Selection biases the prevalence and type of epistasis along adaptive trajectories

The role of epistasis in evolutionary rescue

The process by which adaptive evolution preserves a population threatened with extinction due to environmental changes is known as evolutionary rescue. Several factors determine the fate of those populations, including demography and genetic factors, such as standing genetic variation, gene flow, availability of de novo mutations, and so on. Despite the extensive debate about evolutionary rescue in the current literature, a study about the role of epistasis and the topography of the fitness landscape on the fate of dwindling populations is missing. In the current work, we aim to fill this gap and study the influence of epistasis on the probability of extinction of populations. We present simulation results, and analytical approximations are derived. Counterintuitively, we show that the likelihood of extinction is smaller when the degree of epistasis is higher. The reason underneath is twofold: first, higher epistasis can promote mutations of more significant phenotypic effects, but also, the incongruence between the maps genotype-phenotype and phenotype-fitness turns the fitness landscape at low epistasis more rugged, thus curbing some of its advantages.

Rapid adaptation of recombining populations on tunable fitness landscapes

How does standing genetic variation affect polygenic adaptation in recombining populations? Despite a large body of work in quantitative genetics, epistatic and weak additive fitness effects among simultaneously segregating genetic variants are difficult to capture experimentally or to predict theoretically. In this study, we simulated adaptation on fitness landscapes with tunable ruggedness driven by standing genetic variation in recombining populations. We confirmed that recombination hinders the movement of a population through a rugged fitness landscape. When surveying the effect of epistasis on the fixation of alleles, we found that the combined effects of high ruggedness and high recombination probabilities lead to preferential fixation of alleles that had a high initial frequency. This indicates that positive epistatic alleles escape from being broken down by recombination when they start at high frequency. We further extract direct selection coefficients and pairwise epistasis along the adaptive path. When taking the final fixed genotype as the reference genetic background, we observe that, along the adaptive path, beneficial direct selection appears stronger and pairwise epistasis weaker than in the underlying fitness landscape. Quantitatively, the ratio of epistasis and direct selection is smaller along the adaptive path (≈ 1 ) than expected. Thus, adaptation on a rugged fitness landscape may lead to spurious signals of direct selection generated through epistasis. Our study highlights how the interplay of epistasis and recombination constrains the adaptation of a diverse population to a new environment.

Epistasis and pleiotropy shape biophysical protein subspaces associated with drug resistance

Protein space is a rich analogy for genotype-phenotype maps, where amino acid sequence is organized into a high-dimensional space that highlights the connectivity between protein variants. It is a useful abstraction for understanding the process of evolution, and for efforts to engineer proteins towards desirable phenotypes. Few mentions of protein space consider how protein phenotypes can be described in terms of their biophysical components, nor do they rigorously interrogate how forces like epistasis-describing the nonlinear interaction between mutations and their phenotypic consequences-manifest across these components. In this study, we deconstruct a low-dimensional protein space of a bacterial enzyme (dihydrofolate reductase; DHFR) into "subspaces" corresponding to a set of kinetic and thermodynamic traits [k_{cat}, K_{M}, K_{i}, and T_{m} (melting temperature)]. We then examine how combinations of three mutations (eight alleles in total) display pleiotropy, or unique effects on individual subspace traits. We examine protein spaces across three orthologous DHFR enzymes (Escherichia coli, Listeria grayi, and Chlamydia muridarum), adding a genotypic context dimension through which epistasis occurs across subspaces. In doing so, we reveal that protein space is a deceptively complex notion, and that future applications to bioengineering should consider how interactions between amino acid substitutions manifest across different phenotypic subspaces.

Idiosyncratic and dose-dependent epistasis drives variation in tomato fruit size

Epistasis between genes is traditionally studied with mutations that eliminate protein activity, but most natural genetic variation is in cis-regulatory DNA and influences gene expression and function quantitatively. In this study, we used natural and engineered cis-regulatory alleles in a plant stem-cell circuit to systematically evaluate epistatic relationships controlling tomato fruit size. Combining a promoter allelic series with two other loci, we collected over 30,000 phenotypic data points from 46 genotypes to quantify how allele strength transforms epistasis. We revealed a saturating dose-dependent relationship but also allele-specific idiosyncratic interactions, including between alleles driving a step change in fruit size during domestication. Our approach and findings expose an underexplored dimension of epistasis, in which cis-regulatory allelic diversity within gene regulatory networks elicits nonlinear, unpredictable interactions that shape phenotypes.

Impact of population size on early adaptation in rugged fitness landscapes

Owing to stochastic fluctuations arising from finite population size, known as genetic drift, the ability of a population to explore a rugged fitness landscape depends on its size. In the weak mutation regime, while the mean steady-state fitness increases with population size, we find that the height of the first fitness peak encountered when starting from a random genotype displays various behaviours versus population size, even among small and simple rugged landscapes. We show that the accessibility of the different fitness peaks is key to determining whether this height overall increases or decreases with population size. Furthermore, there is often a finite population size that maximizes the height of the first fitness peak encountered when starting from a random genotype. This holds across various classes of model rugged landscapes with sparse peaks, and in some experimental and experimentally inspired ones. Thus, early adaptation in rugged fitness landscapes can be more efficient and predictable for relatively small population sizes than in the large-size limit. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Epistasis meets pleiotropy in shaping biophysical protein subspaces associated with antimicrobial resistance

Protein space is a rich analogy for genotype-phenotype maps, where amino acid sequence is organized into a high-dimensional space that highlights the connectivity between protein variants. It is a useful abstraction for understanding the process of evolution, and for efforts to engineer proteins towards desirable phenotypes. Few framings of protein space consider how higher-level protein phenotypes can be described in terms of their biophysical dimensions, nor do they rigorously interrogate how forces like epistasis-describing the nonlinear interaction between mutations and their phenotypic consequences-manifest across these dimensions. In this study, we deconstruct a low-dimensional protein space of a bacterial enzyme (dihydrofolate reductase; DHFR) into "subspaces" corresponding to a set of kinetic and thermodynamic traits [(kcat, KM, Ki, and Tm (melting temperature)]. We then examine how three mutations (eight alleles in total) display pleiotropy in their interactions across these subspaces. We extend this approach to examine protein spaces across three orthologous DHFR enzymes (Escherichia coli, Listeria grayi, and Chlamydia muridarum), adding a genotypic context dimension through which epistasis occurs across subspaces. In doing so, we reveal that protein space is a deceptively complex notion, and that the process of protein evolution and engineering should consider how interactions between amino acid substitutions manifest across different phenotypic subspaces.

