Gradients for the evolution of bimatrix games

The evolutionary dynamics of bimatrix games is studied for rescaled partnership games and zero sum games. The former case leads to gradient systems. The selection equations for sexual and asexual reproduction of genotypes corresponding to mixed strategies are analysed. As examples, the origin of anisogamy and cyclic chases for predator-prey coevolution are studied.     

Feasibility of communication in binary signaling games

In signaling games the replicator dynamics does not almost always converge to states of perfect communication. A significant portion of the state space converges to components of Nash equilibria that characterize states of partial communication. Since these components consist of non-hyperbolic rest points, the significance of this result will depend on the dynamic behavior of specific perturbations of the replicator equations. In this paper we study selection-mutation dynamics of signaling games, which may be considered as one plausible perturbation of the replicator dynamics. We find that the long term behavior of the dynamics depends on the mutation rates of senders and receivers and on the relevance of communication.     

Adaptive Significance and Long-Term Survival of Asexual Lineages

Important questions remain about the long-term survival and adaptive significance of eukaryotic asexual lineages. Numerous papers dealing with sex advantages still continued to compare parthenogenetic populations versus sexual populations arguing that sex demonstrates a better fitness. Because asexual lineages do not possess any recombination mechanisms favoring rapid changes in the face of severe environmental conditions, they should be considered as an evolutionary dead-end. Nevertheless, reviewing literature dealing with asexual reproduction, it is possible to draw three stimulating conclusions. (1) Asexual reproduction in eukaryotes considerably differs from prokaryotes which experience recombination but neither meiosis nor syngamy. Recombination and meiosis would be a driving force for sexual reproduction. Eukaryotes should therefore be considered as a continuum of sexual organisms that are more or less capable (and sometimes incapable) of sexual reproduction. (2) Rather than revealing ancestral eukaryotic forms, most known lineages of asexual eukaryotes have lost sex due to a genomic conflict affecting their sexual capacity. Thus, it could be argued that hybridization is a major cause of their asexuality. Asexuality may have evolved as a reproductive mechanism reducing conflict within organisms. (3) It could be proposed that, rather than being generalists, parthenogenetic hybrid lineages could be favored when exploiting peculiar restricted ecological niches, following the “frozen niche variation” model. Although hybrid events may result in sex loss, probably caused by genomic conflict, asexual hybrids could display new original adaptive traits, and the rapid colonization of environments through clonal reproduction could favor their long-term survival, leading to evolutionary changes and hybrid speciation. Examination of the evolutionary history of asexual lineages reveals that evolutionary processes act through transitional stages in which even very small temporary benefits may be enough to counter the expected selective disadvantages.     

A quasispecies approach to the evolution of sexual replication in unicellular organisms

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.     

Genetic Variation in Reproductive Investment Across an Ephemerality Gradient in Daphnia pulex

Species across the tree of life can switch between asexual and sexual reproduction. In facultatively sexual species, the ability to switch between reproductive modes is often environmentally dependent and subject to local adaptation. However, the ecological and evolutionary factors that influence the maintenance and turnover of polymorphism associated with facultative sex remain unclear. We studied the ecological and evolutionary dynamics of reproductive investment in the facultatively sexual model species, Daphnia pulex. We found that patterns of clonal diversity, but not genetic diversity varied among ponds consistent with the predicted relationship between ephemerality and clonal structure. Reconstruction of a multi-year pedigree demonstrated the coexistence of clones that differ in their investment into male production. Mapping of quantitative variation in male production using lab-generated and field-collected individuals identified multiple putative quantitative trait loci (QTL) underlying this trait, and we identified a plausible candidate gene. The evolutionary history of these QTL suggests that they are relatively young, and male limitation in this system is a rapidly evolving trait. Our work highlights the dynamic nature of the genetic structure and composition of facultative sex across space and time and suggests that quantitative genetic variation in reproductive strategy can undergo rapid evolutionary turnover.     

