Selection on recombination in a multi-locus system

The model of Wills and Miller (1976) for selection on recombination rates in finite populations was studied by means of a computer model involving 80 selected loci and a linked or unlinked modifier gene affecting the map length occupied by the selected loci. The selected loci were subject to heterozygote advantage, and multiplicative fitness interactions between loci were assumed. In all cases studied, selection for reduction in recombination out-weighed any selection for increased recombination that may have been present.     

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.     

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.     

Selection, Hitchhiking and Disequilibrium Analysis at Three Linked Loci with Application to Hla Data

The HLA system has been extensively studied from an evolutionary perspective. Although it is clear that selection has acted on the genes in the HLA complex, the nature of this selection has yet to be fully clarified. A study of constrained disequilibrium values is presented that is applicable to HLA and other less polymorphic systems with three or more linked loci, with the purpose of identifying selection events. The method uses the fact that three locus systems impose additional constraints on the range of possible disequilibrium values for any pair of loci. We have thus examined the behavior of the normalized pairwise disequilibrium measures using two locus (D'), and also three locus (D"), constraints on pairwise disequilibria in a three locus system when one of the three loci is under positive selection. The difference between these measures, delta = magnitude of D' - magnitude of D", has a distribution for the two unselected loci differing from that for the selected locus with either of the unselected loci (the hallmark is a high positive value of delta for the two unselected loci). An examination of genetic drift indicates that positive delta values are unlikely to be found in human populations in the absence of selection when recombination is greater than about 0.1%. This measure can thus provide insight into which allele of several linked loci might have been subject to selection. Application of this method to HLA haplotypes from a large French population study (Provinces Francaise) identifies selected alleles on particular haplotypes. Application of a complementary method, disequilibrium pattern analysis also confirms the action of selection on these haplotypes.     

Selection, Generalized Transmission and the Evolution of Modifier Genes. I. the Reduction Principle

Modifier gene models are used to explore the evolution of features of organisms, such as the genetic system, that are not directly involved in the determination of fitness. Recent work has shown that a general "reduction principle" holds in models of selectively neutral modifiers of recombination, mutation, and migration. Here we present a framework for models of modifier genes that shows these reduction results to be part of a more general theory, for which recombination and mutation are special cases. The deterministic forces that affect the genetic composition of a population can be partitioned into two categories: selection and transmission. Selection includes differential viabilities, fertilities, and mating success. Imperfect transmission occurs as a result of such phenomena as recombination, mutation and migration, meiosis, gene conversion, and meiotic drive. Selectively neutral modifier genes affect transmission, and a neutral modifier gene can evolve only by generating association with selected genes whose transmission it affects. We show that, in randomly mating populations at equilibrium, imperfect transmission of selected genes allows a variance in their marginal fitnesses to be maintained. This variance in the marginal fitnesses of selected genes is what drives the evolution of neutral modifier genes. Populations with a variance in marginal fitnesses at equilibrium are always subject to invasion by modifier genes that bring about perfect transmission of the selected genes. It is also found, within certain constraints, that for modifier genes producing what we call "linear variation" in the transmission processes, a new modifier allele can invade a population at equilibrium if it reduces the level of imperfect transmission acting on the selected genes, and will be expelled if it increases the level of imperfect transmission. Moreover, the strength of the induced selection on the modifier gene is shown to range up to the order of the departure of the genetic system from perfect transmission.     

