Neighbor-Joining Uses the Optimal Weight for Net Divergence

A class of phylogenetic clustering methods which calculate net divergences from distance data, but assign differing weights to the net divergences, is defined. The class includes the Neighbor-Joining Method and the Unweighted Pair-Group Method with Arithmetic Mean. The accuracy of some of these methods is studied by computer simulation for the case of four taxa under the additive tree hypothesis. Of these methods and under this hypothesis, it is proved that Neighbor-Joining uses the only weighting for net divergence which is consistent, so that it is the only method in the class which is expected to converge to the correct tree as more data are added. Neighbor-Joining is then compared with Closest Tree on Distances for five taxa by simulation. It is proved that Closest Tree on Distances is equivalent to Neighbor-Joining for four taxa, though it is not when more than four taxa are considered.