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

Fisher's Geometric Model as a Tool to Study Speciation

Interactions between alleles and across environments play an important role in the fitness of hybrids and are at the heart of the speciation process. Fitness landscapes capture these interactions and can be used to model hybrid fitness, helping us to interpret empirical observations and clarify verbal models. Here, we review recent progress in understanding hybridization outcomes through Fisher's geometric model, an intuitive and analytically tractable fitness landscape that captures many fitness patterns observed across taxa. We use case studies to show how the model parameters can be estimated from different types of data and discuss how these estimates can be used to make inferences about the divergence history and genetic architecture. We also highlight some areas where the model's predictions differ from alternative incompatibility-based models, such as the snowball effect and outlier patterns in genome scans.

Unpredictability of the Fitness Effects of Antimicrobial Resistance Mutations Across Environments in Escherichia coli

The evolution of antimicrobial resistance (AMR) in bacteria is a major public health concern, and antibiotic restriction is often implemented to reduce the spread of resistance. These measures rely on the existence of deleterious fitness effects (i.e. costs) imposed by AMR mutations during growth in the absence of antibiotics. According to this assumption, resistant strains will be outcompeted by susceptible strains that do not pay the cost during the period of restriction. The fitness effects of AMR mutations are generally studied in laboratory reference strains grown in standard growth environments; however, the genetic and environmental context can influence the magnitude and direction of a mutation's fitness effects. In this study, we measure how three sources of variation impact the fitness effects of Escherichia coli AMR mutations: the type of resistance mutation, the genetic background of the host, and the growth environment. We demonstrate that while AMR mutations are generally costly in antibiotic-free environments, their fitness effects vary widely and depend on complex interactions between the mutation, genetic background, and environment. We test the ability of the Rough Mount Fuji fitness landscape model to reproduce the empirical data in simulation. We identify model parameters that reasonably capture the variation in fitness effects due to genetic variation. However, the model fails to accommodate the observed variation when considering multiple growth environments. Overall, this study reveals a wealth of variation in the fitness effects of resistance mutations owing to genetic background and environmental conditions, which will ultimately impact their persistence in natural populations.

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.

Changing fitness effects of mutations through long-term bacterial evolution

The distribution of fitness effects of new mutations shapes evolution, but it is challenging to observe how it changes as organisms adapt. Using Escherichia coli lineages spanning 50,000 generations of evolution, we quantify the fitness effects of insertion mutations in every gene. Macroscopically, the fraction of deleterious mutations changed little over time whereas the beneficial tail declined sharply, approaching an exponential distribution. Microscopically, changes in individual gene essentiality and deleterious effects often occurred in parallel; altered essentiality is only partly explained by structural variation. The identity and effect sizes of beneficial mutations changed rapidly over time, but many targets of selection remained predictable because of the importance of loss-of-function mutations. Taken together, these results reveal the dynamic-but statistically predictable-nature of mutational fitness effects.

Environmental modulation of global epistasis in a drug resistance fitness landscape

Interactions between mutations (epistasis) can add substantial complexity to genotype-phenotype maps, hampering our ability to predict evolution. Yet, recent studies have shown that the fitness effect of a mutation can often be predicted from the fitness of its genetic background using simple, linear relationships. This phenomenon, termed global epistasis, has been leveraged to reconstruct fitness landscapes and infer adaptive trajectories in a wide variety of contexts. However, little attention has been paid to how patterns of global epistasis may be affected by environmental variation, despite this variation frequently being a major driver of evolution. This is particularly relevant for the evolution of drug resistance, where antimicrobial drugs may change the environment faced by pathogens and shape their adaptive trajectories in ways that can be difficult to predict. By analyzing a fitness landscape of four mutations in a gene encoding an essential enzyme of P. falciparum (a parasite cause of malaria), here we show that patterns of global epistasis can be strongly modulated by the concentration of a drug in the environment. Expanding on previous theoretical results, we demonstrate that this modulation can be quantitatively explained by how specific gene-by-gene interactions are modified by drug dose. Importantly, our results highlight the need to incorporate potential environmental variation into the global epistasis framework in order to predict adaptation in dynamic environments.

