Since the modern evolutionary synthesis was first proposed early in the twentieth century, attention has focused on assessing the relative contribution of mutation versus natural selection on protein evolution. Here we test a model that yields general quantitative predictions on rates of protein evolution by combining principles of individual energetics with Kimura's neutral theory. The model successfully predicts much of the heterogeneity in rates of protein evolution for diverse eukaryotes (i.e. fishes, amphibians, reptiles, birds, mammals) from different thermal environments. Data also show that the ratio of non-synonymous to synonymous nucleotide substitution is independent of body size, and thus presumably of effective population size. These findings indicate that rates of protein evolution are largely controlled by mutation rates, which in turn are strongly influenced by individual metabolic rate.
The authors make a reference to the neutral theory of molecular evolution. The basic idea behind a neutral model of evolution is that mutation rates are the dominant force behind rates of substitution at the molecular level. In other words, the only parameter you need to predict the rate of substitution is mutation. Substitution is basically the phenomenon whereby allele 1 is at ~100% frequency on a locus within a population at a given time, and at some point in the future allele 2 is at 100% frequency. Allele 2 has substituted for allele 1 at the locus of interest. The sparest formalism for neutral theory would be: Rate of substitution ~ Rate of mutation, derived from: Rate of substitution = Probability of substitution (for a new mutant) X 2 X Effective population size X Rate of mutation Since Probability of substitution = 1/[2 X Effective population size], 2 X Effective population size cancels out.^1 So population size is irrelevant. The authors above suggest that a biophysical parameter, metabolic rate, is a good predictor of the rate of mutation. Science Daily has a summation up. We all know in theory that biology is just a branch of chemistry and physics, but sometimes that theory is realized. 1 - The "2" is because we are assuming this is a diploid case, where each gene comes in two copies. That doubles the sample space across which a mutation could occur