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.     

Fitness valleys constrain HIV‐1's adaptation to its secondary chemokine coreceptor

Fitness valleys, in which mutations at different loci are singly deleterious but jointly beneficial, arise because of reciprocal sign epistasis. Recent theoretical work provides analytical approximations of times to cross fitness valleys via three mechanisms: sequential fixation, stochastic tunnelling and recombination. These times depend critically on the effective population size (N_e). Human immunodeficiency virus type 1 (HIV‐1) encounters fitness valleys in adapting to its secondary cell‐surface chemokine coreceptor, CXCR4. Adaptation to CXCR4 tends to occur late in infection and only in about 50% of patients and is associated with disease progression. It has been hypothesized that the need to cross fitness valleys may explain the delayed and inconsistent adaptation to CXCR4. We have identified four fitness valleys from a previous study of fitness epistasis in adaptation to CXCR4 and use estimates of the within‐patient variance N_e for different patient treatment statuses and infection stages (conditions) to estimate times to cross the valleys. These valleys may be crossed predominantly by stochastic tunnelling, although mean crossing times are consistently longer than the durations of the conditions for which they are calculated. These results were confirmed with stochastic simulation. Simulations show that crossing times for a given condition are highly variable and that for each condition there is a low probability of crossing each valley. These findings support the hypothesis that fitness valleys constrain the adaptation of HIV‐1 to CXCR4. This study provides the first detailed analysis of the evolutionary dynamics associated with empirical fitness valleys.     

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.     

Quantifying the Role of Population Subdivision in Evolution on Rugged Fitness Landscapes

Natural selection drives populations towards higher fitness, but crossing fitness valleys or plateaus may facilitate progress up a rugged fitness landscape involving epistasis. We investigate quantitatively the effect of subdividing an asexual population on the time it takes to cross a fitness valley or plateau. We focus on a generic and minimal model that includes only population subdivision into equivalent demes connected by global migration, and does not require significant size changes of the demes, environmental heterogeneity or specific geographic structure. We determine the optimal speedup of valley or plateau crossing that can be gained by subdivision, if the process is driven by the deme that crosses fastest. We show that isolated demes have to be in the sequential fixation regime for subdivision to significantly accelerate crossing. Using Markov chain theory, we obtain analytical expressions for the conditions under which optimal speedup is achieved: valley or plateau crossing by the subdivided population is then as fast as that of its fastest deme. We verify our analytical predictions through stochastic simulations. We demonstrate that subdivision can substantially accelerate the crossing of fitness valleys and plateaus in a wide range of parameters extending beyond the optimal window. We study the effect of varying the degree of subdivision of a population, and investigate the trade-off between the magnitude of the optimal speedup and the width of the parameter range over which it occurs. Our results, obtained for fitness valleys and plateaus, also hold for weakly beneficial intermediate mutations. Finally, we extend our work to the case of a population connected by migration to one or several smaller islands. Our results demonstrate that subdivision with migration alone can significantly accelerate the crossing of fitness valleys and plateaus, and shed light onto the quantitative conditions necessary for this to occur.     

Recombination Accelerates Adaptation on a Large-Scale Empirical Fitness Landscape in HIV-1

Recombination has the potential to facilitate adaptation. In spite of the substantial body of theory on the impact of recombination on the evolutionary dynamics of adapting populations, empirical evidence to test these theories is still scarce. We examined the effect of recombination on adaptation on a large-scale empirical fitness landscape in HIV-1 based on in vitro fitness measurements. Our results indicate that recombination substantially increases the rate of adaptation under a wide range of parameter values for population size, mutation rate and recombination rate. The accelerating effect of recombination is stronger for intermediate mutation rates but increases in a monotonic way with the recombination rates and population sizes that we examined. We also found that both fitness effects of individual mutations and epistatic fitness interactions cause recombination to accelerate adaptation. The estimated epistasis in the adapting populations is significantly negative. Our results highlight the importance of recombination in the evolution of HIV-I.     

Recombination and the evolution of mutational robustness

Mutational robustness is the degree to which a phenotype, such as fitness, is resistant to mutational perturbations. Since most of these perturbations will tend to reduce fitness, robustness provides an immediate benefit for the mutated individual. However, robust systems decay due to the accumulation of deleterious mutations that would otherwise have been cleared by selection. This decay has received very little theoretical attention. At equilibrium, a population or asexual lineage is expected to have a mutation load that is invariant with respect to the selection coefficient of deleterious alleles, so the benefit of robustness (at the level of the population or asexual lineage) is temporary. However, previous work has shown that robustness can be favoured when robustness loci segregate independently of the mutating loci they act upon. We examine a simple two-locus model that allows for intermediate rates of recombination and inbreeding to show that increasing the effective recombination rate allows for the evolution of greater mutational robustness.     

