ratematrix: AnRpackage for studying evolutionary integration among several traits on phylogenetic trees

Abstract Evolutionary integration occurs when two or more phenotypes evolve in a correlated fashion. Correlated evolution among traits can happen due to genetic constraints, ontogeny, and selection and have an important impact on the trajectory of phenotypic evolution. Phylogenetic trees can be used to study such pattern on macroevolutionary time scales by estimating the strength of evolutionary covariance among traits through time and across clades. However, only few applications implement models to conduct comparative analyses of evolutionary integration. We introduce a Bayesian Markov chain Monte Carlo approach to estimate the evolutionary correlation among two or more traits using the evolutionary rate matrix ( R ). R is a covariance matrix that represents both the rates of evolution of each trait and the structure of evolutionary correlation among traits. Here, we present the R package ratematrix , a resource to test hypotheses of evolutionary integration using multivariate data and phylogenetic trees. ratematrix provides a flexible framework allowing for any number of evolutionary rate matrix regimes fitted to the same phylogenetic tree and it incorporates the uncertainty associated with parameter estimates, ancestral state reconstruction and phylogenetic estimation in the analyses. The ratematrix package uses a novel pruning algorithm that significantly improve computational time. We also provide specific functions that facilitate users to conduct long MCMC analysis when computational resources are limited.