Competition between recombination and epistasis can cause a transition from allele to genotype selection

Polygenic selection to a changing optimum under self-fertilisation

Many traits are polygenic, affected by multiple genetic variants throughout the genome. Selection acting on these traits involves co-ordinated allele-frequency changes at these underlying variants, and this process has been extensively studied in random-mating populations. Yet many species self-fertilise to some degree, which incurs changes to genetic diversity, recombination and genome segregation. These factors cumulatively influence how polygenic selection is realised in nature. Here, we use analytical modelling and stochastic simulations to investigate to what extent self-fertilisation affects polygenic adaptation to a new environment. Our analytical solutions show that while selfing can increase adaptation to an optimum, it incurs linkage disequilibrium that can slow down the initial spread of favoured mutations due to selection interference, and favours the fixation of alleles with opposing trait effects. Simulations show that while selection interference is present, high levels of selfing (at least 90%) aids adaptation to a new optimum, showing a higher long-term fitness. If mutations are pleiotropic then only a few major-effect variants fix along with many neutral hitchhikers, with a transient increase in linkage disequilibrium. These results show potential advantages to self-fertilisation when adapting to a new environment, and how the mating system affects the genetic composition of polygenic selection.

Epistasis, core-genome disharmony, and adaptation in recombining bacteria

Recombination of short DNA fragments via horizontal gene transfer (HGT) can introduce beneficial alleles, create genomic disharmony through negative epistasis, and create adaptive gene combinations through positive epistasis. For non-core (accessory) genes, the negative epistatic cost is likely to be minimal because the incoming genes have not co-evolved with the recipient genome and are frequently observed as tightly linked cassettes with major effects. By contrast, interspecific recombination in the core genome is expected to be rare because disruptive allelic replacement is likely to introduce negative epistasis. Why then is homologous recombination common in the core of bacterial genomes? To understand this enigma, we take advantage of an exceptional model system, the common enteric pathogens Campylobacter jejuni and C. coli that are known for very high magnitude interspecies gene flow in the core genome. As expected, HGT does indeed disrupt co-adapted allele pairings, indirect evidence of negative epistasis. However, multiple HGT events enable recovery of the genome's co-adaption between introgressing alleles, even in core metabolism genes (e.g., formate dehydrogenase). These findings demonstrate that, even for complex traits, genetic coalitions can be decoupled, transferred, and independently reinstated in a new genetic background-facilitating transition between fitness peaks. In this example, the two-step recombinational process is associated with C. coli that are adapted to the agricultural niche.IMPORTANCEGenetic exchange among bacteria shapes the microbial world. From the acquisition of antimicrobial resistance genes to fundamental questions about the nature of bacterial species, this powerful evolutionary force has preoccupied scientists for decades. However, the mixing of genes between species rests on a paradox: 0n one hand, promoting adaptation by conferring novel functionality; on the other, potentially introducing disharmonious gene combinations (negative epistasis) that will be selected against. Taking an interdisciplinary approach to analyze natural populations of the enteric bacteria Campylobacter, an ideal example of long-range admixture, we demonstrate that genes can independently transfer across species boundaries and rejoin in functional networks in a recipient genome. The positive impact of two-gene interactions appears to be adaptive by expanding metabolic capacity and facilitating niche shifts through interspecific hybridization. This challenges conventional ideas and highlights the possibility of multiple-step evolution of multi-gene traits by interspecific introgression.

Rapid adaptation of recombining populations on tunable fitness landscapes

How does standing genetic variation affect polygenic adaptation in recombining populations? Despite a large body of work in quantitative genetics, epistatic and weak additive fitness effects among simultaneously segregating genetic variants are difficult to capture experimentally or to predict theoretically. In this study, we simulated adaptation on fitness landscapes with tunable ruggedness driven by standing genetic variation in recombining populations. We confirmed that recombination hinders the movement of a population through a rugged fitness landscape. When surveying the effect of epistasis on the fixation of alleles, we found that the combined effects of high ruggedness and high recombination probabilities lead to preferential fixation of alleles that had a high initial frequency. This indicates that positive epistatic alleles escape from being broken down by recombination when they start at high frequency. We further extract direct selection coefficients and pairwise epistasis along the adaptive path. When taking the final fixed genotype as the reference genetic background, we observe that, along the adaptive path, beneficial direct selection appears stronger and pairwise epistasis weaker than in the underlying fitness landscape. Quantitatively, the ratio of epistasis and direct selection is smaller along the adaptive path (≈ 1 ) than expected. Thus, adaptation on a rugged fitness landscape may lead to spurious signals of direct selection generated through epistasis. Our study highlights how the interplay of epistasis and recombination constrains the adaptation of a diverse population to a new environment.

Kinetic coevolutionary models predict the temporal emergence of HIV-1 resistance mutations under drug selection pressure

Drug resistance in HIV type 1 (HIV-1) is a pervasive problem that affects the lives of millions of people worldwide. Although records of drug-resistant mutations (DRMs) have been extensively tabulated within public repositories, our understanding of the evolutionary kinetics of DRMs and how they evolve together remains limited. Epistasis, the interaction between a DRM and other residues in HIV-1 protein sequences, is key to the temporal evolution of drug resistance. We use a Potts sequence-covariation statistical-energy model of HIV-1 protein fitness under drug selection pressure, which captures epistatic interactions between all positions, combined with kinetic Monte-Carlo simulations of sequence evolutionary trajectories, to explore the acquisition of DRMs as they arise in an ensemble of drug-naive patient protein sequences. We follow the time course of 52 DRMs in the enzymes protease, RT, and integrase, the primary targets of antiretroviral therapy. The rates at which DRMs emerge are highly correlated with their observed acquisition rates reported in the literature when drug pressure is applied. This result highlights the central role of epistasis in determining the kinetics governing DRM emergence. Whereas rapidly acquired DRMs begin to accumulate as soon as drug pressure is applied, slowly acquired DRMs are contingent on accessory mutations that appear only after prolonged drug pressure. We provide a foundation for using computational methods to determine the temporal evolution of drug resistance using Potts statistical potentials, which can be used to gain mechanistic insights into drug resistance pathways in HIV-1 and other infectious agents.

