B R I E F C O M M U N I C AT I O N doi:10.1111/evo.12470
RUNAWAY COEVOLUTION: ADAPTATION TO HERITABLE AND NONHERITABLE ENVIRONMENTS Devin M. Drown1,2 and Michael J. Wade1 1
Department of Biology, Indiana University, Bloomington, Indiana 47405 2
E-mail: [email protected]
Received February 27, 2014 Accepted June 4, 2014 Populations evolve in response to the external environment, whether abiotic (e.g., climate) or biotic (e.g., other conspecifics). We investigated how adaptation to biotic, heritable environments differs from adaptation to abiotic, nonheritable environments. We found that, for the same selection coefficients, the coadaptive process between genes and heritable environments is much faster than genetic adaptation to an abiotic nonheritable environment. The increased rate of adaptation results from the positive association generated by reciprocal selection between the heritable environment and the genes responding to it. These associations result in a runaway process of adaptive coevolution, even when the genes creating the heritable environment and genes responding to the heritable environment are unlinked. Although tightening the degree of linkage accelerates the coadaptive process, the acceleration caused by a comparable amount of inbreeding is greater, because inbreeding has a cumulative effect on reducing functional recombination over generations. Our results suggest that that adaptation to local abiotic environmental variation may result in the rapid diversification of populations and subsequent reproductive isolation not directly but rather via its effects on heritable environments and the genes responding to them. KEY WORDS:
G × E, genotype by environment, indirect genetic effects.
As Fisher (1958, p. 41) emphasized, populations evolve in response to the external environment, whether abiotic (e.g., climate) or biotic (e.g., other conspecifics or other species): . . . the physical environment may be regarded as constantly deteriorating . . . and this will tend, in the majority of species, constantly to lower the average value of m, the Malthusian parameter of the population increase. Probably more important than the changes in climate will be the evolutionary changes in progress in associated organisms.
Fisher saw the increase in fitness of “competitors and enemies” as a major cause of environmental deterioration. When the associated organisms are conspecifics, they constitute a “heritable environment” (Fisher 1958; West-Eberhard 1979). And, such environments coevolve with the organisms adapting to them. As a result, instead of deteriorating, favorable heritable environments can become more common and population mean fitness can increase. C
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The most common heritable environment is epistasis, sometimes referred to as the “internal environment” (e.g., Jasnos et al. 2008), in which the effect of an allele at one locus depends upon alleles at other loci (Hansen 2013). Genes with conspecific indirect genetic effects (IGE), such as maternal effect genes or sib-social genes, are also common instances of heritable environments (Wolf et al. 1998). Here, variation in heritable environment means variation in the genetic composition of conspecific social partners (Wolf 2000; Bijma 2014). The rate of adaptation to any environment, abiotic or social, depends upon the frequency of that environment and the strength of selection within it. In the context of quantitative genetics, the potential for IGE to accelerate evolution through coadaptation of the individual and its social environment has been discussed elsewhere (e.g., Wolf et al. 1998; Wolf 2003; McGlothlin et al. 2010; Bailey and Moore 2012; Fitzpatrick 2014). Here, we directly compare the relative rates of adaptation to heritable and nonheritable environments
C 2014 The Society for the Study of Evolution. 2014 The Author(s). Evolution Evolution 68-10: 3039–3046
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using a population genetic model framework. By quantifying the relative rates of evolution in this way, we can compare the familiar population genetic theory of genotype-by-environment (G × E) interactions with that of the less familiar theory of IGE. We investigate adaptation to variation in the nonheritable abiotic environment and to variation in three kinds of genetic or heritable environments: the internal genetic environment (epistasis), the maternal genetic environment, and the sib-social genetic environment. The initial rate of adaptation is the same across all environments, abiotic as well as biotic, but differences arise as a result of the evolution of the biotic environment. Selection creates positive associations between beneficial heritable environments and the genes adapting to them, making the coadaptive process self-accelerating or a runaway. That is, selection on one gene results in an increase in the frequency of the genetic environment in which that gene is favored. However, when adapting to a poorer or deteriorating environment, a runaway process does not occur because of the internal antagonism of selective effects. This process is similar to Fisher’s runaway sexual selection in that, via nonrandom mating, genes for female mate preference become associated with the genes for the preferred male trait (Fisher 1958). As a gene for the male trait increases owing to its mating advantage in female mate choice, the female preference gene increases along with it (Lande 1981; Kirkpatrick 1982). Much like our process, the success of the male gene increases the frequency of environment (namely, the female mating preference) in which it is favored. In population genetics theory, epistasis and restricted recombination (i.e., the genetic architecture) play important roles in creating and sustaining linkage disequilibrium (LD), both during adaptation (transient LD) and at equilibrium (Crow and Kimura 2009; Charlesworth and Charlesworth 2010; Gillespie 2010). Our model framework allows us to contrast the impact of population genetic structure and the genetic architecture (with the former being more important than the latter) on rates of adaptation. In models of IGE, which include the maternal and sibling effects, population genetic structure is an essential feature of IGE evolution (Bijma and Wade 2008). For this reason, we vary the degree of inbreeding (within-family mating) relative to random mating, which affects realized recombination rates. We examine the effects of population genetic structure caused by an arbitrary fraction of the population mating within families, while the remainder of the population mates at random. Although a great deal of research has been devoted to examining recombination in relation to LD and epistatic selection, we find that the runaway process of adaptive coevolution between heritable environments and the genes responding to them is more sensitive to inbreeding and other deviations from random mating than it is to linkage. First, we review the standard population genetic G × E model of adaption to an external abiotic, nonheritable environment, such
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as temperature, or more broadly, climate. Next, we extend the one gene external-environment model to two unlinked genes, one for the social environment (the IGE) and the other for adaptation to the social environment (direct effect gene; Moore et al. 1997). Lastly, we model the case of two loci, in which one gene adapts to the genotypic background created by the other, that is, we posit an epistatic interaction between the loci. MODEL
We compare the rate at which individuals adapt to four different kinds of environment (Fig. 1), an external, nongenetic environment and three genetic environments (sib-social, maternal, and epistatic). In each case, we model the evolution of a single gene (A gene) with additive effects on fitness only in the selective environment. In alternative or nonselective environments, the gene is neutral. Allelic variation at this gene permits adaptation to the environment. For adaptation to an external environment, we posit two environments and allow the A gene to have fitness effects only in one of them. This is one of the simplest models of G × E for fitness, and it is often invoked as representative of a species expanding its range to a new environment. To model the genetic environments, we imagine a second gene. For the internal genetic environment, we imagine that the A gene has its fitness effects only in some genotypic backgrounds but not others. Similarly, for maternal and sibling environments, we assume that the A gene manifests its fitness effects only when born of some females, or in the company of some genotypic sib-ships, but not others. Adaptation to an abiotic, nonheritable environment We model adaptation to two contrasting environments, E1 and E2 . The proportion of the population in E1 is e1 , with the remaining fraction, e2 = 1 – e1 , found in E2 . E1 can be a better environment than E2 , meaning that mean fitness for all individuals in E1 is higher by an increment, 2β, where β is ࣙ 0, than it is in E2 . We assume a diploid species with discrete nonoverlapping generations, in which individuals differ genetically from one another in their sensitivity, α, to E1 (but not to E2 ) as determined by alternative alleles, A and a, at a single locus. The frequency of the A allele is PA and that of the a allele is Pa = 1− PA . The alleles act additively so that wAA (E1 ), the fitness of an AA genotype in E1 equals (1 + 2β + 2α); wAa (E1 ) is (1 + 2β + 1α); and waa (E1 ) is (1 + 2β). In E2 , all genotypes have fitnesses equal to 1 (Fig. 1A). This is a G × E model, in which the environmental effect on fitness varies in scale but not in sign. Adaptation to a biotic, heritable environment The sib-social case: We model selection in response to a sib-social environment by assuming that an unlinked, second locus, with alternative alleles, B and b, determines sibling genotype. The
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frequency of this indirect-effect allele B in the population is PB and that of the b allele is Pb = 1 – PB . Individuals express alternative alleles, A and a, which affect their sensitivity, α, to BB (but not to bb) siblings. The alleles act additively as above so that wAA (BB), the fitness of an AA genotype interacting with a BB sibling equals (1 + 2β + 2α), wAa (BB) is (1 + 2β + 1α), and waa (BB) is (1 + 2β). When interacting with a bb sibling, all genotypes have fitness equal to 1 (Fig. 1B). Genotypes interacting with Bb heterozygous siblings have a fitness that is intermediate between their fitnesses with BB and bb siblings. The total fitness of an individual across all sibling interactions is given by weighting by the frequency of the B allele (PB,sib ) within families. The withinfamily frequency of the B allele is affected by the number of mates per females, the apportionment of fertility among multiple male mates, and the degree of within-family (f) as opposed to random (1 – f) mating. Note that the parameterization of selection
in the abiotic and biotic models for locus A is identical (compare Fig. 1A and B). The maternal case: We model the response to a maternal environment by assuming that an unlinked, second locus, with alternative alleles, B and b, determines maternal genotype. The frequency of this indirect-effect allele B in the population is PB and that of the b allele is Pb = 1 – PB . Offspring express alternative alleles, A or a, which affect their sensitivity, α, to BB (but not to bb) mothers. The alleles act additively as above so that wAA (BB), the fitness of an AA offspring genotype of a BB mother equals (1 + 2β + 2α), wAa (BB) is (1 + 2β + 1α), and waa (BB) is (1 + 2β). When born of a bb mother, all offspring genotypes have fitness equal to 1 (Fig. 1C). The offspring of Bb heterozygous mothers have an intermediate fitness between their fitness with BB and bb mothers.
