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Ratios as a size adjustment in morphometrics.

Simple ratios in which a measurement variable is divided by a size variable are commonly used but known to be inadequate for eliminating size correlations from morphometric data. Deficiencies in the simple ratio can be alleviated by incorporating regression coefficients describing the bivariate relationship between the measurement and size variables. Recommendations have included: 1) subtracting the regression intercept to force the bivariate relationship through the origin (intercept-adjusted ratios); 2) exponentiating either the measurement or the size variable using an allometry coefficient to achieve linearity (allometrically adjusted ratios); or 3) both subtracting the intercept and exponentiating (fully adjusted ratios). These three strategies for deriving size-adjusted ratios imply different data models for describing the bivariate relationship between the measurement and size variables (i.e., the linear, simple allometric, and full allometric models, respectively). Algebraic rearrangement of the equation associated with each data model leads to a correctly formulated adjusted ratio whose expected value is constant (i.e., size correlation is eliminated). Alternatively, simple algebra can be used to derive an expected value function for assessing whether any proposed ratio formula is effective in eliminating size correlations. Some published ratio adjustments were incorrectly formulated as indicated by expected values that remain a function of size after ratio transformation. Regression coefficients incorporated into adjusted ratios must be estimated using least-squares regression of the measurement variable on the size variable. Use of parameters estimated by any other regression technique (e.g., major axis or reduced major axis) results in residual correlations between size and the adjusted measurement variable. Correctly formulated adjusted ratios, whose parameters are estimated by least-squares methods, do control for size correlations. The size-adjusted results are similar to those based on analysis of least-squares residuals from the regression of the measurement on the size variable. However, adjusted ratios introduce size-related changes in distributional characteristics (variances) that differentially alter relationships among animals in different size classes.

Animals↗

Multivariate analysis of the sexual dimorphism of the hip bone in a modern human population and in early hominids.

A large sample of hip bones of known sex coming from one modern population is studied morphologically and by multivariate analysis to investigate sexual dimorphism patterns. A principal component analysis of raw data shows that a large amount of the hip bone sexual dimorphism is accounted for by size differences, but that sex-linked shape variation is also very conspicuous and cannot be considered an allometric consequence of differences in body size between the sexes. The PCA of transformed ("shape") variables indicates that the female hip bones are different in those traits associated with a relatively larger pelvic inlet (longer pubic bones, a greater degree of curvature of the iliopectineal line, and more posterior position of the auricular surface), as well as a broader sciatic notch. The analysis of nonmetric traits also shows marked sexual dimorphism in the position of the sacroiliac joint in the iliac bone, in the shape of the sciatic notch, in pubic morphology, and in the presence of the pre-auricular sulcus in females. When the australopithecine AL 288-1 and Sts 14 hip bones are included in the multivariate analysis, they appear as "ultra-females." In particular these early hominids exhibit extraordinarily long pubic bones and iliopectineal lines, which cannot be explained by allometry.

Analysis of Variance↗

Structural adaptations for gliding in mammals with implications for locomotor behavior in paromomyids.

The gliding abilities of paromomyid plesiadapiforms are evaluated through a functional analysis of long bone morphology in a comparative sample of modern gliders and related nongliders. Relationships between body mass, long bone lengths, and long bone midshaft cross-sectional areas are explored. Theory suggests that gliders should have long humeri and femora to improve aspect ratio, and that larger gliders should have relatively longer limb bones than smaller gliders to minimize drag and patagial loading at greater body masses. Comparisons between extant taxa support these predictions: gliders have relatively longer humeri and femora than those of nongliders, and glider long bone lengths scale with positive allometry, while the scaling of nonglider long bones does not differ from isometry. Preliminary analysis of distal to proximal limb segment proportions further suggests that bone lengthening is, to some extent, related to patagial attachment site, although humeri and femora are relatively long in all of the gliders, regardless of attachment site. The proportions of paromomyids relative to those of extant mammals do not support a gliding interpretation for these fossils.

