A bayesian MCMC approach to assess the complete distribution of fitness effects of new mutations: uncovering the potential for adaptive walks in challenging environments

Epistasis facilitates functional evolution in an ancient transcription factor

A protein's genetic architecture - the set of causal rules by which its sequence produces its functions - also determines its possible evolutionary trajectories. Prior research has proposed that the genetic architecture of proteins is very complex, with pervasive epistatic interactions that constrain evolution and make function difficult to predict from sequence. Most of this work has analyzed only the direct paths between two proteins of interest - excluding the vast majority of possible genotypes and evolutionary trajectories - and has considered only a single protein function, leaving unaddressed the genetic architecture of functional specificity and its impact on the evolution of new functions. Here, we develop a new method based on ordinal logistic regression to directly characterize the global genetic determinants of multiple protein functions from 20-state combinatorial deep mutational scanning (DMS) experiments. We use it to dissect the genetic architecture and evolution of a transcription factor's specificity for DNA, using data from a combinatorial DMS of an ancient steroid hormone receptor's capacity to activate transcription from two biologically relevant DNA elements. We show that the genetic architecture of DNA recognition consists of a dense set of main and pairwise effects that involve virtually every possible amino acid state in the protein-DNA interface, but higher-order epistasis plays only a tiny role. Pairwise interactions enlarge the set of functional sequences and are the primary determinants of specificity for different DNA elements. They also massively expand the number of opportunities for single-residue mutations to switch specificity from one DNA target to another. By bringing variants with different functions close together in sequence space, pairwise epistasis therefore facilitates rather than constrains the evolution of new functions.

The distribution of fitness effects during adaptive walks using a simple genetic network

The tempo and mode of adaptation depends on the availability of beneficial alleles. Genetic interactions arising from gene networks can restrict this availability. However, the extent to which networks affect adaptation remains largely unknown. Current models of evolution consider additive genotype-phenotype relationships while often ignoring the contribution of gene interactions to phenotypic variance. In this study, we model a quantitative trait as the product of a simple gene regulatory network, the negative autoregulation motif. Using forward-time genetic simulations, we measure adaptive walks towards a phenotypic optimum in both additive and network models. A key expectation from adaptive walk theory is that the distribution of fitness effects of new beneficial mutations is exponential. We found that both models instead harbored distributions with fewer large-effect beneficial alleles than expected. The network model also had a complex and bimodal distribution of fitness effects among all mutations, with a considerable density at deleterious selection coefficients. This behavior is reminiscent of the cost of complexity, where correlations among traits constrain adaptation. Our results suggest that the interactions emerging from genetic networks can generate complex and multimodal distributions of fitness effects.

The Effects of Mutation and Recombination Rate Heterogeneity on the Inference of Demography and the Distribution of Fitness Effects

Disentangling the effects of demography and selection has remained a focal point of population genetic analysis. Knowledge about mutation and recombination is essential in this endeavor; however, despite clear evidence that both mutation and recombination rates vary across genomes, it is common practice to model both rates as fixed. In this study, we quantify how this unaccounted for rate heterogeneity may impact inference using common approaches for inferring selection (DFE-alpha, Grapes, and polyDFE) and/or demography (fastsimcoal2 and δaδi). We demonstrate that, if not properly modeled, this heterogeneity can increase uncertainty in the estimation of demographic and selective parameters and in some scenarios may result in mis-leading inference. These results highlight the importance of quantifying the fundamental evolutionary parameters of mutation and recombination before utilizing population genomic data to quantify the effects of genetic drift (i.e. as modulated by demographic history) and selection; or, at the least, that the effects of uncertainty in these parameters can and should be directly modeled in downstream inference.

ACIDES: on-line monitoring of forward genetic screens for protein engineering

Forward genetic screens of mutated variants are a versatile strategy for protein engineering and investigation, which has been successfully applied to various studies like directed evolution (DE) and deep mutational scanning (DMS). While next-generation sequencing can track millions of variants during the screening rounds, the vast and noisy nature of the sequencing data impedes the estimation of the performance of individual variants. Here, we propose ACIDES that combines statistical inference and in-silico simulations to improve performance estimation in the library selection process by attributing accurate statistical scores to individual variants. We tested ACIDES first on a random-peptide-insertion experiment and then on multiple public datasets from DE and DMS studies. ACIDES allows experimentalists to reliably estimate variant performance on the fly and can aid protein engineering and research pipelines in a range of applications, including gene therapy.

Unpredictable repeatability in molecular evolution

The extent of parallel evolution at the genotypic level is quantitatively linked to the distribution of beneficial fitness effects (DBFE) of mutations. The standard view, based on light-tailed distributions (i.e., distributions with finite moments), is that the probability of parallel evolution in duplicate populations is inversely proportional to the number of available mutations and, moreover, that the DBFE is sufficient to determine the probability when the number of available mutations is large. Here, we show that when the DBFE is heavy-tailed, as found in several recent experiments, these expectations are defied. The probability of parallel evolution decays anomalously slowly in the number of mutations or even becomes independent of it, implying higher repeatability of evolution. At the same time, the probability of parallel evolution is non-self-averaging—that is, it does not converge to its mean value, even when a large number of mutations are involved. This behavior arises because the evolutionary process is dominated by only a few mutations of high weight. Consequently, the probability varies widely across systems with the same DBFE. Contrary to the standard view, the DBFE is no longer sufficient to determine the extent of parallel evolution, making it much less predictable. We illustrate these ideas theoretically and through analysis of empirical data on antibiotic-resistance evolution.

Co-evolution of interacting proteins through non-contacting and non-specific mutations

Proteins often accumulate neutral mutations that do not affect current functions but can profoundly influence future mutational possibilities and functions. Understanding such hidden potential has major implications for protein design and evolutionary forecasting but has been limited by a lack of systematic efforts to identify potentiating mutations. Here, through the comprehensive analysis of a bacterial toxin-antitoxin system, we identified all possible single substitutions in the toxin that enable it to tolerate otherwise interface-disrupting mutations in its antitoxin. Strikingly, the majority of enabling mutations in the toxin do not contact and promote tolerance non-specifically to many different antitoxin mutations, despite covariation in homologues occurring primarily between specific pairs of contacting residues across the interface. In addition, the enabling mutations we identified expand future mutational paths that both maintain old toxin-antitoxin interactions and form new ones. These non-specific mutations are missed by widely used covariation and machine learning methods. Identifying such enabling mutations will be critical for ensuring continued binding of therapeutically relevant proteins, such as antibodies, aimed at evolving targets.

