Requisite mutational load, pathway epistasis and deterministic mutation accumulation in sexual versus asexual populations.

A measure of the equilibrium load of deleterious mutations is developed that explicitly incorporates the level of genome-wide linkage disequilibrium. This measure, called the requisite mutational load, is based on the minimal net reproductive rate of the least mutated class necessary to prevent the deterministic mutation accumulation. If this minimal net reproductive rate is larger than ecological or physiological constraints allow, then: a) the population is driven to extinction via deterministic mutation accumulation, or b) a mutational Red-Queen ensues with adaptation counterbalancing mutation accumulation. Two population parameters determine the requisite mutational load: a) the equilibrium strength of selection, measured as a selection gradient, and b) the equilibrium opportunity for selection, measured as the variance in number of mutations per genome. The opportunity for selection is decomposed into the accumulation of mutations (average number per genome) and the level of genome-wide linkage disequilibrium. Recombination can substantially reduce the requisite mutational load, compared to clonal reproduction, when there is buffering and/or reinforcing epistasis and also when there is positive assortative mating for fitness. Recombination is advantageous because it reduces the negative (variance reducing) linkage disequilibrium induced by beneficial epistasis. The functional form of the expression for requisite mutational load illustrates why epistasis within pathways, i.e., among closely interacting genes, is a powerful alternative to genome-wide truncation selection, as a means of reducing mutational load.