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.
hadamard conjugation path-sets k3st model phylogenetic trees phylogenetic invariants