A population genetic model for the evolution of synonymous codon usage: patterns and predictions

Patterns of synonymous codon usage are determined by the forces of mutation, selection and drift. We elaborate on previous population genetic models of codon usage to incorporate parameters of population polymorphism, and demonstrate that the degree of codon bias expected in a single sequence picked at random from the population is accurately predicted by previous models, irrespective of population polymorphism. This new model is used to explore the relationships between synonymous codon usage, nucleotide site diversity and the rate of substitution. We derive the equilibrium frequency distribution of weakly selected segregating sites under the infinite-sites model, and the expected nucleotide site diversity. Contrary to intuition, levels of silent-site diversity can increase with the strength of selection acting on codon usage. We also predict the effects of background selection on statistics of synonymous codon usage and derive simple formulae to predict patterns of codon usage at amino acids with more than two synonymous codons, and the effects of variation in selection coefficient between sites within a gene. We show that patterns of silent-site variation and synonymous codon usage on the X chromosome and autosomes in Drosophila are compatible with recessivity of the fitness effects of unpreferred codons. Finally, we suggest that there still exist considerable discrepancies between current models and data.