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predator-prey dynamics using the Rosenzweig-MacArthur-like model in which the Holling type II functional response has been replaced by a predator-dependent family which generalizes many of the commonly used descriptions of predator interference.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.
Jaramillo, Juliana; Chapman, Eric G.; Vega, Fernando E.; Harwood, James D.
2010-03-01
The coffee berry borer, Hypothenemus hampei, is the most important pest of coffee throughout the world, causing losses estimated at US 500 million/year. The thrips Karnyothrips flavipes was observed for the first time feeding on immature stages of H. hampei in April 2008 from samples collected in the Kisii area of Western Kenya. Since the trophic interactions between H. hampei and K. flavipes are carried out entirely within the coffee berry, and because thrips feed by liquid ingestion, we used molecular gut-content analysis to confirm the potential role of K. flavipes as a predator of H. hampei in an organic coffee production system. Species-specific COI primers designed for H. hampei were shown to have a high degree of specificity for H. hampei DNA and did not produce any PCR product from DNA templates of the other insects associated with the coffee agroecosystems. In total, 3,327 K. flavipes emerged from 17,792 H. hampei-infested berries collected from the field between April and September 2008. Throughout the season, 8.3% of K. flavipes tested positive for H. hampei DNA, although at times this figure approached 50%. Prey availability was significantly correlated with prey consumption, thus indicating the potential impact on H. hampei populations.
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.
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.
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.
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...
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.
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
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).
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.
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.
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.
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.
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.
Eid, Tony; Ghostine, Bachir; Kreichaty, Gaby; Daher, Paul; Ghanem, Ismat
2013-05-01
Congenital kyphoscoliosis (CKS) results from abnormal vertebral chondrification. Congenital fibrous bands occur in several locations with variable impact on vertebral development. We report a previously unreported case of a female infant with CKS presenting with an L2 hypoplastic vertebra and a costo-vertebral fibrous band extending to the skin in the form of a dimple. We also describe the therapeutic approach, consisting of surgical excision of the fibrous band and postoperative fulltime bracing, with a 7-year follow-up. We recommend a high index of suspicion in any unusual presentation of CKS and insist on case by case management in such cases.
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.
Poly-epiphyseal overgrowth: description of a previously unreported skeletal dysplasia
Pazzaglia, Ugo E.; Bonaspetti, Giovanni [University of Brescia, Orthopaedic Clinic, Brescia (Italy); Beluffi, Giampiero [Fondazione IRCCS Policlinico San Matteo, Department of Paediatric Radiology, Pavia (Italy); Marchi, Antonietta; Bozzola, Mauro; Savasta, Salvatore [Fondazione IRCCS Policlinico San Matteo, Paediatric Clinic, University of Pavia, Pavia (Italy)
2007-10-15
A skeletal dysplasia with previously unreported features is presented. Its evolution was characterized by growth abnormalities of bones without involvement of other organs. Advanced bone age, increased stature and irregular epiphyseal ossification with stippling of the main long bones were documented. Physeal overgrowth was massive in the left proximal humerus and femur. Furthermore, the hip joint appeared fused with an abundant mass of pathological calcific tissue extending from the femur to the ilium. Pathological epiphyses were characterized by anarchic cartilaginous proliferation with multiple ossification centres, while lamellar bone apposition and remodelling were normal. The observed bone changes were different from those in any previously reported syndrome, metabolic defect or bone dysplasia. However, they clearly indicated a defect of endochondral ossification with some resemblance to phenotypes observed in dysplasia epiphysealis hemimelica. (orig.)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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].
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.
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.
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.
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.
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
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.
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.
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
Kihara, Kumiko; Mori, Kotaro; Suzuki, Shingo; Hosoda, Kazufumi; Yamada, Akito; Matsuyama, Shin-ichi; Kashiwagi, Akiko; Yomo, Tetsuya
2011-03-01
Predator-prey interactions have been found at all levels within ecosystems. Despite their ecological ubiquity and importance, the process of transition to a stable coexistent state has been poorly verified experimentally. To investigate the stabilization process of predator-prey interactions, we previously constructed a reproducible experimental predator-prey system between Dictyostelium discoideum and Escherichia coli, and showed that the phenotypically changed E. coli contributed to stabilization of the system. In the present study, we focused on the transition to stable coexistence of both species after the phenotypic change in E. coli. Analysis of E. coli cells isolated from co-culture plates as single colony enabled us to readily identify the appearance of phenotypically changed E. coli that differed in colony morphology and growth rate. It was also demonstrated that two types of viscous colony, i.e., the dense-type and sparse-type, differing in spatial distribution of both species emerged probabilistically and all of the viscous colonies maintained stably were of the sparse-type. These results suggest that the phenotypically changed E. coli may produce two types of viscous colonies probabilistically. The difference in spatial distribution would affect localized interactions between both species and then cause probabilistic stabilization of predator-prey interactions.
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
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...
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.
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.
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.
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.
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.
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...
Garvie, Marcus R; Burkardt, John; Morgan, Jeff
2015-03-01
We describe simple finite element schemes for approximating spatially extended predator-prey dynamics with the Holling type II functional response and logistic growth of the prey. The finite element schemes generalize 'Scheme 1' in the paper by Garvie (Bull Math Biol 69(3):931-956, 2007). We present user-friendly, open-source MATLAB code for implementing the finite element methods on arbitrary-shaped two-dimensional domains with Dirichlet, Neumann, Robin, mixed Robin-Neumann, mixed Dirichlet-Neumann, and Periodic boundary conditions. Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/ . In addition to discussing the well posedness of the model equations, the results of numerical experiments are presented and demonstrate the crucial role that habitat shape, initial data, and the boundary conditions play in determining the spatiotemporal dynamics of predator-prey interactions. As most previous works on this problem have focussed on square domains with standard boundary conditions, our paper makes a significant contribution to the area.
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.
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.
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.
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.
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.
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.
Echinocandin Failure Case Due to a Previously Unreported FKS1 Mutation in Candida krusei
Jensen, Rasmus Hare; Justesen, Ulrik Stenz; Rewes, Annika
2014-01-01
Echinocandins are the preferred therapy for invasive infections due to Candida krusei. We present here a case of clinical failure involving C. krusei with a characteristic FKS1 hot spot mutation not previously reported in C. krusei that was isolated after 14 days of treatment. Anidulafungin MICs...... were elevated by ≥5 dilution steps above the clinical breakpoint but by only 1 step for a Candida albicans isolate harboring the corresponding mutation, suggesting a notable species-specific difference in the MIC increase conferred by this mutation....
PHACES syndrome: a review of eight previously unreported cases with late arterial occlusions
Bhattacharya, J.J. [Department of Neuroradiology, Institute of Neurological Sciences, Southern General Hospital, 1345 Gowan Road, G51, Glasgow (United Kingdom); Luo, C.B.; Alvarez, H.; Rodesch, G.; Lasjaunias, P.L. [Neuroradiologie Diagnostique et Therapeutique, Hopital de Bicetre, Rue du General Leclerc 78, 94275, Le Kremlin-Bicetre (France); Pongpech, S. [Ramathibodi Hospital, Bangkok (Thailand)
2004-03-01
PHACE and PHACES are acronyms for a syndrome of variable expression comprising posterior cranial fossa malformations, facial haemangiomas, arterial anomalies, aortic coarctation and other cardiac disorders, ocular abnormalities and stenotic arterial disease. We review five girls and three boys aged 1 month-14 years with disorders from this spectrum. Six had large facial haemangiomas but recent reports suggest that small haemangiomas may occur; hence our inclusion of two possible cases. We also focus on the recently recognised feature of progressive intracranial arterial occlusions, present in four of our patients, later than previously recognised, from 4 to 14 years of age. We suggest that many elements of this disorder could reflect an abnormality of cell proliferation and apoptosis. (orig.)
A previously unreported locality record for the Gila monster (Heloderma suspectum)
Lovich, Jeff; Haxel, Gordon
2011-01-01
Although the Gila Monster (Heloderma suspectum) is widely distributed throughout the Sonoran and portions of the Mojave Deserts of the southwestern United States and northwestern Mexico, details of its distribution in California are imperfectly known, due to the apparent rarity of the species in that state. In their review of Gila Monster records for California, Lovich and Beaman (2007) documented only 26 credible sightings during a period of 153 years. In May 2009 another sighting in California was documented by Ruppert (2010a, b) who photographed a specimen in the Providence Mountains, an area known for previous Gila Monster sightings (Lovich and Beaman 2007). In this paper we report the 28th credible record of a Gila Monster in California.
Parker, G.F.; Roberts, D.B. [Univ. of Oxford (United Kingdom)
1996-04-01
Inbred Drosophila melanogaster stocks were surveyed for {alpha}-glucosidases with nondenaturing gel electrophoresis using a fluorogenic substrate to stain the gels. The glucosidase most active under these conditions is polymorphic. We established that the polymorphism is genetic in origin and that the glucosidase was not likely to be a previously characterized enzyme. The gene encoding the enzyme was mapped cytogenetically to 33 A1-2- 33A8-B1, confirming that this is an enzyme not yet reported in D. melanogaster. The enzyme was partially purified by elution from nondenaturing gels, which enable us to establish that it has optimal activity at pH 6 and interacts most strongly with {alpha}- 1 -4 glucosides. A developmental and tissue survey suggested that this enzyme could have a purely digestive role or be involved in carbohydrate metabolism inside the organism. We propose that this enzyme is involved in either starch digestion or glycogen metabolism. 37 refs., 6 figs., 1 tab.
Parker, G F; Roberts, D B
1996-04-01
Inbred Drosophila melanogaster stocks were surveyed for alpha-glucosidases with nondenaturing gel electrophoresis using a fluorogenic substrate to stain the gels. The glucosidase most active under these conditions is polymorphic. We established that the polymorphism is genetic in origin and that the glucosidase was not likely to be a previously characterized enzyme. The gene encoding the enzyme was mapped cytogenetically to 33 A1-2- 33A8-B1, confirming that this is an enzyme not yet reported in D. melanogaster. The enzyme was partially purified by elution from nondenaturing gels, which enabled us to establish that it has optimal activity at pH 6 and interacts most strongly with alpha-1-4 glucosides. A developmental and tissue survey suggested that this enzyme could have a purely digestive role or be involved in carbohydrate metabolism inside the organism. We propose that this enzyme is involved in either starch digestion or glycogen metabolism.
Yokoyama, T; Kobayashi, A; Shimizu, A; Motoyama, H; Miyagawa, S
2015-10-01
An 81-year-old emaciated woman was admitted to our hospital with a one-year history of recurrent bilateral inguinal swellings. Palpable lumps were observed not only in bilateral groin areas, but also on the right iliac fossa (RIF) of her abdomen. During a planned transabdominal preperitoneal laparoscopic herniorrhaphy, a previously unreported form of ventral hernia was observed at a position lateral and cranial to the right internal inguinal ring, which probably corresponded to the palpable lump on the RIF. The hernia orifice was 2 cm in diameter, and a vascular structure ran through the orifice. The contents of the hernia consisted of fatty tissue arising from the retroperitoneal tissue. Routine exploration revealed orifices of the following hernias: left indirect, right direct, bilateral femoral, bilateral obturator, and right Spigelian hernia. Her postoperative course was uneventful and a mass on the right lower quadrant disappeared after operation.
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
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...
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Marras, Stefano; Noda, Takuji; Steffensen, John F; Svendsen, Morten B S; Krause, Jens; Wilson, Alexander D M; Kurvers, Ralf H J M; Herbert-Read, James; Boswell, Kevin M; Domenici, Paolo
2015-10-01
Billfishes are considered among the fastest swimmers in the oceans. Despite early estimates of extremely high speeds, more recent work showed that these predators (e.g., blue marlin) spend most of their time swimming slowly, rarely exceeding 2 m s(-1). Predator-prey interactions provide a context within which one may expect maximal speeds both by predators and prey. Beyond speed, however, an important component determining the outcome of predator-prey encounters is unsteady swimming (i.e., turning and accelerating). Although large predators are faster than their small prey, the latter show higher performance in unsteady swimming. To contrast the evading behaviors of their highly maneuverable prey, sailfish and other large aquatic predators possess morphological adaptations, such as elongated bills, which can be moved more rapidly than the whole body itself, facilitating capture of the prey. Therefore, it is an open question whether such supposedly very fast swimmers do use high-speed bursts when feeding on evasive prey, in addition to using their bill for slashing prey. Here, we measured the swimming behavior of sailfish by using high-frequency accelerometry and high-speed video observations during predator-prey interactions. These measurements allowed analyses of tail beat frequencies to estimate swimming speeds. Our results suggest that sailfish burst at speeds of about 7 m s(-1) and do not exceed swimming speeds of 10 m s(-1) during predator-prey interactions. These speeds are much lower than previous estimates. In addition, the oscillations of the bill during swimming with, and without, extension of the dorsal fin (i.e., the sail) were measured. We suggest that extension of the dorsal fin may allow sailfish to improve the control of the bill and minimize its yaw, hence preventing disturbance of the prey. Therefore, sailfish, like other large predators, may rely mainly on accuracy of movement and the use of the extensions of their bodies, rather than resorting
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.
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.
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.
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.
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.
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.
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.
A Polycycle and Limit Cycles in a Non-Differentiable Predator-Prey Model
E Sáez; I Szántó
2007-05-01
For a non-differentiable predator-prey model, we establish conditions for the existence of a heteroclinic orbit which is part of one contractive polycycle and for some values of the parameters, we prove that the heteroclinic orbit is broken and generates a stable limit cycle. In addition, in the parameter space, we prove that there exists a curve such that the unique singularity in the realistic quadrant of the predator-prey model is a weak focus of order two and by Hopf bifurcations we can have at most two small amplitude limit cycles.
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.
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.
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.
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.
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.
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…
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…
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.
Chaotic dynamics in the Volterra predator-prey model via linked twist maps
Marina Pireddu
2008-01-01
Full Text Available We prove the existence of infinitely many periodic solutions and complicated dynamics, due to the presence of a topological horseshoe, for the classical Volterra predator-prey model with a periodic harvesting. The proof relies on some recent results about chaotic planar maps combined with the study of geometric features which are typical of linked twist maps.
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
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
Tucker, Marlee A; Rogers, Tracey L
2014-12-22
Predator-prey relationships and trophic levels are indicators of community structure, and are important for monitoring ecosystem changes. Mammals colonized the marine environment on seven separate occasions, which resulted in differences in species' physiology, morphology and behaviour. It is likely that these changes have had a major effect upon predator-prey relationships and trophic position; however, the effect of environment is yet to be clarified. We compiled a dataset, based on the literature, to explore the relationship between body mass, trophic level and predator-prey ratio across terrestrial (n = 51) and marine (n = 56) mammals. We did not find the expected positive relationship between trophic level and body mass, but we did find that marine carnivores sit 1.3 trophic levels higher than terrestrial carnivores. Also, marine mammals are largely carnivorous and have significantly larger predator-prey ratios compared with their terrestrial counterparts. We propose that primary productivity, and its availability, is important for mammalian trophic structure and body size. Also, energy flow and community structure in the marine environment are influenced by differences in energy efficiency and increased food web stability. Enhancing our knowledge of feeding ecology in mammals has the potential to provide insights into the structure and functioning of marine and terrestrial communities. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Cross-diffusion induced Turing patterns in a sex-structured predator-prey model
Liu, J.; Zhou, H.; Zhang, Lai
2012-01-01
In this paper, we consider a sex-structured predator-prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray-Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate...