Evolutionary rescue on genotypic fitness landscapes

Populations facing adverse environments, novel pathogens or invasive competitors may be destined to extinction if they are unable to adapt rapidly. Quantitative predictions of the probability of survival through adaptation, evolutionary rescue, have been previously developed for one of the most natural and well-studied mappings from an organism's traits to its fitness, Fisher's geometric model (FGM). While FGM assumes that all possible trait values are accessible via mutation, in many applications only a finite set of rescue mutations will be available, such as mutations conferring resistance to a parasite, predator or toxin. We predict the probability of evolutionary rescue, via de novo mutation, when this underlying genetic structure is included. We find that rescue probability is always reduced when its genetic basis is taken into account. Unlike other known features of the genotypic FGM, however, the probability of rescue increases monotonically with the number of available mutations and approaches the behaviour of the classical FGM as the number of available mutations approaches infinity.

A null model for the distribution of fitness effects of mutations

The distribution of fitness effects (DFE) of new mutations is key to our understanding of many evolutionary processes. Theoreticians have developed several models to help understand the patterns seen in empirical DFEs. Many such models reproduce the broad patterns seen in empirical DFEs but these models often rely on structural assumptions that cannot be tested empirically. Here, we investigate how much of the underlying "microscopic" biological processes involved in the mapping of new mutations to fitness can be inferred from "macroscopic" observations of the DFE. We develop a null model by generating random genotype-to-fitness maps and show that the null DFE is that with the largest possible information entropy. We further show that, subject to one simple constraint, this null DFE is a Gompertz distribution. Finally, we illustrate how the predictions of this null DFE match empirically measured DFEs from several datasets, as well as DFEs simulated from Fisher's geometric model. This suggests that a match between models and empirical data is often not a very strong indication of the mechanisms underlying the mapping of mutation to fitness.

Epistasis decreases with increasing antibiotic pressure but not temperature

Predicting mutational effects is essential for the control of antibiotic resistance (ABR). Predictions are difficult when there are strong genotype-by-environment (G × E), gene-by-gene (G × G or epistatic) or gene-by-gene-by-environment (G × G × E) interactions. We quantified G × G × E effects in Escherichia coli across environmental gradients. We created intergenic fitness landscapes using gene knock-outs and single-nucleotide ABR mutations previously identified to vary in the extent of G × E effects in our environments of interest. Then, we measured competitive fitness across a complete combinatorial set of temperature and antibiotic dosage gradients. In this way, we assessed the predictability of 15 fitness landscapes across 12 different but related environments. We found G × G interactions and rugged fitness landscapes in the absence of antibiotic, but as antibiotic concentration increased, the fitness effects of ABR genotypes quickly overshadowed those of gene knock-outs, and the landscapes became smoother. Our work reiterates that some single mutants, like those conferring resistance or susceptibility to antibiotics, have consistent effects across genetic backgrounds in stressful environments. Thus, although epistasis may reduce the predictability of evolution in benign environments, evolution may be more predictable in adverse environments. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Global epistasis on fitness landscapes

Epistatic interactions between mutations add substantial complexity to adaptive landscapes and are often thought of as detrimental to our ability to predict evolution. Yet, patterns of global epistasis, in which the fitness effect of a mutation is well-predicted by the fitness of its genetic background, may actually be of help in our efforts to reconstruct fitness landscapes and infer adaptive trajectories. Microscopic interactions between mutations, or inherent nonlinearities in the fitness landscape, may cause global epistasis patterns to emerge. In this brief review, we provide a succinct overview of recent work about global epistasis, with an emphasis on building intuition about why it is often observed. To this end, we reconcile simple geometric reasoning with recent mathematical analyses, using these to explain why different mutations in an empirical landscape may exhibit different global epistasis patterns-ranging from diminishing to increasing returns. Finally, we highlight open questions and research directions. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Rate of environmental variation impacts the predictability in evolution

