Deleterious passengers in adapting populations

Synergistic epistasis among cancer drivers can rescue early tumors from the accumulation of deleterious passengers

Epistasis among driver mutations is pervasive and explains relevant features of cancer, such as differential therapy response and convergence towards well-characterized molecular subtypes. Furthermore, a growing body of evidence suggests that tumor development could be hampered by the accumulation of slightly deleterious passenger mutations. In this work, we combined empirical epistasis networks, computer simulations, and mathematical models to explore how synergistic interactions among driver mutations affect cancer progression under the burden of slightly deleterious passengers. We found that epistasis plays a crucial role in tumor development by promoting the transformation of precancerous clones into rapidly growing tumors through a process that is analogous to evolutionary rescue. The triggering of epistasis-driven rescue is strongly dependent on the intensity of epistasis and could be a key rate-limiting step in many tumors, contributing to their unpredictability. As a result, central genes in cancer epistasis networks appear as key intervention targets for cancer therapy.

Dynamics of bacterial recombination in the human gut microbiome

Horizontal gene transfer (HGT) is a ubiquitous force in microbial evolution. Previous work has shown that the human gut is a hotspot for gene transfer between species, but the more subtle exchange of variation within species-also known as recombination-remains poorly characterized in this ecosystem. Here, we show that the genetic structure of the human gut microbiome provides an opportunity to measure recent recombination events from sequenced fecal samples, enabling quantitative comparisons across diverse commensal species that inhabit a common environment. By analyzing recent recombination events in the core genomes of 29 human gut bacteria, we observed widespread heterogeneities in the rates and lengths of transferred fragments, which are difficult to explain by existing models of ecological isolation or homology-dependent recombination rates. We also show that natural selection helps facilitate the spread of genetic variants across strain backgrounds, both within individual hosts and across the broader population. These results shed light on the dynamics of in situ recombination, which can strongly constrain the adaptability of gut microbial communities.

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.

A Countable-Type Branching Process Model for the Tug-of-War Cancer Cell Dynamics

We consider a time-continuous Markov branching process of proliferating cells with a countable collection of types. Among-type transitions are inspired by the Tug-of-War process introduced by McFarland et al. (Proc Natl Acad Sci 111(42):15138-15143, 2014) as a mathematical model for competition of advantageous driver mutations and deleterious passenger mutations in cancer cells. We introduce a version of the model in which a driver mutation pushes the type of the cell L-units up, while a passenger mutation pulls it 1-unit down. The distribution of time to divisions depends on the type (fitness) of cell, which is an integer. The extinction probability given any initial cell type is strictly less than 1, which allows us to investigate the transition between types (type transition) in an infinitely long cell lineage of cells. The analysis leads to the result that under driver dominance, the type transition process escapes to infinity, while under passenger dominance, it leads to a limit distribution. Implications in cancer cell dynamics and population genetics are discussed.

Human deleterious mutation rate implies high fitness variance, with declining mean fitness compensated by rarer beneficial mutations of larger effect

Each new human has an expected Ud = 2 - 10 new deleterious mutations. This deluge of deleterious mutations cannot all be purged, and therefore accumulate in a declining fitness ratchet. Using a novel simulation framework designed to efficiently handle genome-wide linkage disequilibria across many segregating sites, we find that rarer, beneficial mutations of larger effect are sufficient to compensate fitness declines due to the fixation of many slightly deleterious mutations. Drift barrier theory posits a similar asymmetric pattern of fixations to explain ratcheting genome size and complexity, but in our theory, the cause is Ud > 1 rather than small population size. In our simulations, Ud ~2 - 10 generates high within-population variance in relative fitness; two individuals will typically differ in fitness by 15-40%. Ud ~2 - 10 also slows net adaptation by ~13%-39%. Surprisingly, fixation rates are more sensitive to changes in the beneficial than the deleterious mutation rate, e.g. a 10% increase in overall mutation rate leads to faster adaptation; this puts to rest dysgenic fears about increasing mutation rates due to rising paternal age.

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.

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.

Genomic Analysis of SARS-CoV-2 Alpha, Beta and Delta Variants of Concern Uncovers Signatures of Neutral and Non-Neutral Evolution

Due to the emergence of new variants of the SARS-CoV-2 coronavirus, the question of how the viral genomes evolved, leading to the formation of highly infectious strains, becomes particularly important. Three major emergent strains, Alpha, Beta and Delta, characterized by a significant number of missense mutations, provide a natural test field. We accumulated and aligned 4.7 million SARS-CoV-2 genomes from the GISAID database and carried out a comprehensive set of analyses. This collection covers the period until the end of October 2021, i.e., the beginnings of the Omicron variant. First, we explored combinatorial complexity of the genomic variants emerging and their timing, indicating very strong, albeit hidden, selection forces. Our analyses show that the mutations that define variants of concern did not arise gradually but rather co-evolved rapidly, leading to the emergence of the full variant strain. To explore in more detail the evolutionary forces at work, we developed time trajectories of mutations at all 29,903 sites of the SARS-CoV-2 genome, week by week, and stratified them into trends related to (i) point substitutions, (ii) deletions and (iii) non-sequenceable regions. We focused on classifying the genetic forces active at different ranges of the mutational spectrum. We observed the agreement of the lowest-frequency mutation spectrum with the Griffiths-Tavaré theory, under the Infinite Sites Model and neutrality. If we widen the frequency range, we observe the site frequency spectra much more consistently with the Tung-Durrett model assuming clone competition and selection. The coefficients of the fitting model indicate the possibility of selection acting to promote gradual growth slowdown, as observed in the history of the variants of concern. These results add up to a model of genomic evolution, which partly fits into the classical drift barrier ideas. Certain observations, such as mutation "bands" persistent over the epidemic history, suggest contribution of genetic forces different from mutation, drift and selection, including recombination or other genome transformations. In addition, we show that a "toy" mathematical model can qualitatively reproduce how new variants (clones) stem from rare advantageous driver mutations, and then acquire neutral or disadvantageous passenger mutations which gradually reduce their fitness so they can be then outcompeted by new variants due to other driver mutations.

