Data from: Comparing evolutionary rates for different phenotypic traits on a phylogeny using likelihood

In recent years, likelihood-based approaches have been used with increasing frequency to evaluate macroevolutionary hypotheses of phenotypic evolution under distinct evolutionary processes in a phylogenetic context (e.g., Brownian motion, Ornstein-Uhlenbeck, etc.), and to compare one or more evolutionary rates for the same phenotypic trait along a phylogeny. It is also of interest to determine whether one trait evolves at a faster rate than another trait. However, to date no study has compared phylogenetic evolutionary rates between traits using likelihood, because a formal approach has not yet been proposed. In this article, I describe a new likelihood procedure for comparing evolutionary rates for two or more phenotypic traits on a phylogeny. This approach compares the likelihood of a model where each trait evolves at a distinct evolutionary rate to the likelihood of a model where all traits are constrained to evolve at a common evolutionary rate. The method can also account for within-species measurement error and within-species trait covariation if available. Simulations revealed that the method has appropriate Type I error rates and statistical power. Importantly, when compared with existing approaches based on phylogenetically independent contrasts and methods that compare confidence intervals for model parameters, the likelihood method displays preferable statistical properties for a wide range of simulated conditions. Thus, this likelihood-based method extends the phylogenetic comparative biology toolkit and provides evolutionary biologists with a more powerful means of determining when evolutionary rates differ between phenotypic traits. Finally, I provide an empirical example illustrating the approach by comparing rates of evolution for several phenotypic traits in Plethodon salamanders.

近年来，基于似然的方法（likelihood-based approaches）在系统发育框架下的应用频次不断提升，被广泛用于评估不同演化过程下的表型演化宏观演化假说（如布朗运动（Brownian motion）、奥恩斯坦-乌伦贝克模型（Ornstein-Uhlenbeck）等），并可比较系统发育树上同一表型性状的一个或多个演化速率。此外，判断某一性状的演化速率是否快于另一性状也是学界关注的重要研究议题。然而迄今为止，尚无研究通过似然方法开展跨性状的系统发育演化速率比较，因为尚未提出正式的分析框架。

本文提出一种全新的似然分析流程，用于比较系统发育树上两个或多个表型性状的演化速率。该方法将“每个性状以独立专属演化速率演化”的模型似然，与“所有性状被约束为共享同一演化速率”的模型似然进行对比。若有可用数据，该方法还可纳入种内测量误差与种内性状协变情况。

模拟实验结果表明，本方法的一类错误率（Type I error rates）与统计效力（statistical power）均符合统计学要求。尤为重要的是，相较于现有基于系统发育独立对比（phylogenetic independent contrasts）的方法，以及通过比较模型参数置信区间的各类方法，本似然方法在多种模拟场景下均展现出更优的统计性能。因此，这种基于似然的方法拓展了系统发育比较生物学（phylogenetic comparative biology）的分析工具库，为演化生物学家提供了更高效的手段，以判断不同表型性状间的演化速率是否存在差异。

最后，本文以无肺螈属（Plethodon）蝾螈的多个表型性状的演化速率比较为例，展示了该方法的实证应用。