Size-free Shape Research Articles

Three-dimensional geometric morphometric analyses of humerus ecomorphology: New perspectives for paleohabitat reconstruction in carnivorans and ungulates.

Long bone ecomorphology has proven effective for paleohabitat reconstructions across a wide range of mammalian clades. Still, there is no comprehensive framework to allow interpretation of long bone morphological variation within and between different monophyletic groups. Here, we investigated the use of humerus morphometry to classify living members of the orders Carnivora and ungulates based on their preferred habitats. Using geometric morphometrics, we extracted three different kinds of humerus shape data describing interspecific variation with and without accounting for evolutionary allometry and phylogenetic signal. The traditional a priori categorization of species in open, mixed, and closed habitats was employed in combination with selected subsets of shape variables to identify the best-predictive models for habitat adaptation. These were identified based on the statistical performance of phylogenetic and non-phylogenetic discriminant analyses and then applied to predict habitats on a subsample of fossil species. Size-free shape data combined with phylogenetic discriminant analyses showed the highest rate of accuracy in habitat classification for a combined sample of carnivorans and ungulates. Conversely, when the two groups were investigated separately, traditional shape data analyzed with phylogenetic discriminant function analyses provided models with the greatest predictive power. By combining carnivorans and ungulates within the same methodological framework we identified common adaptive features in closed habitat-adapted species that show compressed epiphyses, while open habitat-adapted species have expanded epiphyses. These morphologies evolved to allow significant degree of direction switches during locomotion in closed habitats compared to open habitat-adapted species whose forelimb joints evolved to stabilize articulations for increasing speed.

Beyond CREA: Evolutionary patterns of non-allometric shape variation and divergence in a highly allometric clade of murine rodents.

The shared functions of the skull are thought to result in common evolutionary patterns in mammalian cranial shape. Craniofacial evolutionary allometry (CREA) is a particularly prominent pattern where larger species display proportionally elongate facial skeletons and smaller braincases. It was recently proposed that CREA arises from biomechanical effects of cranial scaling when diets are similar. Thus, deviations from CREA should occur with changes in cranial biomechanics, for example due to dietary change. Here, we test this using 3D geometric morphometric analysis in a dataset of Australian murine crania, which are highly allometric. We contrast allometric and non-allometric variation in the cranium by comparing evolutionary mode, allometry, ordinations, as well as allometry, integration, and modularity in functional modules. We found evidence of stabilising selection in allometry-containing and size-free shape, and substantial non-allometric variation aligned with dietary specialisation in parallel with CREA. Integration among cranial modules was higher, and modularity lower, with size included, but integration between rostrum and cranial vault, which are involved in the CREA pattern, dropped dramatically after size removal. Our results thus support the hypothesis that CREA is a composite arising from selection on cranial function, with substantial non-allometric shape variation occurring alongside CREA where dietary specialisation impacts selection on gnawing function. This emphasises the need to research mammalian cranial evolution in the context of allometric and non-allometric selection on biomechanical function.

Geographical variation in head shape of a Neotropical group of toads: the role of physical environment and relatedness

In this study we review the morphological variation within the Rhinella crucifer species group using geometric morphometrics. We sampled 270 specimens from 78 localities comprising all genetic units delimited for the group. We placed 12 landmarks and 89 semi-landmarks defining morphological structures of the anterior region of the body (head and parotoid glands) on standardized photographs of dorsal aspects of specimens. We checked for the existence of size-free morphological variation using exploratory multivariate analyses and tested for differences among categories (genetic units) using canonical variate analyses. We investigated the effects of relatedness by conducting canonical analyses hierarchically, and tested for phylogenetic signal using reconstruction of morphologies on a tree derived from mitochondrial data. We then corrected for relatedness using phylogenetic principal component analysis, and tested for the influence of the physical environment (temperature, humidity and altitude) with a partial Mantel test of matrix correlation. Our results revealed that there is size-free shape variation in the group. Shape changes are related to specific structures in the head, with landmarks and semi-landmarks highlighting changes in a complementary way. We were able to statistically detect the effect of phylogenetic distance with landmarks when considering the closest genetic units as a single category. A significant proportion of the variation in head shape can be explained by environmental variables, suggesting that conditions of the physical environment should also be considered as a source of morphological variation.

Osteological Variation among Extreme Morphological Forms in the Mexican Salamander Genus Chiropterotriton (Amphibia: Plethodontidae): Morphological Evolution And Homoplasy.

