Use of the Method of Generalized Least Squares in Reconstructing Phylogenies from Sequence Data

The method of generalized least squares provides a flexible method of phylogenetic reconstruction from sequence data, after reducing them to pairwise distances between species, corrected for multiple and back mutation. It gives efficient estimates of the branch lengths of a given tree. It also provides a natural measure of the departure of the observed from the predicted set of distances which has a x2 distribution under the true topology; this fact is used to construct a significance test on the topology and so to determine a "confidence interval" for the set of trees which are compatible with the data. To use this method it is necessary to know the variances and covariances of the corrected pairwise distances. A new method of estimating these variances and covariances empirically is described. The methodology is illustrated using data on the phylogeny of four mammalian orders (with the conclusion that rodents and lagomorphs are not sister groups) and of six primates (with the conclusion that the human/chimp/gorilla trichotomy cannot be resolved with these data alone). ' z (dij-S,)* . This is the method proposed by Cavalli-Sforza and Edwards ( 1967) ; it has been used recently as part of the neighbor-joining method of Saitou and Nei ( 1987) for finding the best-supported tree and as part of the method of Li ( 1989) for testing phylogenetic trees.