Studying Morphological Variation: Exploring the Shape Space in Evolutionary Anthropology

TL;DR

This paper develops a mathematical framework for analyzing morphological variation in primate and mammal bones using differential geometry and machine learning, enabling robust evolutionary shape comparisons.

Contribution

It introduces a comprehensive mathematical approach to compare and analyze anatomical shapes across species, integrating multiple methods into a unified framework.

Findings

Robust shape comparison methods for anatomical surfaces.

Framework for cross-dataset landmark selection and shape classification.

Integration of differential geometry and machine learning for evolutionary morphology.

Abstract

We present results of a long-term team collaboration of mathematicians and biologists. We focus on building a mathematical framework for the shape space constituted by a collection of homologous bones or teeth from many species. The biological application is to quantitative morphological understanding of the evolutionary history of primates in particular, and mammals more generally. Similar to the practice of biologists, we leverage the power of the whole collection for results that are more robust than can be obtained by only pairwise comparisons, using tools from differential geometry and machine learning. This paper concentrates on the mathematical framework. We review methods for comparing anatomical surfaces, discuss the problem of registration and alignment, and address the computation of different distances. Next, we cover broader questions related to cross-dataset landmark selection, shape segmentation, and shape classification analysis. This paper summarizes the work of many team members other than the authors; in this paper that unites (for the first time) all their results in one joint context, space restrictions prevent a full description of the mathematical details, which are thoroughly covered in the original articles. Although our application is to the study of anatomical surfaces, we believe our approach has much wider applicability.