Recommendations for improving statistical inference in population genomics

The field of population genomics has grown rapidly in response to the recent advent of affordable, large-scale sequencing technologies. As opposed to the situation during the majority of the 20th century, in which the development of theoretical and statistical population genetic insights outpaced the generation of data to which they could be applied, genomic data are now being produced at a far greater rate than they can be meaningfully analyzed and interpreted. With this wealth of data has come a tendency to focus on fitting specific (and often rather idiosyncratic) models to data, at the expense of a careful exploration of the range of possible underlying evolutionary processes. For example, the approach of directly investigating models of adaptive evolution in each newly sequenced population or species often neglects the fact that a thorough characterization of ubiquitous nonadaptive processes is a prerequisite for accurate inference. We here describe the perils of these tendencies, present our consensus views on current best practices in population genomic data analysis, and highlight areas of statistical inference and theory that are in need of further attention. Thereby, we argue for the importance of defining a biologically relevant baseline model tuned to the details of each new analysis, of skepticism and scrutiny in interpreting model fitting results, and of carefully defining addressable hypotheses and underlying uncertainties.

Neural networks enable efficient and accurate simulation-based inference of evolutionary parameters from adaptation dynamics

The rate of adaptive evolution depends on the rate at which beneficial mutations are introduced into a population and the fitness effects of those mutations. The rate of beneficial mutations and their expected fitness effects is often difficult to empirically quantify. As these 2 parameters determine the pace of evolutionary change in a population, the dynamics of adaptive evolution may enable inference of their values. Copy number variants (CNVs) are a pervasive source of heritable variation that can facilitate rapid adaptive evolution. Previously, we developed a locus-specific fluorescent CNV reporter to quantify CNV dynamics in evolving populations maintained in nutrient-limiting conditions using chemostats. Here, we use CNV adaptation dynamics to estimate the rate at which beneficial CNVs are introduced through de novo mutation and their fitness effects using simulation-based likelihood-free inference approaches. We tested the suitability of 2 evolutionary models: a standard Wright-Fisher model and a chemostat model. We evaluated 2 likelihood-free inference algorithms: the well-established Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) algorithm, and the recently developed Neural Posterior Estimation (NPE) algorithm, which applies an artificial neural network to directly estimate the posterior distribution. By systematically evaluating the suitability of different inference methods and models, we show that NPE has several advantages over ABC-SMC and that a Wright-Fisher evolutionary model suffices in most cases. Using our validated inference framework, we estimate the CNV formation rate at the GAP1 locus in the yeast Saccharomyces cerevisiae to be 10-4.7 to 10-4 CNVs per cell division and a fitness coefficient of 0.04 to 0.1 per generation for GAP1 CNVs in glutamine-limited chemostats. We experimentally validated our inference-based estimates using 2 distinct experimental methods-barcode lineage tracking and pairwise fitness assays-which provide independent confirmation of the accuracy of our approach. Our results are consistent with a beneficial CNV supply rate that is 10-fold greater than the estimated rates of beneficial single-nucleotide mutations, explaining the outsized importance of CNVs in rapid adaptive evolution. More generally, our study demonstrates the utility of novel neural network-based likelihood-free inference methods for inferring the rates and effects of evolutionary processes from empirical data with possible applications ranging from tumor to viral evolution.

Inferring the distribution of fitness effects in patient-sampled and experimental virus populations: two case studies

We here propose an analysis pipeline for inferring the distribution of fitness effects (DFE) from either patient-sampled or experimentally-evolved viral populations, that explicitly accounts for non-Wright-Fisher and non-equilibrium population dynamics inherent to pathogens. We examine the performance of this approach via extensive power and performance analyses, and highlight two illustrative applications - one from an experimentally-passaged RNA virus, and the other from a clinically-sampled DNA virus. Finally, we discuss how such DFE inference may shed light on major research questions in virus evolution, ranging from a quantification of the population genetic processes governing genome size, to the role of Hill-Robertson interference in dictating adaptive outcomes, to the potential design of novel therapeutic approaches to eradicate within-patient viral populations via induced mutational meltdown.

Revisiting the notion of deleterious sweeps

It has previously been shown that, conditional on its fixation, the time to fixation of a semi-dominant deleterious autosomal mutation in a randomly mating population is the same as that of an advantageous mutation. This result implies that deleterious mutations could generate selective sweep-like effects. Although their fixation probabilities greatly differ, the much larger input of deleterious relative to beneficial mutations suggests that this phenomenon could be important. We here examine how the fixation of mildly deleterious mutations affects levels and patterns of polymorphism at linked sites-both in the presence and absence of interference amongst deleterious mutations-and how this class of sites may contribute to divergence between-populations and species. We find that, while deleterious fixations are unlikely to represent a significant proportion of outliers in polymorphism-based genomic scans within populations, minor shifts in the frequencies of deleterious mutations can influence the proportions of private variants and the value of FST after a recent population split. As sites subject to deleterious mutations are necessarily found in functional genomic regions, interpretations in terms of recurrent positive selection may require reconsideration.

The Adaptive Potential of the Middle Domain of Yeast Hsp90

The distribution of fitness effects (DFEs) of new mutations across different environments quantifies the potential for adaptation in a given environment and its cost in others. So far, results regarding the cost of adaptation across environments have been mixed, and most studies have sampled random mutations across different genes. Here, we quantify systematically how costs of adaptation vary along a large stretch of protein sequence by studying the distribution of fitness effects of the same ≈2,300 amino-acid changing mutations obtained from deep mutational scanning of 119 amino acids in the middle domain of the heat shock protein Hsp90 in five environments. This region is known to be important for client binding, stabilization of the Hsp90 dimer, stabilization of the N-terminal-Middle and Middle-C-terminal interdomains, and regulation of ATPase–chaperone activity. Interestingly, we find that fitness correlates well across diverse stressful environments, with the exception of one environment, diamide. Consistent with this result, we find little cost of adaptation; on average only one in seven beneficial mutations is deleterious in another environment. We identify a hotspot of beneficial mutations in a region of the protein that is located within an allosteric center. The identified protein regions that are enriched in beneficial, deleterious, and costly mutations coincide with residues that are involved in the stabilization of Hsp90 interdomains and stabilization of client-binding interfaces, or residues that are involved in ATPase–chaperone activity of Hsp90. Thus, our study yields information regarding the role and adaptive potential of a protein sequence that complements and extends known structural information.

