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.     

The red queen coupled with directional selection favours the evolution of sex

Why sexual reproduction has evolved to be such a widespread mode of reproduction remains a major question in evolutionary biology. Although previous studies have shown that increased sex and recombination can evolve in the presence of host-parasite interactions (the 'Red Queen hypothesis' for sex), many of these studies have assumed that multiple loci mediate infection vs. resistance. Data suggest, however, that a major locus is typically involved in antigen presentation and recognition. Here, we explore a model where only one locus mediates host-parasite interactions, but a second locus is subject to directional selection. Even though the effects of these genes on fitness are independent, we show that increased rates of sex and recombination are favoured at a modifier gene that alters the rate of genetic mixing. This result occurs because of selective interference in finite populations (the 'Hill-Robertson effect'), which also favours sex. These results suggest that the Red Queen hypothesis may help to explain the evolution of sex by contributing a form of persistent selection, which interferes with directional selection at other loci and thereby favours sex and recombination.     

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.     

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.     

The dynamics of the rec-system in variable environments: haploid selection in a cyclical two-state environment

The dynamics of a 3-locus infinite population with non-overlapping generations and panmixia was studied. Loci are di-allelic: two loci affect fitness under cyclical symmetric haploid selection while the third one is a modifier of recombination (rec-modifier). Selection favors alternatively haplotypes AB and ab or Ab and aB. It has been proven that under alternating selection (when period of selection consists of two generations) a dominant suppressor of recombination is displaced and the allele for non-zero recombination becomes fixed within the population. For populations with inversion heterozygosity within the selective system (i.e. with zero recombination in heterozygote for rec-modifier and non-zero for homozygotes) fixation of one of the alleles (depending on the initial point) at the rec-modifier locus is predicted. For other values of recombination parameters, the behavior of the system was studied numerically. A full bifurcation picture of parameters was obtained. Many of the results related to the case of a two-generation period hold also in the case of longer period lengths.     

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.     

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.     

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.     

Genetic crosses in the apicomplexan parasite Cryptosporidium parvum define recombination parameters

Recombinant progeny lines of Cryptosporidium parvum were generated by coinfecting immunosuppressed mice with two genetically distinct isolates of C. parvum. Progeny lines were obtained from a cross of parental lines MD x TU114 through targeted propagation in mice of progeny oocysts originating from populations lacking one parental allele at one or more loci. For each infection lineage this process was repeated until only a single allele remained for each marker, indicating that the progeny line was clonal. To study genetic recombination, 16 progeny clones were genotyped at 40 loci located on each of the eight chromosomes. The inheritance of parental alleles was significantly skewed towards the more virulent parent isolate MD. A contiguous 476 kb segment of chromosome V displayed MD allele in all progeny recovered, while MD and TU114 alleles were detected at other loci throughout the genome. The absence of alleles from one parental isolate in this chromosomal region may indicate phenotypic selection for the MD allele during the generation of these lines. A range for the meiotic crossover frequency was determined on the basis of 40 markers and the number of meioses estimated to have taken place during the crossing experiment. C. parvum exhibits a high rate of recombination commensurate with other Apicomplexa.     

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.     

Contrasting Roles of Interallelic Recombination at the Hla-a and Hla-B Loci

A statistical study of DNA sequences of alleles at the highly polymorphic class I MHC loci of humans, HLA-A and HLA-B, showed evidence of both large-scale recombination events (involving recombination of exons 1-2 of one allele with exons 3-8 of another) and small-scale recombination events (involving apparent exchange of short DNA segments). The latter events occurred disproportionately in the region of the gene encoding the antigen recognition site (ARS) of the class I molecule. Furthermore, they involved the ARS codons which are under the strongest selection favoring allelic diversity at the amino acid level. Thus, the frequency of recombinant alleles appears to have been increased by some form of balancing selection (such as overdominant selection) favoring heterozygosity in the ARS. These analyses also revealed a striking difference between the A and B loci. Recombination events appear to have occurred about twice as frequently at the B locus, and recombinants at the B locus were significantly more likely to affect polymorphic sites in the ARS. At the A locus, there are well-defined allelic lineages that have persisted since prior to the human-chimpanzee divergence; but at the B locus, there is no evidence for such long-lasting allelic lineages. Thus, relatively frequent interallelic recombination has apparently been a feature of the long-term evolution of the B locus but not of the A locus.     

