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Markov invariants, plethysms, and phylogenetics

Citation

Sumner, JG and Charleston, MA and Jermiin, LS and Jarvis, PD, Markov invariants, plethysms, and phylogenetics, Journal of Theoretical Biology, 253, (3) pp. 601-615. ISSN 0022-5193 (2008) [Refereed Article]


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The definitive version is available at http://www.sciencedirect.com

Official URL: http://www.sciencedirect.com

DOI: doi:10.1016/j.jtbi.2008.04.001

Abstract

We explore model-based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, lthough we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log–Det distance measure. We take as our primary tool group representation theory, and show that it provides a general framework for analyzing Markov processes on trees. From this algebraic perspective, the inherent symmetries of these processes become apparent, and focusing on plethysms, we are able to define Markov invariants and give existence proofs. We give an explicit technique for constructing the invariants, valid for any number of character states and taxa. For phylogenetic trees with three and four leaves, we demonstrate that the corresponding Markov invariants can be fruitfully exploited in applied phylogenetic studies.

Item Details

Item Type:Refereed Article
Keywords:invariants, plethysm, phylogenetics, Schur functions, branching rules
Research Division:Biological Sciences
Research Group:Evolutionary Biology
Research Field:Phylogeny and Comparative Analysis
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Biological Sciences
Author:Sumner, JG (Dr Jeremy Sumner)
Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:55009
Year Published:2008
Funding Support:Australian Research Council (DP0344996)
Web of Science® Times Cited:16
Deposited By:Physics
Deposited On:2009-03-04
Last Modified:2009-06-09
Downloads:0

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