POLYMORPHISM UNDER STOCHASTIC ENVIRONMENTAL VARIATION
Model: We employ a sinusoidal fitness function, since we are interested in the
effects of phenotypic plasticity on the levels of genetic polymorphism under periodic,
predictable environments. In natural populations, however, even though the period of
environmental variation is predicable (typically annual), the severity of environmental
seasons may vary across years. For example, while effects such as average daylight
length are predictable, effects such as average temperature or food abundance may
experience severe perturbations across years. We therefore studied the effects of genomic
storage in the presence of stochastic variation in the severity of each season.
To test robustness of the genomic storage effect against stochastic perturbations in
environmental effects, we examine the effects of random fluctuations around predicted
seasonal effects on the levels of genetic polymorphism via Monte Carlo simulations. We
consider periodic environmental effect on fitness according to
𝑠! = (1 + 𝑣 !! )𝑠max sin 2𝜋
!
!!!
!
,
with a stochastic environmental shift v! 2t # ~ Normal(0,σ), where σ quantifies average
!" #$
C
within-season departure from the unperturbed fitness function. The stochastic
perturbations perturb the geometric mean fitnesses of alleles at both of the loci,
temporarily breaking quasineutrality across the cycle of fitness oscillations at the target
locus. Simulations including stochastic environmental perturbations (σ = 0.05, σ = 0.1, or
σ = 0.2) were performed on a subset of parameters given in the main text with p = 1.
Results: We find that balanced polymorphism arising from genomic storage is
robust to stochastic perturbations in the magnitude fitness oscillations between seasons
(Figure S1). Even with inter-seasonal stochastic variation in the magnitude of oscillations
as large as σ = 0.2, we find the same qualitative pattern of elevated polymorphism as with
a deterministic fitness function (electronic supplementary material Figure S1 top block).
In addition to perturbed environmental effects, we also undertook simulations that
stochastically varied the season length, C. To do so, we randomly skipped or repeated
sinusoidal environmental effect (according to fn. above) for one in ten generations, which
effectively increases or decreases the number of generations per season, randomly. Once
again, the genomic storage effect continued to produce significantly elevated diversity.
These results demonstrate that the genomic storage effect can contribute to
balanced polymorphism in populations that are exposed both to drift and to
environmental perturbations in season severity and duration.
Figure S1. Genomic storage effect
promotes diversity even with stochastic
environmental perturbations. Here, the
periodic environmental effect on fitness
!!!
𝑠! = (1 + 𝑣 !! 𝑠max sin 2𝜋 ! , varied
!
randomly between seasons, with v! 2t # ~
!" #$
C
Normal(0,σ,) drawn each season. In the
bottom block, we also perturbed the
periods of fitness oscillations (C) such
that sinusoidal environmental effect (𝑠! ) is
either repeated or skipped with probability
1/10 in each generation. The ensembleaverage levels of diversity are shown as a
function of the season length (C,
increasing vertically within major blocks),
the expected magnitude of periodic
selection (smax, increasing horizontally
within each panel), and the recombination
rate (r = 0.0001, 0.01, 0.1, 0.25 and 0.5,
varying horizontally within minor blocks),
with p = 1. We simulated an ensemble of
5x107 replicate populations of size N =
105, each run for 100N generations.