Evolution in alternating environments with tunable interlandscape correlations

Natural populations are often exposed to temporally varying environments. Evolutionary dynamics in varying environments have been extensively studied, although understanding the effects of varying selection pressures remains challenging. Here, we investigate how cycling between a pair of statistically related fitness landscapes affects the evolved fitness of an asexually reproducing population. We construct pairs of fitness landscapes that share global fitness features but are correlated with one another in a tunable way, resulting in landscape pairs with specific correlations. We find that switching between these landscape pairs, depending on the ruggedness of the landscape and the interlandscape correlation, can either increase or decrease steady‐state fitness relative to evolution in single environments. In addition, we show that switching between rugged landscapes often selects for increased fitness in both landscapes, even in situations where the landscapes themselves are anticorrelated. We demonstrate that positively correlated landscapes often possess a shared maximum in both landscapes that allows the population to step through sub‐optimal local fitness maxima that often trap single landscape evolution trajectories. Finally, we demonstrate that switching between anticorrelated paired landscapes leads to ergodic‐like dynamics where each genotype is populated with nonzero probability, dramatically lowering the steady‐state fitness in comparison to single landscape evolution.     

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.     

Detecting epistasis from an ensemble of adapting populations

The role that epistasis plays during adaptation remains an outstanding problem, which has received considerable attention in recent years. Most of the recent empirical studies are based on ensembles of replicate populations that adapt in a fixed, laboratory controlled condition. Researchers often seek to infer the presence and form of epistasis in the fitness landscape from the time evolution of various statistics averaged across the ensemble of populations. Here, we provide a rigorous analysis of what quantities, drawn from time series of such ensembles, can be used to infer epistasis for populations evolving under weak mutation on finite‐site fitness landscapes. First, we analyze the mean fitness trajectory—that is, the time course of the ensemble average fitness. We show that for any epistatic fitness landscape and starting genotype, there always exists a non‐epistatic fitness landscape that produces the exact same mean fitness trajectory. Thus, the presence of epistasis is not identifiable from the mean fitness trajectory. By contrast, we show that two other ensemble statistics—the time evolution of the fitness variance across populations, and the time evolution of the mean number of substitutions—can detect certain forms of epistasis in the underlying fitness landscape.     

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.     

Prior evolution in stochastic versus constant temperatures affects RNA virus evolvability at a thermal extreme

It is unclear how historical adaptation versus maladaptation in a prior environment affects population evolvability in a novel habitat. Prior work showed that vesicular stomatitis virus (VSV) populations evolved at constant 37°C improved in cellular infection at both 29°C and 37°C; in contrast, those evolved under random changing temperatures between 29°C and 37°C failed to improve. Here, we tested whether prior evolution affected the rate of adaptation at the thermal‐niche edge: 40°C. After 40 virus generations in the new environment, we observed that populations historically evolved at random temperatures showed greater adaptability. Deep sequencing revealed that most of the newly evolved mutations were de novo. Also, two novel evolved mutations in the VSV glycoprotein and replicase genes tended to co‐occur in the populations previously evolved at constant 37°C, whereas this parallelism was not seen in populations with prior random temperature evolution. These results suggest that prior adaptation under constant versus random temperatures constrained the mutation landscape that could improve fitness in the novel 40°C environment, perhaps owing to differing epistatic effects of new mutations entering genetic architectures that earlier diverged. We concluded that RNA viruses maladapted to their previous environment could “leapfrog” over counterparts of higher fitness, to achieve faster adaptability in a novel environment.     

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.     