Adaptation, Biological↗

Cranial ontogeny of Papio baboons (Papio hamadryas).

Cranial form in subspecies of Papio baboons (Papio hamadryas) varies in relation to size, geography, and sex. However, knowledge about this variation is based mainly on adults, precluding direct assessments of the evolutionary factors that are ultimately responsible for adult shape variation. Consequently, this study tests hypotheses about the development of size and shape differences among subspecies of Papio baboons, anticipating limited evolutionary divergences in the ontogenetic pathways leading to adult endpoints. Geometric morphometric and bivariate allometric analyses are used to explore developmental size and shape variation. Allometric scaling in adult Papio baboons occurs because both sexes and all subspecies follow similar developmental pathways to a variety of adult forms. However, complex allometry contributes to form differences, producing potentially important shape differences that emerge during development. Modest shape differences that are statistically independent of size distinguish chacma baboons (P. h. ursinus) from other forms. A small-headed subspecies, the Kinda baboon (P. h. kindae), also presents a distinctive ontogeny, and may provide insights into the evolution of size change in this species. Variation among subspecies that is statistically independent of size involves the rostrum, zygomatic breadths, and cranial flexion. These features may be related to diet, but the precise biomechanical correlates of baboon form variation remain unclear.

Animals↗

Quantitative analysis of human mandibular shape using three-dimensional geometric morphometrics.

Human mandibular morphology is often thought to reflect mainly function, and to be of lesser value in studies of population history. Previous descriptions of human mandibles showed variation in ramal height and breadth to be the strongest difference among recent human groups. Several mandibular traits that differentiate Neanderthals from modern humans include greater robusticity, a receding symphysis, a large retromolar space, a rounder gonial area, an asymmetric mandibular notch, and a posteriorly positioned mental foramen in Neanderthals. Nevertheless, the degree to which these differences are part of modern human variation and/or are related to size and function remains unclear. The aim of this study was to document geographic and functional patterning in the mandibular shape of recent humans, to assess the effects of allometry on mandibular form, and to quantitatively evaluate proposed "Neanderthal" mandibular traits through comparison with samples of geographically diverse recent humans. Data were collected in the form of three-dimensional coordinates of 28 landmarks. Unlike previous studies, this analysis found that modern human mandibular shape exhibits considerable geographic patterning, with some aspects of mandibular morphology reflecting a climatic gradient, and others, a functional specialization. Population history is also reflected in mandibular form, albeit relatively weakly. Proposed "Neanderthal" traits were found to separate Neanderthal from modern human mandibles successfully in the statistical analysis. Of these, the retromolar gap was found to be related to increased mandibular size in modern humans. The status of this trait as a Neanderthal autapomorphy should therefore be treated with caution.

Anatomy, Comparative↗

Sifaka positional behavior: ontogenetic and quantitative genetic approaches.

In many primate species, hands and feet are large relative to neonatal body weight, and they subsequently exhibit negative allometric growth during ontogeny. Here, data are presented showing that this pattern holds for a wild population of lemur, Verreaux's sifaka (Propithecus verreauxi verreauxi). Using morphometric data collected on this population, it is shown that younger animals possess relatively large hands and feet. This ontogenetic pattern suggests a simple behavioral test: do juvenile animals with their larger, almost adult-sized hands and feet locomote on similarly sized substrates as adult animals? Using locomotor bout sampling, this question was tested by collecting positional behavior data on this population. Results from this test find no differences in locomotor behaviors or substrate use between yearlings and adult animals. To place these results in a broader evolutionary context, heritabilities and selection gradients of hands, feet, and other limb elements for animals in this population were estimated. Among limb elements, heritabilities range from 0.16-0.44, with the foot having the lowest value. Positive directional selection acts most strongly on the foot (directional selection gradient = 0.119). The low heritability and positive selection coefficient indicate that selection has acted, and continues to act, on foot size in young animals. These results are interpreted within a functional context with respect to the development of locomotor coordination: larger feet enable young animals to use "adult-sized" substrates when they move through their habitat. It is suggested that the widespread pattern of negative allometry of the extremities in sifaka and other primates is maintained by selection, and does not simply reflect a primitive developmental pathway that has no adaptive basis.

