Testing Hypotheses of Correlated Evolution Using Phylogenetically Independent Contrasts: Sensitivity to Deviations from Brownian Motion

Abstract

We examined the statistical performance (in terms of type I error rates) of Felsenstein's (1985, Am. Nat. 125:1–15) comparative method of phylogenetically independent contrasts for testing hypotheses about evolutionary correlations of continuous-valued characters. We simulated data along two different phylogenies, one for 15 species of plethodontid salamanders and the other for 49 species of Carnivora and ungulates. We implemented 15 different models of character evolution, 14 of which deviated from Brownian motion, which is in effect assumed by the method. The models studied included the Ornstein–Uhlenbeck process and punctuated equilibrium (change allowed in only one daughter at each bifurcation) both with and without trends and limits on how far phenotypes could evolve. As has been shown in several previous simulation studies, a nonphylogenetic Pearson correlation of species' mean values yielded inflated type I error rates under most models, including that of simple Brownian motion. Independent contrasts yielded acceptable type I error rates under Brownian motion (and in preliminary studies under slight deviations from this model), but they were inflated under most other models. This new result confirms the model dependence of independent contrasts. However, when branch lengths were checked and transformed, then type I error rates of independent contrasts were reduced. Moreover, the maximum observed type I error rates never exceeded twice the nominal P value at α = 0.05. In comparison, the nonphylogenetic correlation tended to yield extremely inflated (and highly variable) type I error rates. These results constitute another demonstration of the general superiority of phylogenetically based statistical methods over nonphylogenetic ones, even under extreme deviations from a Brownian motion model. These results also show the necessity of checking the assumptions of statistical comparative methods and indicate that diagnostic checks and remedial measures can substantially improve the performance of the independent contrasts method.