Protein sequence landscapes are not so simple: on reference-free versus reference-based inference

In a recent preprint, Park, Metzger, and Thornton reanalyze 20 empirical protein sequence-function landscapes using a "reference-free analysis" (RFA) method they recently developed. They argue that these empirical landscapes are simpler and less epistatic than earlier work suggested, and attribute the difference to limitations of the methods used in the original analyses of these landscapes, which they claim are more sensitive to measurement noise, missing data, and other artifacts. Here, we show that these claims are incorrect. Instead, we find that the RFA method introduced by Park et al. is exactly equivalent to the reference-based least-squares methods used in the original analysis of many of these empirical landscapes (and also equivalent to a Hadamard-based approach they implement). Because the reanalyzed and original landscapes are in fact identical, the different conclusions drawn by Park et al. instead reflect different interpretations of the parameters describing the inferred landscapes; we argue that these do not support the conclusion that epistasis plays only a small role in protein sequence-function landscapes.

A dynamical limit to evolutionary adaptation

Natural selection makes evolutionary adaptation possible even if the overwhelming majority of new mutations are deleterious. However, in rapidly evolving populations where numerous linked mutations occur and segregate simultaneously, clonal interference and genetic hitchhiking can limit the efficiency of selection, allowing deleterious mutations to accumulate over time. This can in principle overwhelm the fitness increases provided by beneficial mutations, leading to an overall fitness decline. Here, we analyze the conditions under which evolution will tend to drive populations to higher versus lower fitness. Our analysis focuses on quantifying the boundary between these two regimes, as a function of parameters such as population size, mutation rates, and selection pressures. This boundary represents a state in which adaptation is precisely balanced by Muller's ratchet, and we show that it can be characterized by rapid molecular evolution without any net fitness change. Finally, we consider the implications of global fitness-mediated epistasis and find that under some circumstances, this can drive populations toward the boundary state, which can thus represent a long-term evolutionary attractor.

Evolution of haploid and diploid populations reveals common, strong, and variable pleiotropic effects in non-home environments

Adaptation is driven by the selection for beneficial mutations that provide a fitness advantage in the specific environment in which a population is evolving. However, environments are rarely constant or predictable. When an organism well adapted to one environment finds itself in another, pleiotropic effects of mutations that made it well adapted to its former environment will affect its success. To better understand such pleiotropic effects, we evolved both haploid and diploid barcoded budding yeast populations in multiple environments, isolated adaptive clones, and then determined the fitness effects of adaptive mutations in 'non-home' environments in which they were not selected. We find that pleiotropy is common, with most adaptive evolved lineages showing fitness effects in non-home environments. Consistent with other studies, we find that these pleiotropic effects are unpredictable: they are beneficial in some environments and deleterious in others. However, we do find that lineages with adaptive mutations in the same genes tend to show similar pleiotropic effects. We also find that ploidy influences the observed adaptive mutational spectra in a condition-specific fashion. In some conditions, haploids and diploids are selected with adaptive mutations in identical genes, while in others they accumulate mutations in almost completely disjoint sets of genes.

Inferring sparse structure in genotype-phenotype maps

Correlation among multiple phenotypes across related individuals may reflect some pattern of shared genetic architecture: individual genetic loci affect multiple phenotypes (an effect known as pleiotropy), creating observable relationships between phenotypes. A natural hypothesis is that pleiotropic effects reflect a relatively small set of common "core" cellular processes: each genetic locus affects one or a few core processes, and these core processes in turn determine the observed phenotypes. Here, we propose a method to infer such structure in genotype-phenotype data. Our approach, sparse structure discovery (SSD) is based on a penalized matrix decomposition designed to identify latent structure that is low-dimensional (many fewer core processes than phenotypes and genetic loci), locus-sparse (each locus affects few core processes), and/or phenotype-sparse (each phenotype is influenced by few core processes). Our use of sparsity as a guide in the matrix decomposition is motivated by the results of a novel empirical test indicating evidence of sparse structure in several recent genotype-phenotype datasets. First, we use synthetic data to show that our SSD approach can accurately recover core processes if each genetic locus affects few core processes or if each phenotype is affected by few core processes. Next, we apply the method to three datasets spanning adaptive mutations in yeast, genotoxin robustness assay in human cell lines, and genetic loci identified from a yeast cross, and evaluate the biological plausibility of the core process identified. More generally, we propose sparsity as a guiding prior for resolving latent structure in empirical genotype-phenotype maps.

A dynamical limit to evolutionary adaptation

Natural selection makes evolutionary adaptation possible even if the overwhelming majority of new mutations are deleterious. However, in rapidly evolving populations where numerous linked mutations occur and segregate simultaneously, clonal interference and genetic hitchhiking can limit the efficiency of selection, allowing deleterious mutations to accumulate over time. This can in principle overwhelm the fitness increases provided by beneficial mutations, leading to an overall fitness decline. Here, we analyze the conditions under which evolution will tend to drive populations to higher versus lower fitness. Our analysis focuses on quantifying the boundary between these two regimes, as a function of parameters such as population size, mutation rates, and selection pressures. This boundary represents a state in which adaptation is precisely balanced by Muller's ratchet, and we show that it can be characterized by rapid molecular evolution without any net fitness change. Finally, we consider the implications of global fitness-mediated epistasis, and find that under some circumstances this can drive populations towards the boundary state, which can thus represent a long-term evolutionary attractor.

Social network structure and the spread of complex contagions from a population genetics perspective

Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a nonlinear function of the fraction of the individuals' affected neighbors, such a spreading process becomes a "complex contagion." This nonlinearity does not typically appear with physically spreading infections, but instead can emerge when the concept that is spreading is subject to game theoretical considerations (e.g., for choices of strategy or behavior) or psychological effects such as social reinforcement and other forms of peer influence (e.g., for ideas, preferences, or opinions). Here we study how the stochastic dynamics of such complex contagions are affected by the underlying network structure. Motivated by simulations of complex contagions on real social networks, we present a framework for analyzing the statistics of contagions with arbitrary nonlinear adoption probabilities based on the mathematical tools of population genetics. The central idea is to use an effective lower-dimensional diffusion process to approximate the statistics of the contagion. This leads to a tradeoff between the effects of "selection" (microscopic tendencies for an idea to spread or die out), random drift, and network structure. Our framework illustrates intuitively several key properties of complex contagions: stronger community structure and network sparsity can significantly enhance the spread, while broad degree distributions dampen the effect of selection compared to random drift. Finally, we show that some structural features can exhibit critical values that demarcate regimes where global contagions become possible for networks of arbitrary size. Our results draw parallels between the competition of genes in a population and memes in a world of minds and ideas. Our tools provide insight into the spread of information, behaviors, and ideas via social influence, and highlight the role of macroscopic network structure in determining their fate.

