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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
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
Author:Sumner, JG (Dr Jeremy Sumner)
ID Code:115178
Year Published:2017
Funding Support:Australian Research Council (DP150100088)
Web of Science® Times Cited:1
Deposited By:Mathematics and Physics
Deposited On:2017-03-09
Last Modified:2017-11-15
Downloads:0

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