The impact of high‐order epistasis in the within‐host fitness of a positive‐sense plant RNA virus

RNA viruses are the main source of emerging infectious diseases because of the evolutionary potential bestowed by their fast replication, large population sizes and high mutation and recombination rates. However, an equally important property, which is usually neglected, is the topography of the fitness landscape. How many fitness maxima exist and how well they are connected is especially interesting, as this determines the number of accessible evolutionary pathways. To address this question, we have reconstructed a region of the fitness landscape of tobacco etch potyvirus constituted by mutations observed during the experimental adaptation of the virus to the novel host Arabidopsis thaliana. Fitness was measured for many genotypes and showed the existence of multiple peaks and holes in the landscape. We found prevailing epistatic effects between mutations, with cases of reciprocal sign epistasis being common among pairs of mutations. We also found that high‐order epistasis was as important as pairwise epistasis in their contribution to fitness. Therefore, results suggest that the landscape was rugged due to the existence of holes caused by lethal genotypes, that a very limited number of potential neutral paths exist and that it contained a single adaptive peak.     

Exploring phenotype space through neutral evolution

RNA secondary-structure folding algorithms predict the existence of connected networks of RNA sequences with identical secondary structures. Fitness landscapes that are based on the mapping between RNA sequence and RNA secondary structure hence have many neutral paths. A neutral walk on these fitness landscapes gives access to a virtually unlimited number of secondary structures that are a single point mutation from the neutral path. This shows that neutral evolution explores phenotype space and can play a role in adaptation. Received: 23 December 1995 / Accepted: 17 March 1996     

Historical Contingency Causes Divergence in Adaptive Expression of the lac Operon

Populations of Escherichia coli selected in constant and fluctuating environments containing lactose often adapt by substituting mutations in the lacI repressor that cause constitutive expression of the lac operon. These mutations occur at a high rate and provide a significant benefit. Despite this, eight of 24 populations evolved for 8,000 generations in environments containing lactose contained no detectable repressor mutations. We report here on the basis of this observation. We find that, given relevant mutation rates, repressor mutations are expected to have fixed in all evolved populations if they had maintained the same fitness effect they confer when introduced to the ancestor. In fact, reconstruction experiments demonstrate that repressor mutations have become neutral or deleterious in those populations in which they were not detectable. Populations not fixing repressor mutations nevertheless reached the same fitness as those that did fix them, indicating that they followed an alternative evolutionary path that made redundant the potential benefit of the repressor mutation, but involved unique mutations of equivalent benefit. We identify a mutation occurring in the promoter region of the uspB gene as a candidate for influencing the selective choice between these paths. Our results detail an example of historical contingency leading to divergent evolutionary outcomes.     

The population genetics of adaptation: the adaptation of DNA sequences

I describe several patterns characterizing the genetics of adaptation at the DNA level. Following Gillespie (1983, 1984, 1991), I consider a population presently fixed for the ith best allele at a locus and study the sequential substitution of favorable mutations that results in fixation of the fittest DNA sequence locally available. Given a wild type sequence that is less than optimal, I derive the fitness rank of the next allele typically fixed by natural selection as well as the mean and variance of the jump in fitness that results when natural selection drives a substitution. Looking over the whole series of substitutions required to reach the best allele, I show that the mean fitness jumps occurring throughout an adaptive walk are constrained to a twofold window of values, assuming only that adaptation begins from a reasonably fit allele. I also show that the first substitution and the substitution of largest effect account for a large share of the total fitness increase during adaptation. I further show that the distribution of selection coefficients fixed throughout such an adaptive walk is exponential (ignoring mutations of small effect), a finding reminiscent of that seen in Fisher's geometric model of adaptation. Last, I show that adaptation by natural selection behaves in several respects as the average of two idealized forms of adaptation, perfect and random.     

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     

Coalescent under the evolution of coadaptation

Adaptation to novel environments arises either from new beneficial mutations or by utilizing pre‐existing genetic variation. When standing variation is used as the source of new adaptation, fitness effects of alleles may be altered through an environmental change. Alternatively, changes in epistatic genetic backgrounds may convert formerly neutral mutations into beneficial alleles in the new genetic background. By extending the coalescent theory to describe the genealogical histories of two interacting loci, I here investigated the hitchhiking effect of epistatic selection on the amount and pattern of sequence diversity at the linked neutral regions. Assuming a specific form of epistasis between two new mutations that are independently neutral, but together form a coadapted haplotype, I demonstrate that the footprints of epistatic selection differ markedly between the interacting loci depending on the order and relative timing of the two mutational events, even though both mutations are equally essential for the formation of an adaptive gene combination. Our results imply that even when neutrality tests could detect just a single instance of adaptive substitution, there may, in fact, be numerous other hidden mutations that are left undetected, but still play indispensable roles in the evolution of a new adaptation. We expect that the integration of the coalescent framework into the general theory of polygenic inheritance would clarify the connection between factors driving phenotypic evolution and their consequences on underlying DNA sequence changes, which should further illuminate the evolutionary foundation of coadapted systems.     