Genetic load in sexual and asexual diploids: segregation, dominance and genetic drift

In diploid organisms, sexual reproduction rearranges allelic combinations between loci (recombination) as well as within loci (segregation). Several studies have analyzed the effect of segregation on the genetic load due to recurrent deleterious mutations, but considered infinite populations, thus neglecting the effects of genetic drift. Here, we use single-locus models to explore the combined effects of segregation, selection, and drift. We find that, for partly recessive deleterious alleles, segregation affects both the deterministic component of the change in allele frequencies and the stochastic component due to drift. As a result, we find that the mutation load may be far greater in asexuals than in sexuals in finite and/or subdivided populations. In finite populations, this effect arises primarily because, in the absence of segregation, heterozygotes may reach high frequencies due to drift, while homozygotes are still efficiently selected against; this is not possible with segregation, as matings between heterozygotes constantly produce new homozygotes. If deleterious alleles are partly, but not fully recessive, this causes an excess load in asexuals at intermediate population sizes. In subdivided populations without extinction, drift mostly occurs locally, which reduces the efficiency of selection in both sexuals and asexuals, but does not lead to global fixation. Yet, local drift is stronger in asexuals than in sexuals, leading to a higher mutation load in asexuals. In metapopulations with turnover, global drift becomes again important, leading to similar results as in finite, unstructured populations. Overall, the mutation load that arises through the absence of segregation in asexuals may greatly exceed previous predictions that ignored genetic drift.     

Segregation and the evolution of sex under overdominant selection

The segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.     

Fixation probability in a two-locus model by the ancestral recombination-selection graph

We use the ancestral influence graph (AIG) for a two-locus, two-allele selection model in the limit of a large population size to obtain an analytic approximation for the probability of ultimate fixation of a single mutant allele A. We assume that this new mutant is introduced at a given locus into a finite population in which a previous mutant allele B is already segregating with a wild type at another linked locus. We deduce that the fixation probability increases as the recombination rate increases if allele A is either in positive epistatic interaction with B and allele B is beneficial or in no epistatic interaction with B and then allele A itself is beneficial. This holds at least as long as the recombination fraction and the selection intensity are small enough and the population size is large enough. In particular this confirms the Hill-Robertson effect, which predicts that recombination renders more likely the ultimate fixation of beneficial mutants at different loci in a population in the presence of random genetic drift even in the absence of epistasis. More importantly, we show that this is true from weak negative epistasis to positive epistasis, at least under weak selection. In the case of deleterious mutants, the fixation probability decreases as the recombination rate increases. This supports Muller's ratchet mechanism to explain the accumulation of deleterious mutants in a population lacking recombination.     

The effect of intragenic recombination on the number of alleles in a finite population

A two-site infinite allele model is constructed to study the effect of intragenic recombination on the number of neutral alleles and the distribution of their frequencies in a finite population. The results of theory and Monte Carlo simulation of the two-site model demonstrate that intragenic recombination significantly increases the mean and variance of the number of alleles when the rates of mutation and recombination are as large as the reciprocal of the population size. Data from natural populations indicate that this may be a significant process in generating variation and determining its distribution.     

Sexual antagonism and meiotic drive cause stable linkage disequilibrium and favour reduced recombination on the X chromosome

Sexual antagonism and meiotic drive are sex‐specific evolutionary forces with the potential to shape genomic architecture. Previous theory has found that pairing two sexually antagonistic loci or combining sexual antagonism with meiotic drive at linked autosomal loci augments genetic variation, produces stable linkage disequilibrium (LD) and favours reduced recombination. However, the influence of these two forces has not been examined on the X chromosome, which is thought to be enriched for sexual antagonism and meiotic drive. We investigate the evolution of the X chromosome under both sexual antagonism and meiotic drive with two models: in one, both loci experience sexual antagonism; in the other, we pair a meiotic drive locus with a sexually antagonistic locus. We find that LD arises between the two loci in both models, even when the two loci freely recombine in females and that driving haplotypes will be enriched for male‐beneficial alleles, further skewing sex ratios in these populations. We introduce a new measure of LD, , which accounts for population allele frequencies and is appropriate for instances where these are sex specific. Both models demonstrate that natural selection favours modifiers that reduce the recombination rate. These results inform observed patterns of congealment found on driving X chromosomes and have implications for patterns of natural variation and the evolution of recombination rates on the X chromosome.     

