Sex versus asex: An analysis of the role of variance conversion

The question as to why most complex organisms reproduce sexually remains a very active research area in evolutionary biology. Theories dating back to Weismann have suggested that the key may lie in the creation of increased variability in offspring, causing enhanced response to selection. Under appropriate conditions, selection is known to result in the generation of negative linkage disequilibrium, with the effect of recombination then being to increase genetic variance by reducing these negative associations between alleles. It has therefore been a matter of significant interest to understand precisely those conditions resulting in negative linkage disequilibrium, and to recognise also the conditions in which the corresponding increase in genetic variation will be advantageous. Here, we prove rigorous results for the multi-locus case, detailing the build up of negative linkage disequilibrium, and describing the long term effect on population fitness for models with and without bounds on fitness contributions from individual alleles. Under the assumption of large but finite bounds on fitness contributions from alleles, the non-linear nature of the effect of recombination on a population presents serious obstacles in finding the genetic composition of populations at equilibrium, and in establishing convergence to those equilibria. We describe techniques for analysing the long term behaviour of sexual and asexual populations for such models, and use these techniques to establish conditions resulting in higher fitnesses for sexually reproducing populations.