Modes of Selection in Tumors as Reflected by Two Mathematical Models and Site Frequency Spectra

The tug-of-war model was developed in a series of papers of McFarland and co-authors to account for existence of mutually counteracting rare advantageous driver mutations and more frequent slightly deleterious passenger mutations in cancer. In its original version, it was a state-dependent branching process. Because of its formulation, the tug-of-war model is of importance for tackling the problem as to whether evolution of cancerous tumors is "Darwinian" or "non-Darwinian." We define two Time-Continuous Markov Chain versions of the model, including identical mutation processes but adopting different drift and selection components. In Model A, drift and selection process preserves expected fitness whereas in Model B it leads to non-decreasing expected fitness. We investigate these properties using mathematical analysis and extensive simulations, which detect the effect of the so-called drift barrier in Model B but not in Model A. These effects are reflected in different structure of clone genealogies in the two models. Our work is related to the past theoretical work in the field of evolutionary genetics, concerning the interplay among mutation, drift and selection, in absence of recombination (asexual reproduction), where epistasis plays a major role. Finally, we use the statistics of mutation frequencies known as the Site Frequency Spectra (SFS), to compare the variant frequencies in DNA of sequenced HER2+ breast cancers, to those based on Model A and B simulations. The tumor-based SFS are better reproduced by Model A, pointing out a possible selection pattern of HER2+ tumor evolution. To put our models in context, we carried out an exploratory study of how publicly accessible data from breast, prostate, skin and ovarian cancers fit a range of models found in the literature.

Emergent evolutionary forces in spatial models of luminal growth and their application to the human gut microbiota

The genetic composition of the gut microbiota is constantly reshaped by ecological and evolutionary forces. These strain-level dynamics are challenging to understand because they depend on complex spatial growth processes that take place within a host. Here we introduce a population genetic framework to predict how stochastic evolutionary forces emerge from simple models of microbial growth in spatially extended environments like the intestinal lumen. Our framework shows how fluid flow and longitudinal variation in growth rate combine to shape the frequencies of genetic variants in simulated fecal samples, yielding analytical expressions for the effective generation times, selection coefficients, and rates of genetic drift. We find that over longer timescales, the emergent evolutionary dynamics can often be captured by well-mixed models that lack explicit spatial structure, even when there is substantial spatial variation in species-level composition. By applying these results to the human colon, we find that continuous fluid flow and simple forms of wall growth alone are unlikely to create sufficient bottlenecks to allow large fluctuations in mutant frequencies within a host. We also find that the effective generation times may be significantly shorter than expected from traditional average growth rate estimates. Our results provide a starting point for quantifying genetic turnover in spatially extended settings like the gut microbiota and may be relevant for other microbial ecosystems where unidirectional fluid flow plays an important role.

Gene Regulatory Evolution in Cold-Adapted Fly Populations Neutralizes Plasticity and May Undermine Genetic Canalization

The relationships between adaptive evolution, phenotypic plasticity, and canalization remain incompletely understood. Theoretical and empirical studies have made conflicting arguments on whether adaptive evolution may enhance or oppose the plastic response. Gene regulatory traits offer excellent potential to study the relationship between plasticity and adaptation, and they can now be studied at the transcriptomic level. Here, we take advantage of three closely related pairs of natural populations of Drosophila melanogaster from contrasting thermal environments that reflect three separate instances of cold tolerance evolution. We measure the transcriptome-wide plasticity in gene expression levels and alternative splicing (intron usage) between warm and cold laboratory environments. We find that suspected adaptive changes in both gene expression and alternative splicing tend to neutralize the ancestral plastic response. Further, we investigate the hypothesis that adaptive evolution can lead to decanalization of selected gene regulatory traits. We find strong evidence that suspected adaptive gene expression (but not splicing) changes in cold-adapted populations are more vulnerable to the genetic perturbation of inbreeding than putatively neutral changes. We find some evidence that these patterns may reflect a loss of genetic canalization accompanying adaptation, although other processes including hitchhiking recessive deleterious variants may contribute as well. Our findings augment our understanding of genetic and environmental effects on gene regulation in the context of adaptive evolution.

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.

Evolutionary Dynamics of Asexual Hypermutators Adapting to a Novel Environment

How microbes adapt to a novel environment is a central question in evolutionary biology. Although adaptive evolution must be fueled by beneficial mutations, whether higher mutation rates facilitate the rate of adaptive evolution remains unclear. To address this question, we cultured Escherichia coli hypermutating populations, in which a defective methyl-directed mismatch repair pathway causes a 140-fold increase in single-nucleotide mutation rates. In parallel with wild-type E. coli, populations were cultured in tubes containing Luria-Bertani broth, a complex medium known to promote the evolution of subpopulation structure. After 900 days of evolution, in three transfer schemes with different population-size bottlenecks, hypermutators always exhibited similar levels of improved fitness as controls. Fluctuation tests revealed that the mutation rates of hypermutator lines converged evolutionarily on those of wild-type populations, which may have contributed to the absence of fitness differences. Further genome-sequence analysis revealed that, although hypermutator populations have higher rates of genomic evolution, this largely reflects strong genetic linkage. Despite these linkage effects, the evolved population exhibits parallelism in fixed mutations, including those potentially related to biofilm formation, transcription regulation, and mutation-rate evolution. Together, these results are generally inconsistent with a hypothesized positive relationship between the mutation rate and the adaptive speed of evolution, and provide insight into how clonal adaptation occurs in novel environments.

