Pagel M
School of Mathematical Sciences, Queen Mary and Westfield College, University of London, U.K.
J Theor Biol. 1993 Sep 21;164(2):191-205. doi: 10.1006/jtbi.1993.1148.
Two alternative classes of comparative statistical method differ in the way that the comparative data are used to test for an association between two quantitative traits. Directional comparative methods use reconstructions of the ancestral character states to calculate the changes between ancestral and descendant conditions along the branches of the phylogenetic tree. The set of changes in two or more traits is used to test for evidence of correlated evolution. Cross-sectional techniques do not estimate changes along the branches of the tree, but rather make comparisons across the tips of a phylogeny, or between pairs of extant taxa (or between their higher nodes). These methods, then, study the association between pairs of traits representing the contemporary endpoints of evolution. The best known of the cross-sectional techniques, the species regression, simply regresses the species values of one variable onto those of another. However, it is shown here analytically that directional and cross-sectional methods, despite making very different use of the data, estimate precisely the same evolutionary parameter: the association between the changes in two variables along the branches of the phylogenetic tree. Thus, comparative statistical techniques are able to recover the historical trends of evolution, that is, the ways in which evolution has proceeded along the branches of the phylogenetic tree, from analysis of the variation among the contemporary species of a phylogeny. This means that the choice between the two alternative traditions of comparative study cannot be based upon what the different methods purport to measure, but rather must be based upon the statistical properties of particular methods. In the light of this result, it is discussed here whether there are statistical reasons to prefer some methods over others.
两类不同的比较统计方法在利用比较数据来检验两个数量性状之间的关联方式上存在差异。定向比较方法利用祖先性状状态的重建来计算沿着系统发育树分支的祖先和后代状态之间的变化。两个或更多性状的变化集用于检验协同进化的证据。横断面技术并不估计沿着树分支的变化，而是在系统发育树的末端之间进行比较，或者在成对的现存分类群之间（或它们的上级节点之间）进行比较。因此，这些方法研究代表进化当代终点的成对性状之间的关联。横断面技术中最著名的物种回归，只是将一个变量的物种值对另一个变量的物种值进行回归。然而，本文通过分析表明，定向和横断面方法尽管对数据的使用方式非常不同，但精确估计的是同一个进化参数：沿着系统发育树分支的两个变量变化之间的关联。因此，比较统计技术能够从系统发育当代物种间的变异分析中恢复进化的历史趋势，即进化沿着系统发育树分支进行的方式。这意味着比较研究的两种不同传统之间的选择不能基于不同方法声称要测量的内容，而必须基于特定方法的统计特性。鉴于这一结果，本文讨论了是否存在统计学上的理由更倾向于某些方法而非其他方法。
