Selection for recombination in small populations

Stochastic interplay between mutation and recombination during the acquisition of drug resistance mutations in human immunodeficiency virus type 1

The emergence of drug resistance mutations in human immunodeficiency virus (HIV) has been a major setback in the treatment of infected patients. Besides the high mutation rate, recombination has been conjectured to have an important impact on the emergence of drug resistance. Population genetic theory suggests that in populations limited in size recombination may facilitate the acquisition of beneficial mutations. The viral population in an infected patient may indeed represent such a population limited in size, since current estimates of the effective population size range from 500 to 10(5). To address the effects of limited population size, we therefore expand a previously described deterministic population genetic model of HIV replication by incorporating the stochastic processes that occur in finite populations of infected cells. Using parameter estimates from the literature, we simulate the evolution of drug-resistant viral strains. The simulations show that recombination has only a minor effect on the rate of acquisition of drug resistance mutations in populations with effective population sizes as small as 1,000, since in these populations, viral strains typically fix beneficial mutations sequentially. However, for intermediate effective population sizes (10(4) to 10(5)), recombination can accelerate the evolution of drug resistance by up to 25%. Furthermore, a reduction in population size caused by drug therapy can be overcome by a higher viral mutation rate, leading to a faster evolution of drug resistance.

Analysis of evolution through competitive selection

Recent studies of in vitro evolution of DNA via protein binding indicate that the evolution behavior is qualitatively different in different parameter regimes. I here present a general theory that is valid for a wide range of parameters, and which reproduces and extends previous results. Specifically, the mean-field theory of a general translation-invariant model can be reduced to the basic diffusion equation with a dynamic boundary condition. The simple analytical form yields both quantitatively accurate predictions and valuable insight into the principles involved.

Recombination and speciation

Speciation can be viewed as the evolution of restrictions on the freedom of genetic recombination: new combinations of alleles can be generated within species, but alleles from different species cannot be brought together. Recently, there has been increasing realization that the role of chromosomal rearrangements in speciation might be primarily a result of their influence on recombination. I argue that ideas about the role of recombination in speciation should be considered in the context of the variability of recombination rates and patterns more generally and that genic as well as chromosomal causes of restricted recombination should be considered. I review patterns of variation in recombination rates and theoretical progress in understanding the conditions that favour increased or decreased rates. Although progress has been made in understanding conditions that alter overall rates of recombination, widespread variation in patterns of recombination remains largely unexplained. I consider three models for the role of locally restricted recombination in speciation and the evidence currently supporting them.

Quantitative trait loci and the study of plant domestication

Plant domestication ranks as one of the most important developments in human history, giving human populations the potential to harness unprecedented quantities of the earth's resources. But domestication has also played a more subtle historical role as the foundation of the modern study of evolution and adaptation. Until recently, however, researchers interested in domestication were limited to studying phenotypic changes or the genetics of simple Mendelian traits, when often the characters of most interest--fruit size, yield, height, flowering time, etc.--are quantitative in nature. The goals of this paper are to review some of the recent work on the quantitative genetics of plant domestication, identify some of the common trends found in this literature, and offer some novel interpretations of the data that is currently available.

Adaptation in sexuals vs. asexuals: clonal interference and the Fisher-Muller model

Fisher and Muller's theory that recombination speeds adaptation by eliminating competition among beneficial mutations has proved a popular explanation for the advantage of sex. Recent theoretical studies have attempted to quantify the speed of adaptation under the Fisher-Muller model, partly in an attempt to understand the role of "clonal interference" in microbial experimental evolution. We reexamine adaptation in sexuals vs. asexuals, using a model of DNA sequence evolution. In this model, a modest number of sites can mutate to beneficial alleles and the fitness effects of these mutations are unequal. We study (1) transition probabilities to different beneficial mutations; (2) waiting times to the first and the last substitutions of beneficial mutations; and (3) trajectories of mean fitness through time. We find that some of these statistics are surprisingly similar between sexuals and asexuals. These results highlight the importance of the choice of substitution model in assessing the Fisher-Muller advantage of sex.

