Selection for recombination in small populations

Abortive meiosis in the oogenesis of parthenogenetic Daphnia pulex

Most daphnid species adopt parthenogenesis and sexual reproduction differentially in response to varied environmental cues, resulting in the production of diploid progenies in both cases. Previous studies have reportedly suggested that daphnids produce their parthenogenetic eggs via apomixis; the nuclear division of mature oocytes should be an equational division similar to somatic mitosis. However, it seems premature to conclude that this has been unequivocally established in any daphnids. Therefore, the objective of our research was to precisely reveal the process and mechanism of parthenogenetic oogenesis and maintenance of diploidy in Daphnia pulex through histology, karyology, and immunohistochemistry. We found that, when a parthenogenetic egg entered the first meiosis, division was arrested in the early first anaphase. Then, two half-bivalents, which were dismembered from each bivalent, moved back to the equatorial plate and assembled to form a diploid equatorial plate. Finally, the sister chromatids were separated and moved to opposite poles in the same manner as the second meiotic division followed by the extrusion of one extremely small daughter cell (resembling a polar body). These results suggest that parthenogenetic D. pulex do not adopt typical apomixis. We hypothesize that D. pulex switches reproductive mode depending on whether the egg is fertilized or not.

Higher rates of sex evolve in spatially heterogeneous environments

The evolution and maintenance of sexual reproduction has puzzled biologists for decades. Although this field is rich in hypotheses, experimental evidence is scarce. Some important experiments have demonstrated differences in evolutionary rates between sexual and asexual populations; other experiments have documented evolutionary changes in phenomena related to genetic mixing, such as recombination and selfing. However, direct experiments of the evolution of sex within populations are extremely rare (but see ref. 12). Here we use the rotifer, Brachionus calyciflorus, which is capable of both sexual and asexual reproduction, to test recent theory predicting that there is more opportunity for sex to evolve in spatially heterogeneous environments. Replicated experimental populations of rotifers were maintained in homogeneous environments, composed of either high- or low-quality food habitats, or in heterogeneous environments that consisted of a mix of the two habitats. For populations maintained in either type of homogeneous environment, the rate of sex evolves rapidly towards zero. In contrast, higher rates of sex evolve in populations experiencing spatially heterogeneous environments. The data indicate that the higher level of sex observed under heterogeneity is not due to sex being less costly or selection against sex being less efficient; rather sex is sufficiently advantageous in heterogeneous environments to overwhelm its inherent costs. Counter to some alternative theories for the evolution of sex, there is no evidence that genetic drift plays any part in the evolution of sex in these populations.

Optimal strategy for competence differentiation in bacteria

A phylogenetically diverse subset of bacterial species are naturally competent for transformation by DNA. Transformation entails recombination of genes between different lineages, representing a form of bacterial sex that increases standing genetic variation. We first assess whether homologous recombination by transformation is favored by evolution. Using stochastic population genetic computer simulations in which beneficial and deleterious mutations occur at many loci throughout the whole genome, we find that transformation can increase both the rate of adaptive evolution and the equilibrium level of fitness. Secondly, motivated by experimental observations of Bacillus subtilis, we assume that competence additionally entails a weak persister phenotype, i.e., the rates of birth and death are reduced for these cells. Consequently, persisters evolve more slowly than non-persisters. We show via simulation that strains which stochastically switch into and out of the competent phenotype are evolutionarily favored over strains that express only a single phenotype. Our model's simplicity enables us to derive and numerically solve a system of finite- deterministic equations that describe the evolutionary dynamics. The observed tradeoff between the benefit of recombination and the cost of persistence may explain the previously mysterious observation that only a fractional subpopulation of B. subtilis cells express competence. More generally, this work demonstrates that population genetic forces can give rise to phenotypic diversity even in an unchanging and homogeneous environment.

In certain environmental conditions, populations of the bacterium Bacillus subtilis split into two physiologically distinct phenotypes. While some cells continue to grow and divide, a minority become “competent” for transformation by extracellular DNA. This differentiation process is driven not by genetic differences among cells, but rather by noisy molecular fluctuations. Although the differentiation process is thought to confer an evolutionary advantage, the basis of this advantage has remained elusive until now. We developed computer simulations of the joint dynamics of cell replication, cell death, mutation, and the quasi-sexual transfer of genes through the extracellular DNA pool. We find that bacterial sex via DNA transformation is indirectly favored by evolutionary forces. However, the indirect benefits of sex are counterbalanced by a reduced replication rate. We find that these opposing forces present an evolutionary dilemma best solved when the population splits into the two experimentally observed phenotypes. These results present a mechanism that selects for phenotypic diversity, even in an unchanging and homogeneous environment.

