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

2012/02/29 by Gabriel Cardona, Cardona, Gabriel, Arnau Mir +3 · 1 citation
Agricultural and Biological Sciences · Environmental Science · #Animal Ecology and Behavior Studies #Ecology and Vegetation Dynamics Studies #FOS: Biological sciences #FOS: Mathematics #Plant and animal studies #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Quantitative Methods (q-bio.QM)

paper · pdf · doi:10.48550/arxiv.1202.6573

openalex publication_date 2012/02/29 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Chu-Vandermonde convolution and harmonic number identities

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