Substitution processes in molecular evolution. I. Uniform and clustered substitutions in a haploid model.
J H Gillespie


A computer simulation of the process of nucleotide substitutions in a finite haploid population subject to selection in a randomly fluctuating environment provides a number of unexpected results. For rapidly fluctuating environments, substitutions are more regular than random. A small mutation-rate approximation is used to explain the regularity. The explanation does not depend heavily on the particulars of the haploid model, leading to the conjecture that many symmetrical models of molecular evolution with rapidly changing parameters may exhibit substitutions that are more regular than random. When fitnesses change very slowly, the simulation shows that substitutions are more clumped than random. Here a small-mutation approximation shows that the clustering is due to the increase in fitness that accompanies each successive substitution with a consequent lowering of the effective mutation rate. The two observations taken together suggest that the common observation that amino acid substitutions are clustered in time is due to the presence of parameters that change very slowly.