In the two last decades, we have improved our understanding of the adaptive evolution of natural populations under constant and stable environments. For instance, experimental methods from evolutionary biology have allowed us to explore the structure of fitness landscapes and survey how the landscape properties can constrain the adaptation process. However, understanding how environmental changes can affect adaptation remains challenging. Very little progress has been made with respect to time-varying fitness landscapes. Using the adaptive-walk approximation, we survey the evolutionary process of populations under a scenario of environmental variation. In particular, we investigate how the rate of environmental variation influences the predictability in evolution. We observe that the rate of environmental variation not only changes the duration of adaptive walks towards fitness peaks of the fitness landscape, but also affects the degree of repeatability of both outcomes and evolutionary paths. In general, slower environmental variation increases the predictability in evolution. The accessibility of endpoints is greatly influenced by the ecological dynamics. The dependence of these quantities on the genome size and number of traits is also addressed. To our knowledge, this contribution is the first to use the predictive approach to quantify and understand the impact of the speed of environmental variation on the degree of parallelism of the evolutionary process.

Fitness of evolving bacterial populations is contingent on deep and shallow history but only shallow history creates predictable patterns

Long-term evolution experiments have tested the importance of genetic and environmental factors in influencing evolutionary outcomes. Differences in phylogenetic history, recent adaptation to distinct environments and chance events, all influence the fitness of a population. However, the interplay of these factors on a population's evolutionary potential remains relatively unexplored. We tracked the outcome of 2000 generations of evolution of four natural isolates of Escherichia coli bacteria that were engineered to also create differences in shallow history by adding previously identified mutations selected in a separate long-term experiment. Replicate populations started from each progenitor evolved in four environments. We found that deep and shallow phylogenetic histories both contributed significantly to differences in evolved fitness, though by different amounts in different selection environments. With one exception, chance effects were not significant. Whereas the effect of deep history did not follow any detectable pattern, effects of shallow history followed a pattern of diminishing returns whereby fitter ancestors had smaller fitness increases. These results are consistent with adaptive evolution being contingent on the interaction of several evolutionary forces but demonstrate that the nature of these interactions is not fixed and may not be predictable even when the role of chance is small.

On the incongruence of genotype-phenotype and fitness landscapes

The mapping from genotype to phenotype to fitness typically involves multiple nonlinearities that can transform the effects of mutations. For example, mutations may contribute additively to a phenotype, but their effects on fitness may combine non-additively because selection favors a low or intermediate value of that phenotype. This can cause incongruence between the topographical properties of a fitness landscape and its underlying genotype-phenotype landscape. Yet, genotype-phenotype landscapes are often used as a proxy for fitness landscapes to study the dynamics and predictability of evolution. Here, we use theoretical models and empirical data on transcription factor-DNA interactions to systematically study the incongruence of genotype-phenotype and fitness landscapes when selection favors a low or intermediate phenotypic value. Using the theoretical models, we prove a number of fundamental results. For example, selection for low or intermediate phenotypic values does not change simple sign epistasis into reciprocal sign epistasis, implying that genotype-phenotype landscapes with only simple sign epistasis motifs will always give rise to single-peaked fitness landscapes under such selection. More broadly, we show that such selection tends to create fitness landscapes that are more rugged than the underlying genotype-phenotype landscape, but this increased ruggedness typically does not frustrate adaptive evolution because the local adaptive peaks in the fitness landscape tend to be nearly as tall as the global peak. Many of these results carry forward to the empirical genotype-phenotype landscapes, which may help to explain why low- and intermediate-affinity transcription factor-DNA interactions are so prevalent in eukaryotic gene regulation.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Bacterial fitness landscapes stratify based on proteome allocation associated with discrete aero-types

The fitness landscape is a concept commonly used to describe evolution towards optimal phenotypes. It can be reduced to mechanistic detail using genome-scale models (GEMs) from systems biology. We use recently developed GEMs of Metabolism and protein Expression (ME-models) to study the distribution of Escherichia coli phenotypes on the rate-yield plane. We found that the measured phenotypes distribute non-uniformly to form a highly stratified fitness landscape. Systems analysis of the ME-model simulations suggest that this stratification results from discrete ATP generation strategies. Accordingly, we define "aero-types", a phenotypic trait that characterizes how a balanced proteome can achieve a given growth rate by modulating 1) the relative utilization of oxidative phosphorylation, glycolysis, and fermentation pathways; and 2) the differential employment of electron-transport-chain enzymes. This global, quantitative, and mechanistic systems biology interpretation of fitness landscape formed upon proteome allocation offers a fundamental understanding of bacterial physiology and evolution dynamics.

