Reworking Geometric Morphometrics into a Methodology of Transformation Grids

Abstract Today’s typical application of geometric morphometrics to a quantitative comparison organismal anatomies begins by standardizing samples homologously labelled point configurations for location, orientation, and scale, then renders the ensuing comparisons graphically thin-plate spline as applied group averages, principal components, regression predictions, or canonical variates. The scale-standardization step has recently come under criticism unnecessary indeed inappropriate, at least growth studies. This essay argues similar rethinking centering rotation, replacement interpolant resulting different strategy that leaves unexplained residuals every landmark individually in order simplify interpretation displayed grid whole, “transformation grid” been highlighted true underlying topic ever since D’Arcy Thompson’s celebrated exposition 1917. For analyses involving gradients large this paper all three Procrustes conventions version my two-point registration 1986 [originally Galton’s 1907 (Nature 76:617–618, 1907)]. choice two points interacts with another non-Procrustes concern, interpretability lines coordinate system deformed according fitted polynomial trend rather than an interpolating spline. works examples using previously published midsagittal cranial data; there result new findings pertinent both these classic data sets. A concluding discussion suggests current toolkit morphometrics, centered on shape coordinates splines, is too restricted suit many interpretive purposes evolutionary developmental biology.