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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…
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.
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.
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.
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.
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.
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.
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
Periodic solutions of delayed predator-prey model with the Beddington-DeAngelis functional response
Huo Haifeng [Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050 (China)]. E-mail: hfhuo@lut.cn; Li Wantong [Department of Mathematics, Lanzhou University Lanzhou, Gansu 730000 (China)]. E-mail: wtli@lzu.edu.cn; Nieto, Juan J. [Departamento de Analisis Matematico, Facultad de Matematicas, Universidad de Santiago de Compostela 15782 (Spain)]. E-mail: amnieto@usc.es
2007-07-15
By using the continuation theorem based on Gaines and Mawhin's coincidence degree, sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for a delayed predator-prey model with the Beddington-DeAngelis functional response. Our results are applicable to state dependent and distributed delays.
Effect of a protection zone in the diffusive Leslie predator-prey model
Du, Yihong; Peng, Rui; Wang, Mingxin
In this paper, we consider the diffusive Leslie predator-prey model with large intrinsic predator growth rate, and investigate the change of behavior of the model when a simple protection zone Ω for the prey is introduced. As in earlier work [Y. Du, J. Shi, A diffusive predator-prey model with a protection zone, J. Differential Equations 229 (2006) 63-91; Y. Du, X. Liang, A diffusive competition model with a protection zone, J. Differential Equations 244 (2008) 61-86] we show the existence of a critical patch size of the protection zone, determined by the first Dirichlet eigenvalue of the Laplacian over Ω and the intrinsic growth rate of the prey, so that there is fundamental change of the dynamical behavior of the model only when Ω is above the critical patch size. However, our research here reveals significant difference of the model's behavior from the predator-prey model studied in [Y. Du, J. Shi, A diffusive predator-prey model with a protection zone, J. Differential Equations 229 (2006) 63-91] with the same kind of protection zone. We show that the asymptotic profile of the population distribution of the Leslie model is governed by a standard boundary blow-up problem, and classical or degenerate logistic equations.
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.
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…
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
Predator-Prey Model for Haloes in Saturn’s Rings
Esposito, Larry W.; Madhusudhanan, P.; Colwell, J. E.; Bradley, E.; Sremcevic, M.
2013-10-01
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: 1. Cyclic velocity changes cause the perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; 2. This forms a bright halo around the ILR, if the forcing is strong enough; 3. 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
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
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
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...
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.
Stochastic predator-prey dynamics of transposons in the human genome
Xue, Chi
2016-01-01
Transposable elements (TE) are DNA sequences that can jump from site to site in the genome during the life cycle of a cell, usually encoding the very enzymes which perform their excision. However, some TEs are parasitic, relying on the enzymes produced by the regular TEs. In this case, we show that a stochastic model, which takes into account the small copy numbers of the TEs in a cell, predicts noise-induced predator-prey oscillations with a characteristic time scale that is much longer than the cell replication time, indicating that the state of the predator-prey oscillator is stored in the genome and transmitted to successive generations. Our work demonstrates the important role of number fluctuations in the expression of mobile genetic elements, and shows explicitly how ecological concepts can be applied to the dynamics and fluctuations of living genomes.
Stochastic Predator-Prey Dynamics of Transposons in the Human Genome
Xue, Chi; Goldenfeld, Nigel
2016-11-01
Transposable elements, or transposons, are DNA sequences that can jump from site to site in the genome during the life cycle of a cell, usually encoding the very enzymes which perform their excision. However, some transposons are parasitic, relying on the enzymes produced by the regular transposons. In this case, we show that a stochastic model, which takes into account the small copy numbers of the active transposons in a cell, predicts noise-induced predator-prey oscillations with a characteristic time scale that is much longer than the cell replication time, indicating that the state of the predator-prey oscillator is stored in the genome and transmitted to successive generations. Our work demonstrates the important role of the number fluctuations in the expression of mobile genetic elements, and shows explicitly how ecological concepts can be applied to the dynamics and fluctuations of living genomes.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Segregation process and phase transition in cyclic predator-prey models with even number of species
Szabo, Gyorgy; Sznaider, Gustavo Ariel
2007-01-01
We study a spatial cyclic predator-prey model with an even number of species (for n=4, 6, and 8) that allows the formation of two defective alliances consisting of the even and odd label species. The species are distributed on the sites of a square lattice. The evolution of spatial distribution is governed by iteration of two elementary processes on neighboring sites chosen randomly: if the sites are occupied by a predator-prey pair then the predator invades the prey's site; otherwise the species exchange their site with a probability $X$. For low $X$ values a self-organizing pattern is maintained by cyclic invasions. If $X$ exceeds a threshold value then two types of domains grow up that formed by the odd and even label species, respectively. Monte Carlo simulations indicate the blocking of this segregation process within a range of X for n=8.
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.
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.
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.
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.
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.
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...
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...
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.
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.
NON-CONSTANT POSITIVE STEADY-STATES OF A PREDATOR-PREY-MUTUALIST MODEL
CHEN WENYAN; WANG MINGXIN
2004-01-01
In this paper, the authors deal with the non-constant positive steady-states of a predator-prey-mutualist model with homogeneous Neumann boundary condition. They first give a priori estimates (positive upper and lower bounds) of positive steady-states,and then study the non-existence, the global existence and bifurcation of non-constant positive steady-states as some parameters are varied. Finally the asymptotic behavior of such solutions as d3 →∞ is discussed.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
Asymptotic behavior of a stochastic non-autonomous predator-prey model with impulsive perturbations
Wu, Ruihua; Zou, Xiaoling; Wang, Ke
2015-03-01
This paper is concerned with a stochastic non-autonomous Lotka-Volterra predator-prey model with impulsive effects. The asymptotic properties are examined. Sufficient conditions for persistence and extinction are obtained, our results demonstrate that the impulse has important effects on the persistence and extinction of the species. We also show that the solution is stochastically ultimate bounded under some conditions. Finally, several simulation figures are introduced to confirm our main results.
Matching allele dynamics and coevolution in a minimal predator-prey replicator model
Sardanyes, Josep [Complex Systems Lab (ICREA-UPF), Barcelona Biomedical Research Park (PRBB-GRIB), Dr. Aiguader 88, 08003 Barcelona (Spain)], E-mail: josep.sardanes@upf.edu; Sole, Ricard V. [Complex Systems Lab (ICREA-UPF), Barcelona Biomedical Research Park (PRBB-GRIB), Dr. Aiguader 88, 08003 Barcelona (Spain); Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 (United States)
2008-01-21
A minimal Lotka-Volterra type predator-prey model describing coevolutionary traits among entities with a strength of interaction influenced by a pair of haploid diallelic loci is studied with a deterministic time continuous model. We show a Hopf bifurcation governing the transition from evolutionary stasis to periodic Red Queen dynamics. If predator genotypes differ in their predation efficiency the more efficient genotype asymptotically achieves lower stationary concentrations.
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.
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.
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).
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Neimark-Sacker bifurcation of a two-dimensional discrete-time predator-prey model.
Khan, A Q
2016-01-01
In this paper, we study the dynamics and bifurcation of a two-dimensional discrete-time predator-prey model in the closed first quadrant [Formula: see text]. The existence and local stability of the unique positive equilibrium of the model are analyzed algebraically. It is shown that the model can undergo a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium and an invariant circle will appear. Some numerical simulations are presented to illustrate our theocratical results and numerically it is shown that the unique positive equilibrium of the system is globally asymptotically stable.
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.
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.
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.
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...
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.
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.
Hopf Bifurcation and Stability Analysis for a Predator-prey Model with Time-delay
CHEN Hong-bing
2015-01-01
In this paper, a predator-prey model of three species is investigated, the necessary and sucient of the stable equilibrium point for this model is studied. Further, by introduc-ing a delay as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ cross some critical values. And, the stability and direction of hopf bifurcation are determined by applying the normal form theory and center manifold theory. numerical simulation results are given to support the theoretical predictions. At last, the periodic solution of this system is computed.
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.
Existence and Attractiveness of Order One Periodic Solution of a Holling I Predator-Prey Model
Huidong Cheng
2012-01-01
Full Text Available According to the integrated pest management strategies, a Holling type I functional response predator-prey system concerning state-dependent impulsive control is investigated. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution, and the attractivity of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient than the existing ones for proving the existence and attractiveness of order one periodic solution.
Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion
Xinze Lian
2013-01-01
Full Text Available We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.
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, 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.
An implementation of continuous genetic algorithm in parameter estimation of predator-prey model
Windarto
2016-03-01
Genetic algorithm is an optimization method based on the principles of genetics and natural selection in life organisms. The main components of this algorithm are chromosomes population (individuals population), parent selection, crossover to produce new offspring, and random mutation. In this paper, continuous genetic algorithm was implemented to estimate parameters in a predator-prey model of Lotka-Volterra type. For simplicity, all genetic algorithm parameters (selection rate and mutation rate) are set to be constant along implementation of the algorithm. It was found that by selecting suitable mutation rate, the algorithms can estimate these parameters well.
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.
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
Numerical Solutions of the Multispecies Predator-Prey Model by Variational Iteration Method
Khaled Batiha
2007-01-01
Full Text Available The main objective of the current work was to solve the multispecies predator-prey model. The techniques used here were called the variational iteration method (VIM and the Adomian decomposition method (ADM. The advantage of this work is twofold. Firstly, the VIM reduces the computational work. Secondly, in comparison with existing techniques, the VIM is an improvement with regard to its accuracy and rapid convergence. The VIM has the advantage of being more concise for analytical and numerical purposes. Comparisons with the exact solution and the fourth-order Runge-Kutta method (RK4 show that the VIM is a powerful method for the solution of nonlinear equations.
Sadiq, Faizan A; Li, Yun; Liu, TongJie; Flint, Steve; Zhang, Guohua; He, GuoQing
2016-01-18
Aerobic spore forming bacteria are potential milk powder contaminants and are viewed as indicators of poor quality. A total of 738 bacteria, including both mesophilic and thermophilic, isolated from twenty-five powdered milk samples representative of three types of milk powders in China were analyzed based on the random amplified polymorphic DNA (RAPD) protocol to provide insight into species diversity. Bacillus licheniformis was found to be the most prevalent bacterium with greatest diversity (~43% of the total isolates) followed by Geobacillus stearothermophilus (~21% of the total isolates). Anoxybacillus flavithermus represented only 8.5% of the total profiles. Interestingly, actinomycetes represented a major group of the isolates with the predominance of Laceyella sacchari followed by Thermoactinomyces vulgaris, altogether comprising of 7.3% of the total isolates. Out of the nineteen separate bacterial species (except five unidentified groups) recovered and identified from milk powders, twelve proved to belong to novel or previously unreported species in milk powders. Assessment and characterization of the harmful effects caused by this particular micro-flora on the quality and safety of milk powders will be worth doing in the future.
A Model-Based Approach to Predicting Predator-Prey & Friend-Foe Relationships in Ant Colonies
Narayanaswami, Karthik
2009-01-01
Understanding predator-prey relationships among insects is a challenging task in the domain of insect-colony research. This is due to several factors involved, such as determining whether a particular behavior is the result of a predator-prey interaction, a friend-foe interaction or another kind of interaction. In this paper, we analyze a series of predator-prey and friend-foe interactions in two colonies of carpenter ants to better understand and predict such behavior. Using the data gathered, we have also come up with a preliminary model for predicting such behavior under the specific conditions the experiment was conducted in. In this paper, we present the results of our data analysis as well as an overview of the processes involved.
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.
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.
A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape.
William Gilpin
2017-07-01
Full Text Available In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.
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.
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 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.
Longmire, K.; Glaspie, C.; Seitz, R.
2016-02-01
The study examined the implications of ocean acidification for Mya arenaria and the predator-prey dynamics between M. arenaria and Callinectes sapidus. Clams were subjected to either ambient conditions or acidified conditions and grown over four weeks. Mortality, shell lengths, and biomass (ash-free dry weights) were recorded for clams destructively sampled each week. Clams were subjected to behavioral experiments to determine their response to an approaching physical disturbance. Crabs were exposed to acidified or ambient conditions for 48 hours, and placed in 48 hour mesocosm trials with clams. Shell lengths, mortality and biomass between the ambient and acidified clams were not significantly different between acidified and ambient treatments. Shell ash weights were lower for acidified clams, evidence of shell dissolution. In the behavioral experiment, ocean acidification reduced the ability of clams to respond to a predator stimulus. Lastly, in predator-prey mesocosm trials, in ambient conditions, crabs ate all or none of the available clams, whereas acidified crabs ate all available clams in many trials and ate at least one acidified clam per trial. The early effects of ocean acidification on M. arenaria will manifest in trophic interactions with other species, rather than impacting M. arenaria alone.
Information theory and robotics meet to study predator-prey interactions.
Neri, Daniele; Ruberto, Tommaso; Cord-Cruz, Gabrielle; Porfiri, Maurizio
2017-07-01
Transfer entropy holds promise to advance our understanding of animal behavior, by affording the identification of causal relationships that underlie animal interactions. A critical step toward the reliable implementation of this powerful information-theoretic concept entails the design of experiments in which causal relationships could be systematically controlled. Here, we put forward a robotics-based experimental approach to test the validity of transfer entropy in the study of predator-prey interactions. We investigate the behavioral response of zebrafish to a fear-evoking robotic stimulus, designed after the morpho-physiology of the red tiger oscar and actuated along preprogrammed trajectories. From the time series of the positions of the zebrafish and the robotic stimulus, we demonstrate that transfer entropy correctly identifies the influence of the stimulus on the focal subject. Building on this evidence, we apply transfer entropy to study the interactions between zebrafish and a live red tiger oscar. The analysis of transfer entropy reveals a change in the direction of the information flow, suggesting a mutual influence between the predator and the prey, where the predator adapts its strategy as a function of the movement of the prey, which, in turn, adjusts its escape as a function of the predator motion. Through the integration of information theory and robotics, this study posits a new approach to study predator-prey interactions in freshwater fish.
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.
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.
Spatial dynamics in a predator-prey model with Beddington-DeAngelis functional response.
Zhang, Xiao-Chong; Sun, Gui-Quan; Jin, Zhen
2012-02-01
In this paper spatial dynamics of the Beddington-DeAngelis predator-prey model is investigated. We analyze the linear stability and obtain the condition of Turing instability of this model. Moreover, we deduce the amplitude equations and determine the stability of different patterns. In Turing space, we found that this model has coexistence of H(0) hexagon patterns and stripe patterns, H(π) hexagon patterns, and H(0) hexagon patterns. To better describe the real ecosystem, we consider the ecosystem as an open system and take the environmental noise into account. It is found that noise can decrease the number of the patterns and make the patterns more regular. What is more, noise can induce two kinds of typical pattern transitions. One is from the H(π) hexagon patterns to the regular stripe patterns, and the other is from the coexistence of H(0) hexagon patterns and stripe patterns to the regular stripe patterns. The obtained results enrich the finding in the Beddington-DeAngelis predator-prey model well.
