A standardized effect size for evaluating and comparing the strength of phylogenetic signal

Abstract

Macroevolutionary studies frequently characterize the phylogenetic signal in phenotypes; however, analytical tools for comparing the strength of that signal across traits remain largely underdeveloped. We developed a non-parametric, permutation test for the log-likelihood of an evolutionary model, plus a standardized statistic, (Formula presented.), from this test, which can be considered a phylogenetic signal effect size. This statistic can be used in two-sample tests to compare the strength of phylogenetic signal for multiple traits. We performed simulation experiments that revealed that (Formula presented.) had a linear association with Pagel's (Formula presented.), which could be predicted by tree size, plus could be quickly interpreted as a hypothesis for phylogenetic signal based on a standard normal distribution. We additionally found that the permutation test had greater statistical power for detecting phylogenetic signal than parametric likelihood ratio tests, especially for small trees. The analytical framework we present extends the phylogenetic comparative methods toolkit, allowing for statistical comparison of phylogenetic signal in multiple traits. Future studies could also consider this framework for the comparison of different evolutionary models, especially in light of different null processes.