A comparison of sexual and asexual replication strategies in a simplified model based on the yeast life cycle

This paper develops simplified mathematical models describing the mutation-selection balance for the asexual and sexual replication pathways in Saccharomyces cerevisiae, or Baker’s yeast. The simplified models are based on the single-fitness-peak approximation in quasispecies theory. We assume diploid genomes consisting of two chromosomes, and we assume that each chromosome is functional if and only if its base sequence is identical to some master sequence. The growth and replication of the yeast cells is modeled as a first-order process, with first-order growth rate constants that are determined by whether a given genome consists of zero, one, or two functional chromosomes. In the asexual pathway, we assume that a given diploid cell divides into two diploids. For the sake of generality, our model allows for mitotic recombination and asymmetric chromosome segregation. In the sexual pathway, we assume that a given diploid cell divides into two diploids, each of which then divide into two haploids. The resulting four haploids enter a haploid pool, where they grow and replicate until they meet another haploid with which to fuse. In the sexual pathway, we consider two mating strategies: (1) a selective strategy, where only haploids with functional chromosomes can fuse with one another; (2) a random strategy, where haploids randomly fuse with one another. When the cost for sex is low, we find that the selective mating strategy leads to the highest mean fitness of the population, when compared to all of the other strategies. When the cost for sex is low, sexual replication with random mating also has a higher mean fitness than asexual replication without mitotic recombination or asymmetric chromosome segregation. We also show that, at low replication fidelities, sexual replication with random mating has a higher mean fitness than asexual replication, as long as the cost for sex is low. If the fitness penalty for having a defective chromosome is sufficiently high and the cost for sex sufficiently low, then at low replication fidelities the random mating strategy has a mean fitness that is a factor of larger than the asexual mean fitness. We argue that for yeast, the selective mating strategy is the one that is closer to reality, which if true suggests that sex may provide a selective advantage under considerably more relaxed conditions than previous research has indicated. The results of this paper also suggest that S. cerevisiae switches from asexual to sexual replication when stressed, because stressful growth conditions provide an opportunity for the yeast to clear out deleterious mutations from their genomes. That being said, our model does not contradict theories for the evolution of sex that argue that sex evolved because it allows a population to more easily adapt to changing conditions.     

Can punishment maintain sex?

Individuals who reproduce asexually have a two-fold advantage over their sexually-reproducing counterparts as they are able to reproduce twice as fast. Explaining why sexual reproduction is favoured over asexual reproduction therefore remains an important challenge in evolutionary biology. Various mechanisms involving resistance to parasites, adaptation to novel environments and helping to purge the genome of deleterious mutations have all been proposed as potential mechanisms which could promote the evolution of sex. A recent article has suggested that spiteful males may help to reduce the two-fold advantage of asexual females. Here I discuss this idea, and further ask whether punishment of asexual females by sexual females could be one way in which sexual reproduction could be maintained in groups of animals; in light of recent research on the repression of competition, it could be possible that asexual females which reproduce faster than their sexual counterparts will be punished for using group resources. It may therefore be possible that the behaviour of sexual individuals towards asexual females could have fitness consequences which could potentially reduce the two-fold advantage they gain from reproducing parthenogenetically.     

Molecular evidence for ancient asexuality in timema stick insects

Asexuality is rare in animals in spite of its apparent advantage relative to sexual reproduction, indicating that it must be associated with profound costs [1-9]. One expectation is that reproductive advantages gained by new asexual lineages will be quickly eroded over time [3, 5-7]. Ancient asexual taxa that have evolved and adapted without sex would be "scandalous" exceptions to this rule, but it is often difficult to exclude the possibility that putative asexuals deploy some form of "cryptic" sex, or have abandoned sex more recently than estimated from divergence times to sexual relatives [10]. Here we provide evidence, from high intraspecific divergence of mitochondrial sequence and nuclear allele divergence patterns, that several independently derived Timema stick-insect lineages have persisted without recombination for more than a million generations. Nuclear alleles in the asexual lineages displayed significantly higher intraindividual divergences than in related sexual species. In addition, within two asexuals, nuclear allele phylogenies suggested the presence of two clades, with sequences from the same individual appearing in both clades. These data strongly support ancient asexuality in Timema and validate the genus as an exceptional opportunity to attack the question of how asexual reproduction can be maintained over long periods of evolutionary time.     