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.
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.
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.
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.
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.
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.
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.
Predator-prey model for the self-organization of stochastic oscillators in dual populations
Moradi, Sara; Anderson, Johan; Gürcan, Ozgur D.
A predator-prey model of dual populations with stochastic oscillators is presented. A linear cross-coupling between the two populations is introduced that follows 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 synchronization 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 synchronization of stochastic oscillator is discussed. Sara Moradi has benefited from a mobility grant funded by the Belgian Federal Science Policy Office and the MSCA of the European Commission (FP7-PEOPLE-COFUND-2008 nº 246540).
Predator-prey dynamics stabilised by nonlinearity explain oscillations in dust-forming plasmas
Ross, A. E.; McKenzie, D. R.
2016-04-01
Dust-forming plasmas are ionised gases that generate particles from a precursor. In nature, dust-forming plasmas are found in flames, the interstellar medium and comet tails. In the laboratory, they are valuable in generating nanoparticles for medicine and electronics. Dust-forming plasmas exhibit a bizarre, even puzzling behaviour in which they oscillate with timescales of seconds to minutes. Here we show how the problem of understanding these oscillations may be cast as a predator-prey problem, with electrons as prey and particles as predators. The addition of a nonlinear loss term to the classic Lotka-Volterra equations used for describing the predator-prey problem in ecology not only stabilises the oscillations in the solutions for the populations of electrons and particles in the plasma but also explains the behaviour in more detail. The model explains the relative phase difference of the two populations, the way in which the frequency of the oscillations varies with the concentration of the precursor gas, and the oscillations of the light emission, determined by the populations of both species. Our results demonstrate the value of adopting an approach to a complex physical science problem that has been found successful in ecology, where complexity is always present.
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.
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.
Information theory and robotics meet to study predator-prey interactions
Neri, Daniele; Ruberto, Tommaso; Cord-Cruz, Gabrielle; Porfiri, Maurizio
2017-07-01
Transfer entropy holds promise to advance our understanding of animal behavior, by affording the identification of causal relationships that underlie animal interactions. A critical step toward the reliable implementation of this powerful information-theoretic concept entails the design of experiments in which causal relationships could be systematically controlled. Here, we put forward a robotics-based experimental approach to test the validity of transfer entropy in the study of predator-prey interactions. We investigate the behavioral response of zebrafish to a fear-evoking robotic stimulus, designed after the morpho-physiology of the red tiger oscar and actuated along preprogrammed trajectories. From the time series of the positions of the zebrafish and the robotic stimulus, we demonstrate that transfer entropy correctly identifies the influence of the stimulus on the focal subject. Building on this evidence, we apply transfer entropy to study the interactions between zebrafish and a live red tiger oscar. The analysis of transfer entropy reveals a change in the direction of the information flow, suggesting a mutual influence between the predator and the prey, where the predator adapts its strategy as a function of the movement of the prey, which, in turn, adjusts its escape as a function of the predator motion. Through the integration of information theory and robotics, this study posits a new approach to study predator-prey interactions in freshwater fish.
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.
Uszko, Wojciech; Diehl, Sebastian; Englund, Göran; Amarasekare, Priyanga
2017-04-01
We theoretically explore consequences of warming for predator-prey dynamics, broadening previous approaches in three ways: we include beyond-optimal temperatures, predators may have a type III functional response, and prey carrying capacity depends on explicitly modelled resources. Several robust patterns arise. The relationship between prey carrying capacity and temperature can range from near-independence to monotonically declining/increasing to hump-shaped. Predators persist in a U-shaped region in resource supply (=enrichment)-temperature space. Type II responses yield stable persistence in a U-shaped band inside this region, giving way to limit cycles with enrichment at all temperatures. In contrast, type III responses convey stability at intermediate temperatures and confine cycles to low and high temperatures. Warming-induced state shifts can be predicted from system trajectories crossing stability and persistence boundaries in enrichment-temperature space. Results of earlier studies with more restricted assumptions map onto this graph as special cases. Our approach thus provides a unifying framework for understanding warming effects on trophic dynamics.
Drossel, B; Higgs, P G; McKane, A J
2001-01-01
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large-scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organized criticality.
The scaling of locomotor performance in predator-prey encounters: from fish to killer whales.
Domenici, P
2001-12-01
During predator-prey encounters, a high locomotor performance in unsteady manoeuvres (i.e. acceleration, turning) is desirable for both predators and prey. While speed increases with size in fish and other aquatic vertebrates in continuous swimming, the speed achieved within a given time, a relevant parameter in predator-prey encounters, is size independent. In addition, most parameters indicating high performance in unsteady swimming decrease with size. Both theoretical considerations and data on acceleration suggest a decrease with body size. Small turning radii and high turning rates are indices of maneuverability in space and in time, respectively. Maneuverability decreases with body length, as minimum turning radii and maximum turning rates increase and decrease with body length, respectively. In addition, the scaling of linear performance in fish locomotion may be modulated by turning behaviour, which is an essential component of the escape response. In angelfish, for example, the speed of large fish is inversely related to their turning angle, i.e. fish escaping at large turning angles show lower speed than fish escaping at small turning angles. The scaling of unsteady locomotor performance makes it difficult for large aquatic vertebrates to capture elusive prey by using whole-body attacks, since the overall maneuverability and acceleration of small prey is likely to be superior to that of large predators. Feeding strategies in vertebrate predators can be related to the predator-prey length ratios. At prey-predator ratios higher than approximately 10(-2), vertebrate predators are particulate feeders, while at smaller ratios, they tend to be filter feeders. At intermediate ratios, large aquatic predators may use a variety of feeding methods that aid, or do not involve, whole body attacks. Among these are bubble curtains used by humpback whales to trap fish schools, and tail-slapping of fish by delphinids. Tail slapping by killer whales is discussed as an
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.
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.
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…
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
无
2012-01-01
In this paper,a class of predator-prey model with Crowley-Martin type functional response and time delay is considered.By choosing the delay as a bifurcation parameter,it is shown that Hopf bifurcation occurs as the delay passes through a certain critical value.Some numerical simulations for verifying the main results are also provided.
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.
Neuenfeldt, Stefan; Beyer, Jan
2006-01-01
Aquatic ecosystems are environmentally heterogeneous with features such as fronts or clines of temperature and salinity. This heterogeneity varies over time and is likely to cause changes in predator-prey overlaps, which will affect the diet composition of the predators. We investigated how inflo...
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.
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.
Cooperation can emerge in prisoner's dilemma from a multi-species predator prey replicator dynamic.
Paulson, Elisabeth; Griffin, Christopher
2016-08-01
In this paper we study a generalized variation of the replicator dynamic that involves several species and sub-species that may interact. We show how this dynamic comes about from a specific finite-population model, but also show that one must take into consideration the dynamic nature of the population sizes (and hence proportions) in order to make the model complete. We provide expressions for these population dynamics to produce a kind of multi-replicator dynamic. We then use this replicator dynamic to show that cooperation can emerge as a stable behavior when two species each play prisoner's dilemma as their intra-species game and a form of zero-sum predator prey game as their inter-species game. General necessary and sufficient conditions for cooperation to emerge as stable are provided for a number of game classes. We also showed an example using Hawk-Dove where both species can converge to stable (asymmetric) mixed strategies.
Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model
Xinze Lian
2012-01-01
Full Text Available This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatial distribution of the species with self- and cross-diffusion in a Holling-III ratio-dependent predator-prey model. The diffusion instability of the positive equilibrium of the model with Neumann boundary conditions is discussed. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spots, stripes, and spiral wave pattern replication, which show that reaction-diffusion model is useful to reveal the spatial predation dynamics in the real world.
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.
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.
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.
Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model
Huidong Cheng
2012-01-01
Full Text Available According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.
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.
Ren, Jingli; Li, Xueping
A seasonally forced predator-prey system with generalized Holling type IV functional response is considered in this paper. The influence of seasonal forcing on the system is investigated via numerical bifurcation analysis. Bifurcation diagrams for periodic solutions of periods one and two, containing bifurcation curves of codimension one and bifurcation points of codimension two, are obtained by means of a continuation technique, corresponding to different bifurcation cases of the unforced system illustrated in five bifurcation diagrams. The seasonally forced model exhibits more complex dynamics than the unforced one, such as stable and unstable periodic solutions of various periods, stable and unstable quasiperiodic solutions, and chaotic motions through torus destruction or cascade of period doublings. Finally, some phase portraits and corresponding Poincaré map portraits are given to illustrate these different types of solutions.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Rikvold, Per Arne
2007-01-01
We study an individual-based predator-prey model of biological coevolution, using linear stability analysis and large-scale kinetic Monte Carlo simulations. The model exhibits approximate 1/f noise in diversity and population-size fluctuations, and it generates a sequence of quasi-steady communities in the form of simple food webs. These communities are quite resilient toward the loss of one or a few species, which is reflected in different power-law exponents for the durations of communities and the lifetimes of species. The exponent for the former is near -1, while the latter is close to -2. Statistical characteristics of the evolving communities, including degree (predator and prey) distributions and proportions of basal, intermediate, and top species, compare reasonably with data for real food webs.
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 stochastic predator-prey models with Holling II functional response
Liu, Qun; Zu, Li; Jiang, Daqing
2016-08-01
In this paper, we consider the dynamics of stochastic predator-prey models with Holling II functional response. For the stochastic systems, we firstly establish sufficient conditions for the existence of the globally positive solutions. Then we investigate the asymptotic moment estimations of the positive solutions and study the ultimately bounded in the mean of them. Thirdly, by constructing some suitable Lyapunov functions, we verify that there are unique stationary distributions and they are ergodic. The obtained results show that the systems still retain some stability in the sense of weak stability provided that the intensity of the white noise is relatively small. Finally, some numerical simulations are introduced to illustrate our main results.
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.
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.
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....
Robustness of predator-prey models for confinement regime transitions in fusion plasmas
Zhu, H; Dendy, R O
2013-01-01
Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free energy sources such as temperature gradients. Zero-dimensional models, designed to embody plausible physical narratives for these interactions, can help identify the origin of enhanced energy confinement and of transitions between confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here we extend a successful three-variable (temperature gradient; microturbulence level; one class of coherent structure) model in this genre [M A Malkov and P H Diamond, Phys. Plasmas 16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure. This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree of invariance of the phenomenology generated by the model of Malkov and Diamond,...
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.
Bing Liu; Ying Zhi; Lan-sun Chen
2004-01-01
A mathematical model of a predator-prey model with Ivlev's functional response concerning integrated pest management (IPM)is proposed and analyzed.We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some criticalvalues.Further more,the conditions for the permanence of the system are given.By using bifurcation theory,we show the existence and stability of a positive periodic solution.These results are quite different from those of the corresponding system without impulses.Numerical simulation shows that the system we consider has more complex dynamical behaviors.Finally,it is proved that IPM stragey is more effective than the classical one.
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.
Dynamics of a Stage-Structured Leslie-Gower Predator-Prey Model
Hai-Feng Huo
2011-01-01
Full Text Available A generalized version of the Leslie-Gower predator-prey model that incorporates the prey population structure is introduced. Our results show that the inclusion of (age structure in the prey population does not alter the qualitative dynamics of the model; that is, we identify sufficient conditions for the ‘‘trapping’’ of the dynamics in a biological compact set—albeit the analysis is a bit more challenging. The focus is on the study of the boundedness of solutions and identification of sufficient conditions for permanence. Sufficient conditions for the local stability of the nonnegative equilibria of the model are also derived, and sufficient conditions for the global attractivity of positive equilibrium are obtained. Numerical simulations are used to illustrate our results.
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.
Environmental vs. demographic variability in stochastic lattice predator-prey models
Tauber, Uwe C.
2014-03-01
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. 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.
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...
Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model
Xiaoqin Wang
2013-01-01
Full Text Available We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.
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
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.
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
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
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
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
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
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...
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.
Kroeker, Kristy J; Sanford, Eric; Jellison, Brittany M; Gaylord, Brian
2014-06-01
The influence of environmental change on species interactions will affect population dynamics and community structure in the future, but our current understanding of the outcomes of species interactions in a high-CO2 world is limited. Here, we draw upon emerging experimental research examining the effects of ocean acidification on coastal molluscs to provide hypotheses of the potential impacts of high-CO2 on predator-prey interactions. Coastal molluscs, such as oysters, mussels, and snails, allocate energy among defenses, growth, and reproduction. Ocean acidification increases the energetic costs of physiological processes such as acid-base regulation and calcification. Impacted molluscs can display complex and divergent patterns of energy allocation to defenses and growth that may influence predator-prey interactions; these include changes in shell properties, body size, tissue mass, immune function, or reproductive output. Ocean acidification has also been shown to induce complex changes in chemoreception, behavior, and inducible defenses, including altered cue detection and predator avoidance behaviors. Each of these responses may ultimately alter the susceptibility of coastal molluscs to predation through effects on predator handling time, satiation, and search time. While many of these effects may manifest as increases in per capita predation rates on coastal molluscs, the ultimate outcome of predator-prey interactions will also depend on how ocean acidification affects the specified predators, which also exhibit complex responses to ocean acidification. Changes in predator-prey interactions could have profound and unexplored consequences for the population dynamics of coastal molluscs in a high-CO2 ocean. © 2014 Marine Biological Laboratory.
Cachera, Marie; Villanueva, Ching-maria; Ernande, Bruno; Baheux, Mickael; Rouquette, Manuel; Chambord, Sophie; Lefebvre, Sebastien
2011-01-01
Each species pertains to a given functional niche, depending on its relationships with others species and its interactions with the abiotic environment. Understanding inter-specific interactions is critical to know and predict ecosystems' structure, functioning and dynamics, but also their response to anthropogenic impacts. Predator-prey relationship is one of the main biotic interactions as it both determines the survival of the prey and the predator and is the keystone of food webs. Unra...
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.
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.
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.
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.
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.
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.
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.
Chang Tan
2013-01-01
Full Text Available By piecewise Euler method, a discrete Lotka-Volterra predator-prey model with impulsive effect at fixed moment is proposed and investigated. By using Floquets theorem, we show that a globally asymptotically stable pest-eradication periodic solution exists when the impulsive period is less than some critical value. Further, we prove that the discrete system is permanence if the impulsive period is larger than some critical value. Finally, some numerical experiments are given.
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.
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.
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.
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.
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.
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.
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.
