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.     

Effects of population size and mutation rate on the evolution of mutational robustness

It is often assumed that the efficiency of selection for mutational robustness would be proportional to mutation rate and population size, thus being inefficient in small populations. However, Krakauer and Plotkin (2002) hypothesized that selection in small populations would favor robustness mechanisms, such as redundancy, that mask the effect of deleterious mutations. In large populations, by contrast, selection is more effective at removing deleterious mutants and fitness would be improved by eliminating mechanisms that mask the effect of deleterious mutations and thus impede their removal. Here, we test whether these predictions are supported in experiments with evolving populations of digital organisms. Digital organisms are self-replicating programs that inhabit a virtual world inside a computer. Like their organic counterparts, digital organisms mutate, compete, evolve, and adapt by natural selection to their environment. In this study, 160 populations evolved at different combinations of mutation rate and population size. After 10(4) generations, we measured the mutational robustness of the most abundant genotype in each population. Mutational robustness tended to increase with mutation rate and to decline with population size, although the dependence with population size was in part mediated by a negative relationship between fitness and robustness. These results are independent of whether genomes were constrained to their original length or allowed to change in size.     

MUTATION AND EXTINCTION: THE ROLE OF VARIABLE MUTATIONAL EFFECTS,SYNERGISTIC EPISTASIS,BENEFICIAL MUTATIONS,AND DEGREE OF OUTCROSSING

Recent theoretical studies have illustrated the potential role of spontaneous deleterious mutation as a cause of extinction in small populations. However, these studies have not addressed several genetic issues, which can in principle have a substantial influence on the risk of extinction. These include the presence of synergistic epistasis, which can reduce the rate of mutation accumulation by progressively magnifying the selective effects of mutations, and the occurrence of beneficial mutations, which can offset the effects of previous deleterious mutations. In stochastic simulations of small populations (effective sizes on the order of 100 or less), we show that both synergistic epistasis and the rate of beneficial mutation must be unrealistically high to substantially reduce the risk of extinction due to random fixation of deleterious mutations. However, in analytical calculations based on diffusion theory, we show that in large, outcrossing populations (effective sizes greater than a few hundred), very low levels of beneficial mutation are sufficient to prevent mutational decay. Further simulation results indicate that in populations small enough to be highly vulnerable to mutational decay, variance in deleterious mutational effects reduces the risk of extinction, assuming that the mean deleterious mutational effect is on the order of a few percent or less. We also examine the magnitude of outcrossing that is necessary to liberate a predominantly selfing population from the threat of long-term mutational deterioration. The critical amount of outcrossing appears to be greater than is common in near-obligately selfing plant species, supporting the contention that such species are generally doomed to extinction via random drift of new mutations. Our results support the hypothesis that a long-term effective population size in the neighborhood of a few hundred individuals defines an approximate threshold, below which outcrossing populations are vulnerable to extinction via fixation of deleterious mutations, and above which immunity is acquired.     

Mutant alleles of small effect are primarily responsible for the loss of fitness with slow inbreeding in Drosophila melanogaster.

Multilocus simulation is used to identify genetic models that can account for the observed rates of inbreeding and fitness decline in laboratory populations of Drosophila melanogaster. The experimental populations were maintained under crowded conditions for approximately 200 generations at a harmonic mean population size of Nh approximately 65-70. With a simulated population size of N = 50, and a mean selective disadvantage of homozygotes at individual loci approximately 1-2% or less, it is demonstrated that the mean effective population size over a 200-generation period may be considerably greater than N, with a ratio matching the experimental estimate of Ne/Nh approximately 1.4. The buildup of associative overdominance at electrophoretic marker loci is largely responsible for the stability of gene frequencies and the observed reduction in the rate of inbreeding, with apparent selection coefficients in favor of the heterozygote at neutral marker loci increasing rapidly over the first N generations of inbreeding to values approximately 5-10%. The observed decline in fitness under competitive conditions in populations of size approximately 50 in D. melanogaster therefore primarily results from mutant alleles with mean effects on fitness as homozygotes of sm < or = 0.02. Models with deleterious recessive mutants at the background loci require that the mean selection coefficient against heterozygotes is at most hsm approximately 0.002, with a minimum mutation rate for a single Drosophila autosome 100 cM in length estimated to be in the range 0.05-0.25, assuming an exponential distribution of s. A typical chromosome would be expected to carry at least 100-200 such mutant alleles contributing to the decline in competitive fitness with slow inbreeding.     

