Fitness-dependent mutation rates in finite populations

Mutation rate may be condition dependent, whereby individuals in poor condition, perhaps from high mutation load, have higher mutation rates than individuals in good condition. Agrawal (J. Evol. Biol.15, 2002, 1004) explored the basic properties of fitness-dependent mutation rate (FDMR) in infinite populations and reported some heuristic results for finite populations. The key parameter governing how infinite populations evolve under FDMR is the curvature (k) of the relationship between fitness and mutation rate. We extend Agrawal's analysis to finite populations and consider dominance and epistasis. In finite populations, the probability of long-term existence depends on k. In sexual populations, positive curvature leads to low equilibrium mutation rate, whereas negative curvature results in high mutation rate. In asexual populations, negative curvature results in rapid extinction via 'mutational meltdown', whereas positive curvature sometimes allows persistence. We speculate that fitness-dependent mutation rate may provide the conditions for genetic architecture to diverge between sexual and asexual taxa.     

Mutation-selection balance and the evolutionary advantage of sex and recombination

Mutation-selection balance in a multi-locus system is investigated theoretically, using a modification of Bulmer's infinitesimal model of selection on a normally-distributed quantitative character, taking the number of mutations per individual (n) to represent the character value. The logarithm of the fitness of an individual with n mutations is assumed to be a quadratic, decreasing function of n. The equilibrium properties of infinitely large asexual populations, random-mating populations lacking genetic recombination, and random-mating populations with arbitrary recombination frequencies are investigated. With 'synergistic' epistasis on the scale of log fitness, such that log fitness declines more steeply as n increases, it is shown that equilibrium mean fitness is least for asexual populations. In sexual populations, mean fitness increases with the number of chromosomes and with the map length per chromosome. With 'diminishing returns' epistasis, such that log fitness declines less steeply as n increases, mean fitness behaves in the opposite way. Selection on asexual variants and genes affecting the rate of genetic recombination in random-mating populations was also studied. With synergistic epistasis, zero recombination always appears to be disfavoured, but free recombination is disfavoured when the mutation rate per genome is sufficiently small, leading to evolutionary stability of maps of intermediate length. With synergistic epistasis, an asexual mutant is unlikely to invade a sexual population if the mutation rate per diploid genome greatly exceeds unity. Recombination is selectively disadvantageous when there is diminishing returns epistasis. These results are compared with the results of previous theoretical studies of this problem, and with experimental data.     

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.     

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.     

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.     

Evolution of Bacterial Transformation: Is Sex with Dead Cells Ever Better than No Sex at All?

Computer simulations of bacterial transformation are used to show that, under a wide range of biologically reasonable assumptions, transforming populations undergoing deleterious mutation and selection have a higher mean fitness at equilibrium than asexual populations. The source of transforming DNA, the amount of DNA taken up by each transforming cell, and the relationship between number of mutations and cell viability (the fitness function) are important factors. When the DNA source is living cells, transformation resembles meiotic sex. When the DNA source is cells killed by selection against mutations, transformation increases the average number of mutations per genome but can nevertheless increase the mean fitness of the population at equilibrium. In a model of regulated transformation, in which the most fit cells of a transforming population do not transform, transforming populations are always fitter at equilibrium than asexual populations. These results show that transformation can reduce mutation load.     

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.     

Sex and the Spread of Retrotransposon Ty3 in Experimental Populations of Saccharomyces Cerevisiae

Mobile genetic elements may be molecular parasites that reduce the fitness of individuals that bear them by causing predominantly deleterious mutations, but increase in frequency when rare because transposition increases their rates of transmission to the progeny of crosses between infected and uninfected individuals. If this is true, then the initial spread of a mobile element requires sex. We tested this prediction using the yeast retrotransposon Ty3 and a strain of Saccharomyces cerevisiae lacking Ty3. We infected replicate isogenic sexual and asexual populations with a galactose-inducible Ty3 element at an initial frequency of 1%. In two of six asexual populations, active Ty3 elements increased in frequency to 38 and 86%, due to the spread in each population of a competitively superior mutant carrying a new Ty3 insertion. Ty3 frequencies increased above 80% in all sexual populations in which transposition was induced in haplophase or in diplophase. Ty3 did not increase in frequency when active during both haplophase and diplophase, apparently because of selective sweeps during adaptation to galactose. Repressed Ty3 elements spread in sexual populations, by increasing sexual fitness. These results indicate that active Ty3 elements are more likely to become established in sexual populations than in asexual populations.     