Hopf and steady state bifurcation analysis in a ratio-dependent predator-prey model
Zhang, Lai; Liu, Jia; Banerjee, Malay
2017-03-01
In this paper, we perform spatiotemporal bifurcation analysis in a ratio-dependent predator-prey model and derive explicit conditions for the existence of non-constant steady states that emerge through steady state bifurcation from related constant steady states. These explicit conditions are numerically verified in details and further compared to those conditions ensuring Turing instability. We find that (1) Turing domain is identical to the parametric domain where there exists only steady state bifurcation, which implies that Turing patterns are stable non-constant steady states, but the opposite is not necessarily true; (2) In non-Turing domain, steady state bifurcation and Hopf bifurcation act in concert to determine the emergent spatial patterns, that is, non-constant steady state emerges through steady state bifurcation but it may be unstable if the destabilising effect of Hopf bifurcation counteracts the stabilising effect of diffusion, leading to non-stationary spatial patterns; (3) Coupling diffusion into an ODE model can significantly enrich population dynamics by inducing alternative non-constant steady states (four different states are observed, two stable and two unstable), in particular when diffusion interacts with different types of bifurcation; (4) Diffusion can promote species coexistence by saving species which otherwise goes to extinction in the absence of diffusion.
Flood disturbance and predator-prey effects on regional gradients in species diversity.
Mori, Terutaka; Saitoh, Takashi
2014-01-01
The effects of both abiotic factors and biotic interactions among guilds (i.e., inter-guild effects) have been suggested to be important for understanding spatial variation in species diversity; however, compared to the abiotic effects, the processes by which the inter-guild effects are mediated have been little described. Hence, we investigated stream invertebrate assemblages on Hokkaido Island, Japan, and assessed how the processes of determining regional patterns in species diversity differed among guilds (collector-filterers, collector-gatherers/shredders, scrapers, and predators) by taking both inter-guild and abiotic effects into consideration using Bayesian networks. Collector-gatherers/shredders, collector-filterers, and predators exhibited significant regional gradients in taxonomic richness. Gradients in the former two guilds can be generated by variation in flood disturbance regardless of interactions with other guilds. The gradient in predator taxonomic richness was indirectly related to the disturbance and was directly generated by bottom-up effects through their prey (collector-gatherers/shredders and collector-filterers). We found that not only environmental factors, but also inter-guild effects may be essential for forming the regional gradient in predators, unlike those for collector-gatherers/shredders and collector-filterers. The processes underlying the regional variation in taxonomic richness of the three guilds are interpreted in terms of the "more individuals" hypothesis, facilitation, and predator-prey relationships.
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.
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.
Optimal harvesting policy of predator-prey model with free fishing and reserve zones
Toaha, Syamsuddin; Rustam
2017-03-01
The present paper deals with an optimal harvesting of predator-prey model in an ecosystem that consists of two zones, namely the free fishing and prohibited zones. The dynamics of prey population in the ecosystem can migrate from the free fishing to the prohibited zone and vice versa. The predator and prey populations in the free fishing zone are then harvested with constant efforts. The existence of the interior equilibrium point is analyzed and its stability is determined using Routh-Hurwitz stability test. The stable interior equilibrium point is then related to the problem of maximum profit and the problem of present value of net revenue. We follow the Pontryagin's maximal principle to get the optimal harvesting policy of the present value of the net revenue. From the analysis, we found a critical point of the efforts that makes maximum profit. There also exists certain conditions of the efforts that makes the present value of net revenue becomes maximal. In addition, the interior equilibrium point is locally asymptotically stable which means that the optimal harvesting is reached and the unharvested prey, harvested prey, and harvested predator populations remain sustainable. Numerical examples are given to verify the analytical results.
Analysis of a Stochastic Predator-Prey Model with Applications to Intrahost HIV Genetic Diversity
Leviyang, Sivan
2009-01-01
During an infection, HIV experiences strong selection by immune system T cells. Recent experimental work has shown that MHC escape mutations form an important pathway for HIV to avoid such selection. In this paper, we study a model of MHC escape mutation. The model is a predator-prey model with two prey, composed of two HIV variants, and one predator, the immune system CD8 cells. We assume that one HIV variant is visible to CD8 cells and one is not. The model takes the form of a system of stochastic differential equations. Motivated by well-known results concerning the short life-cycle of HIV intrahost, we assume that HIV population dynamics occur on a faster time scale then CD8 population dynamics. This separation of time scales allows us to analyze our model using an asymptotic approach. Using this model we study the impact of an MHC escape mutation on the population dynamics and genetic evolution of the intrahost HIV population. From the perspective of population dynamics, we show that the competition betw...
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.
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.
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.
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.
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.
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.
Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J
2015-03-01
We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso. We show the resulting method, here called the LSA method, to be an (asymptotically) oracle model selection method. The finite sample performance of the proposed LSA method is investigated with Monte Carlo simulations, in which we examine the percentage of selecting true ODE models, the efficiency of the parameter estimation compared to simply using the full and true models, and coverage probabilities of the estimated confidence intervals for ODE parameters, all of which have satisfactory performances. Our method is also demonstrated by selecting the best predator-prey ODE to model a lynx and hare population dynamical system among some well-known and biologically interpretable ODE models.
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.
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.
On basins of attraction for a predator-prey model via meshless approximation
Francomano, Elisa; Hilker, Frank M.; Paliaga, Marta; Venturino, Ezio
2016-10-01
In this work an epidemiological predator-prey model is studied. It analyzes the spread of an infectious disease with frequency-dependent and vertical transmission within the predator population. In particular we consider social predators, i.e. they cooperate in groups to hunt. The result is a three-dimensional system in which the predator population is divided into susceptible and infected individuals. Studying the dynamical system and bifurcation diagrams, a scenario was identified in which the model shows multistability but the domain of attraction of one equilibrium point can be so small that it is almost the point itself. From a biological point of view it is important to analyze this effect in order to understand under which conditions the population goes extinct or survives. Thus we present a study to analyze the basins of attraction of the stable equilibrium points. This paper addresses the question of finding the point lying on the surface which partitions the phase plane. Therefore a meshless approach has been adopted to produce an approximation of the separatrix manifold.
Predator prey oscillations in a simple cascade model of drift wave turbulence
Berionni, V.; Guercan, Oe. D. [Laboratoire de Physique des Plasmas, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex (France)
2011-11-15
A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separation for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.
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.
Aladeen Al Basheer
2017-01-01
Full Text Available Cannibalism, the act of killing and consumption of conspecifics, is generally considered to be a stabilising process in ODE models of predator-prey systems. On the other hand, Sun et al. were the first to show that cannibalism can cause Turing instability, in the classical Rosenzweig-McArthur two-species PDE model, which is an impossibility without cannibalism. Magnússon’s classic work is the first to show that cannibalism in a structured three-species predator-prey ODE model can actually be destabilising. In the current manuscript we consider the PDE form of the three-species model proposed in Magnússon’s classic work. We prove that, in the absence of cannibalism, Turing instability is an impossibility in this model, for any range of parameters. However, the inclusion of cannibalism can cause Turing instability. Thus, to the best of our knowledge, we report the first cannibalism induced Turing instability result, in spatially explicit three-species age structured predator-prey systems. We also show that, in the classical ODE model proposed by Magnússon, cannibalism can act as a life boat mechanism, for the prey.
Increased autumn rainfall disrupts predator-prey interactions in fragmented boreal forests.
Terraube, Julien; Villers, Alexandre; Poudré, Léo; Varjonen, Rauno; Korpimäki, Erkki
2017-04-01
There is a pressing need to understand how changing climate interacts with land-use change to affect predator-prey interactions in fragmented landscapes. This is particularly true in boreal ecosystems facing fast climate change and intensification in forestry practices. Here, we investigated the relative influence of autumn climate and habitat quality on the food-storing behaviour of a generalist predator, the pygmy owl, using a unique data set of 15 850 prey items recorded in western Finland over 12 years. Our results highlighted strong effects of autumn climate (number of days with rainfall and with temperature forests strengthened the functional response of owls to variations in vole abundance and were more prone to switch from main prey to alternative prey (passerine birds) depending on local climate conditions. High-quality habitat may allow pygmy owls to buffer negative effects of inclement weather and cyclic variation in vole abundance. Additionally, our results evidenced sex-specific trends in body condition, as the scaled mass index of smaller males increased while the scaled mass index of larger females decreased over the study period, probably due to sex-specific foraging strategies and energy requirements. Long-term temporal stability in local vole abundance refutes the hypothesis of climate-driven change in vole abundance and suggests that rainier autumns could reduce the vulnerability of small mammals to predation by pygmy owls. As small rodents are key prey species for many predators in northern ecosystems, our findings raise concern about the impact of global change on boreal food webs through changes in main prey vulnerability. © 2016 John Wiley & Sons Ltd.
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.
Robustness of predator-prey models for confinement regime transitions in fusion plasmas
Zhu, H.; Chapman, S. C.; Dendy, R. O.
2013-04-01
Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free energy sources such as temperature gradients. Zero-dimensional models, designed to embody plausible physical narratives for these interactions, can help to identify the origin of enhanced energy confinement and of transitions between confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here, we extend a successful three-variable (temperature gradient; microturbulence level; one class of coherent structure) model in this genre [M. A. Malkov and P. H. Diamond, Phys. Plasmas 16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure. This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree of invariance of the phenomenology generated by the model of Malkov and Diamond, given this additional physics. We study and compare the long-time behaviour of the three-equation and four-equation systems, their evolution towards the final state, and their attractive fixed points and limit cycles. We explore the sensitivity of paths to attractors. It is found that, for example, an attractive fixed point of the three-equation system can become a limit cycle of the four-equation system. Addressing these questions which we together refer to as "robustness" for convenience is particularly important for models which, as here, generate sharp transitions in the values of system variables which may replicate some key features of confinement transitions. Our results help to establish the robustness of the zero-dimensional model approach to capturing observed confinement phenomenology in tokamak fusion plasmas.
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.
Robustness of predator-prey models for confinement regime transitions in fusion plasmas
Zhu, H. [Department of Physics, Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry CV4 7AL (United Kingdom); Chapman, S. C. [Department of Physics, Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry CV4 7AL (United Kingdom); Department of Mathematics and Statistics, University of Tromso (Norway); Dendy, R. O. [Euratom/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB (United Kingdom); Department of Physics, Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2013-04-15
Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free energy sources such as temperature gradients. Zero-dimensional models, designed to embody plausible physical narratives for these interactions, can help to identify the origin of enhanced energy confinement and of transitions between confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here, we extend a successful three-variable (temperature gradient; microturbulence level; one class of coherent structure) model in this genre [M. A. Malkov and P. H. Diamond, Phys. Plasmas 16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure. This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree of invariance of the phenomenology generated by the model of Malkov and Diamond, given this additional physics. We study and compare the long-time behaviour of the three-equation and four-equation systems, their evolution towards the final state, and their attractive fixed points and limit cycles. We explore the sensitivity of paths to attractors. It is found that, for example, an attractive fixed point of the three-equation system can become a limit cycle of the four-equation system. Addressing these questions which we together refer to as 'robustness' for convenience is particularly important for models which, as here, generate sharp transitions in the values of system variables which may replicate some key features of confinement transitions. Our results help to establish the robustness of the zero-dimensional model approach to capturing observed confinement phenomenology in tokamak fusion plasmas.
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.
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.
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.
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 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.
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.
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.
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.
Muhammad Shakil
2015-12-01
Full Text Available In this paper we aim to develop the modeled equations for different types of mechanism of the predator-prey interactions with the help of a quasi chemical approach while taking a special study case of foxes and rabbits, these mechanisms include autocatalysis mechanism, pair wise interactions and the mechanism of their movements to some free places. The chemical reactions representing the interactions obey the mass action law. The territorial animal like fox is assigned a simple cell as its territory. Under the proper relations between coefficients, this system may demonstrate globally stable dynamics.
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.
Xiao, Qizhen; Dai, Binxiang
2015-10-01
In this paper, we analyze a general predator-prey model with state feedback impulsive harvesting strategies in which the prey species displays a strong Allee effect. We firstly show the existence of order-1 heteroclinic cycle and order-1 positive periodic solutions by using the geometric theory of differential equations for the unperturbed system. Based on the theory of rotated vector fields, the order-1 positive periodic solutions and heteroclinic bifurcation are studied for the perturbed system. Finally, some numerical simulations are provided to illustrate our main results. All the results indicate that the harvesting rate should be maintained at a reasonable range to keep the sustainable development of ecological systems.
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.
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).
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.
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.
无
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.
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.
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.
Liu, Quan-Xing; Jin, Zhen
2006-01-01
Results are reported concerning the formation of spatial patterns in the two-species ratio-dependent predator-prey model driven by spatial colored-noise. The results show that there is a critical value with respect to the intensity of spatial noise for this system when the parameters are in the Turing space, above which the regular spatial patterns appear in two dimensions, but under which there are not regular spatial patterns produced. In particular, we investigate in two-dimensional space ...
Wenjie Qin
2014-01-01
Full Text Available The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Further-more, when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results.
Codron, J; Botha-Brink, J; Codron, D; Huttenlocker, A K; Angielczyk, K D
2017-01-01
Unlike modern mammalian communities, terrestrial Paleozoic and Mesozoic vertebrate systems were characterized by carnivore faunas that were as diverse as their herbivore faunas. The comparatively narrow food base available to carnivores in these paleosystems raises the possibility that predator-prey interactions contributed to unstable ecosystems by driving populations to extinction. Here, we develop a model of predator-prey interactions based on diversity, abundance and body size patterns observed in the Permo-Triassic vertebrate fossil record of the Karoo Basin, South Africa. Our simulations reflect empirical evidence that despite relatively high carnivore: herbivore species ratios, herbivore abundances were sufficient for carnivores to maintain required intake levels through most of the Karoo sequence. However, high mortality rates amongst herbivore populations, even accounting for birth rates of different-sized species, are predicted for assemblages immediately preceding the end-Guadalupian and end-Permian mass extinctions, as well as in the Middle Triassic when archosaurs replaced therapsids as the dominant terrestrial fauna. These results suggest that high rates of herbivore mortality could have played an important role in biodiversity declines leading up to each of these turnover events. Such declines would have made the systems especially vulnerable to subsequent stochastic events and environmental perturbations, culminating in large-scale extinctions.
James, A. R. C. [Alberta Univ., Dept. of Biological Sciences, Edmonton, AB (Canada)
1999-09-30
The influence of timber harvesting, combined with development of the oil and natural gas industry and the resulting environmental changes on predator-prey relationship between wolves and caribou in northeastern Alberta are investigated. To establish the level of influence, two ways of predator-prey relationship were studied: (1) spatial distribution of caribou in relation to alternative prey, commonly moose, which is assumed to reduce the level of wolf predation experienced by caribou populations, and (2) the development of linear corridors which has been hypothesized to increase predation pressure on caribou. With respect to spatial separation it was found that the selection of fen/bog complexes by caribou and the selection of well-drained habitats by moose and wolves resulted in spatial separation, reducing, but not totally eliminating predation pressure on caribou from wolves. Regarding the effect of linear corridors, radio monitoring established that caribou mortalities attribued to wolf predation were higher among caribou that were closer to linear corridors than among caribou that were farther from corridors than random points. These and other related observations led to the conclusion that timber harvesting and increased industrial activity in and near caribou ranges could have significant effect on caribou population dynamics by increasing predation. Managaement implications of these results and various remedial options are discussed. refs. figs.
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.
