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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A selective sweep causes interference over a time  and a genetic distance .Fixation probability of a new mutation with advantage  occurring after an interfering sweep with the same selective advantage . The fixation probability , scaled by its baseline value , is plotted against the scaled map position of the new mutation relative to the interfering sweep, , and its scaled time of occurrence relative to the time at which the interfering sweep reaches frequency , . Note that the relationship between these scaled variables is independent of , as long as . The X marks the time when the interfering sweep is at frequency  for ; it is assumed to follow a deterministic trajectory. The sweep causes the most interference once it becomes common (frequency ), and causes little interference to common alleles (i.e., alleles that arise around the same time or earlier).  is calculated numerically using Eqs. (2) and (3) .
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pgen-1002740-g001: A selective sweep causes interference over a time and a genetic distance .Fixation probability of a new mutation with advantage occurring after an interfering sweep with the same selective advantage . The fixation probability , scaled by its baseline value , is plotted against the scaled map position of the new mutation relative to the interfering sweep, , and its scaled time of occurrence relative to the time at which the interfering sweep reaches frequency , . Note that the relationship between these scaled variables is independent of , as long as . The X marks the time when the interfering sweep is at frequency for ; it is assumed to follow a deterministic trajectory. The sweep causes the most interference once it becomes common (frequency ), and causes little interference to common alleles (i.e., alleles that arise around the same time or earlier). is calculated numerically using Eqs. (2) and (3) .

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.


Limits to the rate of adaptive substitution in sexual populations.

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

A selective sweep causes interference over a time  and a genetic distance .Fixation probability of a new mutation with advantage  occurring after an interfering sweep with the same selective advantage . The fixation probability , scaled by its baseline value , is plotted against the scaled map position of the new mutation relative to the interfering sweep, , and its scaled time of occurrence relative to the time at which the interfering sweep reaches frequency , . Note that the relationship between these scaled variables is independent of , as long as . The X marks the time when the interfering sweep is at frequency  for ; it is assumed to follow a deterministic trajectory. The sweep causes the most interference once it becomes common (frequency ), and causes little interference to common alleles (i.e., alleles that arise around the same time or earlier).  is calculated numerically using Eqs. (2) and (3) .
© Copyright Policy
Related In: Results  -  Collection

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

pgen-1002740-g001: A selective sweep causes interference over a time and a genetic distance .Fixation probability of a new mutation with advantage occurring after an interfering sweep with the same selective advantage . The fixation probability , scaled by its baseline value , is plotted against the scaled map position of the new mutation relative to the interfering sweep, , and its scaled time of occurrence relative to the time at which the interfering sweep reaches frequency , . Note that the relationship between these scaled variables is independent of , as long as . The X marks the time when the interfering sweep is at frequency for ; it is assumed to follow a deterministic trajectory. The sweep causes the most interference once it becomes common (frequency ), and causes little interference to common alleles (i.e., alleles that arise around the same time or earlier). is calculated numerically using Eqs. (2) and (3) .
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.

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