Fig 1.
(A) The total selection coefficient measures the overall effect of selection on an allele including any associations with other sites under selection. (B) When alleles at different sites have different total selection coefficients, selection generates allele frequency divergence. (C) Compared to the binomial variance (proportional to p(1 − p)) created by random genetic drift, the selective variance tends to be more elevated at intermediate frequencies (proportional to [p(1 − p)]2) because the magnitude of selective allele frequency change is proportional to p(1 − p).
Fig 2.
(A) Forward-time population genetic simulations consistently show elevated excess variance under positive selection only. Excess variance defined as Ct(p) − Ct(p*) with major allele frequencies 0.5 < p < 0.55 and 0.9 < p* < 0.95 and t = 10 generations. (B) Under strong negative selection (deleterious mutation rate U = 1/genome/generation, mutation selection coefficient s = −0.05), total selection coefficients are substantial at all frequencies but much stronger for high major allele frequencies resulting in a frequency-independent overall selective divergence like the neutral case. (C) In contrast, the selective divergence
shows clear frequency dependence under positive selection, thus producing excess variance at intermediate frequencies. Population size N = 1000; 100 replicates per parameter combination. Stars indicate which panel A simulations are shown in panels B and C respectively.
Fig 3.
Intermediate frequency SNPs in E&R D. Simulans populations (A [11]; B [12]) have systematically elevated variance coefficients Ct(p) = Var(Δtp|p)/p(1 − p) relative to higher frequency SNPs after one round of evolution and resequencing (t ≈ 10 in A; t ≈ 15 in B), inconsistent with the binomial expectation for neutrally evolving alleles (1).
Ct(p) is calculated in 2.5% major allele frequency bins using all SNPs in the genome (circles). Vertical lines show 95% block bootstrap confidence intervals (1Mb blocks). We subtract the constant minpCt(p) from Ct(p) in each replicate to prevent differences in the overall magnitude of Ct(p) between replicates from obscuring p dependence within each replicate.
Fig 4.
Excess allele frequency variance (a measure of deviation from neutrality defined as Ct(p) − Ct(p*)) accumulates over time in a D. Simulans E&R experiment (A; [11]), but remains relatively flat in a wild D. Melanogaster population (B; S = Spring, F = Fall, LF = Late Fall; 09 = 2009 etc.; [15]).
The excess variance is calculated for intermediate frequency alleles falling within a major allele frequency bin at p = 0.5. In (A), p* = 0.9 and bin width is 2.5%. In (B), p* = 0.8 and bin width is 5%. Vertical lines show 95% block bootstrap confidence intervals (1Mb blocks).
Fig 5.
Total selection coefficients show substantial among-locus variance in Drosophila.
(A-C) Lower bound estimates of calculated from (6) (circles; vertical lines show 95% block bootstrap confidence intervals) are of order 10−4, which implies typical s values of ∼1%. Following the original studies [11, 12, 15], we assume t = 10 (A); t = 15 (B) and t = 10 (C; for both summer and winter).