Nonsynonymous Polymorphism Counts in Bacterial Genomes: a Comparative Examination

Genomic data reveal single-nucleotide polymorphisms (SNPs) that may carry information about the evolutionary history of bacteria. However, it remains unclear what inferences about selection can be made from genomic SNP data. Bacterial species are often sampled during epidemic outbreaks or within hosts during the course of chronic infections. SNPs obtained from genomic analysis of these data are not necessarily fixed. Treating them as fixed during analysis by using measures such as the ratio of nonsynonymous to synonymous evolutionary changes (dN/dS) may lead to incorrect inferences about the strength and direction of selection. In this study, we consider data from a range of whole-genome sequencing studies of bacterial pathogens and explore patterns of nonsynonymous variation to assess whether evidence of selection can be identified by investigating SNP counts alone across multiple WGS studies. We visualize these SNP data in ways that highlight their relationship to neutral baseline expectations. These neutral expectations are based on a simple model of mutation, from which we simulate SNP accumulation to investigate how SNP counts are distributed under alternative assumptions about positive and negative selection. We compare these patterns with empirical SNP data and illustrate the general difficulty of detecting positive selection from SNP data. Finally, we consider whether SNP counts observed at the between-host population level differ from those observed at the within-host level and find some evidence that suggests that dynamics across these two scales are driven by different underlying processes.IMPORTANCE Identifying selection from SNP data obtained from whole-genome sequencing studies is challenging. Some current measures used to identify and quantify selection acting on genomes rely on fixed differences; thus, these are inappropriate for SNP data where variants are not fixed. With the increase in whole-genome sequencing studies, it is important to consider SNP data in the context of evolutionary processes. How SNPs are counted and analyzed can help in understanding mutation accumulation and trajectories of strains. We developed a tool for identifying possible evidence of selection and for comparative analysis with other SNP data. We propose a model that provides a rule-of-thumb guideline and two new visualization techniques that can be used to interpret and compare SNP data. We quantify the expected proportion of nonsynonymous SNPs in coding regions under neutrality and demonstrate its use in identifying evidence of positive and negative selection from simulations and empirical data.

Mutation bias can shape adaptation in large asexual populations experiencing clonal interference

The extended evolutionary synthesis invokes a role for development in shaping adaptive evolution, which in population genetics terms corresponds to mutation-biased adaptation. Critics have claimed that clonal interference makes mutation-biased adaptation rare. We consider the behaviour of two simultaneously adapting traits, one with larger mutation rate U, the other with larger selection coefficient s, using asexual travelling wave models. We find that adaptation is dominated by whichever trait has the faster rate of adaptation v in isolation, with the other trait subject to evolutionary stalling. Reviewing empirical claims for mutation-biased adaptation, we find that not all occur in the 'origin-fixation' regime of population genetics where v is only twice as sensitive to s as to U. In some cases, differences in U are at least ten to twelve times larger than differences in s, as needed to cause mutation-biased adaptation even in the 'multiple mutations' regime. Surprisingly, when U > s in the 'diffusive-mutation' regime, the required sensitivity ratio is also only two, despite pervasive clonal interference. Given two traits with identical v, the benefit of having higher s is surprisingly small, occurring largely when one trait is at the boundary between the origin-fixation and multiple mutations regimes.

High Transcriptional Error Rates Vary as a Function of Gene Expression Level

Errors in gene transcription can be costly, and organisms have evolved to prevent their occurrence or mitigate their costs. The simplest interpretation of the drift barrier hypothesis suggests that species with larger population sizes would have lower transcriptional error rates. However, Escherichia coli seems to have a higher transcriptional error rate than species with lower effective population sizes, for example Saccharomyces cerevisiae. This could be explained if selection in E. coli were strong enough to maintain adaptations that mitigate the consequences of transcriptional errors through robustness, on a gene by gene basis, obviating the need for low transcriptional error rates and associated costs of global proofreading. Here, we note that if selection is powerful enough to evolve local robustness, selection should also be powerful enough to locally reduce error rates. We therefore predict that transcriptional error rates will be lower in highly abundant proteins on which selection is strongest. However, we only expect this result when error rates are high enough to significantly impact fitness. As expected, we find such a relationship between expression and transcriptional error rate for non-C→U errors in E. coli (especially G→A), but not in S. cerevisiae. We do not find this pattern for C→U changes in E. coli, presumably because most deamination events occurred during sample preparation, but do for C→U changes in S. cerevisiae, supporting the interpretation that C→U error rates estimated with an improved protocol, and which occur at rates comparable with E. coli non-C→U errors, are biological.