Reversion is most likely under high mutation supply when compensatory mutations do not fully restore fitness costs

The dynamics of adaptation, reversion, and compensation have been central topics in microbial evolution, and several studies have attempted to resolve the population genetics underlying how these dynamics occur. However, questions remain regarding how certain features-the evolution of mutators and whether compensatory mutations alleviate costs fully or partially-may influence the evolutionary dynamics of compensation and reversion. In this study, we attempt to explain findings from experimental evolution by utilizing computational and theoretical approaches toward a more refined understanding of how mutation rate and the fitness effects of compensatory mutations influence adaptive dynamics. We find that high mutation rates increase the probability of reversion toward the wild type when compensation is only partial. However, the existence of even a single fully compensatory mutation is associated with a dramatically decreased probability of reversion to the wild type. These findings help to explain specific results from experimental evolution, where compensation was observed in nonmutator strains, but reversion (sometimes with compensation) was observed in mutator strains, indicating that real-world compensatory mutations are often unable to fully alleviate the costs associated with adaptation. Our findings emphasize the potential role of the supply and quality of mutations in crafting the dynamics of adaptation and reversal, with implications for theoretical population genetics and for biomedical contexts like the evolution of antibiotic resistance.

The sphingolipid anteome: implications for evolution of the sphingolipid metabolic pathway

Modern cell membranes contain a bewildering complexity of lipids, among them sphingolipids (SLs). Advances in mass spectrometry have led to the realization that the number and combinatorial complexity of lipids, including SLs, is much greater than previously appreciated. SLs are generated de novo by four enzymes, namely serine palmitoyltransferase, 3-ketodihydrosphingosine reductase, ceramide synthase and dihydroceramide Δ4-desaturase 1. Some of these enzymes depend on the availability of specific substrates and cofactors, which are themselves supplied by other complex metabolic pathways. The evolution of these four enzymes is poorly understood and likely depends on the co-evolution of the metabolic pathways that supply the other essential reaction components. Here, we introduce the concept of the 'anteome', from the Latin ante ('before') to describe the network of metabolic ('omic') pathways that must have converged in order for these pathways to co-evolve and permit SL synthesis. We also suggest that current origin of life and evolutionary models lack appropriate experimental support to explain the appearance of this complex metabolic pathway and its anteome.

The mutation effect reaction norm (mu-rn) highlights environmentally dependent mutation effects and epistatic interactions

Since the modern synthesis, the fitness effects of mutations and epistasis have been central yet provocative concepts in evolutionary and population genetics. Studies of how the interactions between parcels of genetic information can change as a function of environmental context have added a layer of complexity to these discussions. Here I introduce the "mutation effect reaction norm" (Mu-RN), a new instrument through which one can analyze the phenotypic consequences of mutations and interactions across environmental contexts. It embodies the fusion of measurements of genetic interactions with the reaction norm, a classic depiction of the performance of genotypes across environments. I demonstrate the utility of the Mu-RN through the signature of a "compensatory ratchet" mutation that undermines reverse evolution of antimicrobial resistance. More broadly, I argue that the mutation effect reaction norm may help us resolve the dynamism and unpredictability of evolution, with implications for theoretical biology, genetic modification technology, and public health. This article is protected by copyright. All rights reserved.

Lanza V, Rodríguez-Beltrán J, Galán JC, San Millán A, Cantón R, Coque TM. Evolutionary Pathways and Trajectories in Antibiotic Resistance

Evolution is the hallmark of life. Descriptions of the evolution of microorganisms have provided a wealth of information, but knowledge regarding "what happened" has precluded a deeper understanding of "how" evolution has proceeded, as in the case of antimicrobial resistance. The difficulty in answering the "how" question lies in the multihierarchical dimensions of evolutionary processes, nested in complex networks, encompassing all units of selection, from genes to communities and ecosystems. At the simplest ontological level (as resistance genes), evolution proceeds by random (mutation and drift) and directional (natural selection) processes; however, sequential pathways of adaptive variation can occasionally be observed, and under fixed circumstances (particular fitness landscapes), evolution is predictable. At the highest level (such as that of plasmids, clones, species, microbiotas), the systems' degrees of freedom increase dramatically, related to the variable dispersal, fragmentation, relatedness, or coalescence of bacterial populations, depending on heterogeneous and changing niches and selective gradients in complex environments. Evolutionary trajectories of antibiotic resistance find their way in these changing landscapes subjected to random variations, becoming highly entropic and therefore unpredictable. However, experimental, phylogenetic, and ecogenetic analyses reveal preferential frequented paths (highways) where antibiotic resistance flows and propagates, allowing some understanding of evolutionary dynamics, modeling and designing interventions. Studies on antibiotic resistance have an applied aspect in improving individual health, One Health, and Global Health, as well as an academic value for understanding evolution. Most importantly, they have a heuristic significance as a model to reduce the negative influence of anthropogenic effects on the environment.

