Philipp Mitteroecker

Advances in Geometric Morphometrics

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.

Linear Discrimination, Ordination, and the Visualization of Selection Gradients in Modern Morphometrics

Linear discriminant analysis (LDA) is a multivariate classification technique frequently applied to morphometric data in various biomedical disciplines. Canonical variate analysis (CVA), the generalization of LDA for multiple groups, is often used in the exploratory style of an ordination technique (a low-dimensional representation of the data). In the rare case when all groups have the same covariance matrix, maximum likelihood classification can be based on these linear functions. Both LDA and CVA require full-rank covariance matrices, which is usually not the case in modern morphometrics. When the number of variables is close to the number of individuals, groups appear separated in a CVA plot even if they are samples from the same population. Hence, reliable classification and assessment of group separation require many more organisms than variables. A simple alternative to CVA is the projection of the data onto the principal components of the group averages (between-group PCA). In contrast to CVA, these axes are orthogonal and can be computed even when the data are not of full rank, such as for Procrustes shape coordinates arising in samples of any size, and when covariance matrices are heterogeneous. In evolutionary quantitative genetics, the selection gradient is identical to the coefficient vector of a linear discriminant function between the populations before vs. after selection. When the measured variables are Procrustes shape coordinates, discriminant functions and selection gradients are vectors in shape space and can be visualized as shape deformations. Except for applications in quantitative genetics and in classification, however, discriminant functions typically offer no interpretation as biological factors.

THE EVOLUTIONARY ROLE OF MODULARITY AND INTEGRATION IN THE HOMINOID CRANIUM

Abstract Patterns of morphological integration and modularity among shape features emerge from genetic and developmental factors with varying pleiotropic effects. Factors or processes affecting morphology only locally may respond to selection more easily than common factors that may lead to deleterious side effects and hence are expected to be more conserved. We briefly review evidence for such global factors in primate cranial development as well as for local factors constrained to either the face or the neurocranium. In a sample comprising 157 crania of Homo sapiens, Pan troglodytes, and Gorilla gorilla, we statistically estimated common and local factors of shape variation from Procrustes coordinates of 347 landmarks and semilandmarks. Common factors with pleiotropic effects on both the face and the neurocranium account for a large amount of shape variation, but mainly by extension or truncation of otherwise conserved developmental pathways. Local factors (modular shape characteristics) have more degrees of freedom for evolutionary change than mere ontogenetic scaling. Cranial shape is similarly integrated during development in all three species, but human evolution involves dissociation among several characteristics. The dissociation has probably been achieved by evolutionary alterations and by the novel emergence of local factors affecting characteristics that are controlled at the same time by the common factors.

Heterochrony and geometric morphometrics: a comparison of cranial growth in Pan paniscus versus Pan troglodytes.

Summary Heterochrony, the classic framework in which to study ontogeny and phylogeny, in essence relies on a univariate concept of shape. Though principal component (PC) plots of multivariate shape data seem to resemble classical bivariate allometric plots, the language of heterochrony cannot be translated directly into general multivariate methodology. We simulate idealized multivariate ontogenetic trajectories and explore their appearance in PC plots of shape space and size–shape space. Only if the trajectories of two related species lie along exactly the same path in shape space can the classic terminology of heterochrony apply and pure dissociation of size change against shape change be detected. Regional heterochrony—the variation of apparent heterochrony by region—implies a dissociation of local growth fields and cannot be identified in an overall PC analysis. We exemplify a geometric morphometric approach to these issues using adult and subadult crania of 48 Pan paniscus and 47 Pan troglodytes specimens. On each specimen, we digitized 47 landmarks and 144 semilandmarks on facial curves and the external neurocranial surface. We reject the hypothesis of global heterochrony in the cranium of Pan as well as regional heterochrony for the lower face, the upper face, and the neurocranium.

Early modern human diversity suggests subdivided population structure and a complex out-of-Africa scenario

The interpretation of genetic evidence regarding modern human origins depends, among other things, on assessments of the structure and the variation of ancient populations. Because we lack genetic data from the time when the first anatomically modern humans appeared, between 200,000 and 60,000 years ago, instead we exploit the phenotype of neurocranial geometry to compare the variation in early modern human fossils with that in other groups of fossil Homo and recent modern humans. Variation is assessed as the mean-squared Procrustes distance from the group average shape in a representation based on several hundred neurocranial landmarks and semilandmarks. We find that the early modern group has more shape variation than any other group in our sample, which covers 1.8 million years, and that they are morphologically similar to recent modern humans of diverse geographically dispersed populations but not to archaic groups. Of the currently competing models of modern human origins, some are inconsistent with these findings. Rather than a single out-of-Africa dispersal scenario, we suggest that early modern humans were already divided into different populations in Pleistocene Africa, after which there followed a complex migration pattern. Our conclusions bear implications for the inference of ancient human demography from genetic models and emphasize the importance of focusing research on those early modern humans, in particular, in Africa.

Second to fourth digit ratio and face shape

The average human male face differs from the average female face in size and shape of the jaws, cheek-bones, lips, eyes and nose. It is possible that this dimorphism is determined by sex steroids such as testosterone (T) and oestrogen (E), and several studies on the perception of such characteristics have been based on this assumption, but those studies focussed mainly on the relationship of male faces with circulating hormone levels; the corresponding biology of the female face remains mainly speculative. This paper is concerned with the relative importance of prenatal T and E levels (assessed via the 2D : 4D finger length ratio, a proxy for the ratio of T/E) and sex in the determination of facial form as characterized by 64 landmark points on facial photographs of 106 Austrians of college age. We found that (i) prenatal sex steroid ratios (in terms of 2D : 4D) and actual chromosomal sex dimorphism operate differently on faces, (ii) 2D : 4D affects male and female face shape by similar patterns, but (iii) is three times more intense in men than in women. There was no evidence that these effects were confounded by allometry or facial asymmetry. Our results suggest that studies on the perception of facial characteristics need to consider differential effects of prenatal hormone exposure and actual chromosomal gender in order to understand how characteristics have come to be rated ‘masculine’ or ‘feminine’ and the consequences of these perceptions in terms of mate preferences.

