Emma R. Schachner
Full Text Available The lungs of birds have long been known to move air in only one direction during both inspiration and expiration through most of the tubular gas-exchanging bronchi (parabronchi. Recently a similar pattern of airflow has been observed in American alligators, a sister taxon to birds. The pattern of flow appears to be due to the arrangement of the primary and secondary bronchi, which, via their branching angles, generate inspiratory and expiratory aerodynamic valves. Both the anatomical similarity of the avian and alligator lung and the similarity in the patterns of airflow raise the possibility that these features are plesiomorphic for Archosauria and therefore did not evolve in response to selection for flapping flight or an endothermic metabolism, as has been generally assumed. To further test the hypothesis that unidirectional airflow is ancestral for Archosauria, we measured airflow in the lungs of the Nile crocodile (Crocodylus niloticus. As in birds and alligators, air flows cranially to caudally in the cervical ventral bronchus, and caudally to cranially in the dorsobronchi in the lungs of Nile crocodiles. We also visualized the gross anatomy of the primary, secondary and tertiary pulmonary bronchi of C. niloticus using computed tomography (CT and microCT. The cervical ventral bronchus, cranial dorsobronchi and cranial medial bronchi display similar characteristics to their proposed homologues in the alligator, while there is considerable variation in the tertiary and caudal group bronchi. Our data indicate that the aspects of the crocodilian bronchial tree that maintain the aerodynamic valves and thus generate unidirectional airflow, are ancestral for Archosauria.
Full Text Available Many of the major locomotor transitions during the evolution of Archosauria, the lineage including crocodiles and birds as well as extinct Dinosauria, were shifts from quadrupedalism to bipedalism (and vice versa. Those occurred within a continuum between more sprawling and erect modes of locomotion and involved drastic changes of limb anatomy and function in several lineages, including sauropodomorph dinosaurs. We present biomechanical computer models of two locomotor extremes within Archosauria in an analysis of joint ranges of motion and the moment arms of the major forelimb muscles in order to quantify biomechanical differences between more sprawling, pseudosuchian (represented the crocodile Crocodylus johnstoni and more erect, dinosaurian (represented by the sauropodomorph Mussaurus patagonicus modes of forelimb function. We compare these two locomotor extremes in terms of the reconstructed musculoskeletal anatomy, ranges of motion of the forelimb joints and the moment arm patterns of muscles across those ranges of joint motion. We reconstructed the three-dimensional paths of 30 muscles acting around the shoulder, elbow and wrist joints. We explicitly evaluate how forelimb joint mobility and muscle actions may have changed with postural and anatomical alterations from basal archosaurs to early sauropodomorphs. We thus evaluate in which ways forelimb posture was correlated with muscle leverage, and how such differences fit into a broader evolutionary context (i.e. transition from sprawling quadrupedalism to erect bipedalism and then shifting to graviportal quadrupedalism. Our analysis reveals major differences of muscle actions between the more sprawling and erect models at the shoulder joint. These differences are related not only to the articular surfaces but also to the orientation of the scapula, in which extension/flexion movements in Crocodylus (e.g. protraction of the humerus correspond to elevation/depression in Mussaurus. Muscle
William G. Parker
Full Text Available Aetosaurians are some of the most common fossils collected from the Upper Triassic Chinle Formation of Arizona, especially at the Petrified Forest National Park (PEFO. Aetosaurians collected from lower levels of the park include Desmatosuchus spurensis, Paratypothorax, Adamanasuchus eisenhardtae, Calyptosuchus wellesi, and Scutarx deltatylus. Four partial skeletons collected from the park between 2002 and 2009 represent the holotype and referred specimens of Scutarx deltatylus. These specimens include much of the carapace, as well as the vertebral column, and shoulder and pelvic girdles, and a new naming convention proposed for osteoderms descriptions better differentiates portions of the carapace and ventral armor. A partial skull from the holotype specimen represents the first aetosaur skull recovered and described from Arizona since the 1930s. The key morphological feature distinguishing Scutarx deltatylus is the presence of a prominent, triangular boss located in the posteromedial corner of the dorsal surface of the dorsal paramedian osteoderms. Scutarx deltatylus can be distinguished from closely related forms Calyptosuchus wellesi and Adamanasuchus eisenhardtae not only morphologically, but also stratigraphically. Thus, Scutarx deltatylus is potentially an index taxon for the upper part of the Adamanian biozone.
Full Text Available Abstract Background The morphological peculiarities of turtles have, for a long time, impeded their accurate placement in the phylogeny of amniotes. Molecular data used to address this major evolutionary question have so far been limited to a handful of markers and/or taxa. These studies have supported conflicting topologies, positioning turtles as either the sister group to all other reptiles, to lepidosaurs (tuatara, lizards and snakes, to archosaurs (birds and crocodiles, or to crocodilians. Genome-scale data have been shown to be useful in resolving other debated phylogenies, but no such adequate dataset is yet available for amniotes. Results In this study, we used next-generation sequencing to obtain seven new transcriptomes from the blood, liver, or jaws of four turtles, a caiman, a lizard, and a lungfish. We used a phylogenomic dataset based on 248 nuclear genes (187,026 nucleotide sites for 16 vertebrate taxa to resolve the origins of turtles. Maximum likelihood and Bayesian concatenation analyses and species tree approaches performed under the most realistic models of the nucleotide and amino acid substitution processes unambiguously support turtles as a sister group to birds and crocodiles. The use of more simplistic models of nucleotide substitution for both concatenation and species tree reconstruction methods leads to the artefactual grouping of turtles and crocodiles, most likely because of substitution saturation at third codon positions. Relaxed molecular clock methods estimate the divergence between turtles and archosaurs around 255 million years ago. The most recent common ancestor of living turtles, corresponding to the split between Pleurodira and Cryptodira, is estimated to have occurred around 157 million years ago, in the Upper Jurassic period. This is a more recent estimate than previously reported, and questions the interpretation of controversial Lower Jurassic fossils as being part of the extant turtles radiation. Conclusions These results provide a phylogenetic framework and timescale with which to interpret the evolution of the peculiar morphological, developmental, and molecular features of turtles within the amniotes.