Yeast population dynamics in Brazilian bioethanol production

The large-scale and nonaseptic fermentation of sugarcane feedstocks into fuel ethanol in biorefineries represents a unique ecological niche, in which the yeast Saccharomyces cerevisiae is the predominant organism. Several factors, such as sugarcane variety, process design, and operating and weather conditions, make each of the ∼400 industrial units currently operating in Brazil a unique ecosystem. Here, we track yeast population dynamics in 2 different biorefineries through 2 production seasons (April to November of 2018 and 2019), using a novel statistical framework on a combination of metagenomic and clonal sequencing data. We find that variation from season to season in 1 biorefinery is small compared to the differences between the 2 units. In 1 biorefinery, all lineages present during the entire production period derive from 1 of the starter strains, while in the other, invading lineages took over the population and displaced the starter strain. However, despite the presence of invading lineages and the nonaseptic nature of the process, all yeast clones we isolated are phylogenetically related to other previously sequenced bioethanol yeast strains, indicating a common origin from this industrial niche. Despite the substantial changes observed in yeast populations through time in each biorefinery, key process indicators remained quite stable through both production seasons, suggesting that the process is robust to the details of these population dynamics.

Epistasis and evolution: recent advances and an outlook for prediction

As organisms evolve, the effects of mutations change as a result of epistatic interactions with other mutations accumulated along the line of descent. This can lead to shifts in adaptability or robustness that ultimately shape subsequent evolution. Here, we review recent advances in measuring, modeling, and predicting epistasis along evolutionary trajectories, both in microbial cells and single proteins. We focus on simple patterns of global epistasis that emerge in this data, in which the effects of mutations can be predicted by a small number of variables. The emergence of these patterns offers promise for efforts to model epistasis and predict evolution.

Genotype-phenotype landscapes for immune-pathogen coevolution

Our immune systems constantly coevolve with the pathogens that challenge them, as pathogens adapt to evade our defense responses, with our immune repertoires shifting in turn. These coevolutionary dynamics take place across a vast and high-dimensional landscape of potential pathogen and immune receptor sequence variants. Mapping the relationship between these genotypes and the phenotypes that determine immune-pathogen interactions is crucial for understanding, predicting, and controlling disease. Here, we review recent developments applying high-throughput methods to create large libraries of immune receptor and pathogen protein sequence variants and measure relevant phenotypes. We describe several approaches that probe different regions of the high-dimensional sequence space and comment on how combinations of these methods may offer novel insight into immune-pathogen coevolution.

The landscape of antibody binding affinity in SARS-CoV-2 Omicron BA.1 evolution

The Omicron BA.1 variant of SARS-CoV-2 escapes convalescent sera and monoclonal antibodies that are effective against earlier strains of the virus. This immune evasion is largely a consequence of mutations in the BA.1 receptor binding domain (RBD), the major antigenic target of SARS-CoV-2. Previous studies have identified several key RBD mutations leading to escape from most antibodies. However, little is known about how these escape mutations interact with each other and with other mutations in the RBD. Here, we systematically map these interactions by measuring the binding affinity of all possible combinations of these 15 RBD mutations (215=32,768 genotypes) to 4 monoclonal antibodies (LY-CoV016, LY-CoV555, REGN10987, and S309) with distinct epitopes. We find that BA.1 can lose affinity to diverse antibodies by acquiring a few large-effect mutations and can reduce affinity to others through several small-effect mutations. However, our results also reveal alternative pathways to antibody escape that does not include every large-effect mutation. Moreover, epistatic interactions are shown to constrain affinity decline in S309 but only modestly shape the affinity landscapes of other antibodies. Together with previous work on the ACE2 affinity landscape, our results suggest that the escape of each antibody is mediated by distinct groups of mutations, whose deleterious effects on ACE2 affinity are compensated by another distinct group of mutations (most notably Q498R and N501Y).

Hierarchical sequence-affinity landscapes shape the evolution of breadth in an anti-influenza receptor binding site antibody

Broadly neutralizing antibodies (bnAbs) that neutralize diverse variants of a particular virus are of considerable therapeutic interest. Recent advances have enabled us to isolate and engineer these antibodies as therapeutics, but eliciting them through vaccination remains challenging, in part due to our limited understanding of how antibodies evolve breadth. Here, we analyze the landscape by which an anti-influenza receptor binding site (RBS) bnAb, CH65, evolved broad affinity to diverse H1 influenza strains. We do this by generating an antibody library of all possible evolutionary intermediates between the unmutated common ancestor (UCA) and the affinity-matured CH65 antibody and measure the affinity of each intermediate to three distinct H1 antigens. We find that affinity to each antigen requires a specific set of mutations - distributed across the variable light and heavy chains - that interact non-additively (i.e., epistatically). These sets of mutations form a hierarchical pattern across the antigens, with increasingly divergent antigens requiring additional epistatic mutations beyond those required to bind less divergent antigens. We investigate the underlying biochemical and structural basis for these hierarchical sets of epistatic mutations and find that epistasis between heavy chain mutations and a mutation in the light chain at the V_H-V_L interface is essential for binding a divergent H1. Collectively, this is the first work to comprehensively characterize epistasis between heavy and light chain mutations and shows that such interactions are both strong and widespread. Together with our previous study analyzing a different class of anti-influenza antibodies, our results implicate epistasis as a general feature of antibody sequence-affinity landscapes that can potentiate and constrain the evolution of breadth.

Towards evolutionary predictions: Current promises and challenges

Evolution has traditionally been a historical and descriptive science, and predicting future evolutionary processes has long been considered impossible. However, evolutionary predictions are increasingly being developed and used in medicine, agriculture, biotechnology and conservation biology. Evolutionary predictions may be used for different purposes, such as to prepare for the future, to try and change the course of evolution or to determine how well we understand evolutionary processes. Similarly, the exact aspect of the evolved population that we want to predict may also differ. For example, we could try to predict which genotype will dominate, the fitness of the population or the extinction probability of a population. In addition, there are many uses of evolutionary predictions that may not always be recognized as such. The main goal of this review is to increase awareness of methods and data in different research fields by showing the breadth of situations in which evolutionary predictions are made. We describe how diverse evolutionary predictions share a common structure described by the predictive scope, time scale and precision. Then, by using examples ranging from SARS-CoV2 and influenza to CRISPR-based gene drives and sustainable product formation in biotechnology, we discuss the methods for predicting evolution, the factors that affect predictability and how predictions can be used to prevent evolution in undesirable directions or to promote beneficial evolution (i.e. evolutionary control). We hope that this review will stimulate collaboration between fields by establishing a common language for evolutionary predictions.

