Hyperiax and Phylogenetic Inference from Shape Data

Abstract: Phylogenetic inference on high-dimensional morphological traits requires algorithms that account for both the nonlinear geometry of the shape data and the phylogenetic tree structure. The Backward Filtering Forward Guiding (BFFG) framework provides smoothing for nonlinear stochastic processes on trees and enables inference of parameters and ancestral states. As practical adoption has been limited by a lack of efficient implementations, we present Hyperiax, an open-source library for tree traversal algorithms and message passing using JAX, designed particularly to support operations needed for BFFG. Hyperiax enables efficient execution of operations on trees with large numbers of nodes and, coupled with the BFFG-specific operations, this allows efficient inference in both discrete-time and stochastic differential equation models. Concretely, we demonstrate that Hyperiax enables parameter inference and ancestral reconstruction for butterfly wing shapes represented by landmarks in two dimensions, and analyses of avian beaks from landmarks in three dimensions. Both cases demonstrate application of BFFG on two substantially larger phylogenetic trees with 850 and 696 nodes with higher resolution shape data (118 two-dimensional landmarks and 79 three-dimensional landmarks, specifically) than previously possible.