Limits...
Limits to the rate of adaptive substitution in sexual populations.

Weissman DB, Barton NH - PLoS Genet. (2012)

Bottom Line: 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.

View Article: PubMed Central - PubMed

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 , where N is the population size, U is the rate of beneficial mutations per genome, and is their mean selective advantage. Heritable variance v in log fitness due to unlinked loci reduces Λ by e⁻⁴(v) under polygamy and e⁻⁸ (v) under monogamy. With a linear genetic map of length R Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on s, N, U, and R only through the baseline density: Λ/R = F (Λ₀/R). Under the approximation that the interference due to different sweeps adds up, we show that Λ/R ~(Λ₀/R) / (1 +2Λ₉/R) , 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 Λ₀/R ~ 1; for higher Λ₀/R , the rate of adaptation grows above R/2, 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.

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Effect of interference among alleles with a distribution of selective advantages.Simulation results for scaled mean probability of fixation  for mutations with exponentially distributed selective advantages (blue circles) and scaled mean selective advantage for successful mutations  (green diamonds), as a function of the baseline density of sweeps  – i.e., the amount of interference. The purple squares shows  for the same parameter values, but with all mutations conferring an identical selective advantage . Allowing for a distribution of selective effects makes little difference in the rate of sweeps, , and the mean selective advantage of sweeps stays close to  (dashed black line), even for strong interference. The theoretical predictions Eqs. (7) and (13) (purple and blue dashed curves, respectively) are accurate for weak interference, but underestimate fixation probability with strong interference. The mutation rate  is varied, with other parameters held constant at , , and mean selective advantage provided by a mutation . All points are averages over 5000 simulated generations. Error bars on the top curve show the standard deviation of  for successful mutations. The standard errors are less than the size of the points.
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pgen-1002740-g007: Effect of interference among alleles with a distribution of selective advantages.Simulation results for scaled mean probability of fixation for mutations with exponentially distributed selective advantages (blue circles) and scaled mean selective advantage for successful mutations (green diamonds), as a function of the baseline density of sweeps – i.e., the amount of interference. The purple squares shows for the same parameter values, but with all mutations conferring an identical selective advantage . Allowing for a distribution of selective effects makes little difference in the rate of sweeps, , and the mean selective advantage of sweeps stays close to (dashed black line), even for strong interference. The theoretical predictions Eqs. (7) and (13) (purple and blue dashed curves, respectively) are accurate for weak interference, but underestimate fixation probability with strong interference. The mutation rate is varied, with other parameters held constant at , , and mean selective advantage provided by a mutation . All points are averages over 5000 simulated generations. Error bars on the top curve show the standard deviation of for successful mutations. The standard errors are less than the size of the points.

Mentions: Above, we have focused on the case in which all beneficial mutations provide the same selective advantage . Using simulations, we have also investigated the effect of allowing exponentially distributed selective advantages. ([10] and [78] conduct similar studies for asexual populations.) Figure 7 shows that for both weak and strong interference, allowing for variation in makes little difference to the rate of adaptation. Populations with an exponential distribution of mutational effects with mean evolve only slightly slower than populations with a fixed value , and show nearly the same scaling with the strength of selection.


Limits to the rate of adaptive substitution in sexual populations.

Weissman DB, Barton NH - PLoS Genet. (2012)

Effect of interference among alleles with a distribution of selective advantages.Simulation results for scaled mean probability of fixation  for mutations with exponentially distributed selective advantages (blue circles) and scaled mean selective advantage for successful mutations  (green diamonds), as a function of the baseline density of sweeps  – i.e., the amount of interference. The purple squares shows  for the same parameter values, but with all mutations conferring an identical selective advantage . Allowing for a distribution of selective effects makes little difference in the rate of sweeps, , and the mean selective advantage of sweeps stays close to  (dashed black line), even for strong interference. The theoretical predictions Eqs. (7) and (13) (purple and blue dashed curves, respectively) are accurate for weak interference, but underestimate fixation probability with strong interference. The mutation rate  is varied, with other parameters held constant at , , and mean selective advantage provided by a mutation . All points are averages over 5000 simulated generations. Error bars on the top curve show the standard deviation of  for successful mutations. The standard errors are less than the size of the points.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3369949&req=5

pgen-1002740-g007: Effect of interference among alleles with a distribution of selective advantages.Simulation results for scaled mean probability of fixation for mutations with exponentially distributed selective advantages (blue circles) and scaled mean selective advantage for successful mutations (green diamonds), as a function of the baseline density of sweeps – i.e., the amount of interference. The purple squares shows for the same parameter values, but with all mutations conferring an identical selective advantage . Allowing for a distribution of selective effects makes little difference in the rate of sweeps, , and the mean selective advantage of sweeps stays close to (dashed black line), even for strong interference. The theoretical predictions Eqs. (7) and (13) (purple and blue dashed curves, respectively) are accurate for weak interference, but underestimate fixation probability with strong interference. The mutation rate is varied, with other parameters held constant at , , and mean selective advantage provided by a mutation . All points are averages over 5000 simulated generations. Error bars on the top curve show the standard deviation of for successful mutations. The standard errors are less than the size of the points.
Mentions: Above, we have focused on the case in which all beneficial mutations provide the same selective advantage . Using simulations, we have also investigated the effect of allowing exponentially distributed selective advantages. ([10] and [78] conduct similar studies for asexual populations.) Figure 7 shows that for both weak and strong interference, allowing for variation in makes little difference to the rate of adaptation. Populations with an exponential distribution of mutational effects with mean evolve only slightly slower than populations with a fixed value , and show nearly the same scaling with the strength of selection.

Bottom Line: 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.

View Article: PubMed Central - PubMed

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 , where N is the population size, U is the rate of beneficial mutations per genome, and is their mean selective advantage. Heritable variance v in log fitness due to unlinked loci reduces Λ by e⁻⁴(v) under polygamy and e⁻⁸ (v) under monogamy. With a linear genetic map of length R Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on s, N, U, and R only through the baseline density: Λ/R = F (Λ₀/R). Under the approximation that the interference due to different sweeps adds up, we show that Λ/R ~(Λ₀/R) / (1 +2Λ₉/R) , 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 Λ₀/R ~ 1; for higher Λ₀/R , the rate of adaptation grows above R/2, 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.

Show MeSH
Related in: MedlinePlus