Self-fertilization and the evolution of recombination

In this article, we study the effect of self-fertilization on the evolution of a modifier allele that alters the recombination rate between two selected loci. We consider two different life cycles: under gametophytic selfing, a given proportion of fertilizations involves gametes produced by the same haploid individual, while under sporophytic selfing, a proportion of fertilizations involves gametes produced by the same diploid individual. Under both life cycles, we derive approximations for the change in frequency of the recombination modifier when selection is weak relative to recombination, so that the population reaches a state of quasi-linkage equilibrium. We find that gametophytic selfing increases the range of epistasis under which increased recombination is favored; however, this effect is substantial only for high selfing rates. Moreover, gametophytic selfing affects the relative influence of different components of epistasis (additive x additive, additive x dominance, dominance x dominance) on the evolution of the modifier. Sporophytic selfing has much stronger effects: even a small selfing rate greatly increases the parameter range under which recombination is favored, when there is negative dominance x dominance epistasis. This effect is due to the fact that selfing generates a correlation in homozygosity at linked loci, which is reduced by recombination.     

Selection on recombination in clines

Computer runs have been done to examine Slatkin's (1975) model for selection on recombination rates in linear sets of populations with environmental changes affecting two loci. In order to determine whether the suggested selection pressures on recombination do, in fact, exist, we follow the changes in frequency at a third locus that is polymorphic for alleles affecting the recombination rate between the two selected loci. With haploid or diploid selection models, there can be selection for increased recombination if the parameter values are chosen suitably, but changes in parameter values often lead to changes in the direction of selection, so that decreased recombination is favored. The selection for increased recombination is usually weak, while that for decreased recombination is frequently much stronger. Weaker selection on the selected loci often leads to increasing selection for decreased recombination.     

The evolutionary advantage of fitness‐dependent recombination in diploids: A deterministic mutation–selection balance model

Recombination's omnipresence in nature is one of the most intriguing problems in evolutionary biology. The question of why recombination exhibits certain general features is no less interesting than that of why it exists at all. One such feature is recombination's fitness dependence (FD). The so far developed population genetics models have focused on the evolution of FD recombination mainly in haploids, although the empirical evidence for this phenomenon comes mostly from diploids. Using numerical analysis of modifier models for infinite panmictic populations, we show here that FD recombination can be evolutionarily advantageous in diploids subjected to purifying selection. We ascribe this advantage to the differential rate of disruption of lower‐ versus higher‐fitness genotypes, which can be manifested in selected systems with at least three loci. We also show that if the modifier is linked to such selected system, it can additionally benefit from modifying this linkage in a fitness‐dependent manner. The revealed evolutionary advantage of FD recombination appeared robust to crossover interference within the selected system, either positive or negative. Remarkably, FD recombination was often favored in situations where any constant nonzero recombination was evolutionarily disfavored, implying a relaxation of the rather strict constraints on major parameters (e.g., selection intensity and epistasis) required for the evolutionary advantage of nonzero recombination formulated by classical models.     

The effect of hitch-hiking on genes linked to a balanced polymorphism in a subdivided population

The effect of multi-allelic balancing selection on nucleotide diversity at linked neutral sites was investigated by simulations of subdivided populations. The motivation is to understand the behaviour of self-recognition systems such as the MHC and plant self-incompatibility. For neutral sites, two types of subdivision are present: (1) into demes (connected by migration), and (2) into classes defined by different functional alleles at the selected locus (connected by recombination). Previous theoretical studies of each type of subdivision separately have shown that each increases diversity, and decreases the relative frequencies of low-frequency variants, at neutral sites or loci. We show here that the two types of subdivision act non-additively when sampling is at the whole population level, and that subdivision produces some non-intuitive results. For instance, in highly subdivided populations, genetic diversity at neutral sites may decrease with tighter linkage to a selected locus or site. Another conclusion is that, if there is population subdivision, balancing selection leads to decreased expected FST values for neutral sites linked to the selected locus. Finally, we show that the ability to detect balancing selection by its effects on linked variation, using tests such as Tajima's D, is reduced when genes in a subdivided population are sampled from the total population, rather than within demes.     

