Additional file 16 of Identification of positive selection in genes is greatly improved by using experimentally informed site-specific models

Clarification of subtleties in the relationship between amino-acid preferences and substitution model equilibrium frequencies. Figure 1 shows the experimentally measured amino-acid preferences and the equilibrium frequencies of the GY94 model. The equilibrium frequencies of the experimentally informed codon models (ExpCM) are given by Eq. 4, and are similar but not identical to the preferences: the ExpCM equilibrium frequencies are also influenced by the unequal number of codons per amino acid, nucleotide mutation biases, and the stringency parameter β. The equilibrium frequencies of the GY94 model already account for the codon/mutation factors. To clarify these distinctions, this figure shows the preferences and equilibrium frequencies of the ExpCM model, and the “all-equal” amino-acid preferences that would lead to the equilibrium frequencies of the GY94 model if the nucleotide frequency parameters in that model are construed as representing mutation-level rather than selection-level processes. Note that the logo plots show the amino-acid frequencies implied by the equilibrium codon frequencies (i.e. the sum of the frequencies of all encoding codons for each amino acid). (PDF 76 kb