Background The morphological peculiarities of turtles have, for a long time, impeded their accurate placement in the phylogeny of amniotes. Molecular data used to address this major evolutionary question have so far been limited to a handful of markers and/or taxa. These studies have supported conflicting topologies, positioning turtles as either the sister group to all other reptiles, to lepidosaurs (tuatara, lizards and snakes), to archosaurs (birds and crocodiles), or to crocodilians. Genome-scale data have been shown to be useful in resolving other debated phylogenies, but no such adequate dataset is yet available for amniotes. Results In this study, we used next-generation sequencing to obtain seven new transcriptomes from the blood, liver, or jaws of four turtles, a caiman, a lizard, and a lungfish. We used a phylogenomic dataset based on 248 nuclear genes (187,026 nucleotide sites) for 16 vertebrate taxa to resolve the origins of turtles. Maximum likelihood and Bayesian concatenation analyses and species tree approaches performed under the most realistic models of the nucleotide and amino acid substitution processes unambiguously support turtles as a sister group to birds and crocodiles. The use of more simplistic models of nucleotide substitution for both concatenation and species tree reconstruction methods leads to the artefactual grouping of turtles and crocodiles, most likely because of substitution saturation at third codon positions. Relaxed molecular clock methods estimate the divergence between turtles and archosaurs around 255 million years ago. The most recent common ancestor of living turtles, corresponding to the split between Pleurodira and Cryptodira, is estimated to have occurred around 157 million years ago, in the Upper Jurassic period. This is a more recent estimate than previously reported, and questions the interpretation of controversial Lower Jurassic fossils as being part of the extant turtles radiation. Conclusions These results provide a phylogenetic framework and timescale with which to interpret the evolution of the peculiar morphological, developmental, and molecular features of turtles within the amniotes. PMID:22839781
William G. Parker
Full Text Available Aetosauria is an early-diverging clade of pseudosuchians (crocodile-line archosaurs that had a global distribution and high species diversity as a key component of various Late Triassic terrestrial faunas. It is one of only two Late Triassic clades of large herbivorous archosaurs, and thus served a critical ecological role. Nonetheless, aetosaur phylogenetic relationships are still poorly understood, owing to an overreliance on osteoderm characters, which are often poorly constructed and suspected to be highly homoplastic. A new phylogenetic analysis of the Aetosauria, comprising 27 taxa and 83 characters, includes more than 40 new characters that focus on better sampling the cranial and endoskeletal regions, and represents the most comprenhensive phylogeny of the clade to date. Parsimony analysis recovered three most parsimonious trees; the strict consensus of these trees finds an Aetosauria that is divided into two main clades: Desmatosuchia, which includes the Desmatosuchinae and the Stagonolepidinae, and Aetosaurinae, which includes the Typothoracinae. As defined Desmatosuchinae now contains Neoaetosauroides engaeus and several taxa that were previously referred to the genus Stagonolepis, and a new clade, Desmatosuchini, is erected for taxa more closely related to Desmatosuchus. Overall support for some clades is still weak, and Partitioned Bremer Support (PBS is applied for the first time to a strictly morphological dataset demonstrating that this weak support is in part because of conflict in the phylogenetic signals of cranial versus postcranial characters. PBS helps identify homoplasy among characters from various body regions, presumably the result of convergent evolution within discrete anatomical modules. It is likely that at least some of this character conflict results from different body regions evolving at different rates, which may have been under different selective pressures.
João Hermínio da Silva
Full Text Available The Araripe Sedimentary Basin is known by the excellence of its fossils, regarding the preservation, diversity, and quantity. Here, we present a spectroscopic analysis using several experimental techniques (X-ray energy dispersion spectroscopy, Fourier-transform infrared spectroscopy as well as X-ray diffraction and thermogravimetric analysis applied in small fragments of bones from the posterior members of a theropod dinosaur. The results agree regarding the different composition of the stone matrix and the fossilized bone, indicating a partial substitution of the material by elements present in the depositional environment. However, differently from what is believed to occur, there is evidence that pyritization is not the only mechanism of fossilization for a specimen of Ipubi formation, but calcification, additionally, plays an important role in the fossil production of this Formation.
Susan M Drymala
Full Text Available Crocodylomorphs originated in the Late Triassic and were the only crocodile-line archosaurs to survive the end-Triassic extinction. Recent phylogenetic analyses suggest that the closest relatives of these generally gracile, small-bodied taxa were a group of robust, large-bodied predators known as rauisuchids implying a problematic morphological gap between early crocodylomorphs and their closest relatives. Here we provide a detailed osteological description of the recently named early diverging crocodylomorph Carnufex carolinensis from the Upper Triassic Pekin Formation of North Carolina and assess its phylogenetic position within the Paracrocodylomorpha. Carnufex displays a mosaic of crocodylomorph, rauisuchid, and dinosaurian characters, as well as highly laminar cranial elements and vertebrae, ornamented dermal skull bones, a large, subtriangular antorbital fenestra, and a reduced forelimb. A phylogenetic analysis utilizing a comprehensive dataset of early paracrocodylomorphs and including seven new characters and numerous modifications to characters culled from the literature recovers Carnufex carolinensis as one of the most basal members of Crocodylomorpha, in a polytomy with two other large bodied taxa (CM 73372 and Redondavenator. The analysis also resulted in increased resolution within Crocodylomorpha and a monophyletic clade containing the holotype and two referred specimens of Hesperosuchus as well as Dromicosuchus. Carnufex occupies a key transition at the origin of Crocodylomorpha, indicating that the morphology typifying early crocodylomorphs appeared before the shift to small body size.
Emily J. Lessner
Full Text Available Rauisuchids are large (2–6 m in length, carnivorous, and quadrupedal pseudosuchian archosaurs closely related to crocodylomorphs. Though geographically widespread, fossils of this clade are relatively rare in Late Triassic assemblages. The middle Norian (∼212 Ma Hayden Quarry of northern New Mexico, USA, in the Petrified Forest Member of the Chinle Formation, has yielded isolated postcranial elements and associated skull elements of a new species of rauisuchid. Vivaron haydeni gen. et. sp. nov. is diagnosed by the presence of two posteriorly directed prongs at the posterior end of the maxilla for articulation with the jugal. The holotype maxilla and referred elements are similar to those of the rauisuchid Postosuchus kirkpatricki from the southwestern United States, but V. haydeni shares several maxillary apomorphies (e.g., a distinct dropoff to the antorbital fossa that is not a ridge, a straight ventral margin, and a well defined dental groove with the rauisuchid Teratosaurus suevicus from the Norian of Germany. Despite their geographic separation, this morphological evidence implies a close phylogenetic relationship between V. haydeni and T. suevicus. The morphology preserved in the new Hayden Quarry rauisuchid V. haydeni supports previously proposed and new synapomorphies for nodes within Rauisuchidae. The discovery of Vivaron haydeni reveals an increased range of morphological disparity for rauisuchids from the low-paleolatitude Chinle Formation and a clear biogeographic connection with high paleolatitude Pangea.
