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

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