Evolution of genetic variability and the advantage of sex and recombination in changing environments.

The role of recombination and sexual reproduction in enhancing adaptation and population persistence in temporally varying environments is investigated on the basis of a quantitative-genetic multilocus model. Populations are finite, subject to density-dependent regulation with a finite growth rate, diploid, and either asexual or randomly mating and sexual with or without recombination. A quantitative trait is determined by a finite number of loci at which mutation generates genetic variability. The trait is under stabilizing selection with an optimum that either changes at a constant rate in one direction, exhibits periodic cycling, or fluctuates randomly. It is shown by Monte Carlo simulations that if the directional-selection component prevails, then freely recombining populations gain a substantial evolutionary advantage over nonrecombining and asexual populations that goes far beyond that recognized in previous studies. The reason is that in such populations, the genetic variance can increase substantially and thus enhance the rate of adaptation. In nonrecombining and asexual populations, no or much less increase of variance occurs. It is explored by simulation and mathematical analysis when, why, and by how much genetic variance increases in response to environmental change. In particular, it is elucidated how this change in genetic variance depends on the reproductive system, the population size, and the selective regime, and what the consequences for population persistence are.     

Sexual selection and its effect on the fixation of an asexual clone

Sexual selection is a powerful and ubiquitous force in sexual populations. It has recently been argued that sexual selection can eliminate the twofold cost of sex even with low genomic mutation rates. By means of differential male mating success, deleterious mutations in males become more deleterious than in females, and it has been shown that sexual selection can drastically reduce the mutational load in a sexual population, with or without any form of epistasis. However, any mechanism that claims to maintain sexual reproduction must be able to prevent the fixation of an asexual mutant clone with a twofold fitness advantage. Here, I show that despite very strong sexual selection, the fixation of an asexual mutant cannot be prevented under reasonable genomic mutation rates. Sexual selection can have a strong effect on the average mutational load in a sexual population, but as it cannot prevent the fixation of an asexual mutant, it is unlikely to play a key role on the maintenance of sexual reproduction.     

Population genetics of complex life-cycle parasites: an illustration with trematodes

Accurate inferences on population genetics data require a sound underlying theoretical null model. Organisms alternating sexual and asexual reproduction during their life-cycle have been largely neglected in theoretical population genetic models, thus limiting the biological interpretation of population genetics parameters measured in natural populations. In this article, we derive the expectations of those parameters for the life-cycle of monoecious trematodes, a group comprising several important human and livestock parasites that obligatorily alternate sexual and asexual reproduction during their life-cycle. We model how migration rates between hosts, sexual and asexual mutation rates, adult selfing rate and the variance in reproductive success of parasites during the clonal phase affect the amount of neutral genetic diversity of the parasite (effective population size) and its apportionment within and between definitive hosts (using F-statistics). We demonstrate, in particular, that variance in reproductive success of clones, a parameter that has been completely overlooked in previous population genetics models, is very important in shaping the distribution of the genetic variability both within and among definitive hosts. Within definitive hosts, the parameter F(IS) (a measure of the deviation from random mating) is decreased by high variance in clonal reproductive success of larvae but increased by high adult self-fertilisation rates. Both clonal multiplication and selfing have similar effects on between-host genetic differentiation (F(ST)). Migration occurring before and after asexual reproduction can have different effects on the patterns of F(IS), depending on values of the other parameters such as the mutation rate. While the model applies to any hermaphroditic organism alternating sexual and clonal reproduction (e.g. many plants), the results are specifically discussed in the light of the limited population genetic data on monoecious trematodes available to date and their previous interpretation. We hope that our model will encourage more empirical population genetics studies on monoecious trematodes and other organisms with similar life-cycles.     

Environmental change,mutational load and the advantage of sexual reproduction

There is evidence that asexual reproduction has a long-term disadvantage when compared to sexual reproduction. This disadvantage is usually assumed to arise from the more efficient incorporation of advantageous mutations by sexual populations. We consider here the effect on asexual and sexual populations of changes in the fitness of harmful mutations. It is shown that the re-establishment of equilibrium following environmental change is generally faster in sexual populations, and that the mutational load experienced by the sexual population can be significantly less during this period than that experienced by an asexual one. Changes in the fitness of harmful mutations may therefore impose a greater long-term disadvantage on asexual populations than those which are sexual.     

