A visual approach to mapping and comparing the distribution of variation through geometrical models

Abstract

One of the main aims of morphometrics is the quantification of differences among biological structures. Many tools (in particular considering geometric morphometrics) have been developed to visualise the results of such quantification, images being the most effective summary for a species with a visual-based system of perception such as humans. The degree of variation of the morphological components is a direct product of at least two different factors: the selective pressure, and the biogical constraints. This is identifiable at different levels, from the systematic (species diversity, species variability) to the individual or anatomical (intraspecific variation or variation of single traits). In this paper, we present a simple and effective approach to map the degree of variation by using landmark superimposition, providing a comparison between different species. The case study is the morphology of the dental occlusal surface, compared between modern and extinct human species. Different parameters of distribution of the coordinates after Procrustes superimposition are used to quantify the degree of variation at each landmark according to a common reference (the overall sample variability), and interpolant functions are then used to provide a general synthesis of the distribution of the values. This approach provides a visual representation of the spatial distribution of the variance within the geometric model. Thus, it entails a rapid and complete perspective of the patterns associated with the de-gree of variation in a given anatomical element. Such visual output may be useful as an interface between the analytical steps (inferential and de-scriptive multivariate statistics) and the following interpretation of results.