Quantifying the Evolutionary Constraints and Potential of Hepatitis C Virus NS5A Protein

RNA viruses, such as hepatitis C virus (HCV), influenza virus, and SARS-CoV-2, are notorious for their ability to evolve rapidly under selection in novel environments. It is known that the high mutation rate of RNA viruses can generate huge genetic diversity to facilitate viral adaptation. However, less attention has been paid to the underlying fitness landscape that represents the selection forces on viral genomes, especially under different selection conditions. Here, we systematically quantified the distribution of fitness effects of about 1,600 single amino acid substitutions in the drug-targeted region of NS5A protein of HCV. We found that the majority of nonsynonymous substitutions incur large fitness costs, suggesting that NS5A protein is highly optimized. The replication fitness of viruses is correlated with the pattern of sequence conservation in nature, and viral evolution is constrained by the need to maintain protein stability. We characterized the adaptive potential of HCV by subjecting the mutant viruses to selection by the antiviral drug daclatasvir at multiple concentrations. Both the relative fitness values and the number of beneficial mutations were found to increase with the increasing concentrations of daclatasvir. The changes in the spectrum of beneficial mutations in NS5A protein can be explained by a pharmacodynamics model describing viral fitness as a function of drug concentration. Overall, our results show that the distribution of fitness effects of mutations is modulated by both the constraints on the biophysical properties of proteins (i.e., selection pressure for protein stability) and the level of environmental stress (i.e., selection pressure for drug resistance).

IMPORTANCE Many viruses adapt rapidly to novel selection pressures, such as antiviral drugs. Understanding how pathogens evolve under drug selection is critical for the success of antiviral therapy against human pathogens. By combining deep sequencing with selection experiments in cell culture, we have quantified the distribution of fitness effects of mutations in hepatitis C virus (HCV) NS5A protein. Our results indicate that the majority of single amino acid substitutions in NS5A protein incur large fitness costs. Simulation of protein stability suggests viral evolution is constrained by the need to maintain protein stability. By subjecting the mutant viruses to selection under an antiviral drug, we find that the adaptive potential of viral proteins in a novel environment is modulated by the level of environmental stress, which can be explained by a pharmacodynamics model. Our comprehensive characterization of the fitness landscapes of NS5A can potentially guide the design of effective strategies to limit viral evolution.

Imposed mutational meltdown as an antiviral strategy

Following widespread infections of the most recent coronavirus known to infect humans, SARS‐CoV‐2, attention has turned to potential therapeutic options. With no drug or vaccine yet approved, one focal point of research is to evaluate the potential value of repurposing existing antiviral treatments, with the logical strategy being to identify at least a short‐term intervention to prevent within‐patient progression, while long‐term vaccine strategies unfold. Here, we offer an evolutionary/population‐genetic perspective on one approach that may overwhelm the capacity for pathogen defense (i.e., adaptation) – induced mutational meltdown – providing an overview of key concepts, review of previous theoretical and experimental work of relevance, and guidance for future research. Applied with appropriate care, including target specificity, induced mutational meltdown may provide a general, rapidly implemented approach for the within‐patient eradication of a wide range of pathogens or other undesirable microorganisms.

Warmer temperatures enhance beneficial mutation effects

Temperature determines the rates of all biochemical and biophysical processes, and is also believed to be a key driver of macroevolutionary patterns. It is suggested that physiological constraints at low temperatures may diminish the fitness advantages of otherwise beneficial mutations; by contrast, relatively high, benign, temperatures allow beneficial mutations to efficiently show their phenotypic effects. To experimentally test this "mutational effects" mechanism, we examined the fitness effects of mutations across a temperature gradient using bacterial genotypes from the early stage of a mutation accumulation experiment with Escherichia coli. While the incidence of beneficial mutations did not significantly change across environmental temperatures, the number of mutations that conferred strong beneficial fitness effects was greater at higher temperatures. The results therefore support the hypothesis that warmer temperatures increase the chance and magnitude of positive selection, with implications for explaining the geographic patterns in evolutionary rates and understanding contemporary evolution under global warming.

Inferring Parameters of the Distribution of Fitness Effects of New Mutations When Beneficial Mutations Are Strongly Advantageous and Rare

Characterizing the distribution of fitness effects (DFE) for new mutations is central in evolutionary genetics. Analysis of molecular data under the McDonald-Kreitman test has suggested that adaptive substitutions make a substantial contribution to between-species divergence. Methods have been proposed to estimate the parameters of the distribution of fitness effects for positively selected mutations from the unfolded site frequency spectrum (uSFS). Such methods perform well when beneficial mutations are mildly selected and frequent. However, when beneficial mutations are strongly selected and rare, they may make little contribution to standing variation and will thus be difficult to detect from the uSFS. In this study, I analyze uSFS data from simulated populations subject to advantageous mutations with effects on fitness ranging from mildly to strongly beneficial. As expected, frequent, mildly beneficial mutations contribute substantially to standing genetic variation and parameters are accurately recovered from the uSFS. However, when advantageous mutations are strongly selected and rare, there are very few segregating in populations at any one time. Fitting the uSFS in such cases leads to underestimates of the strength of positive selection and may lead researchers to false conclusions regarding the relative contribution adaptive mutations make to molecular evolution. Fortunately, the parameters for the distribution of fitness effects for harmful mutations are estimated with high accuracy and precision. The results from this study suggest that the parameters of positively selected mutations obtained by analysis of the uSFS should be treated with caution and that variability at linked sites should be used in conjunction with standing variability to estimate parameters of the distribution of fitness effects in the future.