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.

Ecology, the pace-of-life, epistatic selection and the maintenance of genetic variation in life-history genes

Evolutionary genetics has long struggled with understanding how functional genes under selection remain polymorphic in natural populations. Taking as a starting point that natural selection is ultimately a manifestation of ecological processes, we spotlight an underemphasized and potentially ubiquitous ecological effect that may have fundamental effects on the maintenance of genetic variation. Negative frequency dependency is a well-established emergent property of density dependence in ecology, because the relative profitability of different modes of exploiting or utilizing limiting resources tends to be inversely proportional to their frequency in a population. We suggest that this may often generate negative frequency-dependent selection (NFDS) on major effect loci that affect rate-dependent physiological processes, such as metabolic rate, that are phenotypically manifested as polymorphism in pace-of-life syndromes. When such a locus under NFDS shows stable intermediate frequency polymorphism, this should generate epistatic selection potentially involving large numbers of loci with more minor effects on life-history (LH) traits. When alternative alleles at such loci show sign epistasis with a major effect locus, this associative NFDS will promote the maintenance of polygenic variation in LH genes. We provide examples of the kind of major effect loci that could be involved and suggest empirical avenues that may better inform us on the importance and reach of this process.

Bet-hedging via dispersal aids the evolution of plastic responses to unreliable cues

Adaptive plasticity is expected to evolve when informative cues predict environmental variation. However, plastic responses can be maladaptive even when those cues are informative, if prediction mistakes are shared across members of a generation. These fitness costs can constrain the evolution of plasticity when initial plastic mutants use of cues of only moderate reliability. Here, we model the barriers to the evolution of plasticity produced by these constraints and show that dispersal across a metapopulation can overcome them. Constraints are also lessened, though not eliminated, when plastic responses are free to evolve gradually and in concert with increased reliability. Each of these factors be viewed as a form of bet-hedging: by lessening correlations in the fates of relatives, dispersal acts as diversifying bet-hedging, while producing submaximal responses to a cue can be understood as a conservative bet-hedging strategy. While poor information may constrain the evolution of plasticity, the opportunity for bet-hedging may predict when that constraint can be overcome.

Transcriptome-wide gene-gene interaction associations elucidate pathways and functional enrichment of complex traits

It remains unknown to what extent gene-gene interactions contribute to complex traits. Here, we introduce a new approach using predicted gene expression to perform exhaustive transcriptome-wide interaction studies (TWISs) for multiple traits across all pairs of genes expressed in several tissue types. Using imputed transcriptomes, we simultaneously reduce the computational challenge and improve interpretability and statistical power. We discover (in the UK Biobank) and replicate (in independent cohorts) several interaction associations, and find several hub genes with numerous interactions. We also demonstrate that TWIS can identify novel associated genes because genes with many or strong interactions have smaller single-locus model effect sizes. Finally, we develop a method to test gene set enrichment of TWIS associations (E-TWIS), finding numerous pathways and networks enriched in interaction associations. Epistasis is may be widespread, and our procedure represents a tractable framework for beginning to explore gene interactions and identify novel genomic targets.

Statistical genetics in and out of quasi-linkage equilibrium

This review is about statistical genetics, an interdisciplinary topic between statistical physics and population biology. The focus is on the phase ofquasi-linkage equilibrium(QLE). Our goals here are to clarify under which conditions the QLE phase can be expected to hold in population biology and how the stability of the QLE phase is lost. The QLE state, which has many similarities to a thermal equilibrium state in statistical mechanics, was discovered by M Kimura for a two-locus two-allele model, and was extended and generalized to the global genome scale byNeher&Shraiman (2011). What we will refer to as the Kimura-Neher-Shraiman theory describes a population evolving due to the mutations, recombination, natural selection and possibly genetic drift. A QLE phase exists at sufficiently high recombination rate (r) and/or mutation ratesµwith respect to selection strength. We show how in QLE it is possible to infer the epistatic parameters of the fitness function from the knowledge of the (dynamical) distribution of genotypes in a population. We further consider the breakdown of the QLE regime for high enough selection strength. We review recent results for the selection-mutation and selection-recombination dynamics. Finally, we identify and characterize a new phase which we call the non-random coexistence where variability persists in the population without either fixating or disappearing.

Temporal epistasis inference from more than 3 500 000 SARS-CoV-2 genomic sequences

We use direct coupling analysis (DCA) to determine epistatic interactions between loci of variability of the SARS-CoV-2 virus, segmenting genomes by month of sampling. We use full-length, high-quality genomes from the GISAID repository up to October 2021 for a total of over 3 500 000 genomes. We find that DCA terms are more stable over time than correlations but nevertheless change over time as mutations disappear from the global population or reach fixation. Correlations are enriched for phylogenetic effects, and in particularly statistical dependencies at short genomic distances, while DCA brings out links at longer genomic distance. We discuss the validity of a DCA analysis under these conditions in terms of a transient auasilinkage equilibrium state. We identify putative epistatic interaction mutations involving loci in spike.

Inferring Epistasis from Genetic Time-series Data

Epistasis refers to fitness or functional effects of mutations that depend on the sequence background in which these mutations arise. Epistasis is prevalent in nature, including populations of viruses, bacteria, and cancers, and can contribute to the evolution of drug resistance and immune escape. However, it is difficult to directly estimate epistatic effects from sampled observations of a population. At present, there are very few methods that can disentangle the effects of selection (including epistasis), mutation, recombination, genetic drift, and genetic linkage in evolving populations. Here we develop a method to infer epistasis, along with the fitness effects of individual mutations, from observed evolutionary histories. Simulations show that we can accurately infer pairwise epistatic interactions provided that there is sufficient genetic diversity in the data. Our method also allows us to identify which fitness parameters can be reliably inferred from a particular data set and which ones are unidentifiable. Our approach therefore allows for the inference of more complex models of selection from time-series genetic data, while also quantifying uncertainty in the inferred parameters.

