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Sound Colless-like balance indices for multifurcating trees.
- Source :
-
PLoS ONE . 9/25/2018, Vol. 13 Issue 9, p1-27. 27p. - Publication Year :
- 2018
-
Abstract
- The Colless index is one of the most popular and natural balance indices for bifurcating phylogenetic trees, but it makes no sense for multifurcating trees. In this paper we propose a family of Colless-like balance indices that generalize the Colless index to multifurcating phylogenetic trees. Each is determined by the choice of a dissimilarity D and a weight function . A balance index is sound when the most balanced phylogenetic trees according to it are exactly the fully symmetric ones. Unfortunately, not every Colless-like balance index is sound in this sense. We prove then that taking f(n) = ln(n + e) or f(n) = en as weight functions, the resulting index is sound for every dissimilarity D. Next, for each one of these two functions f and for three popular dissimilarities D (the variance, the standard deviation, and the mean deviation from the median), we find the most unbalanced phylogenetic trees according to with any given number n of leaves. The results show that the growth pace of the function f influences the notion of “balance” measured by the indices it defines. Finally, we introduce our R package “CollessLike,” which, among other functionalities, allows the computation of Colless-like indices of trees and their comparison to their distribution under Chen-Ford-Winkel’s α-γ-model for multifurcating phylogenetic trees. As an application, we show that the trees in TreeBASE do not seem to follow either the uniform model for multifurcating trees or the α-γ-model, for any values of α and γ. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 19326203
- Volume :
- 13
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- PLoS ONE
- Publication Type :
- Academic Journal
- Accession number :
- 131956068
- Full Text :
- https://doi.org/10.1371/journal.pone.0203401