Primary and promiscuous functions coexist during evolutionary innovation through whole protein domain acquisitions

Molecular examples of evolutionary innovation are scarce and generally involve point mutations. Innovation can occur through larger rearrangements, but here experimental data is extremely limited. Integron integrases innovated from double-strand- toward single-strand-DNA recombination through the acquisition of the I2 α-helix. To investigate how this transition was possible, we have evolved integrase IntI1 to what should correspond to an early innovation state by selecting for its ancestral activity. Using synonymous alleles to enlarge sequence space exploration, we have retrieved 13 mutations affecting both I2 and the multimerization domains of IntI1. We circumvented epistasis constraints among them using a combinatorial library that revealed their individual and collective fitness effects. We obtained up to 10⁴-fold increases in ancestral activity with various asymmetrical trade-offs in single-strand-DNA recombination. We show that high levels of primary and promiscuous functions could have initially coexisted following I2 acquisition, paving the way for a gradual evolution toward innovation.

Fitness variation across subtle environmental perturbations reveals local modularity and global pleiotropy of adaptation

Building a genotype-phenotype-fitness map of adaptation is a central goal in evolutionary biology. It is difficult even when adaptive mutations are known because it is hard to enumerate which phenotypes make these mutations adaptive. We address this problem by first quantifying how the fitness of hundreds of adaptive yeast mutants responds to subtle environmental shifts. We then model the number of phenotypes these mutations collectively influence by decomposing these patterns of fitness variation. We find that a small number of inferred phenotypes can predict fitness of the adaptive mutations near their original glucose-limited evolution condition. Importantly, inferred phenotypes that matter little to fitness at or near the evolution condition can matter strongly in distant environments. This suggests that adaptive mutations are locally modular - affecting a small number of phenotypes that matter to fitness in the environment where they evolved - yet globally pleiotropic - affecting additional phenotypes that may reduce or improve fitness in new environments.

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.

Extreme Antagonism Arising from Gene-Environment Interactions

Antagonistic interactions in biological systems, which occur when one perturbation blunts the effect of another, are typically interpreted as evidence that the two perturbations impact the same cellular pathway or function. Yet, this interpretation ignores extreme antagonistic interactions wherein an otherwise deleterious perturbation compensates for the function lost because of a prior perturbation. Here, we report on gene-environment interactions involving genetic mutations that are deleterious in a permissive environment but beneficial in a specific environment that restricts growth. These extreme antagonistic interactions constitute gene-environment analogs of synthetic rescues previously observed for gene-gene interactions. Our approach uses two independent adaptive evolution steps to address the lack of experimental methods to systematically identify such extreme interactions. We apply the approach to Escherichia coli by successively adapting it to defined glucose media without and with the antibiotic rifampicin. The approach identified multiple mutations that are beneficial in the presence of rifampicin and deleterious in its absence. The analysis of transcription shows that the antagonistic adaptive mutations repress a stringent response-like transcriptional program, whereas nonantagonistic mutations have an opposite transcriptional profile. Our approach represents a step toward the systematic characterization of extreme antagonistic gene-drug interactions, which can be used to identify targets to select against antibiotic resistance.

Flux, toxicity, and expression costs generate complex genetic interactions in a metabolic pathway

Our ability to predict the impact of mutations on traits relevant for disease and evolution remains severely limited by the dependence of their effects on the genetic background and environment. Even when molecular interactions between genes are known, it is unclear how these translate to organism-level interactions between alleles. We therefore characterized the interplay of genetic and environmental dependencies in determining fitness by quantifying ~4000 fitness interactions between expression variants of two metabolic genes, starting from various environmentally modulated expression levels. We detect a remarkable variety of interactions dependent on initial expression levels and demonstrate that they can be quantitatively explained by a mechanistic model accounting for catabolic flux, metabolite toxicity, and expression costs. Complex fitness interactions between mutations can therefore be predicted simply from their simultaneous impact on a few connected molecular phenotypes.