The influenza hemagglutinin stem antibody CR9114: Evidence for a narrow evolutionary path towards universal protection

Human monoclonal antibodies (hmAbs) that protect against all influenza A and B strains are considered the road to universal influenza vaccines. Based on publicly-available data, we analyze the mechanistic and structural basis of pan-influenza protection by CR9114, a hemagglutinin (HA) stem-reactive antibody that protects against influenza subtypes from groups A1, A2, and B. The mechanistic basis of CR9114’s universal protection is not limited to in vitro neutralization, as CR9114 also protects in vivo from strains that escape its neutralizing activity: some H2 strains and influenza B. Fusion inhibition, viral egress inhibition, and activation of Fc-mediated effector functions are key contributors to CR9114’s universal protection. A comparative analysis of paratopes – between CR9114 (pan-influenza protection) and structurally similar VH1-69 hmAb CR6261 (influenza A1 protection) – pinpoints the structural basis of pan-influenza protection. CR9114’s heterosubtypic binding is conferred by its ability to bind HA with multiple domains: three HCDR loops and FR3. In contrast to other VH1-69 hmAbs, CR9114 uses a long and polar side chain of tyrosine (Y) residues on its HCDR3 for crucial H-bonds with H3, H5, and B HA. The recognition of a highly conserved epitope by CR9114 results in a high genetic barrier for escape by influenza strains. The nested, hierarchical structure of the mutations between the germline ancestor and CR9114 demonstrates that it is the result of a narrow evolutionary pathway within the B cell population. This rare evolutionary pathway indicates an immuno-recessive epitope and limited opportunity for vaccines to induce a polyclonal CR9114-like response.

Spatial structure alters the site frequency spectrum produced by hitchhiking

The reduction of genetic diversity due to genetic hitchhiking is widely used to find past selective sweeps from sequencing data, but very little is known about how spatial structure affects hitchhiking. We use mathematical modeling and simulations to find the unfolded site frequency spectrum left by hitchhiking in the genomic region of a sweep in a population occupying a 1D range. For such populations, sweeps spread as Fisher waves, rather than logistically. We find that this leaves a characteristic 3-part site frequency spectrum at loci very close to the swept locus. Very low frequencies are dominated by recent mutations that occurred after the sweep and are unaffected by hitchhiking. At moderately low frequencies, there is a transition zone primarily composed of alleles that briefly "surfed" on the wave of the sweep before falling out of the wavefront, leaving a spectrum close to that expected in well-mixed populations. However, for moderate-to-high frequencies, there is a distinctive scaling regime of the site frequency spectrum produced by alleles that drifted to fixation in the wavefront and then were carried throughout the population. For loci slightly farther away from the swept locus on the genome, recombination is much more effective at restoring diversity in 1D populations than it is in well-mixed ones. We find that these signatures of space can be strong even in apparently well-mixed populations with negligible spatial genetic differentiation, suggesting that spatial structure may frequently distort the signatures of hitchhiking in natural populations.

Mutational robustness changes during long-term adaptation in laboratory budding yeast populations

As an adapting population traverses the fitness landscape, its local neighborhood (i.e., the collection of fitness effects of single-step mutations) can change shape because of interactions with mutations acquired during evolution. These changes to the distribution of fitness effects can affect both the rate of adaptation and the accumulation of deleterious mutations. However, while numerous models of fitness landscapes have been proposed in the literature, empirical data on how this distribution changes during evolution remains limited. In this study, we directly measure how the fitness landscape neighborhood changes during laboratory adaptation. Using a barcode-based mutagenesis system, we measure the fitness effects of 91 specific gene disruption mutations in genetic backgrounds spanning 8000–10,000 generations of evolution in two constant environments. We find that the mean of the distribution of fitness effects decreases in one environment, indicating a reduction in mutational robustness, but does not change in the other. We show that these distribution-level patterns result from differences in the relative frequency of certain patterns of epistasis at the level of individual mutations, including fitness-correlated and idiosyncratic epistasis.

Idiosyncratic epistasis leads to global fitness-correlated trends

Epistasis can markedly affect evolutionary trajectories. In recent decades, protein-level fitness landscapes have revealed extensive idiosyncratic epistasis among specific mutations. By contrast, other work has found ubiquitous and apparently nonspecific patterns of global diminishing-returns and increasing-costs epistasis among mutations across the genome. Here, we used a hierarchical CRISPR gene drive system to construct all combinations of 10 missense mutations from across the genome in budding yeast and measured their fitness in six environments. We show that the resulting fitness landscapes exhibit global fitness-correlated trends but that these trends emerge from specific idiosyncratic interactions. We thus provide experimental validation of recent theoretical work arguing that fitness-correlated trends can emerge as the generic consequence of idiosyncratic epistasis.

Population genetics of polymorphism and divergence in rapidly evolving populations

In rapidly evolving populations, numerous beneficial and deleterious mutations can arise and segregate within a population at the same time. In this regime, evolutionary dynamics cannot be analyzed using traditional population genetic approaches that assume that sites evolve independently. Instead, the dynamics of many loci must be analyzed simultaneously. Recent work has made progress by first analyzing the fitness variation within a population, and then studying how individual lineages interact with this traveling fitness wave. However, these "traveling wave" models have previously been restricted to extreme cases where selection on individual mutations is either much faster or much slower than the typical coalescent timescale Tc. In this work, we show how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (Tcs) are neither large nor small compared to one. This enables us to describe the dynamics of populations subject to a wide range of fitness effects, and in particular, in cases where it is not immediately clear which mutations are most important in shaping the dynamics and statistics of genetic diversity. We use this approach to derive new expressions for the fixation probabilities and site frequency spectra of mutations as a function of their scaled fitness effects, along with related results for the coalescent timescale Tc and the rate of adaptation or Muller's ratchet. We find that competition between linked mutations can have a dramatic impact on the proportions of neutral and selected polymorphisms, which is not simply summarized by the scaled selection coefficient Tcs. We conclude by discussing the implications of these results for population genetic inferences.

