The extinction time under mutational meltdown driven by high mutation rates

Mutational meltdown describes an eco‐evolutionary process in which the accumulation of deleterious mutations causes a fitness decline that eventually leads to the extinction of a population. Possible applications of this concept include medical treatment of RNA virus infections based on mutagenic drugs that increase the mutation rate of the pathogen. To determine the usefulness and expected success of such an antiviral treatment, estimates of the expected time to mutational meltdown are necessary. Here, we compute the extinction time of a population under high mutation rates, using both analytical approaches and stochastic simulations. Extinction is the result of three consecutive processes: (a) initial accumulation of deleterious mutations due to the increased mutation pressure; (b) consecutive loss of the fittest haplotype due to Muller''s ratchet; (c) rapid population decline toward extinction. We find accurate analytical results for the mean extinction time, which show that the deleterious mutation rate has the strongest effect on the extinction time. We confirm that intermediate‐sized deleterious selection coefficients minimize the extinction time. Finally, our simulations show that the variation in extinction time, given a set of parameters, is surprisingly small.     

Critical Mutation Rate Has an Exponential Dependence on Population Size in Haploid and Diploid Populations

Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has significant potential in aiding population management to prevent local (and global) extinction events.     

Accumulation of deleterious mutations in small abiotic populations of RNA

The accumulation of slightly deleterious mutations in populations leads to the buildup of a genetic load and can cause the extinction of populations of small size. Mutation-accumulation experiments have been used to study this process in a wide variety of organisms, yet the exact mutational underpinnings of genetic loads and their fitness consequences remain poorly characterized. Here, we use an abiotic system of RNA populations evolving continuously in vitro to examine the molecular events that can instigate a genetic load. By tracking the fitness decline of ligase ribozyme populations with bottleneck sizes between 100 and 3000 molecules, we detected the appearance and subsequent fixation of both slightly deleterious mutations and advantageous mutations. Smaller populations went extinct in significantly fewer generations than did larger ones, supporting the notion of a mutational meltdown. These data suggest that mutation accumulation was an important evolutionary force in the prebiotic RNA world and that mechanisms such as recombination to ameliorate genetic loads may have been in place early in the history of life.     

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.     

MUTATION LOAD AND THE SURVIVAL OF SMALL POPULATIONS

Previous attempts to model the joint action of selection and mutation in finite populations have treated population size as being independent of the mutation load. However, the accumulation of deleterious mutations is expected to cause a gradual reduction in population size. Consequently, in small populations random genetic drift will progressively overpower selection making it easier to fix future mutations. This synergistic interaction, which we refer to as a mutational melt-down, ultimately leads to population extinction. For many conditions, the coefficient of variation of extinction time is less than 0.1, and for species that reproduce by binary fission, the expected extinction time is quite insensitive to population carrying capacity. These results are consistent with observations that many cultures of ciliated protozoans and vertebrate fibroblasts have characteristic extinction times. The model also predicts that clonal lineages are unlikely to survive more than 10⁴ to 10⁵ generations, which is consistent with existing data on parthenogenetic animals. Contrary to the usual view that Muller's ratchet does more damage when selection is weak, we show that the mean extinction time declines as mutations become more deleterious. Although very small sexual populations, such as self-fertilized lines, are subject to mutational meltdowns, recombination effectively eliminates the process when the effective population size exceeds a dozen or so. The concept of the effective mutation load is developed, and several procedures for estimating it are described. It is shown that this load can be reduced substantially when mutational effects are highly variable.     