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The epistatic case: We model epistasis with a framework similar to that of the maternal effect locus above (Fig. 1D). In this case, individuals carrying alternative alleles, A and a, differ in sensitivity, α, to their genotypic background at the unlinked B locus. Alleles at the A locus act additively so that wAABB , the fitness of an AABB genotypes equals (1 + 2β + 2α), wAaBB is (1 + 2β + 1α), and waaBB is (1 + 2β). All A locus genotypes have the same fitness on the bb genotypic background (Fig. 1D). The fitnesses of A locus genotypes on the Bb backgrounds are intermediate between their fitness on the BB and bb backgrounds.
Analyses ANALYTICAL SOLUTIONS
We first analyze the four models with the standard assumption that selection is weak such that α and β are near 0 and the loci assort independently. We assume in all of our cases that the genes act additively, however, under the assumption of weak selection and ignoring second-order (and higher) terms, a multiplicative model of gene interaction would converge on the additive models presented here. We assume that the genotypes are the products of random mating and are initially in Hardy–Weinberg proportions. For the abiotic, nonheritable environment, change in frequency of the direct effect allele, A, equals PA,abiotic =
(αe1 ) PA (1 − PA ) , [1 + 2e1 (β + αPA )]
(1)
where the denominator is mean fitness. The rate of change, PA,abiotic , depends on e1 , the frequency of the selective environment (E1 ) and α, the effect of the A allele on fitness in that environment. The rate of adaptation is faster when the selective environment is more common. However, the rate of adaptation is also sensitive to the value of β. In adaptation to E1 , β appears in the denominator of equation (1), so that increases in β diminish PA,abiotic . We contrast this case with one in which offspring fitness is affected by a biotic, heritable environment. Here, we assume that females mate multiply, so that all families consist of half-sibs. For any of the three cases with a biotic, heritable environment, the change in the frequency of the direct effect allele, A, equals PA,biotic =
(αPB ) PA (1 − PA ) , [1 + 2PB (β + αPA )]
(2)
where the denominator is mean fitness. Note here, that the frequency of the abiotic environment, e1 , has been replaced by the frequency of the biotic environment, PB . As above, the numerator in the rate of change, PA , depends on PB , the frequency of the selective biotic environment and α, the effect of the A allele in that social environment. The models differ, however, in that the
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frequency of the social environment, PB , changes as PA evolves, whereas e1 , the frequency of the abiotic nonheritable environment, E1 , does not. The change in PB equals PB = ρ
(β + αPA ) PB (1 − PB ) , [1 + 2PB (β + αPA )]
(3)
where ρ defines the relatedness between the source of the selective environment and the individual (sib-social, half-sibs, ρ = ¼; maternal, ρ = ½; epistatic, ρ = 1; Linksvayer and Wade 2009). As PB increases according to equation (3), evolution of the A allele is accelerated (cf. eq. 2). For the heritable genetic cases, as β increases, the rate of adaptation increases. This happens because the B allele enhances fitness directly in addition to its spread via hitchhiking on the increase in frequency of the A allele. In contrast, for the external environment case, recall increases in β diminish PA,abiotic because β appears in the denominator of equation (1). Adaptation to a heritable genotypic environment is different because β plays a dual role. It appears in the denominator of equation (2), as well as in the numerator of equation (3). The accelerating effect of β in equation (3) more than outweighs its retarding effect in equation (2). The results across the three different heritable environments are quite similar. Because the relatedness of the heritable environment is stronger in the maternal environment than the sibsocial, the maternal background evolves twice as fast as the sibsocial case. Differently put, as the maternal genetic environment in which A is favored becomes more common, the strength of selection on A (i.e., αPB ) is increased. This, in turn, increases PB, creating a self-accelerating runaway process. However, if we assumed that females were monogamous, then the sib-social case would evolve at the same rate as the maternal case because the relatedness among siblings would be half. Even more so, the epistatic background evolves twice as fast as the maternal background and four times as fast as the sib-social background. Because the feedback between the A and B loci is stronger in the epistatic case, the runaway coevolution between alleles A and B is much more rapid. Runaway coevolution is not a property typically associated with epistatic genes interactions, especially between unlinked genes. We derive the initial generation of LD assuming the initial frequency of alleles at both loci is independent (LD = 0): L D = ρ
α PA (1 − PA ) PB (1 − PB ) . 2 [1 + 2PB (β + αPA )]2 (4)
From equation (4), we see that LD is generated by selection and the sign of LD is dependent only on the sign of α, the selection coefficient on the direct effect locus, because the denominator is squared. The positive LD value links allele B of the heritable
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environment to allele A, the locus adapting to it. Consequently, the biotic, heritable environment (PB ) that favors allele A becomes more common. In turn, this increases the strength of selection on A, represented by (αPB ). This, in turn, increases PB so the coadaptation between A and B is mutually reinforcing, generating positive feedback or a self-accelerating runaway process. NUMERICAL ITERATIONS
We contrasted the rates of adaptation among the four models by plotting numerical iterations (i.e., no weak selection assumption) of the evolutionary process (Fig. 2) using MATLAB (R2010a, The Mathworks). When the external selective environment is rare (e1 = 0.05), the adaptive response to selection, PA,abiotic , is slow (Fig. 2A, black line). In contrast, when the heritable environments (sib-social, maternal, or epistatic) are initially rare (PB = 0.05), the coadaptive dynamics of alleles, A and B, result in much more rapid evolution, with the fixation of the heritable environment PB (Fig. 2B) followed quickly by fixation of PA (Fig. 2A). The entire process is completed long before fixation of A in response to E1 , the abiotic non-heritable environment (Fig. 2A, black line). The coadaptation happens rapidly because selection generates a positive LD between PA and PB (Fig. 2C). Thus, not only does increasing PB accelerate the evolution of PA but the reciprocal is also true: the increase in PA has the effect of increasing selection on the B allele, whether it is a sib-social, a maternal, or an epistatic background. There is thus a positive feedback between alleles at the two different loci. EFFECTS OF INBREEDING AND LINKAGE
We now explore two factors, inbreeding and reduced recombination, that potentially increase LD, thereby accelerating the evolutionary rate. We modified our numerical iterations by allowing a fraction, f, of within-family matings (brother–sister) to occur. The remaining fraction of matings (1 − f) occurred according to the proportions expected from the population genotype frequencies. To calculate the offspring genotypes, we mate each female to the respective weighted average genotype frequencies (f, family-level genotype frequencies; 1 − f, population-level genotype frequencies). Specifically, we explore the range of possibilities from complete random mating to 50% sib-mating (0 ࣘ f ࣘ 0.5). We use, as an illustrative example, the case in which the genetic environment is determined by the maternal genotype (Fig. 3). As expected, because inbreeding maintains genetic associations, increasing the fraction of family-level matings resulted in faster rates of adaptive coevolution. Recombination, by breaking down genetic associations, should weaken the positive feedback between loci. As genes become physically closer and recombination is less frequent, then a smaller fraction of LD built up by selection will be lost at replication. We investigated recombination rates (r) spanning the range
from tight linkage to free recombination (0.02 ࣘ r ࣘ 0.5). Using numerical iterations, we explored the impact of weak recombination in the maternal effects model (Fig. 3). As expected, as recombination rate decreases, the rates of evolution of both the direct and indirect effects loci increase.