Toward an Evolutionarily Appropriate Null Model: Jointly Inferring Demography and Purifying Selection

The question of the relative evolutionary roles of adaptive and nonadaptive processes has been a central debate in population genetics for nearly a century. While advances have been made in the theoretical development of the underlying models, and statistical methods for estimating their parameters from large-scale genomic data, a framework for an appropriate null model remains elusive. A model incorporating evolutionary processes known to be in constant operation, genetic drift (as modulated by the demographic history of the population) and purifying selection, is lacking. Without such a null model, the role of adaptive processes in shaping within- and between-population variation may not be accurately assessed. Here, we investigate how population size changes and the strength of purifying selection affect patterns of variation at "neutral" sites near functional genomic components. We propose a novel statistical framework for jointly inferring the contribution of the relevant selective and demographic parameters. By means of extensive performance analyses, we quantify the utility of the approach, identify the most important statistics for parameter estimation, and compare the results with existing methods. Finally, we reanalyze genome-wide population-level data from a Zambian population of Drosophila melanogaster, and find that it has experienced a much slower rate of population growth than was inferred when the effects of purifying selection were neglected. Our approach represents an appropriate null model, against which the effects of positive selection can be assessed.

Evaluating the contributions of purifying selection and progeny-skew in dictating within-host Mycobacterium tuberculosis evolution

The within-host evolutionary dynamics of tuberculosis (TB) remain unclear, and underlying biological characteristics render standard population genetic approaches based upon the Wright-Fisher model largely inappropriate. In addition, the compact genome combined with an absence of recombination is expected to result in strong purifying selection effects. Thus, it is imperative to establish a biologically relevant evolutionary framework incorporating these factors in order to enable an accurate study of this important human pathogen. Further, such a model is critical for inferring fundamental evolutionary parameters related to patient treatment, including mutation rates and the severity of infection bottlenecks. We here implement such a model and infer the underlying evolutionary parameters governing within-patient evolutionary dynamics. Results demonstrate that the progeny skew associated with the clonal nature of TB severely reduces genetic diversity and that the neglect of this parameter in previous studies has led to significant mis-inference of mutation rates. As such, our results suggest an underlying de novo mutation rate that is considerably faster than previously inferred, and a progeny distribution differing significantly from Wright-Fisher assumptions. This inference represents a more appropriate evolutionary null model, against which the periodic effects of positive selection, associated with drug-resistance for example, may be better assessed.

How Long Does It Take to Fix a Favorable Mutation, and Why Should We Care?

The time taken for a selectively favorable allele to spread through a single population was investigated early in the history of population genetics. The resulting formulas are based on deterministic dynamics, leading to inaccuracies at allele frequencies close to 0 or 1. To remedy this problem, the properties of the stochastic phases at either end point of allele frequency need to be analyzed. This article uses a heuristic approach to determining the expected times spent in the stochastic and deterministic phases of allele frequency trajectories, for a model of weak selection at a single locus that is valid for inbreeding populations and for autosomal and sex-linked inheritance. The net fixation time is surprisingly insensitive to the level of dominance of a favorable mutation, even with random mating. Approximate expressions for the variance of the net fixation time are also obtained, which imply that there can be substantial stochastic effects even in very large populations. The accuracy of the approximations was evaluated by comparisons with computer simulations. The results reveal some areas that need further investigation if a full understanding of selective sweeps is to be obtained, notably the possibility that fixations of slightly deleterious mutations may be affecting variability at closely linked sites.

Comprehensive fitness maps of Hsp90 show widespread environmental dependence

Gene-environment interactions have long been theorized to influence molecular evolution. However, the environmental dependence of most mutations remains unknown. Using deep mutational scanning, we engineered yeast with all 44,604 single codon changes encoding 14,160 amino acid variants in Hsp90 and quantified growth effects under standard conditions and under five stress conditions. To our knowledge, these are the largest determined comprehensive fitness maps of point mutants. The growth of many variants differed between conditions, indicating that environment can have a large impact on Hsp90 evolution. Multiple variants provided growth advantages under individual conditions; however, these variants tended to exhibit growth defects in other environments. The diversity of Hsp90 sequences observed in extant eukaryotes preferentially contains variants that supported robust growth under all tested conditions. Rather than favoring substitutions in individual conditions, the long-term selective pressure on Hsp90 may have been that of fluctuating environments, leading to robustness under a variety of conditions.

Field cricket genome reveals the footprint of recent, abrupt adaptation in the wild

Evolutionary adaptation is generally thought to occur through incremental mutational steps, but large mutational leaps can occur during its early stages. These are challenging to study in nature due to the difficulty of observing new genetic variants as they arise and spread, but characterizing their genomic dynamics is important for understanding factors favoring rapid adaptation. Here, we report genomic consequences of recent, adaptive song loss in a Hawaiian population of field crickets (Teleogryllus oceanicus). A discrete genetic variant, flatwing, appeared and spread approximately 15 years ago. Flatwing erases sound‐producing veins on male wings. These silent flatwing males are protected from a lethal, eavesdropping parasitoid fly. We sequenced, assembled and annotated the cricket genome, produced a linkage map, and identified a flatwing quantitative trait locus covering a large region of the X chromosome. Gene expression profiling showed that flatwing is associated with extensive genome‐wide effects on embryonic gene expression. We found that flatwing male crickets express feminized chemical pheromones. This male feminizing effect, on a different sexual signaling modality, is genetically associated with the flatwing genotype. Our findings suggest that the early stages of evolutionary adaptation to extreme pressures can be accompanied by greater genomic and phenotypic disruption than previously appreciated, and highlight how abrupt adaptation might involve suites of traits that arise through pleiotropy or genomic hitchhiking.

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.

