Cumulative heterozygosity as a measure of diversity. Shown is the ensemble average heterozygosity at a target locus under cyclic selection, interacting with an unlinked modifier locus. Cumulative diversity, ĤT, is represented in color under the black curves. The heterozygosity was recorded in each generation following the introduction of a single copy of a derived allele. In a parameter set with long and severe seasons (C = 100 and smax = 0.5), the cumulative diversity is reduced, compared to neutrality. In a parameter set with shorter and milder seasonality (C = 20 and smax = 0.25) the cumulative diversity is elevated, compared to neutrality. Curves were smoothed via the loess fit [left and center, span = 0.01 (5 × 107 replicates); and right, span = 0.1 (106 replicates)].
The genomic storage effect promotes polymorphism across a broad range of parameter values. (A and B) We explore the effects of cyclic selection and phenotypic plasticity on the levels of cumulative diversity at a target locus (HT in A) and at a modifier locus (HM in B) in Monte Carlo simulations of a Wright–Fisher process with selection and recombination. The ensemble-average levels of cumulative diversity are shown as a function of the season length (C, increasing vertically within major blocks), the magnitude of periodic selection (smax, increasing horizontally within each panel), the plasticity effect size (p, varying vertically across major blocks), and the recombination rate (r = 0.0001, 0.01, 0.1, 0.25 and 0.5, varying horizontally within minor blocks). Control simulations, with one or the other locus monomorphic, are shown in the bottom blocks of A and B. Only the cumulative diversity levels that exceed the respective controls represent the genomic storage effect. We simulated an ensemble of 5 × 107 replicate populations of size N = 105, each with a single novel mutant introduction to each of the loci and run for 100N generations.
Results of the deterministic local stability analysis. Top row shows the estimated leading eigenvalue of the Jacobian for each equilibrium identified numerically. Bottom row shows sample trajectories of allele frequencies at the target (d) and at the modifier (M) locus during three periods of cyclic selection, at a stable polymorphic equilibrium. p = 1 in both rows, and r = 0.5 in the bottom row.
The effect of population size (A) and recurrent mutation (B) on balanced polymorphism under the genomic storage effect. (A) Ensemble average heterozygosity at the target locus over time, with C = 20, r = 0.25, and p = 1 (solid line) or p = 0.75 (dashed line) in a population of size N = 105 (blue) or 106 (red), based on the introduction of a single mutant. A total of 105N replicate simulations were each terminated once polymorphism perished or 100N generations were reached. (B) Ensemble mean heterozygosity, averaged over time, relative to the neutral expectation with recurrent mutation rate Nµ = 10−3 and p = 1 (top), Nµ = 0.1 and p = 1 (middle), and Nµ = 0.1 and p = 0.5 (bottom). We simulated 1000 replicate populations of size N = 105 for Nμ = 10−1 and 20,000 replicate populations of size N = 105 for Nμ = 10−3, each run for 100N generations.