The consequences of facultative sex in a prey adapting to predation

A species reproductive mode, along with its associated costs and benefits, can play a significant role in its evolution and survival. Facultative sexuality, being able to reproduce both sexually and asexually, has been deemed evolutionary favourable as the benefits of either mode may be fully realized. In fact, many studies have focused on identifying the benefits of sex and/or the forces selecting for increased rates of sex using facultative sexual species. The costs of either mode, however, can also have a profound impact on a population's evolutionary trajectory. Here, we used experimental evolution and fitness assays to investigate the consequences of facultative sexuality in prey adapting to predation. Specifically, we compared the adaptive response of algal prey populations exposed to constant rotifer predation and which had alternating cycles of asexual and sexual reproduction where sexual episodes were either facultative (sexual and asexual progeny simultaneously propagated) or obligate (only sexual progeny propagated). We found that prey populations with facultative sexual episodes reached a lower final relative fitness and suffered a greater trade‐off in traits under selection, that is defence and competitive ability, as compared to prey populations with obligate sexual episodes. Our results suggest that costs associated with sexual reproduction (germination time) and asexual reproduction (selection interference) were amplified in the facultative sexual prey populations, leading to a reduction in the net advantage of sexuality. Additionally, we found evidence that the cost of sex was reduced in the obligate sexual prey populations because increased selection for sex was observed via the spontaneous production of sexual cells. These results show that certain costs associated with facultative sexuality can affect an organism's evolutionary trajectory.     

No sex in fungus-farming ants or their crops

Asexual reproduction imposes evolutionary handicaps on asexual species, rendering them prone to extinction, because asexual reproduction generates novel genotypes and purges deleterious mutations at lower rates than sexual reproduction. Here, we report the first case of complete asexuality in ants, the fungus-growing ant Mycocepurus smithii, where queens reproduce asexually but workers are sterile, which is doubly enigmatic because the clonal colonies of M. smithii also depend on clonal fungi for food. Degenerate female mating anatomy, extensive field and laboratory surveys, and DNA fingerprinting implicate complete asexuality in this widespread ant species. Maternally inherited bacteria (e.g. Wolbachia, Cardinium) and the fungal cultivars can be ruled out as agents inducing asexuality. M. smithii societies of clonal females provide a unique system to test theories of parent–offspring conflict and reproductive policing in social insects. Asexuality of both ant farmer and fungal crop challenges traditional views proposing that sexual farmer ants outpace coevolving sexual crop pathogens, and thus compensate for vulnerabilities of their asexual crops. Either the double asexuality of both farmer and crop may permit the host to fully exploit advantages of asexuality for unknown reasons or frequent switching between crops (symbiont reassociation) generates novel ant–fungus combinations, which may compensate for any evolutionary handicaps of asexuality in M. smithii.     

Multiple losses of sex within a single genus of Microsporidia

Background  

Most asexual eukaryotic lineages have arisen recently from sexual ancestors and contain few ecologically distinct species, providing evidence for long-term advantages of sex. Ancient asexual lineages provide rare exceptions to this rule and so can yield valuable information relating to the evolutionary forces underlying the maintenance of sex. Microsporidia are parasitic, unicellular fungi. They include many asexual species which have traditionally been grouped together into large, presumably ancient taxonomic groups. However, these putative ancient asexual lineages have been identified on the basis of morphology, life cycles and small subunit ribosomal RNA (16S rRNA) gene sequences, all of which hold questionable value in accurately inferring phylogenetic relationships among microsporidia.     

Maintenance of sexually dimorphic preadult traits in Marchantia inflexa (Marchantiacae)

Marchantia inflexa, a dioecious thallose liverwort, is sexually dimorphic in clonal expansion traits. We used selection analyses to measure the magnitude and direction of selection on clonal fitness to uncover possible mechanisms for the maintenance of preadult sexually dimorphic characters. We planted replicates of genotypes of female and male M. inflexa in two light environments in a greenhouse and measured morphological and phenological characters associated with growth and asexual reproduction. Timing to onset of asexual reproduction and plant size early in development were under sex-specific selection in a low light environment. Additionally, females exhibited a sex-specific cost of plasticity in the timing of their onset of asexual reproduction in high light. Selection on asexual fitness tended to shift traits toward monomorphism rather than sexual dimorphism, whereas the expressed phenotype of females was congruent with patterns of selection acting on sexual fitness. We detected negative trade-offs between asexual and sexual fitness components in females in one light environment. Opposing selective forces acting on asexual and sexual fitness components may explain how sexual dimorphisms persist in the face of selection for monomorphism in the preadult phase.     

