Title :
Hadamard Conjugation for the Kimura 3ST Model: Combinatorial Proof Using Path Sets
Author :
Hendy, Michael D. ; Snir, Sagi
Author_Institution :
Allan Wilson Centre for Mol. Ecology & Evolution, Massey Univ., Palmerston North
Abstract :
Under a stochastic model of molecular sequence evolution the probability of each possible pattern of a characters is well defined. The Kimura´s three-substitution-types (K3ST) model of evolution, allows analytical expression for these probabilities of by means of the Hadamard conjugation as a function of the phylogeny T and the substitution probabilities on each edge of TM . In this paper we produce a direct combinatorial proof of these results, using pathset distances which generalise pairwise distances between sequences. This interpretation provides us with tools that were proved useful in related problems in the mathematical analysis of sequence evolution.
Keywords :
Hadamard matrices; combinatorial mathematics; evolution (biological); molecular biophysics; physiological models; probability; trees (mathematics); Hadamard conjugation; Kimura 3ST model; combinatorial proof; molecular sequence evolution; path sets; phylogeny T; sequence evolution; stochastic model; substitution probability; three-substitution-types model; Hadamard conjugation; K3ST model; path-sets; phylogenetic invariants; phylogenetic trees; Algorithms; Computer Simulation; DNA Mutational Analysis; Evolution, Molecular; Models, Genetic; Phylogeny; Sequence Analysis, DNA;
Journal_Title :
Computational Biology and Bioinformatics, IEEE/ACM Transactions on
DOI :
10.1109/TCBB.2007.70227
