Seasonally Fluctuating Selection Can Maintain Polymorphism at Many Loci

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 empirical data and to quantify its contribution to maintaining genetic Significance variation in natural populations.

temporal heterogeneity | cyclical selection | genetic diversity | marginal A key question in evolutionary biology is: What maintains overdominance | balancing selection the abundant genetic variation observed in natural populations? 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 balancing 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 | PNAS | Published online October 30, 2017 www.pnas.org/cgi/doi/10.1073/pnas.1702994114 Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 itane al. et Wittmann balance mutation-selection-drift that and pre- (37) than variation assumed genetic viously maintaining selec- to balancing more that contributes suggest tion to appear recent data generally, genomic More population polymorphisms. with balanced ancient shared be also may are SNPs species the sister of of Many populations genome. 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geo- multiplicative single-locus highest the from the in Thus, ations as loci. have other fitness, heterozygotes at mean if those metric of stable independent is are locus polymorphism focal a at dynam- infinite ics allele-frequency an the recombination, in free selection on with multiplicative population selection Under fluctuating trait. additive temporally fully (ii) a multiplicative and (i) loci well-understood: are across cases selection two only far, so and, nsmay utpiaiesaoa eeto sapower- a is selection seasonal multiplicative summary, In fluctuat- seasonally is scenario studied previously second The nontrivial, is case multilocus the to results these Extending niaigta oeo them of some that indicating simulans, Drosophila .melanogaster D. tsvrltm ons egade al. et Bergland points, time several at n oeee ihthe with even some and tesi umrdpnso h umrscore summer the on that depends assume summer and in scenario fitness domi- simple for this allow generalize To we copies. effects, nance allele favored currently of number the function a as computed n be can genotype of multilocus a of fitness n tesi itrdpnso h itrscore winter the on depends winter in fitness and (see winter and summer the with for and homozygous let respectively, loci genotype, allele, of multilocus number winter- given the one a be and For summer-favored one allele. each: favored alleles two with loci symmetric by with fully cycle a yearly with a start having we model later, model explored be various will in season- parameters asymmetry a While in environment. population fluctuating mating ally randomly diploid, a consider We Model Basic discern. to values, hard detectable, and parameter many readily subtle and the or to large on be robust can Depending to fluctuations is individuals offspring. allele-frequency genome, single many require the too not have across does and loci at perturbations, of polymorphism model maintain number can large lift,” is a “segregation mechanism, time call This 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the are three example, the locus locus—for of focal that fitnesses a relative the at by dynamics driven discrete allele-frequency With epistasis. the for generations, accounts and selection of strength the function fitness increasing tonically and mer advantage. heterozygote values allow of not do values and consider only mech- stabilizing we other anisms, of absence can the selection in fluctuating polymorphism temporally to maintain whether respect in interested with scores are seasonal not we the winter, to respect and with summer but fitness, in allele favored rently parameters The s ntebscmdl oiaeitrhnebei hi effects their in interchangeable are loci model, basic the In polymor- multilocus for conditions the above, explained As h eainhpbtentesaoa score seasonal the between relationship The n g 0.5 + s eeain fsme.Tegnm osssof consists genome The summer. of generations n tcatcSimulations Stochastic , s n w + · z and n n = w het + n z w nsme and summer in w het n d = het nwne) n fitness, and winter), in s ntesmls ae tesdpnsol on only depends fitness case, simplest the In . i Y and =1 = L PNAS z w z L. w s ,wihwudcrepn ostandard to correspond would which >1, := d n i := w het ⇔ | n o oegnrlmdl,adthe and model), general more a for uniytedmnneo h cur- the of dominance the quantify n ulse nieOtbr3,2017 30, October online Published w ln(w s h ubro eeoyosloci, heterozygous of number the n + + w g d d eeain fwne followed winter of generations 0.5 + = ) w s w d · · s (z n n X i and het =1 het L hsfnto specifies function This ). z · w hsi h aewhen case the is This . n . ln(w het sgvnb mono- a by given is , d w z nwne,ie,half i.e., winter, in s ewe n 1, and 0 between i z ), and (z = z L w n z s Because . s unlinked and nsum- in | E9933 [1] [3] [2] n w

EVOLUTION PNAS PLUS where wi is the fitness value at locus i. In our model, this is achieved by setting w(z) = exp(z) because then Eq. 3 is fulfilled with wi = exp(1) if locus i is homozygous for the currently favored allele, wi = exp(ds ) or wi = exp(dw ) if it is heterozygous, and wi = exp(0) = 1 if it is homozygous for the currently disfavored allele. With v(z) := ln(w(z)), the multiplicative model is characterized by v 00(z) = 0. We therefore use the second derivative of the logarithm of fitness v 00(z) as a measure of epistasis (see ref. 39 for a similar definition of epistasis). Under positive or synergistic epistasis (v 00(z) > 0), the logarithm of fitness increases faster than linearly with z, and thus selection at a focal locus increases in strength with increasing contribution of the other loci to z. By contrast, under negative or diminishing- returns epistasis (v 00(z) < 0), selection at a focal locus becomes weaker with increasing contribution of other loci to z. We focus on two classes of fitness functions (Fig. 1). The first is of the form w(z) = (1 + z)y [4] Fig. 2. Values of the seasonal score, z, as a function of the dominance parameter, d, for two example four-locus genotypes: a heterozygous inter- with a positive parameter y. Although for y > 1 in Eq. 4, fit- mediate (blue line) and a homozygous intermediate (black solid line). ness increases faster than linearly with increasing z (Fig. 1A), transformation to the logarithmic scale v(z) = y · ln(1 + z) reveals that epistasis is negative for all y (Fig. 1B). Epistasis (v 00) becomes more negative with increasing y, but v 0 and thus the d, which means that