Discussion The frequency of the selective background, abiotic, sib-social, maternal, or epistatic, determines the strength of selection on the direct effect gene. We have shown that genetic adaptation to a heritable environment changes the frequency of that heritable environment, thereby increasing the strength of selection in subsequent generations. In contrast, the frequency of an abiotic, nonheritable environment does not necessarily change as a population adapts to it. As a genetic environment becomes more common, it exerts stronger selection pressure on the responding direct effect gene. This, in turn, leads to a further increase in the frequency of the genetic environment via LD (cf. eqs. 3 and 4). The result is a runaway process of coadaptation akin to the runaway social evolution observed by Breden and Wade (1991) or that observed between the genes for female mate choice and male trait in runaway sexual selection (Lande 1981; Kirkpatrick 1982; cf. Shuster and Wade 2003, which discusses 10 different runaways possible in the context of male–female reproductive interactions). The relative quality of the two environments is determined by β. In our analyses, we assumed that the environment in which the A allele is sensitive, whether nonheritable or heritable, is beneficial or not harmful (i.e., β ࣙ 0). When both α > 0 and β > 0, mean fitness increases when the frequency the A allele increases in the population. In all cases, the heritable environment, beneficial to the adapting organism, increases in frequency via coadaptation. Unlike an environment deteriorating because of an increase in competitors or enemies (Fisher 1958), genetic coadaptation improves the environment. For maternal and sib-social heritable environments, coadaptation accelerates cooperation rather than competition among conspecifics. What happens when there is adaptation to a poorer environment (i.e. β < 0)? In this case, population mean fitness will increase only when αPA > −β. However, for heritable environments, the necessary condition for the coevolution of A and its background, B, is also that αPA > –β. This will not often be the case unless the direct effect of the A allele is unusually large or the A allele appears in the population at a high frequency. Unless these conditions are met, the poorer heritable environment does not spread. Nor do the runaway evolutionary dynamics apply to an allele that decreases fitness in a selective environment (Priest and Wade 2010). If there is an internal antagonism of selective effects such that the A allele decreased fitness in a heritable environment, those environments (i.e., PB ) would become
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Generation Comparison of evolution across the four models: epistatic effects (red lines), maternal effects (green lines), sib-social effects (blue lines), or an abiotic environment (black lines). (A) Plots the frequency of the direct effect allele, PA (solid lines), and the indirect effect allele, PB (dashed lines), or the beneficial environment, e1 (dashed line). The frequency of the E1 environment is fixed at 0.05.
Figure 2.
(B) Plots the LD generated between the direct and indirect effects loci. The direct effect coefficient (α) = 0.1 and the indirect effect coefficient (β) = 0. The initial direct and indirect effect allele frequencies (A, B) = 0.05. There is free recombination between loci (r = 0.5).
rarer as a result of selection against the A allele. That, in turn, weakens future selection on the A allele as its experience of the selective environment declines as the frequency of the selective environment decreases. Selection will be weaker at purging alleles that constitute a deleterious environment (e.g., the B allele when β < 0) leading to higher frequencies of deleterious genes (like the A allele) and deleterious backgrounds (like the B allele) at mutation-selection balance (Phillips and Johnson 1998; Priest and Wade 2010). A second important difference between adaptation to abiotic, nonheritable versus biotic, heritable environments occurs whenever the selective environment itself has a positive effect on fitness (i.e., when β > 0). When one of the abiotic, nonheritable environments is better than the alternative, the rate of adaptive response is reduced. In contrast, when one heritable environment is better than the other, the rate of adaptive response is enhanced; the runaway coadaptive process is accelerated. Hence, adaptive
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evolution to heritable environments should be more rapid than adaptation to external, nongenetic environments. Along these lines, there are opportunities for an interaction between abiotic, nonheritable selective environments and a runaway, coadaptive regulatory process. Consider, for example, competition for scarce resources, a premise central to the logic of Darwinian evolution. Some maternal genotypes might be better than others (i.e., β > 0) in competition for resources for their offspring. At the same time, a population might harbor genes expressed in offspring that are better at eliciting maternal resources. This would lead to a runaway process of coadaptation between the better provisioning mothers and their offspring, allowing more rapid genetic tracking of resource availability (Duckworth 2009). In this way, the adaptive coevolution between the maternal and zygotic genomes allows the regulatory network of early development to adapt rapidly to small changes in the external, abiotic environment.
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Figure 3. Comparison of evolution of a maternal effects model with different amounts of inbreeding (left column) and linkage (right column). Different lines’ colors represent the fraction of family-level mating (f) or rates of recombination (r). (A and B) Plots the frequency
of the direct effect allele, PA (solid lines), and the indirect effect allele, PB (dashed lines). (C and D) Plots the LD generated between the direct and indirect effects loci. The direct effect coefficient (α) = 0.1 and the indirect effect (β) = 0. The initial direct and indirect effect allele frequencies (A, B) = 0.05.
