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.

Drift on holey landscapes as a dominant evolutionary process

An organism's phenotype has been shaped by evolution but the specific processes have to be indirectly inferred for most species. For example, correlations among traits imply the historical action of correlated selection and, more generally, the expression and distribution of traits is expected to be reflective of the adaptive landscapes that have shaped a population. However, our expectations about how quantitative traits-like most behaviors, physiological processes, and life-history traits-should be distributed under different evolutionary processes are not clear. Here, we show that genetic variation in quantitative traits is not distributed as would be expected under dominant evolutionary models. Instead, we found that genetic variation in quantitative traits across six phyla and 60 species (including both Plantae and Animalia) is consistent with evolution across high-dimensional "holey landscapes." This suggests that the leading conceptualizations and modeling of the evolution of trait integration fail to capture how phenotypes are shaped and that traits are integrated in a manner contrary to predictions of dominant evolutionary theory. Our results demonstrate that our understanding of how evolution has shaped phenotypes remains incomplete and these results provide a starting point for reassessing the relevance of existing evolutionary models.

Fully accessible fitness landscape of oncogene-negative lung adenocarcinoma

Cancer genomes are almost invariably complex with genomic alterations cooperating during each step of carcinogenesis. In cancers that lack a single dominant oncogene mutation, cooperation between the inactivation of multiple tumor suppressor genes can drive tumor initiation and growth. Here, we shed light on how the sequential acquisition of genomic alterations generates oncogene-negative lung tumors. We couple tumor barcoding with combinatorial and multiplexed somatic genome editing to characterize the fitness landscapes of three tumor suppressor genes NF1, RASA1, and PTEN, the inactivation of which jointly drives oncogene-negative lung adenocarcinoma initiation and growth. The fitness landscape was surprisingly accessible, with each additional mutation leading to growth advantage. Furthermore, the fitness landscapes remained fully accessible across backgrounds with the inactivation of additional tumor suppressor genes. These results suggest that while predicting cancer evolution will be challenging, acquiring the multiple alterations that drive the growth of oncogene-negative tumors can be facilitated by the lack of constraints on mutational order.

Graph 'texture' features as novel metrics that can summarize complex biological graphs

Objective.Image texture features, such as those derived by Haralicket al, are a powerful metric for image classification and are used across fields including cancer research. Our aim is to demonstrate how analogous texture features can be derived for graphs and networks. We also aim to illustrate how these new metrics summarize graphs, may aid comparative graph studies, may help classify biological graphs, and might assist in detecting dysregulation in cancer.Approach.We generate the first analogies of image texture for graphs and networks. Co-occurrence matrices for graphs are generated by summing over all pairs of neighboring nodes in the graph. We generate metrics for fitness landscapes, gene co-expression and regulatory networks, and protein interaction networks. To assess metric sensitivity we varied discretization parameters and noise. To examine these metrics in the cancer context we compare metrics for both simulated and publicly available experimental gene expression and build random forest classifiers for cancer cell lineage.Main results.Our novel graph 'texture' features are shown to be informative of graph structure and node label distributions. The metrics are sensitive to discretization parameters and noise in node labels. We demonstrate that graph texture features vary across different biological graph topologies and node labelings. We show how our texture metrics can be used to classify cell line expression by lineage, demonstrating classifiers with 82% and 89% accuracy.Significance.New metrics provide opportunities for better comparative analyzes and new models for classification. Our texture features are novel second-order graph features for networks or graphs with ordered node labels. In the complex cancer informatics setting, evolutionary analyses and drug response prediction are two examples where new network science approaches like this may prove fruitful.

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’.

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’.

The community-function landscape of microbial consortia

Quantitatively linking the composition and function of microbial communities is a major aspiration of microbial ecology. Microbial community functions emerge from a complex web of molecular interactions between cells, which give rise to population-level interactions among strains and species. Incorporating this complexity into predictive models is highly challenging. Inspired by a similar problem in genetics of predicting quantitative phenotypes from genotypes, an ecological community-function (or structure-function) landscape could be defined that maps community composition and function. In this piece, we present an overview of our current understanding of these community landscapes, their uses, limitations, and open questions. We argue that exploiting the parallels between both landscapes could bring powerful predictive methodologies from evolution and genetics into ecology, providing a boost to our ability to engineer and optimize microbial consortia.

How development affects evolution

Natural selection acts on developmentally constructed phenotypes, but how does development affect evolution? This question prompts a simultaneous consideration of development and evolution. However, there has been a lack of general mathematical frameworks mechanistically integrating the two, which may have inhibited progress on the question. Here, we use a new mathematical framework that mechanistically integrates development into evolution to analyse how development affects evolution. We show that, while selection pushes genotypic and phenotypic evolution up the fitness landscape, development determines the admissible evolutionary pathway, such that evolutionary outcomes occur at path peaks rather than landscape peaks. Changes in development can generate path peaks, triggering genotypic or phenotypic diversification, even on constant, single-peak landscapes. Phenotypic plasticity, niche construction, extra-genetic inheritance, and developmental bias alter the evolutionary path and hence the outcome. Thus, extra-genetic inheritance can have permanent evolutionary effects by changing the developmental constraints, even if extra-genetically acquired elements are not transmitted to future generations. Selective development, whereby phenotype construction points in the adaptive direction, may induce adaptive or maladaptive evolution depending on the developmental constraints. Moreover, developmental propagation of phenotypic effects over age enables the evolution of negative senescence. Overall, we find that development plays a major evolutionary role.