Animals↗

Three-dimensional structure and evolution of primate primary visual cortex.

In this study, three-dimensional reconstructions of primate primary visual cortex (V1) were used to address questions about its evolution. The three-dimensional shape of V1 in anthropoids is significantly longer and narrower than in strepsirrhines. This difference is an effect of clade and is not due to differences in activity pattern or V1 size. New measurements of V1 volume were also provided in order to reassess V1 size differences between strepsirrhines and anthropoids. It was found that for a given lateral geniculate nucleus (LGN) volume, anthropoids have a significantly larger V1 than strepsirrhines do. This is important since LGN is the principal source of V1's input. Finally, independent contrasts analysis was used to examine the scaling of V1 relative to LGN, the rest of cortex, and the rest of the brain. It was confirmed that V1 scales with positive allometry relative to LGN. A number of possible explanations for scaling are discussed. V1 scaling may have to do with the tendency of large brains to be more compartmentalized than small brains, or V1 scaling might reflect the geometry of information representation.

Animals↗

Interspecies scaling of the monoclonal anti-EGF receptor ior EGF/r3 antibody disposition using allometric paradigm: is it really suitable?

The pharmacokinetic regularity of the murine monoclonal antibody ior EGF/r3 across mammals was studied using allometry. The allometric relationship between the volume of distribution and body weight (W) across mammalian species was characterized by the power equation V(d)=218.8 W(0.84) (r=0.92), and that for clearance by CL=2.96 W(0.76) (r=0.97, excluding the dog). The complex Dedrick plot of the ior EGF/r3 pharmacokinetic data produced a superimposable profile (r=0.73). However, a 4-fold variation was observed between the expected human ior EGF/r3 clearance and the cancer patients' values, using apolysichron time units. The patients showed clearance values that overreached the prediction, and the neoteny phenomena cannot explain such a difference. The pharmacokinetic data from cancer patients, rather than healthy volunteers, suggested any tumour-associated drug clearance process as a possible determinant of the mentioned underestimation. Finally, the results obtained in this study confirmed the potential use of allometric scaling to obtain more insight into the similarities and/or differences of the ior EGF/r3 disposition behaviour among mammals.

Animals↗

Connection matrix of the hippocampal formation: I. The dentate gyrus.

The hippocampal formation presents a special opportunity for realistic neural modeling since its structure, connectivity, and physiology are better understood than that of other cortical components. A review of the quantitative neuroanatomy of the rodent dentate gyrus (DG) is presented in the context of the development of a computational model of its connectivity. The DG is a three-layered folded sheet of neural tissue. This sheet is represented as a rectangle, having a surface area of 37 mm2 and a septotemporal length of 12 mm. Points, representing cell somata, are distributed in the model rectangle in a roughly uniform fashion. Synaptic connectivity is generated by assigning each presynaptic cell a spatial zone representing its axonal arbor. For each postsynaptic cell, a list of potential presynaptic cells is compiled, based on which arbor zones the given postsynaptic cell falls within. An appropriate number of presynaptic inputs are then selected at random. The principal cells of the DG, the granule cells, are represented in the model, as are non-principal cells, including basket cells, chandelier cells, mossy cells, and GABAergic peptidergic polymorphic (GPP) cells. The neurons of layer II of the entorhinal cortex are included also. The DG receives its main extrinsic input from these cells via the perforant path. The basket cells, chandelier cells, and GPP cells receive perforant path and granule cell input and exert both feedforward and feedback inhibition onto the granule cells. Mossy cells receive converging input from granule cells and send their output back primarily to distant septotemporal levels, where they contact both granule cells and non-principal cells. To permit numerical simulations, the model must be scaled down while preserving its anatomical structure. A variety of methods for doing this exist. Hippocampal allometry provides valuable clues in this regard.