Hollis, Karen L
2017-06-01
A behavioural ecological approach to the relationship between pit-digging larval antlions and their common prey, ants, provides yet another example of how the specific ecological niche that species inhabit imposes selection pressures leading to unique behavioural adaptations. Antlions rely on multiple strategies to capture prey with a minimal expenditure of energy and extraordinary efficiency while ants employ several different strategies for avoiding capture, including rescue of trapped nestmates. Importantly, both ants and antlions rely heavily on their capacity for learning, a tool that sometimes is overlooked in predator-prey relationships, leading to the implicit assumption that behavioural adaptations are the result of fixed, hard-wired responses. Nonetheless, like hard-wired responses, learned behaviour, too, is uniquely adapted to the ecological niche, a reminder that the expression of associative learning is species-specific. Beyond the study of ants and antlions, per se, this particular predator-prey relationship reveals the important role that the capacity to learn plays in coevolutionary arms races. Copyright © 2016 Elsevier B.V. All rights reserved.
Panaretou, E; Blythe, J N St J; Conti, M; Brennan, P A
2016-05-01
Fibular free flaps are routinely used to reconstruct segmental mandibular defects after resection. While ossification of the vascular pedicle is uncommon but well reported, to our knowledge, heterotopic ossification remote from the pedicle has not previously been described. We report a case in which this occurred. It serves as a reminder that bony, hard lumps in the neck can present years after reconstruction with a fibular flap.
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.
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.
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.
Argolo, C.; Barros, P.; Tomé, T.; Arashiro, E.; Gleria, Iram; Lyra, M. L.
2016-08-01
We investigate a stochastic lattice model describing a predator-prey system in a fractal scale-free landscape, mimicked by the fractal Sierpinski carpet. We determine the threshold of species coexistence, that is, the critical phase boundary related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. We show that the predators must live longer in order to persist in a fractal habitat. We further performed a finite-size scaling analysis in the vicinity of the absorbing-state phase transition to compute a set of stationary and dynamical critical exponents. Our results indicate that the transition belongs to the directed percolation universality class exhibited by the usual contact process model on the same fractal landscape.
Bifurcation analysis and dimension reduction of a predator-prey model for the L-H transition
Dam, Magnus; Brøns, Morten; Juul Rasmussen, Jens
2013-01-01
The L-H transition denotes a shift to an improved confinement state of a toroidal plasma in a fusion reactor. A model of the L-H transition is required to simulate the time dependence of tokamak discharges that include the L-H transition. A 3-ODE predator-prey type model of the L-H transition...... is investigated with bifurcation theory of dynamical systems. The analysis shows that the model contains three types of transitions: an oscillating transition, a sharp transition with hysteresis, and a smooth transition. The model is recognized as a slow-fast system. A reduced 2-ODE model consisting of the full...... model restricted to the flow on the critical manifold is found to contain all the same dynamics as the full model. This means that all the dynamics in the system is essentially 2-dimensional, and a minimal model of the L-H transition could be a 2-ODE model....
Bifurcation analysis and dimension reduction of a predator-prey model for the L-H transition
Dam, Magnus; Brøns, Morten; Juul Rasmussen, Jens; Naulin, Volker; Xu, Guosheng
2013-10-01
The L-H transition denotes a shift to an improved confinement state of a toroidal plasma in a fusion reactor. A model of the L-H transition is required to simulate the time dependence of tokamak discharges that include the L-H transition. A 3-ODE predator-prey type model of the L-H transition is investigated with bifurcation theory of dynamical systems. The analysis shows that the model contains three types of transitions: an oscillating transition, a sharp transition with hysteresis, and a smooth transition. The model is recognized as a slow-fast system. A reduced 2-ODE model consisting of the full model restricted to the flow on the critical manifold is found to contain all the same dynamics as the full model. This means that all the dynamics in the system is essentially 2-dimensional, and a minimal model of the L-H transition could be a 2-ODE model.
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.
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.
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.
Bifurcation analysis and dimension reduction of a predator-prey model for the L-H transition
Dam, Magnus; Brøns, Morten [Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800 Kgs. Lyngby (Denmark); Juul Rasmussen, Jens; Naulin, Volker [Association Euratom-DTU, Department of Physics, Technical University of Denmark, DTU Risø Campus, DK-4000 Roskilde (Denmark); Xu, Guosheng [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)
2013-10-15
The L-H transition denotes a shift to an improved confinement state of a toroidal plasma in a fusion reactor. A model of the L-H transition is required to simulate the time dependence of tokamak discharges that include the L-H transition. A 3-ODE predator-prey type model of the L-H transition is investigated with bifurcation theory of dynamical systems. The analysis shows that the model contains three types of transitions: an oscillating transition, a sharp transition with hysteresis, and a smooth transition. The model is recognized as a slow-fast system. A reduced 2-ODE model consisting of the full model restricted to the flow on the critical manifold is found to contain all the same dynamics as the full model. This means that all the dynamics in the system is essentially 2-dimensional, and a minimal model of the L-H transition could be a 2-ODE model.
Zhenguo Luo
2014-01-01
Full Text Available An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main 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.
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.
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.
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.
Min Zhao
2012-01-01
Full Text Available The dynamic behaviors of a predator-prey (pest model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.
Nie, Linfei; Teng, Zhidong; Hu, Lin; Peng, Jigen
2009-11-01
According to the economic and biological aspects of renewable resources management, we propose a Lotka-Volterra predator-prey model with state dependent impulsive harvest. By using the Poincaré map, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three under some conditions. Numerical results are carried out to illustrate the feasibility of our main results. The bifurcation diagrams of periodic solutions are obtained by using the numerical simulations, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex.
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.
Reiser, D. [Research Center Jülich GmbH, Institute for Energy and Climate Research—Plasma Physics, D-52425 Jülich (Germany); Ohno, N. [Department of Energy Engineering and Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603 (Japan); Tanaka, H. [National Institute for Fusion Science, Toki 509-5292 (Japan); Vela, L. [Physics Department, Universidad Carlos III de Madrid, Avda de la Universidad 30, 28911-Leganés, Madrid (Spain)
2014-03-15
Three-dimensional global drift fluid simulations are carried out to analyze coherent plasma structures appearing in the NAGDIS-II linear device (nagoya divertor plasma Simulator-II). The numerical simulations reproduce several features of the intermittent spiraling structures observed, for instance, statistical properties, rotation frequency, and the frequency of plasma expulsion. The detailed inspection of the three-dimensional plasma dynamics allows to identify the key mechanism behind the formation of these intermittent events. The resistive coupling between electron pressure and parallel electric field in the plasma source region gives rise to a quasilinear predator-prey like dynamics where the axisymmetric mode represents the prey and the spiraling structure with low azimuthal mode number represents the predator. This interpretation is confirmed by a reduced one-dimensional quasilinear model derived on the basis of the findings in the full three-dimensional simulations. The dominant dynamics reveals certain similarities to the classical Lotka-Volterra cycle.
Reiser, D.; Ohno, N.; Tanaka, H.; Vela, L.
2014-03-01
Three-dimensional global drift fluid simulations are carried out to analyze coherent plasma structures appearing in the NAGDIS-II linear device (nagoya divertor plasma Simulator-II). The numerical simulations reproduce several features of the intermittent spiraling structures observed, for instance, statistical properties, rotation frequency, and the frequency of plasma expulsion. The detailed inspection of the three-dimensional plasma dynamics allows to identify the key mechanism behind the formation of these intermittent events. The resistive coupling between electron pressure and parallel electric field in the plasma source region gives rise to a quasilinear predator-prey like dynamics where the axisymmetric mode represents the prey and the spiraling structure with low azimuthal mode number represents the predator. This interpretation is confirmed by a reduced one-dimensional quasilinear model derived on the basis of the findings in the full three-dimensional simulations. The dominant dynamics reveals certain similarities to the classical Lotka-Volterra cycle.
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.
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
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.
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.
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.
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.
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...
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.
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.
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
Desheng TIAN
2008-01-01
The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.
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.
Sun, Kaibiao; Zhang, Tonghua; Tian, Yuan
2016-09-01
This work presents a pest control predator-prey model, where rate of change in prey density follows a scaling law with exponent less than one and the control is by an integrated management strategy. The aim is to investigate the change in system dynamics and determine a pest control level with minimum control price. First, the dynamics of the proposed model without control is investigated by taking the exponent as an index parameter. And then, to determine the frequency of spraying chemical pesticide and yield releases of the predator, the existence of the order-1 periodic orbit of the control system is discussed in cases. Furthermore, to ensure a certain robustness of the adopted control, i.e., for an inaccurately detected species density or a deviation, the control system could be stabilized at the order-1 periodic orbit, the stability of the order-1 periodic orbit is verified by an stability criterion for a general semi-continuous dynamical system. In addition, to minimize the total cost input in pest control, an optimization problem is formulated and the optimum pest control level is obtained. At last, the numerical simulations with a specific model are carried out to complement the theoretical results.
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.
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.
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.
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.
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.
Kareva, Irina; Berezovskaya, Faina
2015-09-07
It is a well-established fact that tumors up-regulate glucose consumption to meet increasing demands for rapidly available energy by upregulating a purely glycolytic mode of glucose metabolism. What is often neglected is that activated cytotoxic cells of the immune system, integral players in the carcinogenesis process, also come to rely on glycolysis as a primary mode of glucose metabolism. Moreover, while cancer cells can revert back to aerobic metabolism, rapidly proliferating cytotoxic lymphocytes are incapable of performing their function when adequate resources are lacking. Consequently, it is likely that in the tumor microenvironment there may exist competition for shared resources between cancer cells and the cells of the immune system, which may underlie much of tumor-immune dynamics. Proposed here is a model of tumor-immune-glucose interactions, formulated as a predator-prey-common resource type system. The outcome of these interactions ranges from tumor elimination, to tumor dormancy, to unrestrained tumor growth. It is also predicted that the process of tumor escape can be preceded by periods of oscillatory tumor growth. A detailed bifurcation analysis of three subsystems of the model suggest that oscillatory regimes are a result of competition for shared resource (glucose) between the predator (immune cells) and the prey (cancer cells). Existence of competition for nutrients between cancer and immune cells may provide additional mechanistic insight as to why the efficacy of many immunotherapies may be limited.
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.
Taylor, Rachel A; Sherratt, Jonathan A; White, Andrew
2013-12-01
Many natural systems are subject to seasonal environmental change. As a consequence many species exhibit seasonal changes in their life history parameters--such as a peak in the birth rate in spring. It is important to understand how this seasonal forcing affects the population dynamics. The main way in which seasonal models have been studied is through a two dimensional bifurcation approach. We augment this bifurcation approach with extensive simulation in order to understand the potential solution behaviours for a predator-prey system with a seasonally forced prey growth rate. We consider separately how forcing influences the system when the unforced dynamics have either monotonic decay to the coexistence steady state, or oscillatory decay, or stable limit cycles. The range of behaviour the system can exhibit includes multi-year cycles of different periodicities, parameter ranges with coexisting multi-year cycles of the same or different period as well as quasi-periodicity and chaos. We show that the level of oscillation in the unforced system has a large effect on the range of behaviour when the system is seasonally forced. We discuss how the methods could be extended to understand the dynamics of a wide range of ecological and epidemiological systems that are subject to seasonal changes.
Self-organizing patterns maintained by competing associations in a six-species predator-prey model
Szabó, G; Borsos, I
2008-01-01
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The evolution of the spatial distribution of species is governed by iterated invasions between the neighboring predator-prey pairs with species specific rates and by site exchange between the neutral pairs with a probability $X$. This dynamical rule yields the formation of five associations composed of two or three species with proper spatiotemporal patterns. For large $X$ a cyclic dominance can occur between the three two-species associations whereas one of the two three-species associations prevails in the whole system for low values of $X$ in the final state. Within an intermediate range of $X$ all the five associations coexist due to the fact that cyclic invasions between the two-species associations reduce their resistance temporarily against the invasion of three-species a...
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.
Tran, Tam T; Janssens, Lizanne; Dinh, Khuong V; Op de Beeck, Lin; Stoks, Robby
2016-07-01
How evolution may mitigate the effects of global warming and pesticide exposure on predator-prey interactions is directly relevant for vector control. Using a space-for-time substitution approach, we addressed how 4°C warming and exposure to the pesticide endosulfan shape the predation on Culex pipiens mosquitoes by damselfly predators from replicated low- and high-latitude populations. Although warming was only lethal for the mosquitoes, it reduced predation rates on these prey. Possibly, under warming escape speeds of the mosquitoes increased more than the attack efficiency of the predators. Endosulfan imposed mortality and induced behavioral changes (including increased filtering and thrashing and a positional shift away from the bottom) in mosquito larvae. Although the pesticide was only lethal for the mosquitoes, it reduced predation rates by the low-latitude predators. This can be explained by the combination of the evolution of a faster life history and associated higher vulnerabilities to the pesticide (in terms of growth rate and lowered foraging activity) in the low-latitude predators and pesticide-induced survival selection in the mosquitoes. Our results suggest that predation rates on mosquitoes at the high latitude will be reduced under warming unless predators evolve toward the current low-latitude phenotype or low-latitude predators move poleward.
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.
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.
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.
Bifurcation analysis of a discrete-time ratio-dependent predator-prey model with Allee Effect
Cheng, Lifang; Cao, Hongjun
2016-09-01
A discrete-time predator-prey model with Allee effect is investigated in this paper. We consider the strong and the weak Allee effect (the population growth rate is negative and positive at low population density, respectively). From the stability analysis and the bifurcation diagrams, we get that the model with Allee effect (strong or weak) growth function and the model with logistic growth function have somewhat similar bifurcation structures. If the predator growth rate is smaller than its death rate, two species cannot coexist due to having no interior fixed points. When the predator growth rate is greater than its death rate and other parameters are fixed, the model can have two interior fixed points. One is always unstable, and the stability of the other is determined by the integral step size, which decides the species coexistence or not in some extent. If we increase the value of the integral step size, then the bifurcated period doubled orbits or invariant circle orbits may arise. So the numbers of the prey and the predator deviate from one stable state and then circulate along the period orbits or quasi-period orbits. When the integral step size is increased to a critical value, chaotic orbits may appear with many uncertain period-windows, which means that the numbers of prey and predator will be chaotic. In terms of bifurcation diagrams and phase portraits, we know that the complexity degree of the model with strong Allee effect decreases, which is related to the fact that the persistence of species can be determined by the initial species densities.
