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Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels
Citation
Jarvis, PD and Sumner, JG, Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9, (3) pp. 828-836. ISSN 1545-5963 (2012) [Refereed Article]
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Copyright Statement
Copyright 2012 IEEE
Abstract
We consider novel phylogenetic models with rate matrices that arise via the embedding of a progenitor model on a small number of character states, into a target model on a larger number of character states. Adapting representation-theoretic results from recent investigations of Markov invariants for the general rate matrix model, we give a prescription for identifying and counting Markov invariants for such "symmetric embedded" models, and we provide enumerations of these for the first few cases with a small number of character states. The simplest example is a target model on three states, constructed from a general 2 state model; the "2 ↪ 3" embedding. We show that for 2 taxa, there exist two invariants of quadratic degree that can be used to directly infer pairwise distances from observed sequences under this model. A simple simulation study verifies their theoretical expected values, and suggests that, given the appropriateness of the model class, they have superior statistical properties than the standard (log) Det invariant (which is of cubic degree for this case).
Item Details
Item Type: | Refereed Article |
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Keywords: | Markov chains, representation theory |
Research Division: | Mathematical Sciences |
Research Group: | Applied mathematics |
Research Field: | Biological mathematics |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding knowledge |
Objective Field: | Expanding knowledge in the mathematical sciences |
UTAS Author: | Jarvis, PD (Dr Peter Jarvis) |
UTAS Author: | Sumner, JG (Dr Jeremy Sumner) |
ID Code: | 77995 |
Year Published: | 2012 |
Funding Support: | Australian Research Council (DP0877447) |
Web of Science® Times Cited: | 5 |
Deposited By: | Mathematics and Physics |
Deposited On: | 2012-06-12 |
Last Modified: | 2013-07-02 |
Downloads: | 0 |
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