Animals↗

Neurotoxic character of thimerosal and the allometric extrapolation of adult clearance half-time to infants.

The decomposition rate of organomercurials and the potency of the blood-brain barrier increase with the size of the organic radical. Thus methylmercury damages the brain more than thimerosal does, and when intake limits set for methylmercury are applied to thimerosal the safety margin is increased even if the clearances were the same. However, the clearance half-time of ethylmercury in adults is about one-third of the 50 days' clearance half-time of methylmercury given for 60 kg body weight. Moreover, because metabolic rates (e.g. basal metabolism, daily loss of mercury in per cent of body burden) in different weight groups are related to the fractional power of body weight (rule of allometry), mercury clears from the infant body faster than from the adult body. Blood mercury concentrations observed after vaccination showed agreement with allometrically extrapolated concentrations.

Adult↗

Kinematics of cranial ontogeny: heterotopy, heterochrony, and geometric morphometric analysis of growth models.

In this paper, we examine the relationship between the classical concepts of heterotopy, heterochrony and ontogenetic allometry as descriptive and as explanatory categories in the investigation of evolutionary developmental novelty in the hominid skull. We use concepts of kinematic analysis of locomotion to propose a methodological framework for the kinematic analysis of cranial form change during ontogeny. We argue that a combination of geometric-morphometric methods with graphics visualization tools currently represents the most adequate means to analyze the kinematics of ontogeny. Using cranial growth models, we simulate how evolutionary modifications of developmental processes impinge on morphological patterns of ontogeny, and explore how differences in ontogenetic patterns can tentatively be traced back to underlying process differences. Our analyses indicate that minor alterations in growth parameters elicit complex patterns of ontogenetic modification that are difficult to describe with the standard repertoire of heterochronic terminology. The proposed kinematic and model-based approach is used in a comparative analysis of cranial ontogeny in Neanderthals and anatomically modern humans, indicating that early ontogenetic modification of a small set of growth parameters is a major source of evolutionary novelty during hominid evolution.

Animals↗

Comparative postnatal ontogeny of the skull in the australidelphian metatherian Dasyurus albopunctatus (Marsupialia: Dasyuromorpha: Dasyuridae).

We describe the cranial ontogeny of an australidelphian marsupial, Dasyurus albopunctatus, using a combination of qualitative and quantitative approaches. We examined in detail qualitative morphological changes of just-weaned individuals as compared to old adults; specifically, changes in 31 morphological structures (e.g., processes, foramina) and 38 changes in cranial joints. We also interpreted growth-invariant structures in terms of their functional relevance. We performed a multivariate allometry analysis based on 14 cranial measurements taken from 31 specimens encompassing the entire postweaning period. Three variables (height of occipital plate, breadth of braincase, and height of mandible) showed the same allometric trends in D. albopunctatus and the three marsupial species studied previously in the same framework (Didelphis albiventris, Lutreolina crassicaudata, and Dromiciops gliroides). In addition, D. albopunctatus shared allometric trends in two variables (length of the upper postcanine row and length of the orbit) with the microbiotheriid D. gliroides. Most of the growth trends observed are interpreted as linked to the predominantly carnivorous dietary habit of adult D. albopunctatus. Because dasyuromorphians are most likely basal to the major Australasian radiation of marsupials, knowledge of ontogenetic changes in D. albopunctatus may shed light on the evolution of ontogeny in the highly diverse Australasian marsupial fauna.

Animals↗

Bursa tract diverticulum in the hermaphroditic land snail Arianta arbustorum (Stylommatophora: Helicidae): morphology, function, and evolutionary implications.

