Modularity and Morphometrics: Error Rates in Hypothesis Testing
The study of modularity in morphological systems has increased in the past twenty years, parallel to the popularization of geometric morphometrics, which has led to the emergence of different criteria for detecting modularity on landmark data. However, compared to usual covariance matrix estimators, Procrustes estimators have properties that hinder their use. Here, we compare different representations of form, focusing on detecting modularity patterns defined a priori; we also compare two metrics: one derived from traditional morphometrics (MHI) and another that emerged in the context of landmark data (RV). Using Anthropoid skulls, we compare these metrics over three representations of form: interlandmark distances, Procrustes residuals, and local shape variables. Over Procrustes residuals, both tests fail to detect modularity patterns, while in remaining representations they show the distinction between early and late development in skull ontogeny. To estimate type I and II error rates, we built covariance matrices of known structure; these tests indicate that, considering both effect and sample sizes, tests using MHI are more robust than those using RV. However, both metrics have low power when used on Procrustes residuals. Thus, we conclude that the influence of development and function is poorly represented on Procrustes estimators for covariance matrices.