Juan Martin Leardi
Full Text Available Background Macelognathus vagans Marsh, 1884 from the Late Jurassic Morrison Fm. of Wyoming was originally described as a dinosaur by Marsh and in 1971 Ostrom suggested crocodilian affinities. In 2005, Göhlich and collaborators identified new material of this species from Colorado as a basal crocodylomorph. However, a partial skull found in association with mandibular and postcranial remains was not described. Methods Due to the small size and delicate structures within the braincase, micro CT studies were performed on this specimen. The new anatomical information was incorporated in a phylogenetic dataset, expanding both character and taxon sampling. Results This new material reinforces the non-crocodyliform crocodylomorph affinities of Macelognathusas it bears a large otic aperture, unfused frontals and lacks ornamentation on the dorsal cranial bones. The internal structures also support these affinities as this specimen bears traits (i.e., heavily pneumatized and expanded basisphenoid; the presence of additional pneumatic features on the braincase; and the otoccipital-quadrate contact not present in most basal crocodylomorphs. Furthermore, the presence of a wide supraoccipital and a cranioquadrate passage are traits shared with Almadasuchus from the early Late Jurassic of Argentina. Macelognathus was recovered as one of the closest relatives of crocodyliforms, forming a clade (Hallopodidae with two other Late Jurassic taxa (Almadasuchus and Hallopus. Discussion The clade formed by Almadasuchus + Hallopus + Macelognathus, the Hallopodidae, is characterized by a higher degree of suturing of the braincase, posteriorly closed otic aperture (paralleled in mesoeucrocodylians and cursorial adaptations. Also, the phylogenetic position of this lineage of derived crocodylomorphs as the sister group of Crocodyliformes implies a large amount of unsampled record (ghost lineage, at least 50 million years.
Descriptions 7 Stratus fractus of bad weather* or Cumulus fractus of bad weather, or both ( pannus ), usually below Altostratus or Nimbostratus. 8...Cumulonimbus without anvil or fibrous upper part, Cumulus, Stratocumulus, Stratus or pannus . / Stratocumulus, Stratus, Cumulus and Cumulonimbus invisible owing
time before and after) or cumulus fractus of bad weath’er, or both ( pannus ), usually below altostratus or nimbostratus. 8 = Cumulus and stratocumulus...vibrous upper part by cumulus, stratocumulus, stratus or pannus . + . from Surface Marine Observations Tape Deck TDF-11 *Fog All clouds in the 0-50...Fractus of bad weather, cr V both ( pannus ), usually below Alto- stratus or N~imbostratus. The term "bad weather* denotes the conditions which coenerally
Under the armor: X-ray computed tomographic reconstruction of the internal skeleton of Coahomasuchus chathamensis (Archosauria: Aetosauria) from the Upper Triassic of North Carolina, USA, and a phylogenetic analysis of Aetosauria.
Hoffman, Devin K; Heckert, Andrew B; Zanno, Lindsay E
Aetosauria is a clade of heavily armored, quadrupedal omnivorous to herbivorous archosaurs known from the Late Triassic across what was the supercontinent of Pangea. Their abundance in many deposits relative to the paucity of other Triassic herbivores indicates that they were key components of Late Triassic ecosystems. However, their evolutionary relationships remain contentious due, in large part, to their extensive dermal armor, which often obstructs observation of internal skeletal anatomy and limits access to potentially informative characters. In an attempt to address this problem we reanalyzed the holotype of a recently described species of Coahomasuchus , C. chathamensis , from the Sanford sub-basin of North Carolina using computed tomography (CT). CT scans of the holotype specimen clarify preservation of the skeleton, revealing several articulated vertebrae and ribs, an isolated vertebra, left ulna, left scapula, and the right humerus, though none of the material resulted in updated phylogenetic scorings. Reexamination of aetosaur materials from the holotype locality also indicates that several isolated osteoderms and elements of the appendicular skeleton are newly referable. Based on these results, we update the Coahomasuchus chathamensis hypodigm and conduct a revised phylogenetic analysis with improved character scorings for Coahomasuchus and several other aetosaurs. Our study recovers Coahomasuchus in a polytomy with Aetosaurus and the Typothoracinae, in contrast with a recent analysis that recovered Coahomasuchus as a wild-card taxon.
Stensrud, D.J. [NOAA/ERL/National Severe Storms Lab., Norman, OK (United States); Pfeifer, S. [Univ. of Oklahoma, Norman, OK (United States)
The sky over the southern Great Plains Cloud and Atmospheric Radiation Testbed (CART) site of the Atmospheric Radiation Measurement (ARM) Program during the predawn and early morning hours often is partially obstructed by stratocumulus, stratus fractus, or cumulus fractus that are moving rapidly to the north, even through the surface winds are weak. This cloud movement is evidence of the low-level jet (LLJ), a wind speed maximum that occurs in the lowest few kilometers of the atmosphere. Owing to the wide spacing between upper-air sounding sites and the relatively infrequent sounding launches, LLJ evolution has been difficult to observe adequately, even though the effects of LLJs on moisture flux into North America are large. Model simulation of the LLJ is described.
both ( pannus ), usually below fractus of bad weather, or both ( pannus ), usu- Altostratus or Nimbostratus ally below Altostratus or Nimbostratus 8 Cumulus...Stratocumulus, Stratus of an anvil; either accompanied or not by Cu- or pannus mulonimbus without anvil or fibrous upper part, by Cumulus, Stratocumulus...Stratus or pannus CL clouds invisible owing to darkness, fog, / Stratocumulus, Stratus, Cumulus and Cu- blowing dust or sand, or other similar mulonimbus
Nesbitt, Sterling J; Butler, Richard J; Gower, David J
Archosauria and their closest relatives, the non-archosaurian archosauriforms, diversified in the Early and Middle Triassic, soon after the end-Permian extinction. This diversification is poorly documented in most Lower and Middle Triassic rock sequences because fossils of early groups of archosauriforms are relatively rare compared to those of other amniotes. The early Middle Triassic (? late Anisian) Manda beds of southwestern Tanzania form an exception, with early archosaur skeletons being relatively common and preserved as articulated or associated specimens. The Manda archosaur assemblage is exceptionally diverse for the Middle Triassic. However, to date, no non-archosaurian archosauriforms have been reported from these rocks. Here, we name a new taxon, Asperoris mnyama gen. et sp. nov., from the Manda beds and thoroughly describe the only known specimen. The specimen consists of a well-preserved partial skull including tooth-bearing elements (premaxilla, maxilla), the nasal, partial skull roof, and several incomplete elements. All skull elements are covered in an autapomorphic highly rugose sculpturing. A unique combination of character states indicates that A. mnyama lies just outside Archosauria as a stem archosaur within Archosauriformes, but more precise relationships of A. mnyama relative to other early archosauriform clades (e.g., Erythrosuchidae) cannot be determined currently. Asperoris mnyama is the first confirmed non-archosaurian archosauriform from the Manda beds and increases the morphological and taxonomic diversity of early archosauriforms known from the Middle Triassic. The direct association of A. mnyama with species referable to Archosauria demonstrates that non-archosaurian archosauriforms were present during the rise and early diversification of Archosauria. Non-archosaurian archosauriforms and archosaurs co-occur in fossil reptile assemblages across Pangaea from the late Early Triassic to the end of the Late Triassic.
