A semiparametric method to test for correlated evolution in a phylogenetic context

Phylogenetic comparative methods are a broad suite of approaches for studying trait and species diversification using evolutionary trees. In spite of their substantial growth in sophistication and complexity in recent years, among the most commonly-employed phylogenetic comparative method continues to be a simple measure of the evolutionary correlation between variables, while accounting for the statistical non-independence in our data that arises from common descent. The standard parametric phylogenetic approach for measuring the evolutionary correlation between continuously valued characters assumes a model called Brownian motion for the evolution of our traits. Here, we introduce a new semiparametric method that relaxes this assumption by testing for the evolutionary correlation between variables based on contrast ranks, and then obtains a null distribution on the test statistic via random permutation. We show that this approach has reasonable statistical properties: type I error close to the nominal level, and power that is similar to fully parametric methods. We conclude by comparing our new method to related approaches.