Rogers James S
Department of Biological Sciences, University of New Orleans, New Orleans, Louisiana, 70148.
Evolution. 1994 Dec;48(6):2026-2036. doi: 10.1111/j.1558-5646.1994.tb02230.x.
The great increase in the number of phylogenetic studies of a wide variety of organisms in recent decades has focused considerable attention on the balance of phylogenetic trees-the degree to which sister clades within a tree tend to be of equal size-for at least two reasons: (1) the degree of balance of a tree may affect the accuracy of estimates of it; (2) the degree of balance, or imbalance, of a tree may reveal something about the macroevolutionary processes that produced it. In particular, variation among lineages in rates of speciation or extinction is expected to produce trees that are less balanced than those that result from phylogenetic evolution in which each extant species of a group has the same probability of speciation or extinction. Several coefficients for measuring the balance or imbalance of phylogenetic trees have been proposed. I focused on Colless's coefficient of imbalance (7) for its mathematical tractability and ease of interpretation. Earlier work on this statistic produced exact methods only for calculating the expected value. In those studies, the variance and confidence limits, which are necessary for testing the departure of observed values of I from the expected, were estimated by Monte Carlo simulation. I developed recursion equations that allow exact calculation of the mean, variance, skewness, and complete probability distribution of I for two different probability-generating models for bifurcating tree shapes. The Equal-Rates Markov (ERM) model assumes that trees grow by the random speciation and extinction of extant species, with all species that are extant at a given time having the same probability of speciation or extinction. The Equal Probability (EP) model assumes that all possible labeled trees for a given number of terminal taxa have the same probability of occurring. Examples illustrate how these theoretically derived probabilities and parameters may be used to test whether the evolution of a monophyletic group or set of monophyletic groups has proceeded according to a Markov model with equal rates of speciation and extinction among species, that is, whether there has been significant variation among lineages in expected rates of speciation or extinction.
近几十年来，对各种各样生物体的系统发育研究数量大幅增加，这使得人们相当关注系统发育树的平衡性——即一棵树内姐妹分支在多大程度上倾向于大小相等——至少有两个原因：（1）树的平衡程度可能会影响对其估计的准确性；（2）树的平衡或不平衡程度可能揭示有关产生它的宏观进化过程的某些信息。特别是，谱系中物种形成或灭绝速率的差异预计会产生比那些由系统发育进化导致的树平衡性更差的树，在系统发育进化中，一个群体的每个现存物种具有相同的物种形成或灭绝概率。已经提出了几个用于衡量系统发育树平衡或不平衡的系数。我关注科莱斯不平衡系数（7），因为它在数学上易于处理且易于解释。早期关于这个统计量的工作仅产生了用于计算期望值的精确方法。在那些研究中，对于检验观察到的I值与期望值的偏差所必需的方差和置信限，是通过蒙特卡罗模拟估计的。我开发了递归方程，对于二叉树形状的两种不同概率生成模型，这些方程允许精确计算I的均值、方差、偏度和完整概率分布。等速率马尔可夫（ERM）模型假设树通过现存物种的随机物种形成和灭绝而生长，在给定时间现存的所有物种具有相同的物种形成或灭绝概率。等概率（EP）模型假设对于给定数量的终端分类单元，所有可能的标记树出现的概率相同。示例说明了这些从理论上推导出来的概率和参数如何可用于检验一个单系群或一组单系群的进化是否按照物种形成和灭绝速率相等的马尔可夫模型进行，也就是说，谱系之间在预期的物种形成或灭绝速率上是否存在显著差异。
