Analytic solutions for Three-Taxon MLMC trees with variable rates across sites

Benny Chor, Michael Hendy, David Penny

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider the problem of finding the maximum likelihood rooted tree under a molecular clock (MLMC), with three species and 2-state characters under a symmetric model of substitution. For identically distributed rates per site this is probably the simplest phylogenetic estimation problem, and it is readily solved numerically. Analytic solutions, on the other hand, were obtained only recently (Yang, 2000). In this work we provide analytic solutions for any distribution of rates across sites (provided the moment generating function of the distribution is strictly increasing over the negative real numbers). This class of distributions includes, among others, identical rates across sites, as well as the Gamma, the uniform, and the inverse Gaussian distributions. Therefore, our work generalizes Yang’s solution. In addition, our derivation of the analytic solution is substantially simpler. We employ the Hadamard conjugation (Hendy and Penny, 1993) and convexity of an entropy–like function.

Original languageEnglish
Title of host publicationAlgorithms in Bioinformatics - First International Workshop, WABI 2001 Århus Denmark, August 28-31, 2001 Proceedings
EditorsBernard M. E. Moret, Olivier Gascuel
PublisherSpringer Verlag
Pages204-213
Number of pages10
ISBN (Print)3540425160
DOIs
StatePublished - 2001
Externally publishedYes
Event1st International Workshop on Algorithms in Bioinformatics, WABI 2001 - Arhus, Denmark
Duration: 28 Aug 200131 Aug 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2149
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference1st International Workshop on Algorithms in Bioinformatics, WABI 2001
Country/TerritoryDenmark
CityArhus
Period28/08/0131/08/01

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