Quasispecies made simple

Quasispecies are clouds of genotypes that appear in a population at mutation–selection balance. This concept has recently attracted the attention of virologists, because many RNA viruses appear to generate high levels of genetic variation that may enhance the evolution of drug resistance and immune escape. The literature on these important evolutionary processes is, however, quite challenging. Here we use simple models to link mutation–selection balance theory to the most novel property of quasispecies: the error threshold—a mutation rate below which populations equilibrate in a traditional mutation–selection balance and above which the population experiences an error catastrophe, that is, the loss of the favored genotype through frequent deleterious mutations. These models show that a single fitness landscape may contain multiple, hierarchically organized error thresholds and that an error threshold is affected by the extent of back mutation and redundancy in the genotype-to-phenotype map. Importantly, an error threshold is distinct from an extinction threshold, which is the complete loss of the population through lethal mutations. Based on this framework, we argue that the lethal mutagenesis of a viral infection by mutation-inducing drugs is not a true error catastophe, but is an extinction catastrophe.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

Extinction of populations by inbreeding depression under stochastic environments

Inbreeding depression may induce rapid extinction due to positive feedbacks between inbreeding depression and reduction of population size, which is often referred to as extinction vortex by inbreeding depression. The present analysis has demonstrated that the extinction vortex is likely to happen with realistic parameter values of genomic mutation rate of lethals or semilethals, equilibrium population size, intrinsic rate of natural increase, and rate of population decline caused by nongenetic extrinsic factors. Simulation models incorporating stochastic fluctuations of population size further indicated that extinction by inbreeding depression is facilitated by environmental fluctuations in population size. The results suggest that there is a positive interaction between genetic stochasticity and environmental stochasticity for extinction of populations by inbreeding depression. Received: May 10, 1999 / Accepted: November 5, 1999     

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.     

With Allee effects,life for the social carnivore is complicated

Anthropogenic modification of the landscape, resultant habitat loss, and decades of persecution have resulted in severe decline and fragmentation of large carnivore populations worldwide. Infectious disease is also identified as a primary threat to many carnivores. In wildlife species, population demography and group persistence are strongly influenced by group or population size. This is referred to as the Allee effect, in which a population or group is at an increased risk of extinction when the number or density of individuals falls below some threshold due to ecological and/or genetic factors. However, in social mammalian species, the relationship between the number of individuals and the risk of extinction is complicated because aggregation may enhance pathogen exposure and transmission. Although theoretical studies of the interaction between infectious disease transmission and Allee effects reveal important implications for carnivore management and population extinction risk, information about the interaction has yet to be synthesized. In this paper, we assess life history strategies of medium to large carnivore species (≥2.4 kg) and their influence on population dynamics, with a special focus on infectious disease. While declining population trends are observed in 73 % of all carnivores (both social and solitary species), infectious disease is identified as a significant cause of population decline in 45 % of social carnivores and 3 % of solitary carnivores. Furthermore, where carnivores suffer a combination of rapid population decline and infectious disease, Allee effects may be more likely to impact social as compared to solitary carnivore populations. These potentially additive interactions may strongly influence disease transmission dynamics and population persistence potential. Understanding the mechanisms that can result in Allee effects in endangered carnivore populations and the manner in which infectious disease interfaces at this nexus may define the outcome of developed conservation strategies.     