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.     

Recombination can evolve in large finite populations given selection on sufficient loci

It is well known that an allele causing increased recombination is expected to proliferate as a result of genetic drift in a finite population undergoing selection, without requiring other mechanisms. This is supported by recent simulations apparently demonstrating that, in small populations, drift is more important than epistasis in increasing recombination, with this effect disappearing in larger finite populations. However, recent experimental evidence finds a greater advantage for recombination in larger populations. These results are reconciled by demonstrating through simulation without epistasis that for m loci recombination has an appreciable selective advantage over a range of population sizes (am, bm). bm increases steadily with m while am remains fairly static. Thus, however large the finite population, if selection acts on sufficiently many loci, an allele that increases recombination is selected for. We show that as selection acts on our finite population, recombination increases the variance in expected log fitness, causing indirect selection on a recombination-modifying locus. This effect is enhanced in those populations with more loci because the variance in phenotypic fitnesses in relation to the possible range will be smaller. Thus fixation of a particular haplotype is less likely to occur, increasing the advantage of recombination.     

Marker-assisted introgression using non-unique marker alleles I: selection on the presence of linked marker alleles

This paper investigates marker-assisted introgression of a major gene into an outbred line, where identification of the introgressed gene is incomplete because marker alleles are not unique to the base populations (the same marker allele can occur in both donor and recipient population). Those markers are used to identify the introgressed allele as well as the background genotype. The effect of using those markers, as if they were completely informative on the retention of the introgressed allele, was examined over five generations of backcrossing by using a single marker or a marker bracket for different starting frequencies of the marker alleles. Results were calculated by using both a deterministic approach, where selection is only for the desired allele, and by a stochastic approach, where selection is also on background genotype. When marker allele frequencies in donor and recipient population diverged from 1 and 0 (using a diallelic marker), the ability to retain the desired allele rapidly declined. Marker brackets performed notably better than single markers. If selection on background marker genotype was applied, the desired allele could be lost even more quickly than expected at random because the chance that the allele, which is common in the donor line, is present on the locus identifying the introgressed allele and is surrounded by alleles common in the recipient line on the background marker loci, will descend from the donor line (double recombination has taken place), is a lot smaller than the chance that this allele will stem from the recipient line (in which the allele occurs in low frequency). Marker brackets again performed better. Preselection against marker homozygotes (producing uninformative gametes) gave a slightly better retention of the introgressed allele.     

HLA class II linkage disequilibrium and haplotype evolution in the Cayapa Indians of Ecuador.

DNA-based typing of the HLA class II loci in a sample of the Cayapa Indians of Ecuador reveals several lines of evidence that selection has operated to maintain and to diversify the existing level of polymorphism in the class II region. As has been noticed for other Native American groups, the overall level of polymorphism at the DRB1, DQA1, DQB1, and DPB1 loci is reduced relative to that found in other human populations. Nonetheless, the relative evenness in the distribution of allele frequencies at each of the four loci points to the role of balancing selection in the maintenance of the polymorphism. The DQA1 and DQB1 loci, in particular, have near-maximum departures from the neutrality model, which suggests that balancing selection has been especially strong in these cases. Several novel DQA1-DQB1 haplotypes and the discovery of a new DRB1 allele demonstrate an evolutionary tendency favoring the diversification of class II alleles and haplotypes. The recombination interval between the centromeric DPB1 locus and the other class II loci will, in the absence of other forces such as selection, reduce disequilibrium across this region. However, nearly all common alleles were found to be part of DR-DP haplotypes in strong disequilibrium, consistent with the recent action of selection acting on these haplotypes in the Cayapa.