dominance switches between seasons (see selective advantage of having an additional favored allele still Stochastic Simulations for a more general model). For d < 0.5, increases with y for all z. Thus, larger y values correspond to we have “deleterious reversal of dominance” (41), and the cur- overall stronger per-locus selection. rently favored allele is always recessive, whereas for d > 0.5, The second class of fitness functions is of the form we have “beneficial reversal of dominance” (41), and the currently favored allele is always dominant. If d = 0.5, the seasonal q w(z) = exp(z ) [5] score z is additive, not just between loci, but also within loci. Importantly, the value of d also determines the relative fitness of with q ≥ 1. This function reduces to the multiplicative model heterozygous intermediates, multilocus genotypes with the same with q = 1 (cyan lines in Fig. 1) and has positive epistasis with number of summer and winter alleles and at least some heterozy- q > 1 (e.g., magenta lines in Fig. 1). gous loci, compared with homozygous intermediates, which also In summary, fitness is computed in two steps. The first maps have the same number of summer and winter alleles, but are fully the multilocus genotype onto a seasonal score z to which loci homozygous (Fig. 2). For d < 0.5, heterozygous intermediates contribute additively, essentially a generalized counter of the have a lower seasonal score, z, and therefore a lower fitness in number of favored alleles (Eqs. 1 and 2), and the second maps z both seasons than homozygous intermediates. For d = 0.5, het- to fitness (Fig. 1). This two-step process disentangles dominance erozygous and homozygous intermediates have the same score (step 1) from selection strength and epistasis (step 2). and fitness. Finally, for d > 0.5, heterozygous intermediates In our model, genotypes with many summer alleles have a have a higher score and fitness. Interestingly, because d mea- high summer score but a low winter score and vice versa, a form sures dominance not at the scale of fitness but at the scale of of antagonistic pleiotropy. Previous theoretical studies suggest the seasonal score, z, beneficial reversal of dominance for fit- that antagonistic pleiotropy is most likely to maintain polymor- ness is neither sufficient nor necessary for d > 0.5 (SI Appendix, phism if for each trait affected by a locus the respective bene- Fig. S1). ficial allele is dominant (40, 41). Such “reversal of dominance” Multiple mechanisms could underlie a seasonal reversal of also facilitates the maintenance of polymorphism in single-locus dominance. For example, metabolic control theory suggests that models for temporally fluctuating selection (42). Hypothesizing deleterious mutations affecting multistep metabolic pathways that reversal of dominance would also help to maintain poly- are generally recessive (43). If selection is fluctuating such that morphism under multilocus temporally fluctuating selection, we each allele is favored during one season and deleterious in assume that ds and dw in Eq. 1 and 2 take the same value, the other season, we might thus expect a beneficial reversal of dominance. Alternatively, changes in dominance could be medi- ated by seasonal changes in gene expression. But even without A B changes in the genotype–phenotype map, seasonal changes in

6 dominance are possible. In the example scenario in Fig. 3, the [4] y = 4 10 additive seasonal score, z, is a composite phenotype, a weighted [4] y = 2 average of two (also additive) traits—for example, starvation )

z [5] q = 1 ( tolerance and fecundity—and there is antagonistic pleiotropy. w [5] q = 1.5 3 Although the allelic effects on the two traits remain constant 10 throughout the year, d > 0.5 because the relative importance Fitness, Fitness, [4] y = 1 of the traits changes between seasons. This scenario requires changes (though not necessarily a reversal; SI Appendix, Fig. [4] y = 0.5

1 S2A) in dominance with respect to the pleiotropic effects of a 0 5 10 15 20 0246810 0246810locus on the two traits. For example, the winter allele (blue) in Fig. 3 produces higher starvation tolerance and is dominant Seasonal score, z for this trait, whereas it leads to smaller fecundity and is reces- Fig. 1. Examples for fitness functions generated by Eq. 4 or Eq. 5 with sive there. One specific way in which such changes in dominance various parameters. In A, fitness is shown on a linear scale, and in B, on a across pleiotropic effects can arise is via branched enzyme path- logarithmic scale. ways with saturation or feedbacks (44).

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(Fig. of mean if arithmetic the to that equal us the tells of 4) v mean (Fig. arithmetic considerations the ric geometric on its fitness, of on equivalently, logarithm depends or, genotype fitness, a mean of success long-term mean the The and genotypes, possible all for itane al. et Wittmann that loci loci, an For of more 2). number or Fig. even intermediates; one (heterozygous thus condition at this and heterozygous fulfill alleles genotypes winter some and num- always same summer the win- with of the those are for ber fitness all ( mean or geometric epistasis highest allele negative the summer With the for allele. fixed state ter a geo- are in highest loci up the all ends population where have the alleles Therefore, winter fitness. mean only metric or summer (v only either epistasis positive With emerges. score seasonal the (d to loci within contributions restric- when are polymorphism tive maintain can selection fluctuating ally in simulations stochastic section. with next extended the and for checked be here polymorphisms then developed will intuitions stable The for maps. genotype-to-fitness conditions various the intuitive an of develop will to understanding muta- us dynamics the allows that of framework allele-frequency one deterministic assume at the simple arises also mutation that that new We a large enough before role. equilibrate so rare a is play are size not tions population does that drift assume genetic we section, this In Analysis Deterministic the of level the at dominance of reversal beneficial both a to score, is respect seasonal there with 2, homozygote and If fitter 1 traits. the traits homozygote to two closer the are of heterozygotes sea- average between the the switching indicates seasonal traits line two dashed the the The 1 of sons. traits and importance of relative averages traits, the weighted with as two 2, computed and are for summer and pleiotropy winter for antagonistic scores is There inance. 