Osteological variation is recorded among and within four of the most distinctive species of the Mexican salamander genus Chiropterotriton. Analysis of the data is consistent with the monophyletic status of the genus and documents previously unrecorded intraspecific and interspecific variation. Most of the recorded variation involves qualitative and quantitative proportional differences, but four fixed differences constitute autapomorphic states that affirm and diagnose some species (C. dimidiatus, C. magnipes). Osteological variation in 15 characters is analyzed with respect to predictions generated from four hypotheses: 1) phylogeny, 2) adaptation to specific habitats (the four species include cave-dwelling, terrestrial, and arboreal forms), 3) size-free shape, and 4) size. High levels of intraspecific variation suggest that the characters studied are not subject to rigid functional constraints in salamanders, regardless of size. The pattern predicted by the hypothesis based on size differences seen among these four Chiropterotriton species matches most closely the observed pattern of relative skull robustness. Since size change and heterochrony are often associated in plethodontid evolution, it is likely that changes in developmental timing play a role in the morphological transitions among these morphologically diverse taxa. Webbed feet, miniaturization, body shape, and an unusual tarsal arrangement are morphologies exhibited in species of Chiropterotrition that are shown to be homoplastic with other clades of tropical plethodontids. Although extensive homoplasy in salamanders might be seen as a roadblock to unraveling phylogenetic hypotheses, the homologous developmental systems that appear to underlie such homoplasy may reveal common and consistent evolutionary processes at work.

Ancestry estimation in South Africa using craniometrics and geometric morphometrics

Population history and positive assortative mating directs gene flow in such a way that biological differences are recognized among groups. In turn, forensic anthropologists quantify biological differences to estimate ancestry. Some anthropologists argue that highly admixed population groups, such as South African coloureds, cannot achieve acceptable accuracies because within group variance is too large. Whereas ancestry estimation in South Africa has been limited to craniometric data from South African blacks and whites, the current study integrates craniometric and geometric morphometric data from the three largest South African groups.Crania from 377 South African individuals (black=158, white=112, and coloured=107) comprised the sample. Standard measurements were collected and the coordinate data were subjected to Generalized Procrustes Analysis (GPA), which resulted in size-free shape variables (ProCoords). A principal component analysis was used to combine the shape variation captured in the ProCoords (ProCoords PC). Linear discriminant analysis (LDA), using equal priors, stepwise variable selection and leave-one-out cross-validation, was conducted on the ProCoords, the ProCoords PCs, and the traditional craniometric data.The LDA using 18 stepwise selected ProCoords resulted in the highest cross-validated accuracy (89%). Utilization of geometric morphometric data emphasized that the relative location of cranial landmarks was more discriminating than simple linear distances. Regardless of high levels of genetic admixture, South African coloureds are a homogeneous group and morphologically distinct from other contemporaneous South African populations. Furthermore, the present study demonstrated a correspondence between peer-reported race and morphological differences in the crania of black, white, and coloured South Africans.

INTERSPECIFIC PATTERNS OF SKULL VARIATION BETWEEN SYMPATRIC BRAZILIAN VESPER MICE: GEOMETRIC MORPHOMETRICS ASSESSMENT

Sympatric species of vesper mice (Calomys expulsus and C. tener) from the Cerrado biome are often distinguished by their respective sizes. Using geometric morphometrics, we tested if interspecific differences were mainly due to isometric or allometric size variations or allometry-free shape differences. To delimit species groups, we used and compared linear discriminant analysis, calculated on subsets of individuals of known identity, and pattern recognition techniques, needing no prior information on specimens. They both yielded similar results, indicating that patterns of interspecific morphological differences are mainly due to size-free shape differences located at landmarks defined at the suture between the frontals and the parietals and between the latter and the interparietal. Correct specimen identification was obtained with pattern recognition techniques using Gaussian mixture models. Morphological differences also were found between the 2 species analyzed and the newly described C. tocantinsi represented here by its paratypes. The combination of geometric morphometrics and pattern recognition techniques seems suitable for systematic analyses aimed at elucidating interspecific patterns of morphological variation in closely related species in field studies and museum specimens.

