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

2013/01/22 by Gabriel Cardona, Arnau Mir, Cardona, Gabriel +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Earth and Planetary Sciences · Mathematics · #Evolution and Paleontology Studies #Genomics and Phylogenetic Studies #Morphological variations and asymmetry #cs.DM #math.PR #q-bio.PE

paper · pdf · doi:10.48550/arxiv.1301.5131

22 pages

arxiv created 2013/01/22 · arxiv updated 2013/01/23

Abstract

The cophenetic metrics d_φ,p, for p∈ 0∪[1,∞[, are a recent addition to the kit of available distances for the comparison of phylogenetic trees. Based on a fifty years old idea of Sokal and Rohlf, these metrics compare phylogenetic trees on a same set of taxa by encoding them by means of their vectors of cophenetic values of pairs of taxa and depths of single taxa, and then computing the L^p norm of the difference of the corresponding vectors. In this paper we compute the expected value of the square of d_φ,2 on the space of fully resolved rooted phylogenetic trees with n leaves, under the Yule and the uniform probability distributions.

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