"Comparing evolutionary rates between trees, clades and traits"
"The tempo of evolutionary change through time is among the most heavily studied dimensions of macroevolution using phylogenies. Here, we present a simple, likelihood-based method for comparing the rate of phenotypic evolution for continuous characters between trees. Our method is derived from a previous approach published by Brian O'Meara and colleagues in 2006. We examine the statistical performance of the method and find that it suffers from the typical downward bias expected for maximum likelihood estimates of the variance, but only for very small trees. We find that evolutionary rates are estimated with minimal bias for trees of even relatively modest size. We also find that type I error rates based on a likelihood-ratio test are minimally elevated above the nominal level, even for small phylogenies. The type I error rate can be reduced to a level at or below its nominal value by substituting a test-statistic distribution obtained via simulation under the null hypothesis of no difference in evolutionary rate among trees. We discuss the consequences of failing to account for uncertainty in the estimation of species means or in the phylogeny, and describe strategies for taking this uncertainty into consideration during estimation. We also identify how our approach is related to previous methods for comparing the rate of evolution among different clades of a single tree or between different phenotypic traits. Finally, we describe how the method can be applied to different evolutionary models and to discrete characters—options that are already implemented in software. Evolutionary biologists continue to be intrigued by changes in the tempo of phenotypic evolution across the tree of life. The method described herein should be useful for contexts in which changes in the evolutionary rate or process between two or more clades of distant or unknown relationship are of interest. © 2018 The Authors. Methods in Ecology and Evolution © 2018 British Ecological Society"
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