Genetic linkage and natural selection

The prevalence of recombination in eukaryotes poses one of the most puzzling questions in biology. The most compelling general explanation is that recombination facilitates selection by breaking down the negative associations generated by random drift (i.e. Hill-Robertson interference, HRI). I classify the effects of HRI owing to: deleterious mutation, balancing selection and selective sweeps on: neutral diversity, rates of adaptation and the mutation load. These effects are mediated primarily by the density of deleterious mutations and of selective sweeps. Sequence polymorphism and divergence suggest that these rates may be high enough to cause significant interference even in genomic regions of high recombination. However, neither seems able to generate enough variance in fitness to select strongly for high rates of recombination. It is plausible that spatial and temporal fluctuations in selection generate much more fitness variance, and hence selection for recombination, than can be explained by uniformly deleterious mutations or species-wide selective sweeps.

Genome analyses and modelling the relationships between coding density, recombination rate and chromosome length

In the human genomes, recombination frequency between homologous chromosomes during meiosis is highly correlated with their physical length while it differs significantly when their coding density is considered. Furthermore, it has been observed that the recombination events are distributed unevenly along the chromosomes. We have found that many of such recombination properties can be predicted by computer simulations of population evolution based on the Monte Carlo methods. For example, these simulations have shown that the probability of acceptance of the recombination events by selection is higher at the ends of chromosomes and lower in their middle parts. The regions of high coding density are more prone to enter the strategy of haplotype complementation and to form clusters of genes, which are "recombination deserts". The phenomenon of switching in-between the purifying selection and haplotype complementation has a phase transition character, and many relations between the effective population size, coding density, chromosome size and recombination frequency are those of the power law type.

Influence of co-evolution with a parasite, Nosema whitei, and population size on recombination rates and fitness in the red flour beetle, Tribolium castaneum

The high prevalence of meiotic recombination-an important element of sexual reproduction-represents one of the greatest puzzles in biology. The influence of either selection by a co-evolving parasite alone or in combination with genetic drift on recombination rates was tested in the host-parasite system Tribolium castaneum and Nosema whitei. After eight generations, populations with smaller genetic drift had a lower recombination rate than those with high drift whereas parasites had no effect. Interestingly, changes in recombination rate at one site of the chromosome negatively correlated with changes at the adjacent site on the same chromosome indicating an occurrence of crossover interference. The occurrence of spontaneous or plastic changes in recombination rates could be excluded with a separate experiment.

The role of advantageous mutations in enhancing the evolution of a recombination modifier

Although the evolution of recombination is still a major problem in evolutionary genetics, recent theoretical studies have shown that recombination can evolve by breaking down interference ("Hill-Robertson effects") among multiple loci. This leads to selection on a recombination modifier in a population subject to recurrent deleterious mutation. Here, we use computer simulations to investigate the evolution of a recombination modifier under three different scenarios of recurrent mutation in a finite population: (1) mutations are deleterious only, (2) mutations are advantageous only, and (3) there is a mixture of deleterious and advantageous mutations. We also investigate how linkage disequilibrium, the strength of selection acting on a modifier, and effective population size change under the different scenarios. We observe that adding even a small number of advantageous mutations increases the fixation rate of modifiers that increase recombination, especially if the effects of deleterious mutations are weak. However, the strength of selection on a modifier is less than the summed strengths had there been deleterious mutations only and advantageous mutations only.

The evolution of heterochiasmy: the role of sexual selection and sperm competition in determining sex-specific recombination rates in eutherian mammals

Early karyotypic work revealed that female and male recombination rates in many species show pronounced differences, and this pattern of heterochiasmy has also been observed in modern linkage mapping studies. Several hypotheses to explain this phenomenon have been offered, ranging from strictly biological mechanisms related to the gametic differences between the sexes, to more evolutionary models based on sexually antagonistic selection. However, despite the long history of interest in heterochiasmy, empirical data has failed to support any theory or pattern consistently. Here I test two alternative evolutionary hypotheses regarding heterochiasmy across the eutherian mammals, and show that sexual dimorphism, but not sperm competition, is strongly correlated with recombination rate, suggesting that sexual antagonism is an important influence. However, the observed relationship between heterochiasmy and sexual dimorphism runs counter to theoretical predictions, with male recombination higher in species with high levels of sexual dimorphism. This may be the response to male-biased dispersal, which, rather than the static male fitness landscape envisioned in the models tested here, could radically shift optimal male fitness parameters among generations.

Deleterious mutations and selection for sex in finite diploid populations

In diploid populations, indirect benefits of sex may stem from segregation and recombination. Although it has been recognized that finite population size is an important component of selection for recombination, its effects on selection for segregation have been somewhat less studied. In this article, we develop analytical two- and three-locus models to study the effect of recurrent deleterious mutations on a modifier gene increasing sex, in a finite diploid population. The model also incorporates effects of mitotic recombination, causing loss of heterozygosity (LOH). Predictions are tested using multilocus simulations representing deleterious mutations occurring at a large number of loci. The model and simulations show that excess of heterozygosity generated by finite population size is an important component of selection for sex, favoring segregation when deleterious alleles are nearly additive to dominant. Furthermore, sex tends to break correlations in homozygosity among selected loci, which disfavors sex when deleterious alleles are either recessive or dominant. As a result, we find that it is difficult to maintain costly sex when deleterious alleles are recessive. LOH tends to favor sex when deleterious mutations are recessive, but the effect is relatively weak for rates of LOH corresponding to current estimates (of the order 10(-4)-10(-5)).