Identification of a locus under complex positive selection in Drosophila simulans by haplotype mapping and composite-likelihood estimation

The recent action of positive selection is expected to influence patterns of intraspecific DNA sequence variation in chromosomal regions linked to the selected locus. These effects include decreased polymorphism, increased linkage disequilibrium, and an increased frequency of derived variants. These effects are all expected to dissipate with distance from the selected locus due to recombination. Therefore, in regions of high recombination, it should be possible to localize a target of selection to a relatively small interval. Previously described patterns of intraspecific variation in three tandemly arranged, testes-expressed genes (janusA, janusB, and ocnus) in Drosophila simulans included all three of these features. Here we expand the original sample and also survey nucleotide polymorphism at three neighboring loci. On the basis of recombination events between derived and ancestral alleles, we localize the target of selection to a 1.5-kb region surrounding janusB. A composite-likelihood-ratio test based on the spatial distribution and frequency of derived polymorphic variants corroborates this result and provides an estimate of the strength of selection. However, the data are difficult to reconcile with the simplest model of positive selection, whereas a new composite-likelihood method suggests that the data are better described by a model in which the selected allele has not yet gone to fixation.     

The Hill-Robertson effect and the evolution of recombination

In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This "Hill-Robertson effect" generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles.     

Molecular evolution near a two-locus balanced polymorphism

Balancing selection at one locus can increase the amount of selectively neutral variation within neighboring genomic regions. Discrete phenotypic polymorphisms studied in natural populations are frequently determined by sets of interacting genes instead of alternative alleles at single loci. We extend coalescent theory to investigate balancing selection on combinations of linked genes. We find that variation at neutral sites is increased across a much larger genomic region relative to the single-locus models: the entire region lying between the two loci in balanced combination is affected to some degree. Epistatic selection maintains these high levels of neutral variation because it directly opposes the homogenizing effect of recombination. The results of the theory are discussed in relation to published gene sequence data, primarily from Drosophila.     

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.     

Short- and long-term benefits and detriments to recombination under antagonistic coevolution

We explored the evolution of recombination under antagonistic coevolution, concentrating on the equilibrium frequencies of modifier alleles causing recombination in initially nonrecombining populations. We found that the equilibrium level of recombination in the host depended not only on parasite virulence, but also on the strength of the modifier allele, and on whether or not the modifier was physically linked to the parasite interaction loci. Nonetheless, the maximum level of recombination for linked loci at equilibrium was about 0.3 (60% of free recombination) for interactions with highly virulent parasites; the level decreased for unlinked modifiers, and for lower levels of parasite virulence. We conclude that recombination spreads because it provides a combination of an immediate (next-generation) fitness benefit and a delayed (two or more generations) increase in the rate of response to directional selection. The relative impact of these two mechanisms depends on the virulence of parasites early in the spread of the modifier, but a trade-off between the two dictates the equilibrium modifier frequency for all nonzero virulences that we examined. In addition, population mean fitness was higher in populations at intermediate equilibria than populations fixed for free recombination or no recombination. The difference, however, was not enough on its own to overcome the two-fold cost of producing males.     

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.     

Impact of polymorphic transposable elements on linkage disequilibrium along chromosomes

Recombination and selection drive the extent of linkage disequilibrium (LD) among loci and therefore affect the reshuffling of adaptive genetic variation. However, it is poorly known to what extent the enrichment of transposable elements (TEs) in recombinationally‐inert regions reflects their inefficient removal by purifying selection and whether the presence of polymorphic TEs can modify the local recombination rate. In this study, we investigate how TEs and recombination interact at fine scale along chromosomes and possibly support linked selection in natural populations. Whole‐genome sequencing data of 304 individuals from nearby alpine populations of Arabis alpina were used to show that the density of polymorphic TEs is specifically correlated with local LD along chromosomes. Consistent with TEs modifying recombination, the characterization of 28 such LD blocks of up to 5.5 Mb in length revealed strong evidence of selective sweeps at a few loci through either site frequency spectrum or haplotype structure. A majority of these blocks were enriched in genes related to ecologically relevant functions such as responses to cold, salt stress or photoperiodism. In particular, the S‐locus (i.e., supergene responsible for strict outcrossing) was identified in a LD block with high levels of polymorphic TEs and evidence of selection. Another such LD block was enriched in cold‐responding genes and presented evidence of adaptive loci related to photoperiodism and flowering being increasingly linked by polymorphic TEs. These results are consistent with the hypothesis that TEs modify recombination landscapes and thus interact with selection in driving blocks of linked adaptive loci in natural populations.     

