Meiosis and the evolution of recombination at low mutation rates

The classical understanding of recombination is that in large asexual populations with multiplicative fitness, linkage disequilibrium is negligible, and thus there is no selective agent driving an allele for recombination. This has led researchers to recognize the importance of synergistic epistatic selection in generating negative linkage disequilibrium that thereby renders an advantage to recombination. Yet data on such selection is equivocal, and various works have shown that synergistic epistasis per se, when left unquantified in its magnitude or operation, is not sufficient to drive the evolution of recombination. Here we show that neither it, nor any mechanism generating negative linkage disequilibrium among fitness-related loci, is necessary. We demonstrate that a neutral gene for recombination can increase in frequency in a large population under a low mutation rate and strict multiplicative fitness. We work in a parameter range where individuals have, on average, less than one mutation each, yet recombination can still evolve. We demonstrate this in two ways: first, by examining the consequences of recombination correlated with misrepaired DNA damage and, second, by increasing the probability of recombination with declining fitness. Interestingly, the allele spreads without repairing even a single DNA mutation.     

Simulation of the effect of population size on the evolution of the recombination fraction

A study, by means of computer simulation, has been performed on the evolution of recombination rate modifier genes in a system with three diallelic loci (A, B and C). The locus C, selectively neutral, is responsible for the modification of the recombination fraction between the major loci (A and B) which are subjected to selection. Two models have been analysed, the modifier allele being recessive in one of them, and codominant in the other, with infinite and finite populations. Distinct initial genic frequencies of the major loci and different selection coefficients have been utilised. We have found that the frequency of the allele which favours recombination increases in finite populations, and decreases slightly in infinite populations. These results are consistent with previous theory; presumably, selection favours alleles reducing recombination between epistatically interacting loci in a infinite population, since this reduces the breakup of advantageous combinations of alleles. However, in finite populations, selection favours the breakup of the random linkage disequilibria which are produced by random drift.     

Selection for recombination in structured populations

In finite populations, linkage disequilibria generated by the interaction of drift and directional selection (Hill-Robertson effect) can select for sex and recombination, even in the absence of epistasis. Previous models of this process predict very little advantage to recombination in large panmictic populations. In this article we demonstrate that substantial levels of linkage disequilibria can accumulate by drift in the presence of selection in populations of any size, provided that the population is subdivided. We quantify (i) the linkage disequilibrium produced by the interaction of drift and selection during the selective sweep of beneficial alleles at two loci in a subdivided population and (ii) the selection for recombination generated by these disequilibria. We show that, in a population subdivided into n demes of large size N, both the disequilibrium and the selection for recombination are equivalent to that expected in a single population of a size intermediate between the size of each deme (N) and the total size (nN), depending on the rate of migration among demes, m. We also show by simulations that, with small demes, the selection for recombination is stronger than both that expected in an unstructured population (m = 1 - 1/n) and that expected in a set of isolated demes (m = 0). Indeed, migration maintains polymorphisms that would otherwise be lost rapidly from small demes, while population structure maintains enough local stochasticity to generate linkage disequilibria. These effects are also strong enough to overcome the twofold cost of sex under strong selection when sex is initially rare. Overall, our results show that the stochastic theories of the evolution of sex apply to a much broader range of conditions than previously expected.     

SELECTION FOR RECOMBINATION IN SMALL POPULATIONS

Abstract The reasons that sex and recombination are so widespread remain elusive. One popular hypothesis is that sex and recombination promote adaptation to a changing environment. The strongest evidence that increased recombination may evolve because recombination promotes adaptation comes from artificially selected populations. Recombination rates have been found to increase as a correlated response to selection on traits unrelated to recombination in several artificial selection experiments and in a comparison of domesticated and nondomesticated mammals. There are, however, several alternative explanations for the increase in recombination in such populations, including two different evolutionary explanations. The first is that the form of selection is epistatic, generating linkage disequilibria among selected loci, which can indirectly favor modifier alleles that increase recombination. The second is that random genetic drift in selected populations tends to generate disequilibria such that beneficial alleles are often found in different individuals; modifier alleles that increase recombination can bring together such favorable alleles and thus may be found in individuals with greater fitness. In this paper, we compare the evolutionary forces acting on recombination in finite populations subject to strong selection. To our surprise, we found that drift accounted for the majority of selection for increased recombination observed in simulations of small to moderately large populations, suggesting that, unless selected populations are large, epistasis plays a secondary role in the evolution of recombination.     