Our analyses identified the generation of positive LD between the two loci as contributing to the runaway process of coevolution. In some two-locus models and as seen here, selection creates positive LD in which initially there was none (Felsenstein 1981). In standard theory, epistatic selection and recombination act as opposing processes, creating and destroying LD, respectively (Charlesworth and Charlesworth 2010, p. 425). Similarly, we expected that linkage (instead of free recombination) would permit greater values of LD. Our numerical results confirmed this expectation (Fig. 3). Previous studies show that population structure is critical to IGE evolution that inbreeding might contribute to the escalation in response to a genetic environment (Agrawal et al. 2001; Bijma and Wade 2008; McGlothlin et al. 2010). Our numerical results show that increased inbreeding does lead to faster rates of adaptive coevolution. Surprisingly, the effects of inbreeding in accelerating the evolutionary dynamics were stronger than comparable increases in linkage. The addition of only 10% inbreeding generates approximately the same dynamic as an 80% reduction in recombination rate (Fig. 3, blue lines). Moreover, despite the accelerated dynamics, inbreeding creates very little LD in con-
trast to the increase in LD with increasing linkage (Fig. 3, red lines). This may be because the effects of inbreeding are cumulative over generations, reducing the opportunity for recombination by reducing the frequency of double heterozygotes (Crow and Kimura 2009). These results suggest that population structure is more important than genetic architecture in relation to adaptation to a heritable, genetic environment. Our model assumes that the IGE originate from related individuals (e.g., maternal). If we relaxed this assumption and modeled IGEs between unrelated individuals, then we would not expect the same dynamics to occur. However, the introduction of population genetic structure would generate some relatedness within subpopulations and we might recover similar dynamics to those of our models in proportion to FST . A significant implication of our findings is that in subdivided populations it would not be unexpected for different IGEs to runaway for alternative alleles as selection rapidly fixes different combinations. F1 hybrid breakdown, due to IGEs running away in different directions, might then result in diversification and perhaps speciation similar to runaway processes of sexual selection (Lande 1981; Kirkpatrick
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1982; West-Eberhard 1983). It may not be unusual for social beetles to be inbreeding at the low levels simulated and so generate rapid runaway coevolution. Our findings suggest that coadaptation to maternal or epistatic environments may lead to a diversification of populations or species in elements of regulatory gene networks that is more rapid than adaptation via structural genes to alternative abiotic environments (e.g., Badyaev et al. 2002). In the standard scenario, speciation is driven by disruptive selection imposed by different abiotic environments. Under this view, speciation depends upon crossing-type G × E interactions for natural selection to pull a single ancestral species apart, into two reproductively isolated daughter species. One implication of our theory is that adaptation to local abiotic environmental variations by maternal genotypes may result in the rapid diversification of populations as well as their subsequent reproductive isolation owing to incompatibilities between their regulatory gene networks. For example, the rapid diversification of placental mammals may be the result of rapid coadaptation between zygotic genotypes and maternal genetic environments (Bininda-Emonds et al. 2007). Our model is consistent with a scenario whereby increased maternal care and attendant maternal genetic effects contribute to the overall success of mammals and to their relatively rapid diversification. ACKNOWLEDGMENTS We thank Amy Dapper, Ellen Ketterson, Curt Lively, Kristi Montooth, the editor Jon F. Wilkins, and anonymous reviewers for constructive comments on the manuscript. Research reported in this publication was supported by the National Institute of General Medical Science of the National Institutes of Health under award R01GM084238 to MJW. The authors declare that there are no conflicts of interest. DATA ARCHIVING The doi for our data is 10.5061/dryad.qs941. LITERATURE CITED Agrawal, A. F., E. D. Brodie, and M. J. Wade. 2001. On indirect genetic effects in structured populations. Am. Nat. 158:308–323. Badyaev, A. V., G. E. Hill, M. L. Beck, A. A. Dervan, R. A. Duckworth, K. J. McGraw, P. M. Nolan, and L. A. Whittingham. 2002. Sex-biased hatching order and adaptive population divergence in a passerine bird. Science 295:316–318. Bailey, N. W., and A. J. Moore. 2012. Runaway sexual selection without genetic correlations: social environments and flexible mate choice initiate and enhance the fisher process. Evolution 66:2674–2684. Bijma, P. 2014. The quantitative genetics of indirect genetic effects: a selective review of modelling issues. Heredity 112:61–69. Bijma, P., and M. J. Wade. 2008. The joint effects of kin, multilevel selection and indirect genetic effects on response to genetic selection. J. Evol. Biol. 21:1175–1188.
Bininda-Emonds, O. R. P., M. Cardillo, K. E. Jones, R. D. E. MacPhee, R. M. D. Beck, R. Grenyer, S. A. Price, R. A. Vos, J. L. Gittleman, and A. Purvis. 2007. The delayed rise of present-day mammals. Nature 446:507–512. Breden, F., and M. J. Wade. 1991. “Runaway” social evolution: reinforcing selection for inbreeding and altruism. J. Theor. Biol. 153:323–337. Charlesworth, B., and D. Charlesworth. 2010. Elements of evolutionary genetics. Roberts and Company Publishers, Greenwood Village, CO. Crow, J. F., and M. Kimura. 2009. An introduction to population genetics theory. Blackburn Press, Caldwell, NJ. Duckworth, R. A. 2009. Maternal effects and range expansion: a key factor in a dynamic process? Philos. Trans. R. Soc. B Biol. Sci. 364:1075–1086. Felsenstein, J. 1981. Skepticism towards santa rosalia, or why are there so few kinds of animals. Evolution 35:124–138. Fisher, R. A. 1958. The genetical theory of natural selection. Dover Publications, Mineola, NY. Fitzpatrick, B. M. 2014. Symbiote transmission and maintenance of extragenomic associations. Front. Microbiol 5:1–15. Gillespie, J. H. 2010. Population genetics: a concise guide. Johns Hopkins Univ. Press, Baltimore, MD. Hansen, T. F. 2013. Why epistasis is important for selection and adaptation. Evolution 67:3501–3511. Jasnos, L., K. Tomala, D. Paczesniak, and R. Korona. 2008. Interactions between stressful environment and gene deletions alleviate the expected average loss of fitness in yeast. Genetics 178:2105–2111. Kirkpatrick, M. 1982. Sexual selection and the evolution of female choice. Evolution 36:1–12. Lande, R. 1981. Models of speciation by sexual selection on polygenic traits. Proc. Natl. Acad. Sci. USA 78:3721–3725. Linksvayer, T. A., and M. J. Wade. 2009. Genes with social effects are expected to harbor more sequence variation within the between species. Evolution 63:1685–1696. McGlothlin, J. W., A. J. Moore, J. B. Wolf, and E. D. Brodie, III. 2010. Interacting phenotypes and the evolutionary process. III. Social evolution. Evolution 64:2558–2574. Moore, A. J., E. D. Brodie, and J. B. Wolf. 1997. Interacting phenotypes and the evolutionary process. 1. Direct and indirect genetic effects of social interactions. Evolution 51:1352–1362. Phillips, P. C., and N. A. Johnson. 1998. The population genetics of synthetic lethals. Genetics 150:449–458. Priest, N. K., and M. J. Wade. 2010. Maternal-zygotic epistasis and the evolution of genetic diseases. J. Biomed. Biotechnol. 2010:1–13. Shuster, S. M., and M. J. Wade. 2003. Mating systems and strategies. Princeton Univ. Press, Princeton, NJ. West-Eberhard, M. J. 1979. Sexual selection, social competition, and evolution. Proc. Am. Philos. Soc. 123:222–234. ———. 1983. Sexual selection, social competition, and speciation. Q. Rev. Biol. 58:155–183. Wolf, J. B. 2000. Indirect genetic effects and gene interactions. Pp. 158–176 in J. B. Wolf, E. D. Brodie, and M. J. Wade, eds. Epistasis and the evolutionary process. Oxford Univ. Press, Oxford, U.K. ———-. 2003. Genetic architecture and evolutionary constraint when the environment contains genes. Proc. Natl. Acad. Sci. USA 100:4655– 4660. Wolf, J. B., E. D. Brodie, J. M. Cheverud, A. J. Moore, and M. J. Wade. 1998. Evolutionary consequences of indirect genetic effects. Trends Ecol. Evol. 13:64–69.