A bursa tract diverticulum is widespread in the female part of the hermaphroditic reproductive system of stylommatophoran pulmonates. However, the ultrastructure of the diverticulum is unknown and there is only anecdotal evidence for a spermatophore-dissolving function for this organ. In the present study, we examined the ultrastructure of the diverticulum and investigated histological, histochemical, and morphometric changes at different time intervals after mating in the simultaneously hermaphroditic land snail Arianta arbustorum. The diverticulum in this species of snail is a prominent organ, consisting of a luminal columnar epithelium surrounded by a thick layer of connective tissue. During mating, the diverticulum functions as the site of spermatophore uptake. Within the lumen of the diverticulum the spermatophore wall is dissolved or at least partly broken down. The digested material is taken up by epithelial cells and accumulated in molluscan-specific cells of the connective tissue, the so-called rhogocytes. Subsequent to copulation, the total diameter of the diverticulum increases markedly, reaching a maximum size 12 h after mating, while at the same time the thicknesses of the diverticulum wall and diverticulum epithelium decrease. The length of the diverticulum shows a positive allometry and a high phenotypic variation compared to snail size, which suggests that the diverticulum is under directional sexual selection. We propose that the diverticulum in A. arbustorum has evolved in response to selection pressures imposed by divergent evolutionary interests between male and female function.

Animals↗

Evidence at hand: Diversity, functional implications, and locomotor prediction in intrinsic hand proportions of diprotodontian marsupials.

Knowledge about the diversity, locomotor adaptations, and evolution of the marsupial forelimb is limited, resulting in an underrepresentation of marsupials in comparative anatomical literature on mammalian forelimb anatomy. This study investigated hand proportions in the diverse marsupial order Diprotodontia. Fifty-two measurements of 95 specimens representing 47 species, as well as 6 non-diprotodontian specimens, were explored using principal components analysis (PCA). Bootstrapping was used to assess the reliability of the loadings. Phylogenetically independent contrasts and phylogenetic ANOVA were used to test for correlation with size and functional adaptation of forelimbs for locomotor habit, scored as arboreal vs. terrestrial. Analysis of first principal component (PC1) scores revealed significant differences between arboreal and terrestrial species, and was related to relative slenderness of their phalangeal elements. Both locomotor groups displayed allometry along PC1 scores, but with different intercepts such that PC1 discriminated between the two locomotor habits almost completely. PC2 separated some higher-level clades and burrowing species. Analysis of locomotor predictors commonly applied by palaeontologists indicates that ratios between proximal and intermediate phalanges were unsuitable as predictors of arboreality/terrestriality, but the phalangeal index was more effective. From PCA results, a phalangeal slenderness ratio was developed which proved to be a useful discriminator, suggesting that a single unallocated phalanx can be used for an impression of locomotor mode in fossils. Most Diprotodontia are laterally paraxonic or ectaxonic, with the exception of digging species whose hands are medially paraxonic. Our results complement those of studies on placental mammals, suggesting that the demands of arboreality, terrestriality, or frequent digging on intrinsic hand proportions are met with similar anatomical adaptations in marsupials.

Adaptation, Physiological↗

Morphometrics of the skeleton of Dermophis mexicanus (Amphibia: Gymnophiona). Part I. The vertebrae, with comparisons to other species.

Morphometric analysis of vertebral structure in caecilians (Amphibia: Gymnophiona) is presented. Ontogenetic variation in Dermophis mexicanus is analyzed through the 100+ vertebrae composing the column. Vertebral structure in adult D. mexicanus is compared with that in Ichthyophis glutinosus and Typhlonectes compressicauda. Centra of the atlas, second, tenth, 20th, and 50th vertebrae grow at allometrically different rates in D. mexicanus, though the 20th and 50th are not significantly different. Growth appears significantly slower in several dimensions of anterior and posterior vertebrae relative to midtrunk vertebrae in all three species. Mensural patterns throughout the entire column are similar in the terrestrail burrowers D. mexicanus and I. glutinosus; patterns in the aquatic T. compressicauda differ substantially from those of the burrowing species and are strongly influenced by allometry. Of the 112 D. mexicanus examined, 13.4% had vertebral anomalies, usually fusions.