ECOLOGICAL GENETICS OF GYNODIOECY IN SILENE VULGARIS: RELATIVE FITNESS OF FEMALES AND HERMAPHRODITES DURING THE COLONIZATION PROCESS

Recent theoretical models have addressed the influence of metapopulation dynamics on the fitness of females and hermaphrodites in gynodioecious plants. In particular, selection is thought to favor hermaphrodites during population establishment because that sex should be less prone to pollen limitation, especially if self-fertilization is possible. However, inbreeding depression could limit this advantage. In this experimental study of Silene vulgaris, a weedy gynodioecious plant, the fitness of females and hermaphrodites was estimated from seed production in both mixed-sex populations and for individuals isolated from these populations by 20, 40, 80, or 160 m. In mixed populations females display statistically significant greater per capita seed production owing to higher capsule production and higher rates of seed germination. The fitness of both sexes declines with increasing isolation, but at different rates, such that in the 160-m treatment hermaphrodites are by far the more fit sex. Allozyme studies suggest that this differential decline is because the selfing rate in hermaphrodites increases as a function of isolation, at least partially compensating for a decline in the availability of outcross pollen. Overall, the negative effects of pollen limitation on females far outweighs the negative effects of inbreeding depression following selfing in hermaphrodites. Thus, extinction/recolonization dynamics would appear to favor hermaphrodites as long as seed dispersal events exceed some critical distance.     

Effects of founding genetic variation on adaptation to a novel resource

Population genetic theory predicts that adaptation in novel environments is enhanced by genetic variation for fitness. However, theory also predicts that under strong selection, demographic stochasticity can drive populations to extinction before they can adapt. We exposed wheat-adapted populations of the flour beetle (Tribolium castaneum) to a novel suboptimal corn resource, to test the effects of founding genetic variation on population decline and subsequent extinction or adaptation. As previously reported, genetically diverse populations were less likely to go extinct. Here, we show that among surviving populations, genetically diverse groups recovered faster after the initial population decline. Within two years, surviving populations significantly increased their fitness on corn via increased fecundity, increased egg survival, faster larval development, and higher rate of egg cannibalism. However, founding genetic variation only enhanced the increase in fecundity, despite existing genetic variation-and apparent lack of trade-offs-for egg survival and larval development time. Thus, during adaptation to novel habitats the positive impact of genetic variation may be restricted to only a few traits, although change in many life-history traits may be necessary to avoid extinction. Despite severe initial maladaptation and low population size, genetic diversity can thus overcome the predicted high extinction risk in new habitats.     

Pathways to extinction: beyond the error threshold

Since the introduction of the quasispecies and the error catastrophe concepts for molecular evolution by Eigen and their subsequent application to viral populations, increased mutagenesis has become a common strategy to cause the extinction of viral infectivity. Nevertheless, the high complexity of virus populations has shown that viral extinction can occur through several other pathways apart from crossing an error threshold. Increases in the mutation rate enhance the appearance of defective forms and promote the selection of mechanisms that are able to counteract the accelerated appearance of mutations. Current models of viral evolution take into account more realistic scenarios that consider compensatory and lethal mutations, a highly redundant genotype-to-phenotype map, rough fitness landscapes relating phenotype and fitness, and where phenotype is described as a set of interdependent traits. Further, viral populations cannot be understood without specifying the characteristics of the environment where they evolve and adapt. Altogether, it turns out that the pathways through which viral quasispecies go extinct are multiple and diverse.     

