Theoretical foundation of the minimum-evolution method of phylogenetic inference

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.