Data from: Comparing evolutionary rates between trees, clades, & traits

1. The tempo of evolutionary change through time is among the most heavily studied dimensions of macroevolution using phylogenies. 2. 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. 3. 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. 4. 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. 5. 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. 6. 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.1. 随时间推移的进化变化速率，是利用系统发育（phylogeny）开展宏观进化研究时最受广泛关注的研究维度之一。2. 本文提出一种简洁的基于似然的方法，用于对比不同系统发育树间连续性状的表型进化速率。本方法衍生自Brian O’Meara及其同事于2006年发表的一项既往研究方法。3. 本研究对该方法的统计性能进行了评估，结果显示其仅在系统发育树规模极小时，会出现最大似然方差估计中典型的向下偏倚；而当树的规模达到相对适中的水平时，进化速率的估计偏差极小。4. 同时我们发现，基于似然比检验（likelihood-ratio test）的一类错误（type I error）率仅会较名义显著性水平小幅升高，即便针对小型系统发育树亦是如此。若采用基于“树间进化速率无差异”原假设（null hypothesis）下模拟得到的检验统计量分布，可将一类错误率降至名义水平或更低。5. 本研究还探讨了未考虑物种均值估计或系统发育推断自身不确定性所带来的影响，并阐述了在参数估计阶段纳入此类不确定性的实施策略。此外，我们还明确了本方法与既往方法的关联：既往方法要么用于对比单棵系统发育树内不同支系（clades）间的进化速率，要么用于对比不同表型性状的进化速率。最后，我们介绍了该方法如何应用于不同进化模型以及离散性状——相关功能已在配套软件中实现。6. 进化生物学家始终对生命之树范围内表型进化速率的变化动态抱有浓厚兴趣。本文所述方法，可用于探究亲缘关系遥远或未知的两个及以上支系间，进化速率或进化过程存在差异的相关研究场景。