Seasonally fluctuating selection can maintain polymorphism at many loci via segregation lift Meike J. Wittmanna,b,c,1, Alan O. Berglanda,d, Marcus W. Feldmana, Paul S. Schmidte, and Dmitri A. Petrova,1 aDepartment of Biology, Stanford University, Stanford, CA 94305; bFakultat¨ fur¨ Mathematik, Universitat¨ Wien, 1090 Wien, Austria; cFakultat¨ fur¨ Biologie, Universitat¨ Bielefeld, 33615 Bielefeld, Germany; dDepartment of Biology, University of Virginia, Charlottesville, VA 22904; and eDepartment of Biology, University of Pennsylvania, Philadelphia, PA 19104-6313 Edited by M. T. Clegg, University of California, Irvine, CA, and approved October 3, 2017 (received for review March 8, 2017) Most natural populations are affected by seasonal changes in (11) and genotypes (12). In fact, most organisms with multiple temperature, rainfall, or resource availability. Seasonally fluctuat- generations per year experience a particular type of temporal ing selection could potentially make a large contribution to main- heterogeneity: seasonality, for example, in temperature, rainfall, taining genetic polymorphism in populations. However, previous resource availability, or in the abundance of predators, com- theory suggests that the conditions for multilocus polymorphism petitors, or parasites. Even tropical populations usually experi- are restrictive. Here, we explore a more general class of mod- ence some seasonality. For example, flowering and fruiting in els with multilocus seasonally fluctuating selection in diploids. tropical forests is often synchronized within and between tree In these models, the multilocus genotype is mapped to fitness in species, leading to seasonal changes in food availability for ani- two steps. The first mapping is additive across loci and accounts mals (13). Often, there are life-history trade-offs across sea- for the relative contributions of heterozygous and homozygous sons (14, 15). For example, seasons with abundant resource loci—that is, dominance. The second step uses a nonlinear fit- supply might select for investment in reproduction, whereas ness function to account for the strength of selection and epis- stressful seasons may select for investment in survival. Since such tasis. Using mathematical analysis and individual-based simula- life-history traits are usually polygenic, many organisms should tions, we show that stable polymorphism at many loci is possible experience seasonally fluctuating selection at a large number if currently favored alleles are sufficiently dominant. This general of loci. mechanism, which we call “segregation lift,” requires seasonal With discrete generations, the fates of genotypes under tem- changes in dominance, a phenomenon that may arise naturally porally fluctuating selection depend on their geometric mean fit- in situations with antagonistic pleiotropy and seasonal changes in nesses over time (16). In haploids, two alleles generally cannot the relative importance of traits for fitness. Segregation lift works coexist because one will have a higher geometric mean fitness best under diminishing-returns epistasis, is not affected by prob- and eventually go to fixation (ref. 16, but see refs. 17 and 18). lems of genetic load, and is robust to differences in parameters In diploids, polymorphism at a single locus is stable if heterozy- across loci and seasons. Under segregation lift, loci can exhibit gotes have the highest geometric mean fitness (“marginal over- conspicuous seasonal allele-frequency fluctuations, but often fluc- dominance”), although in any particular generation, one of the tuations may be small and hard to detect. An important direction homozygotes might be fittest (16, 19, 20). for future work is to formally test for segregation lift in empiri- cal data and to quantify its contribution to maintaining genetic Significance variation in natural populations. temporal heterogeneity j cyclical selection j genetic diversity j marginal A key question in evolutionary biology is: What maintains overdominance j balancing selection the abundant genetic variation observed in natural popula- tions? Many organisms experience some seasonality in their ver since biologists were first able to detect population habitats, and, if they have multiple generations per year, sea- Egenetic variation at the molecular level, they have been puz- sonally fluctuating selection is a potentially powerful mecha- zled by its abundance in natural populations (1). Dispute over nism to maintain polymorphism. However, previous research the underlying reasons gave rise to two scientific schools (2, 3). has argued that this occurs rarely. Inspired by recent empiri- Proponents of the “(neo)classical” school claim that the bulk of cal findings, we reevaluate the potential of seasonally