Fitness effects of mutation accumulation in a natural outbred population of wild radish (Raphanus raphanistrum): comparison of field and greenhouse environments

Spontaneous deleterious mutation has been measured in a handful of organisms, always under laboratory conditions and usually employing inbred species or genotypes. We report the results of a mutation accumulation experiment with an outbred annual plant, Raphanus raphanistrum, with lifetime fitness measured in both the field and the greenhouse. This is the first study to report the effects of spontaneous mutation measured under field conditions. Two large replicate populations (N(e) approximately 600) were maintained with random mating in the greenhouse under relaxed selection for nine generations before the field assay was performed and ten generations before the greenhouse assay. Each generation, every individual was mated twice, once as a pollen donor and once as a pollen recipient, and a single seed from each plant was chosen randomly to create the next generation. The ancestral population was maintained as seeds at 4 degrees C. Declines in lifetime fitness were observed in both the field (1.7% per generation; P= 0.27) and the greenhouse (0.6% per generation; P= 0.07). Significant increases in additive genetic variance for fitness were found for stems per day, flowers per stem, fruits per flower and seeds per fruit in the field as well as for fruits per flower in the greenhouse. Lack of significance of the fitness decline may be due to the short period of mutation accumulation, the use of outbred populations, or both. The percent declines in fitness are at the high end of the range observed in other mutation accumulation experiments and give some support to the idea that mutational effects may be magnified under harsher field conditions. Thus, measurement of mutational parameters under laboratory conditions may underestimate the effects of mutations in natural populations.     

A comprehensive model of mutations affecting fitness and inferences for Arabidopsis thaliana

As the ultimate source of genetic variation, spontaneous mutation is essential to evolutionary change. Theoretical studies over several decades have revealed the dependence of evolutionary consequences of mutation on specific mutational properties, including genomic mutation rates, U, and the effects of newly arising mutations on individual fitness, s. The recent resurgence of empirical effort to infer these properties for diverse organisms has not achieved consensus. Estimates, which have been obtained by methods that assume mutations are unidirectional in their effects on fitness, are imprecise. Both because a general approach must allow for occurrence of fitness-enhancing mutations, even if these are rare, and because recent evidence demands it, we present a new method for inferring mutational parameters. For the distribution of mutational effects, we retain Keightley's assumption of the gamma distribution, to take advantage of the flexibility of its shape. Because the conventional gamma is one sided, restricting it to unidirectional effects, we include an additional parameter, rho, as an amount it is displaced from zero. Estimation is accomplished by Markov chain Monte Carlo maximum likelihood. Through a limited set of simulations, we verify the accuracy of this approach. We apply it to analyze data on two reproductive fitness components from a 17-generation mutation-accumulation study of a Columbia accession of Arabidopsis thaliana in which 40 lines sampled in three generations were assayed simultaneously. For these traits, U approximately/= 0.1-0.2, with distributions of mutational effects broadly spanning zero, such that roughly half the mutations reduce reproductive fitness. One evolutionary consequence of these results is lower extinction risks of small populations of A. thaliana than expected from the process of mutational meltdown. A comprehensive view of the evolutionary consequences of mutation will depend on quantitatively accounting for fitness-enhancing, as well as fitness-reducing, mutations.     

Understanding the evolutionary fate of finite populations: the dynamics of mutational effects

The most consistent result in more than two decades of experimental evolution is that the fitness of populations adapting to a constant environment does not increase indefinitely, but reaches a plateau. Using experimental evolution with bacteriophage, we show here that the converse is also true. In populations small enough such that drift overwhelms selection and causes fitness to decrease, fitness declines down to a plateau. We demonstrate theoretically that both of these phenomena must be due either to changes in the ratio of beneficial to deleterious mutations, the size of mutational effects, or both. We use mutation accumulation experiments and molecular data from experimental evolution to show that the most significant change in mutational effects is a drastic increase in the rate of beneficial mutation as fitness decreases. In contrast, the size of mutational effects changes little even as organismal fitness changes over several orders of magnitude. These findings have significant implications for the dynamics of adaptation.     

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.     

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.     

