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

Detecting epistasis from an ensemble of adapting populations

The role that epistasis plays during adaptation remains an outstanding problem, which has received considerable attention in recent years. Most of the recent empirical studies are based on ensembles of replicate populations that adapt in a fixed, laboratory controlled condition. Researchers often seek to infer the presence and form of epistasis in the fitness landscape from the time evolution of various statistics averaged across the ensemble of populations. Here, we provide a rigorous analysis of what quantities, drawn from time series of such ensembles, can be used to infer epistasis for populations evolving under weak mutation on finite-site fitness landscapes. First, we analyze the mean fitness trajectory-that is, the time course of the ensemble average fitness. We show that for any epistatic fitness landscape and starting genotype, there always exists a non-epistatic fitness landscape that produces the exact same mean fitness trajectory. Thus, the presence of epistasis is not identifiable from the mean fitness trajectory. By contrast, we show that two other ensemble statistics-the time evolution of the fitness variance across populations, and the time evolution of the mean number of substitutions-can detect certain forms of epistasis in the underlying fitness landscape.

Evaluating the ability of the pairwise joint site frequency spectrum to co-estimate selection and demography

The ability to infer the parameters of positive selection from genomic data has many important implications, from identifying drug-resistance mutations in viruses to increasing crop yield by genetically integrating favorable alleles. Although it has been well-described that selection and demography may result in similar patterns of diversity, the ability to jointly estimate these two processes has remained elusive. Here, we use simulation to explore the utility of the joint site frequency spectrum to estimate selection and demography simultaneously, including developing an extension of the previously proposed Jaatha program (Mathew et al., 2013). We evaluate both complete and incomplete selective sweeps under an isolation-with-migration model with and without population size change (both population growth and bottlenecks). Results suggest that while it may not be possible to precisely estimate the strength of selection, it is possible to infer the presence of selection while estimating accurate demographic parameters. We further demonstrate that the common assumption of selective neutrality when estimating demographic models may lead to severe biases. Finally, we apply the approach we have developed to better characterize the within-host demographic and selective history of human cytomegalovirus (HCMV) infection using published next generation sequencing data.

Viewing protein fitness landscapes through a next-gen lens

High-throughput sequencing has enabled many powerful approaches in biological research. Here, we review sequencing approaches to measure frequency changes within engineered mutational libraries subject to selection. These analyses can provide direct estimates of biochemical and fitness effects for all individual mutations across entire genes (and likely compact genomes in the near future) in genetically tractable systems such as microbes, viruses, and mammalian cells. The effects of mutations on experimental fitness can be assessed using sequencing to monitor time-dependent changes in mutant frequency during bulk competitions. The impact of mutations on biochemical functions can be determined using reporters or other means of separating variants based on individual activities (e.g., binding affinity for a partner molecule can be interrogated using surface display of libraries of mutant proteins and isolation of bound and unbound populations). The comprehensive investigation of mutant effects on both biochemical function and experimental fitness provide promising new avenues to investigate the connections between biochemistry, cell physiology, and evolution. We summarize recent findings from systematic mutational analyses; describe how they relate to a field rich in both theory and experimentation; and highlight how they may contribute to ongoing and future research into protein structure-function relationships, systems-level descriptions of cell physiology, and population-genetic inferences on the relative contributions of selection and drift.

Estimating the Fitness Effects of New Mutations in the Wild Yeast Saccharomyces paradoxus