Richard Fitzpatrick
Full Text Available During the reproductive season, sea turtles use a restricted area in the vicinity of their nesting beaches, making them vulnerable to predation. At Raine Island (Australia, the highest density green turtle Chelonia mydas rookery in the world, tiger sharks Galeocerdo cuvier have been observed to feed on green turtles, and it has been suggested that they may specialise on such air-breathing prey. However there is little information with which to examine this hypothesis. We compared the spatial and temporal components of movement behaviour of these two potentially interacting species in order to provide insight into the predator-prey relationship. Specifically, we tested the hypothesis that tiger shark movements are more concentrated at Raine Island during the green turtle nesting season than outside the turtle nesting season when turtles are not concentrated at Raine Island. Turtles showed area-restricted search behaviour around Raine Island for ∼3-4 months during the nesting period (November-February. This was followed by direct movement (transit to putative foraging grounds mostly in the Torres Straight where they switched to area-restricted search mode again, and remained resident for the remainder of the deployment (53-304 days. In contrast, tiger sharks displayed high spatial and temporal variation in movement behaviour which was not closely linked to the movement behaviour of green turtles or recognised turtle foraging grounds. On average, tiger sharks were concentrated around Raine Island throughout the year. While information on diet is required to determine whether tiger sharks are turtle specialists our results support the hypothesis that they target this predictable and plentiful prey during turtle nesting season, but they might not focus on this less predictable food source outside the nesting season.
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.
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.
The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes.
Hatton, Ian A; McCann, Kevin S; Fryxell, John M; Davies, T Jonathan; Smerlak, Matteo; Sinclair, Anthony R E; Loreau, Michel
2015-09-04
Ecosystems exhibit surprising regularities in structure and function across terrestrial and aquatic biomes worldwide. We assembled a global data set for 2260 communities of large mammals, invertebrates, plants, and plankton. We find that predator and prey biomass follow a general scaling law with exponents consistently near ¾. This pervasive pattern implies that the structure of the biomass pyramid becomes increasingly bottom-heavy at higher biomass. Similar exponents are obtained for community production-biomass relations, suggesting conserved links between ecosystem structure and function. These exponents are similar to many body mass allometries, and yet ecosystem scaling emerges independently from individual-level scaling, which is not fully understood. These patterns suggest a greater degree of ecosystem-level organization than previously recognized and a more predictive approach to ecological theory. Copyright © 2015, American Association for the Advancement of Science.
Apes finding ants: Predator-prey dynamics in a chimpanzee habitat in Nigeria.
Pascual-Garrido, Alejandra; Umaru, Buba; Allon, Oliver; Sommer, Volker
2013-12-01
Some chimpanzee populations prey upon army ants, usually with stick tools. However, how their prey's subterranean nesting and nomadic lifestyle influence the apes' harvesting success is still poorly understood. This is particularly true for chimpanzees (Pan troglodytes ellioti) at Gashaka/Nigeria, which consume army ants (Dorylus rubellus) with much higher frequency than at other sites. We assessed various harvesting and search options theoretically available to the apes. For this, we reconstructed annual consumption patterns from feces and compared the physical characteristics of exploited ant nests with those that were not targeted. Repeated exploitation of a discovered nest is viable only in the short term, as disturbed colonies soon moved to a new site. Moreover, monitoring previously occupied nest cavities is uneconomical, as ants hardly ever re-used them. Thus, the apes have to detect new nests regularly, although colony density is relatively low (1 colony/1.3 ha). Surprisingly, visual search cues seem to be of limited importance because the probability of a nest being exploited was independent of its conspicuousness (presence of excavated soil piles, concealing leaf-litter or vegetation). However, chimpanzees preferentially targeted nests in forests or at the base of food trees, that is, where the apes spend relatively more time and/or where ant colony density is highest. Taken together, our findings suggest that, instead of employing a search strategy based on visual cues or spatial memory, chimpanzee predation on army ants contains a considerable opportunistic element.
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.
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.
Jiang, Jiao; Song, Yongli; Yu, Pei
2016-06-01
In this paper, a Leslie-type predator-prey model with ratio-dependent functional response and Allee effect on prey is considered. We first study the existence of the multiple positive equilibria and their stability. Then we investigate the effect of delay on the distribution of the roots of characteristic equation and obtain the conditions for the occurrence of simple-zero, double-zero and triple-zero singularities. The formulations for calculating the normal form of the triple-zero bifurcation of the delay differential equations are derived. We show that, under certain conditions on the parameters, the system exhibits homoclinic orbit, heteroclinic orbit and periodic orbit.
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...
Li, Jiqiu; Fenton, Andy; Kettley, Lee; Roberts, Phillip; Montagnes, David J S
2013-10-07
We propose that delayed predator-prey models may provide superficially acceptable predictions for spurious reasons. Through experimentation and modelling, we offer a new approach: using a model experimental predator-prey system (the ciliates Didinium and Paramecium), we determine the influence of past-prey abundance at a fixed delay (approx. one generation) on both functional and numerical responses (i.e. the influence of present : past-prey abundance on ingestion and growth, respectively). We reveal a nonlinear influence of past-prey abundance on both responses, with the two responding differently. Including these responses in a model indicated that delay in the numerical response drives population oscillations, supporting the accepted (but untested) notion that reproduction, not feeding, is highly dependent on the past. We next indicate how delays impact short- and long-term population dynamics. Critically, we show that although superficially the standard (parsimonious) approach to modelling can reasonably fit independently obtained time-series data, it does so by relying on biologically unrealistic parameter values. By contrast, including our fully parametrized delayed density dependence provides a better fit, offering insights into underlying mechanisms. We therefore present a new approach to explore time-series data and a revised framework for further theoretical studies.
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.
Bairagi, N; Adak, D
2016-07-01
Parasites play a significant role in trophic interactions and can regulate both predator and prey populations. Mathematical models might be of great use in predicting different system dynamics because models have the potential to predict the system response due to different changes in system parameters. In this paper, we study a predator-prey-parasite (PPP) system where prey population is infected by some micro parasites and predator-prey interaction occurs following Leslie-Gower model with type II response function. Infection spreads following SI type epidemic model with standard incidence rate. The infection process is not instantaneous but mediated by a fixed incubation delay. We study the stability and instability of the endemic equilibrium point of the delay-induced PPP system with respect to two parameters, viz., the force of infection and the length of incubation delay under two cases: (i) the corresponding non-delayed system is stable and (ii) the corresponding non-delayed system is unstable. In the first case, the system populations coexist in stable state for all values of delay if the force of infection is low; or show oscillatory behavior when the force of infection is intermediate and the length of delay crosses some critical value. The system, however, exhibits very complicated dynamics if the force of infection is high, where the system is unstable in absence of delay. In this last case, the system shows oscillatory, stable or chaotic behavior depending on the length of delay.
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.
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.
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.
带有年龄结构的捕食者-食饵模型研究%Research on A Predator-Prey Model with Age-Structure
郑立飞; 赵惠燕
2011-01-01
This paper studies the asymptotic behavior of a predator-prey system with age structure. It is assumed that the transition rate from immature stage to mature stage depends on the density of immature individuals. Also, the larva predator is assumed to consume prey. Conditions for the permanence and extinction of the predator are obtained.%研究带有年龄结构的捕食者-食饵模型的渐近行为.本文所研究的模型假定捕食者从幼年阶段到成年阶段的转变率依赖于幼年种群的密度,还假定幼年捕食者捕食食饵.本文最终给出了有年龄结构的捕食者-食饵模型的捕食者持久和灭绝的若干条件.
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.
Haque, Mainul; Sarwardi, Sahabuddin; Preston, Simon; Venturino, Ezio
2011-11-01
We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition study the bifurcations arising in some selected situations. Threshold values for a few parameters determining the feasibility and stability conditions of some equilibria are discovered and similarly a threshold is identified for the disease to die out. The parameter thresholds under which the system admits a Hopf bifurcation are investigated both in the presence of zero and non-zero time lag. Numerical simulations support our theoretical analysis. Copyright © 2011 Elsevier Inc. All rights reserved.
莫愿斌; 刘付永; 马彦追; 张宇楠
2013-01-01
s: According to the basic glowworm swarm optimization (GSO) algorithm in solving the function of global optimal value existing some problems, such as easy to fall into local optimum, slow convergence and low precision, an artificial glowworm swarm optimization algorithm based biological predator-prey behavior (GSOPP) is proposed. The algorithm through populations chase and escape, and the mutation strategy to speed up the convergence rate, and can obtain a more accurate solution. Finally, the test results of 8 standard test functions show that, the improved GSOPP algorithm than the basic GSO algorithm has Better performance.% 针对基本萤火虫优化(GSO)算法在求解函数全局最优值时，存在着易陷入局部最优、收敛速度慢和求解精度低等问题，提出了1种基于生物捕食-被捕食(Predator-Prey)行为的双种群GSO算法(GSOPP)。该算法通过引入种群间的追逐与逃跑以及变异等策略加快了收敛速度，且能获得精度更高的解。最后，通过对8个标准测试函数进行测试，结果表明，改进后的 GSOPP算法比基本GSO算法有更优的性能。
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.
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.
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.
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.
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.
Central Diabetes Insipidus: A Previously Unreported Side Effect of Temozolomide
Nachtigall, Lisa; Wexler, Deborah; Miller, Karen K.; Klibanski, Anne; Makimura, Hideo
2013-01-01
Context: Temozolomide (TMZ) is an alkylating agent primarily used to treat tumors of the central nervous system. We describe 2 patients with apparent TMZ-induced central diabetes insipidus. Using our institution's Research Patient Database Registry, we identified 3 additional potential cases of TMZ-induced diabetes insipidus among a group of 1545 patients treated with TMZ. Case Presentations: A 53-year-old male with an oligoastrocytoma and a 38-year-old male with an oligodendroglioma each developed symptoms of polydipsia and polyuria approximately 2 months after the initiation of TMZ. Laboratory analyses demonstrated hypernatremia and urinary concentrating defects, consistent with the presence of diabetes insipidus, and the patients were successfully treated with desmopressin acetate. Desmopressin acetate was withdrawn after the discontinuation of TMZ, and diabetes insipidus did not recur. Magnetic resonance imaging of the pituitary and hypothalamus was unremarkable apart from the absence of a posterior pituitary bright spot in both of the cases. Anterior pituitary function tests were normal in both cases. Using the Research Patient Database Registry database, we identified the 2 index cases and 3 additional potential cases of diabetes insipidus for an estimated prevalence of 0.3% (5 cases of diabetes insipidus per 1545 patients prescribed TMZ). Conclusions: Central diabetes insipidus is a rare but reversible side effect of treatment with TMZ. PMID:23928668
Central diabetes insipidus: a previously unreported side effect of temozolomide.
Faje, Alexander T; Nachtigall, Lisa; Wexler, Deborah; Miller, Karen K; Klibanski, Anne; Makimura, Hideo
2013-10-01
Temozolomide (TMZ) is an alkylating agent primarily used to treat tumors of the central nervous system. We describe 2 patients with apparent TMZ-induced central diabetes insipidus. Using our institution's Research Patient Database Registry, we identified 3 additional potential cases of TMZ-induced diabetes insipidus among a group of 1545 patients treated with TMZ. A 53-year-old male with an oligoastrocytoma and a 38-year-old male with an oligodendroglioma each developed symptoms of polydipsia and polyuria approximately 2 months after the initiation of TMZ. Laboratory analyses demonstrated hypernatremia and urinary concentrating defects, consistent with the presence of diabetes insipidus, and the patients were successfully treated with desmopressin acetate. Desmopressin acetate was withdrawn after the discontinuation of TMZ, and diabetes insipidus did not recur. Magnetic resonance imaging of the pituitary and hypothalamus was unremarkable apart from the absence of a posterior pituitary bright spot in both of the cases. Anterior pituitary function tests were normal in both cases. Using the Research Patient Database Registry database, we identified the 2 index cases and 3 additional potential cases of diabetes insipidus for an estimated prevalence of 0.3% (5 cases of diabetes insipidus per 1545 patients prescribed TMZ). Central diabetes insipidus is a rare but reversible side effect of treatment with TMZ.
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.
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.
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.
伍慧玲
2012-01-01
研究一类具有离散时间、外界捕获、毒素作用的捕食-食饵系统,通过运用比较引理和构造恰当的Lyapunov函数,证明了系统的持久性和全局吸引性,最后,我们给出了捕食者、食饵种群绝灭的充分条件.%A discrete predator-prey model with harvesting and toxicity was studied.By using comparison theorem and constructing a suitable Lyapunov function,the permanence and global attractivity of the system were proved.Sufficient conditions for the extinction of the predator and prey were given.
一类具阶段结构的捕食者-食饵模型的渐进性质%Asymptotic Behavior of a Predator-Prey Population Model with Stage-Structure
肖氏武; 王稳地; 金瑜
2007-01-01
This paper studies the asymptotic behavior of a predator-prey system with stage structure. It is assumed that the transition rate from immature stage to mature stage depends on the density of immature individuals. Conditions for the permanence and extinction of the predator are obtained. It is also found that the model admits an orbitally asymptotically stable periodic orbit.%研究了一类具阶段结构的捕食者-食饵模型的渐近性质.文中假设由幼年阶段转化为成年阶段的转化率依赖于幼年个体数量.建立了捕食种群一致持续生存与绝灭的条件.证明了稳定的周期解的存在性.
黄晓鑫; 张天四
2014-01-01
考虑了一类额外食饵补充的随机捕食模型，讨论了随机系统全局正解的存在唯一性，给出了随机模型存在平稳分布的条件，讨论了食饵种群、捕食者种群的绝灭条件。最后通过数值仿真验证了上述结论的正确性。%We consider an additional food provided predator-prey system with stochastic perturbation. There exists a unique positive solution of the system with positive initial value, and the existence of the stochastic model stationary distribution is proved. Moreover, the conditions for the system to be extinct are given and the conclusions are verified by numerical simulation.
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.
An unreported complication of acute pancreatitis
G Muthukumarasamy; V Shanmugam; SR Yule; R Ravindran
2007-01-01
Acute pancreatitis constitutes 3% of all admissions with abdominal pain. There are reports of osteal fat necrosis leading to periosteal reactions and osteolytic lesions following severe pancreatitis, particularly in long bones.A 54-year-old man was admitted to our hospital with acute pancretitis, who later developed spinal discitis secondary to necrotizing pancreatitis. He was treated conservatively with antibiotics and after a month he recovered completely without any neurological deficit.This case is reported for its unusual and unreported spinal complications after acute pancreatitis.
Hitherto unreported Agaricus species of Central India
MAHENDRA KUMAR RAI
2010-11-01
Full Text Available Karwa A, Rai MK. 2010. Hitherto unreported Agaricus species of Central India. Nusantara Bioscience 2: 141-145. Melghat forest region from Central India was surveyed for occurrence of medicinal and culinary mushrooms during the years 2005-2008. Out of total 153 species, ten species of Agaricus were recorded from different localities. Of these, seven species namely Agaricus bitorquis, A. subrufescens, A. augustus, A. placomyces, A. essettei, A. basioanolosus and Agaricus sp. nov (a new species are being reported for the first time from the region. The commercial button mushroom Agaricus bisporus lacks good breeding characters due to its bisporic nature. These wild cousins of the button mushroom can definitely prove to be a good source of genetic manipulations to the existing strains and also to develop new strains with improved characters.
