On the Evolution of Recombination in Haploids and Diploids

In population genetic theory, most analytical and numerical studies of the evolution of recombination have focused on diploid genetics. In studies of the foundations and applications of genetic algorithms (GA's), however, the bit-strings are usually treated as haploid genotypes. This paper compares analytical results for the evolutionary dynamics of modifiers of recombination in haploids with results derived for diploids. The new analytical work addresses the evolution of an allele that controls the rate of recombination between two loci subject to directional selection. It is shown that the fate of a recombination modifier in both haploids and diploids is determined in a complicated way by the sign of the epistasis (interaction in fitness) between the loci, the sign of the initial linkage disequilibrium, and the amount of recombination between the modifier and the genes under selection. This theory is deterministic in that the population is regarded as infinite and no sampling occurs to produce offspring from parents. The second part of the paper takes selection schemes that have been used recently in numerical studies of finite diploid populations and asks how recombination evolves in haploid versions of these models. Although the analysis keeps track of the recombination controlling locus rather than the time until a desired bit-string appears, our result may be of use to the practitioners of GA's. We find that as a rule high recombination evolves more easily when selection is on haploids than it does in the diploid case. This is especially true of Gaussian selection schemes with high recombination recessive to low recombination. When the fitness regime is more jagged, however, the results depend on the level of jaggedness, with high recombination favored under smoother regimes. We also find that the direction of mutation and dominance relationship among the modifying alleles affects the results. Although there remains much to be done in reconciling the two ways of approaching evolutionary properties of genetic operations, many new and interesting questions have emerged from, and will continue to be stimulated by interactions between practitioners of each approach.