The evolution of plastic recombination

Empirical data suggest that recombination rates may change in response to stress. To study the evolution of plastic recombination, we develop a modifier model using the same theoretical framework used to study conventional (nonplastic) modifiers, thus allowing direct comparison. We examine the evolution of plastic recombination in both haploid and diploid systems. In haploids, a plastic modifier spreads by forming associations with selectively favored alleles. Relative to nonplastic effects, selection on the plastic effects of a modifier is both much stronger and less sensitive to the specifics of the selection regime (e.g., epistasis). In contrast, the evolution of plastic recombination in diploids is much more restricted. Selection on plasticity requires the ability to detect DNA damage or cis-trans effects as may occur through maternal effects on fitness.

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.

Persistence and loss of meiotic recombination hotspots

The contradiction between the long-term persistence of the chromosomal hotspots that initiate meiotic recombination and the self-destructive mechanism by which they act strongly suggests that our understanding of recombination is incomplete. This "hotspot paradox" has been reinforced by the finding that biased gene conversion also removes active hotspots from human sperm. To investigate the requirements for hotspot persistence, we developed a detailed computer simulation model of their activity and its evolutionary consequences. With this model, unopposed hotspot activity could drive strong hotspots from 50% representation to extinction within 70 generations. Although the crossing over that hotspots cause can increase population fitness, this benefit was always too small to slow the loss of hotspots. Hotspots could not be maintained by plausible rates of de novo mutation, nor by crossover interference, which alters the frequency and/or spacing of crossovers. Competition among hotspots for activity-limiting factors also did not prevent their extinction, although the rate of hotspot loss was slowed. Key factors were the probability that the initiating hotspot allele is destroyed and the nonmeiotic contributions hotspots make to fitness. Experimental investigation of these deserves high priority, because until the paradox is resolved all components of the mechanism are open to doubt.

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.

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.

Recombination dramatically speeds up evolution of finite populations

We study the role of recombination, in the form of bacterial transformation, in speeding up Darwinian evolution. This is done by adding a new process to a previously studied Markov model of evolution on a smooth fitness landscape; this new process allows alleles to be exchanged with those in the surrounding medium. Our results, both numerical and analytic, indicate that, for a wide range of intermediate population sizes, recombination dramatically speeds up the rate of evolutionary advance.

Comparative genome sequencing of Drosophila pseudoobscura: chromosomal, gene, and cis-element evolution

We have sequenced the genome of a second Drosophila species, Drosophila pseudoobscura, and compared this to the genome sequence of Drosophila melanogaster, a primary model organism. Throughout evolution the vast majority of Drosophila genes have remained on the same chromosome arm, but within each arm gene order has been extensively reshuffled, leading to a minimum of 921 syntenic blocks shared between the species. A repetitive sequence is found in the D. pseudoobscura genome at many junctions between adjacent syntenic blocks. Analysis of this novel repetitive element family suggests that recombination between offset elements may have given rise to many paracentric inversions, thereby contributing to the shuffling of gene order in the D. pseudoobscura lineage. Based on sequence similarity and synteny, 10,516 putative orthologs have been identified as a core gene set conserved over 25-55 million years (Myr) since the pseudoobscura/melanogaster divergence. Genes expressed in the testes had higher amino acid sequence divergence than the genome-wide average, consistent with the rapid evolution of sex-specific proteins. Cis-regulatory sequences are more conserved than random and nearby sequences between the species--but the difference is slight, suggesting that the evolution of cis-regulatory elements is flexible. Overall, a pattern of repeat-mediated chromosomal rearrangement, and high coadaptation of both male genes and cis-regulatory sequences emerges as important themes of genome divergence between these species of Drosophila.

Drift increases the advantage of sex in RNA bacteriophage Phi6

The pervasiveness of sex and recombination remains one of the most enigmatic problems in evolutionary biology. According to many theoretical models, recombination can increase the rate of adaptation by restoring genetic variation. However, the potential for genetic drift to generate conditions that produce this outcome has yet to be studied experimentally. We have designed and performed an experiment that reveals the effects of drift on existing genetic variation by minimizing the influence of variation on beneficial mutation rate. Our experiment was conducted in populations of RNA bacteriophage Phi6 initiated from a common source population at varying bottleneck sizes. The segmented genome of this virus results in genetic exchange between viruses that co-infect the same host cell. In response to selection for growth in a high-temperature environment, sexual lines outperformed their asexual counterparts on average. The advantage of sex attenuated with increasing effective population size, implying that the rate of adaptation was limited by clonal interference among segments caused by drift. This is the first empirical evidence that the advantage of sex during adaptation increases with the intensity of drift.