Temperature affects the repeatability of evolution in the microbial eukaryote Tetrahymena thermophila

Evolutionary biologists have long sought to understand what factors affect the repeatability of adaptive outcomes. To better understand the role of temperature in determining the repeatability of adaptive trajectories, we evolved populations of different genotypes of the ciliate Tetrahymena thermophila at low and high temperatures and followed changes in growth rate over 6,500 generations. As expected, growth rate increased with a decelerating rate for all populations; however, there were differences in the patterns of evolution at the two temperatures. The growth rates of the different genotypes tended to converge as evolution proceeded at both temperatures, but this convergence was quicker and more pronounced at the higher temperature. Additionally, over the first 4,000 generations we found greater repeatability of evolution, in terms of change in growth rate, among replicates of the same genotype at the higher temperature. Finally, we found limited evidence of trade-offs in fitness between temperatures, and an asymmetry in the correlated responses, whereby evolution in a high temperature increases growth rate at the lower temperature significantly more than the reverse. These results demonstrate the importance of temperature in determining the repeatability of evolutionary trajectories for the eukaryotic microbe Tetrahymena thermophila and may provide clues to how temperature affects evolution more generally.

Global epistasis emerges from a generic model of a complex trait

Epistasis between mutations can make adaptation contingent on evolutionary history. Yet despite widespread ‘microscopic’ epistasis between the mutations involved, microbial evolution experiments show consistent patterns of fitness increase between replicate lines. Recent work shows that this consistency is driven in part by global patterns of diminishing-returns and increasing-costs epistasis, which make mutations systematically less beneficial (or more deleterious) on fitter genetic backgrounds. However, the origin of this ‘global’ epistasis remains unknown. Here, we show that diminishing-returns and increasing-costs epistasis emerge generically as a consequence of pervasive microscopic epistasis. Our model predicts a specific quantitative relationship between the magnitude of global epistasis and the stochastic effects of microscopic epistasis, which we confirm by reanalyzing existing data. We further show that the distribution of fitness effects takes on a universal form when epistasis is widespread and introduce a novel fitness landscape model to show how phenotypic evolution can be repeatable despite sequence-level stochasticity.

Idiosyncratic epistasis creates universals in mutational effects and evolutionary trajectories

Patterns of epistasis and shapes of fitness landscapes are of wide interest because of their bearings on a number of evolutionary theories. The common phenomena of slowing fitness increases during adaptations and diminishing returns from beneficial mutations are believed to reflect a concave fitness landscape and a preponderance of negative epistasis. Paradoxically, fitness decreases tend to decelerate and harm from deleterious mutations shrinks during the accumulation of random mutations-patterns thought to indicate a convex fitness landscape and a predominance of positive epistasis. Current theories cannot resolve this apparent contradiction. Here, we show that the phenotypic effect of a mutation varies substantially depending on the specific genetic background and that this idiosyncrasy in epistasis creates all of the above trends without requiring a biased distribution of epistasis. The idiosyncratic epistasis theory explains the universalities in mutational effects and evolutionary trajectories as emerging from randomness due to biological complexity.

Predominance of positive epistasis among drug resistance-associated mutations in HIV-1 protease

Drug-resistant mutations often have deleterious impacts on replication fitness, posing a fitness cost that can only be overcome by compensatory mutations. However, the role of fitness cost in the evolution of drug resistance has often been overlooked in clinical studies or in vitro selection experiments, as these observations only capture the outcome of drug selection. In this study, we systematically profile the fitness landscape of resistance-associated sites in HIV-1 protease using deep mutational scanning. We construct a mutant library covering combinations of mutations at 11 sites in HIV-1 protease, all of which are associated with resistance to protease inhibitors in clinic. Using deep sequencing, we quantify the fitness of thousands of HIV-1 protease mutants after multiple cycles of replication in human T cells. Although the majority of resistance-associated mutations have deleterious effects on viral replication, we find that epistasis among resistance-associated mutations is predominantly positive. Furthermore, our fitness data are consistent with genetic interactions inferred directly from HIV sequence data of patients. Fitness valleys formed by strong positive epistasis reduce the likelihood of reversal of drug resistance mutations. Overall, our results support the view that strong compensatory effects are involved in the emergence of clinically observed resistance mutations and provide insights to understanding fitness barriers in the evolution and reversion of drug resistance.

Environment-dependent costs and benefits of recombination in independently evolved populations of Escherichia coli

Understanding of the causes by which reproductive isolation arises remains limited. We examine the role of adaptation in driving reproductive isolation among 12 Escherichia coli populations evolved in two different environments. We found that, regardless of whether parents were selected in the same or different environments, the average fitness of recombinants was lower than the expected, consistent with a prevailing influence of incompatibility between independently accumulated mutations. Exceptions to this pattern occurred among recombinants of some parents evolved in different environments. These recombinants were less fit than expected in the selective environment of one parent, but more fit than expected in the selective environment of the other parent. Our results indicate that both parallel and divergent adaptation can quickly lead to intrinsic genetic barriers contributing to the initial stages of speciation and show that these barriers can be complex, for example, depending on the environment in which recombinant offspring are tested.

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

The dynamics of evolution is intimately shaped by epistasis - interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary history. A key step is thus developing models that enable study of the effects of past evolution on future evolution. In this work, we introduce a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance. Their Gaussian character allows for tractable computational as well as analytic understanding. We study the properties of these landscapes focusing on the simplest evolutionary process: random adaptive (uphill) walks. Conventional measures of "ruggedness" are shown to not much affect such adaptive walks. Instead, the long-distance statistics of epistasis cause all properties to be highly conditional on past evolution, determining the statistics of the local landscape (the distribution of fitness-effects of available mutations and combinations of these), as well as the global geometry of evolutionary trajectories. In order to further explore the effects of conditioning on past evolution, we model the effects of slowly changing environments. At long times, such fitness "seascapes" cause a statistical steady state with highly intermittent evolutionary dynamics: populations undergo bursts of rapid adaptation, interspersed with periods in which adaptive mutations are rare and the population waits for more new directions to be opened up by changes in the environment. Finally, we discuss prospects for studying more complex evolutionary dynamics and on broader classes of high-dimensional landscapes and seascapes.

