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Phylogenetic tree comparison metrics are an important tool in the study of evolution, and hence the definition of such metrics is an interesting problem in phylogenetics. In a paper in Taxon fifty years ago, Sokal and Rohlf proposed to measure quantitatively the difference between a pair of phylogenetic trees by first encoding them by means of their… (More)

Several indices that measure the degree of balance of a rooted phylogenetic tree have been proposed so far in the literature. In this work we define and study a new index of this kind, which we call the total cophenetic index: the sum, over all pairs of different leaves, of the depth of their lowest common ancestor. This index makes sense for arbitrary… (More)

By Lemma 1, it is enough to prove that the minimum non-zero value of D 0 is 1, and that all pairs T, T ∈ UT n such that D 0 (T, T) = 1 also satisfy that D p (T, T) = 1 for every p 1. As we have seen in Example 2, if we contract a pendant arc in a tree T , we obtain a new tree T such that D p (T, T) = 1, for every p ∈ {0} ∪ [1, ∞[, and this is of course the… (More)

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