Imitating the cost of males: A hypothesis for coexistence of all‐female sperm‐dependent species and their sexual host

All‐female sperm‐dependent species are particular asexual organisms that must coexist with a closely related sexual host for reproduction. However, demographic advantages of asexual over sexual species that have to produce male individuals could lead both to extinction. The unresolved question of their coexistence still challenges and fascinates evolutionary biologists. As an alternative hypothesis, we propose those asexual organisms are afflicted by a demographic cost analogous to the production of males to prevent exclusion of the host. Previously proposed hypotheses stated that asexual individuals relied on a lower fecundity than sexual females to cope with demographic advantage. In contrast, we propose that both sexual and asexual species display the same number of offspring, but half of asexual individuals imitate the cost of sex by occupying ecological niches but producing no offspring. Simulations of population growth in closed systems under different demographic scenarios revealed that only the presence of nonreproductive individuals in asexual females can result in long‐term coexistence. This hypothesis is supported by the fact that half of the females in some sperm‐dependent organisms did not reproduce clonally.     

Segregation and the evolution of sex under overdominant selection

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

ON GENETIC SEGREGATION AND THE EVOLUTION OF SEX

It has recently been argued that because the genetic load borne by an asexual species resulting from segregation, relative to a comparable sexual population, is greater than two, sex can overcome its twofold disadvantage and succeed. We evaluate some of the assumptions underlying this argument and discuss alternative assumptions. Further, we simulate the dynamics of competition between sexual and asexual types. We find that for populations of size 100 and 500 the advantages of segregation do not outweigh the cost of producing males. We conclude that, at least for small populations, drift and the cost of sex govern the evolution of sexuality, not selection or segregation. We believe, however, that if sexual and asexual populations were isolated for a sufficiently long period, segregation might impart a fitness advantage upon sexuals that could compensate for the cost of sex and allow sexuals to outcompete asexuals upon their reunion.     

Physiological dependence on copulation in parthenogenetic females can reduce the cost of sex

Despite the two-fold reproductive advantage of asexual over sexual reproduction, the majority of eukaryotic species are sexual. Why sex is so widespread is still unknown and remains one of the most important unanswered questions in evolutionary biology. Although there are several hypothesized mechanisms for the maintenance of sex, all require assumptions that may limit their applicability. I suggest that the maintenance of sex may be aided by the detrimental retention of ancestral traits related to sexual reproduction in the asexual descendants of sexual taxa. This reasoning is based on the fact that successful reproduction in many obligately sexual species is dependent upon the behavioural, physical and physiological cues that accompany sperm delivery. More specifically, I suggest that although parthenogenetic (asexual) females have no need for sperm per se, parthenogens descended from sexual ancestors may not be able to reach their full reproductive potential in the absence of the various stimuli provided by copulatory behaviour. This mechanism is novel in assuming no intrinsic advantage to producing genetically variable offspring; rather, sex is maintained simply through phylogenetic constraint. I review and synthesize relevant literature and data showing that access to males and copulation increases reproductive output in both sexual and parthenogenetic females. These findings suggest that the current predominance of sexual reproduction, despite its well-documented drawbacks, could in part be due to the retention of physiological dependence on copulatory stimuli in parthenogenetic females.     