Barcoded Bulk QTL mapping reveals highly polygenic and epistatic architecture of complex traits in yeast

Mapping the genetic basis of complex traits is critical to uncovering the biological mechanisms that underlie disease and other phenotypes. Genome-wide association studies (GWAS) in humans and quantitative trait locus (QTL) mapping in model organisms can now explain much of the observed heritability in many traits, allowing us to predict phenotype from genotype. However, constraints on power due to statistical confounders in large GWAS and smaller sample sizes in QTL studies still limit our ability to resolve numerous small-effect variants, map them to causal genes, identify pleiotropic effects across multiple traits, and infer non-additive interactions between loci (epistasis). Here, we introduce barcoded bulk quantitative trait locus (BB-QTL) mapping, which allows us to construct, genotype, and phenotype 100,000 offspring of a budding yeast cross, two orders of magnitude larger than the previous state of the art. We use this panel to map the genetic basis of eighteen complex traits, finding that the genetic architecture of these traits involves hundreds of small-effect loci densely spaced throughout the genome, many with widespread pleiotropic effects across multiple traits. Epistasis plays a central role, with thousands of interactions that provide insight into genetic networks. By dramatically increasing sample size, BB-QTL mapping demonstrates the potential of natural variants in high-powered QTL studies to reveal the highly polygenic, pleiotropic, and epistatic architecture of complex traits.

Dynamics and variability in the pleiotropic effects of adaptation in laboratory budding yeast populations

Evolutionary adaptation to a constant environment is driven by the accumulation of mutations which can have a range of unrealized pleiotropic effects in other environments. These pleiotropic consequences of adaptation can influence the emergence of specialists or generalists, and are critical for evolution in temporally or spatially fluctuating environments. While many experiments have examined the pleiotropic effects of adaptation at a snapshot in time, very few have observed the dynamics by which these effects emerge and evolve. Here, we propagated hundreds of diploid and haploid laboratory budding yeast populations in each of three environments, and then assayed their fitness in multiple environments over 1000 generations of evolution. We find that replicate populations evolved in the same condition share common patterns of pleiotropic effects across other environments, which emerge within the first several hundred generations of evolution. However, we also find dynamic and environment-specific variability within these trends: variability in pleiotropic effects tends to increase over time, with the extent of variability depending on the evolution environment. These results suggest shifting and overlapping contributions of chance and contingency to the pleiotropic effects of adaptation, which could influence evolutionary trajectories in complex environments that fluctuate across space and time.

Binding affinity landscapes constrain the evolution of broadly neutralizing anti-influenza antibodies

Over the past two decades, several broadly neutralizing antibodies (bnAbs) that confer protection against diverse influenza strains have been isolated. Structural and biochemical characterization of these bnAbs has provided molecular insight into how they bind distinct antigens. However, our understanding of the evolutionary pathways leading to bnAbs, and thus how best to elicit them, remains limited. Here, we measure equilibrium dissociation constants of combinatorially complete mutational libraries for two naturally isolated influenza bnAbs (CR9114, 16 heavy-chain mutations; CR6261, 11 heavy-chain mutations), reconstructing all possible evolutionary intermediates back to the unmutated germline sequences. We find that these two libraries exhibit strikingly different patterns of breadth: while many variants of CR6261 display moderate affinity to diverse antigens, those of CR9114 display appreciable affinity only in specific, nested combinations. By examining the extensive pairwise and higher order epistasis between mutations, we find key sites with strong synergistic interactions that are highly similar across antigens for CR6261 and different for CR9114. Together, these features of the binding affinity landscapes strongly favor sequential acquisition of affinity to diverse antigens for CR9114, while the acquisition of breadth to more similar antigens for CR6261 is less constrained. These results, if generalizable to other bnAbs, may explain the molecular basis for the widespread observation that sequential exposure favors greater breadth, and such mechanistic insight will be essential for predicting and eliciting broadly protective immune responses.

The genetic basis of differential autodiploidization in evolving yeast populations

Spontaneous whole-genome duplication, or autodiploidization, is a common route to adaptation in experimental evolution of haploid budding yeast populations. The rate at which autodiploids fix in these populations appears to vary across strain backgrounds, but the genetic basis of these differences remains poorly characterized. Here, we show that the frequency of autodiploidization differs dramatically between two closely related laboratory strains of Saccharomyces cerevisiae, BY4741 and W303. To investigate the genetic basis of this difference, we crossed these strains to generate hundreds of unique F1 segregants and tested the tendency of each segregant to autodiplodize across hundreds of generations of laboratory evolution. We find that variants in the SSD1 gene are the primary genetic determinant of differences in autodiploidization. We then used multiple laboratory and wild strains of S. cerevisiae to show that clonal populations of strains with a functional copy of SSD1 autodiploidize more frequently in evolution experiments, while knocking out this gene or replacing it with the W303 allele reduces autodiploidization propensity across all genetic backgrounds tested. These results suggest a potential strategy for modifying rates of spontaneous whole-genome duplications in laboratory evolution experiments in haploid budding yeast. They may also have relevance to other settings in which eukaryotic genome stability plays an important role, such as biomanufacturing and the treatment of pathogenic fungal diseases and cancers.

Global epistasis emerges from a generic model of a complex trait

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

Phenotypic and molecular evolution across 10,000 generations in laboratory budding yeast populations

Laboratory experimental evolution provides a window into the details of the evolutionary process. To investigate the consequences of long-term adaptation, we evolved 205 Saccharomyces cerevisiae populations (124 haploid and 81 diploid) for ~10,000,000 generations in three environments. We measured the dynamics of fitness changes over time, finding repeatable patterns of declining adaptability. Sequencing revealed that this phenotypic adaptation is coupled with a steady accumulation of mutations, widespread genetic parallelism, and historical contingency. In contrast to long-term evolution in E. coli, we do not observe long-term coexistence or populations with highly elevated mutation rates. We find that evolution in diploid populations involves both fixation of heterozygous mutations and frequent loss-of-heterozygosity events. Together, these results help distinguish aspects of evolutionary dynamics that are likely to be general features of adaptation across many systems from those that are specific to individual organisms and environmental conditions.