Why is cancer not more common? A changing microenvironment may help to explain why, and suggests strategies for anti-cancer therapy

One of the great unsolved puzzles in cancer biology is not why cancers occur, but rather explaining why so few cancers occur compared with the theoretical number that could occur, given the number of progenitor cells in the body and the normal mutation rate. We hypothesized that a contributory explanation is that the tumour microenvironment (TME) is not fixed due to factors such as immune cell infiltration, and that this could impair the ability of neoplastic cells to retain a high enough fitness to become a cancer. The TME has implicitly been assumed to be static in most cancer evolution models, and we therefore developed a mathematical model of spatial cancer evolution assuming that the TME, and thus the optimum cancer phenotype, changes over time. Based on simulations, we show how cancer cell populations adapt to diverse changing TME conditions and fitness landscapes. Compared with static TMEs, which generate neutral dynamics, changing TMEs lead to complex adaptations with characteristic spatio-temporal heterogeneity involving variable fitness effects of driver mutations, subclonal mixing, subclonal competition and phylogeny patterns. In many cases, cancer cell populations fail to grow or undergo spontaneous regression, and even extinction. Our analyses predict that cancer evolution in a changing TME is challenging, and can help to explain why cancer is neither inevitable nor as common as expected. Should cancer driver mutations with effects dependent of the TME exist, they are likely to be selected. Anti-cancer prevention and treatment strategies based on changing the TME are feasible and potentially effective.

The distribution of epistasis on simple fitness landscapes

Fitness interactions between mutations can influence a population's evolution in many different ways. While epistatic effects are difficult to measure precisely, important information is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from a class of simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effect sizes, mutational bias and maladaptation of the wild type. We illustrate our approach by reanalysing a large dataset of mutant effects in a yeast snoRNA (small nucleolar RNA). Though characterized by some large epistatic effects, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have limited influence on the evolutionary dynamics in this system. We also show how the amount of epistasis depends on both the underlying fitness landscape and the distribution of mutations, and so is expected to vary in consistent ways between new mutations, standing variation and fixed mutations.

Recent insights into the genotype-phenotype relationship from massively parallel genetic assays

With the molecular revolution in Biology, a mechanistic understanding of the genotype-phenotype relationship became possible. Recently, advances in DNA synthesis and sequencing have enabled the development of deep mutational scanning assays, capable of scoring comprehensive libraries of genotypes for fitness and a variety of phenotypes in massively parallel fashion. The resulting empirical genotype-fitness maps pave the way to predictive models, potentially accelerating our ability to anticipate the behaviour of pathogen and cancerous cell populations from sequencing data. Besides from cellular fitness, phenotypes of direct application in industry (e.g. enzyme activity) and medicine (e.g. antibody binding) can be quantified and even selected directly by these assays. This review discusses the technological basis of and recent developments in massively parallel genetics, along with the trends it is uncovering in the genotype-phenotype relationship (distribution of mutation effects, epistasis), their possible mechanistic bases and future directions for advancing towards the goal of predictive genetics.

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.

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.

Coadapted genomes and selection on hybrids: Fisher's geometric model explains a variety of empirical patterns

Natural selection plays a variety of roles in hybridization, speciation, and admixture. Most research has focused on two extreme cases: crosses between closely related inbred lines, where hybrids are fitter than their parents, or crosses between effectively isolated species, where hybrids suffer severe breakdown. But many natural populations must fall into intermediate regimes, with multiple types of gene interaction, and these are more difficult to study. Here, we develop a simple fitness landscape model, and show that it naturally interpolates between previous modeling approaches, which were designed for the extreme cases, and invoke either mildly deleterious recessives, or discrete hybrid incompatibilities. Our model yields several new predictions, which we test with genomic data from Mytilus mussels, and published data from plants (Zea, Populus, and Senecio) and animals (Mus, Teleogryllus, and Drosophila). The predictions are generally supported, and the model explains a number of surprising empirical patterns. Our approach enables novel and complementary uses of genome-wide datasets, which do not depend on identifying outlier loci, or "speciation genes" with anomalous effects. Given its simplicity and flexibility, and its predictive successes with a wide range of data, the approach should be readily extendable to other outstanding questions in the study of hybridization.

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.

