Adaptive walks toward a moving optimum

We investigate how the dynamics and outcomes of adaptation by natural selection are affected by environmental stability by simulating adaptive walks in response to an environmental change of fixed magnitude but variable speed. Here we consider monomorphic lineages that adapt by the sequential fixation of beneficial mutations. This is modeled by selecting short RNA sequences for folding stability and secondary structure conservation at increasing temperatures. Using short RNA sequences allows us to describe adaptive outcomes in terms of genotype (sequence) and phenotype (secondary structure) and to follow the dynamics of fitness increase. We find that slower rates of environmental change affect the dynamics of adaptive walks by reducing the fitness effect of fixed beneficial mutations, as well as by increasing the range of time in which the substitutions of largest effect are likely to occur. In addition, adaptation to slower rates of environmental change results in fitter endpoints with fewer possible end phenotypes relative to lineages that adapt to a sudden change. This suggests that care should be taken when experiments using sudden environmental changes are used to make predictions about adaptive responses to gradual change.     

Dynamics of molecular evolution in RNA virus populations depend on sudden versus gradual environmental change

Understanding the dynamics of molecular adaptation is a fundamental goal of evolutionary biology. While adaptation to constant environments has been well characterized, the effects of environmental complexity remain seldom studied. One simple but understudied factor is the rate of environmental change. Here we used experimental evolution with RNA viruses to investigate whether evolutionary dynamics varied based on the rate of environmental turnover. We used whole‐genome next‐generation sequencing to characterize evolutionary dynamics in virus populations adapting to a sudden versus gradual shift onto a novel host cell type. In support of theoretical models, we found that when populations evolved in response to a sudden environmental change, mutations of large beneficial effect tended to fix early, followed by mutations of smaller beneficial effect; as predicted, this pattern broke down in response to a gradual environmental change. Early mutational steps were highly parallel across replicate populations in both treatments. The fixation of single mutations was less common than sweeps of associated “cohorts” of mutations, and this pattern intensified when the environment changed gradually. Additionally, clonal interference appeared stronger in response to a gradual change. Our results suggest that the rate of environmental change is an important determinant of evolutionary dynamics in asexual populations.     

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.     

Population Size Affects Adaptation in Complex Ways: Simulations on Empirical Adaptive Landscapes

Do large populations always outcompete smaller ones? Does increasing the mutation rate have a similar effect to increasing the population size, with respect to the adaptation of a population? How important are substitutions in determining the adaptation rate? In this study, we ask how population size and mutation rate interact to affect adaptation on empirical adaptive landscapes. Using such landscapes, we do not need to make many ad hoc assumption about landscape topography, such as about epistatic interactions among mutations or about the distribution of fitness effects. Moreover, we have a better understanding of all the mutations that occur in a population and their effects on the average fitness of the population than we can know in experimental studies. Our results show that the evolutionary dynamics of a population cannot be fully explained by the population mutation rate \(N\mu\); even at constant \(N\mu\), there can be dramatic differences in the adaptation of populations of different sizes. Moreover, the substitution rate of mutations is not always equivalent to the adaptation rate, because we observed populations adapting to high adaptive peaks without fixing any mutations. Finally, in contrast to some theoretical predictions, even on the most rugged landscapes we study, small population size is never an advantage over larger population size. These result show that complex interactions among multiple factors can affect the evolutionary dynamics of populations, and simple models should be taken with caution.     

Fitness evolution and the rise of mutator alleles in experimental Escherichia coli populations

We studied the evolution of high mutation rates and the evolution of fitness in three experimental populations of Escherichia coli adapting to a glucose-limited environment. We identified the mutations responsible for the high mutation rates and show that their rate of substitution in all three populations was too rapid to be accounted for simply by genetic drift. In two of the populations, large gains in fitness relative to the ancestor occurred as the mutator alleles rose to fixation, strongly supporting the conclusion that mutator alleles fixed by hitchhiking with beneficial mutations at other loci. In one population, no significant gain in fitness relative to the ancestor occurred in the population as a whole while the mutator allele rose to fixation, but a substantial and significant gain in fitness occurred in the mutator subpopulation as the mutator neared fixation. The spread of the mutator allele from rarity to fixation took >1000 generations in each population. We show that simultaneous adaptive gains in both the mutator and wild-type subpopulations (clonal interference) retarded the mutator fixation in at least one of the populations. We found little evidence that the evolution of high mutation rates accelerated adaptation in these populations.     

