Document Detail

Phylogenetic invariants for the general Markov model of sequence mutation.
MedLine Citation:
PMID:  14583169     Owner:  NLM     Status:  MEDLINE    
A phylogenetic invariant for a model of biological sequence evolution along a phylogenetic tree is a polynomial that vanishes on the expected frequencies of base patterns at the terminal taxa. While the use of these invariants for phylogenetic inference has long been of interest, explicitly constructing such invariants has been problematic. We construct invariants for the general Markov model of kappa-base sequence evolution on an n-taxon tree, for any kappa and n. The method depends primarily on the observation that certain matrices defined in terms of expected pattern frequencies must commute, and yields many invariants of degree kappa+1, regardless of the value of n. We define strong and parameter-strong sets of invariants, and prove several theorems indicating that the set of invariants produced here has these properties on certain sets of possible pattern frequencies. Thus our invariants may be sufficient for phylogenetic applications.
Elizabeth S Allman; John A Rhodes
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Mathematical biosciences     Volume:  186     ISSN:  0025-5564     ISO Abbreviation:  Math Biosci     Publication Date:  2003 Dec 
Date Detail:
Created Date:  2003-10-29     Completed Date:  2004-02-05     Revised Date:  2009-11-11    
Medline Journal Info:
Nlm Unique ID:  0103146     Medline TA:  Math Biosci     Country:  United States    
Other Details:
Languages:  eng     Pagination:  113-44     Citation Subset:  IM    
Department of Mathematics and Statistics, University of Southern Maine, 96 Falmouth Street, Portland, ME 04104, USA.
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MeSH Terms
Base Sequence / genetics*
Markov Chains*
Models, Genetic*

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

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