Making Heads or Tails of Combined Landmark Configurations in Geometric Morphometric Data

Abstract

Researchers using geometric morphometric methods can be confronted with a need to combine separate landmark configurations from the same research subjects as a more holistic description of organismal morphology. Combining configurations might be valid if single configurations represent separate anatomical structures that can change position with respect to each other or have been shown to be phenotypically integrated, and researchers would prefer to recognize these structures as one set, rather than multiple sets. However, generalized Procrustes analysis (GPA) scales separate configurations to unit size, meaning that in combination, some attempt to relativize the size of configurations should be made. A few recent studies have calculated the relative size of separate configurations in different ways but there has been no formal consideration for the implications of a priori judgments for how configuration sizes should be weighted, before the synthesis presented here. We offer a general solution for weighting separate configuration centroid sizes when combining them, which captures the intention of different methods thus far proposed. We also demonstrate that under various conditions, weighting via normalized centroid size is fraught with problems, and should be avoided. By contrast, an unweighted approach that seeks to maintain landmark densities in separate configurations provides reliable results. Nevertheless, researchers should realize that combining configurations creates new configurations with landmark covariances that are arbitrary with respect to any real anatomical features. As such, combining landmark configurations should not be a haphazard enterprise under any circumstances.