Allometry for the Twenty-First Century

Abstract

The current literature that attempts to bridge between geometric morphometrics (GMM) and finite element analyses (FEA) of CT-derived data from bones of living animals and fossils appears to lack a sound biotheoretical foundation. To supply the missing rigor, the present article demonstrates a new rhetoric of quantitative inference across the GMM–FEA bridge—a rhetoric bridging form to function when both have been quantified so stringently. The suggested approach is founded on diverse standard textbook examples of the relation between forms and the way strains in them are produced by stresses imposed upon them. One potentially cogent approach to the explanatory purposes driving studies of this class arises from a close scrutiny of the way in which computations in both domains, shape and strain, can be couched as minimizations of a scalar quantity. For GMM, this is ordinary Procrustes shape distance; in FEA, it is the potential energy that is stored in the deformed configuration of the solid form. A hybrid statistical method is introduced requiring that all forms be subjected to the same detailed loading designs (the same “probes”) in a manner careful to accommodate the variations of those same forms before they were stressed. The proper role of GMM is argued to be the construction of regressions for strain energy density on the largest-scale relative warps in order that biological explanations may proceed in terms of the residuals from those regressions: the local residual features of strain energy density. The method, evidently a hierarchical one, might be intuitively apprehended as a geometrical approach to a formal allometric analysis of strain. The essay closes with an exhortation.