Evolution of Microbial Growth Traits Under Serial Dilution

Selection of mutants in a microbial population depends on multiple cellular traits. In serial-dilution evolution experiments, three key traits are the lag time when transitioning from starvation to growth, the exponential growth rate, and the yield (number of cells per unit resource). Here, we investigate how these traits evolve in laboratory evolution experiments using a minimal model of population dynamics, where the only interaction between cells is competition for a single limiting resource. We find that the fixation probability of a beneficial mutation depends on a linear combination of its growth rate and lag time relative to its immediate ancestor, even under clonal interference. The relative selective pressure on growth rate and lag time is set by the dilution factor; a larger dilution factor favors the adaptation of growth rate over the adaptation of lag time. The model shows that yield, however, is under no direct selection. We also show how the adaptation speeds of growth and lag depend on experimental parameters and the underlying supply of mutations. Finally, we investigate the evolution of covariation between these traits across populations, which reveals that the population growth rate and lag time can evolve a nonzero correlation even if mutations have uncorrelated effects on the two traits. Altogether these results provide useful guidance to future experiments on microbial evolution.

pCADD: SNV prioritisation in Sus scrofa

BACKGROUND

In animal breeding, identification of causative genetic variants is of major importance and high economical value. Usually, the number of candidate variants exceeds the number of variants that can be validated. One way of prioritizing probable candidates is by evaluating their potential to have a deleterious effect, e.g. by predicting their consequence. Due to experimental difficulties to evaluate variants that do not cause an amino-acid substitution, other prioritization methods are needed. For human genomes, the prediction of deleterious genomic variants has taken a step forward with the introduction of the combined annotation dependent depletion (CADD) method. In theory, this approach can be applied to any species. Here, we present pCADD (p for pig), a model to score single nucleotide variants (SNVs) in pig genomes.

RESULTS

To evaluate whether pCADD captures sites with biological meaning, we used transcripts from miRNAs and introns, sequences from genes that are specific for a particular tissue, and the different sites of codons, to test how well pCADD scores differentiate between functional and non-functional elements. Furthermore, we conducted an assessment of examples of non-coding and coding SNVs, which are causal for changes in phenotypes. Our results show that pCADD scores discriminate between functional and non-functional sequences and prioritize functional SNVs, and that pCADD is able to score the different positions in a codon relative to their redundancy. Taken together, these results indicate that based on pCADD scores, regions with biological relevance can be identified and distinguished according to their rate of adaptation.

CONCLUSIONS

We present the ability of pCADD to prioritize SNVs in the pig genome with respect to their putative deleteriousness, in accordance to the biological significance of the region in which they are located. We created scores for all possible SNVs, coding and non-coding, for all autosomes and the X chromosome of the pig reference sequence Sscrofa11.1, proposing a toolbox to prioritize variants and evaluate sequences to highlight new sites of interest to explain biological functions that are relevant to animal breeding.

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.

Genomic variation predicts adaptive evolutionary responses better than population bottleneck history

The relationship between population size, inbreeding, loss of genetic variation and evolutionary potential of fitness traits is still unresolved, and large-scale empirical studies testing theoretical expectations are surprisingly scarce. Here we present a highly replicated experimental evolution setup with 120 lines of Drosophila melanogaster having experienced inbreeding caused by low population size for a variable number of generations. Genetic variation in inbred lines and in outbred control lines was assessed by genotyping-by-sequencing (GBS) of pooled samples consisting of 15 males per line. All lines were reared on a novel stressful medium for 10 generations during which body mass, productivity, and extinctions were scored in each generation. In addition, we investigated egg-to-adult viability in the benign and the stressful environments before and after rearing at the stressful conditions for 10 generations. We found strong positive correlations between levels of genetic variation and evolutionary response in all investigated traits, and showed that genomic variation was more informative in predicting evolutionary responses than population history reflected by expected inbreeding levels. We also found that lines with lower genetic diversity were at greater risk of extinction. For viability, the results suggested a trade-off in the costs of adapting to the stressful environments when tested in a benign environment. This work presents convincing support for long-standing evolutionary theory, and it provides novel insights into the association between genetic variation and evolutionary capacity in a gradient of diversity rather than dichotomous inbred/outbred groups.

Interference Effects of Deleterious and Beneficial Mutations in Large Asexual Populations

Linked beneficial and deleterious mutations are known to decrease the fixation probability of a favorable mutation in large asexual populations. While the hindering effect of strongly deleterious mutations on adaptive evolution has been well studied, how weakly deleterious mutations, either in isolation or with superior beneficial mutations, influence the rate of adaptation has not been fully explored. When the selection against the deleterious mutations is weak, the beneficial mutant can fix in many genetic backgrounds, besides the one it arose on. Here, taking this factor into account, I obtain an accurate analytical expression for the fixation probability of a beneficial mutant in an asexual population at mutation-selection balance. I then exploit this result along with clonal interference theory to investigate the joint effect of linked beneficial and deleterious mutations on the rate of adaptation, and identify parameter regions where it is reduced due to interference by either beneficial or deleterious or both types of mutations. I also study the evolution of mutation rates in adapting asexual populations, and find that linked beneficial mutations have a stronger influence than the deleterious mutations on mutator fixation.

Deleterious alleles in the context of domestication, inbreeding, and selection

Each individual has a certain number of harmful mutations in its genome. These mutations can lower the fitness of the individual carrying them, dependent on their dominance and selection coefficient. Effective population size, selection, and admixture are known to affect the occurrence of such mutations in a population. The relative roles of demography and selection are a key in understanding the process of adaptation. These are factors that are potentially influenced and confounded in domestic animals. Here, we hypothesize that the series of events of bottlenecks, introgression, and strong artificial selection associated with domestication increased mutational load in domestic species. Yet, mutational load is hard to quantify, so there are very few studies available revealing the relevance of evolutionary processes. The precise role of artificial selection, bottlenecks, and introgression in further increasing the load of deleterious variants in animals in breeding and conservation programmes remains unclear. In this paper, we review the effects of domestication and selection on mutational load in domestic species. Moreover, we test some hypotheses on higher mutational load due to domestication and selective sweeps using sequence data from commercial pig and chicken lines. Overall, we argue that domestication by itself is not a prerequisite for genetic erosion, indicating that fitness potential does not need to decline. Rather, mutational load in domestic species can be influenced by many factors, but consistent or strong trends are not yet clear. However, methods emerging from molecular genetics allow discrimination of hypotheses about the determinants of mutational load, such as effective population size, inbreeding, and selection, in domestic systems. These findings make us rethink the effect of our current breeding schemes on fitness of populations.