Adapting in larger numbers can increase the vulnerability of Escherichia coli populations to environmental changes

Larger populations generally adapt faster to their existing environment. However, it is unknown if the population size experienced during evolution influences the ability to face sudden environmental changes. To investigate this issue, we subjected replicate Escherichia coli populations of different sizes to experimental evolution in an environment containing a cocktail of three antibiotics. In this environment, the ability to actively efflux molecules outside the cell is expected to be a major fitness‐affecting trait. We found that all the populations eventually reached similar fitness in the antibiotic cocktail despite adapting at different speeds, with the larger populations adapting faster. Surprisingly, although efflux activity (EA) enhanced in the smaller populations, it decayed in the larger ones. The evolution of EA was largely shaped by pleiotropic responses to selection and not by drift. This demonstrates that quantitative differences in population size can lead to qualitative differences (decay/enhancement) in the fate of a character during adaptation to identical environments. Furthermore, the larger populations showed inferior fitness upon sudden exposure to several alternative stressful environments. These observations provide a novel link between population size and vulnerability to environmental changes. Counterintuitively, adapting in larger numbers can render bacterial populations more vulnerable to abrupt environmental changes.     

Selection history and epistatic interactions impact dynamics of adaptation to novel environmental stresses

In rapidly changing environments, selection history may impact the dynamics of adaptation. Mutations selected in one environment may result in pleiotropic fitness trade-offs in subsequent novel environments, slowing the rates of adaptation. Epistatic interactions between mutations selected in sequential stressful environments may slow or accelerate subsequent rates of adaptation, depending on the nature of that interaction. We explored the dynamics of adaptation during sequential exposure to herbicides with different modes of action in Chlamydomonas reinhardtii. Evolution of resistance to two of the herbicides was largely independent of selection history. For carbetamide, previous adaptation to other herbicide modes of action positively impacted the likelihood of adaptation to this herbicide. Furthermore, while adaptation to all individual herbicides was associated with pleiotropic fitness costs in stress-free environments, we observed that accumulation of resistance mechanisms was accompanied by a reduction in overall fitness costs. We suggest that antagonistic epistasis may be a driving mechanism that enables populations to more readily adapt in novel environments. These findings highlight the potential for sequences of xenobiotics to facilitate the rapid evolution of multiple-drug and -pesticide resistance, as well as the potential for epistatic interactions between adaptive mutations to facilitate evolutionary rescue in rapidly changing environments.     

Rate of novel host invasion affects adaptability of evolving RNA virus lineages

Although differing rates of environmental turnover should be consequential for the dynamics of adaptive change, this idea has been rarely examined outside of theory. In particular, the importance of RNA viruses in disease emergence warrants experiments testing how differing rates of novel host invasion may impact the ability of viruses to adaptively shift onto a novel host. To test whether the rate of environmental turnover influences adaptation, we experimentally evolved 144 Sindbis virus lineages in replicated tissue-culture environments, which transitioned from being dominated by a permissive host cell type to a novel host cell type. The rate at which the novel host ‘invaded’ the environment varied by treatment. The fitness (growth rate) of evolved virus populations was measured on each host type, and molecular substitutions were mapped via whole genome consensus sequencing. Results showed that virus populations more consistently reached high fitness levels on the novel host when the novel host ‘invaded’ the environment more gradually, and gradual invasion resulted in less variable genomic outcomes. Moreover, virus populations that experienced a rapid shift onto the novel host converged upon different genotypes than populations that experienced a gradual shift onto the novel host, suggesting a strong effect of historical contingency.     

Mutators, population size, adaptive landscape and the adaptation of asexual populations of bacteria.

Selection of mutator alleles, increasing the mutation rate up to 10, 000-fold, has been observed during in vitro experimental evolution. This spread is ascribed to the hitchhiking of mutator alleles with favorable mutations, as demonstrated by a theoretical model using selective parameters corresponding to such experiments. Observations of unexpectedly high frequencies of mutators in natural isolates suggest that the same phenomenon could occur in the wild. But it remains questionable whether realistic in natura parameter values could also result in selection of mutators. In particular, the main parameters of adaptation, the size of the adapting population and the height and steepness of the adaptive peak characterizing adaptation, are very variable in nature. By simulation approach, we studied the effect of these parameters on the selection of mutators in asexual populations, assuming additive fitness. We show that the larger the population size, the more likely the fixation of mutator alleles. At a large population size, at least four adaptive mutations are needed for mutator fixation; moreover, under stronger selection stronger mutators are selected. We propose a model based on multiple mutations to illustrate how second-order selection can optimize population fitness when few favorable mutations are required for adaptation.     

