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

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

2005-05-28

arxiv.org/abs/q-bio/0505055v2

Biology

Quantitative Biology

Populations and Evolution

Scientific paper

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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