Data from: Multivariate phylogenetic comparative methods: evaluations, comparisons, and recommendations

Recent years have seen increased interest in phylogenetic comparative
analyses of multivariate datasets, but to date the varied proposed
approaches have not been extensively examined. Here we review the
mathematical properties required of any multivariate method, and
specifically evaluate existing multivariate phylogenetic comparative
methods in this context. Phylogenetic comparative methods based on the
full multivariate likelihood are robust to levels of covariation among
trait dimensions and are insensitive to the orientation of the dataset,
but display increasing model misspecification as the number of trait
dimensions increases. This is because the expected evolutionary covariance
matrix (V) used in the likelihood calculations becomes more
ill-conditioned as trait dimensionality increases, and as evolutionary
models become more complex. Thus, these approaches are only appropriate
for datasets with few traits and many species. Methods that summarize
patterns across trait dimensions treated separately (e.g., SURFACE)
incorrectly assume independence among trait dimensions, resulting in
nearly a 100% model misspecification rate. Methods using pairwise
composite likelihood are highly sensitive to levels of trait covariation,
the orientation of the dataset, and the number of trait dimensions. The
consequences of these debilitating deficiencies is that a user can arrive
at differing statistical conclusions, and therefore biological inferences,
simply from a dataspace rotation, like principal component analysis. By
contrast, algebraic generalizations of the standard phylogenetic
comparative toolkit that use the trace of covariance matrices are
insensitive to levels of trait covariation, the number of trait
dimensions, and the orientation of the dataset. Further, when appropriate
permutation tests are used, these approaches display acceptable Type I
error and statistical power. We conclude that methods summarizing
information across trait dimensions, as well as pairwise composite
likelihood methods should be avoided, while algebraic generalizations of
the phylogenetic comparative toolkit provide a useful means of assessing
macroevolutionary patterns in multivariate data. Finally, we discuss areas
in which multivariate phylogenetic comparative methods are still in need
of future development; namely highly multivariate Ornstein-Uhlenbeck
models and approaches for multivariate evolutionary model comparisons.