Understanding the Factors That Shape Patterns of Nucleotide Diversity in the House Mouse Genome

A major goal of population genetics has been to determine the extent by which selection at linked sites influences patterns of neutral nucleotide diversity in the genome. Multiple lines of evidence suggest that diversity is influenced by both positive and negative selection. For example, in many species there are troughs in diversity surrounding functional genomic elements, consistent with the action of either background selection (BGS) or selective sweeps. In this study, we investigated the causes of the diversity troughs that are observed in the wild house mouse genome. Using the unfolded site frequency spectrum, we estimated the strength and frequencies of deleterious and advantageous mutations occurring in different functional elements in the genome. We then used these estimates to parameterize forward-in-time simulations of chromosomes, using realistic distributions of functional elements and recombination rate variation in order to determine whether selection at linked sites can explain the observed patterns of nucleotide diversity. The simulations suggest that BGS alone cannot explain the dips in diversity around either exons or conserved noncoding elements. A combination of BGS and selective sweeps produces deeper dips in diversity than BGS alone, but the inferred parameters of selection cannot fully explain the patterns observed in the genome. Our results provide evidence of sweeps shaping patterns of nucleotide diversity across the mouse genome and also suggest that infrequent, strongly advantageous mutations play an important role in this. The limitations of using the unfolded site frequency spectrum for inferring the frequency and effects of advantageous mutations are discussed.

Predicting microbial growth in a mixed culture from growth curve data

Determining the fitness of specific microbial genotypes has extensive application in microbial genetics, evolution, and biotechnology. While estimates from growth curves are simple and allow high throughput, they are inaccurate and do not account for interactions between costs and benefits accruing over different parts of a growth cycle. For this reason, pairwise competition experiments are the current "gold standard" for accurate estimation of fitness. However, competition experiments require distinct markers, making them difficult to perform between isolates derived from a common ancestor or between isolates of nonmodel organisms. In addition, competition experiments require that competing strains be grown in the same environment, so they cannot be used to infer the fitness consequence of different environmental perturbations on the same genotype. Finally, competition experiments typically consider only the end-points of a period of competition so that they do not readily provide information on the growth differences that underlie competitive ability. Here, we describe a computational approach for predicting density-dependent microbial growth in a mixed culture utilizing data from monoculture and mixed-culture growth curves. We validate this approach using 2 different experiments with Escherichia coli and demonstrate its application for estimating relative fitness. Our approach provides an effective way to predict growth and infer relative fitness in mixed cultures.

The Causes and Consequences of Genetic Interactions (Epistasis)

The same mutation can have different effects in different individuals. One important reason for this is that the outcome of a mutation can depend on the genetic context in which it occurs. This dependency is known as epistasis. In recent years, there has been a concerted effort to quantify the extent of pairwise and higher-order genetic interactions between mutations through deep mutagenesis of proteins and RNAs. This research has revealed two major components of epistasis: nonspecific genetic interactions caused by nonlinearities in genotype-to-phenotype maps, and specific interactions between particular mutations. Here, we provide an overview of our current understanding of the mechanisms causing epistasis at the molecular level, the consequences of genetic interactions for evolution and genetic prediction, and the applications of epistasis for understanding biology and determining macromolecular structures.

On the unfounded enthusiasm for soft selective sweeps II: Examining recent evidence from humans, flies, and viruses

Since the initial description of the genomic patterns expected under models of positive selection acting on standing genetic variation and on multiple beneficial mutations—so-called soft selective sweeps—researchers have sought to identify these patterns in natural population data. Indeed, over the past two years, large-scale data analyses have argued that soft sweeps are pervasive across organisms of very different effective population size and mutation rate—humans, Drosophila, and HIV. Yet, others have evaluated the relevance of these models to natural populations, as well as the identifiability of the models relative to other known population-level processes, arguing that soft sweeps are likely to be rare. Here, we look to reconcile these opposing results by carefully evaluating three recent studies and their underlying methodologies. Using population genetic theory, as well as extensive simulation, we find that all three examples are prone to extremely high false-positive rates, incorrectly identifying soft sweeps under both hard sweep and neutral models. Furthermore, we demonstrate that well-fit demographic histories combined with rare hard sweeps serve as the more parsimonious explanation. These findings represent a necessary response to the growing tendency of invoking parameter-heavy, assumption-laden models of pervasive positive selection, and neglecting best practices regarding the construction of proper demographic null models.

A long-standing debate in evolutionary biology revolves around the role of selective vs. stochastic processes in driving molecular evolution and shaping genetic variation. With the advent of genomics, genome-wide polymorphism data have been utilized to characterize these processes, with a major interest in describing the fraction of genomic variation shaped by positive selection. These genomic scans were initially focused around a hard sweep model, in which selection acts upon rare, newly arising beneficial mutations. Recent years have seen the description of sweeps occurring from both standing and rapidly recurring beneficial mutations, collectively known as soft sweeps. However, common to both hard and soft sweeps is the difficulty in distinguishing these effects from neutral demographic patterns, and disentangling these processes has remained an important field of study within population genetics. Despite this, there is a recent and troubling tendency to neglect these demographic considerations, and to naively fit sweep models to genomic data. Recent realizations of such efforts have resulted in the claim that soft sweeps play a dominant role in shaping genomic variation and in driving adaptation across diverse branches of the tree of life. Here, we reanalyze these findings and demonstrate that a more careful consideration of neutral processes results in highly differing conclusions.

The fitness landscape of the codon space across environments

Fitness landscapes map the relationship between genotypes and fitness. However, most fitness landscape studies ignore the genetic architecture imposed by the codon table and thereby neglect the potential role of synonymous mutations. To quantify the fitness effects of synonymous mutations and their potential impact on adaptation on a fitness landscape, we use a new software based on Bayesian Monte Carlo Markov Chain methods and re-estimate selection coefficients of all possible codon mutations across 9 amino acid positions in Saccharomyces cerevisiae Hsp90 across 6 environments. We quantify the distribution of fitness effects of synonymous mutations and show that it is dominated by many mutations of small or no effect and few mutations of larger effect. We then compare the shape of the codon fitness landscape across amino acid positions and environments, and quantify how the consideration of synonymous fitness effects changes the evolutionary dynamics on these fitness landscapes. Together these results highlight a possible role of synonymous mutations in adaptation and indicate the potential mis-inference when they are neglected in fitness landscape studies.

