Spectral analysis and a closest tree method for genetic sequences
type: Item
instance of: scholarly article
title: Spectral analysis and a closest tree method for genetic sequences
zbMATH Open document ID: 0788.92021
DOI: 10.1016/0893-9659(92)90016-3
published in: Applied Mathematics Letters
publication date: 1993-04-01T00:00:00Z
full work available at URL: spectral-analysis-and-a-closest-tree-method-for-genetic-sequences(b4abc0ca-bd52-4491-8b19-a9559940854f).html
review text: This paper deals with the reconstruction of evolutionary trees from aligned genetic sequences. Nucleotide sequences are assumed to evolve according to Kimura's 3-parameter model [cf. \textit{M. Kimura}, Proc. Natl. Acad. Sci. USA 78, 454-458 (1981; Zbl 0511.92013)] which can be formulated in a group-theoretic context by identifying the set of four nucleotides with the Kleinian group \(\mathbb{Z}_ 2\times \mathbb{Z}_ 2\) and considering colorations of species by elements of this group. The authors define conjugate spectra of sequence data and use discrete Fourier transformation methods to estimate the underlying evolutionary tree. These methods, like the principle of maximum parsimony, have the property of providing a tree which minimizes an explicitly representable function of the data and allow the development of a branch-and-bound algorithm.
Mathematics Subject Classification ID: 92D20
Mathematics Subject Classification ID: 92D15
zbMATH DE Number: 148552
zbMATH Keywords: reconstruction of evolutionary trees
zbMATH Keywords: Kimura's 3-parameter model
zbMATH Keywords: Kleinian group
zbMATH Keywords: colorations of species
zbMATH Keywords: conjugate spectra of sequence data
zbMATH Keywords: discrete Fourier transformation methods
zbMATH Keywords: principle of maximum parsimony
zbMATH Keywords: branch-and-bound algorithm
author: Mike Steel
author: M. D. Hendy
author: László A. Székely
author: Péter L. Erdős
reviewed by: G. Karigl
MaRDI profile type: Publication
OpenAlex ID: W2023187118
cites work: Reconstructing the shape of a tree from observed dissimilarity data
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cites work: A combinatorial description of the closest tree algorithm for finding evolutionary trees
cites work: A Fourier inversion formula for evolutionary trees
cites work: Branch and bound algorithms to determine minimal evolutionary trees
description: scientific article; zbMATH DE number 148552