Reliable Phylogenetic Regressions for Multivariate Comparative Data: Illustration with the MANOVA and Application to the Effect of Diet on Mandible Morphology in Phyllostomid Bats

Understanding what shapes species phenotypes over macroevolutionary timescales from comparative data often requires studying the relationship between phenotypes and putative explanatory factors or testing for differences in phenotypes across species groups. In phyllostomid bats for example, is mandible morphology associated to diet preferences? Performing such analyses depends upon reliable phylogenetic regression techniques and associated tests (e.g., phylogenetic Generalized Least Squares, pGLS, and phylogenetic analyses of variance and covariance, pANOVA, pANCOVA). While these tools are well established for univariate data, their multivariate counterparts are lagging behind. This is particularly true for high-dimensional phenotypic data, such as morphometric data. Here, we implement much-needed likelihood-based multivariate pGLS, pMANOVA, and pMANCOVA, and use a recently developed penalized-likelihood framework to extend their application to the difficult case when the number of traits $p$ approaches or exceeds the number of species $n$. We then focus on the pMANOVA and use intensive simulations to assess the performance of the approach as $p$ increases, under various levels of phylogenetic signal and correlations between the traits, phylogenetic structure in the predictors, and under various types of phenotypic differences across species groups. We show that our approach outperforms available alternatives under all circumstances, with greater power to detect phenotypic differences across species group when they exist, and a lower risk of improperly detecting nonexistent differences. Finally, we provide an empirical illustration of our pMANOVA on a geometric-morphometric data set describing mandible morphology in phyllostomid bats along with data on their diet preferences. Overall our results show significant differences between ecological groups. Our approach, implemented in the R package mvMORPH and illustrated in a tutorial for end-users, provides efficient multivariate phylogenetic regression tools for understanding what shapes phenotypic differences across species. [Generalized least squares; high-dimensional data sets; multivariate phylogenetic comparative methods; penalized likelihood; phenomics; phyllostomid bats; phylogenetic MANOVA; phylogenetic regression.]