The maintenance of sexual reproduction in a structured population

We present the results of a computer simulation model in which a sexual population produces an asexual mutant. We estimate the probability that the new asexual lineage will go extinct. We find that whenever the asexual lineage does not go extinct the sexual population is out-competed, and only asexual individuals remain after a sufficiently long period of time has elapsed. We call this type of outcome an asexual takeover. Our results suggest that, given repeated mutations to asexuality, asexual takeover is likely in an unstructured environment. However, if the environment is subdivided into demes that are connected by migration, then asexual takeover becomes less likely. The probability of asexual takeover declines towards zero as the number of demes increases and as the rate of migration decreases. The reason for this is that asexuality leads to a greater loss of fitness due to mutation and genetic drift, in comparison to what occurs under sexual reproduction. Population subdivision slows the spread of asexual lineages, which allows more time for the genetic degeneration caused by asexuality to take place.     

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.     

MUTATIONAL MELTDOWN IN LABORATORY YEAST POPULATIONS

Abstract.— In small or repeatedly bottlenecked populations, mutations are expected to accumulate by genetic drift, causing fitness declines. In mutational meltdown models, such fitness declines further reduce population size, thus accelerating additional mutation accumulation and leading to extinction. Because the rate of mutation accumulation is determined partly by the mutation rate, the risk and rate of meltdown are predicted to increase with increasing mutation rate. We established 12 replicate populations of Saccharomyces cerevisiae from each of two isogenic strains whose genomewide mutation rates differ by approximately two orders of magnitude. Each population was transferred daily by a fixed dilution that resulted in an effective population size near 250. Fitness declines that reduce growth rates were expected to reduce the numbers of cells transferred after dilution, thus reducing population size and leading to mutational meltdown. Through 175 daily transfers and approximately 2900 generations, two extinctions occurred, both in populations with elevated mutation rates. For one of these populations there is direct evidence that extinction resulted from mutational meltdown: Extinction immediately followed a major fitness decline, and it recurred consistently in replicate populations reestablished from a sample frozen after this fitness decline, but not in populations founded from a predecline sample. Wild‐type populations showed no trend to decrease in size and, on average, they increased in fitness.     

The speed of evolution and maintenance of variation in asexual populations

BACKGROUND: The rate at which beneficial mutations accumulate determines how fast asexual populations evolve, but this is only partially understood. Some recent clonal-interference models suggest that evolution in large asexual populations is limited because smaller beneficial mutations are outcompeted by larger beneficial mutations that occur in different lineages within the same population. This analysis assumes that the important mutations fix one at a time; it ignores multiple beneficial mutations that occur in the lineage of an earlier beneficial mutation, before the first mutation in the series can fix. We focus on the effects of such multiple mutations. RESULTS: Our analysis predicts that the variation in fitness maintained by a continuously evolving population increases as the logarithm of the population size and logarithm of the mutation rate and thus yields a similar logarithmic increase in the speed of evolution. To test these predictions, we evolved asexual budding yeast in glucose-limited media at a range of population sizes and mutation rates. CONCLUSIONS: We find that their evolution is dominated by the accumulation of multiple mutations of moderate effect. Our results agree with our theoretical predictions and are inconsistent with the one-by-one fixation of mutants assumed by recent clonal-interference analysis.     

Mutation accumulation in populations of varying size: large effect mutations cause most mutational decline in the rotifer Brachionus calyciflorus under UV‐C radiation

Theory predicts that fitness decline via mutation accumulation will depend on population size, but there are only a few direct tests of this key idea. To gain a qualitative understanding of the fitness effect of new mutations, we performed a mutation accumulation experiment with the facultative sexual rotifer Brachionus calyciflorus at six different population sizes under UV‐C radiation. Lifetime reproduction assays conducted after ten and sixteen UV‐C radiations showed that while small populations lost fitness, fitness losses diminished rapidly with increasing population size. Populations kept as low as 10 individuals were able to maintain fitness close to the nonmutagenized populations throughout the experiment indicating that selection was able to remove the majority of large effect mutations in small populations. Although our results also seem to imply that small populations are effectively immune to mutational decay, we caution against this interpretation. Given sufficient time, populations of moderate to large size can experience declines in fitness from accumulating weakly deleterious mutations as demonstrated by fitness estimates from simulations and, tentatively, from a long‐term experiment with populations of moderate size. There is mounting evidence to suggest that mutational distributions contain a heavier tail of large effects. Our results suggest that this is also true when the mutational spectrum is altered by UV radiation.     