Predicting the evolution of sex on complex fitness landscapes

Most population genetic theories on the evolution of sex or recombination are based on fairly restrictive assumptions about the nature of the underlying fitness landscapes. Here we use computer simulations to study the evolution of sex on fitness landscapes with different degrees of complexity and epistasis. We evaluate predictors of the evolution of sex, which are derived from the conditions established in the population genetic literature for the evolution of sex on simpler fitness landscapes. These predictors are based on quantities such as the variance of Hamming distance, mean fitness, additive genetic variance, and epistasis. We show that for complex fitness landscapes all the predictors generally perform poorly. Interestingly, while the simplest predictor, Delta Var(HD), also suffers from a lack of accuracy, it turns out to be the most robust across different types of fitness landscapes. Delta Var(HD) is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements. The presence of loci that are not under selection can, however, severely diminish predictor accuracy. Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction.

Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill-Robertson effect and to the joint evolution of helping and punishment

Natural populations are of finite size and organisms carry multilocus genotypes. There are, nevertheless, few results on multilocus models when both random genetic drift and natural selection affect the evolutionary dynamics. In this paper we describe a formalism to calculate systematic perturbation expansions of moments of allelic states around neutrality in populations of constant size. This allows us to evaluate multilocus fixation probabilities (long-term limits of the moments) under arbitrary strength of selection and gene action. We show that such fixation probabilities can be expressed in terms of selection coefficients weighted by mean first passages times of ancestral gene lineages within a single ancestor. These passage times extend the coalescence times that weight selection coefficients in one-locus perturbation formulas for fixation probabilities. We then apply these results to investigate the Hill-Robertson effect and the coevolution of helping and punishment. Finally, we discuss limitations and strengths of the perturbation approach. In particular, it provides accurate approximations for fixation probabilities for weak selection regimes only (Ns < or = 1), but it provides generally good prediction for the direction of selection under frequency-dependent selection.

Footprints of inversions at present and past pseudoautosomal boundaries in human sex chromosomes

The human sex chromosomes have stopped recombining gradually, which has left five evolutionary strata on the X chromosome. Y inversions are thought to have suppressed X–Y recombination but clear evidence is missing. Here, we looked for such evidence by focusing on a region—the X-added region (XAR)—that includes the pseudoautosomal region and the most recent strata 3 to 5. We estimated and analyzed the whole set of parsimonious scenarios of Y inversions given the gene order in XAR and its Y homolog. Comparing these to scenarios for simulated sequences suggests that the strata 4 and 5 were formed by Y inversions. By comparing the X and Y DNA sequences, we found clear evidence of two Y inversions associated with duplications that coincide with the boundaries of strata 4 and 5. Divergence between duplicates is in agreement with the timing of strata 4 and 5 formation. These duplicates show a complex pattern of gene conversion that resembles the pattern previously found for AMELXY, a stratum 3 locus. This suggests that this locus—despite AMELY being unbroken—was possibly involved in a Y inversion that formed stratum 3. However, no clear evidence supporting the formation of stratum 3 by a Y inversion was found, probably because this stratum is too old for such an inversion to be detectable. Our results strongly support the view that the most recent human strata have arisen by Y inversions and suggest that inversions have played a major role in the differentiation of our sex chromosomes.

The evolution of epistasis and its links with genetic robustness, complexity and drift in a phenotypic model of adaptation

The epistatic interactions among mutations have a large effect on the evolution of populations. In this article we provide a formalism under which epistatic interactions among pairs of mutations have a distribution whose mean can be modulated. We find that the mean epistasis is correlated to the effect of mutations or genetic robustness, which suggests that such formalism is in good agreement with most in silico models of evolution where the same pattern is observed. We further show that the evolution of epistasis is highly dependant on the intensity of drift and of how complex the organisms are, and that either positive or negative epistasis could be selected for, depending on the balance between the efficiency of selection and the intensity of drift.

Simulation of DNA sequence evolution under models of recent directional selection

Computer simulation is an essential tool in the analysis of DNA sequence variation for mapping events of recent adaptive evolution in the genome. Various simulation methods are employed to predict the signature of selection in sequence variation. The most informative and efficient method currently in use is coalescent simulation. However, this method is limited to simple models of directional selection. Whole-population forward-in-time simulations are the alternative to coalescent simulations for more complex models. The notorious problem of excessive computational cost in forward-in-time simulations can be overcome by various simplifying amendments. Overall, the success of simulations depends on the creative application of some population genetic theory to the simulation algorithm.