3. Fig. (z v 00 h neana leefeunydnmc eg,fo summer from (e.g., dynamics allele-frequency interannual The ewl rtcnr httecniin ne hc season- which under conditions the that confirm first will We s 00 0 = ) 0 = and oeta ehnsi nepnigfrbnfiilrvra fdom- of reversal beneficial for underpinning mechanistic Potential and ) v ,adlre hno qa to equal or than larger and 4B), (Fig. (z v (z ∗ z = ) See . d w if ) d 0 = s o ie eoyewl esalrta or than smaller be will genotype given a for v i.S2 Fig. Appendix, SI = 00 .5 v d o ealdpof,adalpolymorphism all and proof), detailed a for z < (z w r hsnurl oblnigselection balancing No neutral. thus are s = 0 = esnsieult rsml geomet- simple or inequality Jensen’s ). 0 z ,eulto equal 4A), (Fig. everywhere w .5 sas refrgntpshomozy- genotypes for true also is nEqs. in o lentv scenarios. alternative for 00 v 1 00 > and < z ,tegntpswith genotypes the 0), ,eteetpswith types extreme 0), vrtm is time over .Then, 2). z s = v z (z z w r additive are ∗ hr are There . z ) L s z if + oi This loci. ∗ v z = w 00 v L/2. (z = > SI ∗ L 0 ) utn eeto a ananplmrhs ne additivity under polymorphism fluc- maintain seasonally (d which can in way selection only the tuating be to appears below, detail ocueta oyopimi osbeif possible Eq. is below polymorphism text that conclude see respectively, homozygotes, vored eoe ml,adw a prxmt h eodtr on term second Eq. the of obtain approximate to side can left-hand we the and loci, of small, the that number becomes first the note as this, see Thus, To increases. Eq. loci in of condition number the as 1 For respectively. loci, 100 and For need thus In scores loci. all have at tion allele winter score the has 0 with type one resident the the summer cases, and the both loci with all above, one at the seen fitness, allele have maximum with we genotypes As gous (v mutants. epistasis homozygous by synergistic is fully invaded with possible polymorphism be fittest for the can condition for genotype fixed necessary epis- population a of a case, presence that each the in In polymorphism tasis. maintain also can dominant. is nance allele favored to currently respect the with time dominance any of at reversal that a such be must there is, That (exp(d loci loci. individual other for at erozygotes, values dynamics fitness the the by given affected polymor- not Thus, are for locus conditions one the at epistasis, multiplica- phism without Under i.e., polymorphism. selection, multilocus tive facilitate can 0.5) xrm ye aetehgetaeaelgfins n hstehighest the thus scale, and logarithmic log-fitness a average (C on fitness highest convex mean the geometric is function have average fitness types same the the extreme have if types and all log-fitness then (B); log-linear, average log-fitness is function highest fitness the the if have (A); types intermediate scale, logarithmic around symmetry mirror summer the genotype’s a of function a as score, (gray) fitness of logarithm average the 4. Fig. epista- positive with functions Eq. fitness sis, of class example our Using v z satisfies sible, of value critical The nteohrsao,weesmtnsdfeigi n posi- one in differing mutants whereas season, other the in et eepoewehrdvain rmadtvt (d additivity from deviations whether explore we Next, Logarithm of fitness, ( ) domi- of reversal beneficial a such whether explore we Now, 0 = q A 0 z s 2, = .5). Assuming . h oaih fsme tes(e)adwne tes(le and (blue) fitness winter and (red) fitness summer of logarithm The 5 with d L exp(1) exp(d crit Average Winter Summer /2 v q (d > d 9 ae aus077 .5,ad095 ih1 10, 1, with 0.995, and 0.954, 0.707, values takes d + ) L crit L sawy ufildfor fulfilled always is ) etu bantecondition the obtain thus we 1, = d 2 and − d L q PNAS v Summer score, > , ,tewne cr is score winter the 0.5, ). + 1 (L d (L + q crit exp(1) exp(0) + .I h tesfnto scnaeo the on concave is function fitness the If L/2. − B 0 | twiheteetpsbcm inva- become types extreme which at , d 00 9 + 1 − + 1 ulse nieOtbr3,2017 30, October online Published and > yaTyo xaso rud1 around expansion Taylor a by q + 1 ost infinity, to goes L, · o urnl aoe n disfa- and favored currently for d > exp(0) ,teeaetoflyhomozy- fully two are there 0), L d ) d /2 crit d 1 > o uat oivd,we invade, to mutants For . ) z L ngeneral, in q v s − L = > + (L) d ⇔ 1 noesao n score and season one in L L 1 = L − z q d q w . z > 1. = v n thus and = w (0). C 0 0. d L crit 5. − (d z crit approaches s ,w can we 3), L edn to leading , d ) /2 crit o het- for − | 1)/L E9935 ≤ [6] [9] [7] [8] 6 = z 1. L ,

EVOLUTION PNAS PLUS d q d − 1 1 crit + 1 + q · crit + O = 1. [10] Table 1. Overview of model parameters and the ranges explored L L L2 Parameter Explanation Range explored Multiplying both sides by L and letting L go to infinity, we can g Number of generations per season; 1–20 conclude that dcrit is approximately 1 if the number of loci is a year has 2g generations large. Thus, for fitness functions of the type in Eq. 5 with positive N Population size 100–10,000 epistasis, seasonally fluctuating selection can, in principle, main- L Number of loci 1–500 tain polymorphism at many loci, but the respective favored allele µ Mutation probability per allele copy 10−6 − 10−4 would have to be almost completely dominant, requiring large per generation seasonal changes in dominance. d Dominance parameter 0–1 With diminishing-returns epistasis (v 00 < 0), the fittest pos- y Exponent of the fitness function Eq. 4 0.5–4 sible fully homozygous genotype carries the summer allele at half of the loci and the winter allele at the other half of the loci (assuming an even number of loci). Thus, a necessary condition for polymorphism is that this homozygous intermediate type can smaller than the one for synergistic epistasis in Eq. 9. In addition, L/2 be invaded by mutants. The resident type has score in both we run some simulations for the multiplicative model. seasons whereas mutants differing in one position have scores Additional parameters in the stochastic simulations are the L/2 + d L/2 − 1 + d and . Thus, the resulting necessary condition symmetric mutation probability µ per allele copy per gener- for polymorphism is ation and the population size N . We generally keep popu- w(L/2 + d) · w(L/2 − 1 + d) > w(L/2)2. [11] lation size constant, but also run supplementary simulations with seasonal changes in population size. Table 1 gives an Again, this condition is always fulfilled for d = 1. For fitness overview of the model parameters and the ranges explored. functions of the form Eq. 4 with any exponent y, the critical In most simulated scenarios, selection and dominance effects dominance coefficient dcrit at which homozygous intermediates are strong relative to mutation [w 0(z) and d − 0.5 are much become invasible satisfies larger than the mutation rate µ]. Although natural populations L L L 2 are often larger and mutation rates smaller than the values 1 + + d 1 + − 1 + d = 1 + . [12] 2 crit 2 crit 2 used here, many population genetic processes depend only on the product N µ (e.g., ref. 45). Thus, large populations with This quadratic equation has a negative solution, which is not rel- small mutation rates may be well approximated by computa- evant for our model, and a positive solution tionally more manageable smaller populations with larger muta- s ! tion rates. 