Limits to the Rate of Adaptive Substitution in Sexual Populations

In large populations, many beneficial mutations may be simultaneously available and may compete with one another, slowing adaptation. By finding the probability of fixation of a favorable allele in a simple model of a haploid sexual population, we find limits to the rate of adaptive substitution, [Image: see text], that depend on simple parameter combinations. When variance in fitness is low and linkage is loose, the baseline rate of substitution is [Image: see text], where [Image: see text] is the population size, [Image: see text] is the rate of beneficial mutations per genome, and [Image: see text] is their mean selective advantage. Heritable variance [Image: see text] in log fitness due to unlinked loci reduces [Image: see text] by [Image: see text] under polygamy and [Image: see text] under monogamy. With a linear genetic map of length [Image: see text] Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on [Image: see text], [Image: see text], [Image: see text], and [Image: see text] only through the baseline density: [Image: see text]. Under the approximation that the interference due to different sweeps adds up, we show that [Image: see text], implying that interference prevents the rate of adaptive substitution from exceeding one per centimorgan per 200 generations. Simulations and numerical calculations confirm the scaling argument and confirm the additive approximation for [Image: see text]; for higher [Image: see text], the rate of adaptation grows above [Image: see text], but only very slowly. We also consider the effect of sweeps on neutral diversity and show that, while even occasional sweeps can greatly reduce neutral diversity, this effect saturates as sweeps become more common—diversity can be maintained even in populations experiencing very strong interference. Our results indicate that for some organisms the rate of adaptive substitution may be primarily recombination-limited, depending only weakly on the mutation supply and the strength of selection.