Mir, ArnauRotger, LuciaRossello, Francesc2024-09-062024-09-062018-09-25Mir Torres A, Rotger L, Rossello F. Sound Colless-like balance indices for multifurcating trees. PLoS One. 2018 Sep 25;13(9):e0203401.1932-6203http://hdl.handle.net/20.500.13003/9118https://hdl.handle.net/20.500.12105/22607The 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 C-D,C-f that generalize the Colless index to multifurcating phylogenetic trees. Each C-D,C-f is determined by the choice of a dissimilarity D and a weight function f : N -> R->= 0. 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) = e(n) as weight functions, the resulting index C-D,C-f 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 C-D,C-f 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 alpha-gamma-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 alpha-gamma-model, for any values of alpha and gamma.enghttp://creativecommons.org/licenses/by/4.0/Models, Theoreticalresearch articleAttribution 4.0 International30252858139e020340110.1371/journal.pone.0203401PloS Oneopen accessModelos Teóricos2-s2.0-85054016533445639700007L624010261