Foth, Christian; Ezcurra, Martín D; Sookias, Roland B; Brusatte, Stephen L; Butler, Richard J
Archosauromorpha originated in the middle-late Permian, radiated during the Triassic, and gave rise to the crown group Archosauria, a highly successful clade of reptiles in terrestrial ecosystems over the last 250 million years. However, scientific attention has mainly focused on the diversification of archosaurs, while their stem lineage (i.e. non-archosaurian archosauromorphs) has often been overlooked in discussions of the evolutionary success of Archosauria. Here, we analyse the cranial disparity of late Permian to Early Jurassic archosauromorphs and make comparisons between non-archosaurian archosauromorphs and archosaurs (including Pseudosuchia and Ornithodira) on the basis of two-dimensional geometric morphometrics. Our analysis recovers previously unappreciated high morphological disparity for non-archosaurian archosauromorphs, especially during the Middle Triassic, which abruptly declined during the early Late Triassic (Carnian). By contrast, cranial disparity of archosaurs increased from the Middle Triassic into the Late Triassic, declined during the end-Triassic extinction, but re-expanded towards the end of the Early Jurassic. Our study indicates that non-archosaurian archosauromorphs were highly diverse components of terrestrial ecosystems prior to the major radiation of archosaurs, including dinosaurs, while disparity patterns of the Ladinian and Carnian indicate a gradual faunal replacement of stem archosaurs by the crown group, including a short interval of partial overlap in morphospace during the Ladinian.
de Jong, W W; Zweers, A; Versteeg, M; Dessauer, H C; Goodman, M
The amino acid sequences of the eye lens protein alpha-crystallin A from many mammalian and avian species, two frog species, and a dogfish have provided detailed information about the molecular evolution of this protein and allowed some useful inferences about phylogenetic relationships among these species. We now have isolated and sequenced the alpha-crystallins of the American alligator and the common tegu lizard. The reptilian alpha A chains appear to have evolved as slowly as those of other vertebrates, i.e., at two to three amino acid replacements per 100 residues in 100 Myr. The lack of charged replacements and the general types and distribution of replacements also are similar to those in other vertebrate alpha A chains. Maximum-parsimony analyses of the total data set of 67 vertebrate alpha A sequences support the monophyletic origin of alligator, tegu, and birds and favor the grouping of crocodilians and birds as surviving sister groups in the subclass Archosauria.
Roland B. Sookias
Full Text Available The South African species Euparkeria capensis is of great importance for understanding the early radiation of archosauromorphs (including archosaurs following the Permo–Triassic mass extinction, as most phylogenetic analyses place it as the sister taxon to crown group Archosauria within the clade Archosauriformes. Although a number of species from Lower–Middle Triassic deposits worldwide have been referred to the putative clade Euparkeriidae, the monophyly of Euparkeriidae is controversial and has yet to be demonstrated by quantitative phylogenetic analysis. Three Chinese taxa have been recently suggested to be euparkeriids: Halazhaisuchus qiaoensis, ‘Turfanosuchus shageduensis’, and Wangisuchus tzeyii, all three of which were collected from the Middle Triassic Ermaying Formation of northern China. Here, we reassess the taxonomy and systematics of these taxa. We regard Wangisuchus tzeyii as a nomen dubium, because the holotype is undiagnostic and there is no convincing evidence that the previously referred additional specimens represent the same taxon as the holotype. We also regard ‘Turfanosuchus shageduensis’ as a nomen dubium as we are unable to identify any diagnostic features. We refer the holotype to Archosauriformes, and more tentatively to Euparkeriidae. Halazhaisuchus qiaoensis and the holotype of ‘Turfanosuchus shageduensis’ are resolved as sister taxa in a phylogenetic analysis, and are in turn the sister taxon to Euparkeria capensis, forming a monophyletic Euparkeriidae that is the sister to Archosauria+Phytosauria. This is the first quantitative phylogenetic analysis to recover a non-monospecific, monophyletic Euparkeriidae, but euparkeriid monophyly is only weakly supported and will require additional examination. Given their similar sizes, stratigraphic positions and phylogenetic placement, the holotype of ‘Turfanosuchus shageduensis’ may represent a second individual of Halazhaisuchus qiaoensis, but no
Barton, Christopher C.; Lovejoy, Shaun; Schertzer, Daniel J.; Turcotte, Donald L.
Benoit B. Mandelbrot, who advanced the concept of power law scaling as a fundamental property of a broad range of natural processes and patterns in geophysics, economics, mathematics, and virtually all of science, died on 14 October 2010 in Cambridge, Mass., at the age of 85. Mandelbrot, known as the "father of fractal geometry," was a mathematician who developed the scaling concepts of self-similarity and self-affinity and found examples in spatial, temporal, and size patterns across a broad spectrum of disciplines. He coined the term "fractal" (from the Latin noun "fractus," meaning fragmented) for shapes and patterns that exhibit self-similarity, meaning that they are statistically scale independent. Such shapes are characterized by fractional power law exponents, between the integer (Euclidean) dimensions. He is best known through his books, including Les Objets Fractals: Forme, Hasard et Dimension; Fractals: Form, Chance and Dimension; The Fractal Geometry of Nature; andMultifractals and 1/f Noise: Wild Self-Affinity in Physics [Mandelbrot, 1975, Mandelbrot 1977, Mandelbrot 1982, Mandelbrot 1999].
Narasimha, Roddam; Diwan, Sourabh Suhas; Duvvuri, Subrahmanyam; Sreenivas, K. R.; Bhat, G. S.
