Solvable models of neighbor-dependent nucleotide substitution processes

Details Solvable models of neighbor-dependent nucleotide substitution processes Solvable models of neighbor-dependent nucleotide substitution processes

2005-10-03

arxiv.org/abs/math/0510034v2

Mathematics

Probability

47 pages, minor modifications

Scientific paper

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.

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