Radical amino acid mutations persist longer in the absence of sex

Harmful mutations are ubiquitous and inevitable, and the rate at which these mutations are removed from populations is a critical determinant of evolutionary fate. Closely related sexual and asexual taxa provide a particularly powerful setting to study deleterious mutation elimination because sexual reproduction should facilitate mutational clearance by reducing selective interference between sites and by allowing the production of offspring with different mutational complements than their parents. Here, we compared the rate of removal of conservative (i.e., similar biochemical properties) and radical (i.e., distinct biochemical properties) nonsynonymous mutations from mitochondrial genomes of sexual versus asexual Potamopyrgus antipodarum, a New Zealand freshwater snail characterized by coexisting and ecologically similar sexual and asexual lineages. Our analyses revealed that radical nonsynonymous mutations are cleared at higher rates than conservative changes and that sexual lineages eliminate radical changes more rapidly than asexual counterparts. These results are consistent with reduced efficacy of purifying selection in asexual lineages allowing harmful mutations to remain polymorphic longer than in sexual lineages. Together, these data illuminate some of the population‐level processes contributing to mitochondrial mutation accumulation and suggest that mutation accumulation could influence the outcome of competition between sexual and asexual lineages.     

Aging asexual lineages and the evolutionary maintenance of sex

Finite populations of asexual and highly selfing species suffer from a reduced efficacy of selection. Such populations are thought to decline in fitness over time due to accumulating slightly deleterious mutations or failing to adapt to changing conditions. These within‐population processes that lead nonrecombining species to extinction may help maintain sex and outcrossing through species level selection. Although inefficient selection is proposed to elevate extinction rates over time, previous models of species selection for sex assumed constant diversification rates. For sex to persist, classic models require that asexual species diversify at rates lower than sexual species; the validity of this requirement is questionable, both conceptually and empirically. We extend past models by allowing asexual lineages to decline in diversification rates as they age, that is nonrecombining lineages “senesce” in diversification rates. At equilibrium, senescing diversification rates maintain sex even when asexual lineages, at young ages, diversify faster than their sexual progenitors. In such cases, the age distribution of asexual lineages contains a peak at intermediate values rather than showing the exponential decline predicted by the classic model. Coexistence requires only that the average rate of diversification in asexuals be lower than that of sexuals.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Dynamic mutation-selection balance as an evolutionary attractor

The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that maintains the balanced state. We find that a surprisingly low ε suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes.     

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.     

MUTATIONS DO NOT ACCUMULATE IN ASEXUAL ISOLATES CAPABLE OF GROWTH AND EXTINCTION–MULLER'S RATCHET RE-EXAMINED

The rarity of exclusively asexual species is often attributed to Muller's Ratchet. This supposes that because asexual populations cannot recreate individuals with fewer mutations than the currently least-loaded line, mutations will accumulate in such isolates. However, because the computer models that corroborate this theory have assumed isolate immortality, it is possible that mutations will accumulate only if there is “soft” selection acting on relative, rather than absolute, fitness. Here we, therefore, describe several models in which 200 asexual organisms randomly selected from an infinite population in genetic equilibrium under “hard” selection (acting through absolute fitness), were followed for 100 generations. When there were no limits to the fluctuations in population size, the deterministic distribution of mutations per individual was maintained for 100 (as well as for 200) generations. If population growth was limited by a proportional decrease in fertility of the whole isolate, then the isolates tended to become extinct. The rate of extinction was inversely related to maximum isolate size. When resource limitation at maximum population size had an extra deleterious effect on mutants, then isolates shed the mutant classes. Mutations accumulated (ad inifinitum) in immortal isolates whose population numbers were kept constant by proportionately increasing or decreasing each class's size whenever isolate size ≠ 200. Muller's Ratchet, therefore, operates only when mutations affect the outcome of intraspecific contests, but not the organisms' intrinsic ability to survive in the ecosystem.     

Condition‐dependent mutation rates and sexual selection

‘Good genes’ models of sexual selection show that females can gain indirect benefits for their offspring if male ornaments are condition‐dependent signals of genetic quality. Recurrent deleterious mutation is viewed as a major contributor to variance in genetic quality, and previous theoretical treatments of ‘good genes’ processes have assumed that the influx of new mutations is constant. I propose that this assumption is too simplistic, and that mutation rates vary in ways that are important for sexual selection. Recent data have shown that individuals in poor condition can have higher mutation rates, and I argue that if both male sexual ornaments and mutation rates are condition‐dependent, then females can use male ornamentation to evaluate their mate’s mutation rate. As most mutations are deleterious, females benefit from choosing well‐ornamented mates, as they are less likely to contribute germline‐derived mutations to offspring. I discuss some of the evolutionary ramifications of condition‐dependent mutation rates and sexual selection.