High fraction of silent recombination in a finite-population two-locus neutral birth-death-mutation model

A precise estimate of allele and haplotype polymorphism is of great interest in theoretical population genetics, but also has practical applications, such as bone marrow registries management. Allele polymorphism is driven mainly by point mutations, while haplotype polymorphism is also affected by recombination. Current estimates treat recombination as mutations in an infinite site model. We here show that even in the simple case of two loci in a haploid individual, for a finite population, most recombination events produce existing haplotypes, and as such are silent. Silent recombination considerably reduces the total number of haplotypes expected from the infinite site model for populations that are not much larger than one over the mutation rate. Moreover, in contrast with mutations, the number of haplotypes does not grow linearly with the population size. We hence propose a more accurate estimate of the total number of haplotypes that takes into account silent recombination. We study large-scale human leukocyte antigen (HLA) haplotype frequencies from human populations to show that the current estimated recombination rate in the HLA region is underestimated.

Complex fitness landscape shapes variation in a hyperpolymorphic species

It is natural to assume that patterns of genetic variation in hyperpolymorphic species can reveal large-scale properties of the fitness landscape that are hard to detect by studying species with ordinary levels of genetic variation. Here, we study such patterns in a fungus Schizophyllum commune, the most polymorphic species known. Throughout the genome, short-range linkage disequilibrium (LD) caused by attraction of minor alleles is higher between pairs of nonsynonymous than of synonymous variants. This effect is especially pronounced for pairs of sites that are located within the same gene, especially if a large fraction of the gene is covered by haploblocks, genome segments where the gene pool consists of two highly divergent haplotypes, which is a signature of balancing selection. Haploblocks are usually shorter than 1000 nucleotides, and collectively cover about 10% of the S. commune genome. LD tends to be substantially higher for pairs of nonsynonymous variants encoding amino acids that interact within the protein. There is a substantial correlation between LDs at the same pairs of nonsynonymous mutations in the USA and the Russian populations. These patterns indicate that selection in S. commune involves positive epistasis due to compensatory interactions between nonsynonymous alleles. When less polymorphic species are studied, analogous patterns can be detected only through interspecific comparisons.

Changes to DNA known as mutations may alter how the proteins and other components of a cell work, and thus play an important role in allowing living things to evolve new traits and abilities over many generations. Whether a mutation is beneficial or harmful may differ depending on the genetic background of the individual – that is, depending on other mutations present in other positions within the same gene – due to a phenomenon called epistasis.

Epistasis is known to affect how various species accumulate differences in their DNA compared to each other over time. For example, a mutation that is rare in humans and known to cause disease may be widespread in other primates because its negative effect is canceled out by another mutation that is standard for these species but absent in humans. However, it remains unclear whether epistasis plays a significant part in shaping genetic differences between individuals of the same species.

A type of fungus known as Schizophyllum commune lives on rotting wood and is found across the world. It is one of the most genetically diverse species currently known, so there is a higher chance of pairs of compensatory mutations occurring and persisting for a long time in S. commune than in most other species, providing a unique opportunity to study epistasis.

Here, Stolyarova et al. studied two distinct populations of S. commune, one from the USA and one from Russia. The team found that – unlike in humans, flies and other less genetically diverse species – epistasis maintains combinations of mutations in S. commune that individually would be harmful to the fungus but together compensate for each other. For example, pairs of mutations affecting specific molecules known as amino acids – the building blocks of proteins – that physically interact with each other tended to be found together in the same individuals.

One potential downside of having pairs of compensatory mutations in the genome is that when the organism reproduces, the process of making sex cells may split up these pairs so that harmful mutations are inherited without their partner mutations. Thus, epistasis may have helped shape the way S. commune and other genetically diverse species have evolved.

Genomic variants affecting homoeologous gene expression dosage contribute to agronomic trait variation in allopolyploid wheat

Allopolyploidy greatly expands the range of possible regulatory interactions among functionally redundant homoeologous genes. However, connection between the emerging regulatory complexity and expression and phenotypic diversity in polyploid crops remains elusive. Here, we use diverse wheat accessions to map expression quantitative trait loci (eQTL) and evaluate their effects on the population-scale variation in homoeolog expression dosage. The relative contribution of cis- and trans-eQTL to homoeolog expression variation is strongly affected by both selection and demographic events. Though trans-acting effects play major role in expression regulation, the expression dosage of homoeologs is largely influenced by cis-acting variants, which appear to be subjected to selection. The frequency and expression of homoeologous gene alleles showing strong expression dosage bias are predictive of variation in yield-related traits, and have likely been impacted by breeding for increased productivity. Our study highlights the importance of genomic variants affecting homoeolog expression dosage in shaping agronomic phenotypes and points at their potential utility for improving yield in polyploid crops.

Evolution of resistance under alternative models of selective interference

The use of multiple pesticides or drugs can lead to a simultaneous selection pressure for resistance alleles at different loci. Models of resistance evolution focus on how this can delay the spread of resistance through a population, but often neglect how this can also reduce the probability that a resistance allele spreads. This neglected factor has been studied in a parallel literature as selective interference. Models of interference use alternative constructions of fitness, where selection coefficients from different loci either add or multiply. Although these are equivalent under weak selection, the two constructions make alternative predictions under the strong selection that characterizes resistance evolution. Here, simulations are used to examine the effects of interference on the probability of fixation and time to fixation of a new and strongly beneficial mutation in the presence of another strongly beneficial allele with variable starting frequency. The results from simulations show a complicated pattern of effects. The key result is that, under multiplicativity, the presence of the strongly beneficial allele leads to a small reduction in the probability of fixation for the new beneficial mutation up to ~10%, and a negligible increase in the average time to fixation up to ~2%, whereas under additivity, the effect is more substantial at up to ~50% for the probability of fixation and ~100% for the average time to fixation. Consequently, the effect of interference is only an important feature of resistance evolution under additivity. Current evidence from studies of experimental evolution provides widespread support for the basic features of additivity, which suggests that interference may afford resistance a different pattern of evolution than other adaptations: rather than the gradual and simultaneous selection of many alleles with small effects, the rapid evolution of resistance may involve the sequential selection of alleles with large effects.