Effect of epistasis and linkage on fixation probability in three-locus models: an ancestral recombination-selection graph approach

We study the probability of ultimate fixation of a single new mutant arising in an individual chosen at random at a locus linked to two other loci carrying previously arisen mutations. This is done using the Ancestral Recombination-Selection Graph (ARSG) in a finite population in the limit of a large population size, which is also known as the Ancestral Influence Graph (AIG). An analytical expansion of the fixation probability with respect to population-scaled recombination rates and selection intensities is obtained. The coefficients of the expansion are expressed in terms of the initial state of the population and the epistatic interactions among the selected loci. Under the assumption of weak selection at tightly linked loci, the sign of the leading term, which depends on the signs of epistasis and initial linkage disequilibrium, determines whether an increase in recombination rates increases the chance of ultimate fixation of the new mutant. If mutants are advantageous, this is the case when epistasis is positive or null and the initial linkage disequilibrium is negative, which is an expected state in a finite population under directional selection. Moreover, this is also the case for a neutral mutant modifier coding for higher recombination rates if the same conditions hold at the selected loci. Under the same conditions, deleterious mutants are disfavored for ultimate fixation and neutral modifiers for higher recombination rates still favored. The recombination rates between the modifier locus and the selected loci do not come into play in the leading terms of the approximation for the fixation probability, but they do in higher-order terms.     

Expected Linkage Disequilibrium for a Neutral Locus Linked to a Chromosomal Arrangement

The expected value of the squared linkage disequilibrium is derived for a neutral locus associated with a chromosomal arrangement that is maintained in the population by strong balancing selection. For a given value of recombination, the expected squared linkage disequilibrium is shown to decrease as the intensity of selection maintaining the arrangement increases. The transient behavior of the expected square linkage disequilibrium is also derived. This theory applies to loci that are closely linked to inversions in Drosophila species and to loci closely linked to the differential segments of the translocation complexes in ring-forming species of Oenothera. In both cases the strong linkage disequilibria that have been observed in natural populations can be explained by random drift.     

Background selection and population differentiation

A general analytical formula is derived, which predicts the effects of background selection on population differentiation at a neutral locus as a result of its linkage with selected loci of deleterious mutations. The theory is based on the assumptions of random mating, multiplicative fitness, and weak selection in hermaphrodite plants in the island model of population structure. The analytical results show that Fst at the neutral locus increases as a result of the effects of background selection, regardless of the dependence or independence among linked background selective loci. The increment in Fst is closely related to the magnitude of linkage disequilibria between the neutral locus and selected loci, and can be estimated by the ratio of Fst with background selection to Fst without background selection minus one. The steady-state linkage disequilibrium between a neutral locus and a selected locus in subpopulations, primarily attained by gene flow, decreases with the recombination rate, and can be enhanced when there are dependence among linked selected loci. Monte Carlo computer simulations with two- and three-locus models show that the analytical formulae perform well under general conditions. Application of the present theory may aid in analyzing the genome-wide mapping of the effect of background selection in terms of Fst.     

Assortative mating for fitness and the evolution of recombination

To understand selection on recombination, we need to consider how linkage disequilibria develop and how recombination alters these disequilibria. Any factor that affects the development of disequilibria, including nonrandom mating, can potentially change selection on recombination. Assortative mating is known to affect linkage disequilibria but its effects on the evolution of recombination have not been previously studied. Given that assortative mating for fitness can arise indirectly via a number of biologically realistic scenarios, it is plausible that weak assortative mating occurs across a diverse set of taxa. Using a modifier model, we examine how assortative mating for fitness affects the evolution of recombination under two evolutionary scenarios: selective sweeps and mutation-selection balance. We find there is no net effect of assortative mating during a selective sweep. In contrast, assortative mating could have a large effect on recombination when deleterious alleles are maintained at mutation-selection balance but only if assortative mating is sufficiently strong. Upon considering reasonable values for the number of loci affecting fitness components, the strength of selection, and the mutation rate, we conclude that the correlation in fitness between mates is unlikely to be sufficiently high for assortative mating to affect the evolution of recombination in most species.     