Mutation-Driven Parallel Evolution during Viral Adaptation

Convergent evolution has been demonstrated across all levels of biological organization, from parallel nucleotide substitutions to convergent evolution of complex phenotypes, but whether instances of convergence are the result of selection repeatedly finding the same optimal solution to a recurring problem or are the product of mutational biases remains unsettled. We generated 20 replicate lineages allowed to fix a single mutation from each of four bacteriophage genotypes under identical selective regimes to test for parallel changes within and across genotypes at the levels of mutational effect distributions and gene, protein, amino acid, and nucleotide changes. All four genotypes shared a distribution of beneficial mutational effects best approximated by a distribution with a finite upper bound. Parallel adaptation was high at the protein, gene, amino acid, and nucleotide levels, both within and among phage genotypes, with the most common first-step mutation in each background fixing on an average in 7 of 20 replicates and half of the substitutions in two of the four genotypes occurring at shared sites. Remarkably, the mutation of largest beneficial effect that fixed for each genotype was never the most common, as would be expected if parallelism were driven by selection. In fact, the mutation of smallest benefit for each genotype fixed in a total of 7 of 80 lineages, equally as often as the mutation of largest benefit, leading us to conclude that adaptation was largely mutation-driven, such that mutational biases led to frequent parallel fixation of mutations of suboptimal effect.

Differential strengths of molecular determinants guide environment specific mutational fates

Organisms maintain competitive fitness in the face of environmental challenges through molecular evolution. However, it remains largely unknown how different biophysical factors constrain molecular evolution in a given environment. Here, using deep mutational scanning, we quantified empirical fitness of >2000 single site mutants of the Gentamicin-resistant gene (GmR) in Escherichia coli, in a representative set of physical (non-native temperatures) and chemical (small molecule supplements) environments. From this, we could infer how different biophysical parameters of the mutations constrain molecular function in different environments. We find ligand binding, and protein stability to be the best predictors of mutants' fitness, but their relative predictive power differs across environments. While protein folding emerges as the strongest predictor at minimal antibiotic concentration, ligand binding becomes a stronger predictor of mutant fitness at higher concentration. Remarkably, strengths of environment-specific selection pressures were largely predictable from the degree of mutational perturbation of protein folding and ligand binding. By identifying structural constraints that act as determinants of fitness, our study thus provides coarse mechanistic insights into the environment specific accessibility of mutational fates.

Experimental Determination and Prediction of the Fitness Effects of Random Point Mutations in the Biosynthetic Enzyme HisA

The distribution of fitness effects of mutations is a factor of fundamental importance in evolutionary biology. We determined the distribution of fitness effects of 510 mutants that each carried between 1 and 10 mutations (synonymous and nonsynonymous) in the hisA gene, encoding an essential enzyme in the l-histidine biosynthesis pathway of Salmonella enterica. For the full set of mutants, the distribution was bimodal with many apparently neutral mutations and many lethal mutations. For a subset of 81 single, nonsynonymous mutants most mutations appeared neutral at high expression levels, whereas at low expression levels only a few mutations were neutral. Furthermore, we examined how the magnitude of the observed fitness effects was correlated to several measures of biophysical properties and phylogenetic conservation.We conclude that for HisA: (i) The effect of mutations can be masked by high expression levels, such that mutations that are deleterious to the function of the protein can still be neutral with regard to organism fitness if the protein is expressed at a sufficiently high level; (ii) the shape of the fitness distribution is dependent on the extent to which the protein is rate-limiting for growth; (iii) negative epistatic interactions, on an average, amplified the combined effect of nonsynonymous mutations; and (iv) no single sequence-based predictor could confidently predict the fitness effects of mutations in HisA, but a combination of multiple predictors could predict the effect with a SD of 0.04 resulting in 80% of the mutations predicted within 12% of their observed selection coefficients.

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

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

Additive Phenotypes Underlie Epistasis of Fitness Effects

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

A statistical framework for analyzing deep mutational scanning data

Deep mutational scanning is a widely used method for multiplex measurement of functional consequences of protein variants. We developed a new deep mutational scanning statistical model that generates error estimates for each measurement, capturing both sampling error and consistency between replicates. We apply our model to one novel and five published datasets comprising 243,732 variants and demonstrate its superiority in removing noisy variants and conducting hypothesis testing. Simulations show our model applies to scans based on cell growth or binding and handles common experimental errors. We implemented our model in Enrich2, software that can empower researchers analyzing deep mutational scanning data.

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.

The evolutionary trade-off between stem cell niche size, aging, and tumorigenesis

Many epithelial tissues within multicellular organisms are continually replenished by small independent populations of stem cells largely responsible for maintaining tissue homeostasis. These continually dividing populations are subject to mutations that can lead to tumorigenesis but also contribute to aging. Mutations accumulate in stem cell niches and change the rate of cell division and differentiation; the pace of this process and the fate of specific mutations depend strongly on niche population size. Here, we create a mathematical model of the intestinal stem cell niche, crypt system, and epithelium. We calculate the expected effect of fixed mutations in stem cell niches and their effect on tissue homeostasis throughout the intestinal epithelium over organismal lifetime. We find that, due to the small population size of stem cell niches, mutations predominantly fix via genetic drift and decrease stem cell fitness, leading to niche and tissue attrition, and contributing to organismal aging. We also explore mutation accumulation at various stem cell niche sizes and demonstrate that an evolutionary trade-off exists between niche size, tissue aging, and the risk of tumorigenesis. Further, mouse and human niches exist at a size that minimizes the probability of tumorigenesis, at the expense of accumulating deleterious mutations due to genetic drift. Finally, we show that the trade-off between the probability of tumorigenesis and the extent of aging depends on whether or not mutational effects confer a selective advantage in the stem cell niche.

Inference of the Distribution of Selection Coefficients for New Nonsynonymous Mutations Using Large Samples

The distribution of fitness effects (DFE) has considerable importance in population genetics. To date, estimates of the DFE come from studies using a small number of individuals. Thus, estimates of the proportion of moderately to strongly deleterious new mutations may be unreliable because such variants are unlikely to be segregating in the data. Additionally, the true functional form of the DFE is unknown, and estimates of the DFE differ significantly between studies. Here we present a flexible and computationally tractable method, called Fit∂a∂i, to estimate the DFE of new mutations using the site frequency spectrum from a large number of individuals. We apply our approach to the frequency spectrum of 1300 Europeans from the Exome Sequencing Project ESP6400 data set, 1298 Danes from the LuCamp data set, and 432 Europeans from the 1000 Genomes Project to estimate the DFE of deleterious nonsynonymous mutations. We infer significantly fewer (0.38-0.84 fold) strongly deleterious mutations with selection coefficient |s| > 0.01 and more (1.24-1.43 fold) weakly deleterious mutations with selection coefficient |s| < 0.001 compared to previous estimates. Furthermore, a DFE that is a mixture distribution of a point mass at neutrality plus a gamma distribution fits better than a gamma distribution in two of the three data sets. Our results suggest that nearly neutral forces play a larger role in human evolution than previously thought.

