Natural selection and the molecular clock.

This paper concludes that the statistical properties of protein evolution are compatible with a particular model of evolution by natural selection. The argument begins with a statistical description of the molecular clock based on a Poisson process with a randomly varying tick rate. If the time scale of the change of the tick rate of the molecular clock is assumed to be much less than the average time between substitutions, then it is shown that the substitution process must be episodic, with bursts of substitutions being separated by long periods of time with no substitutions. This analysis generalizes the recent work of Gillespie (1984a). The second part of the argument shows that a simple model of evolution by natural selection--one that incorporates a changing environment, the molecular landscape, and a simple form of epistasis--exhibits dynamics that are identical to those inferred from the statistical analysis. This leads to the conclusion that natural selection is a viable explanation for protein evolution. In addition, a correction formula for multiple substitutions is given that does not require that the substitution process be a Poisson process, and some comments on the inability of the neutral allele theory to account for the dynamics of the substitution process are presented.