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.     

Fitness-associated recombination on rugged adaptive landscapes

A negative correlation between fitness and recombination rates seems to exist in various organisms. In this article we suggest that a correlation of that kind may play an important role in the evolution of complex traits. We study the effects of such fitness-associated recombination (FAR) in a simple two-locus deterministic model, as well as in a multi-loci NK rugged adaptive landscape. In both models studied, FAR results in faster adaptation and higher average population fitness, compared with uniform-rate recombination.     

On the evolutionary advantage of fitness-associated recombination

The adaptive value of recombination remains something of a puzzle. One of the basic problems is that recombination not only creates new and advantageous genetic combinations, but also breaks down existing good ones. A negative correlation between the fitness of an individual and its recombination rate would result in prolonged integrity of fitter genetic combinations while enabling less fit ones to produce new combinations. Such a correlation could be mediated by various factors, including stress responses, age, or direct DNA damage. For haploid population models, we show that an allele for such fitness-associated recombination (FAR) can spread both in asexual populations and in populations reproducing sexually at any uniform recombination rate. FAR also carries an advantage for the population as a whole, resulting in a higher average fitness at mutation-selection balance. These results are demonstrated in populations adapting to new environments as well as in well-adapted populations coping with deleterious mutations. Current experimental results providing evidence for the existence of FAR in nature are discussed.     

Selection, Generalized Transmission and the Evolution of Modifier Genes. I. the Reduction Principle

Modifier gene models are used to explore the evolution of features of organisms, such as the genetic system, that are not directly involved in the determination of fitness. Recent work has shown that a general "reduction principle" holds in models of selectively neutral modifiers of recombination, mutation, and migration. Here we present a framework for models of modifier genes that shows these reduction results to be part of a more general theory, for which recombination and mutation are special cases. The deterministic forces that affect the genetic composition of a population can be partitioned into two categories: selection and transmission. Selection includes differential viabilities, fertilities, and mating success. Imperfect transmission occurs as a result of such phenomena as recombination, mutation and migration, meiosis, gene conversion, and meiotic drive. Selectively neutral modifier genes affect transmission, and a neutral modifier gene can evolve only by generating association with selected genes whose transmission it affects. We show that, in randomly mating populations at equilibrium, imperfect transmission of selected genes allows a variance in their marginal fitnesses to be maintained. This variance in the marginal fitnesses of selected genes is what drives the evolution of neutral modifier genes. Populations with a variance in marginal fitnesses at equilibrium are always subject to invasion by modifier genes that bring about perfect transmission of the selected genes. It is also found, within certain constraints, that for modifier genes producing what we call "linear variation" in the transmission processes, a new modifier allele can invade a population at equilibrium if it reduces the level of imperfect transmission acting on the selected genes, and will be expelled if it increases the level of imperfect transmission. Moreover, the strength of the induced selection on the modifier gene is shown to range up to the order of the departure of the genetic system from perfect transmission.     

Evolution in the real world: stochastic variation and the determinants of fitness in Carlina vulgaris

Empirical studies of life histories often ignore stochastic variation, despite theoretical demonstrations of its potential impact on life-history evolution. Here we use a novel approach to explore the effects of stochastic variation on life-history evolution and estimate the selection pressures operating on the monocarpic perennial Carlina vulgaris, in which flowering may be delayed by up to eight years. The approach is novel in that we use modern theoretical techniques to estimate selection pressures and the fitness landscape from a fully parameterised individual-based model. These approaches take into account temporal variation in demographic rates and density dependence. Analysis of 16 years' data revealed significant temporal variation in growth, mortality, and recruitment in our study population. Flowering was strongly size dependent and, unusually for such a species, also age dependent. Individual-based models of the flowering strategy, parameterized using field data, consistently underestimated the size at flowering, when temporal variation in demographic rates was ignored. In contrast, models that incorporated temporal variation in growth, mortality, and recruitment predicted sizes at flowering not significantly different from those observed in the field. Temporal variation in mortality, which had the largest effect on the flowering strategy, selected for increased size at flowering. An analytical approximation is presented to explain this result, extending the "1-year look-ahead criterion" presented in Rees et al. (2000). A fitness landscape generated by following the fate of rare mutant invaders with a broad range of alternative flowering strategies demonstrated that the observed parameters were adaptive. However, the fitness landscape reveals that approximately equal fitness is achieved by a broad range of strategies, providing a mechanism for the maintenance of genetic variation. To understand how the different parameters that defined our models determine the fitness of rare mutants, we numerically estimated the elasticities and sensitivities of mutant fitness. This demonstrated strong selection on a number of the parameters. Elasticities and sensitivities estimated in constant and random environments were significantly positively correlated, and both were negatively related to the standard error of the parameter. This last result is surprising and, we argue, reflects the genetic and phenotypic responses to selection.     

