Statistical aspects of evolution under natural selection, with implications for the advantage of sexual reproduction

The prevalence of sexual reproduction remains mysterious, as it poses clear evolutionary drawbacks compared to reproducing asexually. Several possible explanations exist, with one of the most likely being that finite population size causes linkage disequilibria to randomly generate and impede the progress of natural selection, and that these are eroded by recombination via sexual reproduction. Previous investigations have either analysed this phenomenon in detail for small numbers of loci, or performed population simulations for many loci. Here we present a quantitative genetic model for fitness, based on the Price Equation, in order to examine the theoretical consequences of randomly generated linkage disequilibria when there are many loci. In addition, most previous work has been concerned with the long-term consequences of deleterious linkage disequilibria for population fitness. The expected change in mean fitness between consecutive generations, a measure of short-term evolutionary success, is shown under random environmental influences to be related to the autocovariance in mean fitness between the generations, capturing the effects of stochastic forces such as genetic drift. Interaction between genetic drift and natural selection, due to randomly generated linkage disequilibria, is demonstrated to be one possible source of mean fitness autocovariance. This suggests a possible role for sexual reproduction in reducing the negative effects of genetic drift, thereby improving the short-term efficacy of natural selection.