Diffeomorphic Independent Contrasts for Ancestral Reconstruction of Shapes

AO_SCPLOWBSTRACTC_SCPLOWAncestral 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 account for landmark correlations within shapes. 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 Felsensteins 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 two existing methods: (1) Linear predictors using Ordinary Least Squares and (2) Ancestral character estimation using maximum likelihood under Brownian Motion and apply DICAROS to a dataset of swallowtail butterfly species (Family Papilonidae, Order Lepiodetra) 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 un-tailed and tailed papilinodae species while also illustrating how images of modern species would look under the DICAROS ancestral reconstruction