Negative frequency-dependent selection and asymmetrical transformation stabilise multi-strain bacterial population structures

Streptococcus pneumoniae can be divided into many strains, each a distinct set of isolates sharing similar core and accessory genomes, which co-circulate within the same hosts. Previous analyses suggested the short-term vaccine-associated dynamics of S. pneumoniae strains may be mediated through multi-locus negative frequency-dependent selection (NFDS), which maintains accessory loci at equilibrium frequencies. Long-term simulations demonstrated NFDS stabilised clonally-evolving multi-strain populations through preventing the loss of variation through drift, based on polymorphism frequencies, pairwise genetic distances and phylogenies. However, allowing symmetrical recombination between isolates evolving under multi-locus NFDS generated unstructured populations of diverse genotypes. Replication of the observed data improved when multi-locus NFDS was combined with recombination that was instead asymmetrical, favouring deletion of accessory loci over insertion. This combination separated populations into strains through outbreeding depression, resulting from recombinants with reduced accessory genomes having lower fitness than their parental genotypes. Although simplistic modelling of recombination likely limited these simulations' ability to maintain some properties of genomic data as accurately as those lacking recombination, the combination of asymmetrical recombination and multi-locus NFDS could restore multi-strain population structures from randomised initial populations. As many bacteria inhibit insertions into their chromosomes, this combination may commonly underlie the co-existence of strains within a niche.

Inferring genetic fitness from genomic data

The genetic composition of a naturally developing population is considered as due to mutation, selection, genetic drift, and recombination. Selection is modeled as single-locus terms (additive fitness) and two-loci terms (pairwise epistatic fitness). The problem is posed to infer epistatic fitness from population-wide whole-genome data from a time series of a developing population. We generate such data in silico and show that in the quasilinkage equilibrium phase of Kimura, Neher, and Shraiman, which pertains at high enough recombination rates and low enough mutation rates, epistatic fitness can be quantitatively correctly inferred using inverse Ising-Potts methods.

Global analysis of more than 50,000 SARS-CoV-2 genomes reveals epistasis between eight viral genes

Genome-wide epistasis analysis is a powerful tool to infer gene interactions, which can guide drug and vaccine development and lead to deeper understanding of microbial pathogenesis. We have considered all complete severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) genomes deposited in the Global Initiative on Sharing All Influenza Data (GISAID) repository until four different cutoff dates, and used direct coupling analysis together with an assumption of quasi-linkage equilibrium to infer epistatic contributions to fitness from polymorphic loci. We find eight interactions, of which three are between pairs where one locus lies in gene ORF3a, both loci holding nonsynonymous mutations. We also find interactions between two loci in gene nsp13, both holding nonsynonymous mutations, and four interactions involving one locus holding a synonymous mutation. Altogether, we infer interactions between loci in viral genes ORF3a and nsp2, nsp12, and nsp6, between ORF8 and nsp4, and between loci in genes nsp2, nsp13, and nsp14. The paper opens the prospect to use prominent epistatically linked pairs as a starting point to search for combinatorial weaknesses of recombinant viral pathogens.

Evolutionary stalling and a limit on the power of natural selection to improve a cellular module

Cells consist of molecular modules which perform vital biological functions. Cellular modules are key units of adaptive evolution because organismal fitness depends on their performance. Theory shows that in rapidly evolving populations, such as those of many microbes, adaptation is driven primarily by common beneficial mutations with large effects, while other mutations behave as if they are effectively neutral. As a consequence, if a module can be improved only by rare and/or weak beneficial mutations, its adaptive evolution would stall. However, such evolutionary stalling has not been empirically demonstrated, and it is unclear to what extent stalling may limit the power of natural selection to improve modules. Here we empirically characterize how natural selection improves the translation machinery (TM), an essential cellular module. We experimentally evolved populations of Escherichia coli with genetically perturbed TMs for 1,000 generations. Populations with severe TM defects initially adapted via mutations in the TM, but TM adaptation stalled within about 300 generations. We estimate that the genetic load in our populations incurred by residual TM defects ranges from 0.5 to 19%. Finally, we found evidence that both epistasis and the depletion of the pool of beneficial mutations contributed to evolutionary stalling. Our results suggest that cellular modules may not be fully optimized by natural selection despite the availability of adaptive mutations.

Pervasive within-host recombination and epistasis as major determinants of the molecular evolution of the foot-and-mouth disease virus capsid

Although recombination is known to occur in foot-and-mouth disease virus (FMDV), it is considered only a minor determinant of virus sequence diversity. Analysis at phylogenetic scales shows inter-serotypic recombination events are rare, whereby recombination occurs almost exclusively in non-structural proteins. In this study we have estimated recombination rates within a natural host in an experimental setting. African buffaloes were inoculated with a SAT-1 FMDV strain containing two major viral sub-populations differing in their capsid sequence. This population structure enabled the detection of extensive within-host recombination in the genomic region coding for structural proteins and allowed recombination rates between the two sub-populations to be estimated. Quite surprisingly, the effective recombination rate in VP1 during the acute infection phase turns out to be about 0.1 per base per year, i.e. comparable to the mutation/substitution rate. Using a high-resolution map of effective within-host recombination in the capsid-coding region, we identified a linkage disequilibrium pattern in VP1 that is consistent with a mosaic structure with two main genetic blocks. Positive epistatic interactions between co-evolved variants appear to be present both within and between blocks. These interactions are due to intra-host selection both at the RNA and protein level. Overall our findings show that during FMDV co-infections by closely related strains, capsid-coding genes recombine within the host at a much higher rate than expected, despite the presence of strong constraints dictated by the capsid structure. Although these intra-host results are not immediately translatable to a phylogenetic setting, recombination and epistasis must play a major and so far underappreciated role in the molecular evolution of the virus at all scales.

There are 7 serotypes of Foot-and-Mouth Disease Virus and multiple strains of each serotype. The emergence of new strains can result in widespread outbreaks of disease and requires new vaccines to be developed. The major mechanisms driving variation are thought to be substitutions in the viral genome. Recombination in the capsid-coding region of the virus genome has been described at phylogenetic scales but not thought to play a major role in generating variants. In the current experiment, a co-infection of African buffaloes with closely related sub-populations of viruses allowed us to detect recombination events. For structural protein-coding sequences, the genetic composition of the population is driven by extensive within-host recombination. During the acute infection phase the intra-host recombination rates of 0.1 per base per year are comparable to the typical mutation rates of the virus. The recombination map reveals two strongly linked regions within the VP1 protein-coding sequence. Epistatic interactions between co-evolved mutations in VP1 are caused by intra-host selection at the RNA and protein level and are present both within and between the two regions. Our findings in this experimental setting support a major role for recombination and epistasis in the intra-host evolution of FMDV.

