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. In joint work with Antonio Montalban, we prove results establishing basic conditions under which negative linkage disequilibrium will be created, and describing the long term effect on population fitness. For infinite population models in which gene fitnesses combine additively with zero-epistasis, we show that, during the process of asexual propagation, a negative linkage disequilibrium will be created and maintained, meaning that an occurrence of recombination at any stage of the process will cause an immediate increase in fitness variance. In contexts where there is a large but finite bound on allele fitnesses, the non-linear nature of the effect of recombination on a population presents serious obstacles in establishing convergence to an equilibrium, or even the positions of fixed points in the corresponding dynamical system. 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.

Sex versus Asex: an analysis of the role of variance conversion, with Antonio Montalban, Theoretical Population Biology, 114, 2017, pdf.