The advantage of recombination when selection is acting at many genetic Loci.

Natural selection can act at many loci across the genome. But as the number of polymorphic loci increases linearly, the number of possible genotypic combinations increases exponentially. Consequently, a finite population - even a very large population - contains only a small sample of all possible multi-locus genotypes. In this paper, we revisit the classic Fisher-Muller models of recombination, taking into account the abundant standing variation that is commonly seen in natural populations. We show that the generation of new genotypic combinations through recombination is an important component of adaptive evolution based on multi-locus selection. Specifically, high-fitness genotypes are expected to be absent from the initial population when the frequencies of favorable alleles at the selected loci are low. But as the allele frequencies rise in response to selection the missing genotypes will be generated by recombination. Given recombination, if the average frequency of the favored alleles at the various selected loci is equal to p, then the expected number of favorable alleles per chromosome will be equal to pL, where L is the number of loci. As the value of p approaches unity at the selected loci, the number of favorable alleles per chromosome will approach a value of L, i.e., at the end of the selection process a favorable allele will be found at all loci. In the absence of recombination, however, selection will be limited to the highest-fitness genotypes that are already present in the initial population. We point out that the fitness of such initial genotypes is far less than the theoretical maximum fitness because they contain a favorable allele at only a fraction of the loci. Consequently, recombination acts to unblock the adaptive response to multi-locus selection in finite populations. Using simulations, we show that the sexual population can withstand invasion by newly-arising asexual clones. These results help explain the maintenance of sexual reproduction in natural populations.