Unraveling the causes of adaptive benefits of synonymous mutations in TEM-1 β-lactamase

While synonymous mutations were long thought to be without phenotypic consequences, there is growing evidence they can affect gene expression, protein folding, and ultimately the fitness of an organism. In only a few cases have the mechanisms by which synonymous mutations affect the phenotype been elucidated. We previously identified 48 mutations in TEM-1 β-lactamase that increased resistance of Escherichia coli to cefotaxime, 10 of which were synonymous. To better understand the molecular mechanisms underlying the beneficial effect of these synonymous mutations, we made a series of measurements for a panel containing the 10 synonymous together with 10 non-synonymous mutations as a reference. Whereas messenger levels were unaffected, we found that total and functional TEM protein levels were higher for 5 out of 10 synonymous mutations. These observations suggest that some of these mutations act on translation or a downstream process. Similar effects were observed for some small-benefit non-synonymous mutations, suggesting a similar causal mechanism. For the synonymous mutations, we found that the cost of resistance scales with TEM protein levels. A resistance landscape for four synonymous mutations revealed strong epistasis: none of the combinations of mutations exceeded the resistance of the largest-effect mutation and there were synthetically neutral combinations. By considering combined effects of these mutations, we could infer that functional TEM protein level is a multi-dimensional phenotype. These results suggest that synonymous mutations may have beneficial effects by increasing the expression of an enzyme with low substrate activity, which may be realized via multiple, yet unknown, post-transcriptional mechanisms.

Sign epistasis caused by hierarchy within signalling cascades

Sign epistasis is a central evolutionary constraint, but its causal factors remain difficult to predict. Here we use the notion of parameterised optima to explain epistasis within a signalling cascade, and test these predictions in Escherichia coli. We show that sign epistasis arises from the benefit of tuning phenotypic parameters of cascade genes with respect to each other, rather than from their complex and incompletely known genetic bases. Specifically, sign epistasis requires only that the optimal phenotypic parameters of one gene depend on the phenotypic parameters of another, independent of other details, such as activating or repressing nature, position within the cascade, intra-genic pleiotropy or genotype. Mutational effects change sign more readily in downstream genes, indicating that optimising downstream genes is more constrained. The findings show that sign epistasis results from the inherent upstream-downstream hierarchy between signalling cascade genes, and can be addressed without exhaustive genotypic mapping.

Sign epistasis clearly constrains evolution, but its causes are difficult to decipher. Here, the authors study epistasis in a signalling cascade, and arrive at a general criterion and understanding of sign epistasis as arising from the inherent hierarchy between signalling cascade components.

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.

Genotypic Complexity of Fisher's Geometric Model

Fisher's geometric model was originally introduced to argue that complex adaptations must occur in small steps because of pleiotropic constraints. When supplemented with the assumption of additivity of mutational effects on phenotypic traits, it provides a simple mechanism for the emergence of genotypic epistasis from the nonlinear mapping of phenotypes to fitness. Of particular interest is the occurrence of reciprocal sign epistasis, which is a necessary condition for multipeaked genotypic fitness landscapes. Here we compute the probability that a pair of randomly chosen mutations interacts sign epistatically, which is found to decrease with increasing phenotypic dimension n, and varies nonmonotonically with the distance from the phenotypic optimum. We then derive expressions for the mean number of fitness maxima in genotypic landscapes comprised of all combinations of L random mutations. This number increases exponentially with L, and the corresponding growth rate is used as a measure of the complexity of the landscape. The dependence of the complexity on the model parameters is found to be surprisingly rich, and three distinct phases characterized by different landscape structures are identified. Our analysis shows that the phenotypic dimension, which is often referred to as phenotypic complexity, does not generally correlate with the complexity of fitness landscapes and that even organisms with a single phenotypic trait can have complex landscapes. Our results further inform the interpretation of experiments where the parameters of Fisher's model have been inferred from data, and help to elucidate which features of empirical fitness landscapes can be described by this model.

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.

