Fig. 3

Classification of the double codon substitutions. a Four combinations of within-codon double substitutions based on the synonymy of the respective ancestral and derived (final) codons, and synonymy of intermediate state codons to the ancestral codons. Each cell represents one of the four combinations of the two intermediates (non) synonymy and the two final states (non) synonymy. When both are synonymous, the combination is noted as SS. When at least one of the intermediates is synonymous to the ancestral codon, whereas the final codon is non-synonymous to the ancestral state, the combination is classified as SN. When one of the intermediates is non-synonymous to the ancestral codon, whereas the final codon is synonymous to the ancestral, the combination is classified as NS. Finally, when both are non-synonymous, the combination is noted as NN. The text colors represent (non) synonymy of the intermediate and final codons compared to the ancestral: brown, synonymous intermediate; red, non-synonymous intermediate; pink, synonymous final; purple, non-synonymous final. The circle colors are different for each class of codon double substitutions and are the same as in other figures: yellow, SS; light orange, SN; light green, NS; and light blue, NN. b Selective pressure in different codon double substitutions classes. Positive, combinations compatible with positive selection, where a codon double substitution has a significantly higher DF than the corresponding double synonymous substitution and the DF is lower in fast compared to slow evolving genes. Negative, combinations compatible with purifying selection, where a codon double substitution has a significantly lower DF than the corresponding double synonymous substitution and the DF is higher in fast compared to slow evolving genes. Neutral, combinations where the codon DF was not significantly different from that of the corresponding synonymous DF and the DF is similar in fast and slow evolving genes. All SS, SN, and NS combinations show compatible results in the comparison of the DF to the double synonymous null models, and in the comparison of the DF between fast and slow evolving genes, and thus are collectively presented as being subject to neutral evolution, negative and positive selection, respectively. However, the NN combinations show conflicting results between the comparison of DF to double synonymous control null models and the comparison of DF between fast and slow evolving genes, and are therefore presented as a combination of positive, negative, and neutral regimes, based on the individual comparisons to the specific null models with the same base composition