Two sides of the same coin: A population genetics perspective on lethal mutagenesis and mutational meltdown

The extinction of RNA virus populations upon application of a mutagenic drug is frequently referred to as evidence for the existence of an error threshold, above which the population cannot sustain the mutational load. To explain the extinction process after reaching this threshold, models of lethal mutagenesis have been proposed, in which extinction is described as a deterministic (and thus population size-independent) process. As a separate body of literature, the population genetics community has developed models of mutational meltdown, which focus on the stochastic (and thus population-size dependent) processes governing extinction. However, recent extensions of both models have blurred these boundaries. Here, we first clarify definitions in terms of assumptions, expectations, and relevant parameter spaces, and then assess similarities and differences. As concepts from both fields converge, we argue for a unified theoretical framework that is focused on the evolutionary processes at play, rather than dispute over terminology.

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.

On the importance of skewed offspring distributions and background selection in virus population genetics

Many features of virus populations make them excellent candidates for population genetic study, including a very high rate of mutation, high levels of nucleotide diversity, exceptionally large census population sizes, and frequent positive selection. However, these attributes also mean that special care must be taken in population genetic inference. For example, highly skewed offspring distributions, frequent and severe population bottleneck events associated with infection and compartmentalization, and strong purifying selection all affect the distribution of genetic variation but are often not taken into account. Here, we draw particular attention to multiple-merger coalescent events and background selection, discuss potential misinference associated with these processes, and highlight potential avenues for better incorporating them into future population genetic analyses.

A Statistical Guide to the Design of Deep Mutational Scanning Experiments

The characterization of the distribution of mutational effects is a key goal in evolutionary biology. Recently developed deep-sequencing approaches allow for accurate and simultaneous estimation of the fitness effects of hundreds of engineered mutations by monitoring their relative abundance across time points in a single bulk competition. Naturally, the achievable resolution of the estimated fitness effects depends on the specific experimental setup, the organism and type of mutations studied, and the sequencing technology utilized, among other factors. By means of analytical approximations and simulations, we provide guidelines for optimizing time-sampled deep-sequencing bulk competition experiments, focusing on the number of mutants, the sequencing depth, and the number of sampled time points. Our analytical results show that sampling more time points together with extending the duration of the experiment improves the achievable precision disproportionately compared with increasing the sequencing depth or reducing the number of competing mutants. Even if the duration of the experiment is fixed, sampling more time points and clustering these at the beginning and the end of the experiment increase experimental power and allow for efficient and precise assessment of the entire range of selection coefficients. Finally, we provide a formula for calculating the 95%-confidence interval for the measurement error estimate, which we implement as an interactive web tool. This allows for quantification of the maximum expected a priori precision of the experimental setup, as well as for a statistical threshold for determining deviations from neutrality for specific selection coefficient estimates.

The genetics of speciation: Insights from Fisher's geometric model

Research in speciation genetics has uncovered many robust patterns in intrinsic reproductive isolation, and fitness landscape models have been useful in interpreting these patterns. Here, we examine fitness landscapes based on Fisher's geometric model. Such landscapes are analogous to models of optimizing selection acting on quantitative traits, and have been widely used to study adaptation and the distribution of mutational effects. We show that, with a few modifications, Fisher's model can generate all of the major findings of introgression studies (including "speciation genes" with strong deleterious effects, complex epistasis and asymmetry), and the major patterns in overall hybrid fitnesses (including Haldane's Rule, the speciation clock, heterosis, hybrid breakdown, and male-female asymmetry in the F1). We compare our approach to alternative modeling frameworks that assign fitnesses to genotypes by identifying combinations of incompatible alleles. In some cases, the predictions are importantly different. For example, Fisher's model can explain conflicting empirical results about the rate at which incompatibilities accumulate with genetic divergence. In other cases, the predictions are identical. For example, the quality of reproductive isolation is little affected by the manner in which populations diverge.

Antiviral drug resistance as an adaptive process

Antiviral drug resistance is a matter of great clinical importance that, historically, has been investigated mostly from a virological perspective. Although the proximate mechanisms of resistance can be readily uncovered using these methods, larger evolutionary trends often remain elusive. Recent interest by population geneticists in studies of antiviral resistance has spurred new metrics for evaluating mutation and recombination rates, demographic histories of transmission and compartmentalization, and selective forces incurred during viral adaptation to antiviral drug treatment. We present up-to-date summaries on antiviral resistance for a range of drugs and viral types, and review recent advances for studying their evolutionary histories. We conclude that information imparted by demographic and selective histories, as revealed through population genomic inference, is integral to assessing the evolution of antiviral resistance as it pertains to human health.

Triallelic Population Genomics for Inferring Correlated Fitness Effects of Same Site Nonsynonymous Mutations

The distribution of mutational effects on fitness is central to evolutionary genetics. Typical univariate distributions, however, cannot model the effects of multiple mutations at the same site, so we introduce a model in which mutations at the same site have correlated fitness effects. To infer the strength of that correlation, we developed a diffusion approximation to the triallelic frequency spectrum, which we applied to data from Drosophila melanogaster We found a moderate positive correlation between the fitness effects of nonsynonymous mutations at the same codon, suggesting that both mutation identity and location are important for determining fitness effects in proteins. We validated our approach by comparing it to biochemical mutational scanning experiments, finding strong quantitative agreement, even between different organisms. We also found that the correlation of mutational fitness effects was not affected by protein solvent exposure or structural disorder. Together, our results suggest that the correlation of fitness effects at the same site is a previously overlooked yet fundamental property of protein evolution.

