m'OLUTIONARY EFFECT OF RECOMllINATION

Crow and Kimura (1965) constructed a model to quantify the arguments originally due to Fisher (1930) and Muller (1932) that recombination accelerates evolution because it enables mutations originally occurring in distinct individuals to be combined in a single descendent. The model contained the assumption that even though the population be large, the mutation rate should be so small that the double mutant may not exist in the same individual (see, also, Crow and Kimura (1969». In particular, Crow and Kimura concluded that the advantage conferred by recombination is greatest when the population is large. Maynard Smith (1968) contested these findings by producing a "counterexample." This consisted of a deterministic two locus model with multiplicative viabilities in which, at any time, the frequency of the double mutant is the same with recombination as without it. In this article, we also treat the completely deterministic model, that is, an effectively infinite population so that chromosome frequencies suffice to describe the population. However, we do not assume that the relative fitness of the double mutant is exactly equal to the product of the relative fitnesses of the single mutants. We consider the case of two loci so that initially the population can be thought of as being all AB. Mutation occurs from A to a and from B to b. Fitnesses of the mutant genotypes are normalized to the original type. We first show that if the mutations are favorable and the double mutant is fitter than expected under simple multiplicity, then the frequency of the double