Environmental heterogeneity enhances clonal interference

Clonal interference (CI) is a phenomenon that may be important in several asexual microbes. It occurs when population sizes are large and mutation rates to new beneficial alleles are of significant magnitude. Here we explore the role of gene flow and spatial heterogeneity in selection strength in the adaptation of asexuals. We consider a subdivided population of individuals that are adapting, through new beneficial mutations, and that migrate between different patches. The fitness effect of each mutation depends on the patch and all mutations considered are assumed to be unconditionally beneficial. We find that spatial variation in selection pressure affects the rate of adaptive evolution and its qualitative effects depend on the level of gene flow. In particular, we find that both low migration and high levels of heterogeneity lead to enhanced CI. In contrast, for high levels of migration the rate of fixation of adaptive mutations is higher when environmental heterogeneity is present. In addition, we observe that the level of fitness variation is higher and simultaneous fixation of multiple mutations tends to occur in the regime of low migration rates and high heterogeneity.     

Surfing on the seascape: Adaptation in a changing environment

The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation‐limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an “adaptive‐walk” approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.     

Long-term experimental evolution in Escherichia coli. V. Effects of recombination with immigrant genotypes on the rate of bacterial evolution

This study builds upon an earlier experiment that examined the dynamics of mean fitness in evolving populations of Escherichia coli in which mutations were the sole source of genetic variation. During thousands of generations in a constant environment, the rate of improvement in mean fitness of these asexual populations slowed considerably from an initially rapid pace. In this study, we sought to determine whether sexual recombination with novel genotypes would reaccelerate the rate of adaption in these populations. To that end, treatment populations were propagated for an additional 1000 generations in the same environment as their ancestors, but they were periodically allowed to mate with an immigrant pool of genetically distinct Hfr (high frequency recombination) donors. These donors could transfer genes to the resident populations by conjugation, but the donors themselves could not grow in the experimental environment. Control populations were propagated under identical conditions, but in the absence of sexual recombination with the donors. All twelve control populations retained the ancestral alleles at every locus that was scored. In contrast, the sexual recombination treatment yielded dramatic increases in genetic variation. Thus, there was a profound effect of recombination on the rate of genetic change. However, the increased genetic variation in the treatment populations had no significant effect on the rate of adaptive evolution, as measured by changes in mean fitness relative to a common competitor. We then considered three hypotheses that might reconcile these two outcomes: recombination pressure, hitchhiking of recombinant genotypes in association with beneficial mutations, and complex selection dynamics whereby certain genotypes may have a selective advantage only within a particular milieu of competitors. The estimated recombination rate was too low to explain the observed rate of genetic change, either alone or in combination with hitchhiking effects. However, we documented comple x ecological interactions among some recombinant genotypes, suggesting that our method for estimating fitness relative to a common competitor might have underestimated the rate of adaptive evolution in the treatment populations.     

Haldane's sieve and adaptation from the standing genetic variation

We consider populations that adapt to a sudden environmental change by fixing alleles found at mutation-selection balance. In particular, we calculate probabilities of fixation for previously deleterious alleles, ignoring the input of new mutations. We find that "Haldane's sieve"--the bias against the establishment of recessive beneficial mutations--does not hold under these conditions. Instead probabilities of fixation are generally independent of dominance. We show that this result is robust to patterns of sex expression for both X-linked and autosomal loci. We further show that adaptive evolution is invariably slower at X-linked than autosomal loci when evolution begins from mutation-selection balance. This result differs from that obtained when adaptation uses new mutations, a finding that may have some bearing on recent attempts to distinguish between hitchhiking and background selection by contrasting the molecular population genetics of X-linked vs. autosomal loci. Last, we suggest a test to determine whether adaptation used new mutations or previously deleterious alleles from the standing genetic variation.     

Geographical patterns of adaptation within a species' range: interactions between drift and gene flow

We use individual-based stochastic simulations and analytical deterministic predictions to investigate the interaction between drift, natural selection and gene flow on the patterns of local adaptation across a fragmented species' range under clinally varying selection. Migration between populations follows a stepping-stone pattern and density decreases from the centre to the periphery of the range. Increased migration worsens gene swamping in small marginal populations but mitigates the effect of drift by replenishing genetic variance and helping purge deleterious mutations. Contrary to the deterministic prediction that increased connectivity within the range always inhibits local adaptation, simulations show that low intermediate migration rates improve fitness in marginal populations and attenuate fitness heterogeneity across the range. Such migration rates are optimal in that they maximize the total mean fitness at the scale of the range. Optimal migration rates increase with shallower environmental gradients, smaller marginal populations and higher mutation rates affecting fitness.     

Population extinction and the genetics of adaptation

Theories of adaptation typically ignore the effect of environmental change on population size. But some environmental challenges--challenges to which populations must adapt--may depress absolute fitness below 1, causing populations to decline. Under this scenario, adaptation is a race; beneficial alleles that adapt a population to the new environment must sweep to high frequency before the population becomes extinct. We derive simple, though approximate, solutions to the probability of successful adaptation (population survival) when adaptation involves new mutations, the standing genetic variation, or a mixture of the two. Our results show that adaptation to such environmental challenges can be difficult when relying on new mutations at one or a few loci, and populations will often decline to extinction.     

