Data from: Inference of adaptive shifts for multivariate correlated traits

To study the evolution of several quantitative traits, the classical
phylogenetic comparative framework consists of a multivariate random
process running along the branches of a phylogenetic tree. The
Ornstein-Uhlenbeck (OU) process is sometimes preferred to the simple
Brownian Motion (BM) as it models stabilizing selection toward an optimum.
The optimum for each trait is likely to be changing over the long periods
of time spanned by large modern phylogenies. Our goal is to automatically
detect the position of these shifts on a phylogenetic tree, while
accounting for correlations between traits, which might exist because of
structural or evolutionary constraints. We show that, in the presence
shifts, phylogenetic Principal Component Analysis (pPCA) fails to
decorrelate traits efficiently, so that any method aiming at finding shift
needs to deal with correlation simultaneously. We introduce here a
simplification of the full multivariate OU model, named scalar OU (scOU),
which allows for noncausal correlations and is still computationally
tractable. We extend the equivalence between the OU and a BM on a
re-scaled tree to our multivariate framework. We describe an Expectation
Maximization algorithm that allows for a maximum likelihood estimation of
the shift positions, associated with a new model selection criterion,
accounting for the identifiability issues for the shift localization on
the tree. The method, freely available as an R-package (PhylogeneticEM) is
fast, and can deal with missing values. We demonstrate its efficiency and
accuracy compared to another state-of-the-art method (l1ou) on a wide
range of simulated scenarios, and use this new framework to re-analyze
recently gathered datasets on New World Monkeys and Anolis lizards.