Crossing the valley of non-intimidating conspicuousness: evolution of warning coloration through the lens of fitness landscapes

The initial evolution of conspicuous aposematism is a longstanding evolutionary paradox: while the benefits of conspicuousness in aposematic signals have been demonstrated, they rely on predators being familiar with the conspicuous signals and avoiding them. In a system dominated by naïve predators, the appearance of conspicuousness would be expected to increase detection and attack rate by the predators. Hence, it is unclear how such signals could become established in a naïve community. We suggest that this problem may usefully be framed in the terms of fitness landscapes, an idea used for conceptualizing the mapping between genotype/phenotype and fitness. The evolution of conspicuousness can be thought of as a special case of valley crossing, which concerns the transition of populations between fitness peaks, when such a transition imposes an initial decrease in fitness. Crypsis may be regarded as a local fitness peak, hindering predators' ability to detect prey; for an unpalatable species, conspicuous aposematism may constitute a higher-still fitness peak, preventing predation attempts altogether and allowing access to niches unavailable to species encumbered by the necessity to remain concealed from predators. However, in order to reach this higher peak, the population must first cross the valley of non-intimidating conspicuousness, in which the prey is conspicuous but the predators are not yet deterred. Using terms borrowed from the concept of fitness landscapes, we categorize several solutions suggested previously in the literature as either concerning changes in the fitness landscape or as illuminating possible ridges connecting the two peaks, which emerge from unconsidered dimensions of the fitness landscape. We suggest that considering this question through the lens of fitness landscapes not only facilitates useful categorization of previously suggested solutions but may also prove useful for thinking about novel ones.

A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and "ruggedness". As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population's evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.

The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and while it is known to slow down the rate of adaptation (when compared to the strong-selection, weak-mutation model with the same parameters), how it affects the shape of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the shape of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the rescaled fitness trajectory (where adaptation speed is measured relative to its value at the start of the experiment), while an enhancement of the beneficial mutation rate does the opposite of slowing it down. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs change in fraction of beneficial mutations).

Modeling sequence-space exploration and emergence of epistatic signals in protein evolution

During their evolution, proteins explore sequence space via an interplay between random mutations and phenotypic selection. Here, we build upon recent progress in reconstructing data-driven fitness landscapes for families of homologous proteins, to propose stochastic models of experimental protein evolution. These models predict quantitatively important features of experimentally evolved sequence libraries, like fitness distributions and position-specific mutational spectra. They also allow us to efficiently simulate sequence libraries for a vast array of combinations of experimental parameters like sequence divergence, selection strength, and library size. We showcase the potential of the approach in reanalyzing two recent experiments to determine protein structure from signals of epistasis emerging in experimental sequence libraries. To be detectable, these signals require sufficiently large and sufficiently diverged libraries. Our modeling framework offers a quantitative explanation for different outcomes of recently published experiments. Furthermore, we can forecast the outcome of time- and resource-intensive evolution experiments, opening thereby a way to computationally optimize experimental protocols.

Systematic dissection of σ70 sequence diversity and function in bacteria

Primary σ⁷⁰ factors are key conserved bacterial regulatory proteins that interact with regulatory DNA to control gene expression. It is, however, poorly understood whether σ⁷⁰ sequence diversity in different bacteria reflects functional differences. Here, we employ comparative and functional genomics to explore the sequence and function relationship of primary σ⁷⁰. Using multiplex automated genome engineering and deep sequencing (MAGE-seq), we generate a saturation mutagenesis library and high-resolution fitness map of E. coli σ⁷⁰ in domains 2-4. Mapping natural σ⁷⁰ sequence diversity to the E. coli σ⁷⁰ fitness landscape reveals significant predicted fitness deficits across σ⁷⁰ orthologs. Interestingly, these predicted deficits are larger than observed fitness changes for 15 σ⁷⁰ orthologs introduced into E. coli. Finally, we use a multiplexed transcriptional reporter assay and RNA sequencing (RNA-seq) to explore functional differences of several σ⁷⁰ orthologs. This work provides an in-depth analysis of σ⁷⁰ sequence and function to improve efforts to understand the evolution and engineering potential of this global regulator.

Evolution in the weak-mutation limit: Stasis periods punctuated by fast transitions between saddle points on the fitness landscape

The gradual character of evolution is a key feature of the Darwinian worldview. However, macroevolutionary events are often thought to occur in a nongradualist manner, in a regime known as punctuated equilibrium, whereby extended periods of evolutionary stasis are punctuated by rapid transitions between states. Here we analyze a simple mathematical model of population evolution on fitness landscapes and show that, for a large population in the weak-mutation limit, the process of adaptive evolution consists of extended periods of stasis, which the population spends around saddle points on the landscape, interrupted by rapid transitions to new saddle points when a beneficial mutation is fixed. Thus, phenomenologically, the default regime of biological evolution seems to closely resemble punctuated equilibrium.