The effect of linkage and population size on inbreeding depression due to mutational load.

Using a stochastic model of a finite population in which there is mutation to partially recessive detrimental alleles at many loci, we study the effects of population size and linkage between the loci on the population mean fitness and inbreeding depression values. Although linkage between the selected loci decreases the amount of inbreeding depression, neither population size nor recombination rate have strong effects on these quantities, unless extremely small values are assumed. We also investigate how partial linkage between the loci that determine fitness affects the invasion of populations by alleles at a modifier locus that controls the selfing rate. In most of the cases studied, the direction of selection on modifiers was consistent with that found in our previous deterministic calculations. However, there was some evidence that linkage between the modifier locus and the selected loci makes outcrossing less likely to evolve; more losses of alleles promoting outcrossing occurred in runs with linkage than in runs with free recombination. We also studied the fate of neutral alleles introduced into populations carrying detrimental mutations. The times to loss of neutral alleles introduced at low frequency were shorter than those predicted for alleles in the absence of selected loci, taking into account the reduction of the effective population size due to inbreeding. Previous studies have been confined to outbreeding populations, and to alleles at frequencies close to one-half, and have found an effect in the opposite direction. It therefore appears that associations between neutral and selected loci may produce effects that differ according to the initial frequencies of the neutral alleles.     

Selection and genetic drift of polymorphisms within the merozoite surface protein-1 gene of Plasmodium falciparum

Intragenic recombination in the merozoite surface protein-1 gene (Msp-1) of Plasmodium falciparum is a major mechanism for allelic variation among natural parasite populations. The frequency of recombination depends on the intensity of transmission in the vector mosquito. In the present study, linkage disequilibrium between polymorphic 'loci' in the 5'- and 3'-regions of Msp-1 was examined in parasite populations from Brazilian Amazon and southern Vietnam and compared with that in a Thai population previously reported. The R2 test identified clusters of linkage disequilibria between the 5'- and 3'-regions, which are different among the three populations. However, the overall strength of linkage disequilibria was stronger in Brazil, a hypoendemic area, than in Vietnam and Thailand, mesoendemic areas, suggesting that linkage disequilibrium in Msp-1 inversely correlates with the intensity of transmission. To investigate possible mechanisms for linkage disequilibrium in Msp-1, we applied the Fst index, which measures the inter-population variance in allele frequency, to 'loci' in Msp-1 among the three populations. The Fst test identified two distinct regions with respect to inter-population allele frequency in Msp-1: one for highly divergent 'loci' in the 5'-region and the other for non-divergent 'loci' in the 3'-region. These results suggest that genetic drift is not the sole mechanism for linkage disequilibrium, but selection operates on 'loci' in the 3'-region in hypo- and mesoendemic areas of malaria.     

The effect of epistasis on the structure of hybrid zones

Within hybrid zones that are maintained by a balance between selection and dispersal, linkage disequilibrium is generated by the mixing of divergent populations. This linkage disequilibrium causes selection on each locus to act on all other loci, thereby steepening clines, and generating a barrier to gene flow. Diffusion models predict simple relations between the strength of linkage disequilibrium and the dispersal rate, sigma, and between the barrier to gene flow, B, and the reduction in mean fitness, W. The aim of this paper is to test the accuracy of these predictions by comparison with an exact deterministic model of unlinked loci (r = 0.5). Disruptive selection acts on the proportion of alleles from the parental populations (p,q): W = exp[-S(4pq)beta], such that the least fit genotype has fitness e-s. Where beta < 1, fitness is reduced for a wide range of intermediate genotypes; where beta > 1, fitness is only reduced for those genotypes close to p = 0.5. Even with strong epistasis, linkage disequilibria are close to sigma 2p'ip'j/rij, where p'i, p'j are the gradients in allele frequency at loci i, j. The barrier to gene flow, which is reflected in the steepening of neutral clines, is given by [formula: see text] where r, the harmonic mean recombination rate between the neural and selected loci, is here 0.5. This is a close approximation for weak selection, but underestimates B for strong selection. The barrier is stronger for small beta, because hybrid fitness is then reduced over a wider range of p. The widths of the selected clines are harder to predict: though simple approximations are accurate for beta = 1, they become inaccurate for extreme beta because, then, fitness changes sharply with p. Estimates of gene number, made from neutral clines on the assumption that selection acts against heterozygotes, are accurate for weak selection when beta = 1; however, for strong selection, gene number is overestimated. For beta > 1, gene number is systematically overestimated and, conversely, when beta < 1, it is underestimated.     