Associate Editor: J. Wilkins
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RUNAWAY COEVOLUTION: ADAPTATION TO HERITABLE AND NONHERITABLE ENVIRONMENTS Devin M. Drown1,2 and Michael J. Wade1 1
Department of Biology, Indiana University, Bloomington, Indiana 47405 2
E-mail: [email protected]
Received February 27, 2014 Accepted June 4, 2014 Populations evolve in response to the external environment, whether abiotic (e.g., climate) or biotic (e.g., other conspecifics). We investigated how adaptation to biotic, heritable environments differs from adaptation to abiotic, nonheritable environments. We found that, for the same selection coefficients, the coadaptive process between genes and heritable environments is much faster than genetic adaptation to an abiotic nonheritable environment. The increased rate of adaptation results from the positive association generated by reciprocal selection between the heritable environment and the genes responding to it. These associations result in a runaway process of adaptive coevolution, even when the genes creating the heritable environment and genes responding to the heritable environment are unlinked. Although tightening the degree of linkage accelerates the coadaptive process, the acceleration caused by a comparable amount of inbreeding is greater, because inbreeding has a cumulative effect on reducing functional recombination over generations. Our results suggest that that adaptation to local abiotic environmental variation may result in the rapid diversification of populations and subsequent reproductive isolation not directly but rather via its effects on heritable environments and the genes responding to them. KEY WORDS:
G × E, genotype by environment, indirect genetic effects.
As Fisher (1958, p. 41) emphasized, populations evolve in response to the external environment, whether abiotic (e.g., climate) or biotic (e.g., other conspecifics or other species): . . . the physical environment may be regarded as constantly deteriorating . . . and this will tend, in the majority of species, constantly to lower the average value of m, the Malthusian parameter of the population increase. Probably more important than the changes in climate will be the evolutionary changes in progress in associated organisms.
Fisher saw the increase in fitness of “competitors and enemies” as a major cause of environmental deterioration. When the associated organisms are conspecifics, they constitute a “heritable environment” (Fisher 1958; West-Eberhard 1979). And, such environments coevolve with the organisms adapting to them. As a result, instead of deteriorating, favorable heritable environments can become more common and population mean fitness can increase. C
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The most common heritable environment is epistasis, sometimes referred to as the “internal environment” (e.g., Jasnos et al. 2008), in which the effect of an allele at one locus depends upon alleles at other loci (Hansen 2013). Genes with conspecific indirect genetic effects (IGE), such as maternal effect genes or sib-social genes, are also common instances of heritable environments (Wolf et al. 1998). Here, variation in heritable environment means variation in the genetic composition of conspecific social partners (Wolf 2000; Bijma 2014). The rate of adaptation to any environment, abiotic or social, depends upon the frequency of that environment and the strength of selection within it. In the context of quantitative genetics, the potential for IGE to accelerate evolution through coadaptation of the individual and its social environment has been discussed elsewhere (e.g., Wolf et al. 1998; Wolf 2003; McGlothlin et al. 2010; Bailey and Moore 2012; Fitzpatrick 2014). Here, we directly compare the relative rates of adaptation to heritable and nonheritable environments
C 2014 The Society for the Study of Evolution. 2014 The Author(s). Evolution Evolution 68-10: 3039–3046
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using a population genetic model framework. By quantifying the relative rates of evolution in this way, we can compare the familiar population genetic theory of genotype-by-environment (G × E) interactions with that of the less familiar theory of IGE. We investigate adaptation to variation in the nonheritable abiotic environment and to variation in three kinds of genetic or heritable environments: the internal genetic environment (epistasis), the maternal genetic environment, and the sib-social genetic environment. The initial rate of adaptation is the same across all environments, abiotic as well as biotic, but differences arise as a result of the evolution of the biotic environment. Selection creates positive associations between beneficial heritable environments and the genes adapting to them, making the coadaptive process self-accelerating or a runaway. That is, selection on one gene results in an increase in the frequency of the genetic environment in which that gene is favored. However, when adapting to a poorer or deteriorating environment, a runaway process does not occur because of the internal antagonism of selective effects. This process is similar to Fisher’s runaway sexual selection in that, via nonrandom mating, genes for female mate preference become associated with the genes for the preferred male trait (Fisher 1958). As a gene for the male trait increases owing to its mating advantage in female mate choice, the female preference gene increases along with it (Lande 1981; Kirkpatrick 1982). Much like our process, the success of the male gene increases the frequency of environment (namely, the female mating preference) in which it is favored. In population genetics theory, epistasis and restricted recombination (i.e., the genetic architecture) play important roles in creating and sustaining linkage disequilibrium (LD), both during adaptation (transient LD) and at equilibrium (Crow and Kimura 2009; Charlesworth and Charlesworth 2010; Gillespie 2010). Our model framework allows us to contrast the impact of population genetic structure and the genetic architecture (with the former being more important than the latter) on rates of adaptation. In models of IGE, which include the maternal and sibling effects, population genetic structure is an essential feature of IGE evolution (Bijma and Wade 2008). For this reason, we vary the degree of inbreeding (within-family mating) relative to random mating, which affects realized recombination rates. We examine the effects of population genetic structure caused by an arbitrary fraction of the population mating within families, while the remainder of the population mates at random. Although a great deal of research has been devoted to examining recombination in relation to LD and epistatic selection, we find that the runaway process of adaptive coevolution between heritable environments and the genes responding to them is more sensitive to inbreeding and other deviations from random mating than it is to linkage. First, we review the standard population genetic G × E model of adaption to an external abiotic, nonheritable environment, such
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as temperature, or more broadly, climate. Next, we extend the one gene external-environment model to two unlinked genes, one for the social environment (the IGE) and the other for adaptation to the social environment (direct effect gene; Moore et al. 1997). Lastly, we model the case of two loci, in which one gene adapts to the genotypic background created by the other, that is, we posit an epistatic interaction between the loci. MODEL
We compare the rate at which individuals adapt to four different kinds of environment (Fig. 1), an external, nongenetic environment and three genetic environments (sib-social, maternal, and epistatic). In each case, we model the evolution of a single gene (A gene) with additive effects on fitness only in the selective environment. In alternative or nonselective environments, the gene is neutral. Allelic variation at this gene permits adaptation to the environment. For adaptation to an external environment, we posit two environments and allow the A gene to have fitness effects only in one of them. This is one of the simplest models of G × E for fitness, and it is often invoked as representative of a species expanding its range to a new environment. To model the genetic environments, we imagine a second gene. For the internal genetic environment, we imagine that the A gene has its fitness effects only in some genotypic backgrounds but not others. Similarly, for maternal and sibling environments, we assume that the A gene manifests its fitness effects only when born of some females, or in the company of some genotypic sib-ships, but not others. Adaptation to an abiotic, nonheritable environment We model adaptation to two contrasting environments, E1 and E2 . The proportion of the population in E1 is e1 , with the remaining fraction, e2 = 1 – e1 , found in E2 . E1 can be a better environment than E2 , meaning that mean fitness for all individuals in E1 is higher by an increment, 2β, where β is ࣙ 0, than it is in E2 . We assume a diploid species with discrete nonoverlapping generations, in which individuals differ genetically from one another in their sensitivity, α, to E1 (but not to E2 ) as determined by alternative alleles, A and a, at a single locus. The frequency of the A allele is PA and that of the a allele is Pa = 1− PA . The alleles act additively so that wAA (E1 ), the fitness of an AA genotype in E1 equals (1 + 2β + 2α); wAa (E1 ) is (1 + 2β + 1α); and waa (E1 ) is (1 + 2β). In E2 , all genotypes have fitnesses equal to 1 (Fig. 1A). This is a G × E model, in which the environmental effect on fitness varies in scale but not in sign. Adaptation to a biotic, heritable environment The sib-social case: We model selection in response to a sib-social environment by assuming that an unlinked, second locus, with alternative alleles, B and b, determines sibling genotype. The
