Hadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof Using Path Sets

Under a stochastic model of molecular sequence evolution the probability of each possible pattern of characters is well defined. The Kimura's three-substitution-types (K3ST) model of evolution allows analytical expression for these probabilities by means of the Hadamard conjugation as a function of the phylogeny T and the substitution probabilities on each edge of T. In this paper, we produce a direct combinatorial proof of these results using path-set distances, which generalize pairwise distances between sequences. This interpretation provides us with tools that have proved useful in related problems in the mathematical analysis of sequence evolution.

• Type: Journal
• Year: 2008
• Where: TCBB
• Authors: Michael D. Hendy, Sagi Snir
• Keywords: Direct Combinatorial Proof, Molecular Sequence Evolution, Sequence Evolution, TCBB 2008