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor,II

In our previous report [Aita, T., Morinaga, S., Hosimi, Y., 2004. Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor I. Bull. Math. Biol. 66, 1371–1403], an analogy between thermodynamics and adaptive walks on a Mt. Fuji-type fitness landscape in an artificial selection system was presented. Introducing the ‘free fitness’ as the sum of a fitness term and an entropy term and ‘evolutionary force’ as the gradient of free fitness on a fitness coordinate, we demonstrated that the adaptive walk (=evolution) is driven by the evolutionary force in the direction in which free fitness increases. In this report, we examine the effect of various modifications of the original model on the properties of the adaptive walk. The modifications were as follows: first, mutation distance d was distributed obeying binomial distribution; second, the selection process obeyed the natural selection protocol; third, ruggedness was introduced to the landscape according to the NK model; fourth, a noise was included in the fitness measurement. The effect of each modification was described in the same theoretical framework as the original model by introducing ‘effective’ quantities such as the effective mutation distance or the effective screening size.     

Evolutionary dynamics of Candida albicans during in vitro evolution

While mechanisms of resistance to major antifungal agents have been characterized in Candida albicans, little is known about the evolutionary trajectories during the emergence of drug resistance. Here, we examined the evolutionary dynamics of C. albicans that evolved in vitro in the presence or absence of fluconazole using the visualizing evolution in real-time (VERT) method, a novel experimental approach that facilitates the systematic isolation of adaptive mutants that arise in the population. We found an increase in the frequency of adaptive events in the presence of fluconazole compared to the no-drug controls. Analysis of the evolutionary dynamics revealed that mutations that led to increased drug resistance appeared frequently and that mutants with increased levels of resistance arose in independent lineages. Interestingly, most adaptive mutants with increased fitness in the presence of the drug did not exhibit a significant fitness decrease in the absence of the drug, supporting the idea that rapid resistance can arise from mutations in strains maintained in the population prior to exposure to the drug.     

Neutral mutation as the source of genetic variation in life history traits

The mechanism underlying the maintenance of adaptive genetic variation is a long-standing question in evolutionary genetics. There are two concepts (mutation-selection balance and balancing selection) which are based on the phenotypic differences between alleles. Mutation - selection balance and balancing selection cannot properly explain the process of gene substitution, i.e. the molecular evolution of quantitative trait loci affecting fitness. I assume that such loci have non-essential functions (small effects on fitness), and that they have the potential to evolve into new functions and acquire new adaptations. Here I show that a high amount of neutral polymorphism at these loci can exist in real populations. Consistent with this, I propose a hypothesis for the maintenance of genetic variation in life history traits which can be efficient for the fixation of alleles with very small selective advantage. The hypothesis is based on neutral polymorphism at quantitative trait loci and both neutral and adaptive gene substitutions. The model of neutral - adaptive conversion (NAC) assumes that neutral alleles are not neutral indefinitely, and that in specific and very rare situations phenotypic (relative fitness) differences between them can appear. In this paper I focus on NAC due to phenotypic plasticity of neutral alleles. The important evolutionary consequence of NAC could be the increased adaptive potential of a population. Loci responsible for adaptation should be fast evolving genes with minimally discernible phenotypic effects, and the recent discovery of genes with such characteristics implicates them as suitable candidates for loci involved in adaptation.     

Fitness effects of derived deleterious mutations in four closely related wild tomato species with spatial structure

A key issue in evolutionary biology is an improved understanding of the genetic mechanisms by which species adapt to various environments. Using DNA sequence data, it is possible to quantify the number of adaptive and deleterious mutations, and the distribution of fitness effects of new mutations (its mean and variance) by simultaneously taking into account the demography of a given species. We investigated how selection functions at eight housekeeping genes of four closely related, outcrossing species of wild tomatoes that are native to diverse environments in western South America (Solanum arcanum, S. chilense, S. habrochaites and S. peruvianum). We found little evidence for adaptive mutations but pervasive evidence for strong purifying selection in coding regions of the four species. In contrast, the strength of purifying selection seems to vary among the four species in non-coding (NC) regions (introns). Using F(ST)-based measures of fixation in subdivided populations, we suggest that weak purifying selection has affected the NC regions of S. habrochaites, S. chilense and S. peruvianum. In contrast, NC regions in S. arcanum show a distribution of fitness effects with mutations being either nearly neutral or very strongly deleterious. These results suggest that closely related species with similar genetic backgrounds but experiencing contrasting environments differ in the variance of deleterious fitness effects.     

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.     

The Properties of Adaptive Walks in Evolving Populations of Fungus

The rarity of beneficial mutations has frustrated efforts to develop a quantitative theory of adaptation. Recent models of adaptive walks, the sequential substitution of beneficial mutations by selection, make two compelling predictions: adaptive walks should be short, and fitness increases should become exponentially smaller as successive mutations fix. We estimated the number and fitness effects of beneficial mutations in each of 118 replicate lineages of Aspergillus nidulans evolving for approximately 800 generations at two population sizes using a novel maximum likelihood framework, the results of which were confirmed experimentally using sexual crosses. We find that adaptive walks do indeed tend to be short, and fitness increases become smaller as successive mutations fix. Moreover, we show that these patterns are associated with a decreasing supply of beneficial mutations as the population adapts. We also provide empirical distributions of fitness effects among mutations fixed at each step. Our results provide a first glimpse into the properties of multiple steps in an adaptive walk in asexual populations and lend empirical support to models of adaptation involving selection towards a single optimum phenotype. In practical terms, our results suggest that the bulk of adaptation is likely to be accomplished within the first few steps.     