Properties of selected mutations and genotypic landscapes under Fisher's geometric model

The fitness landscape—the mapping between genotypes and fitness—determines properties of the process of adaptation. Several small genotypic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here, we generate several testable predictions for the properties of these small genotypic landscapes under Fisher's geometric model of adaptation. When the ancestral strain is far from the fitness optimum, we analytically compute the fitness effect of selected mutations and their epistatic interactions. Epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected, or coselected in an adaptive walk. Simulations show that genotypic landscapes built from Fisher's model are very close to an additive landscape when the ancestral strain is far from the optimum. However, when it is close to the optimum, a large diversity of landscape with substantial roughness and sign epistasis emerged. Strikingly, small genotypic landscapes built from several replicate adaptive walks on the same underlying landscape were highly variable, suggesting that several realizations of small genotypic landscapes are needed to gain information about the underlying architecture of the fitness landscape.     

Multiple adaptive substitutions during evolution in novel environments

We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to be high, here we start the adaptation process with a low fitness corresponding to a population in a stressful novel environment. For generic fitness distributions, using an analytic argument we find that the average number of steps to a local optimum varies logarithmically with the genotype sequence length and increases as the correlations among genotypic fitnesses increase. When the fitnesses are exponentially or uniformly distributed, using an evolution equation for the distribution of population fitness, we analytically calculate the fitness distribution of fixed beneficial mutations and the walk length distribution.     

RNA viruses as complex adaptive systems

RNA viruses have high mutation rates and so their populations exist as dynamic and complex mutant distributions. It has been consistently observed that when challenged with a new environment, viral populations adapt following hyperbolic-like kinetics: adaptation is initially very rapid, but then slows down as fitness reaches an asymptotic value. These adaptive dynamics have been explained in terms of populations moving towards the top of peaks on rugged fitness landscapes. Fitness fluctuations of varying magnitude are observed during adaptation. Often the presence of fluctuations in the evolution of physical systems indicates some form of self-organization, or where many components of the system are simultaneously involved. Here we analyze data from several in vitro evolution experiments carried out with vesicular stomatitis virus (VSV) looking for the signature of criticality and scaling. Long-range fitness correlations have been detected during the adaptive process. We also found that the magnitude of fitness fluctuations, far from being trivial, conform to a Weibull probability distribution function, suggesting that viral adaptation belongs to a broad category of phenomena previously documented in other fields and related with emergence.     

Predictability of evolutionary trajectories in fitness landscapes

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.     

Evolutionary genomics of host adaptation in vesicular stomatitis virus

Populations experiencing similar selection pressures can sometimes diverge in the genetic architectures underlying evolved complex traits. We used RNA virus populations of large size and high mutation rate to study the impact of historical environment on genome evolution, thus increasing our ability to detect repeatable patterns in the evolution of genetic architecture. Experimental vesicular stomatitis virus populations were evolved on HeLa cells, on MDCK cells, or on alternating hosts. Turner and Elena (2000. Cost of host radiation in an RNA virus. Genetics. 156:1465-1470.) previously showed that virus populations evolved in single-host environments achieved high fitness on their selected hosts but failed to increase in fitness relative to their ancestor on the unselected host and that alternating-host-evolved populations had high fitness on both hosts. Here we determined the complete consensus sequence for each evolved population after 95 generations to gauge whether the parallel phenotypic changes were associated with parallel genomic changes. We also analyzed the patterns of allele substitutions to discern whether differences in fitness across hosts arose through true pleiotropy or the presence of not only a mutation that is beneficial in both hosts but also 1 or more mutations at other loci that are costly in the unselected environment (mutation accumulation [MA]). We found that ecological history may influence to what extent pleiotropy and MA contribute to fitness asymmetries across environments. We discuss the degree to which current genetic architecture is expected to constrain future evolution of complex traits, such as host use by RNA viruses.     

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.     