fluctu- genetic variation is due to neutral or weakly deleterious muta- ating selection to simultaneously maintain polymorphism at tions present at an equilibrium between mutation, genetic drift, many loci in the genome. We obtain a more general condition and selection. The neoclassical view admits that selection may for the maintenance of multilocus polymorphism by season- maintain alleles at intermediate frequency at some loci, but ally fluctuating selection. This condition may plausibly be sat- argues that such loci are exceedingly rare on a genomic scale isfied for many species and does not suffer from problems of (2). By contrast, the “balance” school posits that a substan- previous models. tial fraction of variation is maintained by some form of bal- ancing selection [with some controversy over the meaning of Author contributions: M.J.W., A.O.B., M.W.F., P.S.S., and D.A.P. designed research; M.J.W. performed analyses and simulations; A.O.B., M.W.F., and D.A.P. gave input on all aspects “substantial” (3)]—for example, heterozygote advantage (over- of the analyses; P.S.S. gave input on the paper; and M.J.W, A.O.B., M.W.F., and D.A.P. dominance), negative frequency-dependent selection, and spa- wrote the paper. tial or temporal variability in selection pressures (4). The authors declare no conflict of interest. Fifty years later, the debate has not been conclusively set- This article is a PNAS Direct Submission. tled (5, 6), although the majority view is that (nearly) neu- Published under the PNAS license. tral mutations cause most genetic variation, with overdomi- Data deposition: Source code underlying the analyses in this manuscript has been nance playing a relatively minor part, perhaps acting at only deposited in the figshare repository (available at https://doi.org/10.6084/m9.figshare. tens of loci per species (7–9). A mechanism considered more 5142262). common and powerful is spatial environmental heterogeneity. 1To whom correspondence may be addressed. Email: [email protected] Temporal heterogeneity, by contrast, is believed to be of lim- or [email protected]. ited importance (10), despite widespread temporal fluctuations This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. in the strength and direction of selection, both on phenotypes 1073/pnas.1702994114/-/DCSupplemental. E9932–E9941 j PNAS j Published online October 30, 2017 www.pnas.org/cgi/doi/10.1073/pnas.1702994114 Downloaded by guest on September 28, 2021 Extending these results to the multilocus case is nontrivial, alone is not sufficient to reconcile evidence from population PNAS PLUS and, so far, only two cases are well-understood: (i) multiplicative genomics and quantitative genetics (38). Thus, we need to recon- selection across loci and (ii) temporally fluctuating selection on sider the potential of temporally fluctuating selection to maintain a fully additive trait. Under multiplicative selection in an infinite multilocus polymorphism. population with free recombination, the allele-frequency dynam- As explained above, the conditions for multilocus polymor- ics at a focal locus are independent of those at other loci. Thus, phism under seasonally fluctuating selection have been examined polymorphism is stable if heterozygotes have the highest geo- mostly in two narrow cases. Here, we examine a more general metric mean fitness, as in the single-locus case. However, devi- class of seasonal selection models with various forms of domi- ations from multiplicative selection appear to be the rule. In nance and epistasis. Using deterministic mathematical analysis particular, beneficial mutations often exhibit diminishing-returns and stochastic simulations, we show that multilocus polymor- epistasis (21–23). Additionally, there is the potential problem of phism is possible if the currently favored allele at any time is genetic load. Genetic load is commonly defined as the differ- sufficiently dominant, with dominance measured by using a scale ence between the population’s average fitness and the fitness of on which contributions across loci are additive. This mechanism, the fittest possible genotype. Lewontin and Hubby (1) noticed which we call “segregation lift,” can maintain polymorphism at that this value can become unsustainably high if there is strong a large number of loci across the genome, is robust to many heterozygote advantage at many loci. This was a conundrum for model perturbations, and does not require single individuals to the neoclassical school, which was worried that with high genetic have too many offspring. Depending on the parameter values, load, single individuals would have to produce an astronomically allele-frequency fluctuations can be large and readily detectable, large number of offspring. Others have dismissed