Limits to the rate of adaptive substitution in sexual populations.
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Heritable variance v in log fitness due to unlinked loci reduces Λ by e⁻⁴(v) under polygamy and e⁻⁸ (v) under monogamy.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.
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Affiliation: Institute of Science and Technology Austria, Klosterneuburg, Austria. dbw@ist.ac.at
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, Λ, that depend on simple parameter combinations. When variance in fitness is low and linkage is loose, the baseline rate of substitution is Λ₀ = 2NU Related in: MedlinePlus |
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Mentions: The key observation is that alleles are most vulnerable to interference when rare, but cause the most interference when moderately common. (Intuitively, a mutant allele causes the most interference when it is near frequency – frequent enough to significantly affect other alleles, but not so frequent that most other alleles are on the mutant background; see Figure 1 and Figure S3.) We assume that is very large, so that there is a number , such that alleles which are present in copies are established (i.e., are very likely increase to fixation along a roughly deterministic trajectory), while still being at low frequency in the population. This allows to us to make the crucial approximation that each mutation has a negligible effect on other mutations prior to its establishment, separating the roughly deterministic increase of alleles that are destined to fix (and which interfere with the fixation of others) from the stochastic fluctuations of rare alleles. For a given pattern of established sweeps, these rare alleles can be treated as independent branching processes, with fixation probability given by Eq. (2) . Notice that we can rescale Eq. (2) by writing it in terms of , , and , and letting be the difference between the number of beneficial alleles in background and the average number:(4)This rescaled equation does not explicitly depend on , or – only implicitly, through the dependence of and on the genotype frequencies, . This is still true when we average over genotype frequencies to find the scaled version of Eq. (3) . Thus, the scaled probability of fixation of a new mutation that falls on a random genetic background, , depends on , , , and only through their effect on the number and pattern of interfering sweeps. |
View Article: PubMed Central - PubMed
Affiliation: Institute of Science and Technology Austria, Klosterneuburg, Austria. dbw@ist.ac.at