Genetic signature of amphimixis allows for the detection and fine scale localization of sexual reproduction events in a mainly parthenogenetic nematode

Asexuality is an important mode of reproduction in eukaryotic taxa and has a theoretical advantage over sexual reproduction because of the increased ability to propagate genes. Despite this advantage, hidden signs of cryptic sex have been discovered in the genomes of asexual organisms. This has provided an interesting way to address the evolutionary impact of sex in plant and animal populations. However, the identification of rare sexual reproduction events in mainly asexual species has remained a challenging task. We examined the reproductive history in populations of the plant parasitic nematode Xiphinema index by genotyping individuals collected from six grapevine fields using seven microsatellite markers. A high level of linkage disequilibrium and heterozygous excess suggested a clonality rate of 95–100%. However, we also detected rare sexual reproduction events within these highly clonal populations. By combining highly polymorphic markers with an appropriate hierarchical sampling, and using both Bayesian and multivariate analysis with phylogenetic reconstructions, we were able to identify a small number of sexually produced individuals at the overlapping zones between different genetic clusters. This suggested that sexual reproduction was favoured when and where two nematode patches came into contact. Among fields, a high degree of genetic differentiation indicated a low level of gene flow between populations. Rare genotypes that were shared by several populations suggested passive dispersal by human activities, possibly through the introduction of infected plants from nurseries. We conclude that our method can be used to detect and locate sexual events in various predominantly asexual species.     

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 maintenance of sex in parasites

The maintenance of sex is an unresolved paradox in evolutionary biology, given the inherent twofold fitness advantage for asexuals. Parasitic helminths offer a unique opportunity to address this enigma. Parasites that can create novel antigenic strains are able to escape pre-existing host immunity. Viruses produce diversity through mutation with rapid clonal proliferation. The long generation times of helminth parasites prevent them from adopting this strategy. Instead, we argue that sexual reproduction enables parasitic helminths to rapidly generate strain diversity. We use both a stochastic, individual-based model and a simple analytical model to assess the selective value of sexual versus asexual reproduction in helminth parasites. We demonstrate that sexual reproduction can more easily produce and maintain strain diversity than asexual reproduction for long-lived parasites. We also show that sexual parasite populations are resistant to invasion by rare asexual mutants. These results are robust to high levels of cross-immunity between strains. We suggest that the enhancement of strain diversity, despite stochastic extinction of strains, may be critical to the evolutionary success of sex in long-lived parasites.     

ENVIRONMENTAL STRESS AND THE MAINTENANCE OF SEX IN A FRESHWATER SNAIL

Synergism among mutations can lead to an advantage to sexual reproduction, provided mutation rates are high enough (the mutational deterministic hypothesis). Here we tested the idea that competition for food can increase the advantage to sexual reproduction, perhaps by increasing the synergism among mutations in asexual individuals. We compared the survivorship of sexual and asexual snails (Potamopyrgus antipodarum) under two treatments: starved and fed. We predicted higher mortality for asexual snails when starved, but found that sexual and asexual individuals survived at the same rate, independent of treatment. These results suggest that the distribution of sex in this snail may not be explained by variation in competition among populations.     

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.     

Difference in parasite load and nonspecific immune reaction between sexual and gynogenetic forms of Carassius auratus

For coexistence, the sexual form in sexual/asexual complexes needs short-term advantages that can compensate for the two-fold disadvantage of sex. Higher mortality in the asexual form due to a higher parasite load will provide an advantage to the sexual form. In Lake Suwa, Japan, the parasite load (Metagonnimus sp.; Trematoda) of triploid gynogenetic females of Carassius auratus was significantly higher than that of diploid sexual females. In an immunoassay using healthy wild fish that were conditioned for 1 month in laboratory tanks, the nitroblue tetrazolium (NBT) immune reaction of sexual females was significantly higher than that of gynogenetic females. The NBT activity indicates the abundance of oxygen radicals from phagocytes, and hence the level of immune activity of the phagocytes. We suggest that the higher parasite load of the gynogenetic form is in part due to the lower immune activity of the phagocytes (nonspecific immune reaction) in the gynogenetic form compared to the sexual form.     

