A new balance index for phylogenetic trees

Abstract

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 least common ancestor. This index makes sense for arbitrary trees, can be computed in linear time and it has a larger range of values and a greater resolution power than other indices like Colless' or Sackin's. We compute its maximum and minimum values for arbitrary and binary trees, as well as exact formulas for its expected value for binary trees under the Yule and the uniform models of evolution. As a byproduct of this study, we obtain an exact formula for the expected value of the Sackin index under the uniform model, a result that seems to be new in the literature.

24 pages, 2 figures, preliminary version presented at the JBI 2012

References in corpus (2)

• The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance
• The mean value of the squared path-difference distance for rooted phylogenetic trees

Cited by in corpus (9)

• Sound Colless-like balance indices for multifurcating trees
• Tree balance indices: a comprehensive survey
• Exact and approximate limit behaviour of the Yule tree's cophenetic index
• The expected value of the squared euclidean cophenetic metric under the Yule and the uniform models
• The minimum value of the Colless index
• Explicit solution of divide-and-conquer dividing by a half recurrences with polynomial independent term
• Stochastic models in phylogenetic comparative methods: analytical properties and parameter estimation
• Squaring within the Colless index yields a better balance index
• Extremal properties of the Colless balance index for rooted binary trees