Hadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof using Pathsets
Populations and Evolution
2007-05-23 v2
Abstract
In most stochastic models of molecular sequence evolution the probability of each possible pattern of homologous characters at a site is estimated numerically. However in the case of Kimura's three-substitution-types (K3ST) model, these probabilities can be expressed analytically by Hadamard conjugation as a function of the phylogeny T and the substitution probabilities on each edge of T, together with an analytic inverse function. In this paper we produce a direct proof of these results, using pathset distances which generalise pairwise distances between sequences. This interpretation allows us to apply Hadamard conjugation to a number of topical problems in the mathematical analysis of sequence evolution.
Cite
@article{arxiv.q-bio/0505055,
title = {Hadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof using Pathsets},
author = {Michael D. Hendy and Sagi Snir},
journal= {arXiv preprint arXiv:q-bio/0505055},
year = {2007}
}