Rzhetsky A, Nei M
Institute of Molecular Evolutionary Genetics, Pennsylvania State University, University Park 16802.
Mol Biol Evol. 1993 Sep;10(5):1073-95. doi: 10.1093/oxfordjournals.molbev.a040056.
The minimum-evolution (ME) method of phylogenetic inference is based on the assumption that the tree with the smallest sum of branch length estimates is most likely to be the true one. In the past this assumption has been used without mathematical proof. Here we present the theoretical basis of this method by showing that the expectation of the sum of branch length estimates for the true tree is smallest among all possible trees, provided that the evolutionary distances used are statistically unbiased and that the branch lengths are estimated by the ordinary least-squares method. We also present simple mathematical formulas for computing branch length estimates and their standard errors for any unrooted bifurcating tree, with the least-squares approach. As a numerical example, we have analyzed mtDNA sequence data obtained by Vigilant et al. and have found the ME tree for 95 human and 1 chimpanzee (outgroup) sequences. The tree was somewhat different from the neighbor-joining tree constructed by Tamura and Nei, but there was no statistically significant difference between them.
系统发育推断的最小进化（ME）方法基于这样一种假设：分支长度估计值总和最小的树最有可能是真实的树。过去，这一假设在没有数学证明的情况下被使用。在此，我们通过表明在所有可能的树中，真实树的分支长度估计值总和的期望值最小，给出了该方法的理论基础，前提是所使用的进化距离在统计上是无偏的，并且分支长度是通过普通最小二乘法估计的。我们还给出了简单的数学公式，用于使用最小二乘法计算任何无根二叉树的分支长度估计值及其标准误差。作为一个数值示例，我们分析了Vigilant等人获得的线粒体DNA序列数据，并找到了95个人类和1只黑猩猩（外类群）序列的ME树。该树与Tamura和Nei构建的邻接法树有些不同，但它们之间没有统计学上的显著差异。
