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Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels


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

DOI: doi:10.1109/TCBB.2012.24


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
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 (Associate Professor 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

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