  The question as to why most higher organisms reproduce sexually has remained
open despite extensive research, and has been called "the queen of problems in
evolutionary biology". Theories dating back to Weismann have suggested that the
key must lie in the creation of increased variability in offspring, causing
enhanced response to selection. Rigorously quantifying the effects of assorted
mechanisms which might lead to such increased variability, and establishing
that these beneficial effects outweigh the immediate costs of sexual
reproduction has, however, proved problematic. Here we introduce an approach
which does not focus on particular mechanisms influencing factors such as the
fixation of beneficial mutants or the ability of populations to deal with
deleterious mutations, but rather tracks the entire distribution of a
population of genotypes as it moves across vast fitness landscapes. In this
setting simulations now show sex robustly outperforming asex across a broad
spectrum of finite or infinite population models. Concentrating on the additive
infinite populations model, we are able to give a rigorous mathematical proof
establishing that sexual reproduction acts as a more efficient optimiser of
mean fitness, thereby solving the problem for this model. Some of the key
features of this analysis carry through to the finite populations case.
