous for the plant's defense, natural selection on the trait was stronger because in the other populations, most plant individuals were too vulnerable to resist the attacks of the weevil, and their seeds were infested independent of pericarp thickness. We also found that the imbalance between the defensive/offensive armaments and the intensity of natural selection showed clear latitudinal clines. Overall, our results suggest that the imbalance of armament between sympatric prey and predator could determine the strength of local selection and that climatic conditions could affect the local and overall trajectory of coevolutionary arms races.
Spatial heterogeneity, predator cognition, and the evolution of color polymorphism in virtual prey
Bond, Alan B.; Kamil, Alan C.
2006-01-01
Cryptically colored prey species are often polymorphic, occurring in multiple distinctive pattern variants. Visual predators promote such phenotypic variation through apostatic selection, in which they attack more abundant prey types disproportionately often. In heterogeneous environments, disruptive selection to match the coloration of disparate habitat patches could also produce polymorphism, but how apostatic and disruptive selection interact in these circumstances is unknown. Here we repo...
The interaction of spatial scale and predator-prey functional response
Blaine, T.W.; DeAngelis, D.L.
1997-01-01
Predator-prey models with a prey-dependent functional response have the property that the prey equilibrium value is determined only by predator characteristics. However, in observed natural systems (for instance, snail-periphyton interactions in streams) the equilibrium periphyton biomass has been shown experimentally to be influenced by both snail numbers and levels of available limiting nutrient in the water. Hypothesizing that the observed patchiness in periphyton in streams may be part of the explanation for the departure of behavior of the equilibrium biomasses from predictions of the prey-dependent response of the snail-periphyton system, we developed and analyzed a spatially-explicit model of periphyton in which snails were modeled as individuals in their movement and feeding, and periphyton was modeled as patches or spatial cells. Three different assumptions on snail movement were used: (1) random movement between spatial cells, (2) tracking by snails of local abundances of periphyton, and (3) delayed departure of snails from cells to reduce costs associated with movement. Of these assumptions, only the third strategy, based on an herbivore strategy of staying in one patch until local periphyton biomass concentration falls below a certain threshold amount, produced results in which both periphyton and snail biomass increased with nutrient input. Thus, if data are averaged spatially over the whole system, we expect that a ratio-dependent functional response may be observed if the herbivore behaves according to the third assumption. Both random movement and delayed cell departure had the result that spatial heterogeneity of periphyton increased with nutrient input.