On the importance of examining the relationship between shape data and biologically meaningful variables. An example studying allometry with geometric morphometrics

Abstract

Geometric morphometrics (GM) is a tool for the statistical analysis of shape on Cartesian landmark coordinates. However, because GM studies commonly focus on the description of morphological trends within shape space (or morphospace), the predictive power of multivariate statistics to understand morphological change remains underutilized. Here we show the protocols to study allometry in 3D with these tools on a postnatal growth series of the domestic chicken. We contrast three approaches: a ‘traditional’ one in which size variables are compared statistically, a Principal Components Analysis on size and shape scores (Procrustes form space), and a multivariate regression. In the latter approach we further used three different independent factors inherently related to ontogeny: skull centroid size, body weight, and age of the specimens. The results clearly stress the importance of studying shape change in relation to different causal factors (i.e., with regressions), demonstrating that, indeed, any independent variable or variables that make biological sense can be used to understand morphological change with GM