Patterns and Mechanisms of Diminishing Returns from Beneficial Mutations

Diminishing returns epistasis causes the benefit of the same advantageous mutation smaller in fitter genotypes and is frequently observed in experimental evolution. However, its occurrence in other contexts, environment dependence, and mechanistic basis are unclear. Here, we address these questions using 1,005 sequenced segregants generated from a yeast cross. Under each of 47 examined environments, 66-92% of tested polymorphisms exhibit diminishing returns epistasis. Surprisingly, improving environment quality also reduces the benefits of advantageous mutations even when fitness is controlled for, indicating the necessity to revise the global epistasis hypothesis. We propose that diminishing returns originates from the modular organization of life where the contribution of each functional module to fitness is determined jointly by the genotype and environment and has an upper limit, and demonstrate that our model predictions match empirical observations. These findings broaden the concept of diminishing returns epistasis, reveal its generality and potential cause, and have important evolutionary implications.

An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape

Characterizing the fitness landscape, a representation of fitness for a large set of genotypes, is key to understanding how genetic information is interpreted to create functional organisms. Here we determined the evolutionarily-relevant segment of the fitness landscape of His3, a gene coding for an enzyme in the histidine synthesis pathway, focusing on combinations of amino acid states found at orthologous sites of extant species. Just 15% of amino acids found in yeast His3 orthologues were always neutral while the impact on fitness of the remaining 85% depended on the genetic background. Furthermore, at 67% of sites, amino acid replacements were under sign epistasis, having both strongly positive and negative effect in different genetic backgrounds. 46% of sites were under reciprocal sign epistasis. The fitness impact of amino acid replacements was influenced by only a few genetic backgrounds but involved interaction of multiple sites, shaping a rugged fitness landscape in which many of the shortest paths between highly fit genotypes are inaccessible.

An intuitive understanding of protein evolution dictates that, with the exception of adaptive substitutions, amino acid states should be freely exchangeable between the same gene from different species. However, the extent to which this assertion holds true has not been tested in a controlled experiment. Here, we show that whether an amino acid state can be exchanged between orthologues depends on other amino acid states in the same protein. Furthermore, we show that the mode of interaction of amino acid states is multidimensional. Assuming that amino acid replacements influence the protein in several independent ways substantially improves our ability to predict the effect of an amino acid state in a protein sequence that has not been observed in nature.

Effects of Beneficial Mutations in pykF Gene Vary over Time and across Replicate Populations in a Long-Term Experiment with Bacteria

The fitness effects of mutations can depend on the genetic backgrounds in which they occur and thereby influence future opportunities for evolving populations. In particular, mutations that fix in a population might change the selective benefit of subsequent mutations, giving rise to historical contingency. We examine these effects by focusing on mutations in a key metabolic gene, pykF, that arose independently early in the history of 12 Escherichia coli populations during a long-term evolution experiment. Eight different evolved nonsynonymous mutations conferred similar fitness benefits of ∼10% when transferred into the ancestor, and these benefits were greater than the one conferred by a deletion mutation. In contrast, the same mutations had highly variable fitness effects, ranging from ∼0% to 25%, in evolved clones isolated from the populations at 20,000 generations. Two mutations that were moved into these evolved clones conferred similar fitness effects in a given clone, but different effects between the clones, indicating epistatic interactions between the evolved pykF alleles and the other mutations that had accumulated in each evolved clone. We also measured the fitness effects of six evolved pykF alleles in the same populations in which they had fixed, but at seven time points between 0 and 50,000 generations. Variation in fitness effects was high at intermediate time points, and declined to a low level at 50,000 generations, when the mean fitness effect was lowest. Our results demonstrate the importance of genetic context in determining the fitness effects of different beneficial mutations even within the same gene.

Selection for Protein Stability Enriches for Epistatic Interactions

A now classical argument for the marginal thermodynamic stability of proteins explains the distribution of observed protein stabilities as a consequence of an entropic pull in protein sequence space. In particular, most sequences that are sufficiently stable to fold will have stabilities near the folding threshold. Here, we extend this argument to consider its predictions for epistatic interactions for the effects of mutations on the free energy of folding. Although there is abundant evidence to indicate that the effects of mutations on the free energy of folding are nearly additive and conserved over evolutionary time, we show that these observations are compatible with the hypothesis that a non-additive contribution to the folding free energy is essential for observed proteins to maintain their native structure. In particular, through both simulations and analytical results, we show that even very small departures from additivity are sufficient to drive this effect.

Compensatory mutations and epistasis for protein function

Adaptive protein evolution may be facilitated by neutral amino acid mutations that confer no benefit when they first arise but which potentiate subsequent function-altering mutations via direct or indirect structural mechanisms. Theoretical and empirical results indicate that such compensatory interactions (intramolecular epistasis) can exert a strong influence on trajectories of protein evolution. For this reason, assessing the form and prevalence of intramolecular epistasis and characterizing biophysical mechanisms of compensatory interaction are important research goals at the nexus of structural biology and molecular evolution. Here I review recent insights derived from protein-engineering studies, and I describe an approach for identifying and characterizing mechanisms of epistasis that integrates experimental data on structure-function relationships with analyses of comparative sequence data.

Recombination and peak jumping

We show that genetic recombination can be a powerful mechanism for escaping suboptimal peaks. Recent studies of empirical fitness landscapes reveal complex gene interactions and multiple peaks. However, classical work on recombination largely ignores the effect of complex gene interactions. Briefly, we restrict to fitness landscapes where the global peak is difficult to access. If the optimal genotype can be generated by shuffling genes present in the population, then recombination will produce the genotype. If, in addition, recombination is sufficiently rare, then the proportion of the genotype is expected to increase. Specifically, we consider landscapes where shuffling of suboptimal peak genotypes can produce the global peak genotype. The advantage of recombination we identify has no correspondence for 2-locus systems or for smooth landscapes. The effect of recombination indicated is sometimes extreme, also for rare recombination, in the sense that shutting off recombination could result in the organism failing to adapt. A standard question about recombination is whether the mechanism tends to accelerate or decelerate adaptation. However, we argue that extreme effects may be more important than how the majority falls. In a limited sense, our result can be considered a support for Sewall Wright’s view that adaptation sometimes works better in subdivided populations.