How does selfing affect the genetic variance of quantitative traits? An updated meta-analysis on empirical results in angiosperm species

Most theoretical works predict that selfing should reduce the level of additive genetic variance available for quantitative traits within natural populations. Despite a growing number of quantitative genetic studies undertaken during the last two decades, this prediction is still not well supported empirically. To resolve this issue and confirm or reject theoretical predictions, we reviewed quantitative trait heritability estimates from natural plant populations with different rates of self-fertilization and carried out a meta-analysis. In accordance with models of polygenic traits under stabilizing selection, we found that the fraction of additive genetic variance is negatively correlated with the selfing rate. Although the mating system explains a moderate fraction of the variance, the mean reduction of narrow-sense heritability values between strictly allogamous and predominantly selfing populations is strong, around 60%. Because some nonadditive components of genetic variance become selectable under inbreeding, we determine whether self-fertilization affects the relative contribution of these components to genetic variance by comparing narrow-sense heritability estimates from outcrossing populations with broad-sense heritability estimated in autogamous populations. Results suggest that these nonadditive components of variance may restore some genetic variance in predominantly selfing populations; it remains, however, uncertain how these nonadditive components will contribute to adaptation.

Survival of the simplest in microbial evolution

The evolution of microbial and viral organisms often generates clonal interference, a mode of competition between genetic clades within a population. Here we show how interference impacts systems biology by constraining genetic and phenotypic complexity. Our analysis uses biophysically grounded evolutionary models for molecular phenotypes, such as fold stability and enzymatic activity of genes. We find a generic mode of phenotypic interference that couples the function of individual genes and the population’s global evolutionary dynamics. Biological implications of phenotypic interference include rapid collateral system degradation in adaptation experiments and long-term selection against genome complexity: each additional gene carries a cost proportional to the total number of genes. Recombination above a threshold rate can eliminate this cost, which establishes a universal, biophysically grounded scenario for the evolution of sex. In a broader context, our analysis suggests that the systems biology of microbes is strongly intertwined with their mode of evolution.

In asexual populations selection at different genomic loci can interfere with each other. Here, using a biophysical model of molecular evolution the authors show that interference results in long-term degradation of molecular function, an effect that strongly depends on genome size.

Epistasis detectably alters correlations between genomic sites in a narrow parameter window

Different genomic sites evolve inter-dependently due to the combined action of epistasis, defined as a non-multiplicative contribution of alleles at different loci to genome fitness, and the physical linkage of different loci in genome. Both epistasis and linkage, partially compensated by recombination, cause correlations between allele frequencies at the loci (linkage disequilibrium, LD). The interaction and competition between epistasis and linkage are not fully understood, nor is their relative sensitivity to recombination. Modeling an adapting population in the presence of random mutation, natural selection, pairwise epistasis, and random genetic drift, we compare the contributions of epistasis and linkage. For this end, we use a panel of haplotype-based measures of LD and their various combinations calculated for epistatic and non-epistatic pairs separately. We compute the optimal percentages of detected and false positive pairs in a one-time sample of a population of moderate size. We demonstrate that true interacting pairs can be told apart in a sufficiently short genome within a narrow window of time and parameters. Outside of this parameter region, unless the population is extremely large, shared ancestry of individual sequences generates pervasive stochastic LD for non-interacting pairs masking true epistatic associations. In the presence of sufficiently strong recombination, linkage effects decrease faster than those of epistasis, and the detection of epistasis improves. We demonstrate that the epistasis component of locus association can be isolated, at a single time point, by averaging haplotype frequencies over multiple independent populations. These results demonstrate the existence of fundamental restrictions on the protocols for detecting true interactions in DNA sequence sets.

Fast Estimation of Recombination Rates Using Topological Data Analysis

Accurate estimation of recombination rates is critical for studying the origins and maintenance of genetic diversity. Because the inference of recombination rates under a full evolutionary model is computationally expensive, we developed an alternative approach using topological data analysis (TDA) on genome sequences. We find that this method can analyze datasets larger than what can be handled by any existing recombination inference software, and has accuracy comparable to commonly used model-based methods with significantly less processing time. Previous TDA methods used information contained solely in the first Betti number ([Formula: see text]) of a set of genomes, which aims to capture the number of loops that can be detected within a genealogy. These explorations have proven difficult to connect to the theory of the underlying biological process of recombination, and, consequently, have unpredictable behavior under perturbations of the data. We introduce a new topological feature, which we call ψ, with a natural connection to coalescent models, and present novel arguments relating [Formula: see text] to population genetic models. Using simulations, we show that ψ and [Formula: see text] are differentially affected by missing data, and package our approach as TREE (Topological Recombination Estimator). TREE's efficiency and accuracy make it well suited as a first-pass estimator of recombination rate heterogeneity or hotspots throughout the genome. Our work empirically and theoretically justifies the use of topological statistics as summaries of genome sequences and describes a new, unintuitive relationship between topological features of the distribution of sequence data and the footprint of recombination on genomes.

A rigorous measure of genome-wide genetic shuffling that takes into account crossover positions and Mendel's second law

Comparative studies in evolutionary genetics rely critically on evaluation of the total amount of genetic shuffling that occurs during gamete production. Such studies have been hampered by the absence of a direct measure of this quantity. Existing measures consider crossing-over by simply counting the average number of crossovers per meiosis. This is qualitatively inadequate, because the positions of crossovers along a chromosome are also critical: a crossover toward the middle of a chromosome causes more shuffling than a crossover toward the tip. Moreover, traditional measures fail to consider shuffling from independent assortment of homologous chromosomes (Mendel's second law). Here, we present a rigorous measure of genome-wide shuffling that does not suffer from these limitations. We define the parameter [Formula: see text] as the probability that the alleles at two randomly chosen loci are shuffled during gamete production. This measure can be decomposed into separate contributions from crossover number and position and from independent assortment. Intrinsic implications of this metric include the fact that [Formula: see text] is larger when crossovers are more evenly spaced, which suggests a selective advantage of crossover interference. Utilization of [Formula: see text] is enabled by powerful emergent methods for determining crossover positions either cytologically or by DNA sequencing. Application of our analysis to such data from human male and female reveals that (i) [Formula: see text] in humans is close to its maximum possible value of 1/2 and that (ii) this high level of shuffling is due almost entirely to independent assortment, the contribution of which is ∼30 times greater than that of crossovers.