李兵方; 郭改慧; 白云霄
2013-01-01
Under homogeneous Dirichlet boundary conditions, a predator-prey model with predator cannibalism is con-sidered.The existence and uniqueness of positive solutions are presented.By maximum principles and lower-upper solu-tion methods, a prior estimate of positive solutions is firstly obtained.Then by Leray-Schauder theory and resorting to calculate fixed point indices of compact maps in cones, sufficient conditions for coexistence are given.Moreover, the u-niqueness of positive solutions is derived under some conditions.%在齐次Dirichlet边界条件下研究一类种内相食的捕食-食饵模型正解的存在性和惟一性。首先利用极值原理、上下解方法给出正解的先验估计，然后利用Leray-Schauder度理论，通过计算锥映射不动点指标得到正解的存在性，最后利用特征值变分原理给出正解存在的惟一性。
谭德君
2012-01-01
建立一个具有脉冲效应的非自治随机的比例依赖的捕食-食饵模型,通过研究具有脉冲效应的非自治随机系统与无脉冲效应的非自治随机系统的等价性,证明该模型的有界性,均值一致有界和灭绝性等动力学性质.%A model of a non-autonomous ratio-dependent predator-prey system with impulsive effects and random perturbation is builded. The equivalent relation between the solution of non-autonomous stochastic differential system with impulsive effects and that of a corresponding non autonomous stochastic differential system with impulsive effect is researched. Moreover, we prove some dynamic behavior of this system for the boundedness, uniformly bounded in the mean and extinction of this system.
刘开源
2008-01-01
A Leslie-Cower predator-prey model with birth pulse is investigated. By the stroboscopic map, we obtain an exact periodic solution of the system which has Ricker function or Beverton-Holt function. Further, by Floquet theorem and comparison theorem, we discuss the extinction and permanence of the system. Finally, by numeri-cally analyzing the bifurcation diagrams with bifurcation parameter b (or p ), we know birth pulse brings the system complexly dynamic behaviors including period-doubling route, chaos and periodic windows within the chaotic region.%研究了一个具有脉冲出生的Leslie-Gower捕食者-食饵系统的动力学性质.利用频闪映射,得到了带有Ricker和Beverton-Holt函数的脉冲系统准确的周期解.通过Floquet定理和脉冲比较定理,讨论了该系统的灭绝和持久生存.最后,数值分析了以b(p)为分支参数的分支图,得到的结论是脉冲出生会带给系统倍周期分支、混沌以及在混沌带中出现周期窗口等复杂的动力学行为.
史红波; 李万同; 林国
2011-01-01
该文讨论了带有Robin边界条件的一类修正Leslie-Gower型捕食系统,建立了系统共存解的存在性、稳定性与不存在性,并讨论了抛物系统的长时间行为.结果表明,系统中种群的内秉增长率及椭圆问题Robin边界条件下的主特征值在讨论系统正共存解的存在性与不存在性以及种群的灭绝中发挥了重要作用.%This paper is concerned with a modified Leslie-Gower predator-prey system with Robin boundary conditions. The existence/nonexistence and stability of coexistence solutions are obtained. Furthermore, the long-time behavior of parabolic system is also investigated. The results show that the intrinsic growth rates and the principle eigenvalues of the corresponding elliptic problems with respect to the Robin boundary conditions play more important roles than other parameters for the existence/nonexistence of nonconstant positive steady-state solutions and the extinction of the species.
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。
王斌
2011-01-01
Based on the theory of the time scales and topological degree theory, by using continuation theorem of coincidence degree theory and some skills of integral inequalities on time scales, the sufficient condition of the existence of periodic solutions for a non-autonomous predator-prey system with time delays on time scales is obtained. The obtained result has practical significance and application value in ecological management.%在时标理论和拓扑度理论基础之上，通过应用重合度理论的连续定理和一些时标上积分不等式技巧，给出了时标上一类具有可变时滞的非自治捕食者一食饵系统周期解存在性的充分条件。取得的结果在生态管理中具有现实意义和应用价值。
张忠文
2015-01-01
A nonlocal and time-delayed reaction-diffusion predator-prey model was studied, where prey individuals undergo two stages, i.e. immature and mature, and the conversion of consumed from prey biomass to predator biomass has a retardation. The growth of the prey population obeys general Beverton-Holt function. By discussing the principal eigenvalue of nonlocal elliptic problems, we showed an explicit expression of the principal eigenvalue, the suﬃcient conditions for the uniform persistence and global extinction for the model could be established. By the fluctuation method, the global attractivity of the unique positive constant steady state was obtained.%考虑一类带阶段结构的扩散捕食者食饵模型，其中食饵个体经历两个生命阶段，未成熟和成熟阶段，捕食者生物量的转化有一个延迟，食饵生物量的增长遵循一般化的Beverton-Holt函数。就非局部椭圆特征问题的主特征值，建立一致持久性与全局灭绝性。利用波动方法，给出唯一正常数稳态解的全局吸引性。
王志丽; 徐瑞
2015-01-01
A predator-prey model with time delay and Gompertz growth rate is considered.First, the local stability of each feasible equilibrium is established by analyzing the corresponding characteristic equation,and the existence of the Hopf bifurcation at the positive equilibrium is also obtained.Then,by using Lyapunov functional and the iteration scheme,the global asymptotic stability of each feasible equilibrium is discussed.Finally,numerical simulations are carried out to illustrate the theoretical results.%研究一类含有时滞和 Gompertz 增长率的捕食-被捕食模型。首先，通过分析特征方程研究非负平衡点的局部稳点性，并得到 Hopf 分支存在的充分条件；然后，通过构造 Lyapunov 泛函，运用单调迭代方法，讨论非负平衡点的全局渐近稳定性；最后，对所得理论结果进行数值模拟。
陈秀荣; 杨治伟
2012-01-01
利用同伦分析方法,研究了一类分数阶Lotka-volterra捕食模型,得到了该模型近似解的表达式.研究结果表明,同伦分析方法可以简化分数阶方程复杂的求解过程,该方法用于研究分数阶Lotka-volterra捕食模型完全可行,因此,拓宽了同伦分析方法的应用范围.%A fractional-order Lotka-volterra predator-prey model was considered in this study. By use of homotopy analysis method,the approximate solution for the model was obtained. The result shows that the method is reasonable and practical which can simplify the complex processing of finding the model's solution. Therefore, this paper may be extended the application range of the homotopy analysis method.
蒋芮; 刘华; 谢梅; 魏玉梅; 赵仕凤
2016-01-01
This paper studied the dynamic complexity of a class of discrete population model by computer simulation. The autonomous predator-prey system model is established through theoretical derivation, which has Allee effect and Holling II functional effect. The growth states of discrete-time populations are simulated to explore the influence of the parameters’changes to its population size by MATLAB. It also illustrated the importance of Allee effect and Holling II functional in the model of interaction among populations. The research results show that the larger the processing time, the bigger parameter region for stable coexistence population when the processing time is within the effective range. The introduction of Allee effect makes dynamic behavior of the population more complicated, thus increase the extinction risk of predator population. The population appears bifurcation in advance when predator-prey system strongly affected by Allee effect. It will lead to population extinction, if Allee effect increasingly raises. The strong Allee effect is more prone to population extinction. The conclusion of this paper not only enriches the theory of ecology, but also puts forward important basis of conservation ecology.%利用计算机模拟方法研究一类离散种群相互作用模型的动态复杂性。通过理论推导建立食饵具有Allee效应和HollingⅡ型功能反应的自治捕食系统模型，用Matlab软件模拟离散种群的生长状态，探索研究参数的变化对种群大小的影响，阐释Allee效应及HollingⅡ型功能反应在种群间相互作用模型中的重要性。研究结果表明：1)当处理时间处于有效区间内时，处理时间越大种群的稳定共存参数域越大；2)Allee效应的引入使种群的动态行为更为复杂，从而增加了捕食者种群的灭绝风险；3)系统受强Allee效应的影响，种群会出现提前分叉现象，如果继续增加Allee效应就会导致种群灭绝；4)强Allee
Beretta, E; Capasso, V; Rinaldi, F
1988-01-01
The paper contains an extension of the general ODE system proposed in previous papers by the same authors, to include distributed time delays in the interaction terms. The new system describes a large class of Lotka-Volterra like population models and epidemic models with continuous time delays. Sufficient conditions for the boundedness of solutions and for the global asymptotic stability of nontrivial equilibrium solutions are given. A detailed analysis of the epidemic system is given with respect to the conditions for global stability. For a relevant subclass of these systems an existence criterion for steady states is also given.
Chronic pain in Noonan Syndrome: A previously unreported but common symptom.
Vegunta, Sravanthi; Cotugno, Richard; Williamson, Amber; Grebe, Theresa A
2015-12-01
Noonan syndrome (NS) is a multiple malformation syndrome characterized by pulmonic stenosis, cardiomyopathy, short stature, lymphatic dysplasia, craniofacial anomalies, cryptorchidism, clotting disorders, and learning disabilities. Eight genes in the RAS/MAPK signaling pathway are implicated in NS. Chronic pain is an uncommon feature. To investigate the prevalence of pain in NS, we distributed a two-part questionnaire about pain among NS individuals at the Third International Meeting on Genetic Syndromes of the Ras/MAPK Pathway. The first part of the questionnaire queried demographic information among all NS participants. The second part was completed by individuals with chronic pain. Questions included musculoskeletal problems and clinical features of pain. Forty-five questionnaires were analyzed; 53% of subjects were female. Mean age was 17 (2-48) years; 47% had a PTPN11 mutation. Sixty-two percent (28/45) of individuals with NS experienced chronic pain. There was a significant relationship between prevalence of pain and residing in a cold climate (P = 0.004). Pain occurred commonly in extremities/joints and head/trunk, but more commonly in extremities/joints (P = 0.066). Subjects with hypermobile joints were more likely to have pain (P = 0.052). Human growth hormone treatment was not statistically significant among subjects without chronic pain (P = 0.607). We conclude that pain is a frequent and under-recognized clinical feature of NS. Chronic pain may be associated with joint hypermobility and aggravated by colder climate. Our study is a preliminary investigation that should raise awareness about pain as a common symptom in children and adults with NS.
Tavaré Simon
2010-04-01
Full Text Available Abstract Background A key stage for all microarray analyses is the extraction of feature-intensities from an image. If this step goes wrong, then subsequent preprocessing and processing stages will stand little chance of rectifying the matter. Illumina employ random construction of their BeadArrays, making feature-intensity extraction even more important for the Illumina platform than for other technologies. In this paper we show that using raw Illumina data it is possible to identify, control, and perhaps correct for a range of spatial-related phenomena that affect feature-intensity extraction. Results We note that feature intensities can be unnaturally high when in the proximity of a number of phenomena relating either to the images themselves or to the layout of the beads on an array. Additionally we note that beads neighbour beads of the same type more often than one might expect, which may cause concern in some models of hybridization. We highlight issues in the identification of a bead's location, and in particular how this both affects and is affected by its intensity. Finally we show that beads can be wrongly identified in the image on either a local or array-wide scale, with obvious implications for data quality. Conclusions The image processing issues identified will often pass unnoticed by an analysis of the standard data returned from an experiment. We detail some simple diagnostics that can be implemented to identify problems of this nature, and outline approaches to correcting for such problems. These approaches require access to the raw data from the arrays, not just the summarized data usually returned, making the acquisition of such raw data highly desirable.
Min Su Cheong
2010-07-01
Full Text Available We present an unusual case of concurrent occurrence of a multilocular cystic renal cell carcinoma and a leiomyoma in the same kidney of a patient with no evident clinical symptoms. A 38-year-old man was found incidentally to have a cystic right renal mass on computed tomography. Laparoscopic radical nephrectomy was performed under a preoperative diagnosis of cystic renal cell carcinoma. Histology revealed a multilocular cystic renal cell carcinoma and a leiomyoma. This is the first report of this kind of presentation.
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．
张莉敏; 唐玉萍
2010-01-01
探讨一类食饵具有阶段结构和自食作用的非自治捕食系统.利用等价变换,证明此系统在一定条件下的持久生存性;利用Brouwer不动点定理得到系统正周期解在一定条件下的存在性.%A nonautonomous predator-prey system with stage structure and cannibalism for prey is proposed and analyzed. By using equivalent transformations, sufficient conditions are obtained for the permanence of the system. By utilizing Brouwer fixed point theorem, the existence of positive periodic solution is also discussed.
王斌
2013-01-01
在时标理论和拓扑度理论基础之上,通过应用重合度理论的连续定理和时标上积分不等式技巧,给出了时标上一类具有Holling Ⅱ型功能性反应的非自治捕食者-食饵系统周期解的存在性的充分条件.%Based on the theory of the time scales and topological degree theory, by means of continuation theorem of coincidence degree theory and some skills of integral inequalities on time scales, the sufficient condition of the existence of periodic solutions for a non-autonomous predator-prey system Holling type-Ⅱ functional response on time scales has been obtained. The result is of practical significance and application value in ecological management.
曾广钊; 孙丽华
2005-01-01
讨论了一类非自治阶段结构带有消化时滞的两种群捕食模型,其中只有一个种群有阶段结构.本文得到了这个系统能够持久生存的条件.进一步,如果这个系统是周期系统我们证明了在一定条件下系统存在唯一的全局渐近稳定的正周期解.%This paper considered an non-autonomous predator-prey two-species model with digest delay and stage structure in one species. The conditions of perma nence of it are gotten. Furthermore, existence and asymptotically stability of periodic solution have been proved under some assumptions if this model turns out to be a periodic system.
Adams, Darrin A.; Bonauto, David K.
2016-01-01
Background Studies suggest employers underreport injuries to the Bureau of Labor Statistics Survey of Occupational Injuries and Illnesses (SOII); less is known about reporting differences by establishment characteristics. Methods We linked SOII data to Washington State workers’ compensation claims data, using unemployment insurance data to improve linking accuracy. We used multivariable regression models to estimate incidence ratios (IR) of unreported workers’ compensation claims for establishment characteristics. Results An estimated 70% of workers’ compensation claims were reported in SOII. Claims among state and local government establishments were most likely to be reported. Compared to large manufacturing establishments, unreported claims were most common among small educational services establishments (IR = 2.47, 95%CI: 1.52–4.01) and large construction establishments (IR = 2.05, 95%CI: 1.77–2.37). Conclusions Underreporting of workers’ compensation claims to SOII varies by establishment characteristics, obscuring true differences in work injury incidence. Findings may differ from previous research due to differences in study methods. Am. J. Ind. Med. 59:274–289, 2016. © 2016 The Authors. American Journal of Industrial Medicine Published by Wiley Periodicals, Inc. PMID:26792563
Unreported complication of Bravo pH capsule dislodged intothe pyriform sinus
2015-01-01
We report an unexpected, previously unreported complicationof Bravo pH capsule dislodgement. During BravopH testing of a 44-year-old man with gastroesophagealreflux disease, we were unable to endoscopicallyvisualize the capsule attached to the esophageal wallafter deployment. After multiple attempts to detect thecapsule, it was visualized in the left pyriform sinus. Asthere was significant risk for pulmonary dislodgement,ENT and pulmonary physicians were immediatelyconsulted to review options for safe removal. Ultimately,ENT successfully retrieved the capsule with a foreignbody removal forceps. The Bravo pH test is generallya well-tolerated diagnostic tool used to confirm thepresence of abnormal esophageal acid reflux. While fewcomplications have been reported, technical difficultiescan occur, including poor data reception, misplacement,and early dislodgement. Rarely, more serious complicationscan occur, ranging from esophageal wall traumato capsule aspiration. Gastroenterologists performingthis procedure should be aware of the low, but nontrivial,risk of complications.
