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.

Show MeSH

Related in: MedlinePlus

Differing effects of sweeps on selected and neutral alleles.The scaled fixation probability of beneficial alleles and scaled neutral diversity as a function of the baseline density of sweeps . Points show simulation results, curves show analytical approximations. The circles and the black curve are the scaled fixation probability , and show the same data as in Figure 4. The squares and colored curves show the scaled neutral diversity, . At small , beneficial alleles do not interfere with each other, but still reduce neutral diversity substantially. However, increasing  to larger values has little additional effect on neutral diversity, both because interference limits the increase in the number of sweeps ( decreases), and because the combined effect of overlapping sweeps on neutral diversity is less than the sum of their individual effects (the squares lie above the additive analytical approximation). The analytical approximations match the simulation results up to strong interference (), at which point they begin to break down. The squares are the averages over 100 simulation runs; see the Methods for how  was measured. The colored curves show Eq. (9) for  as a function of , with  taken empirically from the simulations. The mutation rate  is varied, with other parameters held constant at , , and . For these parameter values, essentially all interference is caused by tightly-linked loci.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3369949&req=5

pgen-1002740-g006: Differing effects of sweeps on selected and neutral alleles.The scaled fixation probability of beneficial alleles and scaled neutral diversity as a function of the baseline density of sweeps . Points show simulation results, curves show analytical approximations. The circles and the black curve are the scaled fixation probability , and show the same data as in Figure 4. The squares and colored curves show the scaled neutral diversity, . At small , beneficial alleles do not interfere with each other, but still reduce neutral diversity substantially. However, increasing to larger values has little additional effect on neutral diversity, both because interference limits the increase in the number of sweeps ( decreases), and because the combined effect of overlapping sweeps on neutral diversity is less than the sum of their individual effects (the squares lie above the additive analytical approximation). The analytical approximations match the simulation results up to strong interference (), at which point they begin to break down. The squares are the averages over 100 simulation runs; see the Methods for how was measured. The colored curves show Eq. (9) for as a function of , with taken empirically from the simulations. The mutation rate is varied, with other parameters held constant at , , and . For these parameter values, essentially all interference is caused by tightly-linked loci.

Mentions: As shown in Figure 6, Eq. (9) is roughly in agreement with the rate of coalescence observed at a neutral marker locus in simulated populations. Figure 6 also shows the simulation results and the analytical approximation ( Eq. (8) ) for the rate of adaptation, in terms of reduction in the probability of fixation, . We can clearly see the different scalings discussed above: while both neutral diversity and decrease as the baseline density of sweeps increases, they do so in opposite ways. Beneficial mutations are nearly unaffected by interference until approaches one, at which point drops rapidly. Neutral diversity, on the other hand, is strongly reduced even at small , but is nearly independent of for , precisely because interference limits the increase in in this regime. In addition, for very high rates of sweeps, interference between successful sweeps causes their effect on coalescence to be sub-additive, further preserving neutral diversity [66], [67]; a similar effect also limits the reduction in neutral diversity caused by background selection [76], [77].


Limits to the rate of adaptive substitution in sexual populations.

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

Differing effects of sweeps on selected and neutral alleles.The scaled fixation probability of beneficial alleles and scaled neutral diversity as a function of the baseline density of sweeps . Points show simulation results, curves show analytical approximations. The circles and the black curve are the scaled fixation probability , and show the same data as in Figure 4. The squares and colored curves show the scaled neutral diversity, . At small , beneficial alleles do not interfere with each other, but still reduce neutral diversity substantially. However, increasing  to larger values has little additional effect on neutral diversity, both because interference limits the increase in the number of sweeps ( decreases), and because the combined effect of overlapping sweeps on neutral diversity is less than the sum of their individual effects (the squares lie above the additive analytical approximation). The analytical approximations match the simulation results up to strong interference (), at which point they begin to break down. The squares are the averages over 100 simulation runs; see the Methods for how  was measured. The colored curves show Eq. (9) for  as a function of , with  taken empirically from the simulations. The mutation rate  is varied, with other parameters held constant at , , and . For these parameter values, essentially all interference is caused by tightly-linked loci.
© Copyright Policy
Related In: Results  -  Collection

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

pgen-1002740-g006: Differing effects of sweeps on selected and neutral alleles.The scaled fixation probability of beneficial alleles and scaled neutral diversity as a function of the baseline density of sweeps . Points show simulation results, curves show analytical approximations. The circles and the black curve are the scaled fixation probability , and show the same data as in Figure 4. The squares and colored curves show the scaled neutral diversity, . At small , beneficial alleles do not interfere with each other, but still reduce neutral diversity substantially. However, increasing to larger values has little additional effect on neutral diversity, both because interference limits the increase in the number of sweeps ( decreases), and because the combined effect of overlapping sweeps on neutral diversity is less than the sum of their individual effects (the squares lie above the additive analytical approximation). The analytical approximations match the simulation results up to strong interference (), at which point they begin to break down. The squares are the averages over 100 simulation runs; see the Methods for how was measured. The colored curves show Eq. (9) for as a function of , with taken empirically from the simulations. The mutation rate is varied, with other parameters held constant at , , and . For these parameter values, essentially all interference is caused by tightly-linked loci.
Mentions: As shown in Figure 6, Eq. (9) is roughly in agreement with the rate of coalescence observed at a neutral marker locus in simulated populations. Figure 6 also shows the simulation results and the analytical approximation ( Eq. (8) ) for the rate of adaptation, in terms of reduction in the probability of fixation, . We can clearly see the different scalings discussed above: while both neutral diversity and decrease as the baseline density of sweeps increases, they do so in opposite ways. Beneficial mutations are nearly unaffected by interference until approaches one, at which point drops rapidly. Neutral diversity, on the other hand, is strongly reduced even at small , but is nearly independent of for , precisely because interference limits the increase in in this regime. In addition, for very high rates of sweeps, interference between successful sweeps causes their effect on coalescence to be sub-additive, further preserving neutral diversity [66], [67]; a similar effect also limits the reduction in neutral diversity caused by background selection [76], [77].

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