## Abstract

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 language | English |
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Article number | 4359884 |

Pages (from-to) | 461-471 |

Number of pages | 11 |

Journal | IEEE/ACM Transactions on Computational Biology and Bioinformatics |

Volume | 5 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2008 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- Biotechnology
- Genetics
- Applied Mathematics