Abstract
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, , that depend on simple parameter combinations. When variance in fitness is low and linkage is loose, the baseline rate of substitution is , where is the population size, is the rate of beneficial mutations per genome, and is their mean selective advantage. Heritable variance in log fitness due to unlinked loci reduces by under polygamy and under monogamy. With a linear genetic map of length Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on , , , and only through the baseline density: . Under the approximation that the interference due to different sweeps adds up, we show that , 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 ; for higher , the rate of adaptation grows above , 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.
Highlights
In an adapting population, beneficial alleles may be spreading simultaneously at multiple genetic loci
Adaptation may be limited by a lack of beneficial alleles on which selection can act; in such populations, increasing the supply of mutations proportionally increases the rate of adaptation
By analyzing and simulating a simple model of an adapting sexual population, we find that interference prevents the rate of adaptive substitutions from greatly exceeding one substitution per centimorgan in every 200 generations
Summary
Beneficial alleles may be spreading simultaneously at multiple genetic loci. New beneficial mutations usually arise in different individuals, and compete with each other for fixation [1,2] In asexual populations, this ‘‘clonal interference’’ among alleles can drastically reduce the rate of adaptation [3,4,5,6,7,8,9,10,11]. Recombination can speed adaptation by breaking up negative associations among beneficial alleles [1,2] While this effect is implied by Weismann’s explanation for the advantage of sex [12], and was first investigated mathematically nearly half a century ago [13,14,15,16], there has been surprisingly little explicit treatment of the effects of interference on rates of adaptation. This does not correspond to any real organism, but could be realized in principle: it corresponds to a kind of mass meiosis, in which all members of the population take part. (This procedure can be approximated by multiple rounds of random mating with no selection, and is used directly in some genetic algorithms [51].)
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