刘海玉; 罗勇; 胡亦郑
2015-01-01
In this paper, a stage-structured predator-prey model with continuous harvesting and impulsive effect is investigated by means of comparative theorem of impulse differential equation. The dynamic behaviors of the model are considered. The beingness of the periodic solution is discussed and the sufficient conditions of overall attractions and continuous existence of the system for the predator extinct periodic solution turn to be obtained.%运用脉冲微分方程的比较定理，研究了一类具有脉冲扰动与捕食者具有连续收获的时滞捕食-双食饵模型，证明了系统所有解的一致完全有界，讨论了周期解的存在性，得到捕食者灭绝周期解的全局吸引性和系统持续生存的充分条件。
A hitherto unreported disruption of cervical branches of facial artery
Sharma P
2011-03-01
Full Text Available According to its course, the branches of the facial artery are arranged under two headings; cervical component (branches in the digastric triangle and facial component (branches on the face.Variations in the branches of the facial component of the facial artery have been frequently studied and reported. However, variations in the cervical component are rare. A hitherto unreported variant of the cervical component of the facial artery was observed in a 55-year-old male cadaver during routine undergraduate dissection. The facial artery was arising from the external carotid artery as a common trunk with the lingual artery in the right carotid triangle and its ascending palatine and tonsillar branches were arising from the external carotid artery. It is important for surgeons and radiologists to be aware of the normal anatomy of the facial artery and the external carotid artery. Herein, we describe the detailed anatomical features of the variant branching pattern of the right facial artery and its clinical implications.
Marimuthu Munien V BMW Financial Services (SA (PTY LTD Unreported
C van Heerden
2009-12-01
Full Text Available Section 129(1(a read with section 130(1 and 130(3 of the National Credit Act 34 of 2005 (the NCA provides that, as a required procedure before debt enforcement, a credit provider must draw the default to the consumer's notice in writing and propose that the consumer refer the credit agreement to a debt counsellor, alternative dispute resolution agent, consumer court or ombud with jurisdiction, with the intent that the parties resolve any dispute under the agreement or develop and agree on a plan to bring the payments under the agreement up to date. Even though section 129(1(a is silent as to the method by which the default should be brought to the consumer's notice, section 130(1(a provides clarity by requiring the section 129(1(a notice to be delivered. It appears that a credit provider who fails to comply with the provisions of section 129(1(a prior to debt enforcement by means of litigation will be in a procedural predicament as the credit provider will not possess a complete cause of action thus, for instance, rendering the summons excipiable. The crucial question thus appears to be whether or not in a given situation one may say that there was proper compliance with section 129(1(a as this directly affects the existence or absence of a complete and proper cause of action. A number of factors has to be considered in order to address this question, the most important being if the section 129(1(a notice was duly 'delivered'. In this regard two questions are especially relevant:a When exactly can it be said that a section 129(1(a notice was 'delivered' for purposes of the NCA?b Is it necessary for such notice to be received by the consumer in order to constitute proper compliance with the delivery requirement pertaining to section 129(1(a?The above questions were decided on in a recent judgment, Marimuthu Munien v BMW Financial Services (SA (Pty Ltd Case no 16103/08 (KZD (unreported. This article will analyse section 129(1(a of the NCA by inter
Basant Repswal; Anuj Jain; Sunil Gupta; Aditya Aggarwal; Tushar Kohli; Devendra Pathrot
2014-01-01
Fall from height is a common cause of unintentional injuries in children and accounts for 6％ of all trauma-related childhood deaths,usually from head injury.We report a case of a 2-year-old child with multiple fractures of the bilateral lower limbs due to this reason.A child fell from a height of around 15 feet after toppling from a balcony.He developed multiple fractures involving the right femoral shaft,right distal femoral epiphysis (Salter Harris type 2),right distal metaphysis of the tibia and fibula,and undisplaced Salter Harris type 2 epiphyseal injury of the left distal tibia.There were no head,abdominal or spinal injuries.The patient was taken into emergency operation theatre after initial management which consisted of intravenous fluids,blood transfusion,and splintage of both lower limbs.Fracture of the femoral shaft was treated by closed reduction and fixation using two titanium elastic nails.Distal femoral physeal injury required open reduction and fixation with K wires.Distal tibia fractures were closely reduced and managed nonoperatively in both the lower limbs.All the fractures united in four weeks.At the last follow-up,the child had no disability and was able to perform daily activities comfortably.We also proposed the unique mechanism of injury in this report.
Anuj Jain
2014-10-01
Full Text Available 【Abstract】Fall from height is a common cause of unintentional injuries in children and accounts for 6% of all trauma-related childhood deaths, usually from head injury. We report a case of a 2-year-old child with multiple fractures of the bilateral lower limbs due to this reason. A child fell from a height of around 15 feet after toppling from a alcony. He developed multiple fractures involving the right femoral shaft, right distal femoral epiphysis (Salter Harris type 2, right distal metaphysis of the tibia and fi bula, and undisplaced Salter Harris type 2 epiphyseal injury of the left distal tibia. There were no head, abdominal or spinal injuries. The patient was taken into emergency operation theatre after initial management which consisted of intravenous fl uids, blood transfusion, and splintage of both lower limbs. Fracture of the femoral shaft was treated by closed reduction and fixation using two titanium elastic nails. Distal femoral physeal injury required open eduction and fixation with K wires. Distal tibia fractures were closely reduced and managed nonoperatively in both the lower limbs. All the fractures united in four weeks. At the last follow-up, the child had no disability and was able to perform daily ctivities comfortably. We also proposed the unique mechanism of injury in this report. Key words: Multiple bilateral lower limb fractures; Fall; Child
Moore, A B M; McCarthy, I D; Carvalho, G R; Peirce, R
2012-04-01
This paper presents data from the first major survey of the diversity, biology and fisheries of elasmobranchs in the Persian (Arabian) Gulf. Substantial landings of elasmobranchs, usually as gillnet by-catch, were recorded in Kuwait, Qatar and the Emirate of Abu Dhabi (part of the United Arab Emirates), although larger elasmobranchs from targeted line fisheries were landed in Abu Dhabi. The elasmobranch fauna recorded was distinctive and included species that are undescribed, rare and have a highly restricted known distribution. Numerical abundance was dominated by sharks (c. 80%), of which carcharhinids were by far the most important. The milk shark Rhizoprionodon acutus and whitecheek shark Carcharhinus dussumieri together comprised just under half of all recorded individuals. Around 90% of recorded sharks were small (50-90 cm total length, L(T) ) individuals, most of which were mature individuals of species with a small maximum size (shark species) and include some notable differences from other locations in the Indo-West Pacific Ocean. A number of concerns regarding the sustainability of the fishery were highlighted by this study, notably that most of the batoid species recorded are classed by the IUCN Red List as vulnerable, endangered, data deficient or not evaluated. Despite their considerable elasmobranch landings, none of the three countries sampled have developed a 'Shark Plan' as encouraged to do so under the FAO International Plan of Action: Sharks. Furthermore, Kuwait and Qatar currently report zero or no elasmobranch landings to the FAO.
A Case of Acute Myeloid Leukemia with a Previously Unreported Translocation (14; 15 (q32; q13
Mohamad Khawandanah
2014-01-01
Full Text Available Background. We hereby describe what we believe to be the first reported case of t (14; 15 (q32; q13 associated with acute myeloid leukemia (AML. Methods. PubMed, Embase, and OVID search engines were used to review the related literature and similar published cases. Case. A47-year-old female presented in December 2011 with AML (acute myelomonocytic leukemia with normal cytogenetics; molecular testing revealed FLT-3 internal tandem duplication (ITD mutation, while no mutations involving FLT3 D385/I836, NPM1 exon 12, or KIT exons 8 and 17 were detected. She was induced with 7 + 3 (cytarabine + idarubicin and achieved complete remission after a second induction with high-dose cytarabine (HiDAC followed by uneventful consolidation. She presented 19 months after diagnosis with relapsed disease. Of note, at relapse cytogenetic analysis revealed t (14; 15 (q32; q13, while FLT-3 analysis showed a codon D835 mutation (no ITD mutation was detected. She proved refractory to the initial clofarabine-based regimen, so FLAG-idarubicin then was used. She continued to have persistent disease, and she was discharged on best supportive care. Conclusion. Based on this single case of AML with t (14; 15 (q32; q13, this newly reported translocation may be associated with refractory disease.
A previously unreported type of seismic source in the firn layer of the East Antarctic Ice Sheet
Lough, Amanda C.; Barcheck, C. Grace; Wiens, Douglas A.; Nyblade, Andrew; Anandakrishnan, Sridhar
2015-11-01
We identify a unique type of seismic source in the uppermost part of the East Antarctic Ice Sheet recorded by temporary broadband seismic arrays in East Antarctica. These sources, termed "firnquakes," are characterized by dispersed surface wave trains with frequencies of 1-10 Hz detectable at distances up to 1000 km. Events show strong dispersed Rayleigh wave trains and an absence of observable body wave arrivals; most events also show weaker Love waves. Initial events were discovered by standard detection schemes; additional events were then detected with a correlation scanner using the initial arrivals as templates. We locate sources by determining the L2 misfit for a grid of potential source locations using Rayleigh wave arrival times and polarization directions. We then perform a multiple-filter analysis to calculate the Rayleigh wave group velocity dispersion and invert the group velocity for shear velocity structure. The resulting velocity structure is used as an input model to calculate synthetic seismograms. Inverting the dispersion curves yields ice velocity structures consistent with a low-velocity firn layer ~100 m thick and show that velocity structure is laterally variable. The absence of observable body wave phases and the relative amplitudes of Rayleigh waves and noise constrain the source depth to be less than 20 m. The presence of Love waves for most events suggests the source is not isotropic. We propose the events are linked to the formation of small crevasses in the firn, and several events correlate with shallow crevasse fields mapped in satellite imagery.
A new predator of the coffee berry borer, Hypothenemus hampei, was found in the coffee growing area of Kisii in Western Kenya. Field observations, laboratory trials and gut content analysis using molecular tools have confirmed the role of the predatory thrips Karnyothrips flavipes Jones (Phlaeothrip...
A careful evaluation of scout CT lateral radiograph may prevent unreported vertebral fractures
Bazzocchi, Alberto; Spinnato, Paolo [Imaging Division, Clinical Department of Radiological and Histocytopathological Sciences, University of Bologna, Sant’Orsola – Malpighi Hospital, Via Massarenti 9, 40138 Bologna (Italy); Albisinni, Ugo [Department of Radiology, Rizzoli Orthopaedic Institute, Via Pupilli 1, 40136 Bologna (Italy); Battista, Giuseppe [Imaging Division, Clinical Department of Radiological and Histocytopathological Sciences, University of Bologna, Sant’Orsola – Malpighi Hospital, Via Massarenti 9, 40138 Bologna (Italy); Rossi, Cristina [Section of Radiological Sciences, Department of Clinic Sciences, University of Parma, Via Gramsci 14, 43100 Parma (Italy); Guglielmi, Giuseppe, E-mail: g.guglielmi@unifg.it [Department of Radiology, University of Foggia, Viale Luigi Pinto 1, 71100 Foggia (Italy); Department of Radiology, Scientific Institute “Casa Sollievo della Sofferenza” Hospital, Viale Cappuccini 1, 71013 San Giovanni Rotondo, Foggia (Italy)
2012-09-15
Objectives: Our purpose was to review scout CT lateral radiographs to reveal osteoporotic vertebral fractures unreported by radiologists and to explore scout CT as a potential diagnostic tool in the detection of vertebral fractures. Methods: We considered 500 patients (303 males, 197 females, age 64.6 ± 13.5 year-old). Our investigation was firstly focused on scout CT lateral images to detect vertebral fractures with a combined semiquantitative and quantitative diagnostic approach. Findings addressed to vertebral fracture were subsequently confirmed by multiplanar sagittal CT reconstructions. Whenever a vertebral fracture was discovered the radiologist report was read and a collection of patient anamnesis followed to understand whether fractures were already known. Results: In 44/500 patients (8.8%) the evaluation on scout CT was incomplete or limited for patient/technical-based conditions, and 15 were excluded from the analysis. In 67/485 patients (13.8%) 99 vertebral fractures were detected. Among 67 fractured patients only 18 (26.9%) were previously diagnosed by radiologists. However, in the clinical history of 32 patients vertebral fractures were already known. Conclusions: The perception and sensibility to vertebral fractures among radiologists are still poor when the assessment of the spine is not the aim of the examination. Short time spent for the evaluation of scout CT lateral radiographs could improve our accuracy.
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.
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.
Vertebrate predator-prey interactions in a seasonal environment
Schmidt, Niels Martin; Berg, Thomas B; Forchhammer, Mads
2008-01-01
winters, predation by the only remaining predator, the stoat, is insufficient to regulate the lemming population. In the predator-lemming model, seasonality plays an important role in determining the. growth rate of the lemming population as well as the density of the various lemming predators. We...
Spatial geographic mosaic in an aquatic predator-prey network.
Chaves-Campos, Johel; Johnson, Steven G; Hulsey, C Darrin
2011-01-01
The geographic mosaic theory of coevolution predicts 1) spatial variation in predatory structures as well as prey defensive traits, and 2) trait matching in some areas and trait mismatching in others mediated by gene flow. We examined gene flow and documented spatial variation in crushing resistance in the freshwater snails Mexipyrgus churinceanus, Mexithauma quadripaludium, Nymphophilus minckleyi, and its relationship to the relative frequency of the crushing morphotype in the trophically polymorphic fish Herichthys minckleyi. Crushing resistance and the frequency of the crushing morphotype did show spatial variation among 11 naturally replicated communities in the Cuatro Ciénegas valley in Mexico where these species are all endemic. The variation in crushing resistance among populations was not explained by geographic proximity or by genetic similarity in any species. We detected clear phylogeographic patterns and limited gene flow for the snails but not for the fish. Gene flow among snail populations in Cuatro Ciénegas could explain the mosaic of local divergence in shell strength and be preventing the fixation of the crushing morphotype in Herichthys minckleyi. Finally, consistent with trait matching across the mosaic, the frequency of the fish morphotype was negatively correlated with shell crushing resistance likely reflecting the relative disadvantage of the crushing morphotype in communities where the snails exhibit relatively high crushing resistance.
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.
Bifurcations and dynamics of a discrete predator-prey system.
Asheghi, Rasoul
2014-01-01
In this paper, we study the dynamics behaviour of a stratum of plant-herbivore which is modelled through the following F(x, y)=(f(x, y), g(x, y)) two-dimensional map with four parameters defined by [Formula: see text] where x ≥ 0, y ≥ 0, and the real parameters a, b, r, k are all positive. We will focus on the case a ≠ b. We study the stability of fixed points and do the analysis of the period-doubling and the Neimark-Sacker bifurcations in a standard way.
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.
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.