Exact formulas for the variance of several balance indices under the Yule model
Populations and Evolution
2012-10-22 v2 Probability
Quantitative Methods
Abstract
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, the Colless index and the total cophenetic index of binary rooted phylogenetic trees with n leaves. We also obtain the covariance of the Sackin and the total cophenetic index.
Keywords
Cite
@article{arxiv.1202.6573,
title = {Exact formulas for the variance of several balance indices under the Yule model},
author = {Gabriel Cardona and Arnau Mir and Francesc Rossello},
journal= {arXiv preprint arXiv:1202.6573},
year = {2012}
}
Comments
32 pages. The final version will appear in the J. Comp. Biol. v2 covers the Colless index, which did not appear in v1