Extreme heterochiasmy and nascent sex chromosomes in European tree frogs

We investigated sex-specific recombination rates in Hyla arborea, a species with nascent sex chromosomes and male heterogamety. Twenty microsatellites were clustered into six linkage groups, all showing suppressed or very low recombination in males. Seven markers were sex linked, none of them showing any sign of recombination in males (r=0.00 versus 0.43 on average in females). This opposes classical models of sex chromosome evolution, which envision an initially small differential segment that progressively expands as structural changes accumulate on the Y chromosome. For autosomes, maps were more than 14 times longer in females than in males, which seems the highest ratio documented so far in vertebrates. These results support the pleiotropic model of Haldane and Huxley, according to which recombination is reduced in the heterogametic sex by general modifiers that affect recombination on the whole genome.

Localization of the genetic determinants of meiosis suppression in Daphnia pulex

Although approximately 1 in 10,000 animal species is capable of parthenogenetic reproduction, the evolutionary causes and consequences of such transitions remain uncertain. The microcrustacean Daphnia pulex provides a potentially powerful tool for investigating these issues because lineages that are obligately asexual in terms of female function can nevertheless transmit meiosis-suppressing genes to sexual populations via haploid sperm produced by environmentally induced males. The application of association mapping to a wide geographic collection of D. pulex clones suggests that sex-limited meiosis suppression in D. pulex has spread westward from a northeastern glacial refugium, conveyed by a dominant epistatic interaction among the products of at least four unlinked loci, with one entire chromosome being inherited through males in a nearly nonrecombining fashion. With the enormous set of genomic tools now available for D. pulex, these results set the stage for the determination of the functional underpinnings of the conversion of meiosis to a mitotic-like mode of inheritance.

Cut thy neighbor: cyclic birth and death of recombination hotspots via genetic conflict

Most recombination takes place in numerous, localized regions called hotspots. However, empirical evidence indicates that nascent hotspots are susceptible to removal due to biased gene conversion, so it is paradoxical that they should be so widespread. Previous modeling work has shown that hotspots can evolve due to genetic drift overpowering their intrinsic disadvantage. Here we synthesize recent theoretical and empirical results to show how natural selection can favor hotspots. We propose that hotspots are part of a cycle of antagonistic coevolution between two tightly linked chromosomal regions: an inducer region that initiates recombination during meiosis by cutting within a nearby region of DNA and the cut region itself, which can evolve to be resistant to cutting. Antagonistic coevolution between inducers and their cut sites is driven by recurrent episodes of Hill-Robertson interference, genetic hitchhiking, and biased gene conversion.

Nonadditive genetic components in resistance of the red flour beetle Tribolium castanaeum against parasite infection

Genetically coupled antagonistic coevolution between host and parasites can select for the maintenance of recombination in the host. Mechanistically, maintenance of recombination relies on epistatic interactions between resistance genes creating linkage disequilibria (LD). The role of epistasis in host resistance traits is however only partly understood. Therefore, we applied the joint scaling principle to assess epistasis and other nonadditive genetic components of two resistance traits, survival, and parasite spore load, in population crosses of the red flour beetle Tribolium castanaeum under infections with the microsporidian Nosema whitei. We found nonadditive components only in infected populations but not in control populations. The genetic architecture underlying survival under parasite infection was more complex than that of spore load. Accordingly, the observed negative correlation between survival and spore load was mainly based on a correlation between shared additive components. Breakdown of resistance was especially strong in F2 crosses between resistant lines indicating that multiple epistatic routes can lead to the same adaptation. In general, the wide range of nonoverlapping genetic components between crosses indicated that parasite resistance in T. castanaeum can be understood as a multi peaked fitness landscape with epistasis contributing substantially to phenotypic differentiation in resistance.

Recombination increases human immunodeficiency virus fitness, but not necessarily diversity

Recombination can facilitate the accumulation of mutations and accelerate the emergence of resistance to current antiretroviral therapies for human immunodeficiency virus (HIV) infection. Yet, since recombination can also dissociate favourable combinations of mutations, the benefit of recombination to HIV remains in question. The confounding effects of mutation, multiple infections of cells, random genetic drift and fitness selection that underlie HIV evolution render the influence of recombination difficult to unravel. We developed computer simulations that mimic the genomic diversification of HIV within an infected individual and elucidate the influence of recombination. We find, interestingly, that when the effective population size of HIV is small, recombination increases both the diversity and the mean fitness of the viral population. When the effective population size is large, recombination increases viral fitness but decreases diversity. In effect, recombination enhances (lowers) the likelihood of the existence of multi-drug resistant strains of HIV in infected individuals prior to the onset of therapy when the effective population size is small (large). Our simulations are consistent with several recent experimental observations, including the evolution of HIV diversity and divergencein vivo. The intriguing dependencies on the effective population size appear due to the subtle interplay of drift, selection and epistasis, which we discuss in the light of modern population genetics theories. Current estimates of the effective population size of HIV have large discrepancies. Our simulations present an avenue for accurate determination of the effective population size of HIVin vivoand facilitate establishment of the benefit of recombination to HIV.

