Should we expect substitution rate to depend on population size?

The rate of nucleotide substitution is generally believed to be a decreasing function of effective population size, at least for nonsynonymous substitutions. This view was originally based on consideration of slightly deleterious mutations with a fixed distribution of selection coefficients. A realistic model must include the occurrence and fixation of some advantageous mutations that compensate for the loss of fitness due to deleterious substitutions. Some such models, such as so-called "fixed" models, also predict a population size effect on substitution rate. An alternative model, presented here, predicts the near absence of a population size effect on substitution rate. This model is based on concave log-fitness functions and a fixed distribution of mutational effects on the selectively important trait. Simulations of an instance of the model confirm the approximate insensitivity of the substitution rate to population size. Although much experimental evidence has been claimed to support the existence of a population size effect, the body of evidence as a whole is equivocal, and much of the evidence that is supposed to demonstrate such an effect would also suggest that it is very small. Perhaps the proposed model applies well to some genes and not so well to others, and genes therefore vary with regard to the population size effect.