Interior-branch and bootstrap tests of phylogenetic trees

Abstract

We have compared statistical properties of the interior-branch and bootstrap tests of phylogenetic trees when the neighbor-joining tree-building method is used. For each interior branch of a predetermined topology, the interior-branch and bootstrap tests provide the confidence values, P(C) and P(B), respectively, that indicate the extent of statistical support of the sequence cluster generated by the branch. In phylogenetic analysis these two values are often interpreted in the same way, and if P(C) and P(B) arc high (say, ≥0.95), the sequence cluster is regarded as reliable. We have shown that P(C) is in fact the complement of the P-value used in the standard statistical test, but P(B) is not. Actually, the bootstrap test usually underestimates the extent of statistical support of species clusters. the relationship between the confidence values obtained by the two tests varies with both the topology and expected branch lengths of the true (model) tree. The most conspicuous difference between P(C) and P(B) is observed when the true free is starlike, and there is a tendency for the difference to increase as the number of sequences in the tree increases. The reason for this is that the bootstrap test tends to become progressively more conservative as the number of sequences in the tree increases. Unlike the bootstrap, the interior-branch test has the same statistical properties irrespective of the number of sequences used when a predetermined tree is considered. Therefore, the interior-branch test appears to be preferable to the bootstrap test as long as unbiased estimators of evolutionary distances are used. However, when the interior-branch is applied to a tree estimated from a given data set, P(C) may give an overestimate of statistical confidence. For this case, we developed a method for computing a modified version (P(C)) of the P(C) value and showed that this P(C) tends to give a conservative estimate of statistical confidence, though d is not as conservative as P(B). In this paper we have introduced a model in which evolutionary distances between sequences follow a multivariate normal distribution. This model allowed us to study the relationships between the two tests analytically.