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Dimensional reduction for the General Markov Model on phylogenetic trees

Sumner, JG ORCID: 0000-0001-9820-0235 2017 , 'Dimensional reduction for the General Markov Model on phylogenetic trees' , Bulletin of Mathematical Biology, vol. 79 , pp. 619-634 , doi: 10.1007/s11538-017-0249-6.

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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 Type: Article
Authors/Creators:Sumner, JG
Keywords: group theory, phylogenetics, representation theory, Markov chains, affine group
Journal or Publication Title: Bulletin of Mathematical Biology
Publisher: Academic Press Ltd Elsevier Science Ltd
ISSN: 0092-8240
DOI / ID Number: 10.1007/s11538-017-0249-6
Copyright Information:

Copyright 2017 Society for Mathematical Biology

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