1 1 In addition to the basic model, we design a “capped” model dcrit = −1 − L + (2 + L) 1 + . [13] 2 (2 + L)2 to assess the relevance of genetic load. In this model, each individual can be drawn at most 10 times as a parent of individu- From Eq. 13, dcrit decreases as L increases and approaches 0.5 als in the next generation, i.e., contribute at most 10 gametes. as L goes to infinity. The intuition here is that the second deriva- Once an individual has reached that number, its fitness is set to tive of the logarithm of fitness v 00(z) = −y(1 + z)−2 decreases 0 so that it cannot be drawn again. To better understand the role with increasing z. Therefore, for large L, epistasis around the of offspring-number capping, we also run supplementary simu- intermediate type with z = L/2 is weak, and the conditions for lations with a cap of three, the smallest possible value that still polymorphism approach those without epistasis. In other words, allows for differences in offspring number between individuals with increasing L, selection against temporal variation around in the population. the intermediate type becomes weaker, and a smaller change in From the simulation output, we estimate an “effective strength dominance is sufficient to overcome it. of balancing selection” (Materials and Methods and SI Appendix, Our results so far suggest that for a broad class of fitness section S2), which tells us whether and how fast a rare allele functions, seasonally fluctuating selection can maintain polymor- increases in frequency over a full yearly cycle. As expected from phism if in both seasons the respective favored allele is suf- the above theoretical arguments, additive contributions within ficiently dominant. We call this mechanism “segregation lift” loci (d = 0.5) are not conducive to multilocus polymorphism because it is based on a positive aspect of two alleles segregat- (Fig. 5). For even numbers of loci, i.e., situations where both ing at the same locus, as opposed to the negative aspect of seg- homozygous and heterozygous intermediates exist (Fig. 2), the regation load. However, the preceding analysis does not tell us effective strength of balancing selection estimated from the sim- whether polymorphism will be maintained at all loci, or just one ulations is negative, indicating that rare alleles tend to become or a few of them. Also, it is still unclear how efficient segrega- even rarer. For small odd numbers of loci, the effective strength tion lift is at maintaining multilocus polymorphism in finite pop- of balancing selection is positive, but only one or two loci at a ulations with genetic drift and recurrent mutations and whether time fluctuate at intermediate frequency (SI Appendix, Fig. S4). genetic load is a problem. To address these questions, we now As the number of loci increases, the effective strength of balanc- turn to stochastic simulations. ing selection eventually becomes negative even for odd numbers, decreases overall in absolute value, and finally approaches zero Stochastic Simulations (effective neutrality) from below (Fig. 5). This behavior is inde- We use Wright–Fisher type individual-based forward simulations pendent of the exponent, y, of the fitness function Eq. 4. Also, as (see SI Appendix, section S2 for details). That is, for every individ- expected, effective balancing selection (Materials and Methods) ual in a generation independently, two individuals are sampled as emerges if the dominance parameter, d, is larger than a certain parents in proportion to their fitnesses. We focus on diminishing- critical value, which decreases with the number of loci and is only returns fitness functions of type Eq. 4 both because diminishing- weakly influenced by mutation rate (Fig. 6). returns epistasis appears to be more common and plausible (e.g., From now on, we will focus on scenarios with large numbers refs. 21–23) and because the above theoretical arguments sug- of loci. For the case of 100 loci, Fig. 7 shows example allele- gest that it is more conducive to multilocus polymorphism than frequency trajectories for three different dominance parameters, synergistic epistasis. Specifically, the critical dominance parame- d. For small d, each locus is almost fixed either for the summer ter, dcrit , for diminishing-returns epistasis in Eq. 13 is generally or winter allele. For large d, all loci fluctuate at intermediate

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(Fig. neutrality selection: under than balancing slowly of strength effective the For for those with tent (see relative neutrality S2 scenario under selection lifetime the average the in to polymorphism We a (42). of aver- the frequency lifetime (46), age low factor retardation of so-called the periods compute therefore through go regularly where for alleles autocorrelation interesting positive particularly with larger is regimes is selection This fluctuating 46). polymorphism (42, a neutrality of under lifetime than average the that guarantee increasing with increase Both effects 8A). exponent destabilizing (Fig. and stronger stabilizing dominant, becomes the more selection becomes allele balancing favored effective currently the As as 8A). i.e., (Fig. 0.5, unstable negative is is polymorphism selection balancing and of strength func- effective fitness the the recessive, of exponent the of tion, independently 0.5, to close is means even indicate and odd lines successive dashed for run and numbers. always means are Simulations indicate errors. lines standard two Solid (d case loci. additive of the ber in Methods) and als rqec.Teciia oiac parameter, dominance critical The frequency. 