Median-based resistant methods in the current framework of Geometric Morphometrics

Landmark-based geometric morphometric (GM) methods have become a standard in shape analysis. Superimposition of landmark constellations, referenced to the mean, is performed using the least squares criterion under the consensus framework of Generalized Procrustes Analysis (GPA). While effective, especially when combined with multivariate statistics, this approach also has limitations. Specifically, if there is localized variation (if a few landmarks are significantly displaced in relation to the others), the method homogenizes variation to perform an optimal fit that can spread variation randomly, yielding unrealistic results. This limitation has long been recognized and discussed in the literature—especially paleontological—proposing methods based on repeated medians that help checking for such localized variation in landmark constellations. However, the broad establishment of GPA has led to their neglect, potentially compromising interpretations in studies of allometry, integration, and modularity. Two real life examples, one biological (spiders) and one paleobiological (pterosaur skulls), are used to illustrate what "localized variation" means and the effect it can have on the structure of Procrustes shape data, and consequently, on further statistical analyses. The intended message is that median-based resistant methods for landmark superimposition should be re-implemented