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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Related in: MedlinePlus

The distribution of sweeps in time across the genome.Points show the beginnings of simulated selective sweeps. The distribution over time and map length appears approximately uniform. Time is in generations from the beginning of the simulation, and position is map distance in Morgans from the end of the chromosome. In the right panel, the time scale is halved and the length scale is doubled compared to the left panel, illustrating the effect of a doubling of  on the scaled distribution of sweeps that enters into Eq. (4) for the scaled probability of fixation . If we consider a focal mutation occurring in the middle of the chromosome at generation 2500 (the large gold dot), the rescaling changes the interference it experiences from any given sweep (e.g., the one marked by the large purple dot), but the total expected interference from the whole distribution of sweeps remains unchanged. Simulation parameters are chosen such that there is strong interference: , , , .
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pgen-1002740-g002: The distribution of sweeps in time across the genome.Points show the beginnings of simulated selective sweeps. The distribution over time and map length appears approximately uniform. Time is in generations from the beginning of the simulation, and position is map distance in Morgans from the end of the chromosome. In the right panel, the time scale is halved and the length scale is doubled compared to the left panel, illustrating the effect of a doubling of on the scaled distribution of sweeps that enters into Eq. (4) for the scaled probability of fixation . If we consider a focal mutation occurring in the middle of the chromosome at generation 2500 (the large gold dot), the rescaling changes the interference it experiences from any given sweep (e.g., the one marked by the large purple dot), but the total expected interference from the whole distribution of sweeps remains unchanged. Simulation parameters are chosen such that there is strong interference: , , , .

Mentions: We now make the final approximation that sweeps occur at approximately uniformly and independently distributed times and map positions, as they would in the absence of interference. In this case, the distribution, and therefore , depends only on the density, . (The scaled and unscaled densities of sweeps are the same, since the scaling factors for time and for map length cancel; see Figure 2.) There is a subtlety to this argument. If we consider a given set of sweeps, occurring at defined times and map positions, then their effects on a randomly placed mutation would depend on the strength of selection, and our scaling argument would fail. However, because the distribution of sweeps is invariant under rescaling, the fixation probability averaged over all possible configurations of sweeps is unchanged (Figure 2).


Limits to the rate of adaptive substitution in sexual populations.

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

The distribution of sweeps in time across the genome.Points show the beginnings of simulated selective sweeps. The distribution over time and map length appears approximately uniform. Time is in generations from the beginning of the simulation, and position is map distance in Morgans from the end of the chromosome. In the right panel, the time scale is halved and the length scale is doubled compared to the left panel, illustrating the effect of a doubling of  on the scaled distribution of sweeps that enters into Eq. (4) for the scaled probability of fixation . If we consider a focal mutation occurring in the middle of the chromosome at generation 2500 (the large gold dot), the rescaling changes the interference it experiences from any given sweep (e.g., the one marked by the large purple dot), but the total expected interference from the whole distribution of sweeps remains unchanged. Simulation parameters are chosen such that there is strong interference: , , , .
© Copyright Policy
Related In: Results  -  Collection

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

pgen-1002740-g002: The distribution of sweeps in time across the genome.Points show the beginnings of simulated selective sweeps. The distribution over time and map length appears approximately uniform. Time is in generations from the beginning of the simulation, and position is map distance in Morgans from the end of the chromosome. In the right panel, the time scale is halved and the length scale is doubled compared to the left panel, illustrating the effect of a doubling of on the scaled distribution of sweeps that enters into Eq. (4) for the scaled probability of fixation . If we consider a focal mutation occurring in the middle of the chromosome at generation 2500 (the large gold dot), the rescaling changes the interference it experiences from any given sweep (e.g., the one marked by the large purple dot), but the total expected interference from the whole distribution of sweeps remains unchanged. Simulation parameters are chosen such that there is strong interference: , , , .
Mentions: We now make the final approximation that sweeps occur at approximately uniformly and independently distributed times and map positions, as they would in the absence of interference. In this case, the distribution, and therefore , depends only on the density, . (The scaled and unscaled densities of sweeps are the same, since the scaling factors for time and for map length cancel; see Figure 2.) There is a subtlety to this argument. If we consider a given set of sweeps, occurring at defined times and map positions, then their effects on a randomly placed mutation would depend on the strength of selection, and our scaling argument would fail. However, because the distribution of sweeps is invariant under rescaling, the fixation probability averaged over all possible configurations of sweeps is unchanged (Figure 2).

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