Size-free shape differences between male and female Western Australian dragon lizards (Agamidae)

AbstractExamination of size-free body shape for males and females of 41 species of Western Australian dragon lizards (Agamidae) indicate that males generally have a proportionally longer head, and females a proportionally longer abdomen. Principal component and cluster analyses show that size-free body shape differences between males and females are neither uniform nor consistent within the Agamidae, or the genus Ctenophorus. This inconsistency is problematic when linking morphological characteristics with performance traits, use of space, or preferred habitat for species. We recommend that male and female dragons are treated separately in morphological analyses, but acknowledge that this increases the complexity of analyse and interpretations.

Shape of Western Australian dragon lizards (Agamidae)

AbstractFor 41 species of Western Australian agamid lizards, we found that most appendage lengths vary isometrically, so shape is largely independent of size. Of the three methods we used to quantitatively remove the effects of size on shape, the two that use principal component analysis (PCA; Jolicoeur, 1963; Somers, 1986; 1989) provided similar results, whereas regression residuals (against body length) provided a different interpretation. Somers' size-free PCA approach to remove the size-effects was the most useful because it provided 'size-free' scores for each species that were further analysed using other techniques, and its results seemed more biologically meaningful. Some, but not all, of the variation in size-free shape for these lizards could be related to phylogeny, retreat choice and performance traits.

Allometry of workers of the fire ant, Solenopsis invicta

The relationship between worker body size and the shape of their body parts was explored in the polymorphic ant, Solenopsis invicta. The data consisted of 20 measurements of body parts as well as sums of some of these measurements. Size-free shape variables were created by taking the ratios of relevant measures. After log-transformation, these ratios were regressed against the logarithm of total body length, or against the log of the size of the parent part. Slopes of zero indicated that shape did not change with size, and non-zero slopes signaled a size-related change of shape. Across the range of worker sizes, the head length retained a constant proportion to body length, but relative headwidth increased such that head shape changed from a barrel-profile to a somewhat heart-shaped profile. Antennae became relatively smaller, with the club contributing more to this decline than the other parts. The alinotum became relatively shorter and higher (more humped), and the gaster increased in both relative width and length, and therefore in volume. All three pairs of legs were isometric to body length. The component parts of the legs, with one exception, were isometric to their own total leg length. The body of S. invicta is therefore dominated by mostly modest allometries, giving large workers a somewhat different shape than small ones. None of these size-shape relationships was different for different colonies. The functional meaning of these shape changes is unknown, but that does not stop us from speculating.

Allometry of Workers of the Fire Ant, Solenopsis invicta

The relationship between worker body size and the shape of their body parts was explored in the polymorphic ant, Solenopsis invicta. The data consisted of 20 measurements of body parts as well as sums of some of these measurements. Size-free shape variables were created by taking the ratios of relevant measures. After log-transformation, these ratios were regressed against the logarithm of total body length, or against the log of the size of the parent part. Slopes of zero indicated that shape did not change with size, and non-zero slopes signaled a size-related change of shape. Across the range of worker sizes, the head length retained a constant proportion to body length, but relative headwidth increased such that head shape changed from a barrel-profile to a somewhat heart-shaped profile. Antennae became relatively smaller, with the club contributing more to this decline than the other parts. The alinotum became relatively shorter and higher (more humped), and the gaster increased in both relative width and length, and therefore in volume. All three pairs of legs were isometric to body length. The component parts of the legs, with one exception, were isometric to their own total leg length. The body of S. invicta is therefore dominated by mostly modest allometries, giving large workers a somewhat different shape than small ones. None of these size-shape relationships was different for different colonies. The functional meaning of these shape changes is unknown, but that does not stop us from speculating.

Two statistical approaches to nuclei shape and size in a morphometric description of lymph node sections in non‐Hodgkin's lymphoma

An attempt is made to evaluate more clearly the potential contribution of quantitative nuclear profile shape and size measurements to lymph node section histologic description in 70 cases of non-Hodgkin's lymphoma (NHL). The area of nuclear profiles and five nonredundant and size-free shape indices were measured using the THECLA program on a Leitz Texture Analysis System (Leitz-TAS). Two statistical approaches were applied, known respectively as "parametric," (first statistical moments of variable distributions over samples of 200 nuclear profiles) and "nonparametric," which are percentages of nuclear profiles distributed into five "cytological" classes that are defined by shape: round (A), elongated (B), kidney shaped (C), irregular (D) and cleaved (E) nuclear profiles. Both statistical approaches provide proper overall discrimination of the eight histological categories identified with reasonable reliability by pathologists. Above all, the present report discusses the ability of a set of parametric and nonparametric variables to describe NHL cell populations, in an objective and meaningful way, according to nuclei shape. A method of synthesizing multidimensional correlations (CORICO program) is proposed in support of the discussion. Also, the specific descriptive power of each of the variables is described; in particular, it is concluded that there is a close link between the shape and size of the nuclear profiles of the cells.