What's so hot about recombination hotspots?

Recombination is a nearly ubituitous feature of genomes; where and when it occurs can provide insights about its evolution and can affect our ability to identify genes that cause disease

Analytical study of the effect of recombination on evolution via DNA shuffling

DNA shuffling is an evolutionary protocol wherein cycles of selection, recombination, mutation, and amplification are employed to evolve proteins and DNA sequences. Experiments have shown its superiority to traditional protocols which do not employ recombination. Motivated by DNA shuffling, we investigate a multilocus evolutionary model that incorporates selection, recombination, and point mutations. Due to simplicity of the model, for the case of an infinite population we can obtain a full analytical treatment of both its dynamical and equilibrium properties, and study the benefit of recombination explicitly and quantitatively. We also briefly discuss finite-population size corrections.

The evolution of recombination under domestication: a test of two hypotheses

The successful domestication of wild plants has been one of the most important human accomplishments of the last 10,000 yr. Though our empirical knowledge of the genetic mechanisms of plant domestication is still relatively limited, there exists a large body of theory that offers a host of hypotheses on the genetics of domestication. Two of these that have not been addressed concern the role of recombination in the process of domestication. The first predicts an increase in recombination rate through domestication, while the second argues that recombination rate should serve as a preadaptation to domestication. This study makes use of data on chiasma frequencies available from almost a century of plant cytogenetical literature to test these two hypotheses. The results support the hypothesis that domestication selects for an increase in recombination, and in rejecting the preadaptation hypothesis, they suggest directions for future research into the possibility of preadaptation to domestication.

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.

Rates of deleterious mutation and the evolution of sex in Caenorhabditis

A variety of models propose that the accumulation of deleterious mutations plays an important role in the evolution of breeding systems. These models make predictions regarding the relative rates of protein evolution and deleterious mutation in taxa with contrasting modes of reproduction. Here we compare available coding sequences from one obligately outcrossing and two primarily selfing species of Caenorhabditis to explore the potential for mutational models to explain the evolution of breeding system in this clade. If deleterious mutations interact synergistically, the mutational deterministic hypothesis predicts that a high genomic deleterious mutation rate (U) will offset the reproductive disadvantage of outcrossing relative to asexual or selfing reproduction. Therefore, C. elegans and C. briggsae (both largely selfing) should both exhibit lower rates of deleterious mutation than the obligately outcrossing relative C. remanei. Using a comparative approach, we estimate U to be equivalent (and < 1) among all three related species. Stochastic mutational models, Muller's ratchet and Hill-Robertson interference, are expected to cause reductions in the effective population size in species that rarely outcross, thereby allowing deleterious mutations to accumulate at an elevated rate. We find only limited support for more rapid molecular evolution in selfing lineages. Overall, our analyses indicate that the evolution of breeding system in this group is unlikely to be explained solely by available mutational models.

Evolutionary genomics of inversions in Drosophila pseudoobscura: evidence for epistasis

Drosophila pseudoobscura harbors a rich polymorphism for paracentric inversions on the third chromosome, and the clines in the inversion frequencies across the southwestern United States indicate that strong natural selection operates on them. Isogenic inversion strains were made from isofemale lines collected from four localities, and eight molecular markers were mapped on the third chromosome. Nucleotide diversity was measured for these loci and formed the basis of an evolutionary genomic analysis. The loci were differentiated among inversions. The inversions did not show significant differences among populations, however, likely the result of extensive gene flow among populations. Some loci had significant reductions in nucleotide diversity within inversions compared with interspecies divergence, suggesting that these loci are near inversion breakpoints or are near targets of directional selection. Linkage disequilibrium (LD) levels tended to decrease with distance between loci, indicating that some genetic exchange occurs among gene arrangements despite the presence of inversions. In some cases, however, adjacent genes had low levels of interlocus LD and loosely linked genes had high levels of interlocus LD, suggesting strong epistatic selection. Our results support the hypothesis that the inversions of D. pseudoobscura have emerged as suppressors of recombination to maintain positive epistatic relationships among loci within gene arrangements that developed as the species adapted to a heterogeneous environment.