The evolution of recombination in a heterogeneous environment

Most models describing the evolution of recombination have focused on the case of a single population, implicitly assuming that all individuals are equally likely to mate and that spatial heterogeneity in selection is absent. In these models, the evolution of recombination is driven by linkage disequilibria generated either by epistatic selection or drift. Models based on epistatic selection show that recombination can be favored if epistasis is negative and weak compared to directional selection and if the recombination modifier locus is tightly linked to the selected loci. In this article, we examine the joint effects of spatial heterogeneity in selection and epistasis on the evolution of recombination. In a model with two patches, each subject to different selection regimes, we consider the cases of mutation-selection and migration-selection balance as well as the spread of beneficial alleles. We find that including spatial heterogeneity extends the range of epistasis over which recombination can be favored. Indeed, recombination can be favored without epistasis, with negative and even with positive epistasis depending on environmental circumstances. The selection pressure acting on recombination-modifier loci is often much stronger with spatial heterogeneity, and even loosely linked modifiers and free linkage may evolve. In each case, predicting whether recombination is favored requires knowledge of both the type of environmental heterogeneity and epistasis, as none of these factors alone is sufficient to predict the outcome.     

On the evolution of epistasis III: the haploid case with mutation

Whether interaction between genes is better represented by synergistic or antagonistic epistasis has been a focus of experimental research in bacterial population genetics. Our previous research on evolution of modifiers of epistasis in diploid systems has indicated that the strength of positive or negative epistasis should increase provided linkage disequilibrium is maintained. Here we study a modifier of epistasis in fitness between two loci in a haploid system. Epistasis is modified in the neighborhood of a mutation-selection balance. We show that when linkage in the three-locus system is tight, an increase in the frequency of a modifier allele that induces either more negative or more positive epistasis is possible. Epistasis here can be measured on either an additive or multiplicative scale.     

The deviation from linkage equilibrium with multiple loci varying in a stepping-stone cline

The balance between the creation of associations between alleles at different loci by immigration and the convergence to linkage equilibrium due to the recombination process is studied in a theoretical model. The geographical structure of the model is a stepping-stone chain of populations linking two genetically constant source populations. The model assumes an arbitrary number of autosomal loci and considers genetic variation (two alleles at each locus) that is not subject to natural selection. The gene frequencies at each locus will then show a linear cline through the stepping-stone chain of populations. The deviation from linkage equilibrium through the stepping-stone cline is characterized by an equation for linear measures that provide the linkage disequilibrium measures for a given set of loci in terms of the gene frequencies and the linkage disequilibria in the source populations and in terms of the linkage disequilibrium measures through the cline for lower numbers of loci. Numerical examples of this iterative solution are given, and it is shown that the build-up of the higher order Bennett-disequilibria through the cline is considerably more pronounced than the build-up of two-locus disequilibria.     

On the evolution of recombination and meiosis.

Theories on the evolution of recombination in regard to its ability to increase mean fitness require a consistent source of negative linkage disequilibrium among loci affecting fitness to show an advantage to recombination. Here we present evidence that, at least theoretically, genetic variation for recombination can spread in very large populations under a strictly multiplicative-fitness, deleterious-allele model. The model uses only Mendelian genetics in a multi-locus context to show that a dominant gene for recombination can spread when rare and resist invasion when common. In non-equilibrium populations driven by Muller's ratchet, the gene increases its probability of fixation by increasing the probability of being associated with the best individuals. This occurs at an optimal level of recombination. Its action results in both an immediate and a long-term advantage to recombination amongst the proto-meiotic organisms modelled. The genetic mechanism lends itself naturally to a model for the evolution of meiosis, where modern-day gametes are seen as derivative of ancient unicellular organisms.     