Adaptive value of sex in microbial pathogens

Explaining the adaptive value of sex is one of the great outstanding problems in biology. The challenge comes from the difficulty in identifying the benefits provided by sex, which must outweigh the substantial costs of sex. Here, we consider the adaptive value of sex in viruses, bacteria and fungi, and particularly the information available on the adaptive role of sex in pathogenic microorganisms. Our general theme is that the varied aspects of sex in pathogens illustrate the varied issues surrounding the evolution of sex generally. These include, the benefits of sex (in the short- and long-term), as well as the costs of sex (both to the host and to the pathogen). For the benefits of sex (that is, its adaptive value), we consider three hypotheses: (i) sex provides for effective and efficient recombinational repair of DNA damages, (ii) sex provides DNA for food, and (iii) sex produces variation and reduces genetic associations among alleles under selection. Although the evolution of sex in microbial pathogens illustrates these general issues, our paper is not a general review of theories for the evolution of sex in all organisms. Rather, we focus on the adaptive value of sex in microbial pathogens and conclude that in terms of short-term benefits, the DNA repair hypothesis has the most support and is the most generally applicable hypothesis in this group. In particular, recombinational repair of DNA damages may substantially benefit pathogens when challenged by the oxidative defenses of the host. However, in the long-term, sex may help get rid of mutations, increase the rate of adaptation of the population, and, in pathogens, may infrequently create new infective strains. An additional general issue about sex illustrated by pathogens is that some of the most interesting consequences of sex are not necessarily the reasons for which sex evolved. For example, antibiotic resistance may be transferred by bacterial sex, but this transfer is probably not the reason sex evolved in bacteria.

The Red Queen and the persistence of linkage-disequilibrium oscillations in finite and infinite populations

Background

The Red Queen Hypothesis (RQH) suggests that the coevolutionary dynamics of host-parasite systems can generate selection for increased host recombination. Since host-parasite interactions often have a strong genetic basis, recombination between different hosts can increase the fraction of novel and potentially resistant offspring genotypes. A prerequisite for this mechanism is that host-parasite interactions generate persistent oscillations of linkage disequilibria (LD).

Results

We use deterministic and stochastic models to investigate the persistence of LD oscillations and its impact on the RQH. The standard models of the Red Queen dynamics exhibit persistent LD oscillations under most circumstances. Here, we show that altering the standard model from discrete to continuous time or from simultaneous to sequential updating results in damped LD oscillations. This suggests that LD oscillations are structurally not robust. We then show that in a stochastic regime, drift can counteract this dampening and maintain the oscillations. In addition, we show that the amplitude of the oscillations and therefore the strength of the resulting selection for or against recombination are inversely proportional to the size of the (host) population.

Conclusion

We find that host parasite-interactions cannot generally maintain oscillations in the absence of drift. As a consequence, the RQH can strongly depend on population size and should therefore not be interpreted as a purely deterministic hypothesis.

A third-generation microsatellite-based linkage map of the honey bee, Apis mellifera, and its comparison with the sequence-based physical map

The meiotic map of the honey bee is presented, including the main features that emerged from comparisons with the sequence-based physical map. The map is based on 2,008 markers and is about 40 M long, corresponding to a recombination rate of 22 cM/Mb.

Background:

The honey bee is a key model for social behavior and this feature led to the selection of the species for genome sequencing. A genetic map is a necessary companion to the sequence. In addition, because there was originally no physical map for the honey bee genome project, a meiotic map was the only resource for organizing the sequence assembly on the chromosomes.

Results:

We present the genetic (meiotic) map here and describe the main features that emerged from comparison with the sequence-based physical map. The genetic map of the honey bee is saturated and the chromosomes are oriented from the centromeric to the telomeric regions. The map is based on 2,008 markers and is about 40 Morgans (M) long, resulting in a marker density of one every 2.05 centiMorgans (cM). For the 186 megabases (Mb) of the genome mapped and assembled, this corresponds to a very high average recombination rate of 22.04 cM/Mb. Honey bee meiosis shows a relatively homogeneous recombination rate along and across chromosomes, as well as within and between individuals. Interference is higher than inferred from the Kosambi function of distance. In addition, numerous recombination hotspots are dispersed over the genome.

Conclusion:

The very large genetic length of the honey bee genome, its small physical size and an almost complete genome sequence with a relatively low number of genes suggest a very promising future for association mapping in the honey bee, particularly as the existence of haploid males allows easy bulk segregant analysis.

The Hill–Robertson effect: evolutionary consequences of weak selection and linkage in finite populations

The 'Hill-Robertson (HR) effect' describes that linkage between sites under selection will reduce the overall effectiveness of selection in finite populations. Here we discuss the major concepts associated with the HR effect and present results of computer simulations focusing on the linkage effects generated by multiple sites under weak selection. Most models of linkage and selection forecast differences in effectiveness of selection between chromosomes or chromosomal regions involving a number of genes. The abundance and physical clustering of weakly selected mutations across genomes, however, justify the investigation of HR effects at a very local level and we pay particular attention to linkage effects among selected sites of the same gene. Overall, HR effects caused by weakly selected mutations predict differences in effectiveness of selection between genes that differ in exon-intron structures and across genes. Under this scenario, introns might play an advantageous role reducing intragenic HR effects. Finally, we summarize observations that are consistent with local HR effects in Drosophila, discuss potential consequences on population genetic studies and suggest future lines of research.