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.     

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.     

The effects of deleterious mutations in cyclically parthenogenetic organisms

Cyclically parthenogenetic organisms experience benefits of both sexual and asexual reproductive modes in a constant environment. Sexual reproduction generates new genotypes and may facilitate the purging of deleterious mutations whereas asexuality has a two-fold advantage and enables maintenance of well-fitted genotypes. Asexual reproduction can have a drawback as increased linkage may lead to the accumulation of deleterious mutations. This study presents the results of Monte Carlo simulations of small and infinite diploid populations, with deleterious mutations occurring at multiple loci. The recombination rate and the length of the asexual period, interrupted by sexual reproduction, are allowed to vary. Here I show that the fitness of cyclical parthenogenetic population is dependent on the length of the asexual period. Increased length of the asexual period can lead both to increased segregational load following sexual reproduction and to a stronger effect of deleterious mutations on variation at a linked neutral marker, either by reducing or increasing the variation.     

Recombination enhances protein adaptation in Drosophila melanogaster

Evolutionary theory predicts that the rate and level of adaptation will be enhanced in sexual relative to asexual genomes because sexual recombination facilitates the elimination of deleterious mutations and the fixation of beneficial ones by natural selection. To date, the most compelling evidence for this prediction comes from experimental evolution studies and from loci completely lacking recombination, such as those on Y chromosomes, which often show reduced adaptation and even degeneration. Here, by analyzing replacement and silent DNA polymorphism and divergence at 98 loci, I show that recombination increases the efficacy of protein adaptation throughout the genome of the fruit fly Drosophila melanogaster. Genes residing in genomic regions with reduced recombination rates suffer a greater load of segregating, mildly deleterious mutations and fix fewer beneficial mutations than genes residing in regions with higher recombination rates. These findings suggest that the capacity to respond to natural selection varies with recombination rate across the genome, consistent with theory on the evolutionary advantages of sex and recombination.     

The Rate of Compensatory Evolution

A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, k(c), is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, k(c) depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, k(c) is given by the rate at which favorable combinations of double mutants are produced by compensatory mutation. For r>0, k(c) decreases exponentially with r. In contrast, k(c) becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to WRIGHT's shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.     

Multidimensional Epistasis and the Transitory Advantage of Sex

Identifying and quantifying the benefits of sex and recombination is a long-standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional fitness landscapes in the presence of sign epistasis. Here we present a comparative numerical study of sexual and asexual evolutionary dynamics of haploids on tunably rugged model landscapes under strong selection, paying special attention to the temporal development of the evolutionary advantage of recombination and the link between population diversity and the rate of adaptation. We show that the adaptive advantage of recombination on static rugged landscapes is strictly transitory. At early times, an advantage of recombination arises through the possibility to combine individually occurring beneficial mutations, but this effect is reversed at longer times by the much more efficient trapping of recombining populations at local fitness peaks. These findings are explained by means of well-established results for a setup with only two loci. In accordance with the Red Queen hypothesis the transitory advantage can be prolonged indefinitely in fluctuating environments, and it is maximal when the environment fluctuates on the same time scale on which trapping at local optima typically occurs.     

The Effect of Bacterial Recombination on Adaptation on Fitness Landscapes with Limited Peak Accessibility

There is ample empirical evidence revealing that fitness landscapes are often complex: the fitness effect of a newly arisen mutation can depend strongly on the allelic state at other loci. However, little is known about the effects of recombination on adaptation on such fitness landscapes. Here, we investigate how recombination influences the rate of adaptation on a special type of complex fitness landscapes. On these landscapes, the mutational trajectories from the least to the most fit genotype are interrupted by genotypes with low relative fitness. We study the dynamics of adapting populations on landscapes with different compositions and numbers of low fitness genotypes, with and without recombination. Our results of the deterministic model (assuming an infinite population size) show that recombination generally decelerates adaptation on these landscapes. However, in finite populations, this deceleration is outweighed by the accelerating Fisher-Muller effect under certain conditions. We conclude that recombination has complex effects on adaptation that are highly dependent on the particular fitness landscape, population size and recombination rate.     