Evolutionary dynamics of bacteria in the gut microbiome within and across hosts

Gut microbiota are shaped by a combination of ecological and evolutionary forces. While the ecological dynamics have been extensively studied, much less is known about how species of gut bacteria evolve over time. Here, we introduce a model-based framework for quantifying evolutionary dynamics within and across hosts using a panel of metagenomic samples. We use this approach to study evolution in approximately 40 prevalent species in the human gut. Although the patterns of between-host diversity are consistent with quasi-sexual evolution and purifying selection on long timescales, we identify new genealogical signatures that challenge standard population genetic models of these processes. Within hosts, we find that genetic differences that accumulate over 6-month timescales are only rarely attributable to replacement by distantly related strains. Instead, the resident strains more commonly acquire a smaller number of putative evolutionary changes, in which nucleotide variants or gene gains or losses rapidly sweep to high frequency. By comparing these mutations with the typical between-host differences, we find evidence that some sweeps may be seeded by recombination, in addition to new mutations. However, comparisons of adult twins suggest that replacement eventually overwhelms evolution over multi-decade timescales, hinting at fundamental limits to the extent of local adaptation. Together, our results suggest that gut bacteria can evolve on human-relevant timescales, and they highlight the connections between these short-term evolutionary dynamics and longer-term evolution across hosts.

Effective models and the search for quantitative principles in microbial evolution

Microbes evolve rapidly. Yet they do so in idiosyncratic ways, which depend on the specific mutations that are beneficial or deleterious in a given situation. At the same time, some population-level patterns of adaptation are strikingly similar across different microbial systems, suggesting that there may also be simple, quantitative principles that unite these diverse scenarios. We review the search for simple principles in microbial evolution, ranging from the biophysical level to emergent evolutionary dynamics. A key theme has been the use of effective models, which coarse-grain over molecular and cellular details to obtain a simpler description in terms of a few effective parameters. Collectively, these theoretical approaches provide a set of quantitative principles that facilitate understanding, prediction, and potentially control of evolutionary phenomena, though formidable challenges remain due to the ecological complexity of natural populations.

Cancer-mutation network and the number and specificity of driver mutations

Cancer genomics has produced extensive information on cancer-associated genes, but the number and specificity of cancer-driver mutations remains a matter of debate. We constructed a bipartite network in which 7,665 tumors from 30 cancer types are connected via shared mutations in 198 previously identified cancer genes. We show that about 27% of the tumors can be assigned to statistically supported modules, most of which encompass one or two cancer types. The rest of the tumors belong to a diffuse network component suggesting lower gene specificity of driver mutations. Linear regression of the mutational loads in cancer genes was used to estimate the number of drivers required for the onset of different cancers. The mean number of drivers in known cancer genes is approximately two, with a range of one to five. Cancers that are associated with modules had more drivers than those from the diffuse network component, suggesting that unidentified and/or interchangeable drivers exist in the latter.

Analysis of bacterial genomes from an evolution experiment with horizontal gene transfer shows that recombination can sometimes overwhelm selection

Few experimental studies have examined the role that sexual recombination plays in bacterial evolution, including the effects of horizontal gene transfer on genome structure. To address this limitation, we analyzed genomes from an experiment in which Escherichia coli K-12 Hfr (high frequency recombination) donors were periodically introduced into 12 evolving populations of E. coli B and allowed to conjugate repeatedly over the course of 1000 generations. Previous analyses of the evolved strains from this experiment showed that recombination did not accelerate adaptation, despite increasing genetic variation relative to asexual controls. However, the resolution in that previous work was limited to only a few genetic markers. We sought to clarify and understand these puzzling results by sequencing complete genomes from each population. The effects of recombination were highly variable: one lineage was mostly derived from the donors, while another acquired almost no donor DNA. In most lineages, some regions showed repeated introgression and others almost none. Regions with high introgression tended to be near the donors' origin of transfer sites. To determine whether introgressed alleles imposed a genetic load, we extended the experiment for 200 generations without recombination and sequenced whole-population samples. Beneficial alleles in the recipient populations were occasionally driven extinct by maladaptive donor-derived alleles. On balance, our analyses indicate that the plasmid-mediated recombination was sufficiently frequent to drive donor alleles to fixation without providing much, if any, selective advantage.

Genomics of Adaptation Depends on the Rate of Environmental Change in Experimental Yeast Populations

The rate of directional environmental change may have profound consequences for evolutionary dynamics and outcomes. Yet, most evolution experiments impose a sudden large change in the environment, after which the environment is kept constant. We previously cultured replicate Saccharomyces cerevisiae populations for 500 generations in the presence of either gradually increasing or constant high concentrations of the heavy metals cadmium, nickel, and zinc. Here, we investigate how each of these treatments affected genomic evolution. Whole-genome sequencing of evolved clones revealed that adaptation occurred via a combination of SNPs, small indels, and whole-genome duplications and other large-scale structural changes. In contrast to some theoretical predictions, gradual and abrupt environmental change caused similar numbers of genomic changes. For cadmium, which is toxic already at comparatively low concentrations, mutations in the same genes were used for adaptation to both gradual and abrupt increase in concentration. Conversely, for nickel and zinc, which are toxic at high concentrations only, mutations in different genes were used for adaptation depending on the rate of change. Moreover, evolution was more repeatable following a sudden change in the environment, particularly for nickel and zinc. Our results show that the rate of environmental change and the nature of the selection pressure are important drivers of evolutionary dynamics and outcomes, which has implications for a better understanding of societal problems such as climate change and pollution.