DCA for genome-wide epistasis analysis: the statistical genetics perspective

Direct coupling analysis (DCA) is a now widely used method to leverage statistical information from many similar biological systems to draw meaningful conclusions on each system separately. DCA has been applied with great success to sequences of homologous proteins, and also more recently to whole-genome population-wide sequencing data. We here argue that the use of DCA on the genome scale is contingent on fundamental issues of population genetics. DCA can be expected to yield meaningful results when a population is in the quasi-linkage equilibrium (QLE) phase studied by Kimura and others, but not, for instance, in a phase of clonal competition. We discuss how the exponential (Potts model) distributions emerge in QLE, and compare couplings to correlations obtained in a study of about 3000 genomes of the human pathogen Streptococcus pneumoniae.

Structure of multilocus genetic diversity in predominantly selfing populations

Predominantly selfing populations are expected to have reduced effective population sizes due to nonrandom sampling of gametes, demographic stochasticity (bottlenecks or extinction-recolonization), and large scale hitchhiking (reduced effective recombination). Thus, they are expected to display low genetic diversity, which was confirmed by empirical studies. The structure of genetic diversity in predominantly selfing species is dramatically different from outcrossing ones, with populations often dominated by one or a few multilocus genotypes (MLGs) coexisting with several rare genotypes. Therefore, multilocus diversity indices are relevant to describe diversity in selfing populations. Here, we use simulations to provide analytical expectations for multilocus indices and examine whether selfing alone can be responsible for the high-frequency MLGs persistent through time in the absence of selection. We then examine how combining single and multilocus indices of diversity may be insightful to distinguish the effects of selfing, population size, and more complex demographic events (bottlenecks, migration, admixture, or extinction-recolonization). Finally, we examine how temporal changes in MLG frequencies can be insightful to understand the evolutionary trajectory of a given population. We show that combinations of selfing and small demographic sizes can result in high-frequency MLGs, as observed in natural populations. We also show how different demographic scenarios can be distinguished by the parallel analysis of single and multilocus indices of diversity, and we emphasize the importance of temporal data for the study of predominantly selfing populations. Finally, the comparison of our simulations with empirical data on populations of Medicago truncatula confirms the pertinence of our simulation framework.

Sex: The power of randomization

In evolutionary biology, randomness has been perceived as a force that, in and of itself, is capable of inventing: mutation creates new genetic information at random across the genome which leads to phenotypic change, which is then subject to selection. However, in science in general and in computer science in particular, the widespread use of randomness takes a different form. Here, randomization allows for the breaking of pattern, as seen for example in its removal of biases (patterns) by random sampling or random assignment to conditions. Combined with various forms of evaluation, this breaking of pattern becomes an extraordinarily powerful tool, as also seen in many randomized algorithms in computer science. Here we show that this power of randomness is harnessed in nature by sex and recombination. In a finite population, and under the assumption of interactions between genetic variants, sex and recombination allow selection to test how well an allele will perform in a sample of combinations of interacting genetic partners drawn at random from all possible such combinations; consequently, even a small number of tests of genotypes such as takes place in a finite population favors alleles that will most likely perform well in a vast number of yet unrealized genetic combinations. This power of randomization is not manifest in asexual populations.

Slower environmental change hinders adaptation from standing genetic variation

Evolutionary responses to environmental change depend on the time available for adaptation before environmental degradation leads to extinction. Explicit tests of this relationship are limited to microbes where adaptation usually depends on the sequential fixation of de novo mutations, excluding standing variation for genotype-by-environment fitness interactions that should be key for most natural species. For natural species evolving from standing genetic variation, adaptation at slower rates of environmental change may be impeded since the best genotypes at the most extreme environments can be lost during evolution due to genetic drift or founder effects. To address this hypothesis, we perform experimental evolution with self-fertilizing populations of the nematode Caenorhabditis elegans and develop an inference model to describe natural selection on extant genotypes under environmental change. Under a sudden environmental change, we find that selection rapidly increases the frequency of genotypes with high fitness in the most extreme environment. In contrast, under a gradual environmental change selection first favors genotypes that are worse at the most extreme environment. We demonstrate with a second set of evolution experiments that, as a consequence of slower environmental change and thus longer periods to reach the most extreme environments, genetic drift and founder effects can lead to the loss of the most beneficial genotypes. We further find that maintenance of standing genetic variation can retard the fixation of the best genotypes in the most extreme environment because of interference between them. Taken together, these results show that slower environmental change can hamper adaptation from standing genetic variation and they support theoretical models indicating that standing variation for genotype-by-environment fitness interactions critically alters the pace and outcome of adaptation under environmental change.

A novel framework for inferring parameters of transmission from viral sequence data

Transmission between hosts is a critical part of the viral lifecycle. Recent studies of viral transmission have used genome sequence data to evaluate the number of particles transmitted between hosts, and the role of selection as it operates during the transmission process. However, the interpretation of sequence data describing transmission events is a challenging task. We here present a novel and comprehensive framework for using short-read sequence data to understand viral transmission events, designed for influenza virus, but adaptable to other viral species. Our approach solves multiple shortcomings of previous methods for this purpose; for example, we consider transmission as an event involving whole viruses, rather than sets of independent alleles. We demonstrate how selection during transmission and noisy sequence data may each affect naive inferences of the population bottleneck, accounting for these in our framework so as to achieve a correct inference. We identify circumstances in which selection for increased viral transmission may or may not be identified from data. Applying our method to experimental data in which transmission occurs in the presence of strong selection, we show that our framework grants a more quantitative insight into transmission events than previous approaches, inferring the bottleneck in a manner that accounts for selection, both for within-host virulence, and for inherent viral transmissibility. Our work provides new opportunities for studying transmission processes in influenza, and by extension, in other infectious diseases.

