Abstract
Articulating structures, such as the vertebrate skeleton or the segmented arthropod exoskeleton, comprise a majority of the morphological diversity across the eukaryotic tree of life. Quantifying the form of articulating structures is therefore imperative for a fuller understanding of the factors influencing biological form. A wealth of freely available 3D data capturing this morphological diversity is stored in online repositories such as Morphosource, but the geometric morphometric analysis of an articulating structure is impeded by arbitrary differences in the resting positions of its individual articulating elements. In complex articulating structures, where the angles between articulating elements cannot be standardized, landmarks on articulating elements must be Procrustes superimposed independently (locally) and then recombined to quantify variation in the entire articulating structure simultaneously. Here, we discuss recent advances in local superimposition techniques, namely the "matched local superimpositions" approach, which incorporates anatomically accurate relative sizes, positions, and orientations of locally-superimposed landmarks, enabling clearer biological interpretation. We also use simulations to evaluate the consequences of choice of superimposition approach. Our results show that local superimpositions will isolate shape variation within locally-superimposed landmark subsets by sacrificing size and positional variation. They may also create morphometric "modules" when there are none by increasing integration within the locally-superimposed subsets; however, this effect is no greater than the spurious between-module integration created when superimposing landmark subsets (i.e., articulating elements) together. Taken together, our results show that local superimposition techniques differ from conventional Procrustes superimpositions in predictable ways. Finally, we use empirical datasets of the skulls of wrasses and colubriform snakes to highlight the promise of local superimpositions and their utility. Complex articulating structures must be studied, and the only current solution to do so is local superimpositions.