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

Gabriel Cardona; Arnau Mir; Francesc Rossello

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arXiv · 1301.5131

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

Gabriel Cardona·Arnau Mir·Francesc Rossello

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Abstract

The cophenetic metrics $d_{φ,p}$, for $p\in {0}\cup[1,\infty[$, 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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Gabriel Cardona, Arnau Mir, Francesc Rossello. 2013-01-22. The expected value of the squared euclidean cophenetic metric under the Yule and the uniform models. https://arxiv.org/abs/1301.5131

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