Generalizing the Peramorphosis Test to Detect Heterochronic Changes in an Explicit Phylogenetic Framework

Heterochrony, defined as evolutionary changes in developmental timing, is a key mechanism underlying morphological diversification across taxa. Although several quantitative approaches have been developed to detect heterochronic patterns using geometric morphometric data, most are limited to pairwise comparisons among extant species and do not explicitly incorporate phylogenetic structure. Here, we present a phylogenetic extension of the peramorphosis test that enables the inference of heterochronic changes among ancestor–descendant pairs across an entire phylogeny, with ancestral shapes reconstructed by using maximum‐likelihood estimation under a Brownian‐motion model of trait evolution. This extension was implemented in an R script ( phylo.peram.test.R ) available online. The approach combines Procrustes regression to estimate ontogenetic trajectories, prediction of species‐specific offset shapes, and reconstruction of ancestral morphologies. Heterochronic events are inferred by comparing multivariate distances from an archetypic juvenile shape to ancestral and descendant shapes for a given tree branch. To evaluate the robustness of the patterns inferred, the approach implements a bootstrap resampling procedure that propagates within‐species variation through all analytical steps and records the recovery frequencies for each inferred event. We illustrate the method using two published datasets of cranial and head shape in mammals and pythons, respectively. Results are largely congruent with those obtained using PASOS, an alternative phylogenetic approach for testing heterochrony, although some discrepancies arise from differences in the reconstruction of ancestral states and in the criteria used by each method to identify heterochronic changes. Overall, the phylogenetic peramorphosis test provides a robust framework for detecting heterochronic patterns in a comparative context.