Lethal mutagenesis of bacteria

Lethal mutagenesis, the killing of a microbial pathogen with a chemical mutagen, is a potential broad-spectrum antiviral treatment. It operates by raising the genomic mutation rate to the point that the deleterious load causes the population to decline. Its use has been limited to RNA viruses because of their high intrinsic mutation rates. Microbes with DNA genomes, which include many viruses and bacteria, have not been considered for this type of treatment because their low intrinsic mutation rates seem difficult to elevate enough to cause extinction. Surprisingly, models of lethal mutagenesis indicate that bacteria may be candidates for lethal mutagenesis. In contrast to viruses, bacteria reproduce by binary fission, and this property ensures their extinction if subjected to a mutation rate >0.69 deleterious mutations per generation. The extinction threshold is further lowered when bacteria die from environmental causes, such as washout or host clearance. In practice, mutagenesis can require many generations before extinction is achieved, allowing the bacterial population to grow to large absolute numbers before the load of deleterious mutations causes the decline. Therefore, if effective treatment requires rapid population decline, mutation rates 0.69 may be necessary to achieve treatment success. Implications for the treatment of bacteria with mutagens, for the evolution of mutator strains in bacterial populations, and also for the evolution of mutation rate in cancer are discussed.     

About a three states molecular evolution model

The Eigen model of molecular evolution has recently been reconsidered by taking into account the existence of non-reproducing sequences. New results obtained with this model are presented here: several time-scales characterize the population dynamics and the location of the error threshold, shifted towards larger values of the probability of mutation, depends on both the size of the population and time. Thus this model can be used to analyse extinction events. The distribution of individuals in sequence space beyond the threshold is also discussed.     

Genetic loads under fitness‐dependent mutation rates

Abstract Although much theory depends on the genome‐wide rate of deleterious mutations, good estimates of the mutation rate are scarce and remain controversial. Furthermore, mutation rate may not be constant, and a recent study suggests that mutation rates are higher in mildly stressful environments. If mutation rate is a function of condition, then individuals carrying more mutations will tend to be in worse condition and therefore produce more mutations. Here I examine the mean fitnesses of sexual and asexual populations evolving under such condition‐dependent mutation rates. The equilibrium mean fitness of a sexual population depends on the shape of the curve relating fitness to mutation rate. If mutation rate declines synergistically with increasing condition the mean fitness will be much lower than if mutation rate declines at a diminishing rate. In contrast, asexual populations are less affected by condition‐dependent mutation rates. The equilibrium mean fitness of an asexual population only depends on the mutation rate of the individuals in the least loaded class. Because such individuals have high fitness and therefore a low mutation rate, asexual populations experience less genetic load than sexual populations, thus increasing the twofold cost of sex.     

Evolutionary rescue and the limits of adaptation

Populations subject to severe stress may be rescued by natural selection, but its operation is restricted by ecological and genetic constraints. The cost of natural selection expresses the limited capacity of a population to sustain the load of mortality or sterility required for effective selection. Genostasis expresses the lack of variation that prevents many populations from adapting to stress. While the role of relative fitness in adaptation is well understood, evolutionary rescue emphasizes the need to recognize explicitly the importance of absolute fitness. Permanent adaptation requires a range of genetic variation in absolute fitness that is broad enough to provide a few extreme types capable of sustained growth under a stress that would cause extinction if they were not present. This principle implies that population size is an important determinant of rescue. The overall number of individuals exposed to selection will be greater when the population declines gradually under a constant stress, or is progressively challenged by gradually increasing stress. In gradually deteriorating environments, survival at lethal stress may be procured by prior adaptation to sublethal stress through genetic correlation. Neither the standing genetic variation of small populations nor the mutation supply of large populations, however, may be sufficient to provide evolutionary rescue for most populations.     

Fluctuations of Fitness Distributions and the Rate of Muller's Ratchet

The accumulation of deleterious mutations is driven by rare fluctuations that lead to the loss of all mutation free individuals, a process known as Muller's ratchet. Even though Muller's ratchet is a paradigmatic process in population genetics, a quantitative understanding of its rate is still lacking. The difficulty lies in the nontrivial nature of fluctuations in the fitness distribution, which control the rate of extinction of the fittest genotype. We address this problem using the simple but classic model of mutation selection balance with deleterious mutations all having the same effect on fitness. We show analytically how fluctuations among the fittest individuals propagate to individuals of lower fitness and have dramatically amplified effects on the bulk of the population at a later time. If a reduction in the size of the fittest class reduces the mean fitness only after a delay, selection opposing this reduction is also delayed. This delayed restoring force speeds up Muller's ratchet. We show how the delayed response can be accounted for using a path-integral formulation of the stochastic dynamics and provide an expression for the rate of the ratchet that is accurate across a broad range of parameters.     