Sex and adaptation in a changing environment.

In this study we consider a mathematical model of a sexual population that lives in a changing environment. We find that a low rate of environmental change can produce a very large increase in genetic variability. This may help to explain the high levels of heritability observed in many natural populations. We also study asexuality and find that a modest rate of environmental change can be very damaging to an asexual population, while leaving a sexual population virtually unscathed. Furthermore, in a changing environment, the advantages of sexuality over asexuality can be much greater than suggested by most previous studies. Our analysis applies in the case of very large populations, where stochastic forces may be neglected.     

Muller's ratchet and the accumulation of favourable mutations

Under the influence of recurrent deleterious mutation and selection, asexual and sexual populations reach a deterministic equilibrium with individuals carrying 0,1,2,. . . harmful mutations. When a favourable mutation (aA) occurs in an asexual population it will usually occur in an individual who has one or more (k) deleterious mutations. Muller's ratchet then applies as A will thereafter never occur in an individual with less than k mutations. If the selective advantage of A is less than the selective disadvantage of k harmful mutations then A will not spread. If it is greater it may spread carrying k deleterious mutations to fixation. Sexual populations are not affected in this way. A will spread through the population experiencing genomes with 0,1,2,. . . deleterious mutations in accordance with the deterministic equilibrium.     

The ecology and genetics of fitness in Chlamydomonas. XIII. Fitness of long-term sexual and asexual populations in benign environments

We measured the mean fitness of populations of Chlamydomonas reinhardtii maintained in the laboratory as obligately sexual or asexual populations for about 100 sexual cycles and about 1000 asexual generations. Sexuality (random gamete fusion followed by meiosis) is expected to reduce mutational load and increase mean fitness by combining deleterious mutations from different lines of descent. We found no evidence for this process of mutation clearance: the mean fitness of sexual populations did not exceed that of asexual populations, whether measured through competition or in pure culture. We found instead that sexual progeny suffer an immediate loss in fitness, and that sexual lines maintain genetic variance for fitness. We suggest that sexual populations at equilibrium with selection in a benign environment may be mixtures of several or many epistatic genotypes with nearly equal fitness. Recombination between these genotypes reduces mean fitness and creates genetic variance for fitness. This may provide fuel for continued selection should the environment change.     

A Ruby in the Rubbish: Beneficial Mutations, Deleterious Mutations and the Evolution of Sex

This study presents a mathematical model in which a single beneficial mutation arises in a very large population that is subject to frequent deleterious mutations. The results suggest that, if the population is sexual, then the deleterious mutations will have little effect on the ultimate fate of the beneficial mutation. However, if most offspring are produced asexually, then the probability that the beneficial mutation will be lost from the population may be greatly enhanced by the deleterious mutations. Thus, sexual populations may adapt much more quickly than populations where most reproduction is asexual. Some of the results were produced using computer simulation methods, and a technique was developed that allows treatment of arbitrarily large numbers of individuals in a reasonable amount of computer time. This technique may be of prove useful for the analysis of a wide variety of models, though there are some constraints on its applicability. For example, the technique requires that reproduction can be described by Poisson processes.     

The Tangled Bank: The maintenance of sexual reproduction through competitive interactions

The maintenance of sexual reproduction is discussed using a model based on the familiar Lotka-Volterra competition equations. Both the equilibrium and the stability conditions that allow a sexual population to resist invasion by a single asexual clone are considered. The equilibrium conditions give results similar to previous models: When the cost of sex, within phenotype niche width, and environmental variance are low, the sexual population coexists with the asexual clone and remains at a high density. However, the asexual clone is never completely excluded. Analysis of the stability conditions shows a different picture: The introduction of an asexual clone considerably reduces the stability of the community. However, owing to its larger total niche width, the sexual population exists partly in a “competitor-free space” where the asexual clone has almost no influence on the outcome of the interactions. Therefore the asexual clone is less stable than the sexual population and has a higher probability of extinction. In contrast, the sexual population does not become extinct, since the extreme phenotypes remain at a stable, though low, density, and the central phenotypes, where stability is low, are recreated every generation through recombination. I therefore conclude that the ecological conditions under which sexual reproduction is favored over asexual reproduction are fairly easily attained and are more general than previous analyses had suggested.     