5. Fig. itane al. et Wittmann iha fsrn-ubrcpo 0 h eut o h capped the for results the 10, of cap offspring-number an With effective an compute we fluctuations, seasonal quantify To not does frequency in increase to alleles rare for tendency A o ealdmtoooy.Terslsfr10lc r consis- are loci 100 for results The methodology). detailed for d y .For 8A). (Fig. > fetv tegho aacn eeto (b selection balancing of strength Effective N y oyopimudrsgeainlf sls more lost is lift segregation under polymorphism 0.5, = Fg 8A). (Fig. 1,000, y ftefins ucinEq. function fitness the of g = d 15, d < d utain r o ssrn,presum- strong, as not are fluctuations , µ .Freape for example, For ). > .. ftecretyfvrdall is allele favored currently the if i.e., 0.5, = 0.5 0.0001. Fg ) tapasta h cap- the that appears It 8). (Fig. = d )a ucino h num- the of function a as 0.5) n nraewt increas- with increase and z ihnagnrto (SI generation a within , 4 Fg 8 (Fig. section Appendix, SI d d e d 0 = and nEq. in nrae beyond increases crit .7 C ih10loci 100 with , IAppendix, SI and and 14 in y .For D). Materi- 0 = .5, ± t fflcutosaldces Fg ) ouainsz hardly size effective and Population selection 9). balancing (Fig. of strength decrease effective predictabil- all influences and fluctuations magnitude the of and ity factor, retardation the tion, with and to model returns robust less seems S17). model Fig. Appendix, multiplicative (SI asymmetry the mean model, arithmetic returns an parameter requires polymorphism dominance stable that gesting for parameter, arises dominance then morphism summer the dominance varied parameter, the dominance and in winter asymmetry the fixed of we effects parameters, the explore ( To size S15). population Fig. in changes seasonal Appendix are (SI there (SI when winter function, other and fitness summer the the between of than differs exponent generations the when more S13); has Fig. Appendix, season one when e.g., , Appendix (SI behaves model model diminishing-returns multiplicative S10 the Fig. capped to num- the similarly offspring that Appendix, by more (SI weakened so are fixation capping, effects to these ber go of alleles Both S12). that Fig. large so sometimes the under are fitness in variance ( larger rea- model is when The multiplicative there even that positive. be is one, to selection appears below fac- balancing son often of retardation is strength the effective model Also, the multiplicative 10. the of for cap tor offspring-number even versions, an model with uncapped larger and multi- otherwise capped the with between but for crit- differences S10), holds Fig. the , Appendix also remains (SI result model 0.5 plicative This However, parameter. S9). dominance Fig. simulations ical Appendix, capped (SI and seen uncapped are quan- substantial between three, differences to set titative for is fitter cap offspring-number times the 4.9 When and times individual 1.2 fit average (see least on was the population than the fitter in individual fittest the etta h nigo tbemliou oyopimfor polymorphism multilocus stable of finding d the that gest iesrnt fblnigslcin(b selection balancing of strength tive 6. Fig. eso oii oecmlx(i.5,ol vnvle o h ubro loci of number the for values even only 5), here. (Fig. included complex are more is loci of bers averages represent if if morphism) polymorphism) (stable positive is > iha nraignme flc ne h diminishing- the under loci of number increasing an With diinlsmltosfrtedmnsigrtrsmdlsug- model diminishing-returns the for simulations Additional d eto S4 section Appendix, SI crit rtclvleo h oiac parameter, dominance the of value Critical ). ≈ 0.5 d < d tl od ne aiu om fasymmetry, of forms various under holds still N crit ± = ybl ersn en cosrpiae,adlines and replicates, across means represent Symbols . w tnaderr.Sneteptenfrodnum- odd for pattern the Since errors. standard two 1,000, PNAS n htfluctuations that and ) S11 Fig. Appendix, SI ..Cmae ihtediminishing- the with Compared >0.5. d y d > | s = 0. ulse nieOtbr3,2017 30, October online Published o uprighuitcanalysis). heuristic supporting a for > 2, h tegho aacn selec- balancing of strength the 5, d g 0.6 e > = nEq. in d 15. ,sug- S16), Fig. Appendix, (SI crit n eaie(ntbepoly- (unstable negative and , 14 in aeil n Methods), and Materials d crit uhta h effec- the that such , d ;and S14); Fig. , s tbepoly- Stable . IAppendix, SI d w | t0.4 at , y E9937 4 = y ,

EVOLUTION PNAS PLUS A B C allele and add the number of heterozygous loci weighted by a dominance parameter. The resulting seasonal score is then mapped to fitness via a monotonically increasing function which accounts for strength of selection and epistasis. The previously studied cases of multiplicative selection and selection on a fully additive phenotype are special cases of our model. We identify a general mechanism, segregation lift, by which seasonally fluctuating selection can maintain polymorphism at tens or hundreds Frequency of winter allele 0.0 0.4 0.8 of unlinked loci. Segregation lift requires that the average dom- Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Fall Spring Spring Spring Spring Spring Spring Spring Spring Spring Spring Spring Spring Spring Spring Spring inance parameter of the currently favored allele—the summer allele in summer and the winter allele in winter—is sufficiently Fig. 7. Three examples of allele-frequency trajectories for N = 1,000, large. Individuals with many heterozygous loci then have higher L = 100, g = 15, y = 4, µ = 10−4, and d = 0.15 (A), d = 0.5(B), and d = 0.65 (C). Only 10 randomly selected loci (shown in different colors) out of 100 loci scores in both seasons than individuals with the same number of are shown for 5 years (150 generations) in the middle of the simulation run summer and winter alleles, but more homozygous loci. Unlike (years 301–305). in previously studied additive models, fully homozygous types thus cannot fix in the population, and multilocus polymorphism is maintained. In some cases, segregation lift may also be inter- selection coefficient, measures which are based on average preted as a type of phenotypic plasticity, where more heterozy- allele-frequency changes (Fig. 9 A and C), but large populations gous genotypes can better adjust to both summer and winter maintain polymorphism for longer (Fig. 9B) and have more pre- environments. dictable allele-frequency fluctuations (Fig. 9D). In small popula- The critical value of the dominance parameter required to tions, polymorphism can even be lost slightly faster than under maintain polymorphism, dcrit , depends mostly on the type of neutrality (Fig. 9B). epistasis and on the number of loci. Without epistasis, i.e., for Finally, we consider a generalized model where parameters multiplicative selection, dcrit is 0.5. With synergistic epistasis, it vary across loci and