Diffeomorphic Independent Contrasts for Ancestral Reconstruction of Shapes

Ancestral state reconstruction is a fundamental challenge in evolutionary biology, requiring methods that can capture complex morphological changes while accounting for phylogenetic relationships. Current approaches are based on linear assumptions that often oversimplify the spatial relationships between anatomical features and fail to incorporate landmark correlations within shapes directly in the modeling. Here, we introduce a novel method that combines the ability of Large Deformation Diffeomorphic Metric Mapping (LDDMM) to model smooth, invertible transformations between shapes while preserving the relationships between landmarks with Felsenstein's Independent Contrasts (IC) to iteratively reconstruct ancestral shapes along the branches of a phylogenetic tree. We call this method Diffeomorphic Independent Contrasts for Ancestral Reconstruction of Shapes (DICAROS). We validate DICAROS against three existing methods: (1) linear predictors using Ordinary Least Squares (2) ancestral character estimation using maximum likelihood under Brownian Motion and (3) ridge archetypal penalized likelihood. We apply DICAROS to a dataset of swallowtail butterfly species (Family Papilionidae, Order Lepidoptera) to reconstruct the ancestral shape and visualize evolutionary trajectories in a phylomorphospace from the contrasts. We conclude that DICAROS outperforms the existing methods in terms of accuracy and provides a more accurate reconstruction of the ancestral shape for non-symmetric phylogenetic trees. With DICAROS we show a transition between untailed and tailed Papilionidae species while also illustrating how images of modern species would look under the DICAROS ancestral reconstruction.