QUANTITATIVE GENETICS AND POPULATION DYNAMICS

This study examines the dynamics of a competition and a host-parasite model in which the interactions are determined by quantitative characters. Both models are extensions of one-dimensional difference equations that can exhibit complicated dynamics. Compared to these basic models, the phenotypic variability given by the quantitative characters reduces the size of the density fluctuations in asexual populations. With sexual reproduction, which is described by modeling the genetics of the quantitative character explicitly with many haploid loci that determine the character additively, this reduction in fitness variance is magnified. Moreover, quantitative genetics can induce simple dynamics. For example, the sexual population can have a two-cycle when the asexual system is chaotic. This paper discusses the consequences for the evolution of sex. The higher mean growth rate implied by the lower fitness variance in sexual populations is an advantage that can overcome a twofold intrinsic growth rate of asexuals. The advantage is bigger when the asexual population contains only a subset of the phenotypes present in the sexual population, which conforms with the tangled bank theory for the evolution of sex and shows that tangled bank effects also occur in host-parasite systems. The results suggest that explicitly describing the genetics of a quantitative character leads to more flexible models than the usual assumption of normal character distributions, and therefore to a better understanding of the character's impact on population dynamics.     

The evolution of sex is favoured during adaptation to new environments

Both theory and experiments have demonstrated that sex can facilitate adaptation, potentially yielding a group-level advantage to sex. However, it is unclear whether this process can help solve the more difficult problem of the maintenance of sex within populations. Using experimental populations of the facultatively sexual rotifer Brachionus calyciflorus, we show that rates of sex evolve to higher levels during adaptation but then decline as fitness plateaus. To assess the fitness consequences of genetic mixing, we directly compare the fitnesses of sexually and asexually derived genotypes that naturally occur in our experimental populations. Sexually derived genotypes are more fit than asexually derived genotypes when adaptive pressures are strong, but this pattern reverses as the pace of adaptation slows, matching the pattern of evolutionary change in the rate of sex. These fitness assays test the net effect of sex but cannot be used to disentangle whether selection on sex arises because highly sexual lineages become associated with different allele combinations or with different allele frequencies than less sexual lineages (i.e., "short-" or "long-term" effects, respectively). We infer which of these mechanisms provides an advantage to sex by performing additional manipulations to obtain fitness distributions of sexual and asexual progeny arrays from unbiased parents (rather than from naturally occurring, and thereby evolutionarily biased, parents). We find evidence that sex breaks down adaptive gene combinations, resulting in lower average fitness of sexual progeny (i.e., a short-term disadvantage to sex). As predicted by theory, the advantage to sex arises because sexually derived progeny are more variable in fitness, allowing for faster adaptation. This "long-term advantage" builds over multiple generations, eventually resulting in higher fitness of sexual types.     

Why reproduce sexually?

There is reason to believe that intense selection, such that only a small minority at the top of the fitness distribution has any appreciable chance of survival, can sometimes give sexual reproduction an immediate (one-life-cycle) advantage over asexual. The advantage must be great enough to balance the 50% loss of genetic material in meiosis.One model shows the advantage to be frequency-dependent in life cycles in which there are several asexual generations and one sexual. The observed frequency of sexual reproduction in such a life cycle is explained as an evolutionary equilibrium by this model. In another model the optimum frequency of asexual reproduction drops to zero as fecundity and competition increase. This explains the exclusively sexual reproduction of such fecund organism as elms and oysters. Once lost, asexual reproduction may be difficult to evolve secondarily. This explains the presence of such exclusively sexual, low-fecundity organisms as the higher vertebrates.     

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.     

