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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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Copyright Statement
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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 |
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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 |
UTAS Author: | Sumner, JG (Dr Jeremy Sumner) |
UTAS Author: | Jarvis, PD (Dr Peter Jarvis) |
ID Code: | 55009 |
Year Published: | 2008 |
Funding Support: | Australian Research Council (DP0344996) |
Web of Science® Times Cited: | 17 |
Deposited By: | Physics |
Deposited On: | 2009-03-04 |
Last Modified: | 2009-06-09 |
Downloads: | 0 |
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