Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, E-07122 Spain.
Math Biosci. 2018 Jan;295:73-85. doi: 10.1016/j.mbs.2017.11.007. Epub 2017 Nov 16.
The cophenetic metrics d, 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 norm of the difference of the corresponding vectors. In this paper we compute the expected value of the square of d on the space of fully resolved rooted phylogenetic trees with n leaves, under the Yule and the uniform probability distributions.
当$p\in{0}\cup[1,\infty)$时，基于协方差度量$d$是最近添加到比较系统发育树的可用距离的工具。这些度量基于 Sokal 和 Rohlf 五十年前的想法，通过它们的协方差值向量和单个体taxa 的深度来编码同一组taxa 的系统发育树，然后计算对应向量的 L 范数的差。在本文中，我们在 Yule 和均匀概率分布下，计算具有 n 个叶子的完全解析的有根系统发育树空间中 d 的平方的期望值。