The dynamics of molecular evolution over 60,000 generations

The outcomes of evolution are determined by a stochastic dynamical process that governs how mutations arise and spread through a population. However, it is difficult to observe these dynamics directly over long periods and across entire genomes. Here we analyse the dynamics of molecular evolution in twelve experimental populations of Escherichia coli, using whole-genome metagenomic sequencing at five hundred-generation intervals through sixty thousand generations. Although the rate of fitness gain declines over time, molecular evolution is characterized by signatures of rapid adaptation throughout the duration of the experiment, with multiple beneficial variants simultaneously competing for dominance in each population. Interactions between ecological and evolutionary processes play an important role, as long-term quasi-stable coexistence arises spontaneously in most populations, and evolution continues within each clade. We also present evidence that the targets of natural selection change over time, as epistasis and historical contingency alter the strength of selection on different genes. Together, these results show that long-term adaptation to a constant environment can be a more complex and dynamic process than is often assumed.

The Damaging Effect of Passenger Mutations on Cancer Progression

Genomic instability and high mutation rates cause cancer to acquire numerous mutations and chromosomal alterations during its somatic evolution; most are termed passengers because they do not confer cancer phenotypes. Evolutionary simulations and cancer genomic studies suggest that mildly deleterious passengers accumulate and can collectively slow cancer progression. Clinical data also suggest an association between passenger load and response to therapeutics, yet no causal link between the effects of passengers and cancer progression has been established. To assess this, we introduced increasing passenger loads into human cell lines and immunocompromised mouse models. We found that passengers dramatically reduced proliferative fitness (∼3% per Mb), slowed tumor growth, and reduced metastatic progression. We developed new genomic measures of damaging passenger load that can accurately predict the fitness costs of passengers in cell lines and in human breast cancers. We conclude that genomic instability and an elevated load of DNA alterations in cancer is a double-edged sword: it accelerates the accumulation of adaptive drivers, but incurs a harmful passenger load that can outweigh driver benefit. The effects of passenger alterations on cancer fitness were unrelated to enhanced immunity, as our tests were performed either in cell culture or in immunocompromised animals. Our findings refute traditional paradigms of passengers as neutral events, suggesting that passenger load reduces the fitness of cancer cells and slows or prevents progression of both primary and metastatic disease. The antitumor effects of chemotherapies can in part be due to the induction of genomic instability and increased passenger load. Cancer Res; 77(18); 4763-72. ©2017 AACR.

Mistranslation can enhance fitness through purging of deleterious mutations

Phenotypic mutations are amino acid changes caused by mistranslation. How phenotypic mutations affect the adaptive evolution of new protein functions is unknown. Here we evolve the antibiotic resistance protein TEM-1 towards resistance on the antibiotic cefotaxime in an Escherichia coli strain with a high mistranslation rate. TEM-1 populations evolved in such strains endow host cells with a general growth advantage, not only on cefotaxime but also on several other antibiotics that ancestral TEM-1 had been unable to deactivate. High-throughput sequencing of TEM-1 populations shows that this advantage is associated with a lower incidence of weakly deleterious genotypic mutations. Our observations show that mistranslation is not just a source of noise that delays adaptive evolution. It could even facilitate adaptive evolution by exacerbating the effects of deleterious mutations and leading to their more efficient purging. The ubiquity of mistranslation and its effects render mistranslation an important factor in adaptive protein evolution.

Mistranslation results in amino acid changes in proteins known as phenotypic mutations and these occur at a much higher rate than DNA mutations. Here, the authors show that mistranslation can increase the response to directional selection by exacerbating the fitness effects of deleterious DNA mutations.

Dynamics and Fate of Beneficial Mutations Under Lineage Contamination by Linked Deleterious Mutations

Beneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldane's application of single-type branching process theory showed that genetic drift alone could cause the extinction of newly arising beneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations and might further increase their extinction probability. Here, we model the lineage dynamics of a newly arising beneficial mutation as a multitype branching process. Our approach accounts for the combined effects of drift and the stochastic accumulation of linked deleterious mutations, which we call lineage contamination We first study the lineage-contamination phenomenon in isolation, deriving dynamics and survival probabilities (the complement of extinction probabilities) of beneficial lineages. We find that survival probability is zero when [Formula: see text] where U is deleterious mutation rate and [Formula: see text] is the selective advantage of the beneficial mutation in question, and is otherwise depressed below classical predictions by a factor bounded from below by [Formula: see text] We then put the lineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection. We find that, under the combined effects of lineage contamination and background selection, ensemble survival probability is never zero but is depressed below classical predictions by a factor bounded from below by [Formula: see text] where [Formula: see text] is mean selective advantage of beneficial mutations, and [Formula: see text] This factor, and other bounds derived from it, are independent of the fitness effects of deleterious mutations. At high enough mutation rates, lineage contamination can depress fixation probabilities to values that approach zero. This fact suggests that high mutation rates can, perhaps paradoxically, (1) alleviate competition among beneficial mutations, or (2) potentially even shut down the adaptive process. We derive critical mutation rates above which these two events become likely.