Change of Genetic Architecture in Response to Sex

A traditional view is that sexual reproduction increases the potential for phenotypic evolution by expanding the range of genetic variation upon which natural selection can act. However, when nonadditive genetic effects and genetic disequilibria underlie a genetic system, genetic slippage (a change in the mean genotypic value contrary to that promoted by selection) in response to sex may occur. Additionally, depending on whether natural selection is predominantly stabilizing or disruptive, recombination may either enhance or reduce the level of expressed genetic variance. Thus, the role of sexual reproduction in the dynamics of phenotypic evolution depends heavily upon the nature of natural selection and the genetic system of the study population. In the present study, on a permanent lake Daphnia pulicaria population, sexual reproduction resulted in significant genetic slippage and a significant increase in expressed genetic variance for several traits. These observations provide evidence for substantial genetic disequilibria and nonadditive genetic effects underlying the genetic system of the study population. From these results, the fitness function of the previous clonal selection phase is inferred to be directional and/or stabilizing. The data are also used to infer the effects of natural selection on the mean and the genetic variance of the population.     

Maintaining evolvability

Although molecular methods, such as QTL mapping, have revealed a number of loci with large effects, it is still likely that the bulk of quantitative variability is due to multiple factors, each with small effect. Typically, these have a large additive component. Conventional wisdom argues that selection, natural or artificial, uses up additive variance and thus depletes its supply. Over time, the variance should be reduced, and at equilibrium be near zero. This is especially expected for fitness and traits highly correlated with it. Yet, populations typically have a great deal of additive variance, and do not seem to run out of genetic variability even after many generations of directional selection. Long-term selection experiments show that populations continue to retain seemingly undiminished additive variance despite large changes in the mean value. I propose that there are several reasons for this. (i) The environment is continually changing so that what was formerly most fit no longer is. (ii) There is an input of genetic variance from mutation, and sometimes from migration. (iii) As intermediate-frequency alleles increase in frequency towards one, producing less variance (as p → 1, p(1 − p) → 0), others that were originally near zero become more common and increase the variance. Thus, a roughly constant variance is maintained. (iv) There is always selection for fitness and for characters closely related to it. To the extent that the trait is heritable, later generations inherit a disproportionate number of genes acting additively on the trait, thus increasing genetic variance. For these reasons a selected population retains its ability to evolve. Of course, genes with large effect are also important. Conspicuous examples are the small number of loci that changed teosinte to maize, and major phylogenetic changes in the animal kingdom. The relative importance of these along with duplications, chromosome rearrangements, horizontal transmission and polyploidy is yet to be determined. It is likely that only a case-by-case analysis will provide the answers. Despite the difficulties that complex interactions cause for evolution in Mendelian populations, such populations nevertheless evolve very well. Longlasting species must have evolved mechanisms for coping with such problems. Since such difficulties do not arise in asexual populations, a comparison of epistatic patterns in closely related sexual and asexual species might provide some important insights.     

Mutation Load under Vegetative Reproduction and Cytoplasmic Inheritance

For reasons that remain unclear, even multicellular organisms usually originate from a single cell. Here I consider the balance between deleterious mutations and selection against them in a population with obligate vegetative reproduction, when every offspring is initiated by more than one cell of a parent. The mutation load depends on the genomic deleterious mutation rate U, strictness of selection, number of cells which initiate an offspring n, and the relatedness among the initial cells. The load grows with increasing U, n and strictness of selection, and declines when an offspring is initiated by more closely related cells. If Un >> 1, the load under obligate vegetative reproduction may be substantially higher than under sexual or asexual reproduction, which may account for its rarity. In nature obligate vegetative reproduction seems to be more common and long term in taxa whose cytological features ensure a relatively low load under it. The same model also describes the mutation load under two other modes of inheritance: (1) uniparental transmission of organelles and (2) reproduction by division of multinuclear cells, where each daughter cell receives many nuclei. The load declines substantially when the deleterious mutation rate per organelle genome gets lower or when the number of nuclei in a cell sometimes drops. This may explain the small sizes of organelle genomes in sexual lineages and the presence of karyonic cycles in asexual unicellular multinuclear eukaryotes.     

