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
dataset 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.