A mathematical analysis of the evolution of a large population under the weak-mutation limit shows that such a population would spend most of the time in stasis in the vicinity of saddle points on the fitness landscape. The periods of stasis are punctuated by fast transitions, in lnN_e/s time (N_e, effective population size; s, selection coefficient of a mutation), when a new beneficial mutation is fixed in the evolving population, which accordingly moves to a different saddle, or on much rarer occasions from a saddle to a local peak. Phenomenologically, this mode of evolution of a large population resembles punctuated equilibrium (PE) whereby phenotypic changes occur in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but the phenotype does not change substantially. Theoretically, PE has been linked to self-organized criticality (SOC), a model in which the size of “avalanches” in an evolving system is power-law-distributed, resulting in increasing rarity of major events. Here we show, however, that a PE-like evolutionary regime is the default for a very simple model of an evolving population that does not rely on SOC or any other special conditions.

Efficient inference, potential, and limitations of site-specific substitution models

Natural selection imposes a complex filter on which variants persist in a population resulting in evolutionary patterns that vary greatly along the genome. Some sites evolve close to neutrally, while others are highly conserved, allow only specific states, or only change in concert with other sites. On one hand, such constraints on sequence evolution can be to infer biological function, one the other hand they need to be accounted for in phylogenetic reconstruction. Phylogenetic models often account for this complexity by partitioning sites into a small number of discrete classes with different rates and/or state preferences. Appropriate model complexity is typically determined by model selection procedures. Here, we present an efficient algorithm to estimate more complex models that allow for different preferences at every site and explore the accuracy at which such models can be estimated from simulated data. Our iterative approximate maximum likelihood scheme uses information in the data efficiently and accurately estimates site-specific preferences from large data sets with moderately diverged sequences and known topology. However, the joint estimation of site-specific rates, and site-specific preferences, and phylogenetic branch length can suffer from identifiability problems, while ignoring variation in preferences across sites results in branch length underestimates. Site-specific preferences estimated from large HIV pol alignments show qualitative concordance with intra-host estimates of fitness costs. Analysis of these substitution models suggests near saturation of divergence after a few hundred years. Such saturation can explain the inability to infer deep divergence times of HIV and SIVs using molecular clock approaches and time-dependent rate estimates.

Inferring Future Landscapes: Sampling the Local Optima Level

Connection patterns among Local Optima Networks (LONs) can inform heuristic design for optimisation. LON research has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON sampling algorithms are therefore important. In this article, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Using machine learning, we use estimated LON features to predict search performance for competitive heuristics used in the QAP domain. The results show that by using random forest regression, LON construction algorithms produce fitness landscape features which can explain almost all search variance. We find that LON samples better relate to search than enumerated LONs do. The importance of fitness levels of sampled LONs in search predictions is crystallised. Features from LONs produced by different algorithms are combined in predictions for the first time, with promising results for this "super-sampling": a model to predict tabu search success explained 99% of variance. Arguments are made for the use-case of each LON algorithm and for combining the exploitative process of one with the exploratory optimisation of the other.

Molecular Biology and Evolution of Cancer: From Discovery to Action

Cancer progression is an evolutionary process. During this process, evolving cancer cell populations encounter restrictive ecological niches within the body, such as the primary tumor, circulatory system, and diverse metastatic sites. Efforts to prevent or delay cancer evolution-and progression-require a deep understanding of the underlying molecular evolutionary processes. Herein we discuss a suite of concepts and tools from evolutionary and ecological theory that can inform cancer biology in new and meaningful ways. We also highlight current challenges to applying these concepts, and propose ways in which incorporating these concepts could identify new therapeutic modes and vulnerabilities in cancer.

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.

Fitness Effects of Single Amino Acid Insertions and Deletions in TEM-1 β-Lactamase

Short insertions and deletions (InDels) are a common type of mutation found in nature and a useful source of variation in protein engineering. InDel events have important consequences in protein evolution, often opening new pathways for adaptation. However, much less is known about the effects of InDels compared to point mutations and amino acid substitutions. In particular, deep mutagenesis studies on the distribution of fitness effects of mutations have focused almost exclusively on amino acid substitutions. Here, we present a near-comprehensive analysis of the fitness effects of single amino acid InDels in TEM-1 β-lactamase. While we found InDels to be largely deleterious, partially overlapping deletion-tolerant and insertion-tolerant regions were observed throughout the protein, especially in unstructured regions and at the end of helices. The signal sequence of TEM-1 tolerated InDels more than the mature protein. Most regions of the protein tolerated insertions more than deletions, but a few regions tolerated deletions more than insertions. We examined the relationship between InDel tolerance and a variety of measures to help understand its origin. These measures included evolutionary variation in β-lactamases, secondary structure identity, tolerance to amino acid substitutions, solvent accessibility, and side-chain weighted contact number. We found secondary structure, weighted contact number, and evolutionary variation in class A beta-lactamases to be the somewhat predictive of InDel fitness effects.