Strategy selection in structured populations

Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix . We study a mutation and selection process. For weak selection strategy A is favored over B if and only if σa+b>c+σd. This means the effect of population structure on strategy selection can be described by a single parameter, σ. We present the values of σ for various examples including the well-mixed population, games on graphs, games in phenotype space and games on sets. We give a proof for the existence of such a σ, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between σ and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, σ, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games.     

Assortative mating for fitness and the evolution of recombination

To understand selection on recombination, we need to consider how linkage disequilibria develop and how recombination alters these disequilibria. Any factor that affects the development of disequilibria, including nonrandom mating, can potentially change selection on recombination. Assortative mating is known to affect linkage disequilibria but its effects on the evolution of recombination have not been previously studied. Given that assortative mating for fitness can arise indirectly via a number of biologically realistic scenarios, it is plausible that weak assortative mating occurs across a diverse set of taxa. Using a modifier model, we examine how assortative mating for fitness affects the evolution of recombination under two evolutionary scenarios: selective sweeps and mutation-selection balance. We find there is no net effect of assortative mating during a selective sweep. In contrast, assortative mating could have a large effect on recombination when deleterious alleles are maintained at mutation-selection balance but only if assortative mating is sufficiently strong. Upon considering reasonable values for the number of loci affecting fitness components, the strength of selection, and the mutation rate, we conclude that the correlation in fitness between mates is unlikely to be sufficiently high for assortative mating to affect the evolution of recombination in most species.     

The Evolution of Epistasis and the Advantage of Recombination in Populations of Bacteriophage T4

Experiments reported here test two hypotheses about the evolution of recombination: first, the Fisher-Muller concept that sexual organisms respond to selection more rapidly than do asexual ones, and second, that epistasis is more likely to evolve in the absence of recombination. Populations of bacteriophage T4 were selected by the drug proflavine in discrete generations and the change in mean population fitness was monitored. Three separate selection series yielded results supporting the Fisher-Muller hypothesis. The amount of epistasis evolved was measured by partitioning the T4 map into regions and comparing the sum of the proflavine resistances of each region with the resistance of the whole. Significantly more interactions were found in phage isolated from the populations with lower total recombination than in those from populations with higher recombination. The degree to which these experiments fit preconceived notions about natural selection suggests that microorganisms may be advantageously used in other population genetics experiments.     

Selection for recombination in partially self-fertilizing populations

This paper confirms Holden's (1979) suggestion that certain types of fitness interactions between a pair of loci in partially self-fertilizing populations may promote selection for increased recombination between them. Our results are based on both algebraic and computer calculations of the fate of alleles at a third locus, which control the level of recombination between the selected pair. We also show that the behavior of the population mean fitness as a function of recombination fraction is not necessarily an indicator of the direction of selection on recombination in partially selfing populations.     

The one-third law of evolutionary dynamics

Evolutionary game dynamics in finite populations provide a new framework for studying selection of traits with frequency-dependent fitness. Recently, a "one-third law" of evolutionary dynamics has been described, which states that strategy A fixates in a B-population with selective advantage if the fitness of A is greater than that of B when A has a frequency 13. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the "number"13 is not understood. In this paper we provide an intuitive explanation by studying the underlying stochastic processes. We find that in one invasion attempt, an individual interacts on average with B-players twice as often as with A-players, which yields the one-third law. We also show that the one-third law implies that the average Malthusian fitness of A is positive.     

