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

Abstract

ABSTRACTUnderstanding what shapes species phenotypes over macroevolutionary time scales from comparative data requires the use of 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 well-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 a greater power to detect phenotypic differences across species group when they exist, and a low risk to improperly detect inexistent differences. Finally, we provide an empirical illustration of our pMANOVA on a geometric-morphometric dataset describing mandible morphology in phyllostomid bats along with data on their diet preferences. Our approach, implemented in the R package mvMORPH, provides efficient multivariate phylogenetic regression tools for understanding what shapes phenotypic differences across species.