Emergence of long-term balanced polymorphism under cyclic selection of spatially variable magnitude

Abstract

A fundamental question in evolutionary biology is what promotes genetic variation at nonneutral loci, a major precursor to adaptation in changing environments. In particular, balanced polymorphism under realistic evolutionary models of temporally varying environments in finite natural populations remains to be demonstrated. Here, we propose a novel mechanism of balancing selection under temporally varying fitnesses. Using forward-in-time computer simulations and mathematical analysis, we show that cyclic selection that spatially varies in magnitude, such as along an environmental gradient, can lead to elevated levels of nonneutral genetic polymorphism in finite populations. Balanced polymorphism is more likely with an increase in gene flow, magnitude and period of fitness oscillations, and spatial heterogeneity. This polymorphism-promoting effect is robust to small systematic fitness differences between competing alleles or to random environmental perturbation. Furthermore, we demonstrate analytically that protected polymorphism arises as spatially heterogeneous cyclic fitness oscillations generate a type of storage effect that leads to negative frequency dependent selection. Our findings imply that spatially variable cyclic environments can promote elevated levels of nonneutral genetic variation in natural populations.

Phenotypic plasticity promotes balanced polymorphism in periodic environments by a genomic storage effect

“…Note that such stable polymorphic equilibrium, where selection pushes allele frequencies toward intermediate values, implies a form of negative frequency dependence. This is analogous to the results of Gulisija and Kim (2015), which demonstrated negative frequency dependence in the context of a spatially heterogeneous cyclic selection. The range of parameter values for which stable equilibria are observed in deterministic analyses is somewhat larger than the range of balanced polymorphism observed in finite populations.…”

“…Likewise, at the modifier locus these control simulations quantify cumulative diversity that arises from a direct selective benefit of the modifier allele, over the course of its sweep to fixation. In our eventual analysis, we attribute elevated diversity to the genomic storage effect only if cumulative diversity levels at both loci exceed those observed in these control simulations and also exceed the neutral expectation.Control simulation 1: Target locus in the absence of phenotypic plasticity: In the absence of the modifier allele, cyclic selection results in diversity levels at the target locus, H T , that are similar to or less thanĤ neutral (Figure 2, bottom left), a pattern described in detail in Gulisija and Kim (2015).Control simulation 2: Plasticity modifier locus in the absence of diversity at the target locus: Cumulative diversity levels at the plasticity modifier locus in the absence of polymorphism at the target locus,Ĥ M,control , typically exceed H neutral and they range up to 2Ĥ neutral (Figure 2, bottom right). This elevation in H is due to the selective advantage of the modifier allele (see Population genetic model), which increases its fixation probability.…”

“…However, the underlying mechanisms maintaining genetic polymorphism in these cases are unclear. Theoretical possibilities that predict balanced polymorphism in varying environments include heterozygous advantage [geometric mean overdominance, which cannot occur in haploids (Dempster 1955;Haldane and Jayakar 1963;Gillespie 1973Gillespie , 1974], overlapping generations with age-/stage-specific selection or seed banks (Ellner and Hairston 1994;Turelli et al 2001;Svardal et al 2011), density regulation with resource competition (Dean 2005;Yi and Dean 2013), or these mechanisms in combination with spatial heterogeneity in selection (Gillespie 1974(Gillespie , 1975Ewing 1979;Gulisija and Kim 2015;Svardal et al 2015). Despite these developments, balancing selection due to temporally varying selection has not been widely accepted in population genetic literature probably because early models were criticized due to their failure to maintain polymorphism under genetic drift (Hedrick 1976).…”

“…Theoretical possibilities that predict balanced polymorphism in varying environments include heterozygous advantage [geometric mean overdominance, which cannot occur in haploids (Dempster 1955;Haldane and Jayakar 1963;Gillespie 1973Gillespie , 1974], overlapping generations with age-/stage-specific selection or seed banks (Ellner and Hairston 1994;Turelli et al 2001;Svardal et al 2011), density regulation with resource competition (Dean 2005;Yi and Dean 2013), or these mechanisms in combination with spatial heterogeneity in selection (Gillespie 1974(Gillespie , 1975Ewing 1979;Gulisija and Kim 2015;Svardal et al 2015). Despite these developments, balancing selection due to temporally varying selection has not been widely accepted in population genetic literature probably because early models were criticized due to their failure to maintain polymorphism under genetic drift (Hedrick 1976).The storage effect, initially recognized in studies of species coexistence in community ecology (Chesson and Warner 1981;Chesson 1985Chesson , 2000, presents a key mechanism underlying balanced genetic polymorphism in populations with overlapping generations and stage-specific selection or in combination with spatial heterogeneity (Ellner and Hairston 1994;Turelli et al 2001;Gulisija and Kim 2015;Svardal et al 2015). The basic idea is that a fraction of the population, in a specific life stage or a patch of habitat where adverse effects of selection are diminished, can "store" polymorphism until conditions change.…”

“…Although the storage effect was originally studied in a deterministic framework, Svardal et al (2011Svardal et al ( , 2015 demonstrated a storage effect in finite populations experiencing overlapping generations and fluctuating selection, while Gulisija and Kim (2015) demonstrated balanced polymorphisms in finite populations under periodic selection and discrete generations, where a portion of a population is exposed to a decreased magnitude of environmental oscillation. Moreover, Gulisija and Kim (2015) showed that the effect arises even in the presence of geometric mean selective advantage/disadvantage between the competing alleles. While it is clear that heterogeneous varying selection can lead to the storage effect under various fitness scenarios, past studies have focused on the storage effect arising from age/ stage or spatial heterogeneity in varying selection pressures.…”