Diminishing-returns epistasis among random beneficial mutations in a multicellular fungus

Adaptive evolution ultimately is fuelled by mutations generating novel genetic variation. Non-additivity of fitness effects of mutations (called epistasis) may affect the dynamics and repeatability of adaptation. However, understanding the importance and implications of epistasis is hampered by the observation of substantial variation in patterns of epistasis across empirical studies. Interestingly, some recent studies report increasingly smaller benefits of beneficial mutations once genotypes become better adapted (called diminishing-returns epistasis) in unicellular microbes and single genes. Here, we use Fisher's geometric model (FGM) to generate analytical predictions about the relationship between the effect size of mutations and the extent of epistasis. We then test these predictions using the multicellular fungus Aspergillus nidulans by generating a collection of 108 strains in either a poor or a rich nutrient environment that each carry a beneficial mutation and constructing pairwise combinations using sexual crosses. Our results support the predictions from FGM and indicate negative epistasis among beneficial mutations in both environments, which scale with mutational effect size. Hence, our findings show the importance of diminishing-returns epistasis among beneficial mutations also for a multicellular organism, and suggest that this pattern reflects a generic constraint operating at diverse levels of biological organization.

Selecting among three basic fitness landscape models: Additive, multiplicative and stickbreaking

Fitness landscapes map genotypes to organismal fitness. Their topographies depend on how mutational effects interact - epistasis - andare important for understanding evolutionary processes such as speciation, the rate of adaptation, the advantage of recombination, and the predictability versus stochasticity of evolution. The growing amount of data has made it possible to better test landscape models empirically. We argue that this endeavor will benefit from the development and use of meaningful basic models against which to compare more complex models. Here we develop statistical and computational methods for fitting fitness data from mutation combinatorial networks to three simple models: additive, multiplicative and stickbreaking. We employ a Bayesian framework for doing model selection. Using simulations, we demonstrate that our methods work and we explore their statistical performance: bias, error, and the power to discriminate among models. We then illustrate our approach and its flexibility by analyzing several previously published datasets. An R-package that implements our methods is available in the CRAN repository under the name Stickbreaker.

Additive Phenotypes Underlie Epistasis of Fitness Effects

Gene interactions, or epistasis, play a large role in determining evolutionary outcomes. The ruggedness of fitness landscapes, and thus the predictability of evolution and the accessibility of high-fitness genotypes, is determined largely by the pervasiveness of epistasis and the degree of correlation between similar genotypes. We created all possible pairings of three sets of five beneficial first-step mutations fixed during adaptive walks under three different regimes: selection on growth rate alone, on growth rate and thermal stability, and on growth rate and pH stability. All 30 double-mutants displayed negative, antagonistic epistasis with regard to growth rate and fitness, but positive epistasis and additivity were common for the stability phenotypes. This suggested that biophysically simple phenotypes, such as capsid stability, may on average behave more additively than complex phenotypes like viral growth rate. Growth rate epistasis was also smaller in magnitude when the individual effects of single mutations were smaller. Significant sign epistasis, such that the effect of a mutation that is beneficial in the wild-type background is deleterious in combination with a second mutation, emerged more frequently in intragenic mutational pairings than in intergenic pairs, and was evident in nearly half of the double-mutants, indicating that the fitness landscape is moderately uncorrelated and of intermediate ruggedness. Together, our results indicated that mutations may interact additively with regard to phenotype when considered at a basic, biophysical level, but that epistasis arises as a result of pleiotropic interactions between the individual components of complex phenotypes and diminishing returns arising from intermediate phenotypic optima.

Diminishing-returns epistasis decreases adaptability along an evolutionary trajectory

Populations evolving in constant environments exhibit declining adaptability. Understanding the basis of this pattern could reveal underlying processes determining the repeatability of evolutionary outcomes. In principle, declining adaptability can be due to a decrease in the effect size of beneficial mutations, a decrease in the rate at which they occur, or some combination of both. By evolving Escherichia coli populations started from different steps along a single evolutionary trajectory, we show that declining adaptability is best explained by a decrease in the size of available beneficial mutations. This pattern reflected the dominant influence of negative genetic interactions that caused new beneficial mutations to confer smaller benefits in fitter genotypes. Genome sequencing revealed that starting genotypes that were more similar to one another did not exhibit greater similarity in terms of new beneficial mutations, supporting the view that epistasis acts globally, having a greater influence on the effect than on the identity of available mutations along an adaptive trajectory. Our findings provide support for a general mechanism that leads to predictable phenotypic evolutionary trajectories.

The genotype-phenotype map of an evolving digital organism

To understand how evolving systems bring forth novel and useful phenotypes, it is essential to understand the relationship between genotypic and phenotypic change. Artificial evolving systems can help us understand whether the genotype-phenotype maps of natural evolving systems are highly unusual, and it may help create evolvable artificial systems. Here we characterize the genotype-phenotype map of digital organisms in Avida, a platform for digital evolution. We consider digital organisms from a vast space of 10¹⁴¹ genotypes (instruction sequences), which can form 512 different phenotypes. These phenotypes are distinguished by different Boolean logic functions they can compute, as well as by the complexity of these functions. We observe several properties with parallels in natural systems, such as connected genotype networks and asymmetric phenotypic transitions. The likely common cause is robustness to genotypic change. We describe an intriguing tension between phenotypic complexity and evolvability that may have implications for biological evolution. On the one hand, genotypic change is more likely to yield novel phenotypes in more complex organisms. On the other hand, the total number of novel phenotypes reachable through genotypic change is highest for organisms with simple phenotypes. Artificial evolving systems can help us study aspects of biological evolvability that are not accessible in vastly more complex natural systems. They can also help identify properties, such as robustness, that are required for both human-designed artificial systems and synthetic biological systems to be evolvable.

