Martins Emilia P, Garland Theodore
Department of Zoology, University of Wisconsin, Madison, WI, 53706, USA.
Evolution. 1991 May;45(3):534-557. doi: 10.1111/j.1558-5646.1991.tb04328.x.
We use computer simulation to compare the statistical properties of several methods that have been proposed for estimating the evolutionary correlation between two continuous traits, and define alternative evolutionary correlations that may be of interest. We focus on Felsenstein's (1985) method and some variations of it and on several "minimum evolution" methods (of which the procedure of Huey and Bennett [1987] is a special case), as compared with a nonphylogenetic correlation. The last, a simple correlation of trait values across the tips of a phylogeny, virtually always yields inflated Type I error rates, relatively low power, and relatively poor estimates of evolutionary correlations. We therefore cannot recommend its use. In contrast, Felsenstein's (1985) method yields acceptable significance tests, high power, and good estimates of what we term the input correlation and the standardized realized evolutionary correlation, given complete phylogenetic information and knowledge of the rate and mode of character change (e.g., gradual and proportional to time ["Brownian motion"] or punctuational, with change only at speciation events). Inaccurate branch length information may affect any method adversely, but only rarely does it cause Felsenstein's (1985) method to perform worse than do the others tested. Other proposed methods generally yield inflated Type I error rates and have lower power. However, certain minimum evolution methods (although not the specific procedure used by Huey and Bennett [1987]) often provide more accurate estimates of what we term the unstandardized realized evolutionary correlation, and their use is recommended when estimation of this correlation is desired. We also demonstrate how correct Type I error rates can be obtained for any method by reference to an empirical null distribution derived from computer simulations, and provide practical suggestions on choosing an analytical method, based both on the evolutionary correlation of interest and on the availability of branch lengths and knowledge of the model of evolutionary change appropriate for the characters being analyzed. Computer programs that implement the various methods and that will simulate (correlated) character evolution along a known phylogeny are available from the authors on request. These programs can be used to test the effectiveness of any new methods that might be proposed, and to check the generality of our conclusions with regard to other phylogenies.
我们使用计算机模拟来比较几种已被提出用于估计两个连续性状之间进化相关性的方法的统计特性，并定义可能令人感兴趣的替代进化相关性。我们重点关注费尔斯滕森（1985年）的方法及其一些变体，以及几种“最小进化”方法（其中休伊和贝内特[1987年]的程序是一个特例），并与非系统发育相关性进行比较。最后一种方法，即系统发育末端性状值的简单相关性，几乎总是导致第一类错误率膨胀、功效相对较低以及进化相关性估计相对较差。因此，我们不建议使用它。相比之下，在有完整的系统发育信息以及性状变化速率和模式（例如，渐进且与时间成比例[“布朗运动”]或间断性的，仅在物种形成事件时发生变化）的知识的情况下，费尔斯滕森（1985年）的方法能得出可接受的显著性检验、高功效以及对我们所称的输入相关性和标准化实现进化相关性的良好估计。不准确的分支长度信息可能对任何方法都产生不利影响，但很少会导致费尔斯滕森（1985年）的方法比其他测试方法表现更差。其他提出的方法通常会导致第一类错误率膨胀且功效较低。然而，某些最小进化方法（尽管不是休伊和贝内特[1987年]使用的具体程序）通常能提供对我们所称的未标准化实现进化相关性更准确的估计，当需要估计这种相关性时，建议使用这些方法。我们还展示了如何通过参考从计算机模拟得出的经验性零分布为任何方法获得正确的第一类错误率，并基于感兴趣的进化相关性以及分支长度的可用性和适合所分析性状的进化变化模型的知识，提供关于选择分析方法的实用建议。应作者要求可提供实现各种方法并能沿着已知系统发育模拟（相关）性状进化的计算机程序。这些程序可用于测试可能提出的任何新方法的有效性，并检验我们关于其他系统发育得出的结论的普遍性。