High-resolution lineage tracking reveals travelling wave of adaptation in laboratory yeast

In rapidly adapting asexual populations, including many microbial pathogens and viruses, numerous mutant lineages often compete for dominance within the population^1-5. These complex evolutionary dynamics determine the outcomes of adaptation, but have been difficult to observe directly. Previous studies have used whole-genome sequencing to follow molecular adaptation^6-10; however, these methods have limited resolution in microbial populations. Here we introduce a renewable barcoding system to observe evolutionary dynamics at high resolution in laboratory budding yeast. We find nested patterns of interference and hitchhiking even at low frequencies. These events are driven by the continuous appearance of new mutations that modify the fates of existing lineages before they reach substantial frequencies. We observe how the distribution of fitness within the population changes over time, and find a travelling wave of adaptation that has been predicted by theory^11-17. We show that clonal competition creates a dynamical 'rich-get-richer' effect: fitness advantages that are acquired early in evolution drive clonal expansions, which increase the chances of acquiring future mutations. However, less-fit lineages also routinely leapfrog over strains of higher fitness. Our results demonstrate that this combination of factors, which is not accounted for in existing models of evolutionary dynamics, is critical in determining the rate, predictability and molecular basis of adaptation.

Higher-fitness yeast genotypes are less robust to deleterious mutations

Natural selection drives populations toward higher fitness, but second-order selection for adaptability and mutational robustness can also influence evolution. In many microbial systems, diminishing-returns epistasis contributes to a tendency for more-fit genotypes to be less adaptable, but no analogous patterns for robustness are known. To understand how robustness varies across genotypes, we measure the fitness effects of hundreds of individual insertion mutations in a panel of yeast strains. We find that more-fit strains are less robust: They have distributions of fitness effects with lower mean and higher variance. These differences arise because many mutations have more strongly deleterious effects in faster-growing strains. This negative correlation between fitness and robustness implies that second-order selection for robustness will tend to conflict with first-order selection for fitness.

Best practices in near-infrared fluorescence imaging with indocyanine green (NIRF/ICG)-guided robotic urologic surgery: a systematic review-based expert consensus

PURPOSE

The aim of the present study is to investigate the impact of the near-infrared (NIRF) technology with indocyanine green (ICG) in robotic urologic surgery by performing a systematic literature review and to provide evidence-based expert recommendations on best practices in this field.

METHODS

All English language publications on NIRF/ICG-guided robotic urologic procedures were evaluated. We followed the PRISMA (Preferred Reporting Items for Systematic Review and Meta-Analyses) statement to evaluate PubMed^®, Scopus^® and Web of Science™ databases (up to April 2019). Experts in the field provided detailed pictures and intraoperative video-clips of different NIRF/ICG-guided robotic surgeries with recommendations for each procedure. A unique QRcode was generated and linked to each underlying video-clip. This new exclusive feature makes the present the first "dynamic paper" that merges text and figure description with their own video providing readers an innovative, immersive, high-quality and user-friendly experience.

RESULTS

Our electronic search identified a total of 576 papers. Of these, 36 studies included in the present systematic review reporting the use of NIRF/ICG in robotic partial nephrectomy (n = 13), robotic radical prostatectomy and lymphadenectomy (n = 7), robotic ureteral re-implantation and reconstruction (n = 5), robotic adrenalectomy (n = 4), robotic radical cystectomy (n = 3), penectomy and robotic inguinal lymphadenectomy (n = 2), robotic simple prostatectomy (n = 1), robotic kidney transplantation (n = 1) and robotic sacrocolpopexy (n = 1).

CONCLUSION

NIRF/ICG technology has now emerged as a safe, feasible and useful tool that may facilitate urologic robotic surgery. It has been shown to improve the identification of key anatomical landmarks and pathological structures for oncological and non-oncological procedures. Level of evidence is predominantly low. Larger series with longer follow-up are needed, especially in assessing the quality of the nodal dissection and the feasibility of the identification of sentinel nodes and the impact of these novel technologies on long-term oncological and functional outcomes.

Evolthon: A community endeavor to evolve lab evolution

In experimental evolution, scientists evolve organisms in the lab, typically by challenging them to new environmental conditions. How best to evolve a desired trait? Should the challenge be applied abruptly, gradually, periodically, sporadically? Should one apply chemical mutagenesis, and do strains with high innate mutation rate evolve faster? What are ideal population sizes of evolving populations? There are endless strategies, beyond those that can be exposed by individual labs. We therefore arranged a community challenge, Evolthon, in which students and scientists from different labs were asked to evolve Escherichia coli or Saccharomyces cerevisiae for an abiotic stress—low temperature. About 30 participants from around the world explored diverse environmental and genetic regimes of evolution. After a period of evolution in each lab, all strains of each species were competed with one another. In yeast, the most successful strategies were those that used mating, underscoring the importance of sex in evolution. In bacteria, the fittest strain used a strategy based on exploration of different mutation rates. Different strategies displayed variable levels of performance and stability across additional challenges and conditions. This study therefore uncovers principles of effective experimental evolutionary regimens and might prove useful also for biotechnological developments of new strains and for understanding natural strategies in evolutionary arms races between species. Evolthon constitutes a model for community-based scientific exploration that encourages creativity and cooperation.

This Community Page article describes Evolthon; a first-of-its-kind community-based effort, involving about 30 participant labs around the world, aiming to explore the best strategy for evolving microorganisms to cope with an environmental challenge.

Experimental Studies of Evolutionary Dynamics in Microbes

Evolutionary dynamics in laboratory microbial evolution experiments can be surprisingly complex. In the past two decades, observations of these dynamics have challenged simple models of adaptation and have shown that clonal interference, hitchhiking, ecological diversification, and contingency are widespread. In recent years, advances in high-throughput strain maintenance and phenotypic assays, the dramatically reduced cost of genome sequencing, and emerging methods for lineage barcoding have made it possible to observe evolutionary dynamics at unprecedented resolution. These new methods can now begin to provide detailed measurements of key aspects of fitness landscapes and of evolutionary outcomes across a range of systems. These measurements can highlight challenges to existing theoretical models and guide new theoretical work towards the complications that are most widely important.

Recombination Alters the Dynamics of Adaptation on Standing Variation in Laboratory Yeast Populations

The rates and selective effects of beneficial mutations, together with population genetic factors such as population size and recombination rate, determine the outcomes of adaptation and the signatures this process leaves in patterns of genetic diversity. Previous experimental studies of microbial evolution have focused primarily on initially clonal populations, finding that adaptation is characterized by new strongly selected beneficial mutations that sweep rapidly to fixation. Here, we study evolution in diverse outcrossed yeast populations, tracking the rate and genetic basis of adaptation over time. We combine time-serial measurements of fitness and allele frequency changes in 18 populations of budding yeast evolved at different outcrossing rates to infer the drivers of adaptation on standing genetic variation. In contrast to initially clonal populations, we find that adaptation is driven by a large number of weakly selected, linked variants. Populations undergoing different rates of outcrossing make use of this selected variation differently: whereas asexual populations evolve via rapid, inefficient, and highly variable fixation of clones, sexual populations adapt continuously by gradually breaking down linkage disequilibrium between selected variants. Our results demonstrate how recombination can sustain adaptation over long timescales by inducing a transition from selection on genotypes to selection on individual alleles, and show how pervasive linked selection can affect evolutionary dynamics.