An extreme test of mutational meltdown shows mutational firm up instead

Traditionally, the accumulation of new deleterious mutations in populations or species in low numbers is expected to lead to a reduction in fitness and mutational meltdown, but in this study the opposite was observed. Beginning with a highly inbred populations of Drosophila melanogaster, new mutations that accumulated in experiments of two females and two males or of one female and one male each generation for 52 generations did not cause a decline in progeny numbers over time. Only two lines went extinct among 52 tested lines. In three of four experiments there was a significant increase in progeny numbers over time (mutational firm up), which had to be due to new beneficial, compensatory, overdominant, or back mutations.     

The effect of spontaneous mutations on competitive ability

Understanding the impact of spontaneous mutations on fitness has many theoretical and practical applications in biology. Although mutational effects on individual morphological or life‐history characters have been measured in several classic genetic model systems, there are few estimates of the rate of decline due to mutation for complex fitness traits. Here, we estimate the effects of mutation on competitive ability, an important complex fitness trait, in a model system for ecological and evolutionary genomics, Daphnia. Competition assays were performed to compare fitness between mutation‐accumulation (MA) lines and control lines from eight different genotypes from two populations of Daphnia pulicaria after 30 and 65 generations of mutation accumulation. Our results show a fitness decline among MA lines relative to controls as expected, but highlight the influence of genomic background on this effect. In addition, in some assays, MA lines outperform controls providing insight into the frequency of beneficial mutations.     

MULLER'S RATCHET AND MUTATIONAL MELTDOWNS

We extend our earlier work on the role of deleterious mutations in the extinction of obligately asexual populations. First, we develop analytical models for mutation accumulation that obviate the need for time-consuming computer simulations in certain ranges of the parameter space. When the number of mutations entering the population each generation is fairly high, the number of mutations per individual and the mean time to extinction can be predicted using classical approaches in quantitative genetics. However, when the mutation rate is very low, a fixation-probability approach is quite effective. Second, we show that an intermediate selection coefficient (s) minimizes the time to extinction. The critical value of s can be quite low, and we discuss the evolutionary implications of this, showing that increased sensitivity to mutation and loss of capacity for DNA repair can be selectively advantageous in asexual organisms. Finally, we consider the consequences of the mutational meltdown for the extinction of mitochondrial lineages in sexual species.     

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.     

Rapid mutational declines of viability in Drosophila

High rates of mildly deleterious mutation could cause the extinction of small populations, reduce neutral genetic variation and provide an evolutionary advantage for sex. In the first attempts to estimate the rate of mildly deleterious mutation, Mukai and Ohnishi allowed spontaneous mutations to accumulate on D. melanogaster second chromosomes shielded from recombination and selection. Viability of the shielded chromosomes appeared to decline rapidly, implying a deleterious mutation rate on the order of one per zygote per generation. These results have been challenged, however; at issue is whether Mukai and Ohnishi may have confounded viability declines caused by mutation with declines resulting from environmental changes or other extraneous factors. Here, using a method not sensitive to non-mutational viability changes, I reanalyse the previous mutation-accumulation (MA) experiments, and report the results of a new one. I show that in each of four experiments, including Mukai's two experiments, viability declines due to mildly deleterious mutations were rapid. The results give no support for the view that Mukai overestimated the declines. Although there is substantial variation in estimates of genomic mutation rates from the experiments, this variation is probably due to some combination of sampling error, strain differences and differences in assay conditions, rather than to failure to distinguish mutational and non-mutational viability changes.     

The Interaction between Selection,Demography and Selfing and How It Affects Population Viability

Population extinction due to the accumulation of deleterious mutations has only been considered to occur at small population sizes, large sexual populations being expected to efficiently purge these mutations. However, little is known about how the mutation load generated by segregating mutations affects population size and, eventually, population extinction. We propose a simple analytical model that takes into account both the demographic and genetic evolution of populations, linking population size, density dependence, the mutation load, and self-fertilisation. Analytical predictions were found to be relatively good predictors of population size and probability of population viability when verified using an explicit individual based stochastic model. We show that initially large populations do not always reach mutation-selection balance and can go extinct due to the accumulation of segregating deleterious mutations. Population survival depends not only on the relative fitness and demographic stochasticity, but also on the interaction between the two. When deleterious mutations are recessive, self-fertilisation affects viability non-monotonically and genomic cold-spots could favour the viability of outcrossing populations.     