Clouds are the largest source of uncertainty in climate science, and remain a weak link in modeling tropical circulation. A major challenge is to establish connections between particulate microphysics and macroscale turbulent dynamics in cumulus clouds. Here we address the issue from the latter standpoint. First we show how to create bench-scale flows that reproduce a variety of cumulus-cloud forms (including two genera and three species), and track complete cloud life cycles—e.g., from a “cauliflower” congestus to a dissipating fractus. The flow model used is a transient plume with volumetric diabatic heating scaled dynamically to simulate latent-heat release from phase changes in clouds. Laser-based diagnostics of steady plumes reveal Riehl–Malkus type protected cores. They also show that, unlike the constancy implied by early self-similar plume models, the diabatic heating raises the Taylor entrainment coefficient just above cloud base, depressing it at higher levels. This behavior is consistent with cloud-dilution rates found in recent numerical simulations of steady deep convection, and with aircraft-based observations of homogeneous mixing in clouds. In-cloud diabatic heating thus emerges as the key driver in cloud development, and could well provide a major link between microphysics and cloud-scale dynamics. PMID:21918112
Narasimha, R.; Diwan, S.; Subrahmanyam, D.; Sreenivas, K. R.; Bhat, G. S.
A variety of cumulus cloud flows, including congestus (both shallow bubble and tall tower types), mediocris and fractus have been generated in a water tank by simulating the release of latent heat in real clouds. The simulation is achieved through ohmic heating, injected volumetrically into the flow by applying suitable voltages between diametral cross-sections of starting jets and plumes of electrically conducting fluid (acidified water). Dynamical similarity between atmospheric and laboratory cloud flows is achieved by duplicating values of an appropriate non-dimensional heat release number. Velocity measurements, made by laser instrumentation, show that the Taylor entrainment coefficient generally increases just above the level of commencement of heat injection (corresponding to condensation level in the real cloud). Subsequently the coefficient reaches a maximum before declining to the very low values that characterize tall cumulus towers. The experiments also simulate the protected core of real clouds. Cumulus Congestus : Atmospheric cloud (left), simulated laboratory cloud (right). Panels below show respectively total heat injected and vertical profile of heating in the laboratory cloud.
crownward archosauriforms than to proterosuchids, and several species are found widespread along the archosauromorph tree, some being nested within Archosauria (e.g., “Chasmatosaurus ultimus,” Youngosuchus). Doswelliids and proterochampsids are recovered as more closely related to each other than to other archosauromorphs, forming a large clade (Proterochampsia) of semi-aquatic to aquatic forms that includes the bizarre genus Vancleavea. Euparkeria is one of the sister-taxa of the clade composed of proterochampsians and archosaurs. The putative Indian archosaur Yarasuchus is recovered in a polytomy with Euparkeria and more crownward archosauriforms, and as more closely related to the Russian Dongusuchus than to other species. Phytosaurs are recovered as the sister-taxa of all other pseudosuchians, thus being nested within Archosauria. PMID:27162705
Dimensão fractal na quantificação do grau de rejeição celular miocárdica pós-transplante cardíaco Fractal dimension in quantifying the degree of myocardial cellular rejection after cardiac transplantation
Roberto Douglas Moreira
Full Text Available INTRODUÇÃO: O termo "fractal" é derivado do latim fractus, que significa "irregular" ou "quebrado", considerando a estrutura observada como tendo uma dimensão não-inteira. Há muitos estudos que empregaram a Dimensão Fractal (DF como uma ferramenta de diagnóstico. Um dos métodos mais comuns para o seu estudo é a "Box-plot counting" (Método de contagem de caixas. OBJETIVO: O objetivo do estudo foi tentar estabelecer a contribuição da DF na quantificação da rejeição celular miocárdica após o transplante cardíaco. MÉTODOS: Imagens microscópicas digitalizadas foram capturadas na resolução 800x600 (aumento de 100x. A DF foi calculada com auxílio do "software ImageJ", com adaptações. A classificação dos graus de rejeição foi de acordo com a "Sociedade Internacional de Transplante Cardíaco e Pulmonar" (ISHLT 2004. O relatório final do grau de rejeição foi confirmado e redefinido após exaustiva revisão das lâminas por um patologista experiente externo. No total, 658 lâminas foram avaliadas, com a seguinte distribuição entre os graus de rejeição (R: 335 (0R, 214 (1R, 70 (2R, 39 (3R. Os dados foram analisados estatisticamente com os testes Kruskal-Wallis e curvas ROC sendo considerados significantes valores de P INTRODUCTION: The term "Fractal" is derived from the Latin fractus meaning "irregular" or "broken" considering the observed structure with a non-integer dimension. There are many studies which employed the Fractal Dimension (FD as a diagnostic tool. One of the most common methods for its study is the "Box Counting Method". OBJECTIVE: The aim of the present study was to try to establish the contribution of FD in the quantification of myocardial cellular rejection after cardiac transplantation. METHODS: Microscopic digital images were captured at 800x600 resolution (magnification 100x. FD was calculated with the aid of "ImageJ software" with adaptations. The classification of the degrees of rejection was in
Pritchard, Adam C.; Nesbitt, Sterling J.
The Triassic Period saw the first appearance of numerous amniote lineages (e.g. Lepidosauria, Archosauria, Mammalia) that defined Mesozoic ecosystems following the end Permian Mass Extinction, as well as the first major morphological diversification of crown-group reptiles. Unfortunately, much of our understanding of this event comes from the record of large-bodied reptiles (total body length > 1 m). Here we present a new species of drepanosaurid (small-bodied, chameleon-like diapsids) from the Upper Triassic Chinle Formation of New Mexico. Using reconstructions of micro-computed tomography data, we reveal the three-dimensional skull osteology of this clade for the first time. The skull presents many archaic anatomical traits unknown in Triassic crown-group reptiles (e.g. absence of bony support for the external ear), whereas other traits (e.g. toothless rostrum, anteriorly directed orbits, inflated endocranium) resemble derived avian theropods. A phylogenetic analysis of Permo-Triassic diapsids supports the hypothesis that drepanosaurs are an archaic lineage that originated in the Permian, far removed from crown-group Reptilia. The phylogenetic position of drepanosaurids indicates the presence of archaic Permian clades among Triassic small reptile assemblages and that morphological convergence produced a remarkably bird-like skull nearly 100 Myr before one is known to have emerged in Theropoda.