Genetic variation in adaptability and pleiotropy in budding yeast

Evolution can favor organisms that are more adaptable, provided that genetic variation in adaptability exists. Here, we quantify this variation among 230 offspring of a cross between diverged yeast strains. We measure the adaptability of each offspring genotype, defined as its average rate of adaptation in a specific environmental condition, and analyze the heritability, predictability, and genetic basis of this trait. We find that initial genotype strongly affects adaptability and can alter the genetic basis of future evolution. Initial genotype also affects the pleiotropic consequences of adaptation for fitness in a different environment. This genetic variation in adaptability and pleiotropy is largely determined by initial fitness, according to a rule of declining adaptability with increasing initial fitness, but several individual QTLs also have a significant idiosyncratic role. Our results demonstrate that both adaptability and pleiotropy are complex traits, with extensive heritable differences arising from naturally occurring variation.

Follow-up after focal therapy in renal masses: an international multidisciplinary Delphi consensus project

PURPOSE

To establish consensus on follow-up (FU) after focal therapy (FT) in renal masses. To formulate recommendations to aid in clinical practice and research.

METHODS

Key topics and questions for consensus were identified from a systematic literature research. A Web-based questionnaire was distributed among participants selected based on their contribution to the literature and/or known expertise. Three rounds according to the Delphi method were performed online. Final discussion was conducted during the "8th International Symposium on Focal Therapy and Imaging in Prostate and Kidney Cancer" among an international multidisciplinary expert panel.

RESULTS

Sixty-two participants completed all three rounds of the online questionnaire. The panel recommended a minimum follow-up of 5 years, preferably extended to 10 years. The first FU was recommended at 3 months, with at least two imaging studies in the first year. Imaging was recommended biannually during the second year and annually thereafter. The panel recommended FU by means of CT scan with slice thickness ≤3 mm (at least three phases with excretory phase if suspicion of collecting system involvement) or mpMRI. Annual checkup for pulmonary metastasis by CT thorax was advised. Outside study protocols, biopsy during follow-up should only be performed in case of suspicion of residual/persistent disease or radiological recurrence.

CONCLUSIONS

The consensus led to clear FU recommendations after FT of renal masses supported by a multidisciplinary expert panel. In spite of the low level of evidence, these recommendations can guide clinicians and create uniformity in the follow-up practice and for clinical research purposes.

Sex speeds adaptation by altering the dynamics of molecular evolution

Sex and recombination are pervasive throughout nature despite their substantial costs¹. Understanding the evolutionary forces that maintain these phenomena is a central challenge in biology^2,3. One longstanding hypothesis argues that sex is beneficial because recombination speeds adaptation⁴. Theory has proposed a number of distinct population genetic mechanisms that could underlie this advantage. For example, sex can promote the fixation of beneficial mutations either by alleviating interference competition (the Fisher-Muller effect)^5,6 or by separating them from deleterious load (the ruby in the rubbish effect)^7,8. Previous experiments confirm that sex can increase the rate of adaptation^9–17, but these studies did not observe the evolutionary dynamics that drive this effect at the genomic level. Here, we present the first comparison between the sequence-level dynamics of adaptation in experimental sexual and asexual populations, which allows us to identify the specific mechanisms by which sex speeds adaptation. We find that sex alters the molecular signatures of evolution by changing the spectrum of mutations that fix, and confirm theoretical predictions that it does so by alleviating clonal interference. We also show that substantially deleterious mutations hitchhike to fixation in adapting asexual populations. In contrast, recombination prevents such mutations from fixing. Our results demonstrate that sex both speeds adaptation and alters its molecular signature by allowing natural selection to more efficiently sort beneficial from deleterious mutations.

Genomic investigations of evolutionary dynamics and epistasis in microbial evolution experiments

Microbial evolution experiments enable us to watch adaptation in real time, and to quantify the repeatability and predictability of evolution by comparing identical replicate populations. Further, we can resurrect ancestral types to examine changes over evolutionary time. Until recently, experimental evolution has been limited to measuring phenotypic changes, or to tracking a few genetic markers over time. However, recent advances in sequencing technology now make it possible to extensively sequence clones or whole-population samples from microbial evolution experiments. Here, we review recent work exploiting these techniques to understand the genomic basis of evolutionary change in experimental systems. We first focus on studies that analyze the dynamics of genome evolution in microbial systems. We then survey work that uses observations of sequence evolution to infer aspects of the underlying fitness landscape, concentrating on the epistatic interactions between mutations and the constraints these interactions impose on adaptation.

Crowded growth leads to the spontaneous evolution of semistable coexistence in laboratory yeast populations

Identifying the mechanisms that create and maintain biodiversity is a central challenge in biology. Stable diversification of microbial populations often requires the evolution of differences in resource utilization. Alternatively, coexistence can be maintained by specialization to exploit spatial heterogeneity in the environment. Here, we report spontaneous diversification maintained by a related but distinct mechanism: crowding avoidance. During experimental evolution of laboratory Saccharomyces cerevisiae populations, we observed the repeated appearance of "adherent" (A) lineages able to grow as a dispersed film, in contrast to their crowded "bottom-dweller" (B) ancestors. These two types stably coexist because dispersal reduces interference competition for nutrients among kin, at the cost of a slower maximum growth rate. This tradeoff causes the frequencies of the two types to oscillate around equilibrium over the course of repeated cycles of growth, crowding, and dispersal. However, further coevolution of the A and B types can perturb and eventually destroy their coexistence over longer time scales. We introduce a simple mathematical model of this "semistable" coexistence, which explains the interplay between ecological and evolutionary dynamics. Because crowded growth generally limits nutrient access in biofilms, the mechanism we report here may be broadly important in maintaining diversity in these natural environments.

A genomic and evolutionary approach reveals non-genetic drug resistance in malaria

BACKGROUND

Drug resistance remains a major public health challenge for malaria treatment and eradication. Individual loci associated with drug resistance to many antimalarials have been identified, but their epistasis with other resistance mechanisms has not yet been elucidated.