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frequency of this indirect-effect allele B in the population is PB and that of the b allele is Pb = 1 – PB . Individuals express alternative alleles, A and a, which affect their sensitivity, α, to BB (but not to bb) siblings. The alleles act additively as above so that wAA (BB), the fitness of an AA genotype interacting with a BB sibling equals (1 + 2β + 2α), wAa (BB) is (1 + 2β + 1α), and waa (BB) is (1 + 2β). When interacting with a bb sibling, all genotypes have fitness equal to 1 (Fig. 1B). Genotypes interacting with Bb heterozygous siblings have a fitness that is intermediate between their fitnesses with BB and bb siblings. The total fitness of an individual across all sibling interactions is given by weighting by the frequency of the B allele (PB,sib ) within families. The withinfamily frequency of the B allele is affected by the number of mates per females, the apportionment of fertility among multiple male mates, and the degree of within-family (f) as opposed to random (1 – f) mating. Note that the parameterization of selection
in the abiotic and biotic models for locus A is identical (compare Fig. 1A and B). The maternal case: We model the response to a maternal environment by assuming that an unlinked, second locus, with alternative alleles, B and b, determines maternal genotype. The frequency of this indirect-effect allele B in the population is PB and that of the b allele is Pb = 1 – PB . Offspring express alternative alleles, A or a, which affect their sensitivity, α, to BB (but not to bb) mothers. The alleles act additively as above so that wAA (BB), the fitness of an AA offspring genotype of a BB mother equals (1 + 2β + 2α), wAa (BB) is (1 + 2β + 1α), and waa (BB) is (1 + 2β). When born of a bb mother, all offspring genotypes have fitness equal to 1 (Fig. 1C). The offspring of Bb heterozygous mothers have an intermediate fitness between their fitness with BB and bb mothers.
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The epistatic case: We model epistasis with a framework similar to that of the maternal effect locus above (Fig. 1D). In this case, individuals carrying alternative alleles, A and a, differ in sensitivity, α, to their genotypic background at the unlinked B locus. Alleles at the A locus act additively so that wAABB , the fitness of an AABB genotypes equals (1 + 2β + 2α), wAaBB is (1 + 2β + 1α), and waaBB is (1 + 2β). All A locus genotypes have the same fitness on the bb genotypic background (Fig. 1D). The fitnesses of A locus genotypes on the Bb backgrounds are intermediate between their fitness on the BB and bb backgrounds.
Analyses ANALYTICAL SOLUTIONS
We first analyze the four models with the standard assumption that selection is weak such that α and β are near 0 and the loci assort independently. We assume in all of our cases that the genes act additively, however, under the assumption of weak selection and ignoring second-order (and higher) terms, a multiplicative model of gene interaction would converge on the additive models presented here. We assume that the genotypes are the products of random mating and are initially in Hardy–Weinberg proportions. For the abiotic, nonheritable environment, change in frequency of the direct effect allele, A, equals PA,abiotic =
(αe1 ) PA (1 − PA ) , [1 + 2e1 (β + αPA )]
(1)
where the denominator is mean fitness. The rate of change, PA,abiotic , depends on e1 , the frequency of the selective environment (E1 ) and α, the effect of the A allele on fitness in that environment. The rate of adaptation is faster when the selective environment is more common. However, the rate of adaptation is also sensitive to the value of β. In adaptation to E1 , β appears in the denominator of equation (1), so that increases in β diminish PA,abiotic . We contrast this case with one in which offspring fitness is affected by a biotic, heritable environment. Here, we assume that females mate multiply, so that all families consist of half-sibs. For any of the three cases with a biotic, heritable environment, the change in the frequency of the direct effect allele, A, equals PA,biotic =
(αPB ) PA (1 − PA ) , [1 + 2PB (β + αPA )]
(2)
where the denominator is mean fitness. Note here, that the frequency of the abiotic environment, e1 , has been replaced by the frequency of the biotic environment, PB . As above, the numerator in the rate of change, PA , depends on PB , the frequency of the selective biotic environment and α, the effect of the A allele in that social environment. The models differ, however, in that the
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frequency of the social environment, PB , changes as PA evolves, whereas e1 , the frequency of the abiotic nonheritable environment, E1 , does not. The change in PB equals PB = ρ
(β + αPA ) PB (1 − PB ) , [1 + 2PB (β + αPA )]
(3)
where ρ defines the relatedness between the source of the selective environment and the individual (sib-social, half-sibs, ρ = ¼; maternal, ρ = ½; epistatic, ρ = 1; Linksvayer and Wade 2009). As PB increases according to equation (3), evolution of the A allele is accelerated (cf. eq. 2). For the heritable genetic cases, as β increases, the rate of adaptation increases. This happens because the B allele enhances fitness directly in addition to its spread via hitchhiking on the increase in frequency of the A allele. In contrast, for the external environment case, recall increases in β diminish PA,abiotic because β appears in the denominator of equation (1). Adaptation to a heritable genotypic environment is different because β plays a dual role. It appears in the denominator of equation (2), as well as in the numerator of equation (3). The accelerating effect of β in equation (3) more than outweighs its retarding effect in equation (2). The results across the three different heritable environments are quite similar. Because the relatedness of the heritable environment is stronger in the maternal environment than the sibsocial, the maternal background evolves twice as fast as the sibsocial case. Differently put, as the maternal genetic environment in which A is favored becomes more common, the strength of selection on A (i.e., αPB ) is increased. This, in turn, increases PB, creating a self-accelerating runaway process. However, if we assumed that females were monogamous, then the sib-social case would evolve at the same rate as the maternal case because the relatedness among siblings would be half. Even more so, the epistatic background evolves twice as fast as the maternal background and four times as fast as the sib-social background. Because the feedback between the A and B loci is stronger in the epistatic case, the runaway coevolution between alleles A and B is much more rapid. Runaway coevolution is not a property typically associated with epistatic genes interactions, especially between unlinked genes. We derive the initial generation of LD assuming the initial frequency of alleles at both loci is independent (LD = 0): L D = ρ
α PA (1 − PA ) PB (1 − PB ) . 2 [1 + 2PB (β + αPA )]2 (4)
From equation (4), we see that LD is generated by selection and the sign of LD is dependent only on the sign of α, the selection coefficient on the direct effect locus, because the denominator is squared. The positive LD value links allele B of the heritable
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environment to allele A, the locus adapting to it. Consequently, the biotic, heritable environment (PB ) that favors allele A becomes more common. In turn, this increases the strength of selection on A, represented by (αPB ). This, in turn, increases PB so the coadaptation between A and B is mutually reinforcing, generating positive feedback or a self-accelerating runaway process. NUMERICAL ITERATIONS
We contrasted the rates of adaptation among the four models by plotting numerical iterations (i.e., no weak selection assumption) of the evolutionary process (Fig. 2) using MATLAB (R2010a, The Mathworks). When the external selective environment is rare (e1 = 0.05), the adaptive response to selection, PA,abiotic , is slow (Fig. 2A, black line). In contrast, when the heritable environments (sib-social, maternal, or epistatic) are initially rare (PB = 0.05), the coadaptive dynamics of alleles, A and B, result in much more rapid evolution, with the fixation of the heritable environment PB (Fig. 2B) followed quickly by fixation of PA (Fig. 2A). The entire process is completed long before fixation of A in response to E1 , the abiotic non-heritable environment (Fig. 2A, black line). The coadaptation happens rapidly because selection generates a positive LD between PA and PB (Fig. 2C). Thus, not only does increasing PB accelerate the evolution of PA but the reciprocal is also true: the increase in PA has the effect of increasing selection on the B allele, whether it is a sib-social, a maternal, or an epistatic background. There is thus a positive feedback between alleles at the two different loci. EFFECTS OF INBREEDING AND LINKAGE
We now explore two factors, inbreeding and reduced recombination, that potentially increase LD, thereby accelerating the evolutionary rate. We modified our numerical iterations by allowing a fraction, f, of within-family matings (brother–sister) to occur. The remaining fraction of matings (1 − f) occurred according to the proportions expected from the population genotype frequencies. To calculate the offspring genotypes, we mate each female to the respective weighted average genotype frequencies (f, family-level genotype frequencies; 1 − f, population-level genotype frequencies). Specifically, we explore the range of possibilities from complete random mating to 50% sib-mating (0 ࣘ f ࣘ 0.5). We use, as an illustrative example, the case in which the genetic environment is determined by the maternal genotype (Fig. 3). As expected, because inbreeding maintains genetic associations, increasing the fraction of family-level matings resulted in faster rates of adaptive coevolution. Recombination, by breaking down genetic associations, should weaken the positive feedback between loci. As genes become physically closer and recombination is less frequent, then a smaller fraction of LD built up by selection will be lost at replication. We investigated recombination rates (r) spanning the range
from tight linkage to free recombination (0.02 ࣘ r ࣘ 0.5). Using numerical iterations, we explored the impact of weak recombination in the maternal effects model (Fig. 3). As expected, as recombination rate decreases, the rates of evolution of both the direct and indirect effects loci increase.
