Soft sweeps: molecular population genetics of adaptation from standing genetic variation

Abstract

A population can adapt to a rapid environmental change or habitat expansion in two ways. It may adapt either through new beneficial mutations that subsequently sweep through the population or by using alleles from the standing genetic variation. We use diffusion theory to calculate the probabilities for selective adaptations and find a large increase in the fixation probability for weak substitutions, if alleles originate from the standing genetic variation. We then determine the parameter regions where each scenario-standing variation vs. new mutations-is more likely. Adaptations from the standing genetic variation are favored if either the selective advantage is weak or the selection coefficient and the mutation rate are both high. Finally, we analyze the probability of "soft sweeps," where multiple copies of the selected allele contribute to a substitution, and discuss the consequences for the footprint of selection on linked neutral variation. We find that soft sweeps with weaker selective footprints are likely under both scenarios if the mutation rate and/or the selection coefficient is high.

Figure 1.—

Fixation probabilities from a single new mutation (dashed line) and from a single segregating allele (solid line). Note that α_b is measured on a logarithmic scale.

Figure 2.—

The probability of fixation from mutation-selection-drift balance, P_sgv, for a range of mutation and selection parameters. Solid lines show approximation Equation 8 and dotted lines show the deterministic approximation Equation 10. Solid circles are simulation results. Ninety-five percent confidence intervals are contained in the circles.

Figure 2.—

The probability of fixation from mutation-selection-drift balance, P_sgv, for a range of mutation and selection parameters. Solid lines show approximation Equation 8 and dotted lines show the deterministic approximation Equation 10. Solid circles are simulation results. Ninety-five percent confidence intervals are contained in the circles.

Figure 2.—

The probability of fixation from mutation-selection-drift balance, P_sgv, for a range of mutation and selection parameters. Solid lines show approximation Equation 8 and dotted lines show the deterministic approximation Equation 10. Solid circles are simulation results. Ninety-five percent confidence intervals are contained in the circles.

Figure 2.—

The probability of fixation from mutation-selection-drift balance, P_sgv, for a range of mutation and selection parameters. Solid lines show approximation Equation 8 and dotted lines show the deterministic approximation Equation 10. Solid circles are simulation results. Ninety-five percent confidence intervals are contained in the circles.

Figure 3.—

The probability that an adaptive substitution is from the standing genetic variation (Pr_sgv). Simulation data with 95% confidence intervals are compared to the analytical approximation Equation 14.

Figure 3.—

The probability that an adaptive substitution is from the standing genetic variation (Pr_sgv). Simulation data with 95% confidence intervals are compared to the analytical approximation Equation 14.

Figure 3.—

The probability that an adaptive substitution is from the standing genetic variation (Pr_sgv). Simulation data with 95% confidence intervals are compared to the analytical approximation Equation 14.

Figure 3.—

The probability that an adaptive substitution is from the standing genetic variation (Pr_sgv). Simulation data with 95% confidence intervals are compared to the analytical approximation Equation 14.

Figure 4.—

The probability that an adaptive substitution stems from the standing genetic variation Pr_sgv in a population with a bottleneck at the time of the environmental change. Dashed lines show a simple reduction in population size by a factor 100 without recovery. Simulation circles and solid lines are for the opposite case of strong logistic recovery (for parameters see main text). The lines follow from the simple analytical approximation Equation 14 with the bottleneck correction R_α → R_α/B_sgv and α_b → α_b/B_new in the term proportional to G. Direct numerical integration of Equations 5 and 6 with the same bottleneck correction produces a slightly better fit.

Figure 4.—

The probability that an adaptive substitution stems from the standing genetic variation Pr_sgv in a population with a bottleneck at the time of the environmental change. Dashed lines show a simple reduction in population size by a factor 100 without recovery. Simulation circles and solid lines are for the opposite case of strong logistic recovery (for parameters see main text). The lines follow from the simple analytical approximation Equation 14 with the bottleneck correction R_α → R_α/B_sgv and α_b → α_b/B_new in the term proportional to G. Direct numerical integration of Equations 5 and 6 with the same bottleneck correction produces a slightly better fit.

Figure 4.—

The probability that an adaptive substitution stems from the standing genetic variation Pr_sgv in a population with a bottleneck at the time of the environmental change. Dashed lines show a simple reduction in population size by a factor 100 without recovery. Simulation circles and solid lines are for the opposite case of strong logistic recovery (for parameters see main text). The lines follow from the simple analytical approximation Equation 14 with the bottleneck correction R_α → R_α/B_sgv and α_b → α_b/B_new in the term proportional to G. Direct numerical integration of Equations 5 and 6 with the same bottleneck correction produces a slightly better fit.

Figure 4.—

The probability that an adaptive substitution stems from the standing genetic variation Pr_sgv in a population with a bottleneck at the time of the environmental change. Dashed lines show a simple reduction in population size by a factor 100 without recovery. Simulation circles and solid lines are for the opposite case of strong logistic recovery (for parameters see main text). The lines follow from the simple analytical approximation Equation 14 with the bottleneck correction R_α → R_α/B_sgv and α_b → α_b/B_new in the term proportional to G. Direct numerical integration of Equations 5 and 6 with the same bottleneck correction produces a slightly better fit.

Figure 5.—

The probability that multiple copies from the standing genetic variation contribute to a substitution, P_mult. Solid lines correspond to Equation 18 and dotted lines to the deterministic approximation Equation 19.

Figure 5.—

The probability that multiple copies from the standing genetic variation contribute to a substitution, P_mult. Solid lines correspond to Equation 18 and dotted lines to the deterministic approximation Equation 19.

Figure 5.—

The probability that multiple copies from the standing genetic variation contribute to a substitution, P_mult. Solid lines correspond to Equation 18 and dotted lines to the deterministic approximation Equation 19.

Figure 5.—

The probability that multiple copies from the standing genetic variation contribute to a substitution, P_mult. Solid lines correspond to Equation 18 and dotted lines to the deterministic approximation Equation 19.

Figure 6.—

The probability that multiple copies with independent origin contribute to a substitution, P_ind. Lines correspond to Equation 20; symbols represent simulation data. Circles represent fixations from the standing genetic variation without new mutational input after time T; squares include new mutations. Triangles represent fixations from recurrent new mutations only.

Figure 6.—

The probability that multiple copies with independent origin contribute to a substitution, P_ind. Lines correspond to Equation 20; symbols represent simulation data. Circles represent fixations from the standing genetic variation without new mutational input after time T; squares include new mutations. Triangles represent fixations from recurrent new mutations only.