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.