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.     

The influence of neighborhood size and habitat shape on the accumulation of deleterious mutations.

To examine the impact of genetic neighborhood size and habitat shape on genetic load and the accumulation of deleterious mutation, individual-based simulations were performed in continuously distributed habitats. The risk of extinction increased as both the area of the habitat and the neighborhood size decreased. When the neighborhood area became smaller than the habitat area, habitat shape also began to influence the risk of extinction by mutation loads, expected time to extinction being shorter in longer and narrower habitats than in a square habitat. Both the number of homozygous deleterious loci per individual and the mutation load in the population increased as the neighborhood size and total population size decreased. Neighborhood size and total population size both independently affected the average number of homozygous deleterious loci per individual. In addition, as the ratio of the long to the short side of the rectangle of a habitat increased, the average number of homozygous deleterious loci increased. When the areas of the habitats were held constant, the average number of homozygous loci and the mutation loads were smallest for a regular square and largest for the longest, narrowest habitat. These results suggest that the spatial genetic structure of an individual is an important factor in the accumulation of deleterious mutations and the risk of extinction by mutation meltdown.     

Quantifying the extinction vortex

We developed a database of 10 wild vertebrate populations whose declines to extinction were monitored over at least 12 years. We quantitatively characterized the final declines of these well-monitored populations and tested key theoretical predictions about the process of extinction, obtaining two primary results. First, we found evidence of logarithmic scaling of time-to-extinction as a function of population size for each of the 10 populations. Second, two lines of evidence suggested that these extinction-bound populations collectively exhibited dynamics akin to those theoretically proposed to occur in extinction vortices. Specifically, retrospective analyses suggested that a population size of n individuals within a decade of extinction was somehow less valuable to persistence than the same population size was earlier. Likewise, both year-to-year rates of decline and year-to-year variability increased as the time-to-extinction decreased. Together, these results provide key empirical insights into extinction dynamics, an important topic that has received extensive theoretical attention.     

Mating patterns influence vulnerability to the extinction vortex

Earth's biodiversity is undergoing mass extinction due to anthropogenic compounding of environmental, demographic and genetic stresses. These different stresses can trap populations within a reinforcing feedback loop known as the extinction vortex, in which synergistic pressures build upon one another through time, driving down population viability. Sexual selection, the widespread evolutionary force arising from competition, choice and reproductive variance within animal mating patterns could have vital consequences for population viability and the extinction vortex: (a) if sexual selection reinforces natural selection to fix ‘good genes’ and purge ‘bad genes’, then mating patterns encouraging competition and choice may help protect populations from extinction; (b) by contrast, if mating patterns create load through evolutionary or ecological conflict, then population viability could be further reduced by sexual selection. We test between these opposing theories using replicate populations of the model insect Tribolium castaneum exposed to over 10 years of experimental evolution under monogamous versus polyandrous mating patterns. After a 95‐generation history of divergence in sexual selection, we compared fitness and extinction of monogamous versus polyandrous populations through an experimental extinction vortex comprising 15 generations of cycling environmental and genetic stresses. Results showed that lineages from monogamous evolutionary backgrounds, with limited opportunities for sexual selection, showed rapid declines in fitness and complete extinction through the vortex. By contrast, fitness of populations from the history of polyandry, with stronger opportunities for sexual selection, declined slowly, with 60% of populations surviving by the study end. The three vortex stresses of (a) nutritional deprivation, (b) thermal stress and (c) genetic bottlenecking had similar impacts on fitness declines and extinction risk, with an overall sigmoid decline in survival through time. We therefore reveal sexual selection as an important force behind lineages facing extinction threats, identifying the relevance of natural mating patterns for conservation management.