Hadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof using Pathsets

Michael D. Hendy; Sagi Snir

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Hadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof using Pathsets

Michael D. Hendy·Sagi Snir

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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.

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Michael D. Hendy, Sagi Snir. 2005-11-03. Hadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof using Pathsets. https://arxiv.org/abs/q-bio/0505055

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