Quantitative genetic variation in Daphnia: temporal changes in genetic architecture

Nonadditive genetic variation and genetic disequilibrium are two important factors that influence the evolutionary trajectory of natural populations. We assayed quantitative genetic variation in a temporary-pond-dwelling population of Daphnia pulex over a full season to examine the role of nonadditive genetic variation and genetic disequilibrium in determining the short-term evolutionary trajectory of a cyclic parthenogen. Quantitative traits were influenced by three factors: (1) clonal selection significantly changed the population mean phenotype during the course of the growing season; (2) sexual reproduction and recombination led to significant changes in life-history trait means and the levels of expressed genetic variation, implying the presence of substantial nonadditive genetic variation and genetic disequilibrium; and (3) Egg-bank effects were found to be an important component of the realized year-to-year change. Additionally, we examined the impact of genetic disequilibria induced by clonal selection on the genetic (co)variance structure with a common principal components model. Clonal selection caused significant changes in the (co)variance structure that were eliminated by a single bout of random mating, suggesting that a build-up of disequilibria was the primary source of changes in the (co)variance structure. The results of this study highlight the complexity of natural selection operating on populations that undergo alternating phases of sexual and asexual reproduction.     

Mutation accumulation in space and the maintenance of sexual reproduction

The maintenance of sexual reproduction remains one of the major puzzles of evolutionary biology, since, all else being equal, an asexual mutant should have a twofold fitness advantage over the sexual wildtype. Most theories suggest that sex helps either to purge deleterious mutations, or to adapt to changing environments. Both mechanisms have their limitations if they act in isolation because they require either high genomic mutation rates or very virulent pathogens, and it is therefore often thought that they must act together to maintain sex. Typically, however, these theories have in common that they are not based on spatial processes. Here, we show that local dispersal and local competition can explain the maintenance of sexual reproduction as a means of purging deleterious mutations. Using a spatially explicit individual-based model, we find that even with reasonably low genomic mutation rates and large total population sizes, asexual clones cannot invade a sexual population. Our results demonstrate how spatial processes affect mutation accumulation such that it can fully erode the twofold benefit of asexuality faster than an asexual clone can take over a sexual population. Thus, the cost of sex is generally overestimated in models that ignore the effects of space on mutation accumulation.     

EVOLUTION OF TRADE-OFFS BETWEEN SEXUAL AND ASEXUAL PHASES AND THE ROLE OF REPRODUCTIVE PLASTICITY IN THE GENETIC ARCHITECTURE OF APHID LIFE HISTORIES

Life‐history theory postulates that evolution is constrained by trade‐offs (i.e., negative genetic correlations) among traits that contribute to fitness. However, in organisms with complex life cycles, trade‐offs may drastically differ between phases, putatively leading to different evolutionary trajectories. Here, we tested this possibility by examining changes in life‐history traits in an aphid species that alternates asexual and sexual reproduction in its life cycle. The quantitative genetics of reproductive and dispersal traits was studied in 23 lineages (genotypes) of the bird cherry‐oat aphid Rhopalosiphum padi, during both the sexual and asexual phases, which were induced experimentally under specific environmental conditions. We found large and significant heritabilities (broad‐sense) for all traits and several negative genetic correlations between traits (trade‐offs), which are related to reproduction (i.e., numbers of the various sexual or asexual morphs) or dispersal (i.e., numbers of winged or wingless morphs). These results suggest that R. padi exhibits lineage specialization both in reproductive and dispersal strategies. In addition, we found important differences in the structure of genetic variance–covariance matrices ( G ) between phases. These differences were due to two large, negative genetic correlations detected during the asexual phase only: (1) between fecundity and age at maturity and (2) between the production of wingless and winged parthenogenetic females. We propose that this differential expression in genetic architecture results from a reallocation scheme during the asexual phase, when sexual morphs are not produced. We also found significant G × E interaction and nonsignificant genetic correlations across phases, indicating that genotypes could respond independently to selection in each phase. Our results reveal a rather unique situation in which the same population and even the same genotypes express different genetic (co)variation under different environmental conditions, driven by optimal resource allocation criteria.     