RESULTS

We previously described two mutations in the cytoplasmic prolyl-tRNA synthetase (cPRS) gene that confer resistance to halofuginone. We describe here the evolutionary trajectory of halofuginone resistance of two independent drug resistance selections in Plasmodium falciparum. Using this novel methodology, we discover an unexpected non-genetic drug resistance mechanism that P. falciparum utilizes before genetic modification of the cPRS. P. falciparum first upregulates its proline amino acid homeostasis in response to halofuginone pressure. We show that this non-genetic adaptation to halofuginone is not likely mediated by differential RNA expression and precedes mutation or amplification of the cPRS gene. By tracking the evolution of the two drug resistance selections with whole genome sequencing, we further demonstrate that the cPRS locus accounts for the majority of genetic adaptation to halofuginone in P. falciparum. We further validate that copy-number variations at the cPRS locus also contribute to halofuginone resistance.

CONCLUSIONS

We provide a three-step model for multi-locus evolution of halofuginone drug resistance in P. falciparum. Informed by genomic approaches, our results provide the first comprehensive view of the evolutionary trajectory malaria parasites take to achieve drug resistance. Our understanding of the multiple genetic and non-genetic mechanisms of drug resistance informs how we will design and pair future anti-malarials for clinical use.

A genomic and evolutionary approach reveals non-genetic drug resistance in malaria

Background

Drug resistance remains a major public health challenge for malaria treatment and eradication. Individual loci associated with drug resistance to many antimalarials have been identified, but their epistasis with other resistance mechanisms has not yet been elucidated.

Results

We previously described two mutations in the cytoplasmic prolyl-tRNA synthetase (cPRS) gene that confer resistance to halofuginone. We describe here the evolutionary trajectory of halofuginone resistance of two independent drug resistance selections in Plasmodium falciparum. Using this novel methodology, we discover an unexpected non-genetic drug resistance mechanism that P. falciparum utilizes before genetic modification of the cPRS. P. falciparum first upregulates its proline amino acid homeostasis in response to halofuginone pressure. We show that this non-genetic adaptation to halofuginone is not likely mediated by differential RNA expression and precedes mutation or amplification of the cPRS gene. By tracking the evolution of the two drug resistance selections with whole genome sequencing, we further demonstrate that the cPRS locus accounts for the majority of genetic adaptation to halofuginone in P. falciparum. We further validate that copy-number variations at the cPRS locus also contribute to halofuginone resistance.

Conclusions

We provide a three-step model for multi-locus evolution of halofuginone drug resistance in P. falciparum. Informed by genomic approaches, our results provide the first comprehensive view of the evolutionary trajectory malaria parasites take to achieve drug resistance. Our understanding of the multiple genetic and non-genetic mechanisms of drug resistance informs how we will design and pair future anti-malarials for clinical use.

Electronic supplementary material

The online version of this article (doi:10.1186/s13059-014-0511-2) contains supplementary material, which is available to authorized users.

Flexible gene pools

Rapid genetic exchange leads to mosaic genomes in cyanobacterial populations [Also see Report by Rosen et al. ]

Inexpensive multiplexed library preparation for megabase-sized genomes

Whole-genome sequencing has become an indispensible tool of modern biology. However, the cost of sample preparation relative to the cost of sequencing remains high, especially for small genomes where the former is dominant. Here we present a protocol for rapid and inexpensive preparation of hundreds of multiplexed genomic libraries for Illumina sequencing. By carrying out the Nextera tagmentation reaction in small volumes, replacing costly reagents with cheaper equivalents, and omitting unnecessary steps, we achieve a cost of library preparation of $8 per sample, approximately 6 times cheaper than the standard Nextera XT protocol. Furthermore, our procedure takes less than 5 hours for 96 samples. Several hundred samples can then be pooled on the same HiSeq lane via custom barcodes. Our method will be useful for re-sequencing of microbial or viral genomes, including those from evolution experiments, genetic screens, and environmental samples, as well as for other sequencing applications including large amplicon, open chromosome, artificial chromosomes, and RNA sequencing.

The competition between simple and complex evolutionary trajectories in asexual populations

BACKGROUND

On rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial "uphill" mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the evolutionary process determine the probability that evolution will take any specific path among a variety of competing possible trajectories. Understanding this evolutionary choice is essential if we are to understand the outcomes and predictability of adaptation on rugged landscapes.

RESULTS

We present a simple model to analyze the probability that evolution will eschew immediately uphill paths in favor of crossing fitness valleys or plateaus that lead to higher fitness but less accessible genotypes. We calculate how this probability depends on the population size, mutation rates, and relevant selection pressures, and compare our analytical results to Wright-Fisher simulations.

CONCLUSION

We find that the probability of valley crossing depends nonmonotonically on population size: intermediate size populations are most likely to follow a "greedy" strategy of acquiring immediately beneficial mutations even if they lead to evolutionary dead ends, while larger and smaller populations are more likely to cross fitness valleys to reach distant advantageous genotypes. We explicitly identify the boundaries between these different regimes in terms of the relevant evolutionary parameters. Above a certain threshold population size, we show that the probability that the population finds the more distant peak depends only on a single simple combination of the relevant parameters.

Functional characterization of bacteria isolated from ancient arctic soil exposes diverse resistance mechanisms to modern antibiotics

Using functional metagenomics to study the resistomes of bacterial communities isolated from different layers of the Canadian high Arctic permafrost, we show that microbial communities harbored diverse resistance mechanisms at least 5,000 years ago. Among bacteria sampled from the ancient layers of a permafrost core, we isolated eight genes conferring clinical levels of resistance against aminoglycoside, β-lactam and tetracycline antibiotics that are naturally produced by microorganisms. Among these resistance genes, four also conferred resistance against amikacin, a modern semi-synthetic antibiotic that does not naturally occur in microorganisms. In bacteria sampled from the overlaying active layer, we isolated ten different genes conferring resistance to all six antibiotics tested in this study, including aminoglycoside, β-lactam and tetracycline variants that are naturally produced by microorganisms as well as semi-synthetic variants produced in the laboratory. On average, we found that resistance genes found in permafrost bacteria conferred lower levels of resistance against clinically relevant antibiotics than resistance genes sampled from the active layer. Our results demonstrate that antibiotic resistance genes were functionally diverse prior to the anthropogenic use of antibiotics, contributing to the evolution of natural reservoirs of resistance genes.