Pervasive Pairwise Intragenic Epistasis among Sequential Mutations in TEM-1 β-Lactamase

Interactions between mutations play a central role in shaping the fitness landscape, but a clear picture of intragenic epistasis has yet to emerge. To further reveal the prevalence and patterns of intragenic epistasis, we present a survey of epistatic interactions between sequential mutations in TEM-1 β-lactamase. We measured the fitness effect of ~12,000 pairs of consecutive amino acid substitutions and used our previous study of the fitness effects of single amino acid substitutions to calculate epistasis for over 8000 mutation pairs. Since sequential mutations are prone to physically interact, we postulated that our study would be surveying specific epistasis instead of nonspecific epistasis. We found widespread negative epistasis, especially in beta-strands, and a high frequency of negative sign epistasis among individually beneficial mutations. Negative epistasis (52%) occurred 7.6 times as frequently as positive epistasis (6.8%). Buried residues experienced more negative epistasis that surface-exposed residues. However, TEM-1 exhibited a couple of hotspots for positive epistasis, most notably L221/ R222 at which many combinations of mutations positively interacted. This study is the first to systematically examine pairwise epistasis throughout an entire protein performing its native function in its native host.

Computational Complexity as an Ultimate Constraint on Evolution

Experiments show that evolutionary fitness landscapes can have a rich combinatorial structure due to epistasis. For some landscapes, this structure can produce a computational constraint that prevents evolution from finding local fitness optima-thus overturning the traditional assumption that local fitness peaks can always be reached quickly if no other evolutionary forces challenge natural selection. Here, I introduce a distinction between easy landscapes of traditional theory where local fitness peaks can be found in a moderate number of steps, and hard landscapes where finding local optima requires an infeasible amount of time. Hard examples exist even among landscapes with no reciprocal sign epistasis; on these semismooth fitness landscapes, strong selection weak mutation dynamics cannot find the unique peak in polynomial time. More generally, on hard rugged fitness landscapes that include reciprocal sign epistasis, no evolutionary dynamics-even ones that do not follow adaptive paths-can find a local fitness optimum quickly. Moreover, on hard landscapes, the fitness advantage of nearby mutants cannot drop off exponentially fast but has to follow a power-law that long-term evolution experiments have associated with unbounded growth in fitness. Thus, the constraint of computational complexity enables open-ended evolution on finite landscapes. Knowing this constraint allows us to use the tools of theoretical computer science and combinatorial optimization to characterize the fitness landscapes that we expect to see in nature. I present candidates for hard landscapes at scales from single genes, to microbes, to complex organisms with costly learning (Baldwin effect) or maintained cooperation (Hankshaw effect). Just how ubiquitous hard landscapes (and the corresponding ultimate constraint on evolution) are in nature becomes an open empirical question.

On the deformability of an empirical fitness landscape by microbial evolution

A fitness landscape is a map between the genotype and its reproductive success in a given environment. The topography of fitness landscapes largely governs adaptive dynamics, constraining evolutionary trajectories and the predictability of evolution. Theory suggests that this topography can be deformed by mutations that produce substantial changes to the environment. Despite its importance, the deformability of fitness landscapes has not been systematically studied beyond abstract models, and little is known about its reach and consequences in empirical systems. Here we have systematically characterized the deformability of the genome-wide metabolic fitness landscape of the bacterium Escherichia coli Deformability is quantified by the noncommutativity of epistatic interactions, which we experimentally demonstrate in mutant strains on the path to an evolutionary innovation. Our analysis shows that the deformation of fitness landscapes by metabolic mutations rarely affects evolutionary trajectories in the short range. However, mutations with large environmental effects produce long-range landscape deformations in distant regions of the genotype space that affect the fitness of later descendants. Our results therefore suggest that, even in situations in which mutations have strong environmental effects, fitness landscapes may retain their power to forecast evolution over small mutational distances despite the potential attenuation of that power over longer evolutionary trajectories. Our methods and results provide an avenue for integrating adaptive and eco-evolutionary dynamics with complex genetics and genomics.

Local Fitness Landscapes Predict Yeast Evolutionary Dynamics in Directionally Changing Environments

The fitness landscape is a concept that is widely used for understanding and predicting evolutionary adaptation. The topography of the fitness landscape depends critically on the environment, with potentially far-reaching consequences for evolution under changing conditions. However, few studies have assessed directly how empirical fitness landscapes change across conditions, or validated the predicted consequences of such change. We previously evolved replicate yeast populations in the presence of either gradually increasing, or constant high, concentrations of the heavy metals cadmium (Cd), nickel (Ni), and zinc (Zn), and analyzed their phenotypic and genomic changes. Here, we reconstructed the local fitness landscapes underlying adaptation to each metal by deleting all repeatedly mutated genes both by themselves and in combination. Fitness assays revealed that the height, and/or shape, of each local fitness landscape changed considerably across metal concentrations, with distinct qualitative differences between unconditionally (Cd) and conditionally toxic metals (Ni and Zn). This change in topography had particularly crucial consequences in the case of Ni, where a substantial part of the individual mutational fitness effects changed in sign across concentrations. Based on the Ni landscape analyses, we made several predictions about which mutations had been selected when during the evolution experiment. Deep sequencing of population samples from different time points generally confirmed these predictions, demonstrating the power of landscape reconstruction analyses for understanding and ultimately predicting evolutionary dynamics, even under complex scenarios of environmental change.