Expansion load and the evolutionary dynamics of a species range

Expanding populations incur a mutation burden, the so-called expansion load. Using a mixture of individual-based simulations and analytical modeling, we study the expansion load process in models where population growth depends on the population's fitness (i.e., hard selection). We show that expansion load can severely slow down expansions and limit a species' range, even in the absence of environmental variation. We also study the effect of recombination on the dynamics of a species range and on the evolution of mean fitness on the wave front. If recombination is strong, mean fitness on front approaches an equilibrium value at which the effects of fixed mutations cancel each other out. The equilibrium rate at which new demes are colonized is similar to the rate at which beneficial mutations spread through the core. Without recombination, the dynamics is more complex, and beneficial mutations from the core of the range can invade the front of the expansion, which results in irregular and episodic expansion. Although the rate of adaptation is generally higher in recombining organisms, the mean fitness on the front may be larger in the absence of recombination because high-fitness individuals from the core have a higher chance to invade the front. Our findings have important consequences for the evolutionary dynamics of species ranges as well as on the role and the evolution of recombination during range expansions.

The implications of small stem cell niche sizes and the distribution of fitness effects of new mutations in aging and tumorigenesis

Somatic tissue evolves over a vertebrate's lifetime due to the accumulation of mutations in stem cell populations. Mutations may alter cellular fitness and contribute to tumorigenesis or aging. The distribution of mutational effects within somatic cells is not known. Given the unique regulatory regime of somatic cell division, we hypothesize that mutational effects in somatic tissue fall into a different framework than whole organisms; one in which there are more mutations of large effect. Through simulation analysis, we investigate the fit of tumor incidence curves generated using exponential and power‐law distributions of fitness effects (DFE) to known tumorigenesis incidence. Modeling considerations include the architecture of stem cell populations, that is, a large number of very small populations, and mutations that do and do not fix neutrally in the stem cell niche. We find that the typically quantified DFE in whole organisms is sufficient to explain tumorigenesis incidence. Further, deleterious mutations are predicted to accumulate via genetic drift, resulting in reduced tissue maintenance. Thus, despite there being a large number of stem cells throughout the intestine, its compartmental architecture leads to the accumulation of deleterious mutations and significant aging, making the intestinal stem cell niche a prime example of Muller's Ratchet.

Greedy adaptive walks on a correlated fitness landscape

We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length L. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant neighbors of the current genotype until a local fitness maximum is reached. The landscape is of the rough mount Fuji type, which means that the fitness value assigned to a sequence is the sum of a random and a deterministic component. The random components are independent and identically distributed random variables, and the deterministic component varies linearly with the distance to a reference sequence. The deterministic fitness gradient c is a parameter that interpolates between the limits of an uncorrelated random landscape (c=0) and an effectively additive landscape (c→∞). When the random fitness component is chosen from the Gumbel distribution, explicit expressions for the distribution of the number of steps taken by the greedy walk are obtained, and it is shown that the walk length varies non-monotonically with the strength of the fitness gradient when the starting point is sufficiently close to the reference sequence. Asymptotic results for general distributions of the random fitness component are obtained using extreme value theory, and it is found that the walk length attains a non-trivial limit for L→∞, different from its values for c=0 and c=∞, if c is scaled with L in an appropriate combination.

Can the experimental evolution programme help us elucidate the genetic basis of adaptation in nature?

There have been a variety of approaches taken to try to characterize and identify the genetic basis of adaptation in nature, spanning theoretical models, experimental evolution studies and direct tests of natural populations. Theoretical models can provide formalized and detailed hypotheses regarding evolutionary processes and patterns, from which experimental evolution studies can then provide important proofs of concepts and characterize what is biologically reasonable. Genetic and genomic data from natural populations then allow for the identification of the particular factors that have and continue to play an important role in shaping adaptive evolution in the natural world. Further to this, experimental evolution studies allow for tests of theories that may be difficult or impossible to test in natural populations for logistical and methodological reasons and can even generate new insights, suggesting further refinement of existing theories. However, as experimental evolution studies often take place in a very particular set of controlled conditions--that is simple environments, a small range of usually asexual species, relatively short timescales--the question remains as to how applicable these experimental results are to natural populations. In this review, we discuss important insights coming from experimental evolution, focusing on four key topics tied to the evolutionary genetics of adaptation, and within those topics, we discuss the extent to which the experimental work compliments and informs natural population studies. We finish by making suggestions for future work in particular a need for natural population genomic time series data, as well as the necessity for studies that combine both experimental evolution and natural population approaches.

A Balance between Inhibitor Binding and Substrate Processing Confers Influenza Drug Resistance

The therapeutic benefits of the neuraminidase (NA) inhibitor oseltamivir are dampened by the emergence of drug resistance mutations in influenza A virus (IAV). To investigate the mechanistic features that underlie resistance, we developed an approach to quantify the effects of all possible single-nucleotide substitutions introduced into important regions of NA. We determined the experimental fitness effects of 450 nucleotide mutations encoding positions both surrounding the active site and at more distant sites in an N1 strain of IAV in the presence and absence of oseltamivir. NA mutations previously known to confer oseltamivir resistance in N1 strains, including H275Y and N295S, were adaptive in the presence of drug, indicating that our experimental system captured salient features of real-world selection pressures acting on NA. We identified mutations, including several at position 223, that reduce the apparent affinity for oseltamivir in vitro. Position 223 of NA is located adjacent to a hydrophobic portion of oseltamivir that is chemically distinct from the substrate, making it a hotspot for substitutions that preferentially impact drug binding relative to substrate processing. Furthermore, two NA mutations, K221N and Y276F, each reduce susceptibility to oseltamivir by increasing NA activity without altering drug binding. These results indicate that competitive expansion of IAV in the face of drug pressure is mediated by a balance between inhibitor binding and substrate processing.

The consequences of not accounting for background selection in demographic inference

Recently, there has been increased awareness of the role of background selection (BGS) in both data analysis and modelling advances. However, BGS is still difficult to take into account because of tractability issues with simulations and difficulty with nonequilibrium demographic models. Often, simple rescaling adjustments of effective population size are used. However, there has been neither a proper characterization of how BGS could bias or shift inference when not properly taken into account, nor a thorough analysis of whether rescaling is a sufficient solution. Here, we carry out extensive simulations with BGS to determine biases and behaviour of demographic inference using an approximate Bayesian approach. We find that results can be positively misleading with significant bias, and describe the parameter space in which BGS models replicate observed neutral nonequilibrium expectations.