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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Reduction in fixation probability only depends on baseline density of sweeps.The scaled probability of fixation of a beneficial mutation, , plotted as a function of the strength of selection, .  is varied along with , so that the ratio  (and therefore ) is held constant. Circles show simulation results and curves show the analytical approximation given by Eq. (8) . The scaled probability of fixation is nearly constant until  becomes large enough that unlinked sweeps become important . ,  is shown in purple; ,  is shown in gold; ,  is shown in blue.  for all points and curves. Note that for , Eq. (8) slightly overestimates the amount of interference, because the chromosome is short enough that boundary effects must be considered. All simulations were run until the rate of substitution approached a steady value, and then continued until at least 1000 substitutions accumulated. The standard error is less than the radius of the points.
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pgen-1002740-g003: Reduction in fixation probability only depends on baseline density of sweeps.The scaled probability of fixation of a beneficial mutation, , plotted as a function of the strength of selection, . is varied along with , so that the ratio (and therefore ) is held constant. Circles show simulation results and curves show the analytical approximation given by Eq. (8) . The scaled probability of fixation is nearly constant until becomes large enough that unlinked sweeps become important . , is shown in purple; , is shown in gold; , is shown in blue. for all points and curves. Note that for , Eq. (8) slightly overestimates the amount of interference, because the chromosome is short enough that boundary effects must be considered. All simulations were run until the rate of substitution approached a steady value, and then continued until at least 1000 substitutions accumulated. The standard error is less than the radius of the points.

Mentions: We still face a difficulty, however, in that the locations and times of sweeps are not independent: because the amount of interference varies stochastically over the genome and through time, we expect them to be overdispersed. The scaling argument will still hold if the effects of different sweeps add up (the approximation developed below), or if the distribution in scaled time and map length is non-uniform but still depends on the population parameters only through . We show by simulation that the heuristic scaling argument is in fact accurate (Figure 3 and Figure 4), and that distribution of sweeps is close to uniform even for very strong interference (Figure 2). This may seem somewhat puzzling – sweeps should preferentially begin at loci and times that are experiencing less interference. However, when sweeps are rare, most of the genome experiences almost no interference in most generations, and thus little variation in the amount of interference. Conversely, when sweeps are common, most of the genome experiences substantial interference from multiple sweeps in most generations, and the stochastic variations in the amount of interference experienced from locus to locus and generation to generation are small compared to this average effect.


Limits to the rate of adaptive substitution in sexual populations.

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

Reduction in fixation probability only depends on baseline density of sweeps.The scaled probability of fixation of a beneficial mutation, , plotted as a function of the strength of selection, .  is varied along with , so that the ratio  (and therefore ) is held constant. Circles show simulation results and curves show the analytical approximation given by Eq. (8) . The scaled probability of fixation is nearly constant until  becomes large enough that unlinked sweeps become important . ,  is shown in purple; ,  is shown in gold; ,  is shown in blue.  for all points and curves. Note that for , Eq. (8) slightly overestimates the amount of interference, because the chromosome is short enough that boundary effects must be considered. All simulations were run until the rate of substitution approached a steady value, and then continued until at least 1000 substitutions accumulated. The standard error is less than the radius of the points.
© Copyright Policy
Related In: Results  -  Collection

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

pgen-1002740-g003: Reduction in fixation probability only depends on baseline density of sweeps.The scaled probability of fixation of a beneficial mutation, , plotted as a function of the strength of selection, . is varied along with , so that the ratio (and therefore ) is held constant. Circles show simulation results and curves show the analytical approximation given by Eq. (8) . The scaled probability of fixation is nearly constant until becomes large enough that unlinked sweeps become important . , is shown in purple; , is shown in gold; , is shown in blue. for all points and curves. Note that for , Eq. (8) slightly overestimates the amount of interference, because the chromosome is short enough that boundary effects must be considered. All simulations were run until the rate of substitution approached a steady value, and then continued until at least 1000 substitutions accumulated. The standard error is less than the radius of the points.
Mentions: We still face a difficulty, however, in that the locations and times of sweeps are not independent: because the amount of interference varies stochastically over the genome and through time, we expect them to be overdispersed. The scaling argument will still hold if the effects of different sweeps add up (the approximation developed below), or if the distribution in scaled time and map length is non-uniform but still depends on the population parameters only through . We show by simulation that the heuristic scaling argument is in fact accurate (Figure 3 and Figure 4), and that distribution of sweeps is close to uniform even for very strong interference (Figure 2). This may seem somewhat puzzling – sweeps should preferentially begin at loci and times that are experiencing less interference. However, when sweeps are rare, most of the genome experiences almost no interference in most generations, and thus little variation in the amount of interference. Conversely, when sweeps are common, most of the genome experiences substantial interference from multiple sweeps in most generations, and the stochastic variations in the amount of interference experienced from locus to locus and generation to generation are small compared to this average effect.

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