Beneficial mutation selection balance and the effect of linkage on positive selection

When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population concurrently. In an asexual population, these different mutant lineages interfere and not all can fix simultaneously. In addition, further beneficial mutations can accumulate in mutant lineages while these are still a minority of the population. In this article, we analyze the dynamics of such multiple mutations and the interplay between multiple mutations and interference between clones. These result in substantial variation in fitness accumulating within a single asexual population. The amount of variation is determined by a balance between selection, which destroys variation, and beneficial mutations, which create more. The behavior depends in a subtle way on the population parameters: the population size, the beneficial mutation rate, and the distribution of the fitness increments of the potential beneficial mutations. The mutation-selection balance leads to a continually evolving population with a steady-state fitness variation. This variation increases logarithmically with both population size and mutation rate and sets the rate at which the population accumulates beneficial mutations, which thus also grows only logarithmically with population size and mutation rate. These results imply that mutator phenotypes are less effective in larger asexual populations. They also have consequences for the advantages (or disadvantages) of sex via the Fisher-Muller effect; these are discussed briefly.

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.

The evolution of condition-dependent sex in the face of high costs

Facultatively sexual organisms often engage in sex more often when in poor condition. We show that such condition-dependent sex carries evolutionary advantages and can explain the evolution of sexual reproduction even when sex entails high costs. Specifically, we show that alleles promoting individuals of low fitness to have sex more often than individuals of high fitness spread through a population. Such alleles are more likely to segregate out of bad genetic backgrounds and onto good genetic backgrounds, where they tend to remain. This "abandon-ship" mechanism provides a plausible model for the evolution and maintenance of facultative sex.

Fitness declines in Tobacco etch virus upon serial bottleneck transfers

It has been well established that populations of RNA viruses transmitted throughout serial bottlenecks suffer from significant fitness declines as a consequence of the accumulation of deleterious mutations by the onset of Muller's ratchet. Bottlenecks are unavoidably linked to different steps of the infectious cycle of most plant RNA viruses, such as vector-mediated transmissions and systemic colonization of new leaves. Here we report evidence for fitness declines by the accumulation of deleterious mutations in the potyvirus Tobacco etch virus (TEV). TEV was inoculated into the nonsystemic host Chenopodium quinoa, and local lesions were isolated and used to initiate 20 independent mutation accumulation lineages. Weekly, a random lesion from each lineage was isolated and used to inoculate the next set of plants. At each transfer, the Malthusian growth rate was estimated. After 11 consecutive transfers, all lineages suffered significant fitness losses, and one even became extinct. The average rate of fitness decline was 5% per day. The average pattern of fitness decline was consistent with antagonistic epistasis between deleterious mutations, as postulated for antiredundant genomes. Temporal fitness fluctuations were not explained by random noise but reflected more complex underlying processes related to emergence and self-organization phenomena.

The speed of evolution and maintenance of variation in asexual populations

BACKGROUND

The rate at which beneficial mutations accumulate determines how fast asexual populations evolve, but this is only partially understood. Some recent clonal-interference models suggest that evolution in large asexual populations is limited because smaller beneficial mutations are outcompeted by larger beneficial mutations that occur in different lineages within the same population. This analysis assumes that the important mutations fix one at a time; it ignores multiple beneficial mutations that occur in the lineage of an earlier beneficial mutation, before the first mutation in the series can fix. We focus on the effects of such multiple mutations.

RESULTS

Our analysis predicts that the variation in fitness maintained by a continuously evolving population increases as the logarithm of the population size and logarithm of the mutation rate and thus yields a similar logarithmic increase in the speed of evolution. To test these predictions, we evolved asexual budding yeast in glucose-limited media at a range of population sizes and mutation rates.

CONCLUSIONS

We find that their evolution is dominated by the accumulation of multiple mutations of moderate effect. Our results agree with our theoretical predictions and are inconsistent with the one-by-one fixation of mutants assumed by recent clonal-interference analysis.

The evolution of sex: empirical insights into the roles of epistasis and drift

Despite many years of theoretical and experimental work, the explanation for why sex is so common as a reproductive strategy continues to resist understanding. Recent empirical work has addressed key questions in this field, especially regarding rates of mutation accumulation in sexual and asexual organisms, and the roles of negative epistasis and drift as sources of adaptive constraint in asexually reproducing organisms. At the same time, new ideas about the evolution of sexual recombination are being tested, including intriguing suggestions of an important interplay between sex and genetic architecture, which indicate that sex and recombination could have affected their own evolution.

