Codon phylogenetic distance

We develop here an analytical evolution model based on a trinucleotide mutation matrix 64x64 with nine substitution parameters associated with the three types of substitutions in the three trinucleotide sites and with non-zero elements on its main diagonal. It generalizes the previous models based on the nucleotide mutation matrices 4x4 and the trinucleotide mutation matrices 64x64 with zero elements on its main diagonal. It determines at some time t the exact occurrence probabilities of trinucleotides mutating randomly according to these nine substitution parameters. Furthermore, applications of this model allow to generalize an evolutionary analytical solution of the common circular code of eukaryotes and prokaryotes and also to derive a codon phylogenetic distance.