Hadamard conjugation for the Kimura 3ST model: Combinatorial proof using path sets

Michael D. Hendy, Sagi Snir

Research output: Contribution to journalArticlepeer-review


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 phytogeny 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.

Original languageEnglish
Article number4359884
Pages (from-to)461-471
Number of pages11
JournalIEEE/ACM Transactions on Computational Biology and Bioinformatics
Issue number3
StatePublished - Jul 2008
Externally publishedYes


  • Hadamard conjugation
  • K3ST model
  • Path-sets
  • Phylogenetic invariants
  • Phylogenetic trees

ASJC Scopus subject areas

  • Applied Mathematics
  • Genetics
  • Biotechnology


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