Weak Epistasis May Drive Adaptation in Recombining Bacteria

The impact of epistasis on the evolution of multi-locus traits depends on recombination. While sexually reproducing eukaryotes recombine so frequently that epistasis between polymorphisms is not considered to play a large role in short-term adaptation, many bacteria also recombine, some to the degree that their populations are described as "panmictic" or "freely recombining." However, whether this recombination is sufficient to limit the ability of selection to act on epistatic contributions to fitness is unknown. We quantify homologous recombination in five bacterial pathogens and use these parameter estimates in a multilocus model of bacterial evolution with additive and epistatic effects. We find that even for highly recombining species (e.g., Streptococcus pneumoniae or Helicobacter pylori), selection on weak interactions between distant mutations is nearly as efficient as for an asexual species, likely because homologous recombination typically transfers only short segments. However, for strong epistasis, bacterial recombination accelerates selection, with the dynamics dependent on the amount of recombination and the number of loci. Epistasis may thus play an important role in both the short- and long-term adaptive evolution of bacteria, and, unlike in eukaryotes, is not limited to strong effect sizes, closely linked loci, or other conditions that limit the impact of recombination.

The Influence of Higher-Order Epistasis on Biological Fitness Landscape Topography

The effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We conclude by highlighting opportunities for further theoretical and experimental work dissecting the influence that epistasis of all orders has on fitness landscape topography and on the efficiency of evolution by natural selection.

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

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

Rapid adaptation in large populations with very rare sex: Scalings and spontaneous oscillations

Genetic exchange in microbes and other facultative sexuals can be rare enough that evolution is almost entirely asexual and populations almost clonal. But the benefits of genetic exchange depend crucially on the diversity of genotypes in a population. How very rare recombination together with the accumulation of new mutations shapes the diversity of large populations and gives rise to faster adaptation is still poorly understood. This paper analyzes a particularly simple model: organisms with two asexual chromosomes that can reassort during rare matings that occur at a rate r. The speed of adaptation for large population sizes, N, is found to depend on the ratio ∼log(Nr)∕log(N). For larger populations, the r needed to yield the same speed decreases as a power of N. Remarkably, the population undergoes spontaneous oscillations alternating between phases when the fittest individuals are created by mutation and when they are created by reassortment, which - in contrast to conventional regimes - decreases the diversity. Between the two phases, the mean fitness jumps rapidly. The oscillatory dynamics and the strong fluctuations this induces have implications for the diversity and coalescent statistics. The results are potentially applicable to large microbial populations, especially viruses that have a small number of chromosomes. Some of the key features may be more broadly applicable for large populations with other types of rare genetic exchange.

Polygenicity and Epistasis Underlie Fitness-Proximal Traits in the Caenorhabditis elegans Multiparental Experimental Evolution (CeMEE) Panel

Understanding the genetic basis of complex traits remains a major challenge in biology. Polygenicity, phenotypic plasticity, and epistasis contribute to phenotypic variance in ways that are rarely clear. This uncertainty can be problematic for estimating heritability, for predicting individual phenotypes from genomic data, and for parameterizing models of phenotypic evolution. Here, we report an advanced recombinant inbred line (RIL) quantitative trait locus mapping panel for the hermaphroditic nematode Caenorhabditis elegans, the C. elegans multiparental experimental evolution (CeMEE) panel. The CeMEE panel, comprising 507 RILs at present, was created by hybridization of 16 wild isolates, experimental evolution for 140-190 generations, and inbreeding by selfing for 13-16 generations. The panel contains 22% of single-nucleotide polymorphisms known to segregate in natural populations, and complements existing C. elegans mapping resources by providing fine resolution and high nucleotide diversity across > 95% of the genome. We apply it to study the genetic basis of two fitness components, fertility and hermaphrodite body size at time of reproduction, with high broad-sense heritability in the CeMEE. While simulations show that we should detect common alleles with additive effects as small as 5%, at gene-level resolution, the genetic architectures of these traits do not feature such alleles. We instead find that a significant fraction of trait variance, approaching 40% for fertility, can be explained by sign epistasis with main effects below the detection limit. In congruence, phenotype prediction from genomic similarity, while generally poor ([Formula: see text]), requires modeling epistasis for optimal accuracy, with most variance attributed to the rapidly evolving chromosome arms.

Sex in a test tube: testing the benefits of in vitro recombination

The origin and evolution of sex, and the associated role of recombination, present a major problem in biology. Sex typically involves recombination of closely related DNA or RNA sequences, which is fundamentally a random process that creates but also breaks up beneficial allele combinations. Directed evolution experiments, which combine in vitro mutation and recombination protocols with in vitro or in vivo selection, have proved to be an effective approach for improving functionality of nucleic acids and enzymes. As this approach allows extreme control over evolutionary conditions and parameters, it also facilitates the detection of small or position-specific recombination benefits and benefits associated with recombination between highly divergent genotypes. Yet, in vitro approaches have been largely exploratory and motivated by obtaining improved end products rather than testing hypotheses of recombination benefits. Here, we review the various experimental systems and approaches used by in vitro studies of recombination, discuss what they say about the evolutionary role of recombination, and sketch their potential for addressing extant questions about the evolutionary role of sex and recombination, in particular on complex fitness landscapes. We also review recent insights into the role of 'extracellular recombination' during the origin of life.This article is part of the themed issue 'Weird sex: the underappreciated diversity of sexual reproduction'.

Variability in fitness effects can preclude selection of the fittest

Evolutionary biologists often predict the outcome of natural selection on an allele by measuring its effects on lifetime survival and reproduction of individual carriers. However, alleles affecting traits like sex, evolvability, and cooperation can cause fitness effects that depend heavily on differences in the environmental, social, and genetic context of individuals carrying the allele. This variability makes it difficult to summarize the evolutionary fate of an allele based solely on its effects on any one individual. Attempts to average over this variability can sometimes salvage the concept of fitness. In other cases evolutionary outcomes can only be predicted by considering the entire genealogy of an allele, thus limiting the utility of individual fitness altogether. We describe a number of intriguing new evolutionary phenomena that have emerged in studies that explicitly model long-term lineage dynamics and discuss implications for the evolution of infectious diseases.

