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.     

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.     

EVOLUTIONARY FEEDBACKS BETWEEN REPRODUCTIVE MODE AND MUTATION RATE EXACERBATE THE PARADOX OF SEX

Evolutionary theory suggests that low mutation rates should favor the persistence of asexuals. Additionally, given the observation that most nonneutral mutations are deleterious, asexuality may strengthen selection for reduced mutation rates. This reciprocal relationship raises the possibility of a positive feedback loop between sex and mutation rate. We explored the consequences of this evolutionary feedback with an individual‐based model in which a sexual population is continually challenged by the introduction of asexual clones. We found that asexuals were more likely to spread in a population when mutation rates were able to evolve relative to a model in which mutation rates were held constant. In fact, under evolving mutation rates, asexuals were able to spread to fixation even when sexuals faced no cost of sex whatsoever. The added success of asexuals was the result of their ability to evolve lower mutation rates and thereby slow the process of mutation accumulation that otherwise limited their spread. Given the existence of ample mutation rate variation in natural populations, our findings show that the evolutionary feedback between sex and mutation rate may intensify the “paradox of sex,” supporting the argument that deleterious mutation accumulation alone is likely insufficient to overcome the reproductive advantage of asexual competitors in the short term.     

Mutation accumulation in space and the maintenance of sexual reproduction

The maintenance of sexual reproduction remains one of the major puzzles of evolutionary biology, since, all else being equal, an asexual mutant should have a twofold fitness advantage over the sexual wildtype. Most theories suggest that sex helps either to purge deleterious mutations, or to adapt to changing environments. Both mechanisms have their limitations if they act in isolation because they require either high genomic mutation rates or very virulent pathogens, and it is therefore often thought that they must act together to maintain sex. Typically, however, these theories have in common that they are not based on spatial processes. Here, we show that local dispersal and local competition can explain the maintenance of sexual reproduction as a means of purging deleterious mutations. Using a spatially explicit individual-based model, we find that even with reasonably low genomic mutation rates and large total population sizes, asexual clones cannot invade a sexual population. Our results demonstrate how spatial processes affect mutation accumulation such that it can fully erode the twofold benefit of asexuality faster than an asexual clone can take over a sexual population. Thus, the cost of sex is generally overestimated in models that ignore the effects of space on mutation accumulation.     

Eco-evolutionary feedbacks,adaptive dynamics and evolutionary rescue theory

Adaptive dynamics theory has been devised to account for feedbacks between ecological and evolutionary processes. Doing so opens new dimensions to and raises new challenges about evolutionary rescue. Adaptive dynamics theory predicts that successive trait substitutions driven by eco-evolutionary feedbacks can gradually erode population size or growth rate, thus potentially raising the extinction risk. Even a single trait substitution can suffice to degrade population viability drastically at once and cause ‘evolutionary suicide’. In a changing environment, a population may track a viable evolutionary attractor that leads to evolutionary suicide, a phenomenon called ‘evolutionary trapping’. Evolutionary trapping and suicide are commonly observed in adaptive dynamics models in which the smooth variation of traits causes catastrophic changes in ecological state. In the face of trapping and suicide, evolutionary rescue requires that the population overcome evolutionary threats generated by the adaptive process itself. Evolutionary repellors play an important role in determining how variation in environmental conditions correlates with the occurrence of evolutionary trapping and suicide, and what evolutionary pathways rescue may follow. In contrast with standard predictions of evolutionary rescue theory, low genetic variation may attenuate the threat of evolutionary suicide and small population sizes may facilitate escape from evolutionary traps.     

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.     

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.     

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.     

ROLE OF SEX AND MIGRATION IN ADAPTATION TO SINK ENVIRONMENTS

Understanding the effects of sex and migration on adaptation to novel environments remains a key problem in evolutionary biology. Using a single‐cell alga Chlamydomonas reinhardtii, we investigated how sex and migration affected rates of evolutionary rescue in a sink environment, and subsequent changes in fitness following evolutionary rescue. We show that sex and migration affect both the rate of evolutionary rescue and subsequent adaptation. However, their combined effects change as the populations adapt to a sink habitat. Both sex and migration independently increased rates of evolutionary rescue, but the effect of sex on subsequent fitness improvements, following initial rescue, changed with migration, as sex was beneficial in the absence of migration but constraining adaptation when combined with migration. These results suggest that sex and migration are beneficial during the initial stages of adaptation, but can become detrimental as the population adapts to its environment.     