Density dependence, lifespan and the evolutionary dynamics of longevity

Longevity is a life-history trait that is shaped by natural selection. Evolution will shape mortality trajectories and lifespans, but until now the evolutionary analysis of longevity is based principally on a density-independent (Euler-Lotka) framework. The effects of density dependence on the evolution of lifespan and mortality remain largely unexplored. We investigate the influence of different population demographies on the evolution of longevity, and show how these can be linked to adaptive radiations. We present a range of models to explore the intraspecific and interspecific density effects on longevity and, consequently, diversification. We show how the magnitude, type, and timing of mutation can also affect fitness, invasion and diversification. We argue that fitness of alternative strategies under a range of different demographic structures leads to flat, as opposed to rugged, landscapes and that these flat fitness surfaces are important in the evolution of lifespan and senescence.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Low Selection Pressure Aids the Evolution of Cooperative Ribozyme Mutations in Cells

Understanding the evolution of functional RNA molecules is important for our molecular understanding of biology. Here we tested experimentally how two evolutionary parameters, selection pressure and recombination, influenced the evolution of an evolving RNA population. This was done using four parallel evolution experiments that employed low or gradually increasing selection pressure, and recombination events either at the end or dispersed throughout the evolution. As model system, a trans-splicing group I intron ribozyme was evolved in Escherichia coli cells over 12 rounds of selection and amplification, including mutagenesis and recombination. The low selection pressure resulted in higher efficiency of the evolved ribozyme populations, whereas differences in recombination did not have a strong effect. Five mutations were responsible for the highest efficiency. The first mutation swept quickly through all four evolving populations, whereas the remaining four mutations accumulated later and more efficiently under low selection pressure. To determine why low selection pressure aided this evolution, all evolutionary intermediates between the wild type and the 5-mutation variant were constructed, and their activities at three different selection pressures were determined. The resulting fitness profiles showed a high cooperativity among the four late mutations, which can explain why high selection pressure led to inefficient evolution. These results show experimentally how low selection pressure can benefit the evolution of cooperative mutations in functional RNAs.     

Mutation-selection equilibrium in games with multiple strategies

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n×n games in the limit of weak selection.     

Adaption,neutrality and life-course diversity

Heterogeneity among individuals in fitness components is what selection acts upon. Evolutionary theories predict that selection in constant environments acts against such heterogeneity. But observations reveal substantial non-genetic and also non-environmental variability in phenotypes. Here, we examine whether there is a relationship between selection pressure and phenotypic variability by analysing structured population models based on data from a large and diverse set of species. Our findings suggest that non-genetic, non-environmental variation is in general neither truly neutral, selected for, nor selected against. We find much variations among species and populations within species, with mean patterns suggesting nearly neutral evolution of life-course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates. Our analysis suggests we are only at the beginning of understanding the evolution and maintenance of non-genetic non-environmental variation.     

Evolution of variance in offspring number: The effects of population size and migration

It was shown by Gillespie [1974. Am. Nat. 108, 145–151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is {ei65-1}, where w is the mean fitness, {ei65-2} is the variance in offspring number, and N is the total population size. The model also predicts that if a strategy has a higher arithmetic mean fitness and a higher variance than the competitor, the outcome of selection will depend on the population size (with larger population sizes favoring the highvariance, high-mean genotype). This suggests that for metapopulation sizes favoring the high-variance, high-mean genotype). This suggests that for metapopulations with large numbers of (relatively) small demes, a strategy with lower variance and lower mean may be favored if the migration rate is low while higher migration rates (consistent with a larger effective population size) favor the opposite strategy. Individual-based simulation confirms that this is indeed the case for an island model of migration, though the effect of migration differs greatly depending on whether migration precedes or follows selection. It is noted in the appendix that while Gillespie [1974. Am. Nat. 108, 145–151] does seem to be heuristically accurate, it is not clear that the definition of effective fitness follows from his derivation.     