Crispel, Pierre; Roberts, Gregory
In this study, we present a novel method of identifying and geolocalizing cloud field elements from a portable all-sky camera stereo network based on the ground and oriented towards zenith. The methodology is mainly based on stereophotogrammetry which is a 3-D reconstruction technique based on triangulation from corresponding stereo pixels in rectified images. In cases where clouds are horizontally separated, identifying individual positions is performed with segmentation techniques based on hue filtering and contour detection algorithms. Macroscopic cloud field characteristics such as cloud layer base heights and velocity fields are also deduced. In addition, the methodology is fitted to the context of measurement campaigns which impose simplicity of implementation, auto-calibration, and portability. Camera internal geometry models are achieved a priori in the laboratory and validated to ensure a certain accuracy in the peripheral parts of the all-sky image. Then, stereophotogrammetry with dense 3-D reconstruction is applied with cameras spaced 150 m apart for two validation cases. The first validation case is carried out with cumulus clouds having a cloud base height at 1500 m a.g.l. The second validation case is carried out with two cloud layers: a cumulus fractus layer with a base height at 1000 m a.g.l. and an altocumulus stratiformis layer with a base height of 2300 m a.g.l. Velocity fields at cloud base are computed by tracking image rectangular patterns through successive shots. The height uncertainty is estimated by comparison with a Vaisala CL31 ceilometer located on the site. The uncertainty on the horizontal coordinates and on the velocity field are theoretically quantified by using the experimental uncertainties of the cloud base height and camera orientation. In the first cumulus case, segmentation of the image is performed to identify individuals clouds in the cloud field and determine the horizontal positions of the cloud centers.
Tzika, Athanasia C; Ullate-Agote, Asier; Grbic, Djordje; Milinkovitch, Michel C
Despite the availability of deep-sequencing techniques, genomic and transcriptomic data remain unevenly distributed across phylogenetic groups. For example, reptiles are poorly represented in sequence databases, hindering functional evolutionary and developmental studies in these lineages substantially more diverse than mammals. In addition, different studies use different assembly and annotation protocols, inhibiting meaningful comparisons. Here, we present the "Reptilian Transcriptomes Database 2.0," which provides extensive annotation of transcriptomes and genomes from species covering the major reptilian lineages. To this end, we sequenced normalized complementary DNA libraries of multiple adult tissues and various embryonic stages of the leopard gecko and the corn snake and gathered published reptilian sequence data sets from representatives of the four extant orders of reptiles: Squamata (snakes and lizards), the tuatara, crocodiles, and turtles. The LANE runner 2.0 software was implemented to annotate all assemblies within a single integrated pipeline. We show that this approach increases the annotation completeness of the assembled transcriptomes/genomes. We then built large concatenated protein alignments of single-copy genes and inferred phylogenetic trees that support the positions of turtles and the tuatara as sister groups of Archosauria and Squamata, respectively. The Reptilian Transcriptomes Database 2.0 resource will be updated to include selected new data sets as they become available, thus making it a reference for differential expression studies, comparative genomics and transcriptomics, linkage mapping, molecular ecology, and phylogenomic analyses involving reptiles. The database is available at www.reptilian-transcriptomes.org and can be enquired using a wwwblast server installed at the University of Geneva. © The Author(s) 2015. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Greenwold, Matthew J; Sawyer, Roger H
The archosauria consist of two living groups, crocodilians, and birds. Here we compare the structure, expression, and phylogeny of the beta (β)-keratins in two crocodilian genomes and two avian genomes to gain a better understanding of the evolutionary origin of the feather β-keratins. Unlike squamates such as the green anole with 40 β-keratins in its genome, the chicken and zebra finch genomes have over 100 β-keratin genes in their genomes, while the American alligator has 20 β-keratin genes, and the saltwater crocodile has 21 β-keratin genes. The crocodilian β-keratins are similar to those of birds and these structural proteins have a central filament domain and N- and C-termini, which contribute to the matrix material between the twisted β-sheets, which form the 2-3 nm filament. Overall the expression of alligator β-keratin genes in the integument increases during development. Phylogenetic analysis demonstrates that a crocodilian β-keratin clade forms a monophyletic group with the avian scale and feather β-keratins, suggesting that avian scale and feather β-keratins along with a subset of crocodilian β-keratins evolved from a common ancestral gene/s. Overall, our analyses support the view that the epidermal appendages of basal archosaurs used a diverse array of β-keratins, which evolved into crocodilian and avian specific clades. In birds, the scale and feather subfamilies appear to have evolved independently in the avian lineage from a subset of archosaurian claw β-keratins. The expansion of the avian specific feather β-keratin genes accompanied the diversification of birds and the evolution of feathers. Copyright © 2013 Wiley Periodicals, Inc.
Background Extant sauropsids (reptiles and birds) are divided into two major lineages, the lineage of Testudines (turtles) and Archosauria (crocodilians and birds) and the lineage of Lepidosauria (tuatara, lizards, worm lizards and snakes). Karyotypes of these sauropsidan groups generally consist of macrochromosomes and microchromosomes. In chicken, microchromosomes exhibit a higher GC-content than macrochromosomes. To examine the pattern of intra-genomic GC heterogeneity in lepidosaurian genomes, we constructed a cytogenetic map of the Japanese four-striped rat snake (Elaphe quadrivirgata) with 183 cDNA clones by fluorescence in situ hybridization, and examined the correlation between the GC-content of exonic third codon positions (GC3) of the genes and the size of chromosomes on which the genes were localized. Results Although GC3 distribution of snake genes was relatively homogeneous compared with those of the other amniotes, microchromosomal genes showed significantly higher GC3 than macrochromosomal genes as in chicken. Our snake cytogenetic map also identified several conserved segments between the snake macrochromosomes and the chicken microchromosomes. Cross-species comparisons revealed that GC3 of most snake orthologs in such macrochromosomal segments were GC-poor (GC3 < 50%) whereas those of chicken orthologs in microchromosomes were relatively GC-rich (GC3 ≥ 50%). Conclusion Our results suggest that the chromosome size-dependent GC heterogeneity had already occurred before the lepidosaur-archosaur split, 275 million years ago. This character was probably present in the common ancestor of lepidosaurs and but lost in the lineage leading to Anolis during the diversification of lepidosaurs. We also identified several genes whose GC-content might have been influenced by the size of the chromosomes on which they were harbored over the course of sauropsid evolution. PMID:23140509
Shaffer, H Bradley; McCartney-Melstad, Evan; Near, Thomas J; Mount, Genevieve G; Spinks, Phillip Q
Accurate time-calibrated phylogenies are the centerpiece of many macroevolutionary studies, and the relationship between the size and scale of molecular data sets and the density and accuracy of fossil calibrations is a key element of time tree studies. Here, we develop a target capture array specifically for living turtles, compare its efficiency to an ultraconserved element (UCE) dataset, and present a time-calibrated molecular phylogeny based on 539 nuclear loci sequenced from 26 species representing the breadth of living turtle diversity plus outgroups. Our gene array, based on three fully sequenced turtle genomes, is 2.4 times more variable across turtles than a recently published UCE data set for an identical subset of 13 species, confirming that taxon-specific arrays return more informative data per sequencing effort than UCEs. We used our genomic data to estimate the ages of living turtle clades including a mid-late Triassic origin for crown turtles and a mid-Carboniferous split of turtles from their sister group, Archosauria. By specifically excluding several of the earliest potential crown turtle fossils and limiting the age of fossil calibration points to the unambiguous crown lineage Caribemys oxfordiensis from the Late Jurassic (Oxfordian, 163.5-157.3Ma) we corroborate a relatively ancient age for living turtles. We also provide novel age estimates for five of the ten testudine families containing more than a single species, as well as several intrafamilial clades. Most of the diversity of crown turtles appears to date to the Paleogene, well after the Cretaceous-Paleogene mass extinction 66mya. Copyright © 2017 Elsevier Inc. All rights reserved.