The nature of selection acting on a population is in large measure determined by the distribution of fitness effects of new mutations. In this study, we use DNA sequences from four closely related clades of Saccharomyces paradoxus and Saccharomyces cerevisiae to identify and polarize new mutations and estimate their fitness effects. By progressively restricting the analyses to narrower categories of sites, we further seek to characterize sites with predictable mutational effects, that is, unconditionally deleterious, neutral or beneficial. Consistent with previous studies on S. paradoxus, we have failed to find evidence for mutations with beneficial effects, even in regions that were divergent in two outgroup clades, perhaps a consequence of the relatively unchallenged, predominantly asexual and highly inbred lifestyle of this species. On the other hand, there is abundant evidence of deleterious mutations, varying in severity of effect from strongly deleterious to very mild, particularly in regions conserved in the outgroup taxa, indicating a history of persistent purifying selection. Narrowing the analysis down to individual amino acids reduces further the range of effects: for example, mutations changing cysteine are predicted to be nearly always strongly deleterious, whereas those changing arginine, serine, and tyrosine are expected to be nearly neutral. The proportion of mutations with deleterious effects for a particular amino acid is correlated with long-term stasis of that amino acid among highly divergent sequences from a variety of organisms, showing that functionality of sites tends to persist through the diversification of clades and that our findings are also relevant to longer evolutionary times and other taxa.

Contingency and entrenchment in protein evolution under purifying selection

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

Software for the analysis and visualization of deep mutational scanning data

BACKGROUND

Deep mutational scanning is a technique to estimate the impacts of mutations on a gene by using deep sequencing to count mutations in a library of variants before and after imposing a functional selection. The impacts of mutations must be inferred from changes in their counts after selection.

RESULTS

I describe a software package, dms_tools, to infer the impacts of mutations from deep mutational scanning data using a likelihood-based treatment of the mutation counts. I show that dms_tools yields more accurate inferences on simulated data than simply calculating ratios of counts pre- and post-selection. Using dms_tools, one can infer the preference of each site for each amino acid given a single selection pressure, or assess the extent to which these preferences change under different selection pressures. The preferences and their changes can be intuitively visualized with sequence-logo-style plots created using an extension to weblogo.

CONCLUSIONS

dms_tools implements a statistically principled approach for the analysis and subsequent visualization of deep mutational scanning data.

The distribution of fitness effects in an uncertain world

The distribution of fitness effects (DFE) among new mutations plays a critical role in adaptive evolution and the maintenance of genetic variation. Although fitness landscape models predict several key features of the DFE, most theory to date focuses on predictable environmental conditions, while ignoring stochastic environmental fluctuations that feature prominently in the ecology of many organisms. Here, we derive an extension of Fisher's geometric model that incorporates two common effects of environmental variation: (1) nonadaptive genotype-by-environment interactions (G × E), in which the phenotype of a given genotype varies across environmental contexts; and (2) random fluctuation of the fitness optimum, which generates fluctuating selection. We show that both factors cause a mismatch between the DFE within single generations and the distribution of geometric mean fitness effects (averaged over multiple generations) that governs long-term evolutionary change. Such mismatches permit strong evolutionary constraints-despite an abundance of beneficial fitness variation within single environmental contexts-and to conflicting DFE estimates from direct versus indirect inference methods. Finally, our results suggest an intriguing parallel between the genetics and ecology of evolutionary constraints, with environmental fluctuations and pleiotropy placing qualitatively similar limits on the availability of adaptive genetic variation.

The rule of declining adaptability in microbial evolution experiments

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

Protein evolution. Pervasive degeneracy and epistasis in a protein-protein interface

Mapping protein sequence space is a difficult problem that necessitates the analysis of 20(N) combinations for sequences of length N. We systematically mapped the sequence space of four key residues in the Escherichia coli protein kinase PhoQ that drive recognition of its substrate PhoP. We generated a library containing all 160,000 variants of PhoQ at these positions and used a two-step selection coupled to next-generation sequencing to identify 1659 functional variants. Our results reveal extensive degeneracy in the PhoQ-PhoP interface and epistasis, with the effect of individual substitutions often highly dependent on context. Together, epistasis and the genetic code create a pattern of connectivity of functional variants in sequence space that likely constrains PhoQ evolution. Consequently, the diversity of PhoQ orthologs is substantially lower than that of functional PhoQ variants.

Thinking too positive? Revisiting current methods of population genetic selection inference

In the age of next-generation sequencing, the availability of increasing amounts and improved quality of data at decreasing cost ought to allow for a better understanding of how natural selection is shaping the genome than ever before. However, alternative forces, such as demography and background selection (BGS), obscure the footprints of positive selection that we would like to identify. In this review, we illustrate recent developments in this area, and outline a roadmap for improved selection inference. We argue (i) that the development and obligatory use of advanced simulation tools is necessary for improved identification of selected loci, (ii) that genomic information from multiple time points will enhance the power of inference, and (iii) that results from experimental evolution should be utilized to better inform population genomic studies.