Detecting High-Order Epistasis in Nonlinear Genotype-Phenotype Maps

High-order epistasis has been observed in many genotype-phenotype maps. These multi-way interactions between mutations may be useful for dissecting complex traits and could have profound implications for evolution. Alternatively, they could be a statistical artifact. High-order epistasis models assume the effects of mutations should add, when they could in fact multiply or combine in some other nonlinear way. A mismatch in the “scale” of the epistasis model and the scale of the underlying map would lead to spurious epistasis. In this article, we develop an approach to estimate the nonlinear scales of arbitrary genotype-phenotype maps. We can then linearize these maps and extract high-order epistasis. We investigated seven experimental genotype-phenotype maps for which high-order epistasis had been reported previously. We find that five of the seven maps exhibited nonlinear scales. Interestingly, even after accounting for nonlinearity, we found statistically significant high-order epistasis in all seven maps. The contributions of high-order epistasis to the total variation ranged from 2.2 to 31.0%, with an average across maps of 12.7%. Our results provide strong evidence for extensive high-order epistasis, even after nonlinear scale is taken into account. Further, we describe a simple method to estimate and account for nonlinearity in genotype-phenotype maps.

Widespread Genetic Incompatibilities between First-Step Mutations during Parallel Adaptation of Saccharomyces cerevisiae to a Common Environment

Independently evolving populations may adapt to similar selection pressures via different genetic changes. The interactions between such changes, such as in a hybrid individual, can inform us about what course adaptation may follow and allow us to determine whether gene flow would be facilitated or hampered following secondary contact. We used Saccharomyces cerevisiae to measure the genetic interactions between first-step mutations that independently evolved in the same biosynthetic pathway following exposure to the fungicide nystatin. We found that genetic interactions are prevalent and predominantly negative, with the majority of mutations causing lower growth when combined in a double mutant than when alone as a single mutant (sign epistasis). The prevalence of sign epistasis is surprising given the small number of mutations tested and runs counter to expectations for mutations arising in a single biosynthetic pathway in the face of a simple selective pressure. Furthermore, in one third of pairwise interactions, the double mutant grew less well than either single mutant (reciprocal sign epistasis). The observation of reciprocal sign epistasis among these first adaptive mutations arising in the same genetic background indicates that partial postzygotic reproductive isolation could evolve rapidly between populations under similar selective pressures, even with only a single genetic change in each. The nature of the epistatic relationships was sensitive, however, to the level of drug stress in the assay conditions, as many double mutants became fitter than the single mutants at higher concentrations of nystatin. We discuss the implications of these results both for our understanding of epistatic interactions among beneficial mutations in the same biochemical pathway and for speciation.

Fisher's geometrical model and the mutational patterns of antibiotic resistance across dose gradients

Fisher's geometrical model (FGM) has been widely used to depict the fitness effects of mutations. It is a general model with few underlying assumptions that gives a large and comprehensive view of adaptive processes. It is thus attractive in several situations, for example adaptation to antibiotics, but comes with limitations, so that more mechanistic approaches are often preferred to interpret experimental data. It might be possible however to extend FGM assumptions to better account for mutational data. This is theoretically challenging in the context of antibiotic resistance because resistance mutations are assumed to be rare. In this article, we show with Escherichia coli how the fitness effects of resistance mutations screened at different doses of nalidixic acid vary across a dose-gradient. We found experimental patterns qualitatively consistent with the basic FGM (rate of resistance across doses, gamma distributed costs) but also unexpected patterns such as a decreasing mean cost of resistance with increasing screen dose. We show how different extensions involving mutational modules and variations in trait covariance across environments, can be discriminated based on these data. Overall, simple extensions of the FGM accounted well for complex mutational effects of resistance mutations across antibiotic doses.

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.

Competition and fixation of cohorts of adaptive mutations under Fisher geometrical model

One of the simplest models of adaptation to a new environment is Fisher’s Geometric Model (FGM), in which populations move on a multidimensional landscape defined by the traits under selection. The predictions of this model have been found to be consistent with current observations of patterns of fitness increase in experimentally evolved populations. Recent studies investigated the dynamics of allele frequency change along adaptation of microbes to simple laboratory conditions and unveiled a dramatic pattern of competition between cohorts of mutations, i.e., multiple mutations simultaneously segregating and ultimately reaching fixation. Here, using simulations, we study the dynamics of phenotypic and genetic change as asexual populations under clonal interference climb a Fisherian landscape, and ask about the conditions under which FGM can display the simultaneous increase and fixation of multiple mutations—mutation cohorts—along the adaptive walk. We find that FGM under clonal interference, and with varying levels of pleiotropy, can reproduce the experimentally observed competition between different cohorts of mutations, some of which have a high probability of fixation along the adaptive walk. Overall, our results show that the surprising dynamics of mutation cohorts recently observed during experimental adaptation of microbial populations can be expected under one of the oldest and simplest theoretical models of adaptation—FGM.

