The triples distance for rooted bifurcating phylogenetic trees

We investigated the triples distance as a measure of the distance between two rooted bifurcating phylogenetic trees. The triples distance counts the number of subtrees of three taxa that are different in the two trees. Exact expressions are given for the mean and variance of the sampling distribution of this distance measure. Also, a normal approximation is proved under the class of label-invariant models on the distribution of trees. The theory is applied to the usage of the triples distance as a statistic for testing the null hypothesis that the similarities in two trees can be explained by independent random structures. In an example, two phytogenies that describe the same seven species of chloroccalean zoosporic green algae are compared: one phytogeny based on morphological characteristics and one based on ribosomal RNA gene sequence data.