may be asymmetric between seasons. Inde- is close to one when there are multiple loci. With diminishing- pendently, for each locus l, we draw four parameters: Summer returns epistasis, the type of epistasis that appears most common, ∆ ∆ effect size s,l and winter effect size w,l are drawn from a log- dcrit , is substantially larger than 0.5 with few loci, but quickly normal distribution. For this, we draw a pair of parameters from approaches 0.5 as the number of loci increases. a bivariate normal distribution with mean 0, SD 1, and corre- lation coefficient 0.9, and then apply the exponential function Robustness and Plausibility of Segregation Lift as a Mechanism to each of them. Summer and winter dominance parameters, to Maintain Variation. Segregation lift requires that dominance ds,l and dw,l , are drawn independently from a uniform distribu- changes over time such that the currently favored allele is on PL tion on [0,1]. Seasonal scores are then computed as z = l=1 cl , average at least slightly dominant with respect to the seasonal where the contribution cl of locus l in summer is 0 for winter– winter homozygotes, ds,l ∆s,l for heterozygotes, and ∆s,l for summer–summer homozygotes. Winter contributions are computed analogously. Because all effect sizes ∆ are positive, all loci AB exhibit a trade-off between summer and winter effects. We use y = 4 here because it led to the most stable polymorphism in the basic model. The results indicate that polymorphisms with different parameters can be maintained in the same population, with their allele frequencies fluctuating on various trajectories (Fig. 10A). With a sufficiently high total number of loci, hundreds of stable polymorphisms (positive expected frequency change of a rare allele; see SI Appendix, section S2 for details) can be maintained in populations of biologically plausible size (Fig. 10B). The number of CD loci classified as stable depends only weakly on population size. However, only a small proportion of the polymorphisms classified as stable also exhibit detectable allele-frequency fluctuations, defined as changes in the expected direction by at least 5% in at least half of the seasons (Fig. 10 C and D). The number of detectable polymorphisms is highest at an intermediate total number of loci and increases with population size (Fig. 10D). Detectable polymorphisms tend to have larger summer and winter effect sizes than polymorphisms that are only stable (Fig. 10E). Compared with unstable polymorphisms, stable polymorphisms are more balanced in their summer and winter effect sizes −16 (two-sample t-test on | ln(∆s,l /∆w,l )|, p < 2.2 · 10 ; Fig. 10E; Fig. 8. Influence of the dominance parameter d on effective strength of see also SI Appendix, Fig. S18). Many stable polymorphisms have balancing selection (A; be, Eq. 14, Materials and Methods), retardation fac- asymmetric dominance parameters, but for almost all of them, tor (B), magnitude of fluctuations (C; se, Eq. 15, Materials and Methods), detectable or not, the average dominance parameter across sea- and predictability of fluctuations (D). Symbols indicate averages across repli- sons is >0.5 (Fig. 10F). cates for the uncapped vs. capped model variant (often overlapping), and solid vs. dashed lines in A, C, and D indicate the respective means ± two Discussion standard errors. Lines in B simply connect maximum-likelihood estimates obtained jointly from all replicates. N = 1,000, L = 100, g = 15, µ = 10−4. We study a simple model for seasonally fluctuating selection that See SI Appendix, Fig. S5 for more detailed information on the distribution maps the multilocus genotype to fitness in two steps. First, we and frequency dependence of seasonal allele frequency changes. The verti- count the number of loci homozygous for the currently favored cal gray lines are at d = 0.5. Bal. sel., balancing selection; exp., expected.

E9938 | www.pnas.org/cgi/doi/10.1073/pnas.1702994114 Wittmann et al. Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 inlf srbs lot ikg ewe eetdlc.Sneour relationship Since particular loci. a selected has between function linkage Fig. fitness to diminishing-returns also Appendix, robust (SI is lift robust tion more even in polymor- varies lift S2B of likely segregation maintenance the seasonality by make of phism could loci which strength time, across the and parameters reality, space dominance In and 10). sizes (Fig. effect in variation loci those at is 10F stable seasons across generally parameter dominance is average whose polymorphism sum- winter, between differs and parameter Appendix, mer dominance (SI the model When multiplicative S17). the Fig. under than so in appar- S13–S15), more size asymmetries Figs. ently Appendix , population to (SI or winter and and selection, 6) summer of between (Fig. strength rate generations, of mutation robust number the surprisingly in are changes lift to segregation via fluctuating polymorphism seasonally stable as see genome should the we in those that show, sites ones polymorphisms. we the many as and, then fluctu- be dominance, are under of still reversal lost may appropriate are basis with there polymorphisms per-site of selection, a on majority ating rare if vast even are the However, dominance score. and in particu- seasonal changes in the required are, of scale dominance the relevant in the changes required on common is lar how work out theoretical find and to empirical More be (48). to For appear common environments across con- expression far. gene salinity for dominance so across experimental fitness In studies for (47). ditions dominance empirical of reversal relevant beneficial copepod few the in only dominance. instance, there in been Unfortunately, changes small. mecha- are have such changes potential produce required several the plausibly Moreover, are can there that above, nisms discussed As score. C ( fluctuations of magnitude (A; (B), selection factor retardation balancing Methods), of and strength effective on loci 9. Fig. itane al. et Wittmann quantified. be to small 15, too was polymorphism of loss in of that Note replicates. all from in Lines (in errors standard in two lines and replicates across averages indicate 15, CD AB ntefcldmnsigrtrsseai,tecniin for conditions the scenario, diminishing-returns focal the In µ .Symbols (D). fluctuations of predictability and Methods), and Materials and n e.4) uuewr ed oepoewehrsegrega- whether explore to needs work Future 40). ref. and = 10 nuneo ouainsz n h ubro esnlyselected seasonally of number the and size population of Influence B i.S16 Fig. Appendix, SI −4 ipycnetmxmmlklho siae bandjointly obtained estimates maximum-likelihood connect simply a.sl,blnigslcin x. expected. exp., selection; balancing sel., Bal. . 