Sexual selection and alternative mating behaviours generate demographic stochasticity in small populations.

Recent theory predicts that environmental variation and small population size facilitate the coexistence of alternative phenotypes despite unequal mean fitness. However, traditional studies of reproductive strategies often assume that the stability of alternative mating behaviours relies on equal male fitness. We present results from field observations and experimental manipulations of thermal resources on territories demonstrating the coexistence of alternative reproductive behaviours with unequal fitness. The side-blotched lizard Uta stansburiana exhibits two alternative strategies for territoriality: "usurp" and "defend". Paternity analysis revealed significantly greater mean fitness for "usurpers" than "defenders" in our study of natural variation. Moreover, variance in fitness was significantly higher for usurpers on both experimental and natural plots, implying that "usurp" is a risky strategy with potentially large pay-offs or none at all. We show theoretically that significantly higher variance in usurper fitness can allow for coexistence with defenders despite higher mean fitness of usurpers. This coexistence is facilitated by small population size. Our results have general implications for the evolution of alternative strategies and the maintenance of genetic diversity in small populations.     

Long-term experimental evolution in Escherichia coli. V. Effects of recombination with immigrant genotypes on the rate of bacterial evolution

This study builds upon an earlier experiment that examined the dynamics of mean fitness in evolving populations of Escherichia coli in which mutations were the sole source of genetic variation. During thousands of generations in a constant environment, the rate of improvement in mean fitness of these asexual populations slowed considerably from an initially rapid pace. In this study, we sought to determine whether sexual recombination with novel genotypes would reaccelerate the rate of adaption in these populations. To that end, treatment populations were propagated for an additional 1000 generations in the same environment as their ancestors, but they were periodically allowed to mate with an immigrant pool of genetically distinct Hfr (high frequency recombination) donors. These donors could transfer genes to the resident populations by conjugation, but the donors themselves could not grow in the experimental environment. Control populations were propagated under identical conditions, but in the absence of sexual recombination with the donors. All twelve control populations retained the ancestral alleles at every locus that was scored. In contrast, the sexual recombination treatment yielded dramatic increases in genetic variation. Thus, there was a profound effect of recombination on the rate of genetic change. However, the increased genetic variation in the treatment populations had no significant effect on the rate of adaptive evolution, as measured by changes in mean fitness relative to a common competitor. We then considered three hypotheses that might reconcile these two outcomes: recombination pressure, hitchhiking of recombinant genotypes in association with beneficial mutations, and complex selection dynamics whereby certain genotypes may have a selective advantage only within a particular milieu of competitors. The estimated recombination rate was too low to explain the observed rate of genetic change, either alone or in combination with hitchhiking effects. However, we documented comple x ecological interactions among some recombinant genotypes, suggesting that our method for estimating fitness relative to a common competitor might have underestimated the rate of adaptive evolution in the treatment populations.     

Why babies look like their daddies: paternity uncertainty and the evolution of self-deception in evaluating family resemblance

It has been suggested that in a socially monogamous system where fathers invest in their mate's offspring but paternity is far from certain, it will be adaptive on the part of infants to conceal their father's identity; but the opposite claim has also been made that this is against the genetic interests of the fathers, and a high frequency of adulterine births will select instead for paternal resemblance. In this article, I present a simple theoretical model that suggests that neonatal anonymity benefits fathers, mothers, and children. Once anonymity becomes established, however, all babies start paying the cost of paternity uncertainty, that is, the reduction in paternal care due to fathers not knowing whether they have truly sired their mate's offspring. By diminishing the fitness of babies, such a cost bounces back as lowered fitness for parents as well. We should then expect the evolution of maternal strategies directed to decrease paternity uncertainty, in the form of instinctive and unsolicited comments on babies' resemblance to their putative fathers. In contradiction to the widespread belief that it would be in fathers' interest to be skeptical of these allegations, the model suggests that, under conditions of infant anonymity, fathers will actually promote their own fitness by believing their spouses. Received in revised form: 5 September 2001 Electronic Publication