Variances and covariances of squared linkage disequilibria in finite populations

Analysis of linkage disequilibrium D among restriction sites or bases in DNA sequences, arising from mutations in finite populations, depends on a knowledge of the variance-covariance structure of measures such as D2 between different pairs of sites. This requires evaluation of the eighth moments of gene frequencies among two, three, and four loci, and the necessary methodology is derived here and results are computed. While primary emphasis is placed on disequilibrium arising from mutation or gene conversion, the methodology also allows for the joint effects of only drift and recombination. Numerical results confirm that squared linkage disequilibria can have high variances and covariances.     

The Evolution of Recombination: Removing the Limits to Natural Selection

One of the oldest hypotheses for the advantage of recombination is that recombination allows beneficial mutations that arise in different individuals to be placed together on the same chromosome. Unless recombination occurs, one of the beneficial alleles is doomed to extinction, slowing the rate at which adaptive mutations are incorporated within a population. We model the effects of a modifier of recombination on the fixation probability of beneficial mutations when beneficial alleles are segregating at other loci. We find that modifier alleles that increase recombination do increase the fixation probability of beneficial mutants and subsequently hitchhike along as the mutants rise in frequency. The strength of selection favoring a modifier that increases recombination is proportional to λ(2)Sδr/r when linkage is tight and λ(2)S(3)δ r/N when linkage is loose, where λ is the beneficial mutation rate per genome per generation throughout a population of size N, S is the average mutant effect, r is the average recombination rate, and δr is the amount that recombination is modified. We conclude that selection for recombination will be substantial only if there is tight linkage within the genome or if many loci are subject to directional selection as during periods of rapid evolutionary change.     

Linkage Disequilibrium in Subdivided Populations

The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m(1) + m(2)) - (m(1) + m(2))(2), whichever is smaller, where r is the recombination value and m(1) and m(2) are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.     

Linkage Disequilibrium in Natural and Experimental Populations of Drosophila Melanogaster

We have studied linkage disequilibrium in Drosophila melanogaster in two samples from a wild population and in four large laboratory populations derived from the wild samples. We have assayed four polymorphic enzyme loci, fairly closely linked in the third chromosome: Sod Est-6, Pgm, and Odh. The assay method used allows us to identify the allele associations separately in each of the two homologous chromosomes from each male sampled. We have detected significant linkage disequilibrium between two loci in 16.7% of the cases in the wild samples and in 27.8% of the cases in the experimental populations, considerably more than would be expected by chance alone. We have also found three-locus disequilibria in more instances than would be expected by chance. Some disequilibria present in the wild samples disappear in the experimental populations derived from them, but new ones appear over the generations. The effective population sizes required to generate the observed disequilibria by randomness range from 40 to more than 60,000 individuals in the natural population, depending on which locus pair is considered, and from 100 to more than 60,000 in the experimental populations. These population sizes are unrealistic; the fact that different locus-pairs yield disparate estimates within the same population argues against the likelihood that the disequilibria may have arisen as a consequence of population bottlenecks. Migration, or population mixing, cannot be excluded as the process generating the disequilibria in the wild samples, but can in the experimental populations. We conclude that linkage disequilibrium in these populations is most likely due to natural selection acting on the allozymes, or on loci very tightly linked to them.     

Hill–Robertson interference maintained by Red Queen dynamics favours the evolution of sex

Although it is well established theoretically that selective interference among mutations (Hill–Robertson interference) favours meiotic recombination, genomewide mean rates of mutation and strengths of selection appear too low to support this as the mechanism favouring recombination in nature. A possible solution to this discrepancy between theory and observation is that selection is at least intermittently very strong due to the antagonistic coevolution between a host and its parasites. The Red Queen theory posits that such coevolution generates fitness epistasis among loci, which generates negative linkage disequilibrium among beneficial mutations, which in turn favours recombination. This theory has received only limited support. However, Red Queen dynamics without epistasis may provide the ecological conditions that maintain strong and frequent selective interference in finite populations that indirectly selects for recombination. This hypothesis is developed here through the simulation of Red Queen dynamics. This approach required the development of a method to calculate the exact frequencies of multilocus haplotypes after recombination. Simulations show that recombination is favoured by the moderately weak selection of many loci involved in the interaction between a host and its parasites, which results in substitution rates that are compatible with empirical estimates. The model also reproduces the previously reported rapid increase in the rate of outcrossing in Caenorhabditis elegans coevolving with a bacterial pathogen.