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...