The evolution of sexual reproduction as a repair mechanism part II. Mathematical treatment of the wheel model and its significance for real systems

The dynamics of populations of self-replicating, hierarchically structured individuals, exposed to accidents which destroy their sub-units, is analyzed mathematically, specifically with regard to the roles of redundancy and sexual repair. The following points emerge from this analysis: 1. A population of individuals with redundant sub-structure has no intrinsic steady-state point; it tends to either zero or infinity depending on a critical accident rate alpha c. 2. Increased redundancy renders populations less accident prone initially, but population decline is steeper if alpha is greater than a fixed value alpha d. 3. Periodic, sexual repair at system-specific intervals prevents continuous decline and stabilizes the population insofar as it will now oscillate between two fixed population levels. 4. The stabilizing sexual interval increases with increased complexity provided this is accompanied by appropriate levels of redundancy. 5. The model closely simulates the dynamics of heterosis effects. 6. Repair fitness is a population fitness: the chance of an individual being repaired is a function of the statistical make-up of the population as a whole at the particular period. Populations living at alpha greater than alpha c either engage in sexual repair at the appropriate time or they die out. 7. The mathematical properties of the model illustrate mechanisms which possibly played a role in the evolution of a mortal soma in relation to sexual reproduction.     

Antagonistic coevolution with parasites increases the cost of host deleterious mutations

The fitness consequences of deleterious mutations are sometimes greater when individuals are parasitized, hence parasites may result in the more rapid purging of deleterious mutations from host populations. The significance of host deleterious mutations when hosts and parasites antagonistically coevolve (reciprocal evolution of host resistance and parasite infectivity) has not previously been experimentally investigated. We addressed this by coevolving the bacterium Pseudomonas fluorescens and a parasitic bacteriophage in laboratory microcosms, using bacteria with high and low mutation loads. Directional coevolution between bacterial resistance and phage infectivity occurred in all populations. Bacterial population fitness, as measured by competition experiments with ancestral genotypes in the absence of phage, declined with time spent coevolving. However, this decline was significantly more rapid in bacteria with high mutation loads, suggesting the cost of bacterial resistance to phage was greater in the presence of deleterious mutations (synergistic epistasis). As such, resistance to phage was more costly to evolve in the presence of a high mutation load. Consistent with these data, bacteria with high mutation loads underwent less rapid directional coevolution with their phage populations, and showed lower levels of resistance to their coevolving phage populations. These data suggest that coevolution with parasites increases the rate at which deleterious mutations are purged from host populations.     

Evolutionary rescue can prevent extinction following environmental change

The ubiquity of global change and its impacts on biodiversity poses a clear and urgent challenge for evolutionary biologists. In many cases, environmental change is so widespread and rapid that individuals can neither accommodate to them physiologically nor migrate to a more favourable site. Extinction will ensue unless the population adapts fast enough to counter the rate of decline. According to theory, whether populations can be rescued by evolution depends upon several crucial variables: population size, the supply of genetic variation, and the degree of maladaptation to the new environment. Using techniques in experimental evolution we tested the conditions for evolutionary rescue (ER). Hundreds of yeast populations were exposed to normally lethal concentrations of salt in conditions, where the frequency of rescue mutations was estimated and population size was manipulated. In a striking match with theory, we show that ER is possible, and that the recovery of the population may occur within 25 generations. We observed a clear threshold in population size for ER whereby the ancestral population size must be sufficiently large to counter stochastic extinction and contain resistant individuals. These results demonstrate that rapid evolution is an important component of the response of small populations to environmental change.