Solvable models of neighbor-dependent nucleotide substitution processes - Archive ouverte HAL
Article Dans Une Revue Mathematical Biosciences Année : 2008

Solvable models of neighbor-dependent nucleotide substitution processes

Jean Bérard
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Didier Piau
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Résumé

We prove that a wide class of models of Markov neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotide substitutions recently introduced and studied empirically by molecular biologists. We show that the polynucleotide frequencies at equilibrium solve explicit finite-size linear systems. Finally, the dynamics of the process and the distribution at equilibrium exhibit some stringent, rather unexpected, independence properties. For example, nucleotide sites at distance at least three evolve independently, and the sites, if encoded as purines and pyrimidines, evolve independently.

Dates et versions

hal-00078644 , version 1 (06-06-2006)

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Citer

Jean Bérard, Jean-Baptiste Gouéré, Didier Piau. Solvable models of neighbor-dependent nucleotide substitution processes. Mathematical Biosciences, 2008, 211 (1), pp.56-88. ⟨10.1016/j.mbs.2007.10.001⟩. ⟨hal-00078644⟩
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