Exact formulas for the variance of several balance indices under the Yule model

Details Exact formulas for the variance of several balance indices under the Yule model Exact formulas for the variance of several balance indices under the Yule model

2012-02-29

arxiv.org/abs/1202.6573v1

Biology

Quantitative Biology

Populations and Evolution

17 pages

Scientific paper

One of the main applications of balance indices is in tests of null models of evolutionary processes. The knowledge of an exact formula for a statistic of a balance index, holding for any number n of leaves, is necessary in order to use this statistic in tests of this kind involving trees of any size. In this paper we obtain exact formulas for the variance under the Yule model of the Sackin index and the total cophenetic index of binary rooted phylogenetic trees with n leaves. We also obtain the covariance of these indices.

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