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Evolution in Changing Environments: Modifiers of Mutation, Recombination, and Migration

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Evolution in Changing Environments: Modifiers of Mutation, Recombination, and Migration Evolution in changing environments: Modifiers of mutation, recombination, and migration Oana Carjaa,1, Uri Libermanb, and Marcus W. Feldmana,1 aDepartment of Biology, Stanford University, Stanford, CA 94305-5020; and bSchool of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel Contributed by Marcus W. Feldman, September 13, 2014 (sent for review June 20, 2014; reviewed by Lee Altenberg and Lilach Hadany) The production and maintenance of genetic and phenotypic di- because, when the selective environment varies between positive versity under temporally fluctuating selection and the signatures and negative epistasis, the linkage disequilibrium is often of the of environmental changes in the patterns of this variation have opposite sign to the current epistasis. This lag between epistasis been important areas of focus in population genetics. On one hand, and linkage disequilibrium leads to a mismatch between hap- periods of constant selection pull the genetic makeup of popula- lotypes that are most fit and those that are more common, and tions toward local fitness optima. On the other, to cope with recombination should be favored because it breaks apart the cur- changes in the selection regime, populations may evolve mecha- rently maladapted allele combinations and combines alleles that nisms that create a diversity of genotypes. By tuning the rates at might constitute a fitter haplotype in the future (14, 17, 22, 23). which variability is produced—such as the rates of recombination, Environmental fluctuations can also affect the evolution of the mutation rate. In bacteria, stress can increase the mutation rate mutation, or migration—populations may increase their long-term by inducing mutagenic mechanisms such as the SOS transcrip- adaptability. Here we use theoretical models to gain insight into tional response (24, 25) or contingency loci (26). Theoretical how the rates of these three evolutionary forces are shaped by studies have considered both plastic increases in the mutation fluctuating selection. We compare and contrast the evolution of rate in response to stress (27) and also nonplastic mutation rates recombination, mutation, and migration under similar patterns that evolve in synchrony with the rate of environmental change. of environmental change and show that these three sources of When selection fluctuates periodically and symmetrically be- phenotypic variation are surprisingly similar in their response to tween two states with different optimal genotypes, the mutation changing selection. We show that the shape, size, variance, and rate between allelic states should evolve to approximately 1=n, EVOLUTION asymmetry of environmental fluctuation have different but pre- where n is the number of generations between temporal envi- dictable effects on evolutionary dynamics. ronmental changes (28, 29). However, numerical simulations showed that the stable mutation rate became zero as the variance in fluctuating selection | modifier genes | recombination rate | the length of selective cycles increased, or if there were asymmetries migration rate | mutation rate in selection pressure between the two environmental states (30). Variability in selection has also been shown to affect the nder constant selection, a large haploid population is ex- evolutionarily stable migration rate. When selection is hetero- pected to evolve toward a local fitness maximum. However, geneous in space but not in time and without variation in the U intensity of kin competition (31), migrants cannot displace lo- in natural populations selection may not be constant over time cally adapted individuals and there is selection against migration due, for example, to ecological changes, spatial variability, changes (32, 33). This has been shown in population genetic models of in environment, or even shifts in the genetic background (1). Under temporal and spatial heterogeneity in the direction and strength Significance of selection, a population may evolve mechanisms that create and maintain phenotypic diversity, thus increasing the long-term adaptability of the population (2–7). These mechanisms may in- Environmental variability is known to promote the evolution clude changes in the rates at which genetic variability is produced, of mechanisms that increase phenotypic diversity. The evolu- such as the rates of recombination, mutation, and migration (8). tion of recombination, mutation, and migration, which endow Understanding how population genetic dynamics are shaped a population with the needed genetic and phenotypic vari- by changing selection has constituted an important component of ability, has been a focus of study in population genetics for research in mathematical evolutionary theory over the past five more than five decades. Theoretical approaches have focused decades. These studies have addressed such issues as the re- on conditions for the evolution of recombination, mutation, lationship between fluctuations in selection and the dynamics of and migration when environments change periodically and evolution and how these fluctuations are reflected in the pattern with symmetric selection pressures. Here we extend these of genotypic frequency variation (9–12). models to incorporate random and asymmetric selection. We One important contributor to the pattern of genetic diversity is compare and contrast how fluctuating selection affects the recombination, which can affect variation by bringing together or stable rates of these three evolutionary forces and highlight breaking apart combinations of alleles. Recombination may ac- surprising similarities in their evolution under fluctuating se- celerate adaptation by expediting the removal of combinations of lection. This study offers insights into the role of environmen- deleterious alleles from the population, but also slow it down by tal duration, shape, and randomness in predicting the long- breaking apart favorable interactions among genes (13–18). The term evolutionary advantage of recombination, mutation, and prevalence of recombination in nature has stimulated theoretical migration. efforts to explore the evolution of the recombination rate under a wide variety of modeling assumptions (14–20). Most expla- Author contributions: O.C., U.L., and M.W.F. designed research; O.C., U.L., and M.W.F. nations of the advantage of sex and/or recombination involve performed research; O.C., U.L., and M.W.F. contributed new reagents/analytic tools; O.C., either allowing assembly of favored multilocus haplotypes from U.L., and M.W.F. analyzed data; and O.C., U.L., and M.W.F. wrote the paper. combinations of epistatically interacting mutations (19–21), or Reviewers: L.A., The KLI; and L.H., Tel Aviv University. adapting to a changing environment (14, 22, 23). The authors declare no conflict of interest. Charlesworth (14) showed that for a diploid genetic system, 1To whom correspondence may be addressed. Email: [email protected] or mfeldman@ when the sign of the linkage disequilibrium varies cyclically stanford.edu. in time, increased recombination may be favored if the period This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. of environmental fluctuation is strictly larger than two. This is 1073/pnas.1417664111/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1417664111 PNAS Early Edition | 1of6 Downloaded by guest on October 2, 2021 selection in multipatch environments with patch-dependent se- ordered as above and the modifier locus located on one side of lection of alleles (34–36), and in ecological analyses of the evo- the two major loci, let R be the recombination rate between the lution of dispersal (37–43). Migration is suppressed because, in modifier locus and the two major loci. We assume no interference the absence of temporal variation, it limits the ability of pop- between recombination events occurring in the two intervals ulations to adapt to local environmental conditions (44). With separating the two major loci and between the modifier locus and temporal variability in selection however, migration can increase the nearest major locus. the level of local adaptation (45) and higher rates of migration Assume two possible types of selection regimes T1 and T2, may be favored (46–50). such that the fitnesses, irrespective of the genotype at the M=m Here we use the framework of modifier theory to study how locus, can be represented as follows: environmental fluctuation affects the rates of recombination, Genotype AB Ab aB ab mutation, and migration. A modifier approach to study the evo- lution of genetic systems was first introduced by Nei (51) and Environment T1 11+ s1 1 + s1 1 Feldman (52) in models for the evolution of recombination. They Environment T2 1 + s2 111+ s2 analyzed the consequences of indirect selection on recombination between genes under viability selection. This approach is based on Thus, if s1, s2 > 0, the genotypes that are fittest in one envi- the assumption that genetic variation exists in the rate of re- ronment are less fit in the other. Increased recombination should combination; such genetic variation has been demonstrated using be favored because, at every environmental change, recombinant heritability measurements and observed differences between sexes offspring are more fit than the nonrecombinant ones (also see or closely related species (53–55). Recombination and mutation refs. 14, 18, 22, and 23). have been shown to be extremely variable across a species’ ge- nome, with areas of low recombination or mutation,
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