Drift Barriers to Quality Control When Genes Are Expressed at Different Levels

Gene expression is imperfect, sometimes leading to toxic products. Solutions take two forms: globally reducing error rates, or ensuring that the consequences of erroneous expression are relatively harmless. The latter is optimal, but because it must evolve independently at so many loci, it is subject to a stringent "drift barrier"-a limit to how weak the effects of a deleterious mutation s can be, while still being effectively purged by selection, expressed in terms of the population size N of an idealized population such that purging requires s < -1/N In previous work, only large populations evolved the optimal local solution, small populations instead evolved globally low error rates, and intermediate populations were bistable, with either solution possible. Here, we take into consideration the fact that the effectiveness of purging varies among loci, because of variation in gene expression level, and variation in the intrinsic vulnerabilities of different gene products to error. The previously found dichotomy between the two kinds of solution breaks down, replaced by a gradual transition as a function of population size. In the extreme case of a small enough population, selection fails to maintain even the global solution against deleterious mutations, explaining the nonmonotonic relationship between effective population size and transcriptional error rate that was recently observed in experiments on Escherichia coli, Caenorhabditis elegans, and Buchnera aphidicola.

The Nonstationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation

Various models describe asexual evolution by mutation, selection, and drift. Some focus directly on fitness, typically modeling drift but ignoring or simplifying both epistasis and the distribution of mutation effects (traveling wave models). Others follow the dynamics of quantitative traits determining fitness (Fisher's geometric model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift. In all cases, predictions are typically obtained in high or low mutation rate limits and for long-term stationary regimes, thus losing information on transient behaviors and the effect of initial conditions. Here, we connect fitness-based and trait-based models into a single framework, and seek explicit solutions even away from stationarity. The expected fitness distribution is followed over time via its cumulant generating function, using a deterministic approximation that neglects drift. In several cases, explicit trajectories for the full fitness distribution are obtained for arbitrary mutation rates and standing variance. For nonepistatic mutations, especially with beneficial mutations, this approximation fails over the long term but captures the early dynamics, thus complementing stationary stochastic predictions. The approximation also handles several diminishing returns epistasis models (e.g., with an optimal genotype); it can be applied at and away from equilibrium. General results arise at equilibrium, where fitness distributions display a "phase transition" with mutation rate. Beyond this phase transition, in Fisher's geometric model, the full trajectory of fitness and trait distributions takes a simple form; robust to the details of the mutant phenotype distribution. Analytical arguments are explored regarding why and when the deterministic approximation applies.

A Comparison of the Costs and Benefits of Bacterial Gene Expression

To study how a bacterium allocates its resources, we compared the costs and benefits of most (86%) of the proteins in Escherichia coli K-12 during growth in minimal glucose medium. The cost or investment in each protein was estimated from ribosomal profiling data, and the benefit of each protein was measured by assaying a library of transposon mutants. We found that proteins that are important for fitness are usually highly expressed, and 95% of these proteins are expressed at above 13 parts per million (ppm). Conversely, proteins that do not measurably benefit the host (with a benefit of less than 5% per generation) tend to be weakly expressed, with a median expression of 13 ppm. In aggregate, genes with no detectable benefit account for 31% of protein production, or about 22% if we correct for genetic redundancy. Although some of the apparently unnecessary expression could have subtle benefits in minimal glucose medium, the majority of the burden is due to genes that are important in other conditions. We propose that at least 13% of the cell's protein is "on standby" in case conditions change.

Evolution of Mutation Rates in Rapidly Adapting Asexual Populations

Mutator and antimutator alleles often arise and spread in both natural microbial populations and laboratory evolution experiments. The evolutionary dynamics of these mutation rate modifiers are determined by indirect selection on linked beneficial and deleterious mutations. These indirect selection pressures have been the focus of much earlier theoretical and empirical work, but we still have a limited analytical understanding of how the interplay between hitchhiking and deleterious load influences the fates of modifier alleles. Our understanding is particularly limited when clonal interference is common, which is the regime of primary interest in laboratory microbial evolution experiments. Here, we calculate the fixation probability of a mutator or antimutator allele in a rapidly adapting asexual population, and we show how this quantity depends on the population size, the beneficial and deleterious mutation rates, and the strength of a typical driver mutation. In the absence of deleterious mutations, we find that clonal interference enhances the fixation probability of mutators, even as they provide a diminishing benefit to the overall rate of adaptation. When deleterious mutations are included, natural selection pushes the population toward a stable mutation rate that can be suboptimal for the adaptation of the population as a whole. The approach to this stable mutation rate is not necessarily monotonic: even in the absence of epistasis, selection can favor mutator and antimutator alleles that "overshoot" the stable mutation rate by substantial amounts.

Tempo and mode of genome evolution in a 50,000-generation experiment

Adaptation by natural selection depends on the rates, effects, and interactions of many mutations, making it difficult to determine what proportion of mutations in an evolving lineage are beneficial. We analysed 264 complete genomes from 12 Escherichia coli populations to characterize their dynamics over 50,000 generations. The populations that retained the ancestral mutation rate support a model where most fixed mutations are beneficial, the fraction of beneficial mutations declines as fitness rises, and neutral mutations accumulate at a constant rate. We also compared these populations to mutation-accumulation lines evolved under a bottlenecking regime that minimizes selection. Nonsynonymous mutations, intergenic mutations, insertions, and deletions are overrepresented in the long-term populations, further supporting the inference that most mutations that reached high frequency were favoured by selection. These results illuminate the shifting balance of forces that govern genome evolution in populations adapting to a new environment.

The Genetic Cost of Neanderthal Introgression

Approximately 2-4% of genetic material in human populations outside Africa is derived from Neanderthals who interbred with anatomically modern humans. Recent studies have shown that this Neanderthal DNA is depleted around functional genomic regions; this has been suggested to be a consequence of harmful epistatic interactions between human and Neanderthal alleles. However, using published estimates of Neanderthal inbreeding and the distribution of mutational fitness effects, we infer that Neanderthals had at least 40% lower fitness than humans on average; this increased load predicts the reduction in Neanderthal introgression around genes without the need to invoke epistasis. We also predict a residual Neanderthal mutational load in non-Africans, leading to a fitness reduction of at least 0.5%. This effect of Neanderthal admixture has been left out of previous debate on mutation load differences between Africans and non-Africans. We also show that if many deleterious mutations are recessive, the Neanderthal admixture fraction could increase over time due to the protective effect of Neanderthal haplotypes against deleterious alleles that arose recently in the human population. This might partially explain why so many organisms retain gene flow from other species and appear to derive adaptive benefits from introgression.