Microbial evolution. Global epistasis makes adaptation predictable despite sequence-level stochasticity

Epistatic interactions between mutations can make evolutionary trajectories contingent on the chance occurrence of initial mutations. We used experimental evolution in Saccharomyces cerevisiae to quantify this contingency, finding differences in adaptability among 64 closely related genotypes. Despite these differences, sequencing of 104 evolved clones showed that initial genotype did not constrain future mutational trajectories. Instead, reconstructed combinations of mutations revealed a pattern of diminishing-returns epistasis: Beneficial mutations have consistently smaller effects in fitter backgrounds. Taken together, these results show that beneficial mutations affecting a variety of biological processes are globally coupled; they interact strongly, but only through their combined effect on fitness. As a consequence, fitness evolution follows a predictable trajectory even though sequence-level adaptation is stochastic.

Genetic diversity in the interference selection limit

Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. Here, we describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, similar to models of quantitative genetics, molecular evolution is determined by the variance in fitness within the population, defined over an effectively asexual segment of the genome (a "linkage block"). We exploit this insensitivity in a new "coarse-grained" coalescent framework, which approximates the effects of many weakly selected mutations with a smaller number of strongly selected mutations that create the same variance in fitness. This approximation generates accurate and efficient predictions for silent site variability when interference is common. However, these results suggest that there is reduced power to resolve individual selection pressures when interference is sufficiently widespread, since a broad range of parameters possess nearly identical patterns of silent site variability.

Pervasive genetic hitchhiking and clonal interference in forty evolving yeast populations

The dynamics of adaptation determine which mutations fix in a population, and hence how reproducible evolution will be. This is central to understanding the spectra of mutations recovered in the evolution of antibiotic resistance, the response of pathogens to immune selection, and the dynamics of cancer progression. In laboratory evolution experiments, demonstrably beneficial mutations are found repeatedly, but are often accompanied by other mutations with no obvious benefit. Here we use whole-genome whole-population sequencing to examine the dynamics of genome sequence evolution at high temporal resolution in 40 replicate Saccharomyces cerevisiae populations growing in rich medium for 1,000 generations. We find pervasive genetic hitchhiking: multiple mutations arise and move synchronously through the population as mutational 'cohorts'. Multiple clonal cohorts are often present simultaneously, competing with each other in the same population. Our results show that patterns of sequence evolution are driven by a balance between these chance effects of hitchhiking and interference, which increase stochastic variation in evolutionary outcomes, and the deterministic action of selection on individual mutations, which favours parallel evolutionary solutions in replicate populations.

Spatial population expansion promotes the evolution of cooperation in an experimental Prisoner's Dilemma

Cooperation is ubiquitous in nature, but explaining its existence remains a central interdisciplinary challenge. Cooperation is most difficult to explain in the Prisoner's Dilemma game, where cooperators always lose in direct competition with defectors despite increasing mean fitness. Here we demonstrate how spatial population expansion, a widespread natural phenomenon, promotes the evolution of cooperation. We engineer an experimental Prisoner's Dilemma game in the budding yeast Saccharomyces cerevisiae to show that, despite losing to defectors in nonexpanding conditions, cooperators increase in frequency in spatially expanding populations. Fluorescently labeled colonies show genetic demixing of cooperators and defectors, followed by increase in cooperator frequency as cooperator sectors overtake neighboring defector sectors. Together with lattice-based spatial simulations, our results suggest that spatial population expansion drives the evolution of cooperation by (1) increasing positive genetic assortment at population frontiers and (2) selecting for phenotypes maximizing local deme productivity. Spatial expansion thus creates a selective force whereby cooperator-enriched demes overtake neighboring defector-enriched demes in a "survival of the fastest." We conclude that colony growth alone can promote cooperation and prevent defection in microbes. Our results extend to other species with spatially restricted dispersal undergoing range expansion, including pathogens, invasive species, and humans.

Fluctuations in fitness distributions and the effects of weak linked selection on sequence evolution

Evolutionary dynamics and patterns of molecular evolution are strongly influenced by selection on linked regions of the genome, but our quantitative understanding of these effects remains incomplete. Recent work has focused on predicting the distribution of fitness within an evolving population, and this forms the basis for several methods that leverage the fitness distribution to predict the patterns of genetic diversity when selection is strong. However, in weakly selected populations random fluctuations due to genetic drift are more severe, and neither the distribution of fitness nor the sequence diversity within the population are well understood. Here, we briefly review the motivations behind the fitness-distribution picture, and summarize the general approaches that have been used to analyze this distribution in the strong-selection regime. We then extend these approaches to the case of weak selection, by outlining a perturbative treatment of selection at a large number of linked sites. This allows us to quantify the stochastic behavior of the fitness distribution and yields exact analytical predictions for the sequence diversity and substitution rate in the limit that selection is weak.

Dynamic mutation-selection balance as an evolutionary attractor

The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that maintains the balanced state. We find that a surprisingly low ε suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes.

Distortions in genealogies due to purifying selection

Purifying selection can substantially alter patterns of molecular evolution. Its main effect is to reduce overall levels of genetic variation, leading to a reduced effective population size. However, it also distorts genealogies relative to neutral expectations. A structured coalescent method has been used to describe this effect, and forms the basis for numerical methods and simulations. In this study, we extend this approach by making the additional approximation that lineages may be treated independently, which is valid only in the strong selection regime. We show that in this regime, the distortions due to purifying selection can be described by a time-dependent effective population size and mutation rate, confirming earlier intuition. We calculate simple analytical expressions for these functions, N(e)(t) and U(e)(t). These results allow us to describe the structure of genealogies in a population under strong purifying selection as equivalent to a purely neutral population with varying population size and mutation rate, thereby enabling the use of neutral methods of inference and estimation for populations in the strong selection regime.

Population subdivision and adaptation in asexual populations of Saccharomyces cerevisiae

Population subdivision limits competition between individuals, which can have a profound effect on adaptation. Subdivided populations maintain more genetic diversity at any given time compared to well-mixed populations, and thus "explore" larger parts of the genotype space. At the same time, beneficial mutations take longer to spread in such populations, and thus subdivided populations do not "exploit" discovered mutations as efficiently as well-mixed populations. Whether subdivision inhibits or promotes adaptation in a given environment depends on the relative importance of exploration versus exploitation, which in turn depends on the structure of epistasis among beneficial mutations. Here we investigate the relative importance of exploration versus exploitation for adaptation by evolving 976 independent asexual populations of budding yeast with several degrees of geographic subdivision. We find that subdivision systematically inhibits adaptation: even the luckiest demes in subdivided populations on average fail to discover genotypes that are fitter than those discovered by well-mixed populations. Thus, exploitation of discovered mutations is more important for adaptation in our system than a thorough exploration of the mutational neighborhood, and increasing subdivision slows adaptation.