A generalization of substitution evolution models of nucleotides to genetic motifs

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.