Two results about the Sackin and Colless indices for phylogenetic trees and their shapes
type: Item
instance of: scholarly article
title: Two results about the Sackin and Colless indices for phylogenetic trees and their shapes
author: Gary Goh
author: Michael Fuchs
author: Louxin Zhang
published in: Journal of Mathematical Biology
publication date: 2022-12-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/2201.10958
review text: The authors find the asymptotic behaviour of the expectation of the Sackin and Colless indices for the uniform tree model. They find that both behave as \(\pi^{1/2}\lambda^{-1}n^{3/2}\) for large \(n\), where \(n\) is the number of tips of the tree, and \(\lambda\approx 1.1300337163\), is a constant. For phylogenetic trees, under the uniform model, the expectation of the Sackin index was derived in [\textit{A. Mir} et al., Math. Biosci. 241, No. 1, 125--136 (2013; Zbl 1303.92084)] in closed form. The difference in the models is that while a \emph{phylogenetic tree} has labelled leaves, the considered in the work \textit{tree} does not. In the work here, the authors propose an alternative proof of the above closed form result for uniform phylogenetic trees. The asymptotic behaviour of the expectation of the Sackin and Colless indices for uniform phylogenetic trees is known to be also \(\pi^{1/2}n^{3/2}\).
reviewed by: Krzysztof Bartoszek
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 05A16
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 7629595
zbMATH Keywords: phylogenetics
zbMATH Keywords: tree balance
zbMATH Keywords: Sackin index
zbMATH Keywords: Colless index
zbMATH Keywords: asymptotic analysis
MaRDI profile type: Publication
OpenAlex ID: W4309878767
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DOI: 10.1007/S00285-022-01831-2
description: scientific article; zbMATH DE number 7629595