Evolution probabilities and phylogenetic distance of dinucleotides

We develop here an analytical evolution model based on a dinucleotide mutation matrix 16×1616×16 with six substitution parameters associated with the three types of substitutions in the two dinucleotide sites. It generalizes the previous models based on the nucleotide mutation matrices 4×44×4. It determines at some time t the exact occurrence probabilities of dinucleotides mutating randomly according to these six substitution parameters. Furthermore, several properties and two applications of this model allow to derive 16 evolutionary analytical solutions of dinucleotides and also a dinucleotide phylogenetic distance. Finally, based on this mathematical model, the SED (Stochastic Evolution of Dinucleotides) web server has been developed for deriving evolutionary analytical solutions of dinucleotides.