Comparative Analyses of Phenotypic Trait Covariation within and among Populations

Many morphological, behavioral, physiological, and life-history traits covary across the biological scales of individuals, populations, and species. However, the processes that cause traits to covary also change over these scales, challenging our ability to use patterns of trait covariance to infer process. Trait relationships are also widely assumed to have generic functional relationships with similar evolutionary potentials, and even though many different trait relationships are now identified, there is little appreciation that these may influence trait covariation and evolution in unique ways. We use a trait-performance-fitness framework to classify and organize trait relationships into three general classes, address which ones more likely generate trait covariation among individuals in a population, and review how selection shapes phenotypic covariation. We generate predictions about how trait covariance changes within and among populations as a result of trait relationships and in response to selection and consider how these can be tested with comparative data. Careful comparisons of covariation patterns can narrow the set of hypothesized processes that cause trait covariation when the form of the trait relationship and how it responds to selection yield clear predictions about patterns of trait covariation. We discuss the opportunities and limitations of comparative approaches to evaluate hypotheses about the evolutionary causes and consequences of trait covariation and highlight the importance of evaluating patterns within populations replicated in the same and in different selective environments. Explicit hypotheses about trait relationships are key to generating effective predictions about phenotype and its evolution using covariance data.

Specificity Effects of Amino Acid Substitutions in Promiscuous Hydrolases: Context-Dependence of Catalytic Residue Contributions to Local Fitness Landscapes in Nearby Sequence Space

Catalytic promiscuity can facilitate evolution of enzyme functions-a multifunctional catalyst may act as a springboard for efficient functional adaptation. We test the effect of single mutations on multiple activities in two groups of promiscuous AP superfamily members to probe this hypothesis. We quantify the effect of site-saturating mutagenesis of an analogous, nucleophile-flanking residue in two superfamily members: an arylsulfatase (AS) and a phosphonate monoester hydrolase (PMH). Statistical analysis suggests that no one physicochemical characteristic alone explains the mutational effects. Instead, these effects appear to be dominated by their structural context. Likewise, the effect of changing the catalytic nucleophile itself is not reaction-type-specific. Mapping of "fitness landscapes" of four activities onto the possible variation of a chosen sequence position revealed tremendous potential for respecialization of AP superfamily members through single-point mutations, highlighting catalytic promiscuity as a powerful predictor of adaptive potential.

Trade-offs between enzyme fitness and solubility illuminated by deep mutational scanning

Proteins are marginally stable, and an understanding of the sequence determinants for improved protein solubility is highly desired. For enzymes, it is well known that many mutations that increase protein solubility decrease catalytic activity. These competing effects frustrate efforts to design and engineer stable, active enzymes without laborious high-throughput activity screens. To address the trade-off between enzyme solubility and activity, we performed deep mutational scanning using two different screens/selections that purport to gauge protein solubility for two full-length enzymes. We assayed a TEM-1 beta-lactamase variant and levoglucosan kinase (LGK) using yeast surface display (YSD) screening and a twin-arginine translocation pathway selection. We then compared these scans with published experimental fitness landscapes. Results from the YSD screen could explain 37% of the variance in the fitness landscapes for one enzyme. Five percent to 10% of all single missense mutations improve solubility, matching theoretical predictions of global protein stability. For a given solubility-enhancing mutation, the probability that it would retain wild-type fitness was correlated with evolutionary conservation and distance to active site, and anticorrelated with contact number. Hybrid classification models were developed that could predict solubility-enhancing mutations that maintain wild-type fitness with an accuracy of 90%. The downside of using such classification models is the removal of rare mutations that improve both fitness and solubility. To reveal the biophysical basis of enhanced protein solubility and function, we determined the crystallographic structure of one such LGK mutant. Beyond fundamental insights into trade-offs between stability and activity, these results have potential biotechnological applications.

How Good Are Statistical Models at Approximating Complex Fitness Landscapes?

Fitness landscapes determine the course of adaptation by constraining and shaping evolutionary trajectories. Knowledge of the structure of a fitness landscape can thus predict evolutionary outcomes. Empirical fitness landscapes, however, have so far only offered limited insight into real-world questions, as the high dimensionality of sequence spaces makes it impossible to exhaustively measure the fitness of all variants of biologically meaningful sequences. We must therefore revert to statistical descriptions of fitness landscapes that are based on a sparse sample of fitness measurements. It remains unclear, however, how much data are required for such statistical descriptions to be useful. Here, we assess the ability of regression models accounting for single and pairwise mutations to correctly approximate a complex quasi-empirical fitness landscape. We compare approximations based on various sampling regimes of an RNA landscape and find that the sampling regime strongly influences the quality of the regression. On the one hand it is generally impossible to generate sufficient samples to achieve a good approximation of the complete fitness landscape, and on the other hand systematic sampling schemes can only provide a good description of the immediate neighborhood of a sequence of interest. Nevertheless, we obtain a remarkably good and unbiased fit to the local landscape when using sequences from a population that has evolved under strong selection. Thus, current statistical methods can provide a good approximation to the landscape of naturally evolving populations.