The phenotype of an organism comprises the set of morphological and functional traits encoded by its genome. In natural evolving systems, phenotypes are organized into mutationally connected networks of genotypes, which increase the likelihood for an evolving population to encounter novel adaptive phenotypes (i.e., its evolvability). We do not know whether artificial systems, such as self-replicating and evolving computer programs—digital organisms—are more or less evolvable than natural systems. By studying how genotypes map onto phenotypes in digital organisms, we characterize many commonalities between natural and artificial evolving systems. In addition, we show that phenotypic complexity can both facilitate and constrain evolution, which harbors lessons not only for designing evolvable artificial systems, but also for synthetic biology.

On the (un)predictability of a large intragenic fitness landscape

The study of fitness landscapes, which aims at mapping genotypes to fitness, is receiving ever-increasing attention. Novel experimental approaches combined with next-generation sequencing (NGS) methods enable accurate and extensive studies of the fitness effects of mutations, allowing us to test theoretical predictions and improve our understanding of the shape of the true underlying fitness landscape and its implications for the predictability and repeatability of evolution. Here, we present a uniquely large multiallelic fitness landscape comprising 640 engineered mutants that represent all possible combinations of 13 amino acid-changing mutations at 6 sites in the heat-shock protein Hsp90 in Saccharomyces cerevisiae under elevated salinity. Despite a prevalent pattern of negative epistasis in the landscape, we find that the global fitness peak is reached via four positively epistatic mutations. Combining traditional and extending recently proposed theoretical and statistical approaches, we quantify features of the global multiallelic fitness landscape. Using subsets of the data, we demonstrate that extrapolation beyond a known part of the landscape is difficult owing to both local ruggedness and amino acid-specific epistatic hotspots and that inference is additionally confounded by the nonrandom choice of mutations for experimental fitness landscapes.

Extensively Parameterized Mutation-Selection Models Reliably Capture Site-Specific Selective Constraint

The mutation-selection model of coding sequence evolution has received renewed attention for its use in estimating site-specific amino acid propensities and selection coefficient distributions. Two computationally tractable mutation-selection inference frameworks have been introduced: One framework employs a fixed-effects, highly parameterized maximum likelihood approach, whereas the other employs a random-effects Bayesian Dirichlet Process approach. While both implementations follow the same model, they appear to make distinct predictions about the distribution of selection coefficients. The fixed-effects framework estimates a large proportion of highly deleterious substitutions, whereas the random-effects framework estimates that all substitutions are either nearly neutral or weakly deleterious. It remains unknown, however, how accurately each method infers evolutionary constraints at individual sites. Indeed, selection coefficient distributions pool all site-specific inferences, thereby obscuring a precise assessment of site-specific estimates. Therefore, in this study, we use a simulation-based strategy to determine how accurately each approach recapitulates the selective constraint at individual sites. We find that the fixed-effects approach, despite its extensive parameterization, consistently and accurately estimates site-specific evolutionary constraint. By contrast, the random-effects Bayesian approach systematically underestimates the strength of natural selection, particularly for slowly evolving sites. We also find that, despite the strong differences between their inferred selection coefficient distributions, the fixed- and random-effects approaches yield surprisingly similar inferences of site-specific selective constraint. We conclude that the fixed-effects mutation-selection framework provides the more reliable software platform for model application and future development.

Epistasis in protein evolution

The structure, function, and evolution of proteins depend on physical and genetic interactions among amino acids. Recent studies have used new strategies to explore the prevalence, biochemical mechanisms, and evolutionary implications of these interactions-called epistasis-within proteins. Here we describe an emerging picture of pervasive epistasis in which the physical and biological effects of mutations change over the course of evolution in a lineage-specific fashion. Epistasis can restrict the trajectories available to an evolving protein or open new paths to sequences and functions that would otherwise have been inaccessible. We describe two broad classes of epistatic interactions, which arise from different physical mechanisms and have different effects on evolutionary processes. Specific epistasis-in which one mutation influences the phenotypic effect of few other mutations-is caused by direct and indirect physical interactions between mutations, which nonadditively change the protein's physical properties, such as conformation, stability, or affinity for ligands. In contrast, nonspecific epistasis describes mutations that modify the effect of many others; these typically behave additively with respect to the physical properties of a protein but exhibit epistasis because of a nonlinear relationship between the physical properties and their biological effects, such as function or fitness. Both types of interaction are rampant, but specific epistasis has stronger effects on the rate and outcomes of evolution, because it imposes stricter constraints and modulates evolutionary potential more dramatically; it therefore makes evolution more contingent on low-probability historical events and leaves stronger marks on the sequences, structures, and functions of protein families.

Epistasis and the Structure of Fitness Landscapes: Are Experimental Fitness Landscapes Compatible with Fisher's Geometric Model?

The fitness landscape defines the relationship between genotypes and fitness in a given environment and underlies fundamental quantities such as the distribution of selection coefficient and the magnitude and type of epistasis. A better understanding of variation in landscape structure across species and environments is thus necessary to understand and predict how populations will adapt. An increasing number of experiments investigate the properties of fitness landscapes by identifying mutations, constructing genotypes with combinations of these mutations, and measuring the fitness of these genotypes. Yet these empirical landscapes represent a very small sample of the vast space of all possible genotypes, and this sample is often biased by the protocol used to identify mutations. Here we develop a rigorous statistical framework based on Approximate Bayesian Computation to address these concerns and use this flexible framework to fit a broad class of phenotypic fitness models (including Fisher's model) to 26 empirical landscapes representing nine diverse biological systems. Despite uncertainty owing to the small size of most published empirical landscapes, the inferred landscapes have similar structure in similar biological systems. Surprisingly, goodness-of-fit tests reveal that this class of phenotypic models, which has been successful so far in interpreting experimental data, is a plausible in only three of nine biological systems. More precisely, although Fisher's model was able to explain several statistical properties of the landscapes-including the mean and SD of selection and epistasis coefficients-it was often unable to explain the full structure of fitness landscapes.