Exceptional cryptic diversity and multiple origins of parthenogenesis in a freshwater ostracod

The persistence of asexual reproduction in many taxa depends on a balance between the origin of new asexual lineages and the extinction of old ones. This turnover determines the diversity of extant asexual populations and so influences the interaction between sexual and asexual modes of reproduction. Species with mixed reproduction, like the freshwater ostracod (Crustacea) morphospecies Eucypris virens, are a good model to examine these dynamics. This species is also a geographic parthenogen, in which sexual females and males co-exist with asexual females in the circum-Mediterranean area only, whereas asexual females occur all over Europe. A molecular phylogeny of E. virens based on the mitochondrial COI and 16S fragments is presented. It is characterised by many distinct clusters of haplotypes which are either exclusively sexual or asexual, with only one exception, and are often separated by deep branches. Analysis of the phylogeny reveals an astonishing cryptic diversity, which indicates the existence of a species complex with more than 40 cryptic taxa. We therefore suggest a revision of the single species status of E. virens. The phylogeny indicates multiple transitions from diverse sexual ancestor populations to asexuality. Although many transitions appear to be ancient, we argue that this may be an artefact of the existence of unsampled or extinct sexual lineages.     

Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect

The adaptation of large asexual populations is hampered by the competition between independently arising beneficial mutations in different individuals, which is known as clonal interference. In classic work, Fisher and Muller proposed that recombination provides an evolutionary advantage in large populations by alleviating this competition. Based on recent progress in quantifying the speed of adaptation in asexual populations undergoing clonal interference, we present a detailed analysis of the Fisher–Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each and multiplicative (nonepistatic) fitness effects. We solve the deterministic, infinite population dynamics exactly and show that, for a particular, natural mutation scheme, the speed of adaptation in sexuals is twice as large as in asexuals. This result is argued to hold for any nonzero value of the rate of recombination. Guided by the infinite population result and by previous work on asexual adaptation, we postulate an expression for the speed of adaptation in finite sexual populations that agrees with numerical simulations over a wide range of population sizes and recombination rates. The ratio of the sexual to asexual adaptation speed is a function of population size that increases in the clonal interference regime and approaches 2 for extremely large populations. The simulations also show that the imbalance between the numbers of accumulated mutations at the two loci is strongly suppressed even by a small amount of recombination. The generalization of the model to an arbitrary number L of loci is briefly discussed. If each offspring samples the alleles at each locus from the gene pool of the whole population rather than from two parents, the ratio of the sexual to asexual adaptation speed is approximately equal to L in large populations. A possible realization of this scenario is the reassortment of genetic material in RNA viruses with L genomic segments.     

Asexual Experimental Evolution of Yeast Does Not Curtail Transposable Elements

Compared with asexual reproduction, sex facilitates the transmission of transposable elements (TEs) from one genome to another, but boosts the efficacy of selection against deleterious TEs. Thus, theoretically, it is unclear whether sex has a positive net effect on TE’s proliferation. An empirical study concluded that sex is at the root of TE’s evolutionary success because the yeast TE load was found to decrease rapidly in approximately 1,000 generations of asexual but not sexual experimental evolution. However, this finding contradicts the maintenance of TEs in natural yeast populations where sexual reproduction occurs extremely infrequently. Here, we show that the purported TE load reduction during asexual experimental evolution is likely an artifact of low genomic sequencing coverages. We observe stable TE loads in both sexual and asexual experimental evolution from multiple yeast data sets with sufficient coverages. To understand the evolutionary dynamics of yeast TEs, we turn to asexual mutation accumulation lines that have been under virtually no selection. We find that both TE transposition and excision rates per generation, but not their difference, tend to be higher in environments where yeast grows more slowly. However, the transposition rate is not significantly higher than the excision rate and the variance of the TE number among natural strains is close to its neutral expectation, suggesting that selection against TEs is at best weak in yeast. We conclude that the yeast TE load is maintained largely by a transposition–excision balance and that the influence of sex remains unclear.     