Recombination Speeds Adaptation by Reducing Competition between Beneficial Mutations in Populations of Escherichia coli

Identification of the selective forces contributing to the origin and maintenance of sex is a fundamental problem in biology. The Fisher–Muller model proposes that sex is advantageous because it allows beneficial mutations that arise in different lineages to recombine, thereby reducing clonal interference and speeding adaptation. I used the F plasmid to mediate recombination in the bacterium Escherichia coli and measured its effect on adaptation at high and low mutation rates. Recombination increased the rate of adaptation ∼3-fold more in the high mutation rate treatment, where beneficial mutations had to compete for fixation. Sequencing of candidate loci revealed the presence of a beneficial mutation in six high mutation rate lines. In the absence of recombination, this mutation took longer to fix and, over the course of its substitution, conferred a reduced competitive advantage, indicating interference between competing beneficial mutations. Together, these results provide experimental support for the Fisher–Muller model and demonstrate that plasmid-mediated gene transfer can accelerate bacterial adaptation.     

THE INEVITABILITY OF UNCONDITIONALLY DELETERIOUS SUBSTITUTIONS DURING ADAPTATION

Studies on the genetics of adaptation from new mutations typically neglect the possibility that a deleterious mutation might fix. Nonetheless, here we show that, in many regimes, the first mutation to fix is most often deleterious, even when fitness is expected to increase in the long term. In particular, we prove that this phenomenon occurs under weak mutation for any house‐of‐cards model with an equilibrium distribution. We find that the same qualitative results hold under Fisher's geometric model. We also provide a simple intuition for the surprising prevalence of unconditionally deleterious substitutions during early adaptation. Importantly, the phenomenon we describe occurs on fitness landscapes without any local maxima and is therefore distinct from “valley crossing.” Our results imply that the common practice of ignoring deleterious substitutions leads to qualitatively incorrect predictions in many regimes. Our results also have implications for the substitution process at equilibrium and for the response to a sudden decrease in population size.     

Impact of epistasis and pleiotropy on evolutionary adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.     

The effect of population bottlenecks on mutation rate evolution in asexual populations

In the absence of recombination, a mutator allele can spread through a population by hitchhiking with beneficial mutations that appear in its genetic background. Theoretical studies over the past decade have shown that the survival and fixation probability of beneficial mutations can be severely reduced by population size bottlenecks. Here, we use computational modelling and evolution experiments with the yeast S. cerevisiae to examine whether population bottlenecks can affect mutator dynamics in adapting asexual populations. In simulation, we show that population bottlenecks can inhibit mutator hitchhiking with beneficial mutations and are most effective at lower beneficial mutation supply rates. We then subjected experimental populations of yeast propagated at the same effective population size to three different bottleneck regimes and observed that the speed of mutator hitchhiking was significantly slower at smaller bottlenecks, consistent with our theoretical expectations. Our results, thus, suggest that bottlenecks can be an important factor in mutation rate evolution and can in certain circumstances act to stabilize or, at least, delay the progressive elevation of mutation rates in asexual populations. Additionally, our findings provide the first experimental support for the theoretically postulated effect of population bottlenecks on beneficial mutations and demonstrate the usefulness of studying mutator frequency dynamics for understanding the underlying dynamics of fitness‐affecting mutations.     

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.     

Reciprocal sign epistasis between frequently experimentally evolved adaptive mutations causes a rugged fitness landscape

The fitness landscape captures the relationship between genotype and evolutionary fitness and is a pervasive metaphor used to describe the possible evolutionary trajectories of adaptation. However, little is known about the actual shape of fitness landscapes, including whether valleys of low fitness create local fitness optima, acting as barriers to adaptive change. Here we provide evidence of a rugged molecular fitness landscape arising during an evolution experiment in an asexual population of Saccharomyces cerevisiae. We identify the mutations that arose during the evolution using whole-genome sequencing and use competitive fitness assays to describe the mutations individually responsible for adaptation. In addition, we find that a fitness valley between two adaptive mutations in the genes MTH1 and HXT6/HXT7 is caused by reciprocal sign epistasis, where the fitness cost of the double mutant prohibits the two mutations from being selected in the same genetic background. The constraint enforced by reciprocal sign epistasis causes the mutations to remain mutually exclusive during the experiment, even though adaptive mutations in these two genes occur several times in independent lineages during the experiment. Our results show that epistasis plays a key role during adaptation and that inter-genic interactions can act as barriers between adaptive solutions. These results also provide a new interpretation on the classic Dobzhansky-Muller model of reproductive isolation and display some surprising parallels with mutations in genes often associated with tumors.