Epistasis and the Dynamics of Reversion in Molecular Evolution

Recent studies of protein evolution contend that the longer an amino acid substitution is present at a site, the less likely it is to revert to the amino acid previously occupying that site. Here we study this phenomenon of decreasing reversion rates rigorously and in a much more general context. We show that, under weak mutation and for arbitrary fitness landscapes, reversion rates decrease with time for any site that is involved in at least one epistatic interaction. Specifically, we prove that, at stationarity, the hazard function of the distribution of waiting times until reversion is strictly decreasing for any such site. Thus, in the presence of epistasis, the longer a particular character has been absent from a site, the less likely the site will revert to its prior state. We also explore several examples of this general result, which share a common pattern whereby the probability of having reverted increases rapidly at short times to some substantial value before becoming almost flat after a few substitutions at other sites. This pattern indicates a characteristic tendency for reversion to occur either almost immediately after the initial substitution or only after a very long time.

Benefit of transferred mutations is better predicted by the fitness of recipients than by their ecological or genetic relatedness

The effect of a mutation depends on its interaction with the genetic background in which it is assessed. Studies in experimental systems have demonstrated that such interactions are common among beneficial mutations and often follow a pattern consistent with declining evolvability of more fit genotypes. However, these studies generally examine the consequences of interactions between a small number of focal mutations. It is not clear, therefore, that findings can be extrapolated to natural populations, where new mutations may be transferred between genetically divergent backgrounds. We build on work that examined interactions between four beneficial mutations selected in a laboratory-evolved population of Escherichia coli to test how they interact with the genomes of diverse natural isolates of the same species. We find that the fitness effect of transferred mutations depends weakly on the genetic and ecological similarity of recipient strains relative to the donor strain in which the mutations were selected. By contrast, mutation effects were strongly inversely correlated to the initial fitness of the recipient strain. That is, there was a pattern of diminishing returns whereby fit strains benefited proportionally less from an added mutation. Our results strengthen the view that the fitness of a strain can be a major determinant of its ability to adapt. They also support a role for barriers of transmission, rather than differential selection of transferred DNA, as an explanation of observed phylogenetically determined patterns of restricted recombination among E. coli strains.

Survival of the Curviest: Noise-Driven Selection for Synergistic Epistasis

A major goal of human genetics is to elucidate the genetic architecture of human disease, with the goal of fueling improvements in diagnosis and the understanding of disease pathogenesis. The degree to which epistasis, or non-additive effects of risk alleles at different loci, accounts for common disease traits is hotly debated, in part because the conditions under which epistasis evolves are not well understood. Using both theory and evolutionary simulation, we show that the occurrence of common diseases (i.e. unfit phenotypes with frequencies on the order of 1%) can, under the right circumstances, be expected to be driven primarily by synergistic epistatic interactions. Conditions that are necessary, collectively, for this outcome include a strongly non-linear phenotypic landscape, strong (but not too strong) selection against the disease phenotype, and "noise" in the genotype-phenotype map that is both environmental (extrinsic, time-correlated) and developmental (intrinsic, uncorrelated) and, in both cases, neither too little nor too great. These results suggest ways in which geneticists might identify, a priori, those disease traits for which an "epistatic explanation" should be sought, and in the process better focus ongoing searches for risk alleles.

Strong Selection Significantly Increases Epistatic Interactions in the Long-Term Evolution of a Protein

Epistatic interactions between residues determine a protein’s adaptability and shape its evolutionary trajectory. When a protein experiences a changed environment, it is under strong selection to find a peak in the new fitness landscape. It has been shown that strong selection increases epistatic interactions as well as the ruggedness of the fitness landscape, but little is known about how the epistatic interactions change under selection in the long-term evolution of a protein. Here we analyze the evolution of epistasis in the protease of the human immunodeficiency virus type 1 (HIV-1) using protease sequences collected for almost a decade from both treated and untreated patients, to understand how epistasis changes and how those changes impact the long-term evolvability of a protein. We use an information-theoretic proxy for epistasis that quantifies the co-variation between sites, and show that positive information is a necessary (but not sufficient) condition that detects epistasis in most cases. We analyze the “fossils” of the evolutionary trajectories of the protein contained in the sequence data, and show that epistasis continues to enrich under strong selection, but not for proteins whose environment is unchanged. The increase in epistasis compensates for the information loss due to sequence variability brought about by treatment, and facilitates adaptation in the increasingly rugged fitness landscape of treatment. While epistasis is thought to enhance evolvability via valley-crossing early-on in adaptation, it can hinder adaptation later when the landscape has turned rugged. However, we find no evidence that the HIV-1 protease has reached its potential for evolution after 9 years of adapting to a drug environment that itself is constantly changing. We suggest that the mechanism of encoding new information into pairwise interactions is central to protein evolution not just in HIV-1 protease, but for any protein adapting to a changing environment.

Evolution is often viewed as a process that occurs “mutation by mutation”, suggesting that the effect of each mutation is independent of that of others. However, in reality the effect of a mutation often depends on the context of other mutations, a dependence known as “epistasis”. Even though epistasis can constrain protein evolution, it is actually very common. Such interactions are particularly pervasive in proteins that evolve resistance to a drug via mutations that create defects, and that must be repaired with compensatory mutations. We study how epistasis between protein residues evolves over time in a new and changing environment, and compare these findings to protein evolution in a constant environment. We analyze the sequences of the human immunodeficiency virus type 1 (HIV-1) protease enzyme collected over a period of 9 years from patients treated with anti-viral drugs (as well as from patients that went untreated), and find that epistasis between residues continues to increase as more potent anti-viral drugs enter the market, while epistasis is unchanging in the proteins exposed to a constant environment. Yet, the proteins adapting to the changing landscape do not appear to be constrained by the epistatic interactions and continue to manage to evade new drugs.