Phenotypic variation,sexual reproduction and evolutionary population dynamics

I studied the effects of introducing phenotypic variation into a well-known single species model for a population with discrete, non-overlapping generations. The phenotypes differed in their dynamic behaviour. The analysis was made under the assumption that the population was in an evolutionary stable state. Differences in the timing of the competitive impacts of the phenotypes on each other had a strong simplifying effect on the dynamics. This result could also be applied to competition between species. The effect of sexual reproduction on the dynamics of the population was analysed by assuming the simplest genetic model of one locus with two alleles. Sexual reproduction made the system much more stable in the (mathematical) sense that the number of attractors was reduced and their basins of attraction enlarged. In a dominant system sex tended to increase the frequency of the recessive allele, and in an overdominant system it induced gene frequencies of 1/2. Whether the attractors in the dominant system tended to be simpler or more complex than the attractors in the asexual system depended on the phenotype of the recessive homozygote. The overdominant sexual system tended to have simpler dynamics than the corresponding asexual population. A 2-locus model was used to study whether sexuals can invade an asexual population and vice versa. One locus coded for sexual and asexual reproduction, while the other coded for the dynamics. Enhanced stability through sexual reproduction seemed to be the reason why there was a clear asymmetry favouring sex in this evolutionary context.     

Thelytokous Parthenogenesis in the Fungus-Gardening Ant Mycocepurus smithii (Hymenoptera: Formicidae)

The general prevalence of sexual reproduction over asexual reproduction among organisms testifies to the evolutionary benefits of recombination, such as accelerated adaptation to changing environments and elimination of deleterious mutations. Documented instances of asexual reproduction in groups otherwise dominated by sexual reproduction challenge evolutionary biologists to understand the special circumstances that might confer an advantage to asexual reproductive strategies. Here we report one such instance of asexual reproduction in the ants. We present evidence for obligate thelytoky in the asexual fungus-gardening ant, Mycocepurus smithii, in which queens produce female offspring from unfertilized eggs, workers are sterile, and males appear to be completely absent. Obligate thelytoky is implicated by reproductive physiology of queens, lack of males, absence of mating behavior, and natural history observations. An obligate thelytoky hypothesis is further supported by the absence of evidence indicating sexual reproduction or genetic recombination across the species'' extensive distribution range (Mexico-Argentina). Potential conflicting evidence for sexual reproduction in this species derives from three Mycocepurus males reported in the literature, previously regarded as possible males of M. smithii. However, we show here that these specimens represent males of the congeneric species M. obsoletus, and not males of M. smithii. Mycocepurus smithii is unique among ants and among eusocial Hymenoptera, in that males seem to be completely absent and only queens (and not workers) produce diploid offspring via thelytoky. Because colonies consisting only of females can be propagated consecutively in the laboratory, M. smithii could be an adequate study organism a) to test hypotheses of the population-genetic advantages and disadvantages of asexual reproduction in a social organism and b) inform kin conflict theory.For a Portuguese translation of the abstract, please see Abstract S1.     

Density,parasitism, and sexual reproduction are strongly correlated in lake Daphnia populations

Many organisms can reproduce both asexually and sexually. For cyclical parthenogens, periods of asexual reproduction are punctuated by bouts of sexual reproduction, and the shift from asexual to sexual reproduction has large impacts on fitness and population dynamics. We studied populations of Daphnia dentifera to determine the amount of investment in sexual reproduction as well as the factors associated with variation in investment in sex. To do so, we tracked host density, infections by nine different parasites, and sexual reproduction in 15 lake populations of D. dentifera for 3 years. Sexual reproduction was seasonal, with male and ephippial female production beginning as early as late September and generally increasing through November. However, there was substantial variation in the prevalence of sexual individuals across populations, with some populations remaining entirely asexual throughout the study period and others shifting almost entirely to sexual females and males. We found strong relationships between density, prevalence of infection, parasite species richness, and sexual reproduction in these populations. However, strong collinearity between density, parasitism, and sexual reproduction means that further work will be required to disentangle the causal mechanisms underlying these relationships.     

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.     

Does Sex-Selective Predation Stabilize or Destabilize Predator-Prey Dynamics?

Background

Little is known about the impact of prey sexual dimorphism on predator-prey dynamics and the impact of sex-selective harvesting and trophy hunting on long-term stability of exploited populations.