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(Fig. >0.5 y Materials ; = s e 4, nEq. in g ± = napdmdlaemr usata,btee hn balancing then, even or but cap substantial, number more are offspring model and smaller capped uncapped the much between differences a selection, multiplicative With with vari- fitness. vari- small relatively in small with to ance relatively together function, and, to fitness population diminishing-returns leads the the within origi- loci scores the seasonal unlinked results at in of for ance segregation The number results independent role. large the Apparently, important a match model. an closely uncapped model play segre- nal, capped to of our genetic case appear for the however, not In epistasis, does concern. diminishing-returns load potential with a lift is gation load genetic loci, strength. selection various and for epistasis allowing should of functions work combinations fitness future general selection, more consider of also strength and epistasis between nlydanfo nfr itiuino h ntsur.Parameters: square. unit the on distribution uniform y a from drawn probability inally sampling also (F the (see isocline. of ters outermost 75% the with inside of distribution, mass shape sampling the runs indicate original simulation isoclines the ten Oval parameters. over drawn results independently pooled with shows plot The polymorphisms. ble (E detectable. (C also are sizes. ∆ that population polymorphisms total for different the only of for but function a loci as of polymorphisms stable simulation number ( of one number in seasons. Average polymorphisms (B) and stable run. loci for trajectories across allele-frequency vary of parameters when fluctuations 10. Fig. EF CD AB = l ,w hnvrteei aacn eeto talrenme of number large a at selection balancing is there Whenever 4, s umrefc size, effect summer vs. , g = tblt fplmrhs n eetblt fallele-frequency of detectability and polymorphism of Stability 10, .Tedmnneprmtr eeorig- were parameters dominance The S19). Fig. Appendix, SI µ = 10 −4 PNAS n in and ∆ | l A, , s ulse nieOtbr3,2017 30, October online Published o tbeaddtcal n nysta- only and detectable and stable for , C, and E, orsodn oiac parame- dominance Corresponding ) N F = 10,000, and itrefc size, effect Winter ) sin As D) L = Snapshot A) 100. A | and E9939 B,

EVOLUTION PNAS PLUS selection emerges for d > 0.5. Thus, unrealistically large off- ness measurements of different single-locus genotypes in a com- spring numbers are not required for stable multilocus polymor- mon genetic background. In an ideal situation, with fitness mea- phism via segregation lift. surements for many different multilocus genotypes at different times, we could use statistical methods such as machine learn- Magnitude and Detectability of Allele-Frequency Fluctuations. In ing to jointly estimate parameters of the fitness function, effect addition to stable polymorphism, segregation lift can also pro- sizes, and dominance parameters and thereby assess whether or duce strong and predictable seasonal fluctuations in allele not there is segregation lift. Such statistical approaches could frequencies. The magnitude of these fluctuations, however, also take into account the existence of several multiplicative decreases with the number of loci under selection. Thus, the fitness components, each with a set of contributing loci that number of detectable polymorphisms may be maximized at an might exhibit segregation lift and epistatic interactions. In prac- intermediate number of loci (Fig. 10). In SI Appendix, section S3, tice, however, measuring fitness is challenging in itself. One pro- we use a heuristic mathematical argument to explore the rela- ductive direction could be to stock a large number of outdoor tionship between number of loci and magnitude of fluctuations mesocosms, each with a different multilocus genotype, and track in a population of infinite size. As the number of loci goes to fitness over multiple seasons. However, apart from the logistic infinity, the effective strength of selection at each locus is pre- challenges, we do not know a priori which loci to focus on. Com- dicted to go to zero, i.e., effective neutrality. This is because ing up with a meaningful and feasible way to empirically get at more loci lead to higher overall seasonal scores, z, which under the scale of the seasonal score z and estimate the relevant domi- diminishing-returns epistasis leads to weaker average selection nance parameters is thus an important research direction arising pressures at each locus. Thus, even if segregation lift contributes from this study. An alternative approach is to make predictions substantially to maintaining polymorphism at a large number of for the genetic footprint of selection in linked neutral regions, loci, it is not necessarily easy to detect individual selected loci e.g., look at diversity levels, site-frequency spectra, and patterns based on their allele-frequency fluctuations. Future research will of linkage disequilibrium, and use these empirically more acces- need to explore new ways of detecting such subtle seasonal allele- sible patterns to distinguish between multiple possible models. frequency fluctuations at many loci, perhaps based on their col- lective behavior rather than on patterns at individual sites. Conclusions We identify segregation lift as a general mechanism by which sea- Empirical Evidence, Alternative Hypotheses, and Potential Tests sonally fluctuating selection can maintain polymorphism at hun- for Segregation Lift. As mentioned above, a recent pooled- dreds of unlinked loci in populations of biologically reasonable sequencing study by Bergland et al. (36) detected strong seasonal size. Segregation lift circumvents the problems associated with allele-frequency fluctuations at hundreds of sites in a temperate maintenance of polymorphism under stabilizing selection and population of D. melanogaster. At many sites, allele frequencies does not require highly heterozygous individuals to have unre- fluctuated by ∼10% over a single season of ∼10 generations, alistically many offspring. Given the ubiquity of environmental and many of the polymorphisms appear to be long-term stable. fluctuations, segregation lift could make a substantial contribu- Based on our results, segregation lift could potentially explain tion to genetic variation in natural populations of many taxa. An these observations, but caution