How mutational epistasis impairs predictability in protein evolution and design

There has been much debate about the extent to which mutational epistasis, that is, the dependence of the outcome of a mutation on the genetic background, constrains evolutionary trajectories. The degree of unpredictability introduced by epistasis, due to the non-additivity of functional effects, strongly hinders the strategies developed in protein design and engineering. While many studies have addressed this issue through systematic characterization of evolutionary trajectories within individual enzymes, the field lacks a consensus view on this matter. In this work, we performed a comprehensive analysis of epistasis by analyzing the mutational effects from nine adaptive trajectories toward new enzymatic functions. We quantified epistasis by comparing the effect of mutations occurring between two genetic backgrounds: the starting enzyme (for example, wild type) and the intermediate variant on which the mutation occurred during the trajectory. We found that most trajectories exhibit positive epistasis, in which the mutational effect is more beneficial when it occurs later in the evolutionary trajectory. Approximately half (49%) of functional mutations were neutral or negative on the wild-type background, but became beneficial at a later stage in the trajectory, indicating that these functional mutations were not predictable from the initial starting point. While some cases of strong epistasis were associated with direct interaction between residues, many others were caused by long-range indirect interactions between mutations. Our work highlights the prevalence of epistasis in enzyme adaptive evolution, in particular positive epistasis, and suggests the necessity of incorporating mutational epistasis in protein engineering and design to create highly efficient catalysts.

The population genetics of drug resistance evolution in natural populations of viral, bacterial and eukaryotic pathogens

Drug resistance is a costly consequence of pathogen evolution and a major concern in public health. In this review, we show how population genetics can be used to study the evolution of drug resistance and also how drug resistance evolution is informative as an evolutionary model system. We highlight five examples from diverse organisms with particular focus on: (i) identifying drug resistance loci in the malaria parasite Plasmodium falciparum using the genomic signatures of selective sweeps, (ii) determining the role of epistasis in drug resistance evolution in influenza, (iii) quantifying the role of standing genetic variation in the evolution of drug resistance in HIV, (iv) using drug resistance mutations to study clonal interference dynamics in tuberculosis and (v) analysing the population structure of the core and accessory genome of Staphylococcus aureus to understand the spread of methicillin resistance. Throughout this review, we discuss the uses of sequence data and population genetic theory in studying the evolution of drug resistance.

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.

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.

Constraints on adaptation of Escherichia coli to mixed-resource environments increase over time

Can a population evolved in two resources reach the same fitness in both as specialist populations evolved in each of the individual resources? This question is central to theories of ecological specialization, the maintenance of genetic variation, and sympatric speciation, yet relatively few experiments have examined costs of generalism over long-term adaptation. We tested whether selection in environments containing two resources limits a population's ability to adapt to the individual resources by comparing the fitness of replicate Escherichia coli populations evolved for 6000 generations in the presence of glucose or lactose alone (specialists), or in varying presentations of glucose and lactose together (generalists). We found that all populations had significant fitness increases in both resources, though the magnitude and rate of these increases differed. For the first 4000 generations, most generalist populations increased in fitness as quickly in the individual resources as the corresponding specialist populations. From 5000 generations, however, a widespread cost of adaptation affected all generalists, indicating a growing constraint on their abilities to adapt to two resources simultaneously. Our results indicate that costs of generalism are prevalent, but may influence evolutionary trajectories only after a period of cost-free adaptation.

Contingency and entrenchment in protein evolution under purifying selection

The phenotypic effect of an allele at one genetic site may depend on alleles at other sites, a phenomenon known as epistasis. Epistasis can profoundly influence the process of evolution in populations and shape the patterns of protein divergence across species. Whereas epistasis between adaptive substitutions has been studied extensively, relatively little is known about epistasis under purifying selection. Here we use computational models of thermodynamic stability in a ligand-binding protein to explore the structure of epistasis in simulations of protein sequence evolution. Even though the predicted effects on stability of random mutations are almost completely additive, the mutations that fix under purifying selection are enriched for epistasis. In particular, the mutations that fix are contingent on previous substitutions: Although nearly neutral at their time of fixation, these mutations would be deleterious in the absence of preceding substitutions. Conversely, substitutions under purifying selection are subsequently entrenched by epistasis with later substitutions: They become increasingly deleterious to revert over time. Our results imply that, even under purifying selection, protein sequence evolution is often contingent on history and so it cannot be predicted by the phenotypic effects of mutations assayed in the ancestral background.

Epistasis constrains mutational pathways of hemoglobin adaptation in high-altitude pikas

A fundamental question in evolutionary genetics concerns the roles of mutational pleiotropy and epistasis in shaping trajectories of protein evolution. This question can be addressed most directly by using site-directed mutagenesis to explore the mutational landscape of protein function in experimentally defined regions of sequence space. Here, we evaluate how pleiotropic trade-offs and epistatic interactions influence the accessibility of alternative mutational pathways during the adaptive evolution of hemoglobin (Hb) function in high-altitude pikas (Mammalia: Lagomorpha). By combining ancestral protein resurrection with a combinatorial protein-engineering approach, we examined the functional effects of sequential mutational steps in all possible pathways that produced an increased Hb–O₂ affinity. These experiments revealed that the effects of mutations on Hb–O₂ affinity are highly dependent on the temporal order in which they occur: Each of three β-chain substitutions produced a significant increase in Hb–O₂ affinity on the ancestral genetic background, but two of these substitutions produced opposite effects when they occurred as later steps in the pathway. The experiments revealed pervasive epistasis for Hb–O₂ affinity, but affinity-altering mutations produced no significant pleiotropic trade-offs. These results provide insights into the properties of adaptive substitutions in naturally evolved proteins and suggest that the accessibility of alternative mutational pathways may be more strongly constrained by sign epistasis for positively selected biochemical phenotypes than by antagonistic pleiotropy.

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.