Morphometric heterochrony and the evolution of growth

Heterochrony has been an influential perspective on the evolution of morphologies, a circumstance mostly due to a strategic shift of the theory to the analysis of growth and measurable traits. A difficulty in testing hypotheses of heterochrony in the morphometric realm, and therefore in establishing its evolutionary relevance, has been the absence of an explicit criterion of homology in comparisons supposed to reveal paedomorphosis and peramorphosis. Based on the formalism of ontogenetic and allometric trajectories, we defined a criterion of primary homology in the context of morphometric characters that requires only a comparison between metric traits from ontogenetic series of two or more taxa. On the one hand, such a criterion allows for the calculation of values of shape slopes and allometric coefficients in descendants supposedly affected by changes in ontogenetic timing, thereby supplying an analytical tool for testing hypotheses of heterochrony. On the other hand, the concept of morphometric homology establishes the descriptive limits of paedomorphosis and peramorphosis, showing, for example, that the model of sequential hypermorphosis applied to the evolution of human encephalization is not within the descriptive scope of the morphological markers of heterochrony. Sequential hypermorphosis is a successful model of morphometric evolution, as further illustrated by the match between our mathematical deductions and the empirical results obtained by analyses of brain growth data. By exploring the properties of multiphasic polynomial functions, we deduce equations that define the relationship between developmental delay or acceleration and their effect on adult brain size. Together with the primary criterion of homology, we demonstrate that sequential hypermorphosis could generate the large modern human brain, but such brain is neither paedomorphic nor peramorphic. Our approach based on homology and allometry indicates that the evolution of growth is richer in phenomena than heterochrony can account for, and accordingly we argue that morphometric theory can expand its descriptive and heuristic scope by looking beyond the limits imposed by paedomorphosis and peramorphosis.