Abstract
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.
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