Tunably Rugged Landscapes With Known Maximum and Minimum

We propose NM landscapes as a new class of tunably rugged benchmark problems. NM landscapes are well defined on alphabets of any arity, including both discrete and real-valued alphabets, include epistasis in a natural and transparent manner, are proven to have known value and location of the global maximum and, with some additional constraints, are proven to also have a known global minimum. Empirical studies are used to illustrate that, when coefficients are selected from a recommended distribution, the ruggedness of NM landscapes is smoothly tunable and correlates with several measures of search difficulty. We discuss why these properties make NM landscapes preferable to both NK landscapes and Walsh polynomials as benchmark landscape models with tunable epistasis.

Biophysical principles predict fitness landscapes of drug resistance

Fitness landscapes of drug resistance constitute powerful tools to elucidate mutational pathways of antibiotic escape. Here, we developed a predictive biophysics-based fitness landscape of trimethoprim (TMP) resistance for Escherichia coli dihydrofolate reductase (DHFR). We investigated the activity, binding, folding stability, and intracellular abundance for a complete set of combinatorial DHFR mutants made out of three key resistance mutations and extended this analysis to DHFR originated from Chlamydia muridarum and Listeria grayi We found that the acquisition of TMP resistance via decreased drug affinity is limited by a trade-off in catalytic efficiency. Protein stability is concurrently affected by the resistant mutants, which precludes a precise description of fitness from a single molecular trait. Application of the kinetic flux theory provided an accurate model to predict resistance phenotypes (IC50) quantitatively from a unique combination of the in vitro protein molecular properties. Further, we found that a controlled modulation of the GroEL/ES chaperonins and Lon protease levels affects the intracellular steady-state concentration of DHFR in a mutation-specific manner, whereas IC50 is changed proportionally, as indeed predicted by the model. This unveils a molecular rationale for the pleiotropic role of the protein quality control machinery on the evolution of antibiotic resistance, which, as we illustrate here, may drastically confound the evolutionary outcome. These results provide a comprehensive quantitative genotype-phenotype map for the essential enzyme that serves as an important target of antibiotic and anticancer therapies.

Identifying Features of Fitness Landscapes and Relating Them to Problem Difficulty

Complex combinatorial problems are most often optimised with heuristic solvers, which usually deliver acceptable results without any indication of the quality obtained. Recently, predictive diagnostic optimisation was proposed as a means of characterising the fitness landscape while optimising a combinatorial problem. The scalars produced by predictive diagnostic optimisation appear to describe the difficulty of the problem with relative reliability. In this study, we record more scalars that may be helpful in determining problem difficulty during the optimisation process and analyse these in combination with other well-known landscape descriptors by using exploratory factor analysis on four landscapes that arise from different search operators, applied to a varied set of quadratic assignment problem instances. Factors are designed to capture properties by combining the collinear variances of several variables. The extracted factors can be interpreted as the features of landscapes detected by the variables, but disappoint in their weak correlations with the result quality achieved by the optimiser, which we regard as the most reliable indicator of difficulty available. It appears that only the prediction error of predictive diagnostic optimisation has a strong correlation with the quality of the results produced, followed by a medium correlation of the fitness distance correlation of the local optima.

Population genomics of intrapatient HIV-1 evolution

Many microbial populations rapidly adapt to changing environments with multiple variants competing for survival. To quantify such complex evolutionary dynamics in vivo, time resolved and genome wide data including rare variants are essential. We performed whole-genome deep sequencing of HIV-1 populations in 9 untreated patients, with 6-12 longitudinal samples per patient spanning 5-8 years of infection. The data can be accessed and explored via an interactive web application. We show that patterns of minor diversity are reproducible between patients and mirror global HIV-1 diversity, suggesting a universal landscape of fitness costs that control diversity. Reversions towards the ancestral HIV-1 sequence are observed throughout infection and account for almost one third of all sequence changes. Reversion rates depend strongly on conservation. Frequent recombination limits linkage disequilibrium to about 100 bp in most of the genome, but strong hitch-hiking due to short range linkage limits diversity.

Collective behaviour, uncertainty and environmental change

A central aspect of cultural evolutionary theory concerns how human groups respond to environmental change. Although we are painting with a broad brush, it is fair to say that prior to the twenty-first century, adaptation often happened gradually over multiple human generations, through a combination of individual and social learning, cumulative cultural evolution and demographic shifts. The result was a generally resilient and sustainable population. In the twenty-first century, however, considerable change happens within small portions of a human generation, on a vastly larger range of geographical and population scales and involving a greater degree of horizontal learning. As a way of gauging the complexity of societal response to environmental change in a globalized future, we discuss several theoretical tools for understanding how human groups adapt to uncertainty. We use our analysis to estimate the limits of predictability of future societal change, in the belief that knowing when to hedge bets is better than relying on a false sense of predictability.

