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A simple method for estimating and testing phylogenetic trees under the principle of minimum evolution (ME) is presented. The basic procedure of this method is first to obtain the neighbor-joining (NJ) tree by Saitou and Nei’s method and then to search for a tree with the minimum value of the sum (S) of branch lengths by examining all trees that are closely related to the NJ tree. Once the ME tree is identified, a statistical test is conducted for the difference in S between this tree and other closely related trees. The mathematical method required for conducting this test is developed by using the least-squares approach. Computer simulation has shown that this method identifies the correct tree with a high probability, as long as the number of nucleotides examined is sufficiently large. It has also been shown that the topology of the NJ tree is almost always identical with that of the ME tree. A method for obtaining least-squares estimates (and their standard errors) of branch lengths for a given topology is also presented. This method can be used for testing the reliability of the branching pattern of the ME tree. However, the statistical test of S values is more powerful in rejecting incorrect trees than is the branch-length test or bootstrapping. Furthermore, both a mathematical method for computing the number of trees with a given value of topological difference from the NJ tree and a computer algorithm for identifying all the topologies are developed.
Rzhetsky et al. (Tue,) studied this question.