Chang J T
Yale University Statistics Department, New Haven, Connecticut 06520-8290, USA.
Math Biosci. 1996 Jun;134(2):189-215. doi: 10.1016/0025-5564(95)00172-7.
A fundamental problem in reconstructing the evolutionary history of a set of species is to infer the topology of the evolutionary tree that relates those species. A statistical method for estimating such a topology from character data is called consistent if, given data from more and more characters, the method is sure to converge to the true topology. A number of popular methods are based on modeling the evolution of each character as a Markov process along the evolutionary tree. The standard models further assume that each character has in fact evolved according to the same Markov process. This homogeneity assumption is unrealistic; for example, different types of characters are known to experience substitutions at different rates. Certain distance and maximum likelihood methods for topology estimation have been shown to be consistent under the homogeneity assumption. Here we give examples showing that these methods can fail to be consistent when the homogeneity assumption is relaxed. The examples are very simple, requiring only four taxa, binary characters, and characters that evolve at two different rates.
重建一组物种的进化历史时的一个基本问题是推断联系这些物种的进化树的拓扑结构。如果给定越来越多性状的数据，一种从性状数据估计这种拓扑结构的统计方法能够确保收敛到真实拓扑结构，那么该方法就被称为是一致的。许多流行的方法基于将每个性状的进化建模为沿着进化树的马尔可夫过程。标准模型进一步假设每个性状实际上都是按照相同的马尔可夫过程进化的。这种同质性假设是不现实的；例如，已知不同类型的性状以不同的速率发生替换。某些用于拓扑结构估计的距离法和最大似然法已被证明在同质性假设下是一致的。在这里，我们给出一些例子，表明当放松同质性假设时，这些方法可能不一致。这些例子非常简单，只需要四个分类单元、二元性状以及以两种不同速率进化的性状。
