The expected value under the Yule model of the squared path-difference distance

Abstract

The path-difference metric is one of the oldest and most popular distances for the comparison of phylogenetic trees, but its statistical properties are still quite unknown. In this paper we compute the expected value under the Yule model of evolution of its square on the space of fully resolved rooted phylogenetic trees with n leaves. This complements previous work by Steel-Penny and Mir-Rosselló, who computed this mean value for fully resolved unrooted and rooted phylogenetic trees, respectively, under the uniform distribution.

The expected value of the squared cophenetic metric under the Yule and the uniform models

“…[28] This makes it necessary to study the distribution of the metric, or, at least, to have a formula for the expected value of the metric for any number n of leaves. The distribution of several metrics has been studied so far: see, for instance, [5,6,16,17,28].…”