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 analysiscan 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.

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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 heterochronyFthe variation of apparent heterochrony by regionFimplies 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.

The evolutionary process leading to human brain globularity was gradual and paralleled the emergence of behavioral modernity.