Construction of linear invariants in phylogenetic inference
type: Item
instance of: scholarly article
title: Construction of linear invariants in phylogenetic inference
zbMATH Open document ID: 0772.92013
DOI: 10.1016/0025-5564(92)90045-X
author: Yun-Xin Fu
author: Wen-Hsiung Li
published in: Mathematical Biosciences
publication date: 1992-09-27T00:00:00Z
review text: Linear invariants in phylogenetic studies are useful for developing statistical tests of hypotheses on the topology of phylogenetic trees. A linear invariant is defined as a random variable on the set of all nucleotide configurations of an \(n\)-species tree, whose expectation is zero under a semigroup of substitution matrices for the given tree. A new recursive method is presented for constructing linear invariants by expressing their expectation as a compound bilinear form, i.e. a linear form such that all corresponding matrix elements again can be written as bilinear forms. In that way all invariants of an \(n\)-species tree can be derived analytically from those of an \((n-1)\)-species subtree. All linear invariants of trees for 2, 3, 4 and 5 species are derived. The number of linear invariants for a tree is found to increase rapidly with the number of species.
Mathematics Subject Classification ID: 92D20
Mathematics Subject Classification ID: 92D10
zbMATH DE Number: 64803
zbMATH Keywords: phylogenetic trees
zbMATH Keywords: set of all nucleotide configurations of an \(n\)- species tree
zbMATH Keywords: semigroup of substitution matrices
zbMATH Keywords: linear invariants
zbMATH Keywords: compound bilinear form
reviewed by: G. Karigl
MaRDI profile type: Publication
Wikidata QID: Q42611425
cites work: Necessary conditions for the method of inferring phylogeny by linear invariants
full work available at URL: 0025-5564(92)90045-x
OpenAlex ID: W2001415322
description: scientific article; zbMATH DE number 64803