Metabolism at evolutionary optimal States

Metabolism is generally required for cellular maintenance and for the generation of offspring under conditions that support growth. The rates, yields (efficiencies), adaptation time and robustness of metabolism are therefore key determinants of cellular fitness. For biotechnological applications and our understanding of the evolution of metabolism, it is necessary to figure out how the functional system properties of metabolism can be optimized, via adjustments of the kinetics and expression of enzymes, and by rewiring metabolism. The trade-offs that can occur during such optimizations then indicate fundamental limits to evolutionary innovations and bioengineering. In this paper, we review several theoretical and experimental findings about mechanisms for metabolic optimization.

Protein folding and binding can emerge as evolutionary spandrels through structural coupling

Binding interactions between proteins and other molecules mediate numerous cellular processes, including metabolism, signaling, and gene regulation. These interactions often evolve in response to changes in the protein's chemical or physical environment (such as the addition of an antibiotic). Several recent studies have shown the importance of folding stability in constraining protein evolution. Here we investigate how structural coupling between folding and binding--the fact that most proteins can only bind their targets when folded--gives rise to an evolutionary coupling between the traits of folding stability and binding strength. Using a biophysical and evolutionary model, we show how these protein traits can emerge as evolutionary "spandrels" even if they do not confer an intrinsic fitness advantage. In particular, proteins can evolve strong binding interactions that have no functional role but merely serve to stabilize the protein if its misfolding is deleterious. Furthermore, such proteins may have divergent fates, evolving to bind or not bind their targets depending on random mutational events. These observations may explain the abundance of apparently nonfunctional interactions among proteins observed in high-throughput assays. In contrast, for proteins with both functional binding and deleterious misfolding, evolution may be highly predictable at the level of biophysical traits: adaptive paths are tightly constrained to first gain extra folding stability and then partially lose it as the new binding function is developed. These findings have important consequences for our understanding of how natural and engineered proteins evolve under selective pressure.

A framework for inferring fitness landscapes of patient-derived viruses using quasispecies theory

Fitness is a central quantity in evolutionary models of viruses. However, it remains difficult to determine viral fitness experimentally, and existing in vitro assays can be poor predictors of in vivo fitness of viral populations within their hosts. Next-generation sequencing can nowadays provide snapshots of evolving virus populations, and these data offer new opportunities for inferring viral fitness. Using the equilibrium distribution of the quasispecies model, an established model of intrahost viral evolution, we linked fitness parameters to the composition of the virus population, which can be estimated by next-generation sequencing. For inference, we developed a Bayesian Markov chain Monte Carlo method to sample from the posterior distribution of fitness values. The sampler can overcome situations where no maximum-likelihood estimator exists, and it can adaptively learn the posterior distribution of highly correlated fitness landscapes without prior knowledge of their shape. We tested our approach on simulated data and applied it to clinical human immunodeficiency virus 1 samples to estimate their fitness landscapes in vivo. The posterior fitness distributions allowed for differentiating viral haplotypes from each other, for determining neutral haplotype networks, in which no haplotype is more or less credibly fit than any other, and for detecting epistasis in fitness landscapes. Our implemented approach, called QuasiFit, is available at http://www.cbg.ethz.ch/software/quasifit.

A systematic survey of an intragenic epistatic landscape

Mutations are the source of evolutionary variation. The interactions of multiple mutations can have important effects on fitness and evolutionary trajectories. We have recently described the distribution of fitness effects of all single mutations for a nine-amino-acid region of yeast Hsp90 (Hsp82) implicated in substrate binding. Here, we report and discuss the distribution of intragenic epistatic effects within this region in seven Hsp90 point mutant backgrounds of neutral to slightly deleterious effect, resulting in an analysis of more than 1,000 double mutants. We find negative epistasis between substitutions to be common, and positive epistasis to be rare--resulting in a pattern that indicates a drastic change in the distribution of fitness effects one step away from the wild type. This can be well explained by a concave relationship between phenotype and genotype (i.e., a concave shape of the local fitness landscape), suggesting mutational robustness intrinsic to the local sequence space. Structural analyses indicate that, in this region, epistatic effects are most pronounced when a solvent-inaccessible position is involved in the interaction. In contrast, all 18 observations of positive epistasis involved at least one mutation at a solvent-exposed position. By combining the analysis of evolutionary and biophysical properties of an epistatic landscape, these results contribute to a more detailed understanding of the complexity of protein evolution.