The number of mutations selected during adaptation in a laboratory population of Saccharomyces cerevisiae

There is currently limited empirical and theoretical support for the prevailing view that adaptation typically results from the fixation of many mutations, each with small phenotypic effects. Recent theoretical work suggests that, on the contrary, most of the phenotypic change during an episode of adaptation can result from the selection of a few mutations with relatively large effects. I studied the genetics of adaptation by populations of budding yeast to a culture regime of daily hundredfold dilution and transfer in a glucose-limited minimal liquid medium. A single haploid genotype isolated after 2000 generations showed a 76% fitness increase over its ancestor. This evolved haploid was crossed with its ancestor, and tetrad dissections were used to isolate a complete series of six meiotic tetrads. The Castle-Wright estimator of the number of loci at which adaptive mutations had been selected, modified to account for linkage and variation among mutations in the size of their effect, is 4.4. The estimate for a second haploid genotype, isolated from a separate population and with a fitness gain of 60%, was 2.7 loci. Backcrosses to the ancestor with the first evolved genotype support the inference that adaptation resulted primarily from two to five mutations. These backcrosses also indicated that deleterious mutations had hitchhiked with adaptive mutations in this evolved genotype.     

The rate of fitness-valley crossing in sexual populations

Biological traits result in part from interactions between different genetic loci. This can lead to sign epistasis, in which a beneficial adaptation involves a combination of individually deleterious or neutral mutations; in this case, a population must cross a "fitness valley" to adapt. Recombination can assist this process by combining mutations from different individuals or retard it by breaking up the adaptive combination. Here, we analyze the simplest fitness valley, in which an adaptation requires one mutation at each of two loci to provide a fitness benefit. We present a theoretical analysis of the effect of recombination on the valley-crossing process across the full spectrum of possible parameter regimes. We find that low recombination rates can speed up valley crossing relative to the asexual case, while higher recombination rates slow down valley crossing, with the transition between the two regimes occurring when the recombination rate between the loci is approximately equal to the selective advantage provided by the adaptation. In large populations, if the recombination rate is high and selection against single mutants is substantial, the time to cross the valley grows exponentially with population size, effectively meaning that the population cannot acquire the adaptation. Recombination at the optimal (low) rate can reduce the valley-crossing time by up to several orders of magnitude relative to that in an asexual population.     

FISHER'S GEOMETRIC MODEL WITH A MOVING OPTIMUM

Fisher's geometric model has been widely used to study the effects of pleiotropy and organismic complexity on phenotypic adaptation. Here, we study a version of Fisher's model in which a population adapts to a gradually moving optimum. Key parameters are the rate of environmental change, the dimensionality of phenotype space, and the patterns of mutational and selectional correlations. We focus on the distribution of adaptive substitutions, that is, the multivariate distribution of the phenotypic effects of fixed beneficial mutations. Our main results are based on an “adaptive‐walk approximation,” which is checked against individual‐based simulations. We find that (1) the distribution of adaptive substitutions is strongly affected by the ecological dynamics and largely depends on a single composite parameter γ, which scales the rate of environmental change by the “adaptive potential” of the population; (2) the distribution of adaptive substitution reflects the shape of the fitness landscape if the environment changes slowly, whereas it mirrors the distribution of new mutations if the environment changes fast; (3) in contrast to classical models of adaptation assuming a constant optimum, with a moving optimum, more complex organisms evolve via larger adaptive steps.     

Selective neutrality and enzyme kinetics

This article appeals to a recent theory of enzyme evolution to show that the properties, neutral or adaptive, which characterize the observed allelic variation in natural populations can be inferred from the functional parameters, substrate specificity, and reaction rate. This study delineates the following relations between activity variables, and the forces—adaptive or neutral—determining allelic variation: (1) Enzymes with broad substrate specificity: The observed polymorphism is adaptive; mutations in this class of enzymes can result in increased fitness of the organism and hence be relevant for positive selection. (2) Enzymes with absolute substrate specificity and diffusion-controlled rates: Observed allelic variation will be absolutely neutral; mutations in this class of enzymes will be either deleterious or have no effect on fitness. (3) Enzymes with absolute or group specificity and nondiffusion-controlled rates: Observed variation will be partially neutral; mutants which are selectively neutral may become advantageous under an appropriate environmental condition or different genetic background. We illustrate each of the relations between kinetic properties and evolutionary states with examples drawn from enzymes whose evolutionary dynamics have been intensively studied. Received: 12 December 1996 / Accepted: 22 April 1997     

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.