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

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

2012-03-12

arxiv.org/abs/1203.2503v1

Biology

Quantitative Biology

Populations and Evolution

10 pages, extended version of a paper submitted to Applied Mathematics Letter

Scientific paper

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-Rossell\'o, who computed this mean value for fully resolved unrooted and rooted phylogenetic trees, respectively, under the uniform distribution.

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