Effects of selection stringency on the outcomes of directed evolution.

Directed evolution makes mutant lineages compete in climbing complicated sequence-function landscapes. Given this underlying complexity it is unclear how selection stringency, a ubiquitous parameter of directed evolution, impacts the outcome. Here we approach this question in terms of the fitnesses of the candidate variants at each round and the heterogeneity of their distributions of fitness effects. We show that even if the fittest mutant is most likely to yield the fittest mutants in the next round of selection, diversification can improve outcomes by sampling a larger variety of fitness effects. We find that heterogeneity in fitness effects between variants, larger population sizes, and evolution over a greater number of rounds all encourage diversification.

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.

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.

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.

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.

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 VH-VL 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.

Compensatory epistasis maintains ACE2 affinity in SARS-CoV-2 Omicron BA.1.

The Omicron BA.1 variant emerged in late 2021 and quickly spread across the world. Compared to the earlier SARS-CoV-2 variants, BA.1 has many mutations, some of which are known to enable antibody escape. Many of these antibody-escape mutations individually decrease the spike receptor-binding domain (RBD) affinity for ACE2, but BA.1 still binds ACE2 with high affinity. The fitness and evolution of the BA.1 lineage is therefore driven by the combined effects of numerous mutations. Here, we systematically map the epistatic interactions between the 15 mutations in the RBD of BA.1 relative to the Wuhan Hu-1 strain. Specifically, we measure the ACE2 affinity of all possible combinations of these 15 mutations (215 = 32,768 genotypes), spanning all possible evolutionary intermediates from the ancestral Wuhan Hu-1 strain to BA.1. We find that immune escape mutations in BA.1 individually reduce ACE2 affinity but are compensated by epistatic interactions with other affinity-enhancing mutations, including Q498R and N501Y. Thus, the ability of BA.1 to evade immunity while maintaining ACE2 affinity is contingent on acquiring multiple interacting mutations. Our results implicate compensatory epistasis as a key factor driving substantial evolutionary change for SARS-CoV-2 and are consistent with Omicron BA.1 arising from a chronic infection.

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.

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.