Epistasis between deleterious mutations and the evolution of recombination

Epistasis and the evolution of recombination are closely intertwined: epistasis generates linkage disequilibria (i.e. statistical associations between alleles), whereas recombination breaks them up. The mutational deterministic hypothesis (MDH) states that high recombination rates are maintained because the breaking up of linkage disequilibria generated by negative epistasis enables more efficient purging of deleterious mutations. However, recent theoretical and experimental work challenges the MDH. Experimental evidence suggests that negative epistasis, required by the MDH, is relatively uncommon. On the theoretical side, population genetic models suggest that, compared with the combined effects of drift and selection, epistasis generates a negligible amount of linkage disequilibria. Here, we assess these criticisms and discuss to what extent they invalidate the MDH as an explanation for the evolution of recombination.

The evolution of sex and recombination in response to abiotic or coevolutionary fluctuations in epistasis

Evolutionary biologists have identified several factors that could explain the widespread phenomena of sex and recombination. One hypothesis is that host-parasite interactions favor sex and recombination because they favor the production of rare genotypes. A problem with many of the early models of this so-called Red Queen hypothesis is that several factors are acting together: directional selection, fluctuating epistasis, and drift. It is thus difficult to identify what exactly is selecting for sex in these models. Is one factor more important than the others or is it the synergistic action of these different factors that really matters? Here we focus on the analysis of a simple model with a single mechanism that might select for sex: fluctuating epistasis. We first analyze the evolution of sex and recombination when the temporal fluctuations are driven by the abiotic environment. We then analyze the evolution of sex and recombination in a two-species coevolutionary model, where directional selection is absent (allele frequencies remain fixed) and temporal variation in epistasis is induced by coevolution with the antagonist species. In both cases we contrast situations with weak and strong selection and derive the evolutionarily stable (ES) recombination rate. The ES recombination rate is most sensitive to the period of the cycles, which in turn depends on the strength of epistasis. In particular, more virulent parasites cause more rapid cycles and consequently increase the ES recombination rate of the host. Although the ES strategy is maximized at an intermediate period, some recombination is favored even when fluctuations are very slow. By contrast, the amplitude of the cycles has no effect on the ES level of sex and recombination, unless sex and recombination are costly, in which case higher-amplitude cycles allow the evolution of higher rates of sex and recombination. In the coevolutionary model, the amount of recombination in the interacting species also has a large effect on the ES, with evolution favoring higher rates of sex and recombination than in the interacting species. In general, the ES recombination rate is less than or equal to the recombination rate that would maximize mean fitness. We also discuss the effect of migration when sex and recombination evolve in a metapopulation. We find that intermediate parasite migration rates maximize the degree of local adaptation of the parasite and lead to a higher ES recombination rate in the host.

Selection by parasites may increase host recombination frequency

Meiotic recombination destroys successful genotypes and it is therefore thought to evolve only under a very limited set of conditions. Here, we experimentally show that recombination rates across two linkage groups of the host, the red flour beetle Tribolium castaneum, increase with exposure to the microsporidian parasite, Nosema whitei, particularly when parasites were allowed to coevolve with their hosts. Selection by randomly varied parasites resulted in smaller effects, while directional selection for insecticide resistance initially reduced recombination slightly. These results, at least tentatively, suggest that short-term benefits of recombination--and thus the evolution of sex--may be related to parasitism.

An evolutionary view of human recombination

Recombination has essential functions in mammalian meiosis, which impose several constraints on the recombination process. However, recent studies have shown that, in spite of these roles, recombination rates vary tremendously among humans, and show marked differences between humans and closely related species. These findings provide important insights into the determinants of recombination rates and raise new questions about the selective pressures that affect recombination over different genomic scales, with implications for human genetics and evolutionary biology.

Evolution of sex: why do organisms shuffle their genotypes?

Sexual processes alter associations among alleles. To understand the evolution of sex, we need to know both the short-term and long-term consequences of changing these genetic associations. Ultimately, we need to identify which evolutionary forces--for example, selection, genetic drift, migration--are responsible for building the associations affected by sex.

Interference among deleterious mutations favours sex and recombination in finite populations

Sex and recombination are widespread, but explaining these phenomena has been one of the most difficult problems in evolutionary biology. Recombination is advantageous when different individuals in a population carry different advantageous alleles. By bringing together advantageous alleles onto the same chromosome, recombination speeds up the process of adaptation and opposes the fixation of harmful mutations by means of Muller's ratchet. Nevertheless, adaptive substitutions favour sex and recombination only if the rate of adaptive mutation is high, and Muller's ratchet operates only in small or asexual populations. Here, by tracking the fate of modifier alleles that alter the frequency of sex and recombination, we show that background selection against deleterious mutant alleles provides a stochastic advantage to sex and recombination that increases with population size. The advantage arises because, with low levels of recombination, selection at other loci severely reduces the effective population size and genetic variance in fitness at a focal locus (the Hill-Robertson effect), making a population less able to respond to selection and to rid itself of deleterious mutations. Sex and recombination reveal the hidden genetic variance in fitness by combining chromosomes of intermediate fitness to create chromosomes that are relatively free of (or are loaded with) deleterious mutations. This increase in genetic variance within finite populations improves the response to selection and generates a substantial advantage to sex and recombination that is fairly insensitive to the form of epistatic interactions between deleterious alleles. The mechanism supported by our results offers a robust and broadly applicable explanation for the evolutionary advantage of recombination and can explain the spread of costly sex.