Transition from positive to neutral in mutation fixation along with continuing rising fitness in thermal adaptive evolution

It remains to be determined experimentally whether increasing fitness is related to positive selection, while stationary fitness is related to neutral evolution. Long-term laboratory evolution in Escherichia coli was performed under conditions of thermal stress under defined laboratory conditions. The complete cell growth data showed common continuous fitness recovery to every 2°C or 4°C stepwise temperature upshift, finally resulting in an evolved E. coli strain with an improved upper temperature limit as high as 45.9°C after 523 days of serial transfer, equivalent to 7,560 generations, in minimal medium. Two-phase fitness dynamics, a rapid growth recovery phase followed by a gradual increasing growth phase, was clearly observed at diverse temperatures throughout the entire evolutionary process. Whole-genome sequence analysis revealed the transition from positive to neutral in mutation fixation, accompanied with a considerable escalation of spontaneous substitution rate in the late fitness recovery phase. It suggested that continually increasing fitness not always resulted in the reduction of genetic diversity due to the sequential takeovers by fit mutants, but caused the accumulation of a considerable number of mutations that facilitated the neutral evolution.     

Effects of selective neutrality on the evolution of molecular species

We introduce a model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of phenomena seen in RNA sequence-structure maps are present also in our general model. Examples are the occurrence of ''common'' structures that occupy a fraction of the genotype space which tends to unity as the length of the genotype increases, and the formation of percolating neutral networks that cover the genotype space in such a way that a member of such a network can be found within a small radius of any point in the space. We also describe a number of new phenomena that appear to be general properties of systems possessing selective neutrality. In particular, we show that the maximum fitness attained during the adaptive walk of a population evolving on such a fitness landscape increases with increasing degree of neutrality, and is directly related to the fitness of the most fit percolating network.     

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.     

Compensatory mutations cause excess of antagonistic epistasis in RNA secondary structure folding

Background

The rate at which fitness declines as an organism's genome accumulates random mutations is an important variable in several evolutionary theories. At an intuitive level, it might seem natural that random mutations should tend to interact synergistically, such that the rate of mean fitness decline accelerates as the number of random mutations is increased. However, in a number of recent studies, a prevalence of antagonistic epistasis (the tendency of multiple mutations to have a mitigating rather than reinforcing effect) has been observed.

Results

We studied in silico the net amount and form of epistatic interactions in RNA secondary structure folding by measuring the fraction of neutral mutants as a function of mutational distance d. We found a clear prevalence of antagonistic epistasis in RNA secondary structure folding. By relating the fraction of neutral mutants at distance d to the average neutrality at distance d, we showed that this prevalence derives from the existence of many compensatory mutations at larger mutational distances.

Conclusions

Our findings imply that the average direction of epistasis in simple fitness landscapes is directly related to the density with which fitness peaks are distributed in these landscapes.

     

Forecasting of phenotypic and genetic outcomes of experimental evolution in Pseudomonas protegens

Experimental evolution with microbes is often highly repeatable under identical conditions, suggesting the possibility to predict short-term evolution. However, it is not clear to what degree evolutionary forecasts can be extended to related species in non-identical environments, which would allow testing of general predictive models and fundamental biological assumptions. To develop an extended model system for evolutionary forecasting, we used previous data and models of the genotype-to-phenotype map from the wrinkly spreader system in Pseudomonas fluorescens SBW25 to make predictions of evolutionary outcomes on different biological levels for Pseudomonas protegens Pf-5. In addition to sequence divergence (78% amino acid and 81% nucleotide identity) for the genes targeted by mutations, these species also differ in the inability of Pf-5 to make cellulose, which is the main structural basis for the adaptive phenotype in SBW25. The experimental conditions were changed compared to the SBW25 system to test if forecasts were extendable to a non-identical environment. Forty-three mutants with increased ability to colonize the air-liquid interface were isolated, and the majority had reduced motility and was partly dependent on the Pel exopolysaccharide as a structural component. Most (38/43) mutations are expected to disrupt negative regulation of the same three diguanylate cyclases as in SBW25, with a smaller number of mutations in promoter regions, including an uncharacterized polysaccharide synthase operon. A mathematical model developed for SBW25 predicted the order of the three main pathways and the genes targeted by mutations, but differences in fitness between mutants and mutational biases also appear to influence outcomes. Mutated regions in proteins could be predicted in most cases (16/22), but parallelism at the nucleotide level was low and mutational hot spot sites were not conserved. This study demonstrates the potential of short-term evolutionary forecasting in experimental populations and provides testable predictions for evolutionary outcomes in other Pseudomonas species.