is warranted for several reasons. important question for future work is how we can use modern First, with hundreds of seasonal SNPs and only few chromo- molecular biology and sequencing technologies to test for seg- somes, there will necessarily be substantial linkage between some regation lift and thus make progress on solving the puzzle of of the sites. Second, the distribution and dynamics of dominance genetic variation. effects at the seasonally selected loci are still unknown. Finally, it is not completely clear whether the observed magnitude of allele- Materials and Methods frequency fluctuations can be explained by our segregation lift For the basic model and the capped model, we assess stability of polymor- model, where fluctuations are often more subtle (Fig. 10 C and phism by estimating an effective strength of balancing selection, be, from D, but see Fig. 7C). Based on our current knowledge, we there- the year-to-year allele-frequency dynamics. For this, we fit a standard bal- fore cannot claim that the empirical observations by Bergland et ancing selection model (55) of the form al. (36) are explained by segregation lift. Future work will need to empirically test this model and possible alternatives. ∆y x = bex(1 − x)(1 − 2x) [14] One alternative is that genetic variation is not really sta- to average changes in allele frequency over one yearly cycle, ∆ x (see SI bly maintained, but simply induced by recurrent mutation, with y Appendix, section S2 for details). Positive values of be indicate that rare selection responsible only for the seasonal fluctuations (31, 49), alleles tend to become more common in the long run, whereas negative or by recurrent immigration from other subpopulations where values indicate that rare alleles tend to become even more rare. Second, we either winter- or summer-favored alleles dominate. However, quantify the magnitude of fluctuations over individual seasons. For this, we in the case of the Drosophila observations, this was considered fit a standard directional selection model (55) unlikely (36). Alternative mechanisms that could lead to both ∆ = − fluctuations and long-term stability are (i) differential responses sx sex(1 x), [15]

to fluctuating resource concentrations and population densities with an effective selection coefficient se, to average allele-frequency (17, 50–52) and (ii) a so-called “temporal storage effect” where changes over one season, ∆sx (SI Appendix, section S2). genetic variation can be buffered by a long-lasting life-history To obtain a measure for statistical uncertainty in our results, we run 10 stage on which selection does not act, or by some other pro- replicates for every parameter combination and calculate effective strength tected state (51, 53, 54). However, these mechanisms are more of balancing selection, be, and effective selection coefficient, se, indepen- commonly studied in ecology as mechanisms for species coexis- dently for each replicate. We do the same for the predictability of fluctu- tence, and it is unclear whether they can maintain polymorphism ations, i.e., the proportion of seasons in which a locus changes its allele frequency in the expected direction. In all three cases, we report the mean at multiple loci in diploids. over replicates ± two standard errors of the mean. To obtain retardation In future empirical tests for segregation lift, a main challenge factors, we run 100 replicates until polymorphism is lost at one of the loci will be that the pivotal dominance parameter, d, is not rela- or a maximum time of 500 years is reached. From the times of loss for the tive to fitness but relative to the seasonal score, z, which medi- replicates, we obtain maximum-likelihood estimators for the rate of loss of ates between multilocus genotype and fitness, and is itself not polymorphism (see SI Appendix, section S2 for details). directly measurable. Since the shape of the fitness function, w, C++ simulation code and supporting R scripts are available at https://doi. is also generally unknown, it is not possible to infer d from fit- org/10.6084/m9.figshare.5142262.

E9940 | www.pnas.org/cgi/doi/10.1073/pnas.1702994114 Wittmann et al. Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 8 gaa F htokM 21)Mtto od h teso niiul npopula- in individuals of fitness The load: Mutation (2012) MC genetic Whitlock AF, the Agrawal and selection 28. natural that size, polymorphisms Population (1968) balanced MH of Williamson number JRG, Turner The (1967) 27. WF Bodmer TE, Reed JA, Sved 26. dynamics temporal The time: about It’s (2009) SM Carlson JD, heterogeneous DiBattista in AM, Siepielski polymorphism Genetic 11. (1976) EP Ewing ME, Ginevan PW, Hedrick 10. 5 ika D(97 eeoi samjrcueo eeoyoiyi nature. in heterozygosity of cause major a selection. as natural Heterosis of (1967) cost the RD and Milkman fitness adapta- On 25. makes (1967) epistasis epista- W Global Feller Negative (2014) MM 24. (2011) Desai ER, TF Jerison DP, Cooper Rice S, RE, Kryazhimskiy Lenski 23. D, Schneider DM, Dinh AI, Khan 22. Segr NF, Delaney HC, Chiu HH, Chou 21. environments. random in Polymorphism (1973) JH Gillespie heterogeneity.20. genetic of maintain Maintenance selection (1955) ER frequency-independent Dempster does When 19. (2017) NH Barton R, Novak 18. direction. varying of selection to due Polymorphism (1963) SD Jayakar JBS, variation Haldane Seasonal (2015) PS 16. Schmidt MS, Heschel KR, O’Brien SS, Watson EL, Behrman 15. of maintenance the and heterogeneity Environmental forests– (2006) DR tropical Conde of PS, Schmidt phenology The 14. (1993) SJ Wright JW, Terborgh CP, pop- Schaik natural in van selection of 13. consequences genetic The (2016) RD Barrett TJ, Thurman 12. 7 enA,Lha ,Y 21)Futaigslcini h Moran. the in selection Fluctuating (2017) X Yi C, Lehman AM, Dean 17. itane al. et Wittmann eso ...slbrtr,a ela w nnmu eiwr.Simulations reviewers. anonymous two Kolodny, as Oren well as Polechov laboratory, Hermisson, D.A.P.’s Jitka of Pennings, Joachim bers Pleuni Nichols, Desai, Richard Michael McLaren, Mike thank we manuscript, ACKNOWLEDGMENTS. .HdikP 21)Wa steeiec o eeoyoeavnaeselection? advantage heterozygote for evidence M, Croze the is 9. What (2012) PW Hedrick 8. .AtaaS cmd ,SnavS(05 iie oefrblnigselection. balancing for role limited A (2005) S Sunyaev S, Schmidt S, Asthana selection: 7. balancing by maintained variation Polygenic (2004) NH Barton M, Turelli 6. .Bro ,KihlyP(02 nesadn uniaiegntcvariation. genetic quantitative Understanding (2002) P Keightley controversy. 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