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Dimensional reduction for the General Markov Model on phylogenetic trees
Citation
Sumner, JG, Dimensional reduction for the General Markov Model on phylogenetic trees, Bulletin of Mathematical Biology, 79 pp. 619-634. ISSN 0092-8240 (2017) [Refereed Article]
Copyright Statement
Copyright 2017 Society for Mathematical Biology
DOI: doi:10.1007/s11538-017-0249-6
Abstract
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence in the full space. We discuss potential applications including the computation of split (edge) weights on phylogenetic trees from observed sequence data.
Item Details
Item Type: | Refereed Article |
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Keywords: | group theory, phylogenetics, representation theory, Markov chains, affine group |
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: | Sumner, JG (Associate Professor Jeremy Sumner) |
ID Code: | 115178 |
Year Published: | 2017 |
Funding Support: | Australian Research Council (DP150100088) |
Web of Science® Times Cited: | 2 |
Deposited By: | Mathematics and Physics |
Deposited On: | 2017-03-09 |
Last Modified: | 2018-04-27 |
Downloads: | 0 |
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