Regional dissociated heterochrony in multivariate analysis

Heterochrony, the classic framework to study ontogeny and phylogeny, in essence relies on a univariate concept of shape. Though principal component 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 demonstrate their behavior in principal component plots in shape space and in size-shape space. The concept of "dissociation", which is conventionally regarded as a change in the relationship between shape change and size change, appears to be algebraically the same as regional dissociation - the variation of apparent heterochrony by region. Only if the trajectories of two related species lie along exactly the same path in shape space can the classic terminology of heterochrony apply so that pure dissociation of size change against shape change can be detected. We demonstrate a geometric morphometric approach to these issues using adult and subadult crania of 48 Pan paniscus and 47 P. troglodytes. On each specimen we digitized 47 landmarks and 144 semilandmarks on ridge curves and the external neurocranial surface. The relation between these two species' growth trajectories is too complex for a simple summary in terms of global heterochrony.