Methodology and Principal Findings

We review the quantitative evidence for sex-selective predation and study its long-term consequences using several simple predator-prey models. These models can be also interpreted in terms of feedback between harvesting effort and population size of the harvested species under open-access exploitation. Among the 81 predator-prey pairs found in the literature, male bias in predation is 2.3 times as common as female bias. We show that long-term effects of sex-selective predation depend on the interplay of predation bias and prey mating system. Predation on the ‘less limiting’ prey sex can yield a stable predator-prey equilibrium, while predation on the other sex usually destabilizes the dynamics and promotes population collapses. For prey mating systems that we consider, males are less limiting except for polyandry and polyandrogyny, and male-biased predation alone on such prey can stabilize otherwise unstable dynamics. On the contrary, our results suggest that female-biased predation on polygynous, polygynandrous or monogamous prey requires other stabilizing mechanisms to persist.

Conclusions and Significance

Our modelling results suggest that the observed skew towards male-biased predation might reflect, in addition to sexual selection, the evolutionary history of predator-prey interactions. More focus on these phenomena can yield additional and interesting insights as to which mechanisms maintain the persistence of predator-prey pairs over ecological and evolutionary timescales. Our results can also have implications for long-term sustainability of harvesting and trophy hunting of sexually dimorphic species.     

Evolution as a critical component of plankton dynamics

Microevolution is typically ignored as a factor directly affecting ongoing population dynamics. We show here that density-dependent natural selection has a direct and measurable effect on a planktonic predator-prey interaction. We kept populations of Brachionus calyciflorus, a monogonont rotifer that exhibits cyclical parthenogenesis, in continuous flow-through cultures (chemostats) for more than 900 days. Initially, females frequently produced male offspring, especially at high population densities. We observed rapid evolution, however, towards low propensity to reproduce sexually, and by 750 days, reproduction had become entirely asexual. There was strong selection favouring asexual reproduction because, under the turbulent chemostat regime, males were unable to mate with females, produced no offspring, and so had zero fitness. In replicated chemostat experiments we found that this evolutionary process directly influenced the population dynamics. We observed very specific but reproducible plankton dynamics which are explained well by a mathematical model that explicitly includes evolution. This model accounts for both asexual and sexual reproduction and treats the propensity to reproduce sexually as a quantitative trait under selection. We suggest that a similar amalgam of ecological and evolutionary mechanisms may drive the dynamics of rapidly reproducing organisms in the wild.     

Does Sex Speed Up Evolutionary Rate and Increase Biodiversity?

Most empirical and theoretical studies have shown that sex increases the rate of evolution, although evidence of sex constraining genomic and epigenetic variation and slowing down evolution also exists. Faster rates with sex have been attributed to new gene combinations, removal of deleterious mutations, and adaptation to heterogeneous environments. Slower rates with sex have been attributed to removal of major genetic rearrangements, the cost of finding a mate, vulnerability to predation, and exposure to sexually transmitted diseases. Whether sex speeds or slows evolution, the connection between reproductive mode, the evolutionary rate, and species diversity remains largely unexplored. Here we present a spatially explicit model of ecological and evolutionary dynamics based on DNA sequence change to study the connection between mutation, speciation, and the resulting biodiversity in sexual and asexual populations. We show that faster speciation can decrease the abundance of newly formed species and thus decrease long-term biodiversity. In this way, sex can reduce diversity relative to asexual populations, because it leads to a higher rate of production of new species, but with lower abundances. Our results show that reproductive mode and the mechanisms underlying it can alter the link between mutation, evolutionary rate, speciation and biodiversity and we suggest that a high rate of evolution may not be required to yield high biodiversity.     

Stochastic evolutionary dynamics of bimatrix games

Evolutionary game dynamics of two-player asymmetric games in finite populations is studied. We consider two roles in the game, roles α and β. α-players and β-players interact and gain payoffs. The game is described by a pair of matrices, which is called bimatrix. One's payoff in the game is interpreted as its fecundity, thus strategies are subject to natural selection. In addition, strategies can randomly mutate to others. We formulate a stochastic evolutionary game dynamics of bimatrix games as a frequency-dependent Moran process with mutation. We analytically derive the stationary distribution of strategies under weak selection. Our result provides a criterion for equilibrium selection in general bimatrix games.