The Ontogenetic Trajectory of the Phenotypic Covariance Matrix, with Examples from Craniofacial Shape in Rats and Humans

Many classic quantitative genetic theories assume the covariance structure among adult phenotypic traits to be relatively static during evolution. But the cross-sectional covariance matrix arises from the joint variation of a large range of developmental processes and hence is not constant over the period during which a population of developing organisms is actually exposed to selection. To examine how development shapes the phenotypic covariance structure, we ordinate the age-specific covariance matrices of shape coordinates for craniofacial growth in rats and humans. The metric that we use for this purpose is given by the square root of the summed squared log relative eigenvalues. This is the natural metric on the space of positive-definite symmetric matrices, which we introduce and justify in a biometric context. In both species, the covariance matrices appear to change continually throughout the full period of postnatal development. The resulting ontogenetic trajectories alter their direction at major changes of the developmental programs whereas they are fairly straight in between. Consequently, phenotypic covariance matrices—and thus also response to selection—should be expected to vary both over ontogenetic and phylogenetic time scales as different phenotypes are necessarily produced by different developmental pathways.

Sexual dimorphism of the human mandible and its association with dental development

The present study investigates whether the human mandible is sexually dimorphic during early postnatal development and whether early dimorphic features persist during subsequent ontogeny. We also examine whether mandibular dimorphism is linked to dimorphism of dental development. Dense CT-derived mandibular meshes of 84 females and 75 males, ranging from birth to adulthood, were analyzed using geometric morphometric methods. On the basis of the specimens chronological ages and mineralization stages of the deciduous and permanent teeth, we compute dental age as proxy for dental development by the additive conjoint measurement method. By birth, males have, on average, more advanced age-specific shapes than females. However, sex differences decrease quickly as females catch up via a different association between shape and size. This leads to an almost complete reduction of sexual dimorphism between the ages of 4 and 14. From puberty to adulthood, males are characterized by allometric shape changes while the shape of the female mandible continues to change even after size has ceased to increase. Dimorphism of dental maturation becomes visible only at puberty. Sexual dimorphism, concentrated at the ramus and the mental region during the earliest ontogenetic stages and again at adulthood, is not associated with the development of the teeth. At puberty there is a simultaneous peak in size increase, shape development, and dental maturation likely controlled by the surge of sex hormones with a dimorphic onset age. We argue that the infant and adult dimorphism of the mental region may be associated with the development of supralaryngeal structures.

Craniofacial sexual dimorphism patterns and allometry among extant hominids.

Craniofacial sexual dimorphism in primates varies in both magnitude and pattern among species. In the past two decades, there has been an increasing emphasis in exploring the correlations of these patterns with taxonomy and the variation in patterns within and among the craniofacial regions. Scrutinising these relationships for hominids, we decompose the craniofacial morphology in five taxa: Homo sapiens, Pan paniscus, Pan troglodytes, Gorilla gorilla and Pongo pygmaeus. 3D coordinates of 35 traditional landmarks and 61 semilandmarks, covering five ridge curves, are measured for each of 268 adult and sub-adult specimens and analysed using geometric morphometric methods. A multivariate analysis in size-shape space shows that ontogenetic scaling contributes to the development of sexual dimorphism in all five taxa, but to a varying extent. In absolute as well as in relative terms P. pygmaeus shows the greatest allometric component, followed by G. gorilla. Homo is intermediate, while in Pan the non-allometric constituent part contributes a large fraction to the actual sexual dimorphism, most markedly in the pygmy chimpanzee. An eigendecomposition of the five vectors of sexual dimorphism reveals two dimensions independent of allometry. One separates orang-utan sexual dimorphism from the African apes and Homo, and the other differentiates between the great apes and Homo with Pan mediating. We discuss these patterns and speculate on their use as characters for taxonomic analysis in the fossil record.

How to Explore Morphological Integration in Human Evolution and Development

Most studies in evolutionary developmental biology focus on large-scale evolutionary processes using experimental or molecular approaches, whereas evolutionary quantitative genetics provides mathematical models of the influence of heritable phenotypic variation on the short-term response to natural selection. Studies of morphological integration typically are situated in-between these two styles of explanation. They are based on the consilience of observed phenotypic covariances with qualitative developmental, functional, or evolutionary models. Here we review different forms of integration along with multiple other sources of phenotypic covariances, such as geometric and spatial dependencies among measurements. We discuss one multivariate method [partial least squares analysis (PLS)] to model phenotypic covariances and demonstrate how it can be applied to study developmental integration using two empirical examples. In the first example we use PLS to study integration between the cranial base and the face in human postnatal development. Because the data are longitudinal, we can model both cross-sectional integration and integration of growth itself, i.e., how cross-sectional variance and covariance is actually generated in the course of ontogeny. We find one factor of developmental integration (connecting facial size and the length of the anterior cranial base) that is highly canalized during postnatal development, leading to decreasing cross-sectional variance and covariance. A second factor (overall cranial length to height ratio) is less canalized and leads to increasing (co)variance. In a second example, we examine the evolutionary significance of these patterns by comparing cranial integration in humans to that in chimpanzees.