Discussion The frequency of the selective background, abiotic, sib-social, maternal, or epistatic, determines the strength of selection on the direct effect gene. We have shown that genetic adaptation to a heritable environment changes the frequency of that heritable environment, thereby increasing the strength of selection in subsequent generations. In contrast, the frequency of an abiotic, nonheritable environment does not necessarily change as a population adapts to it. As a genetic environment becomes more common, it exerts stronger selection pressure on the responding direct effect gene. This, in turn, leads to a further increase in the frequency of the genetic environment via LD (cf. eqs. 3 and 4). The result is a runaway process of coadaptation akin to the runaway social evolution observed by Breden and Wade (1991) or that observed between the genes for female mate choice and male trait in runaway sexual selection (Lande 1981; Kirkpatrick 1982; cf. Shuster and Wade 2003, which discusses 10 different runaways possible in the context of male–female reproductive interactions). The relative quality of the two environments is determined by β. In our analyses, we assumed that the environment in which the A allele is sensitive, whether nonheritable or heritable, is beneficial or not harmful (i.e., β ࣙ 0). When both α > 0 and β > 0, mean fitness increases when the frequency the A allele increases in the population. In all cases, the heritable environment, beneficial to the adapting organism, increases in frequency via coadaptation. Unlike an environment deteriorating because of an increase in competitors or enemies (Fisher 1958), genetic coadaptation improves the environment. For maternal and sib-social heritable environments, coadaptation accelerates cooperation rather than competition among conspecifics. What happens when there is adaptation to a poorer environment (i.e. β < 0)? In this case, population mean fitness will increase only when αPA > −β. However, for heritable environments, the necessary condition for the coevolution of A and its background, B, is also that αPA > –β. This will not often be the case unless the direct effect of the A allele is unusually large or the A allele appears in the population at a high frequency. Unless these conditions are met, the poorer heritable environment does not spread. Nor do the runaway evolutionary dynamics apply to an allele that decreases fitness in a selective environment (Priest and Wade 2010). If there is an internal antagonism of selective effects such that the A allele decreased fitness in a heritable environment, those environments (i.e., PB ) would become
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Figure 2.
(B) Plots the LD generated between the direct and indirect effects loci. The direct effect coefficient (α) = 0.1 and the indirect effect coefficient (β) = 0. The initial direct and indirect effect allele frequencies (A, B) = 0.05. There is free recombination between loci (r = 0.5).
rarer as a result of selection against the A allele. That, in turn, weakens future selection on the A allele as its experience of the selective environment declines as the frequency of the selective environment decreases. Selection will be weaker at purging alleles that constitute a deleterious environment (e.g., the B allele when β < 0) leading to higher frequencies of deleterious genes (like the A allele) and deleterious backgrounds (like the B allele) at mutation-selection balance (Phillips and Johnson 1998; Priest and Wade 2010). A second important difference between adaptation to abiotic, nonheritable versus biotic, heritable environments occurs whenever the selective environment itself has a positive effect on fitness (i.e., when β > 0). When one of the abiotic, nonheritable environments is better than the alternative, the rate of adaptive response is reduced. In contrast, when one heritable environment is better than the other, the rate of adaptive response is enhanced; the runaway coadaptive process is accelerated. Hence, adaptive
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evolution to heritable environments should be more rapid than adaptation to external, nongenetic environments. Along these lines, there are opportunities for an interaction between abiotic, nonheritable selective environments and a runaway, coadaptive regulatory process. Consider, for example, competition for scarce resources, a premise central to the logic of Darwinian evolution. Some maternal genotypes might be better than others (i.e., β > 0) in competition for resources for their offspring. At the same time, a population might harbor genes expressed in offspring that are better at eliciting maternal resources. This would lead to a runaway process of coadaptation between the better provisioning mothers and their offspring, allowing more rapid genetic tracking of resource availability (Duckworth 2009). In this way, the adaptive coevolution between the maternal and zygotic genomes allows the regulatory network of early development to adapt rapidly to small changes in the external, abiotic environment.
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Figure 3. Comparison of evolution of a maternal effects model with different amounts of inbreeding (left column) and linkage (right column). Different lines’ colors represent the fraction of family-level mating (f) or rates of recombination (r). (A and B) Plots the frequency
of the direct effect allele, PA (solid lines), and the indirect effect allele, PB (dashed lines). (C and D) Plots the LD generated between the direct and indirect effects loci. The direct effect coefficient (α) = 0.1 and the indirect effect (β) = 0. The initial direct and indirect effect allele frequencies (A, B) = 0.05.