Stress-induced mutagenesis and complex adaptation

Because mutations are mostly deleterious, mutation rates should be reduced by natural selection. However, mutations also provide the raw material for adaptation. Therefore, evolutionary theory suggests that the mutation rate must balance between adaptability—the ability to adapt—and adaptedness—the ability to remain adapted. We model an asexual population crossing a fitness valley and analyse the rate of complex adaptation with and without stress-induced mutagenesis (SIM)—the increase of mutation rates in response to stress or maladaptation. We show that SIM increases the rate of complex adaptation without reducing the population mean fitness, thus breaking the evolutionary trade-off between adaptability and adaptedness. Our theoretical results support the hypothesis that SIM promotes adaptation and provide quantitative predictions of the rate of complex adaptation with different mutational strategies.     

Antagonistic coevolution limits population persistence of a virus in a thermally deteriorating environment

Understanding the conditions under which rapid evolutionary adaptation can prevent population extinction in deteriorating environments (i.e. evolutionary rescue) is a crucial aim in the face of global climate change. Despite a rapidly growing body of work in this area, little attention has been paid to the importance of interspecific coevolutionary interactions. Antagonistic coevolution commonly observed between hosts and parasites is likely to retard evolutionary rescue because it often reduces population sizes, and results in the evolution of costly host defence and parasite counter-defence. We used experimental populations of a bacterium Pseudomonas fluorescens SBW25 and a bacteriophage virus (SBW25Φ2), to study how host-parasite coevolution impacts viral population persistence in the face of gradually increasing temperature, an environmental stress for the virus but not the bacterium. The virus persisted much longer when it evolved in the presence of an evolutionarily constant host genotype (i.e. in the absence of coevolution) than when the bacterium and virus coevolved. Further experiments suggest that both a reduction in population size and costly infectivity strategies contributed to viral extinction as a result of coevolution. The results highlight the importance of interspecific evolutionary interactions for the evolutionary responses of populations to global climate change.     

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.     

Quantifying the genomic decay paradox due to Muller's ratchet in human mitochondrial DNA

The observation of high mitochondrial mutation rates in human pedigrees has led to the question of how such an asexual genetic system can survive the accumulation of slightly deleterious mutations caused by Muller's ratchet. I define a null model to quantify in unprecedented detail the threat from extinction caused by Muller's ratchet. This model is general enough to explore the biological significance of Muller's ratchet in various species where its operation has been suspected. For increased precision over a wide range of parameter space I employ individual-based simulations run by evolution@home, the first global computing system for evolutionary biology. After compiling realistic values for the key parameters in human mitochondrial DNA (mtDNA) I find that a surprisingly large range of biologically realistic parameter combinations would lead to the extinction of the human line over a period of 20 million years - if accepted wisdom about mtDNA and Muller's ratchet is correct. The resulting genomic decay paradox complements a similar threat from extinction due to mutation accumulation in nuclear DNA and suggests evaluation of unconventional explanations for long-term persistence. A substantial list of potential solutions is given, including compensatory back mutations, mutation rate heterogeneity and occasional recombination in mtDNA. Future work will have to explore which of these actually solves the paradox. Nonetheless, the results presented here provide yet another reason to minimize anthropogenic increase of mutation rates.     

EVOLUTIONARY RESPONSES TO ENVIRONMENTAL CHANGES: HOW DOES COMPETITION AFFECT ADAPTATION?

The role and importance of ecological interactions for evolutionary responses to environmental changes is to large extent unknown. Here it is shown that interspecific competition may slow down rates of adaptation substantially and fundamentally change patterns of adaptation to long-term environmental changes. In the model investigated here, species compete for resources distributed along an ecological niche space. Environmental change is represented by a slowly moving resource maximum and evolutionary responses of single species are compared with responses of coalitions of two and three competing species. In scenarios with two and three species, species that are favored by increasing resource availability increase in equilibrium population size whereas disfavored species decline in size. Increased competition makes it less favorable for individuals of a disfavored species to occupy a niche close to the maximum and reduces the selection pressure for tracking the moving resource distribution. Individual-based simulations and an analysis using adaptive dynamics show that the combination of weaker selection pressure and reduced population size reduces the evolutionary rate of the disfavored species considerably. If the resource landscape moves stochastically, weak evolutionary responses cause large fluctuations in population size and thereby large extinction risk for competing species, whereas a single species subject to the same environmental variability may track the resource maximum closely and maintain a much more stable population size. Other studies have shown that competitive interactions may amplify changes in mean population sizes due to environmental changes and thereby increase extinction risks. This study accentuates the harmful role of competitive interactions by illustrating that they may also decrease rates of adaptation. The slowdown in evolutionary rates caused by competition may also contribute to explain low rates of morphological change in spite of large environmental fluctuations found in fossil records.     

Avoiding extinction under nonlinear environmental change: models of evolutionary rescue with plasticity

Rapid environmental changes are putting numerous species at risk of extinction. For migration-limited species, persistence depends on either phenotypic plasticity or evolutionary adaptation (evolutionary rescue). Current theory on evolutionary rescue typically assumes linear environmental change. Yet accelerating environmental change may pose a bigger threat. Here, we present a model of a species encountering an environment with accelerating or decelerating change, to which it can adapt through evolution or phenotypic plasticity (within-generational or transgenerational). We show that unless either form of plasticity is sufficiently strong or adaptive genetic variation is sufficiently plentiful, accelerating or decelerating environmental change increases extinction risk compared to linear environmental change for the same mean rate of environmental change.     