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.

Liberating genetic variance through sex

Genetic variation in fitness is the fundamental prerequisite for adaptive evolutionary change. If there is no variation in survival and reproduction or if this variation has no genetic basis, then the composition of a population will not evolve over time. Consequently, the factors influencing genetic variation in fitness have received close attention from evolutionary biologists. One key factor is the mode of reproduction. Indeed, it has long been thought that sex enhances fitness variation and that this explains the ubiquity of sexual reproduction among eukaryotes. Nevertheless, theoretical studies have demonstrated that sex need not always increase genetic variation in fitness. In particular, if fitness interactions among beneficial alleles (epistasis) are positive, sex can reduce genetic variance in fitness. Empirical data have been sorely needed to settle the issue of whether sex does enhance fitness variation. A recent flurry of studies[1-4] has demonstrated that sex and recombination do dramatically increase genetic variation in fitness and consequently the rate of adaptive evolution. Interpreted in light of evolutionary theory, these studies rule out positive in these experiments epistasis as a major source of genetic associations. Further studies are needed, however, to tease apart other possible sources.

The evolution of sex dimorphism in recombination

Sex dimorphism in recombination is widespread on both sex chromosomes and autosomes. Various hypotheses have been proposed to explain these dimorphisms. Yet no theoretical model has been explored to determine how heterochiasmy--the autosomal dimorphism--could evolve. The model presented here shows three circumstances in which heterochiasmy is likely to evolve: (i) a male-female difference in haploid epistasis, (ii) a male-female difference in cis-epistasis minus trans-epistasis in diploids, or (iii) a difference in epistasis between combinations of genes inherited maternally or paternally. These results hold even if sources of linkage disequilibria besides epistasis, such as migration or Hill-Robertson interference, are considered and shed light on previous verbal models of sex dimorphism in recombination rates. Intriguingly, these results may also explain why imprinted regions on the autosomes of humans or sheep are particularly heterochiasmate.

Ecological stress and sex evolution in soil microfungi

The elucidation of the origin and maintenance of sex is a major unsolved problem in evolutionary biology. A number of hypotheses have been elaborated, but the scarcity of empirical data limits further progress. During recent years, the general inclination has changed towards pluralistic models of sex evolution, due partly to an increased diversity of studied organisms. Fungi are among the most promising organisms for testing sexual causation, as demonstrated in recent laboratory experiments. However, reconciling theory and evidence necessitates critical field observations. Here, we report new estimates of the distribution of morphologically sexual and asexual soil microfungi in nature, which indicate a remarkable trend towards increased sexuality with increasing climatic stress.

Sex releases the speed limit on evolution

Explaining the evolutionary maintenance of sex remains a key problem in evolutionary biology. One potential benefit of sex is that it may allow a more rapid adaptive response when environmental conditions change, by increasing the efficiency with which selection can fix beneficial mutations. Here I show that sex can increase the rate of adaptation in the facultatively sexual single-celled chlorophyte Chlamydomonas reinhardtii, but that the benefits of sex depend crucially on the size of the population that is adapting: sex has a marked effect in large populations but little effect in small populations. Several mechanisms have been proposed to explain the benefits of sex in a novel environment, including stochastic effects in small populations, clonal interference and epistasis between beneficial alleles. These results indicate that clonal interference is important in this system.

Experimental tests of the adaptive significance of sexual recombination

Numerous theories have been proposed to explain the advantages of sexual recombination the exchange of hereditary material between different genomes or homologous chromosomes. Many of these candidate benefits have been evaluated in controlled laboratory experiments, which, collectively, strongly indicate that sexual recombination provides important long-term advantages.

Resolving the paradox of sex and recombination

Sexual reproduction and recombination are ubiquitous. However, a large body of theoretical work has shown that these processes should only evolve under a restricted set of conditions. New studies indicate that this discrepancy might result from the fact that previous models have ignored important complexities that face natural populations, such as genetic drift and the spatial structure of populations.