We generalize here the classical stochastic substitution models of nucleotides to genetic motifs of any size. This generalized model gives the analytical occurrence probabilities of genetic motifs as a function of a substitution matrix containing up to three formal parameters (substitution rates) per motif site and of an initial occurrence probability vector of genetic motifs. The evolution direction can be direct (past-present) or inverse (present-past). This extension has been made due to the identification of a Kronecker relation between the nucleotide substitution matrices and the motif substitution matrices. The evolution models for motifs of size 4 (tetranucleotides) and 5 (pentanucleotides) are now included in the SEGM (Stochastic Evolution of Genetic Motifs) web server.
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