Dynamic RNA Fitness Landscapes of a Group I Ribozyme during Changes to the Experimental Environment

Fitness landscapes of protein and RNA molecules can be studied experimentally using high-throughput techniques to measure the functional effects of numerous combinations of mutations. The rugged topography of these molecular fitness landscapes is important for understanding and predicting natural and experimental evolution. Mutational effects are also dependent upon environmental conditions, but the effects of environmental changes on fitness landscapes remains poorly understood. Here, we investigate the changes to the fitness landscape of a catalytic RNA molecule while changing a single environmental variable that is critical for RNA structure and function. Using high-throughput sequencing of in vitro selections, we mapped a fitness landscape of the Azoarcus group I ribozyme under eight different concentrations of magnesium ions (1–48 mM MgCl₂). The data revealed the magnesium dependence of 16,384 mutational neighbors, and from this, we investigated the magnesium induced changes to the topography of the fitness landscape. The results showed that increasing magnesium concentration improved the relative fitness of sequences at higher mutational distances while also reducing the ruggedness of the mutational trajectories on the landscape. As a result, as magnesium concentration was increased, simulated populations evolved toward higher fitness faster. Curve-fitting of the magnesium dependence of individual ribozymes demonstrated that deep sequencing of in vitro reactions can be used to evaluate the structural stability of thousands of sequences in parallel. Overall, the results highlight how environmental changes that stabilize structures can also alter the ruggedness of fitness landscapes and alter evolutionary processes.     

The evolution of mutation rate in finite asexual populations

In this article, we model analytically the evolution of mutation rate in asexual organisms. Three selective forces are present. First, everything else being equal, individuals with higher mutation rate have a larger fitness, thanks to the energy and time saved by not replicating DNA accurately. Second, as a flip side, the genome of these individuals is replicated with errors that may negatively affect fitness. Third, and conversely, replication errors have a potential benefit if beneficial mutations are to be generated. Our model describes the fate of modifiers of mutation rate under the three forces and allows us to predict the long-term evolutionary trajectory of mutation rate. We obtain three major results. First, in asexuals, the needs for both adaptation and genome preservation are not evolutionary forces that can stabilize mutation rate at an intermediate optimum. When adaptation has a significant role, it primarily destabilizes mutation rate and yields the emergence of strong-effect mutators. Second, in contrast to what is usually believed, the appearance of modifiers with large mutation rate is more likely when the fitness cost of each deleterious mutation is weak, because the cost of replication errors is then paid after a delay. Third, in small populations, and even if adaptations are needed, mutation rate is always blocked at the minimum attainable level, because the rate of adaptation is too slow to play a significant role. Only populations whose size is above a critical mass see their mutation rate affected by the need for adaptation.     

Theoretical perspectives on the statics and dynamics of species' borders in patchy environments

Understanding range limits is a fundamental problem in ecology and evolutionary biology. In 1963, Mayr argued that "contaminating" gene flow from central populations constrained adaptation in marginal populations, preventing range expansion, while in 1984, Bradshaw suggested that absence of genetic variation prevented species from occurring everywhere. Understanding stability of range boundaries requires unraveling the interplay of demography, gene flow, and evolution of populations in concrete landscape settings. We walk through a set of interrelated spatial scenarios that illustrate interesting complexities of this interplay. To motivate our individual-based model results, we consider a hypothetical zooplankter in a landscape of discrete water bodies coupled by dispersal. We examine how patterns of dispersal influence adaptation in sink habitats where conditions are outside the species' niche. The likelihood of observing niche evolution (and thus range expansion) over any given timescale depends on (1) the degree of initial maladaptation; (2) pattern (pulsed vs. continuous, uni- vs. bidirectional), timing (juvenile vs. adult), and rate of dispersal (and hence population size); (3) mutation rate; (4) sexuality; and (5) the degree of heterogeneity in the occupied range. We also show how the genetic architecture of polygenic adaptation is influenced by the interplay of selection and dispersal in heterogeneous landscapes.     