Towards genetic markers in animal populations as biomonitors for human-induced environmental change

Genetic markers provide potentially sensitive indicators of changes in environmental conditions because the genetic constitution of populations is normally altered well before populations become extinct. Genetic indicators in populations include overall genetic diversity, genetic changes in traits measured at the phenotypic level, and evolution at specific loci under selection. While overall genetic diversity has rarely been successfully related to environmental conditions, genetically based changes in traits have now been linked to the presence of toxins and both local and global temperature shifts. Candidate loci for monitoring stressors are emerging from information on how specific genes influence traits, and from screens of random loci across environmental gradients. Drosophila research suggests that chromosomal regions under recent intense selection can be identified from patterns of molecular variation and a high frequency of transposable element insertions. Allele frequency changes at candidate loci have been linked to pesticides, pollutants and climate change. Nevertheless, there are challenges in interpreting allele frequencies in populations, particularly when a large number of loci control a trait and when interactions between alleles influence trait expression. To meet these challenges, population samples should be collected for longitudinal studies, and experimental programmes should be undertaken to link variation at candidate genes to ecological processes.     

The advantages of segregation and the evolution of sex

In diploids, sexual reproduction promotes both the segregation of alleles at the same locus and the recombination of alleles at different loci. This article is the first to investigate the possibility that sex might have evolved and been maintained to promote segregation, using a model that incorporates both a general selection regime and modifier alleles that alter an individual's allocation to sexual vs. asexual reproduction. The fate of different modifier alleles was found to depend strongly on the strength of selection at fitness loci and on the presence of inbreeding among individuals undergoing sexual reproduction. When selection is weak and mating occurs randomly among sexually produced gametes, reductions in the occurrence of sex are favored, but the genome-wide strength of selection is extremely small. In contrast, when selection is weak and some inbreeding occurs among gametes, increased allocation to sexual reproduction is expected as long as deleterious mutations are partially recessive and/or beneficial mutations are partially dominant. Under strong selection, the conditions under which increased allocation to sex evolves are reversed. Because deleterious mutations are typically considered to be partially recessive and weakly selected and because most populations exhibit some degree of inbreeding, this model predicts that higher frequencies of sex would evolve and be maintained as a consequence of the effects of segregation. Even with low levels of inbreeding, selection is stronger on a modifier that promotes segregation than on a modifier that promotes recombination, suggesting that the benefits of segregation are more likely than the benefits of recombination to have driven the evolution of sexual reproduction in diploids.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

A chip off the old block: a model for the evolution of genomic imprinting via selection for parental similarity

A consequence of genomic imprinting is that offspring are more similar to one parent than to the other, depending on which parent's genes are inactivated in those offspring. We hypothesize that genomic imprinting may have evolved at some loci because of selection to be similar to the parent of one sex or the other. We construct and analyze an evolutionary-genetic model of a two-locus two-deme system, in which one locus codes for a character under local selection and the second locus is a potential cis-acting modifier of imprinting. A proportion of males only migrate between demes every generation, and prebreeding males are less fit, on average, than females. We examine the conditions in which an imprinting modifier allele can invade a population fixed for a nonimprinting modifier allele and vice versa. We find that the conditions under which the imprinting modifier invades are biologically restrictive (high migration rates and high values of recombination between the two loci) and thus this hypothesis is unlikely to explain the evolution of imprinting. Our modeling also shows that, as with several other hypotheses, polymorphism of imprinting status may evolve under certain circumstances, a feature not predicted by verbal accounts.