The impact of macroscopic epistasis on long-term evolutionary dynamics

Genetic interactions can strongly influence the fitness effects of individual mutations, yet the impact of these epistatic interactions on evolutionary dynamics remains poorly understood. Here we investigate the evolutionary role of epistasis over 50,000 generations in a well-studied laboratory evolution experiment in Escherichia coli. The extensive duration of this experiment provides a unique window into the effects of epistasis during long-term adaptation to a constant environment. Guided by analytical results in the weak-mutation limit, we develop a computational framework to assess the compatibility of a given epistatic model with the observed patterns of fitness gain and mutation accumulation through time. We find that a decelerating fitness trajectory alone provides little power to distinguish between competing models, including those that lack any direct epistatic interactions between mutations. However, when combined with the mutation trajectory, these observables place strong constraints on the set of possible models of epistasis, ruling out many existing explanations of the data. Instead, we find that the data are consistent with a "two-epoch" model of adaptation, in which an initial burst of diminishing-returns epistasis is followed by a steady accumulation of mutations under a constant distribution of fitness effects. Our results highlight the need for additional DNA sequencing of these populations, as well as for more sophisticated models of epistasis that are compatible with all of the experimental data.

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.

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

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

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 is strongly influenced by rare mutations of large effect in a microbial mutation accumulation experiment

Our understanding of the evolutionary consequences of mutation relies heavily on estimates of the rate and fitness effect of spontaneous mutations generated by mutation accumulation (MA) experiments. We performed a classic MA experiment in which frequent sampling of MA lines was combined with whole genome resequencing to develop a high-resolution picture of the effect of spontaneous mutations in a hypermutator (ΔmutS) strain of the bacterium Pseudomonas aeruginosa. After ∼644 generations of mutation accumulation, MA lines had accumulated an average of 118 mutations, and we found that average fitness across all lines decayed linearly over time. Detailed analyses of the dynamics of fitness change in individual lines revealed that a large fraction of the total decay in fitness (42.3%) was attributable to the fixation of rare, highly deleterious mutations (comprising only 0.5% of fixed mutations). Furthermore, we found that at least 0.64% of mutations were beneficial and probably fixed due to positive selection. The majority of mutations that fixed (82.4%) were base substitutions and we failed to find any signatures of selection on nonsynonymous or intergenic mutations. Short indels made up a much smaller fraction of the mutations that were fixed (17.4%), but we found evidence of strong selection against indels that caused frameshift mutations in coding regions. These results help to quantify the amount of natural selection present in microbial MA experiments and demonstrate that changes in fitness are strongly influenced by rare mutations of large effect.

Influenza virus drug resistance: a time-sampled population genetics perspective

The challenge of distinguishing genetic drift from selection remains a central focus of population genetics. Time-sampled data may provide a powerful tool for distinguishing these processes, and we here propose approximate Bayesian, maximum likelihood, and analytical methods for the inference of demography and selection from time course data. Utilizing these novel statistical and computational tools, we evaluate whole-genome datasets of an influenza A H1N1 strain in the presence and absence of oseltamivir (an inhibitor of neuraminidase) collected at thirteen time points. Results reveal a striking consistency amongst the three estimation procedures developed, showing strongly increased selection pressure in the presence of drug treatment. Importantly, these approaches re-identify the known oseltamivir resistance site, successfully validating the approaches used. Enticingly, a number of previously unknown variants have also been identified as being positively selected. Results are interpreted in the light of Fisher's Geometric Model, allowing for a quantification of the increased distance to optimum exerted by the presence of drug, and theoretical predictions regarding the distribution of beneficial fitness effects of contending mutations are empirically tested. Further, given the fit to expectations of the Geometric Model, results suggest the ability to predict certain aspects of viral evolution in response to changing host environments and novel selective pressures.