Body form differences between the Enos Lake species pair of threespine sticklebacks (Gasterosteus aculeatus complex)

Two ecologically and morphologically divergent species of the Gasterosteus aculeatus (threespine stickleback) species complex occur in Enos Lake, Vancouver Island, British Columbia. The limnetic species swims in open water most of the time and feeds on plankton, and the benthic species lives near the shore in a structurally complex environment where it eats larger benthic prey. Based on design criteria inferred from hydrodynamic considerations, from other fishes, or from other populations of Gasterosteus, and on ecological differences between the two species, we expected that limnetic sticklebacks would have a more fusiform body, longer pectoral fins and snout, and larger eyes. Although some of these expected differences had been observed in a previous study of this species pair, others were verified for the first time in this study. Shape divergence between our samples results both from allometric trends coupled with differences in overall mean size and from size-free shape differences. Standard length is a poor proxy for general size (i.e., the first principal component of the morphometric variables) because several major features which differ between the species are dorsoventrally oriented. The marked morphometric divergence between these species has probably evolved within about the past 13 000 years, since deglaciation of Vancouver Island.

Multivariate Discrimination by Shape in Relation to Size

Humphries, J. M., F. L. Bookstein, B. Chernoff, G. R. Smith, R. L. Elder, and S. G. Poss (Museum of Zoology, Centerfor Human Growth and Development, Museum of Paleontology, and Division of Biological Sciences, The University of Michigan, Ann Arbor, Michigan 48109) 1981. Multivariate discrimination by shape in relation to size. Syst. Zool., 30:291-308.-The diverse methods for analyzing size-free shape differences tend to be guided by computational expediency rather than geometric principles. We question the use of ratios and ad hoc combinations of spatially unrelated measures. Neither are linear discriminant functions or series of independent regressions helpful to the visualization of shape differences. A bridge is needed between traditional quantitative methods and the geometrical analysis of shape. In principle any measured transects between landmarks of a form can serve as characters in a morphometric analysis. Systematic studies use a highly non-random sample of these, particularly biased regarding geometrical information. We suggest defining size and shape in terms of factors-estimates of common to a universe of measured distances. The model presented here calculates a linear combination of variables that quantifies shape differences among populations, independent of size. In analyses in which the first two principal components confound size and shape, size is removed from one axis with shear coefficients derived from regression of general size on principal components centered by group. The general size factor is estimated by the principal axis of the within-group covariance matrix of the log-transformed data. Residuals from the regression of general size on the transformed axes approximate a shape-discriminating factor that is uncorrelated with size within group and displays the interpopulation shape differences borne by the first two principal components. The results bear a direct and interpretable correspondence to biorthogonal analysis of shape difference. [Multivariate analysis; principal components; discriminant functions; morphometrics; size-free shape; allometry; fishes.] Systematists need procedures that allow them to discriminate among groups of organisms that vary in size. The groups included in a study can be chosen a priori (e.g., several species or geographic populations within a species) or a posteriori (as a conclusion resulting from some method of analysis). However the groups are chosen, it has long been considered desirable to discriminate among them on the basis of size-free shape derived from distance measures. The terms shape and size have been used in various and sometimes conflicting ways (Huxley, 1932; Thompson, 1942; Simpson, Roe and Lewontin, 1960; Gould, 1966; Mosimann, 1970; Sprent, 1972; Bookstein, 1978). We construe size and shape not as measured variables, but as general factors, linear combinations most parsimoniously accounting for the associations among the distance measures. Size, in particular, is not a single variable such as biomass or a standard length, but a factor which, when called upon to predict all the distance measures within a population, leaves the smallest mean squared residual. We prefer a factor whose algebraic form acknowledges the allometric relationship (Jolicoeur, 1963). Our shape discriminators need to be independent of size (Flessa and Bray, 1977; Mosimann and James, 1979) in order to partition out the effects of growth (e.g., individuals of differing age and size). In general, shape can be defined as the geometry of the organism after information about position, scale, and orientation has been removed (Bookstein, 1978:8). There is then an endless variety of shape remaining. While the quantification of size as a general factor de-