Weak selection on synonymous codons substantially inflates dN/dS estimates in bacteria.

Synonymous codon substitutions are not always selectively neutral as revealed by several types of analyses, including studies of codon usage patterns among genes. We analyzed codon usage in 13 bacterial genomes sampled from across a large order of bacteria, Enterobacterales, and identified presumptively neutral and selected classes of synonymous substitutions. To estimate substitution rates, given a neutral/selected classification of synonymous substitutions, we developed a flexible [Formula: see text] substitution model that allows multiple classes of synonymous substitutions. Under this multiclass synonymous substitution (MSS) model, the denominator of [Formula: see text] includes only the strictly neutral class of synonymous substitutions. On average, the value of [Formula: see text] under the MSS model was 80% of that under the standard codon model in which all synonymous substitutions are assumed to be neutral. The indication is that conventional [Formula: see text] analyses overestimate these values and thus overestimate the frequency of positive diversifying selection and underestimate the strength of purifying selection. To quantify the strength of selection necessary to explain this reduction, we developed a model of selected compensatory codon substitutions. The reduction in synonymous substitution rate, and thus the contribution that selection makes to codon bias variation among genes, can be adequately explained by very weak selection, with a mean product of population size and selection coefficient, [Formula: see text].