Schroeter, Elena R; DeHart, Caroline J; Cleland, Timothy P; Zheng, Wenxia; Thomas, Paul M; Kelleher, Neil L; Bern, Marshall; Schweitzer, Mary H
Sequence data from biomolecules such as DNA and proteins, which provide critical information for evolutionary studies, have been assumed to be forever outside the reach of dinosaur paleontology. Proteins, which are predicted to have greater longevity than DNA, have been recovered from two nonavian dinosaurs, but these results remain controversial. For proteomic data derived from extinct Mesozoic organisms to reach their greatest potential for investigating questions of phylogeny and paleobiology, it must be shown that peptide sequences can be reliably and reproducibly obtained from fossils and that fragmentary sequences for ancient proteins can be increasingly expanded. To test the hypothesis that peptides can be repeatedly detected and validated from fossil tissues many millions of years old, we applied updated extraction methodology, high-resolution mass spectrometry, and bioinformatics analyses on a Brachylophosaurus canadensis specimen (MOR 2598) from which collagen I peptides were recovered in 2009. We recovered eight peptide sequences of collagen I: two identical to peptides recovered in 2009 and six new peptides. Phylogenetic analyses place the recovered sequences within basal archosauria. When only the new sequences are considered, B. canadensis is grouped more closely to crocodylians, but when all sequences (current and those reported in 2009) are analyzed, B. canadensis is placed more closely to basal birds. The data robustly support the hypothesis of an endogenous origin for these peptides, confirm the idea that peptides can survive in specimens tens of millions of years old, and bolster the validity of the 2009 study. Furthermore, the new data expand the coverage of B. canadensis collagen I (a 33.6% increase in collagen I alpha 1 and 116.7% in alpha 2). Finally, this study demonstrates the importance of reexamining previously studied specimens with updated methods and instrumentation, as we obtained roughly the same amount of sequence data as the
Richard J Butler
been present in these taxa (and secondarily lost in extant crocodilians and was potentially primitive for Archosauria as a whole.
Allen, Vivian; Bates, Karl T; Li, Zhiheng; Hutchinson, John R
Locomotion in living birds (Neornithes) has two remarkable features: feather-assisted flight, and the use of unusually crouched hindlimbs for bipedal support and movement. When and how these defining functional traits evolved remains controversial. However, the advent of computer modelling approaches and the discoveries of exceptionally preserved key specimens now make it possible to use quantitative data on whole-body morphology to address the biomechanics underlying this issue. Here we use digital body reconstructions to quantify evolutionary trends in locomotor biomechanics (whole-body proportions and centre-of-mass position) across the clade Archosauria. We use three-dimensional digital reconstruction to estimate body shape from skeletal dimensions for 17 archosaurs along the ancestral bird line, including the exceptionally preserved, feathered taxa Microraptor, Archaeopteryx, Pengornis and Yixianornis, which represent key stages in the evolution of the avian body plan. Rather than a discrete transition from more-upright postures in the basal-most birds (Avialae) and their immediate outgroup deinonychosauria, our results support hypotheses of a gradual, stepwise acquisition of more-crouched limb postures across much of theropod evolution, although we find evidence of an accelerated change within the clade Maniraptora (birds and their closest relatives, such as deinonychosaurs). In addition, whereas reduction of the tail is widely accepted to be the primary morphological factor correlated with centre-of-mass position and, hence, evolution of hindlimb posture, we instead find that enlargement of the pectoral limb and several associated trends have a much stronger influence. Intriguingly, our support for the onset of accelerated morpho-functional trends within Maniraptora is closely correlated with the evolution of flight. Because we find that the evolution of enlarged forelimbs is strongly linked, via whole-body centre of mass, to hindlimb function during
Full Text Available The initial control of viral infection in a host is dominated by a very well orchestrated early innate immune system; however, very little is known about the ability of a host to control viral infection outside of mammals. The reptiles offer an evolutionary bridge between the fish and mammals, with the crocodile having evolved from the archosauria clade that included the dinosaurs, and being the largest living reptile species. Using an RNA-seq approach, we have defined the dynamic changes of a passaged primary crocodile cell line to stimulation with both RNA and DNA viral mimics. Cells displayed a marked upregulation of many genes known to be involved in the mammalian response to viral infection, including viperin, Mx1, IRF7, IRF1, and RIG-I with approximately 10% of the genes being uncharacterized transcripts. Both pathway and genome analysis suggested that the crocodile may utilize the main known mammalian TLR and cytosolic antiviral RNA signaling pathways, with the pathways being responsible for sensing DNA viruses less clear. Viral mimic stimulation upregulated the type I interferon, IFN-Omega, with many known antiviral interferon-stimulated genes also being upregulated. This work demonstrates for the first time that reptiles show functional regulation of many known and unknown antiviral pathways and effector genes. An enhanced knowledge of these ancient antiviral pathways will not only add to our understanding of the host antiviral innate response in non-mammalian species, but is critical to fully comprehend the complexity of the mammalian innate immune response to viral infection.