Adaptation in tunably rugged fitness landscapes: the rough Mount Fuji model

Much of the current theory of adaptation is based on Gillespie's mutational landscape model (MLM), which assumes that the fitness values of genotypes linked by single mutational steps are independent random variables. On the other hand, a growing body of empirical evidence shows that real fitness landscapes, while possessing a considerable amount of ruggedness, are smoother than predicted by the MLM. In the present article we propose and analyze a simple fitness landscape model with tunable ruggedness based on the rough Mount Fuji (RMF) model originally introduced by Aita et al. in the context of protein evolution. We provide a comprehensive collection of results pertaining to the topographical structure of RMF landscapes, including explicit formulas for the expected number of local fitness maxima, the location of the global peak, and the fitness correlation function. The statistics of single and multiple adaptive steps on the RMF landscape are explored mainly through simulations, and the results are compared to the known behavior in the MLM model. Finally, we show that the RMF model can explain the large number of second-step mutations observed on a highly fit first-step background in a recent evolution experiment with a microvirid bacteriophage.

Fitness landscape of sympatric pupfishes a useful tool for visualizing speciation

Arguably the most useful model of evolution emerged from the mind of Sewall Wright when he invented the fitness landscape (Wright 1932). In a recent issue of Molecular Ecology, Martin & Feinstein (2014) investigate the genetics and demographic history of an adaptive radiation of pupfish on San Salvador Island. Since the founder species colonized the island 10,000 years ago, two descendent species have appeared and in several lakes all three species (a durophage, a scale-eater, and the generalist ancestral form) coexist. The three species are thought to occupy three distinct fitness peaks. The durophage and generalists' peaks are close, whereas the scale-eater's peak is predicted to be distant and separated from the other two by a deep valley. Consistent with this view, gene flow between the two species on close fitness peaks is greater than the gene flow between these two species and the third species on a more distant peak. Correspondingly, the inferred fitness landscape predicts progress towards speciation, with more limited separation of species on close peaks, and that speciation is more complete for the scale-eater. The article provides an illustrative example of the power afforded by analysis of large numbers of SNPs for estimating key parameters underlying evolutionary divergence.

The genetics of speciation: are complex incompatibilities easier to evolve?

Reproductive isolation can evolve readily when genotypes containing incompatible alleles are connected by chains of fit intermediates. Experimental crosses show that such Dobzhansky-Muller incompatibilities (DMIs) are often complex (involving alleles at three or more loci) and asymmetrical (such that reciprocal introgressions have very different effects on fitness). One possible explanation is that asymmetrical and complex DMIs are 'easier to evolve', because they block fewer of the possible evolutionary paths between the parental genotypes. To assess this argument, we model evolutionary divergence in allopatry and calculate the delays to divergence caused by DMIs of different kinds. We find that the number of paths is sometimes, though not always, a reliable predictor of the time to divergence. In particular, we find limited support for the idea that symmetrical DMIs take longer to evolve, but this applies largely to two-locus symmetrical DMIs (which leave no path of fit intermediates). Symmetrical complex DMIs can also delay divergence, but only in a limited region of parameter space. In most other cases, the presence and form of DMIs have little influence on times to divergence, and so we argue that ease of evolution is unlikely to be important in explaining the experimental data.

Magnitude and sign epistasis among deleterious mutations in a positive-sense plant RNA virus

How epistatic interactions between mutations determine the genetic architecture of fitness is of central importance in evolution. The study of epistasis is particularly interesting for RNA viruses because of their genomic compactness, lack of genetic redundancy, and apparent low complexity. Moreover, interactions between mutations in viral genomes determine traits such as resistance to antiviral drugs, virulence and host range. In this study we generated 53 Tobacco etch potyvirus genotypes carrying pairs of single-nucleotide substitutions and measured their separated and combined deleterious fitness effects. We found that up to 38% of pairs had significant epistasis for fitness, including both positive and negative deviations from the null hypothesis of multiplicative effects. Interestingly, the sign of epistasis was correlated with viral protein-protein interactions in a model network, being predominantly positive between linked pairs of proteins and negative between unlinked ones. Furthermore, 55% of significant interactions were cases of reciprocal sign epistasis (RSE), indicating that adaptive landscapes for RNA viruses maybe highly rugged. Finally, we found that the magnitude of epistasis correlated negatively with the average effect of mutations. Overall, our results are in good agreement to those previously reported for other viruses and further consolidate the view that positive epistasis is the norm for small and compact genomes that lack genetic robustness.

Modeling evolutionary landscapes: mutational stability, topology, and superfunnels in sequence space

Random mutations under neutral or near-neutral conditions are studied by considering plausible evolutionary trajectories on "neutral nets"-i.e., collections of sequences (genotypes) interconnected via single-point mutations encoding for the same ground-state structure (phenotype). We use simple exact lattice models for the mapping between sequence and conformational spaces. Densities of states based on model intrachain interactions are determined by exhaustive conformational enumeration. We compare results from two very different interaction schemes to ascertain robustness of the conclusions. In both models, sequences in a majority of neutral nets center around a single "prototype sequence" of maximum mutational stability, tolerating the largest number of neutral mutations. General analytical considerations show that these topologies by themselves lead to higher steady-state evolutionary populations at prototype sequences. On average, native thermodynamic stability increases toward a maximum at the prototype sequence, resulting in funnel-like arrangements of native stabilities in sequence space. These observations offer a unified perspective on sequence design, native stability, and mutational stability of proteins. These principles are generalizable from native stability to any measure of fitness provided that its variation with respect to mutations is essentially smooth.