Genetic variation and asexual reproduction in the facultatively parthenogenetic cockroach Nauphoeta cinerea: implications for the evolution of sex

Asexual reproduction could offer up to a two‐fold fitness advantage over sexual reproduction, yet higher organisms usually reproduce sexually. Even in facultatively parthenogenetic species, where both sexual and asexual reproduction is sometimes possible, asexual reproduction is rare. Thus, the debate over the evolution of sex has focused on ecological and mutation‐elimination advantages of sex. An alternative explanation for the predominance of sex is that it is difficult for an organism to accomplish asexual reproduction once sexual reproduction has evolved. Difficulty in returning to asexuality could reflect developmental or genetic constraints. Here, we investigate the role of genetic factors in limiting asexual reproduction in Nauphoeta cinerea, an African cockroach with facultative parthenogenesis that nearly always reproduces sexually. We show that when N. cinerea females do reproduce asexually, offspring are genetically identical to their mothers. However, asexual reproduction is limited to a nonrandom subset of the genotypes in the population. Only females that have a high level of heterozygosity are capable of parthenogenetic reproduction and there is a strong familial influence on the ability to reproduce parthenogenetically. Although the mechanism by which genetic variation facilitates asexual reproduction is unknown, we suggest that heterosis may facilitate the switch from producing haploid meiotic eggs to diploid, essentially mitotic, eggs.     

Genetic variation of geminiviruses: comparison between sexual and asexual host plant populations

One of the most promising hypotheses for the evolution of sex is that sexual reproduction is advantageous because it increases the rate of adaptive evolution in response to parasites. To investigate this advantage of sex, we compared genetic variation of geminiviruses infecting sexual and asexual populations of Eupatorium (Asteraceae). The infection frequency was 37.5% in the sexual population and 87.8% in the asexual population. The lower infection frequency in the sexual population might be the result of higher genetic diversity of host plants. If geminiviruses have diverged to counter defence systems of genetically variable hosts, genetic diversity of viruses is expected to be higher in sexual host populations than in asexual host populations. To test this expectation, we used single-strand conformation polymorphism (SSCP) analysis to examine genetic diversity of the geminiviruses in a DNA region containing the open-reading frame (ORF) C4 gene, which is known to function as a host range determinant. As predicted, higher genetic diversity of viruses was observed in the sexual population: three SSCP types were found in the asexual population while six types were found in the sexual population. Sequencing of the polymerase chain reaction (PCR) products revealed further genetic diversity. Phylogenetic analysis of the sequences showed that the SSCP types belonged to four different clades. Several SSCP types from the same clade were found in the sexual population, whereas the asexual population included only one SSCP type from each clade. Amino acid replacements of ORF C4 are suggested to be accelerated in the sexual population. This evidence supports the hypothesis that sexual reproduction is advantageous as a defence against epidemic disease.     

THE MAINTENANCE OF SEX BY GROUP SELECTION

The traditional group-selection model for the maintenance of sex is based upon the assumption that the long-term evolutionary benefits of sexual reproduction result in asexual lineages having a higher extinction rate than sexual species. This model is reexamined, as is a related model that incorporates the possibility that sexual and asexual lines differ in their speciation rates. In these models, the long-term advantage of sex is opposed by a strong short-term disadvantage arising from the twofold reproductive cost of producing males. It is shown that once some sexual lines become established, then group selection can act to maintain sex despite its short-term disadvantage. The short-term disadvantage is included in the model by assuming that, if asexual individuals arise by mutation within a previously completely sexual species, then the asexuals quickly displace their sexual conspecifics and the species is transformed to asexuality. The probability of this event is given by the transition rate, u_s. If the value of u_s varies between lineages, then one of the effects of group selection is to favor groups (i.e., species) with the lowest values of u_s. This occurs because lines that do convert to asexuality (because of a high u_s) are doomed to a high rate of extinction, and in the long term only those that do not convert to asexuality (because of a low u_s) survive. The net result of group selection is that sex is maintained because of its lower extinction rate (or higher speciation rate) and because asexual mutants only rarely arise.