title: Dimensional Reduction for the General Markov Model on Phylogenetic Trees.
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.
authors.affiliation: School of Physical Sciences, Mathematics, University of Tasmania, Private Bag 37, GPO, Hobart, TAS, 7001, Australia. Jeremy.Sumner@utas.edu.au.
authors.forename: Jeremy G
authors.identifier: 0000-0001-9820-0235
authors.initials: JG
authors.lastname: Sumner
mesh_terms: D005075:Biological Evolution; D008390:Markov Chains; D055641:Mathematical Concepts; D008957:Models, Genetic; D010802:Phylogeny
keywords: Affine group; Markov chains; Representation theory