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.

The population genetics of drug resistance evolution in natural populations of viral, bacterial and eukaryotic pathogens

Drug resistance is a costly consequence of pathogen evolution and a major concern in public health. In this review, we show how population genetics can be used to study the evolution of drug resistance and also how drug resistance evolution is informative as an evolutionary model system. We highlight five examples from diverse organisms with particular focus on: (i) identifying drug resistance loci in the malaria parasite Plasmodium falciparum using the genomic signatures of selective sweeps, (ii) determining the role of epistasis in drug resistance evolution in influenza, (iii) quantifying the role of standing genetic variation in the evolution of drug resistance in HIV, (iv) using drug resistance mutations to study clonal interference dynamics in tuberculosis and (v) analysing the population structure of the core and accessory genome of Staphylococcus aureus to understand the spread of methicillin resistance. Throughout this review, we discuss the uses of sequence data and population genetic theory in studying the evolution of drug resistance.

Weakly Deleterious Mutations and Low Rates of Recombination Limit the Impact of Natural Selection on Bacterial Genomes

Free-living bacteria are usually thought to have large effective population sizes, and so tiny selective differences can drive their evolution. However, because recombination is infrequent, “background selection” against slightly deleterious alleles should reduce the effective population size (N_e) by orders of magnitude. For example, for a well-mixed population with 10¹² individuals and a typical level of homologous recombination (r/m = 3, i.e., nucleotide changes due to recombination [r] occur at 3 times the mutation rate [m]), we predict that N_e is <10⁷. An argument for high N_e values for bacteria has been the high genetic diversity within many bacterial “species,” but this diversity may be due to population structure: diversity across subpopulations can be far higher than diversity within a subpopulation, which makes it difficult to estimate N_e correctly. Given an estimate of N_e, standard population genetics models imply that selection should be sufficient to drive evolution if N_e × s is >1, where s is the selection coefficient. We found that this remains approximately correct if background selection is occurring or when population structure is present. Overall, we predict that even for free-living bacteria with enormous populations, natural selection is only a significant force if s is above 10⁻⁷ or so.

Because bacteria form huge populations with trillions of individuals, the simplest theoretical prediction is that the better allele at a site would predominate even if its advantage was just 10⁻⁹ per generation. In other words, virtually every nucleotide would be at the local optimum in most individuals. A more sophisticated theory considers that bacterial genomes have millions of sites each and selection events on these many sites could interfere with each other, so that only larger effects would be important. However, bacteria can exchange genetic material, and in principle, this exchange could eliminate the interference between the evolution of the sites. We used simulations to confirm that during multisite evolution with realistic levels of recombination, only larger effects are important. We propose that advantages of less than 10⁻⁷ are effectively neutral.

Obstruction of adaptation in diploids by recessive, strongly deleterious alleles

Recessive deleterious mutations are common, causing many genetic disorders in humans and producing inbreeding depression in the majority of sexually reproducing diploids. The abundance of recessive deleterious mutations in natural populations suggests they are likely to be present on a chromosome when a new adaptive mutation occurs, yet the dynamics of recessive deleterious hitchhikers and their impact on adaptation remains poorly understood. Here we model how a recessive deleterious mutation impacts the fate of a genetically linked dominant beneficial mutation. The frequency trajectory of the adaptive mutation in this case is dramatically altered and results in what we have termed a "staggered sweep." It is named for its three-phased trajectory: (i) Initially, the two linked mutations have a selective advantage while rare and will increase in frequency together, then (ii), at higher frequencies, the recessive hitchhiker is exposed to selection and can cause a balanced state via heterozygote advantage (the staggered phase), and (iii) finally, if recombination unlinks the two mutations, then the beneficial mutation can complete the sweep to fixation. Using both analytics and simulations, we show that strongly deleterious recessive mutations can substantially decrease the probability of fixation for nearby beneficial mutations, thus creating zones in the genome where adaptation is suppressed. These mutations can also significantly prolong the number of generations a beneficial mutation takes to sweep to fixation, and cause the genomic signature of selection to resemble that of soft or partial sweeps. We show that recessive deleterious variation could impact adaptation in humans and Drosophila.

The evolutionarily stable distribution of fitness effects

The distribution of fitness effects (DFE) of new mutations is a key parameter in determining the course of evolution. This fact has motivated extensive efforts to measure the DFE or to predict it from first principles. However, just as the DFE determines the course of evolution, the evolutionary process itself constrains the DFE. Here, we analyze a simple model of genome evolution in a constant environment in which natural selection drives the population toward a dynamic steady state where beneficial and deleterious substitutions balance. The distribution of fitness effects at this steady state is stable under further evolution and provides a natural null expectation for the DFE in a population that has evolved in a constant environment for a long time. We calculate how the shape of the evolutionarily stable DFE depends on the underlying population genetic parameters. We show that, in the absence of epistasis, the ratio of beneficial to deleterious mutations of a given fitness effect obeys a simple relationship independent of population genetic details. Finally, we analyze how the stable DFE changes in the presence of a simple form of diminishing-returns epistasis.

The impact of macroscopic epistasis on long-term evolutionary dynamics

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