Effects of intra-gene fitness interactions on the benefit of sexual recombination

Whereas spontaneous point mutation operates on nucleotides individually, sexual recombination manipulates the set of nucleotides within an allele as an essentially particulate unit. In principle, these two different scales of variation enable selection to follow fitness gradients in two different spaces: in nucleotide sequence space and allele sequence space respectively. Epistasis for fitness at these two scales, between nucleotides and between genes, may be qualitatively different and may significantly influence the advantage of mutation-based and recombination-based evolutionary trajectories respectively. We examine scenarios where the genetic sequence within a gene strongly influences the fitness effect of a mutation in that gene, whereas epistatic interactions between sites in different genes are weak or absent. We find that, in cases where beneficial alleles of a gene differ from one another at several nucleotide sites, sexual populations can exhibit enormous benefit compared with asexual populations: not only discovering fit genotypes faster than asexual populations, but also discovering high-fitness genotypes that are effectively not evolvable in asexual populations.

Why have sex? The population genetics of sex and recombination

One of the greatest puzzles in evolutionary biology is the high frequency of sexual reproduction and recombination. Given that individuals surviving to reproductive age have genomes that function in their current environment, why should they risk shuffling their genes with those of another individual? Mathematical models are especially important in developing predictions about when sex and recombination can evolve, because it is difficult to intuit the outcome of evolution with several interacting genes. Interestingly, theoretical analyses have shown that it is often quite difficult to identify conditions that favour the evolution of high rates of sex and recombination. For example, fitness interactions among genes (epistasis) can favour sex and recombination but only if such interactions are negative, relatively weak and not highly variable. One reason why an answer to the paradox of sex has been so elusive is that our models have focused unduly on populations that are infinite in size, unstructured and isolated from other species. Yet most verbal theories for sex and recombination consider a finite number of genotypes evolving in a biologically and/or physically complex world. Here, we review various hypotheses for why sex and recombination are so prevalent and discuss theoretical results indicating which of these hypotheses is most promising.

Pronounced differences of recombination activity at the sex determination locus of the honeybee, a locus under strong balancing selection

Recombination decreases the association of linked nucleotide sites and can influence levels of polymorphism in natural populations. When coupled with selection, recombination may relax potential conflict among linked genes, a concept that has played a central role in research on the evolution of recombination. The sex determination locus (SDL) of the honeybee is an informative example for exploring the combined forces of recombination, selection, and linkage on sequence evolution. Balancing selection at SDL is very strong and homozygous individuals at SDL are eliminated by worker bees. The recombination rate is increased up to four times that of the genomewide average in the region surrounding SDL. Analysis of nucleotide diversity (pi) reveals a sevenfold increase of polymorphism within the sex determination gene complementary sex determiner (csd) that rapidly declines within 45 kb to levels of genomewide estimates. Although no recombination was observed within SDL, which contains csd, analyses of heterogeneity, shared polymorphic sites, and linkage disequilibrium (LD) show that recombination has contributed to the evolution of the 5' part of some csd sequences. Gene conversion, however, has not obviously contributed to the evolution of csd sequences. The local control of recombination appears to be related to SDL function and mode of selection. The homogenizing force of recombination is reduced within SDL, which preserves allelic differences and specificity, while the increase of recombination activity around SDL relaxes conflict between SDL and linked genes.

A comparison of parasite loads on asexual and sexual Phoxinus (Pisces: Cyprinidae)

In light of the inherent disadvantages of sexual reproduction, the existence of sex is often seen as a paradox. There are a variety of hypothetical benefits of sexual reproduction that may balance its disadvantages. The Red Queen hypothesis proposes that sexually reproducing species are better able to evolve resistance to parasites than asexually reproducing species. A prediction of the Red Queen hypothesis is that a parasite should evolve to preferentially exploit an asexual species over a sexual species. To test this central prediction of the Red Queen hypothesis, intensity of infection by the parasite Gyrodactylus eos Mayes, 1977 (Monogenea) was compared between sympatric asexual and sexual fish species in the genus Phoxinus Rafinesque, 1820. In each lake where these species coexist, the asexual fish should suffer higher intensities of infection than the sexual fish. In the majority of lakes sampled, there were more parasites on asexual than sexual fish.

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 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.

Analytic approach to the evolutionary effects of genetic exchange

We present an approximate analytic study of our previously introduced model of evolution including the effects of genetic exchange. This model is motivated by the process of bacterial transformation. We solve for the velocity, the rate of increase of fitness, as a function of the fixed population size, N. We find the velocity increases with ln N, eventually saturating at an N which depends on the strength of the recombination process. The analytical treatment is seen to agree well with direct numerical simulations of our model equations.