The problem of counting sites in the estimation of the synonymous and nonsynonymous substitution rates: implications for the correlation between the synonymous substitution rate and codon usage bias

Most methods for estimating the rate of synonymous and nonsynonymous substitution per site define a site as a mutational opportunity: the proportion of sites that are synonymous is equal to the proportion of mutations that would be synonymous under the model of evolution being considered. Here we demonstrate that this definition of a site can give misleading results and that a physical definition of site should be used in some circumstances. We illustrate our point by reexamining the relationship between codon usage bias and the synonymous substitution rate. It has recently been shown that the rate of synonymous substitution, calculated using the Goldman-Yang method, which encapsulates the mutational-opportunity definition of a site at a high level of sophistication, is either positively correlated or uncorrelated to synonymous codon bias in Drosophila. Using other methods, which account for synonymous codon bias but define a site physically, we show that there is a negative correlation between the synonymous substitution rate and codon bias and that the lack of a negative correlation using the Goldman-Yang method is due to the way in which the number of synonymous sites is counted. We also show that there is a positive correlation between the synonymous substitution rate and third position GC content in mammals, but that the relationship is considerably weaker than that obtained using the Goldman-Yang method. We argue that the Goldman-Yang method is misleading in this context and conclude that methods that rely on a mutational-opportunity definition of a site should be used with caution.