A balance index for phylogenetic trees based on quartets

Coronado, TM; Mir, Arnau; Rosselló, Francesc; Valiente, Gabriel

doi:10.1101/276816

Cited by 5 publications

(8 citation statements)

References 21 publications

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“…Several balance indices have been proposed so far to quantify the balance of a phylogenetic tree. The two most popular ones are the Colless index [4], which only works for bifurcating trees, and the Sackin index [17,20], which can be used on multifurcating trees, but there are many others: see for instance [5,10,11,20] and [6, pp. 562-563].…”

Section: Introductionmentioning

confidence: 99%

Sound colless-like balance indices for multifurcating trees

Mir

García

Rosselló

2018

Preprint

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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 C D,f , which depend on a dissimilarity D and a function f : N → R 0 , that generalize the Colless index to multifurcating phylogenetic trees. We provide two functions f such that the most balanced phylogenetic trees according to the corresponding indices C D,f are exactly the fully symmetric ones. 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 determine the range of values of C D,f on the sets of phylogenetic trees with a given number n of leaves. We end the paper by assessing the performance of one of these indices on TreeBASE and using it to show that the trees in this database do not seem to follow either the uniform model for multifurcating trees or the α-γ-model, for any values of α and γ.

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Section: Introductionmentioning

confidence: 99%

Sound colless-like balance indices for multifurcating trees

Mir

García

Rosselló

2018

Preprint

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“…Before we can introduce and analyze the new symmetry nodes index, we first remind the reader of some basic concepts, which will be used throughout this manuscript. 1 The cherry index is usually simply defined as the number of cherries in a rooted binary tree. We could have considered this index and, analogously, define the symmetry nodes index as the number of symmetry nodes in a rooted binary tree.…”

Section: Preliminariesmentioning

confidence: 99%

“…For decades, various balance indices have been used and discussed as a tool to measure the degree of asymmetry in trees like genealogies or phylogenies that are, for instance, reconstructed based on genetical data (see, for example, [1,2,3,4,5,6]). Their application can give insights into diversification rate variation [7], influences like fertility inheritance and selection [8,9] or effects of different tree reconstruction methods [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

“…After analyzing combinatorial and extremal properties of the new index, SN I will be compared to the modified cherry index mCI, which counts how many leaves of the tree T are not in a cherry, 1 as well as to the J index, which counts the number of imbalanced nodes in a tree. In particular, we will fully characterize the shapes of minimal and maximal trees for SN I, mCI and J, and we will also provide the minimal and maximal values of these indices, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Measuring tree balance using symmetry nodes -- a new balance index and its extremal properties

Kersting¹,

Fischer²

2021

Preprint

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Effects like selection in evolution as well as fertility inheritance in the development of populations can lead to a higher degree of asymmetry in evolutionary trees than expected under a null hypothesis. To identify and quantify such influences, various balance indices were proposed in the phylogenetic literature and have been in use for decades. However, so far no balance index was based on the number of symmetry nodes, even though symmetry nodes play an important role in other areas of mathematical phylogenetics and despite the fact that symmetry nodes are a quite natural way to measure balance or symmetry of a given tree. The aim of this manuscript is thus twofold: First, we will introduce the symmetry nodes index as an index for measuring balance of phylogenetic trees and analyze its extremal properties. We also show that this index can be calculated in linear time. This new index turns out to be a generalization of a simple and well-known balance index, namely the cherry index, as well as a specialization of another, less established, balance index, namely Rogers' J index. Thus, it is the second objective of the present manuscript to compare the new symmetry nodes index to these two indices and to underline its advantages. In order to do so, we will derive some extremal properties of the cherry index and Rogers' J index along the way and thus complement existing studies on these indices. Moreover, we used the programming language R to implement all three indices in the software package symmeTree, which has been made publicly available.

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“…If we can bound the probability of obtaining Bal 4 then we will have a complete characterization of all distributions in EX ∞ 4 . Theorem 14 in [4] will be the main tool to achieve this. Theorem 4.1.…”

Section: Multinomial Modelmentioning

confidence: 99%

Exchangeable and Sampling Consistent Distributions on Rooted Binary Trees

Hollering¹,

Sullivant²

2019

Preprint

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We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling consistent and exchangeable distributions on n leaf phylogenetic trees is a polytope. We use this polytope to show that the set of all exchangeable and infinite sampling consistent distributions on 4 leaf phylogenetic trees is exactly Aldous' beta-splitting model and give a description of some of the vertices for the polytope of distributions on 5 leaves. We also introduce a new semialgebraic set of exchangeable and sampling consistent models we call the multinomial model and use it to characterize the set of exchangeable and sampling consistent distributions.

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A balance index for phylogenetic trees based on quartets

Cited by 5 publications

References 21 publications

Sound colless-like balance indices for multifurcating trees

Sound colless-like balance indices for multifurcating trees

Measuring tree balance using symmetry nodes -- a new balance index and its extremal properties

Exchangeable and Sampling Consistent Distributions on Rooted Binary Trees

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