Empirical Complexities in the Genetic Foundations of Lethal Mutagenesis

From population genetics theory, elevating the mutation rate of a large population should progressively reduce average fitness. If the fitness decline is large enough, the population will go extinct in a process known as lethal mutagenesis. Lethal mutagenesis has been endorsed in the virology literature as a promising approach to viral treatment, and several in vitro studies have forced viral extinction with high doses of mutagenic drugs. Yet only one empirical study has tested the genetic models underlying lethal mutagenesis, and the theory failed on even a qualitative level. Here we provide a new level of analysis of lethal mutagenesis by developing and evaluating models specifically tailored to empirical systems that may be used to test the theory. We first quantify a bias in the estimation of a critical parameter and consider whether that bias underlies the previously observed lack of concordance between theory and experiment. We then consider a seemingly ideal protocol that avoids this bias—mutagenesis of virions—but find that it is hampered by other problems. Finally, results that reveal difficulties in the mere interpretation of mutations assayed from double-strand genomes are derived. Our analyses expose unanticipated complexities in testing the theory. Nevertheless, the previous failure of the theory to predict experimental outcomes appears to reside in evolutionary mechanisms neglected by the theory (e.g., beneficial mutations) rather than from a mismatch between the empirical setup and model assumptions. This interpretation raises the specter that naive attempts at lethal mutagenesis may augment adaptation rather than retard it.     

The fate of transposable elements in asexual populations

Sexual reproduction and recombination are important for maintaining a stable copy number of transposable elements (TEs). In sexual populations, elements can be contained by purifying selection against host carriers with higher element copy numbers; however, in the absence of sex and recombination, asexual populations could be driven to extinction by an unchecked proliferation of TEs. Here we provide a theoretical framework for analyzing TE dynamics under asexual reproduction. Analytic results show that, in an infinite asexual population, an equilibrium in copy number is achieved if no element excision is possible, but that all TEs are eliminated if there is some excision. In a finite population, computer simulations demonstrate that small populations are driven to extinction by a Muller's ratchet-like process of element accumulation, but that large populations can be cured of vertically transmitted TEs, even with excision rates well below transposition rates. These results may have important consequences for newly arisen asexual lineages and may account for the lack of deleterious retrotransposons in the putatively ancient asexual bdelloid rotifers.     

THE ADAPTATION RATE OF ASEXUALS: DELETERIOUS MUTATIONS,CLONAL INTERFERENCE AND POPULATION BOTTLENECKS

The rate at which a population adapts to its environment is a cornerstone of evolutionary theory, and recent experimental advances in microbial populations have renewed interest in predicting and testing this rate. Efforts to understand the adaptation rate theoretically are complicated by high mutation rates, to both beneficial and deleterious mutations, and by the fact that beneficial mutations compete with each other in asexual populations (clonal interference). Testable predictions must also include the effects of population bottlenecks, repeated reductions in population size imposed by the experimental protocol. In this contribution, we integrate previous work that addresses each of these issues, developing an overall prediction for the adaptation rate that includes: beneficial mutations with probabilistically distributed effects, deleterious mutations of arbitrary effect, population bottlenecks, and clonal interference.     

The effect of mating system on invasiveness: some genetic load may be advantageous when invading new environments

The role of adaptation in determining invasion success has been acknowledged recently, notably through the accumulation of case studies of rapid evolution during bioinvasions. Despite this growing body of empirical evidence, there is still a need to develop the theoretical background of invasions with adaptation. Specifically, the impact of mating system on the dynamics of adaptation during invasion of a new environment remains only partially understood. Here, we analyze a simulation demo-genetic model of bioinvasion accounting for partial asexuality rates. We simulate two levels of recurrent immigration from a source population at mutation–drift–selection equilibrium to a new empty environment with a different adaptive landscape (black-hole sink). Adaptation relies on a quantitative trait coded explicitly by 10 loci under mutation, selection and genetic drift. Using this model, we confirm previous results on the positive effects on invasiveness of migration, mutation and similarity of local phenotypic optima. We further show how the invasion dynamics of the introduced population is affected by the rate of asexuality. Purely asexual species have lower invasion success in terms of probability and time to invasion than species with other mating systems. Among species with mixed mating systems, the greatest invasiveness is observed for species with high asexual rates. We suggest that this pattern is due to inflated genetic variance in the source population through the Hill-Robertson effect (i.e., clonal interference). An interesting consequence is that species with the highest genetic load in their source environment have greatest invasiveness in the new environment.