Our analyses identified the generation of positive LD between the two loci as contributing to the runaway process of coevolution. In some two-locus models and as seen here, selection creates positive LD in which initially there was none (Felsenstein 1981). In standard theory, epistatic selection and recombination act as opposing processes, creating and destroying LD, respectively (Charlesworth and Charlesworth 2010, p. 425). Similarly, we expected that linkage (instead of free recombination) would permit greater values of LD. Our numerical results confirmed this expectation (Fig. 3). Previous studies show that population structure is critical to IGE evolution that inbreeding might contribute to the escalation in response to a genetic environment (Agrawal et al. 2001; Bijma and Wade 2008; McGlothlin et al. 2010). Our numerical results show that increased inbreeding does lead to faster rates of adaptive coevolution. Surprisingly, the effects of inbreeding in accelerating the evolutionary dynamics were stronger than comparable increases in linkage. The addition of only 10% inbreeding generates approximately the same dynamic as an 80% reduction in recombination rate (Fig. 3, blue lines). Moreover, despite the accelerated dynamics, inbreeding creates very little LD in con-
trast to the increase in LD with increasing linkage (Fig. 3, red lines). This may be because the effects of inbreeding are cumulative over generations, reducing the opportunity for recombination by reducing the frequency of double heterozygotes (Crow and Kimura 2009). These results suggest that population structure is more important than genetic architecture in relation to adaptation to a heritable, genetic environment. Our model assumes that the IGE originate from related individuals (e.g., maternal). If we relaxed this assumption and modeled IGEs between unrelated individuals, then we would not expect the same dynamics to occur. However, the introduction of population genetic structure would generate some relatedness within subpopulations and we might recover similar dynamics to those of our models in proportion to FST . A significant implication of our findings is that in subdivided populations it would not be unexpected for different IGEs to runaway for alternative alleles as selection rapidly fixes different combinations. F1 hybrid breakdown, due to IGEs running away in different directions, might then result in diversification and perhaps speciation similar to runaway processes of sexual selection (Lande 1981; Kirkpatrick
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1982; West-Eberhard 1983). It may not be unusual for social beetles to be inbreeding at the low levels simulated and so generate rapid runaway coevolution. Our findings suggest that coadaptation to maternal or epistatic environments may lead to a diversification of populations or species in elements of regulatory gene networks that is more rapid than adaptation via structural genes to alternative abiotic environments (e.g., Badyaev et al. 2002). In the standard scenario, speciation is driven by disruptive selection imposed by different abiotic environments. Under this view, speciation depends upon crossing-type G × E interactions for natural selection to pull a single ancestral species apart, into two reproductively isolated daughter species. One implication of our theory is that adaptation to local abiotic environmental variations by maternal genotypes may result in the rapid diversification of populations as well as their subsequent reproductive isolation owing to incompatibilities between their regulatory gene networks. For example, the rapid diversification of placental mammals may be the result of rapid coadaptation between zygotic genotypes and maternal genetic environments (Bininda-Emonds et al. 2007). Our model is consistent with a scenario whereby increased maternal care and attendant maternal genetic effects contribute to the overall success of mammals and to their relatively rapid diversification. ACKNOWLEDGMENTS We thank Amy Dapper, Ellen Ketterson, Curt Lively, Kristi Montooth, the editor Jon F. Wilkins, and anonymous reviewers for constructive comments on the manuscript. Research reported in this publication was supported by the National Institute of General Medical Science of the National Institutes of Health under award R01GM084238 to MJW. The authors declare that there are no conflicts of interest. DATA ARCHIVING The doi for our data is 10.5061/dryad.qs941. LITERATURE CITED Agrawal, A. F., E. D. Brodie, and M. J. Wade. 2001. On indirect genetic effects in structured populations. Am. Nat. 158:308–323. Badyaev, A. V., G. E. Hill, M. L. Beck, A. A. Dervan, R. A. Duckworth, K. J. McGraw, P. M. Nolan, and L. A. Whittingham. 2002. Sex-biased hatching order and adaptive population divergence in a passerine bird. Science 295:316–318. Bailey, N. W., and A. J. Moore. 2012. Runaway sexual selection without genetic correlations: social environments and flexible mate choice initiate and enhance the fisher process. Evolution 66:2674–2684. Bijma, P. 2014. The quantitative genetics of indirect genetic effects: a selective review of modelling issues. Heredity 112:61–69. Bijma, P., and M. J. Wade. 2008. The joint effects of kin, multilevel selection and indirect genetic effects on response to genetic selection. J. Evol. Biol. 21:1175–1188.
Bininda-Emonds, O. R. P., M. Cardillo, K. E. Jones, R. D. E. MacPhee, R. M. D. Beck, R. Grenyer, S. A. Price, R. A. Vos, J. L. Gittleman, and A. Purvis. 2007. The delayed rise of present-day mammals. Nature 446:507–512. Breden, F., and M. J. Wade. 1991. “Runaway” social evolution: reinforcing selection for inbreeding and altruism. J. Theor. Biol. 153:323–337. Charlesworth, B., and D. Charlesworth. 2010. Elements of evolutionary genetics. Roberts and Company Publishers, Greenwood Village, CO. Crow, J. F., and M. Kimura. 2009. An introduction to population genetics theory. Blackburn Press, Caldwell, NJ. Duckworth, R. A. 2009. Maternal effects and range expansion: a key factor in a dynamic process? Philos. Trans. R. Soc. B Biol. Sci. 364:1075–1086. Felsenstein, J. 1981. Skepticism towards santa rosalia, or why are there so few kinds of animals. Evolution 35:124–138. Fisher, R. A. 1958. The genetical theory of natural selection. Dover Publications, Mineola, NY. Fitzpatrick, B. M. 2014. Symbiote transmission and maintenance of extragenomic associations. Front. Microbiol 5:1–15. Gillespie, J. H. 2010. Population genetics: a concise guide. Johns Hopkins Univ. Press, Baltimore, MD. Hansen, T. F. 2013. Why epistasis is important for selection and adaptation. Evolution 67:3501–3511. Jasnos, L., K. Tomala, D. Paczesniak, and R. Korona. 2008. Interactions between stressful environment and gene deletions alleviate the expected average loss of fitness in yeast. Genetics 178:2105–2111. Kirkpatrick, M. 1982. Sexual selection and the evolution of female choice. Evolution 36:1–12. Lande, R. 1981. Models of speciation by sexual selection on polygenic traits. Proc. Natl. Acad. Sci. USA 78:3721–3725. Linksvayer, T. A., and M. J. Wade. 2009. Genes with social effects are expected to harbor more sequence variation within the between species. Evolution 63:1685–1696. McGlothlin, J. W., A. J. Moore, J. B. Wolf, and E. D. Brodie, III. 2010. Interacting phenotypes and the evolutionary process. III. Social evolution. Evolution 64:2558–2574. Moore, A. J., E. D. Brodie, and J. B. Wolf. 1997. Interacting phenotypes and the evolutionary process. 1. Direct and indirect genetic effects of social interactions. Evolution 51:1352–1362. Phillips, P. C., and N. A. Johnson. 1998. The population genetics of synthetic lethals. Genetics 150:449–458. Priest, N. K., and M. J. Wade. 2010. Maternal-zygotic epistasis and the evolution of genetic diseases. J. Biomed. Biotechnol. 2010:1–13. Shuster, S. M., and M. J. Wade. 2003. Mating systems and strategies. Princeton Univ. Press, Princeton, NJ. West-Eberhard, M. J. 1979. Sexual selection, social competition, and evolution. Proc. Am. Philos. Soc. 123:222–234. ———. 1983. Sexual selection, social competition, and speciation. Q. Rev. Biol. 58:155–183. Wolf, J. B. 2000. Indirect genetic effects and gene interactions. Pp. 158–176 in J. B. Wolf, E. D. Brodie, and M. J. Wade, eds. Epistasis and the evolutionary process. Oxford Univ. Press, Oxford, U.K. ———-. 2003. Genetic architecture and evolutionary constraint when the environment contains genes. Proc. Natl. Acad. Sci. USA 100:4655– 4660. Wolf, J. B., E. D. Brodie, J. M. Cheverud, A. J. Moore, and M. J. Wade. 1998. Evolutionary consequences of indirect genetic effects. Trends Ecol. Evol. 13:64–69.
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