Evolutionary traction: the cost of adaptation and the evolution of sex

The advantage of sexual reproduction remains a puzzle for evolutionary biologists. Everything else being equal, asexual populations are expected to have twice the number of offspring produced by similar sexual populations. Yet, asexual species are uncommon among higher eukaryotes. In models assuming small populations, high mutation rates, or frequent environmental changes, sexual reproduction seems to have at least a two-fold advantage over asexuality. But the advantage of sex for large populations, low mutation rates, and rare or mild environmental changes remains a conundrum. Here we show that without recombination, rare advantageous mutations can result in increased accumulation of deleterious mutations ('evolutionary traction'), which explains the long-term advantage of sex under a wide parameter range.     

The fate of transposable elements in asexual populations

Sexual reproduction and recombination are important for maintaining a stable copy number of transposable elements (TEs). In sexual populations, elements can be contained by purifying selection against host carriers with higher element copy numbers; however, in the absence of sex and recombination, asexual populations could be driven to extinction by an unchecked proliferation of TEs. Here we provide a theoretical framework for analyzing TE dynamics under asexual reproduction. Analytic results show that, in an infinite asexual population, an equilibrium in copy number is achieved if no element excision is possible, but that all TEs are eliminated if there is some excision. In a finite population, computer simulations demonstrate that small populations are driven to extinction by a Muller's ratchet-like process of element accumulation, but that large populations can be cured of vertically transmitted TEs, even with excision rates well below transposition rates. These results may have important consequences for newly arisen asexual lineages and may account for the lack of deleterious retrotransposons in the putatively ancient asexual bdelloid rotifers.     

Stabilizing selection,mutational bias,and the evolution of sex*

Stabilizing selection around a fixed phenotypic optimum is expected to disfavor sexual reproduction, since asexually reproducing organisms can maintain a higher fitness at equilibrium, while sex disrupts combinations of compensatory mutations. This conclusion rests on the assumption that mutational effects on phenotypic traits are unbiased, that is, mutation does not tend to push phenotypes in any particular direction. In this article, we consider a model of stabilizing selection acting on an arbitrary number of polygenic traits coded by bialellic loci, and show that mutational bias may greatly reduce the mean fitness of asexual populations compared with sexual ones in regimes where mutations have weak to moderate fitness effects. Indeed, mutation and drift tend to push the population mean phenotype away from the optimum, this effect being enhanced by the low effective population size of asexual populations. In a second part, we present results from individual‐based simulations showing that positive rates of sex are favored when mutational bias is present, while the population evolves toward complete asexuality in the absence of bias. We also present analytical (QLE) approximations for the selective forces acting on sex in terms of the effect of sex on the mean and variance in fitness among offspring.     

Anisogamy,sexual selection,and the evolution and maintenance of sex

Summary In the present paper we distinguish between two aspects of sexual reproduction. Genetic recombination is a universal features of the sexual process. It is a primitive condition found in simple, single-celled organisms, as well as in higher plants and animals. Its function is primarily to repair genetic damage and eliminate deleterious mutations. Recombination also produces new variation, however, and this can provide the basis for adaptive evolutionary change in spatially and temporally variable environments.The other feature usually associated with sexual reproduction, differentiated male and female roles, is a derived condition, largely restricted to complex, diploid, multicellular organisms. The evolution of anisogamous gametes (small, mobile male gametes containing only genetic material, and large, relatively immobile female gametes containing both genetic material and resources for the developing offspring) not only established the fundamental basis for maleness and femaleness, it also led to an asymmetry between the sexes in the allocation of resources to mating and offspring. Whereas females allocate their resources primarily to offspring, the existence of many male gametes for each female one results in sexual selection on males to allocate their resources to traits that enhance success in competition for fertilizations. A consequence of this reproductive competition, higher variance in male than female reproductive success, results in more intense selection on males.The greater response of males to both stabilizing and directional selection constitutes an evolutionary advantage of males that partially compensates for the cost of producing them. The increased fitness contributed by sexual selection on males will complement the advantages of genetic recombination for DNA repair and elimination of deleterious mutations in any outcrossing breeding system in which males contribute only genetic material to their offspring. Higher plants and animals tend to maintain sexual reproduction in part because of the enhanced fitness of offspring resulting from sexual selection at the level of individual organisms, and in part because of the superiority of sexual populations in competition with asexual clones.     

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.