Life-history evolution in spatially heterogeneous environments,with and without phenotypic plasticity

Summary The formulation of Kawecki and Stearns (1993) adapted for sexual populations is used to characterize lifehistory evolution in spatially heterogeneous environments comprising a number of distinct habitats. Three types of evolutionary outcome/optimal strategy are distinguished, appertaining to populations with phenotypic plasticity, populations without it (here called aplastic) and to populations that are reproductively isolated. In general plastic and isolated optima differ, but do not differ if none of the habitats provide source or sink populations. Plastic, aplastic and isolated optima are calculated and compared in three numerical examples representing trade-offs involving reproductive effort, egg size and defence. Locating the aplastic optimum involves numerical construction of a fitness landscape showing how allelic fitness depends on aplastic strategy and on the relative frequencies of the habitats. In all three examples the aplastic optimum lies between or almost between the plastic optima. In two cases the aplastic optimum switches abruptly between the plastic optima as the relative frequencies of the habitats change, and in the third case the switch is gradual. The abruptness or otherwise of the switch depends on the position and structure of the valleys in the fitness landscape and this in turn depends on how sharply the fitness peaks are differentiated.     

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.     

The Ability of Flux Balance Analysis to Predict Evolution of Central Metabolism Scales with the Initial Distance to the Optimum

The most powerful genome-scale framework to model metabolism, flux balance analysis (FBA), is an evolutionary optimality model. It hypothesizes selection upon a proposed optimality criterion in order to predict the set of internal fluxes that would maximize fitness. Here we present a direct test of the optimality assumption underlying FBA by comparing the central metabolic fluxes predicted by multiple criteria to changes measurable by a ¹³C-labeling method for experimentally-evolved strains. We considered datasets for three Escherichia coli evolution experiments that varied in their length, consistency of environment, and initial optimality. For ten populations that were evolved for 50,000 generations in glucose minimal medium, we observed modest changes in relative fluxes that led to small, but significant decreases in optimality and increased the distance to the predicted optimal flux distribution. In contrast, seven populations evolved on the poor substrate lactate for 900 generations collectively became more optimal and had flux distributions that moved toward predictions. For three pairs of central metabolic knockouts evolved on glucose for 600–800 generations, there was a balance between cases where optimality and flux patterns moved toward or away from FBA predictions. Despite this variation in predictability of changes in central metabolism, two generalities emerged. First, improved growth largely derived from evolved increases in the rate of substrate use. Second, FBA predictions bore out well for the two experiments initiated with ancestors with relatively sub-optimal yield, whereas those begun already quite optimal tended to move somewhat away from predictions. These findings suggest that the tradeoff between rate and yield is surprisingly modest. The observed positive correlation between rate and yield when adaptation initiated further from the optimum resulted in the ability of FBA to use stoichiometric constraints to predict the evolution of metabolism despite selection for rate.     

Evolutionary accessibility of mutational pathways

Functional effects of different mutations are known to combine to the total effect in highly nontrivial ways. For the trait under evolutionary selection ('fitness'), measured values over all possible combinations of a set of mutations yield a fitness landscape that determines which mutational states can be reached from a given initial genotype. Understanding the accessibility properties of fitness landscapes is conceptually important in answering questions about the predictability and repeatability of evolutionary adaptation. Here we theoretically investigate accessibility of the globally optimal state on a wide variety of model landscapes, including landscapes with tunable ruggedness as well as neutral 'holey' landscapes. We define a mutational pathway to be accessible if it contains the minimal number of mutations required to reach the target genotype, and if fitness increases in each mutational step. Under this definition accessibility is high, in the sense that at least one accessible pathway exists with a substantial probability that approaches unity as the dimensionality of the fitness landscape (set by the number of mutational loci) becomes large. At the same time the number of alternative accessible pathways grows without bounds. We test the model predictions against an empirical 8-locus fitness landscape obtained for the filamentous fungus Aspergillus niger. By analyzing subgraphs of the full landscape containing different subsets of mutations, we are able to probe the mutational distance scale in the empirical data. The predicted effect of high accessibility is supported by the empirical data and is very robust, which we argue reflects the generic topology of sequence spaces. Together with the restrictive assumptions that lie in our definition of accessibility, this implies that the globally optimal configuration should be accessible to genome wide evolution, but the repeatability of evolutionary trajectories is limited owing to the presence of a large number of alternative mutational pathways.