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.

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.

Diverse phenotypic and genetic responses to short-term selection in evolving Escherichia coli populations

Beneficial mutations fuel adaptation by altering phenotypes that enhance the fit of organisms to their environment. However, the phenotypic effects of mutations often depend on ecological context, making the distribution of effects across multiple environments essential to understanding the true nature of beneficial mutations. Studies that address both the genetic basis and ecological consequences of adaptive mutations remain rare. Here, we characterize the direct and pleiotropic fitness effects of a collection of 21 first-step beneficial mutants derived from naïve and adapted genotypes used in a long-term experimental evolution of Escherichia coli. Whole-genome sequencing was able to identify the majority of beneficial mutations. In contrast to previous studies, we find diverse fitness effects of mutations selected in a simple environment and few cases of genetic parallelism. The pleiotropic effects of these mutations were predominantly positive but some mutants were highly antagonistic in alternative environments. Further, the fitness effects of mutations derived from the adapted genotypes were dramatically reduced in nearly all environments. These findings suggest that many beneficial variants are accessible from a single point on the fitness landscape, and the fixation of alternative beneficial mutations may have dramatic consequences for niche breadth reduction via metabolic erosion.

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.

The rule of declining adaptability in microbial evolution experiments

One of the most recurrent observations after two decades of microbial evolution experiments regards the dynamics of fitness change. In a given environment, low-fitness genotypes are recurrently observed to adapt faster than their more fit counterparts. Since adaptation is the main macroscopic outcome of Darwinian evolution, studying its patterns of change could potentially provide insight into key issues of evolutionary theory, from fixation dynamics to the genetic architecture of organisms. Here, we re-analyze several published datasets from experimental evolution with microbes and show that, despite large differences in the origin of the data, a pattern of inverse dependence of adaptability with fitness clearly emerges. In quantitative terms, it is remarkable to observe little if any degree of idiosyncrasy across systems as diverse as virus, bacteria and yeast. The universality of this phenomenon suggests that its emergence might be understood from general principles, giving rise to the exciting prospect that evolution might be statistically predictable at the macroscopic level. We discuss these possibilities in the light of the various theories of adaptation that have been proposed and delineate future directions of research.

The Utility of Fisher's Geometric Model in Evolutionary Genetics

The accumulation of data on the genomic bases of adaptation has triggered renewed interest in theoretical models of adaptation. Among these models, Fisher Geometric Model (FGM) has received a lot of attention over the last two decades. FGM is based on a continuous multidimensional phenotypic landscape, but it is for the emerging properties of individual mutation effects that it is mostly used. Despite an apparent simplicity and a limited number of parameters, FGM integrates a full model of mutation and epistatic interactions that allows the study of both beneficial and deleterious mutations, and subsequently the fate of evolving populations. In this review, I present the different properties of FGM and the qualitative and quantitative support they have received from experimental evolution data. I later discuss how to estimate the different parameters of the model and outline some future directions to connect FGM and the molecular determinants of adaptation.

The probability of improvement in Fisher's geometric model: a probabilistic approach

Fisher developed his geometric model to support the micro-mutationalism hypothesis which claims that small mutations are more likely to be beneficial and therefore to contribute to evolution and adaptation. While others have provided a general solution to the model using geometric approaches, we derive an equivalent general solution using a probabilistic approach. Our approach to Fisher's geometric model provides alternative intuition and interpretation of the solution in terms of the model's parameters: for mutation to improve a phenotype, its relative beneficial effect must be larger than the ratio of its total effect and twice the difference between the current phenotype and the optimal one. Our approach provides new insight into this classical model of adaptive evolution.