Amphibians↗

Size and shape of the mandibular condyle in primates.

The relationships between the size of the articular surface of the mandibular condyle and masticatory muscle size, tooth size, diet, and biomechanical variables associated with mastication were studied by taking 12 measurements on skulls of 253 adult female anthropoid primates, including three to ten specimens from each of 32 species. In regressions of condylar length, width, or area against body weight, logarithmic transformations substantially improve the fit of the equations compared with untransformed data. There is a strong relationship between condylar measurements and body weight, with all correlations being .94 or higher. The slopes of the allometric regressions of length, width, and area of the condylar head indicate slight positive allometry with body size. Folivorous primates have smaller condyles than frugivorous primates, and colobines have smaller condyles than cebids, cercopithecines, or hominoids. When colobines are eliminated, the differences between frugivores and folivores are not significant. However, the two species with the relatively largest condyles are Pongo pygmaeus and Cercocebus torquatus, suggesting that there may be a relationship between unusually large condylar dimensions and the ability to crack hard nuts between the teeth. Cranial features having strong positive correlations with condylar dimensions include facial prognathism, maxillary incisor size, maxillary postcanine area, mandibular ramus breadth, and temporal fossa area. These data are interpreted as indicating that relatively large condyles are associated with relatively large masticatory muscles, relatively inefficient mandibular biomechanics, and a large dentition. These relationships support the growing evidence that the temporomandibular joint is a stress-bearing joint in normal function.

Animals↗

Coarctation of the stapedial artery: an unusual adaptive response to competing functional demands in the middle ear of some eutherians.

In primitive eutherians, the stapedial artery is the primary supplier of blood to the nonneural tissues of the head. Beyond a certain body size, the stapedial artery can no longer function as the sole supplier to its original territory because the diameter of its stem is limited by the size of the intercrural foramen of the stapes, which exhibits strong negative allometry. Some eutherians have extended the upper limit that the diameter of the stapedial stem can attain by developing a coarctation (narrowing) at the transcrual portion of the vessel. In the Norway rat (Rattus norvegicus) and the golden hamster (Mesocricetus auratus) the coarctation develops in postnatal life and is evidently caused by a retardation in growth that keeps the diameter of the vessel at infantile dimensions. In the rat, additional reduction in the external diameter is produced by a thinning of the tunica media of the arterial wall. A comfortable gap between the wall of the artery and the sides of the intercrural foramen is maintained that most likely facilitates the attenuation of potentially disruptive low-frequency vibrations produced by the arterial pressure pulse. The only negative side effect of a coarctation in rat-sized animals is that resistance to flow is increased and volume flow rate is concomitantly diminished. The coarctation does not create flow disturbances downstream of the constriction. One possible additional benefit of the coarctation is a flattening out of the arterial pressure pulse. It is speculated that the capacity to develop a coarctation once a certain body size is reached is an ancient trait that dates at least as far back as the Early Cretaceous.

Animals↗

Differential scaling of the long bones in the terrestrial carnivora and other mammals.

We measured the lengths and diameters of four long bones from 118 terrestrial carnivoran species using museum specimens. Though intrafamilial regressions scaled linearly, nearly all intraordinal regressions scaled non-linearly. The observed non-linear scaling of bone dimensions within this order results from a systematic decrease in intrafamilial allometric slope with increasing body size. A change in limb posture (more upright in larger species) to maintain similar peak bone stresses may allow the nearly isometric scaling of skeletal dimensions observed in smaller sized mammals (below about 100 kg). However, strong positive allometry is consistently observed in a number of large terrestrial mammals (the largest Carnivora, the large Bovidae, and the Ceratomorpha). This suggests that the capacity to compensate for size increases through alteration of limb posture is limited in extremely large-sized mammals, such that radical changes in bone shape are required to maintain similar levels of peak bone stress.

Animals↗