Turner, Alan H; Pritchard, Adam C; Matzke, Nicholas J
Estimating divergence times on phylogenies is critical in paleontological and neontological studies. Chronostratigraphically-constrained fossils are the only direct evidence of absolute timing of species divergence. Strict temporal calibration of fossil-only phylogenies provides minimum divergence estimates, and various methods have been proposed to estimate divergences beyond these minimum values. We explore the utility of simultaneous estimation of tree topology and divergence times using BEAST tip-dating on datasets consisting only of fossils by using relaxed morphological clocks and birth-death tree priors that include serial sampling (BDSS) at a constant rate through time. We compare BEAST results to those from the traditional maximum parsimony (MP) and undated Bayesian inference (BI) methods. Three overlapping datasets were used that span 250 million years of archosauromorph evolution leading to crocodylians. The first dataset focuses on early Sauria (31 taxa, 240 chars.), the second on early Archosauria (76 taxa, 400 chars.) and the third on Crocodyliformes (101 taxa, 340 chars.). For each dataset three time-calibrated trees (timetrees) were calculated: a minimum-age timetree with node ages based on earliest occurrences in the fossil record; a 'smoothed' timetree using a range of time added to the root that is then averaged over zero-length internodes; and a tip-dated timetree. Comparisons within datasets show that the smoothed and tip-dated timetrees provide similar estimates. Only near the root node do BEAST estimates fall outside the smoothed timetree range. The BEAST model is not able to overcome limited sampling to correctly estimate divergences considerably older than sampled fossil occurrence dates. Conversely, the smoothed timetrees consistently provide node-ages far older than the strict dates or BEAST estimates for morphologically conservative sister-taxa when they sit on long ghost lineages. In this latter case, the relaxed-clock model appears to
Fabiano C. Lima
Full Text Available O crânio representa uma estrutura única e complexa dos vertebrados, sendo foco relevante objeto de estudos morfológicos e sistemáticos. Embora os crocodilianos constituam um importante grupo representante dos Archosauria, nossos conhecimentos acerca de seu desenvolvimento e homologias ainda são escassos. Aqui descrevemos uma sequência detalhada de ossificação dos ossos do crânio de Caiman yacare (Daudin, 1802, objetivando contribuir com informações de foco anatômico. Coletaram-se ao acaso embriões em intervalos regulares durante todo o período de incubação, sendo estes posteriormente submetidos a protocolo de diafanização e coloração de ossos. O padrão de ossificação em C. yacare segue parâmetros gerais em répteis e outros tetrápodes. Os primeiros centros de ossificação correspondem aos ossos dérmicos, envolvidos com funções primárias como a alimentação e respiração (e.g. maxila, dentário, esplenial, angular, pterigoide, ectopterigoide e jugal, incluindo ainda os dentes. Os ossos da porção dorsal do neurocrânio se ossificam posteriormente, evidenciando uma fontanela cranial que permanece até o momento da eclosão. Os ossos parietal, frontal e opstótico possuem mais de um centro de ossificação que se fundem durante a ontogenia. O centro de ossificação do parisfenoide está ausente, e apenas um centro de ossificação está presente para o basisfenoide. A porção posterior do crânio é formada por centros de substituição do condrocrânio que se ossificam em estágios posteriores.
Alan H Turner
Full Text Available Estimating divergence times on phylogenies is critical in paleontological and neontological studies. Chronostratigraphically-constrained fossils are the only direct evidence of absolute timing of species divergence. Strict temporal calibration of fossil-only phylogenies provides minimum divergence estimates, and various methods have been proposed to estimate divergences beyond these minimum values. We explore the utility of simultaneous estimation of tree topology and divergence times using BEAST tip-dating on datasets consisting only of fossils by using relaxed morphological clocks and birth-death tree priors that include serial sampling (BDSS at a constant rate through time. We compare BEAST results to those from the traditional maximum parsimony (MP and undated Bayesian inference (BI methods. Three overlapping datasets were used that span 250 million years of archosauromorph evolution leading to crocodylians. The first dataset focuses on early Sauria (31 taxa, 240 chars., the second on early Archosauria (76 taxa, 400 chars. and the third on Crocodyliformes (101 taxa, 340 chars.. For each dataset three time-calibrated trees (timetrees were calculated: a minimum-age timetree with node ages based on earliest occurrences in the fossil record; a 'smoothed' timetree using a range of time added to the root that is then averaged over zero-length internodes; and a tip-dated timetree. Comparisons within datasets show that the smoothed and tip-dated timetrees provide similar estimates. Only near the root node do BEAST estimates fall outside the smoothed timetree range. The BEAST model is not able to overcome limited sampling to correctly estimate divergences considerably older than sampled fossil occurrence dates. Conversely, the smoothed timetrees consistently provide node-ages far older than the strict dates or BEAST estimates for morphologically conservative sister-taxa when they sit on long ghost lineages. In this latter case, the relaxed
Li, Zhiheng; Clarke, Julia A
early evolution of the clade. Hyoid simplification has been linked to ingestion of large prey items, and this shift in hyoid-related feeding ecology may occur in early archosauriform evolution. A second transformation in hyoid morphology occurs within the crocodilian stem lineage after the split from birds. In Crocodyliformes, deflections in the ceratobrachials become more pronounced. The morphology of the hyoid in Archosauriformes indicates that aspects of the hyolingual apparatus in extant crocodilians are derived, including a strong deflection near the midpoint of the ceratobranchials, and their condition should not be treated as ancestral for Archosauria. © 2015 Anatomical Society.
Timm, L.C.; Reichardt, K.; Oliveira Santos Bacchi, O.
Dimensional analysis refers to the study of the dimensions that characterize physical entities, like mass, force and energy. Classical mechanics is based on three fundamental entities, with dimensions MLT, the mass M, the length L and the time T. The combination of these entities gives rise to derived entities, like volume, speed and force, of dimensions L 3 , LT -1 , MLT -2 , respectively. In other areas of physics, four other fundamental entities are defined, among them the temperature θ and the electrical current I. The parameters that characterize physical phenomena are related among themselves by laws, in general of quantitative nature, in which they appear as measures of the considered physical entities. The measure of an entity is the result of its comparison with another one, of the same type, called unit. Maps are also drawn in scale, for example, in a scale of 1:10,000, 1 cm 2 of paper can represent 10,000 m 2 in the field. Entities that differ in scale cannot be compared in a simple way. Fractal geometry, in contrast to the Euclidean geometry, admits fractional dimensions. The term fractal is defined in Mandelbrot (1982) as coming from the Latin fractus, derived from frangere which signifies to break, to form irregular fragments. The term fractal is opposite to the term algebra (from the Arabic: jabara) which means to join, to put together the parts. For Mandelbrot, fractals are non topologic objects, that is, objects which have as their dimension a real, non integer number, which exceeds the topologic dimension. For the topologic objects, or Euclidean forms, the dimension is an integer (0 for the point, 1 for a line, 2 for a surface, and 3 for a volume). The fractal dimension of Mandelbrot is a measure of the degree of irregularity of the object under consideration. It is related to the speed by which the estimate of the measure of an object increases as the measurement scale decreases. An object normally taken as uni-dimensional, like a piece of a