The Evolutionary Interplay between Adaptation and Self-Fertilization

Genome-wide surveys of nucleotide polymorphisms, obtained from next-generation sequencing, have uncovered numerous examples of adaptation in self-fertilizing organisms, especially regarding changes to climate, geography, and reproductive systems. Yet existing models for inferring attributes of adaptive mutations often assume idealized outcrossing populations, which risks mischaracterizing properties of these variants. Recent theoretical work is emphasizing how various aspects of self-fertilization affects adaptation, yet empirical data on these properties are lacking. We review theoretical and empirical studies demonstrating how self-fertilization alters the process of adaptation, illustrated using examples from current sequencing projects. We propose ideas for how future research can more accurately quantify aspects of adaptation in self-fertilizers, including incorporating the effects of standing variation, demographic history, and polygenic adaptation.

Analysis of large-scale next-generation sequencing datasets are finding more examples of adaptive evolution at the genomic level.

Advances in theoretical work has demonstrated how self-fertilisation affects different aspects of adaptation in these organisms, compared to outcrossers.

Current software and statistical methods do not take different mating systems into account, which risks mischaracterising the presence or strength of adaptive mutations from genome scans.

Development of new mathematical and statistical methods that explicitly consider self-fertilization and associated demographic effects will enable researchers to more accurately quantify adaptation in these organisms.

Hill-Robertson interference maintained by Red Queen dynamics favours the evolution of sex

Although it is well established theoretically that selective interference among mutations (Hill-Robertson interference) favours meiotic recombination, genomewide mean rates of mutation and strengths of selection appear too low to support this as the mechanism favouring recombination in nature. A possible solution to this discrepancy between theory and observation is that selection is at least intermittently very strong due to the antagonistic coevolution between a host and its parasites. The Red Queen theory posits that such coevolution generates fitness epistasis among loci, which generates negative linkage disequilibrium among beneficial mutations, which in turn favours recombination. This theory has received only limited support. However, Red Queen dynamics without epistasis may provide the ecological conditions that maintain strong and frequent selective interference in finite populations that indirectly selects for recombination. This hypothesis is developed here through the simulation of Red Queen dynamics. This approach required the development of a method to calculate the exact frequencies of multilocus haplotypes after recombination. Simulations show that recombination is favoured by the moderately weak selection of many loci involved in the interaction between a host and its parasites, which results in substitution rates that are compatible with empirical estimates. The model also reproduces the previously reported rapid increase in the rate of outcrossing in Caenorhabditis elegans coevolving with a bacterial pathogen.

SAMFIRE: multi-locus variant calling for time-resolved sequence data

An increasingly common method for studying evolution is the collection of time-resolved short-read sequence data. Such datasets allow for the direct observation of rapid evolutionary processes, as might occur in natural microbial populations and in evolutionary experiments. In many circumstances, evolutionary pressure acting upon single variants can cause genomic changes at multiple nearby loci. SAMFIRE is an open-access software package for processing and analyzing sequence reads from time-resolved data, calling important single- and multi-locus variants over time, identifying alleles potentially affected by selection, calculating linkage disequilibrium statistics, performing haplotype reconstruction and exploiting time-resolved information to estimate the extent of uncertainty in reported genomic data.

AVAILABILITY AND IMPLEMENTATION

C ++ code may be found at https://github.com/cjri/samfire/

CONTACT

chris.illingworth@gen.cam.ac.uk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity

The immune system has developed a number of distinct complex mechanisms to shape and control the antibody repertoire. One of these mechanisms, the affinity maturation process, works in an evolutionary-like fashion: after binding to a foreign molecule, the antibody-producing B-cells exhibit a high-frequency mutation rate in the genome region that codes for the antibody active site. Eventually, cells that produce antibodies with higher affinity for their cognate antigen are selected and clonally expanded. Here, we propose a new statistical approach based on maximum entropy modeling in which a scoring function related to the binding affinity of antibodies against a specific antigen is inferred from a sample of sequences of the immune repertoire of an individual. We use our inference strategy to infer a statistical model on a data set obtained by sequencing a fairly large portion of the immune repertoire of an HIV-1 infected patient. The Pearson correlation coefficient between our scoring function and the IC50 neutralization titer measured on 30 different antibodies of known sequence is as high as 0.77 (p-value 10-6), outperforming other sequence- and structure-based models.

Scaling properties of evolutionary paths in a biophysical model of protein adaptation

The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of fitness landscapes and evolutionary paths. We first consider evolution on a simple Mount Fuji fitness landscape, focusing on how the length and predictability of evolutionary paths scale with the coarse-grained sequence length and alphabet. We obtain simple scaling relations for both the weak- and strong-selection limits, with a non-trivial crossover regime at intermediate selection strengths. We apply these results to evolution on a biophysical fitness landscape that describes how proteins evolve new binding interactions while maintaining their folding stability. We combine the scaling relations with numerical calculations for coarse-grained protein sequences to obtain quantitative properties of the model for realistic binding interfaces and a full amino acid alphabet.

A framework for inferring fitness landscapes of patient-derived viruses using quasispecies theory

Fitness is a central quantity in evolutionary models of viruses. However, it remains difficult to determine viral fitness experimentally, and existing in vitro assays can be poor predictors of in vivo fitness of viral populations within their hosts. Next-generation sequencing can nowadays provide snapshots of evolving virus populations, and these data offer new opportunities for inferring viral fitness. Using the equilibrium distribution of the quasispecies model, an established model of intrahost viral evolution, we linked fitness parameters to the composition of the virus population, which can be estimated by next-generation sequencing. For inference, we developed a Bayesian Markov chain Monte Carlo method to sample from the posterior distribution of fitness values. The sampler can overcome situations where no maximum-likelihood estimator exists, and it can adaptively learn the posterior distribution of highly correlated fitness landscapes without prior knowledge of their shape. We tested our approach on simulated data and applied it to clinical human immunodeficiency virus 1 samples to estimate their fitness landscapes in vivo. The posterior fitness distributions allowed for differentiating viral haplotypes from each other, for determining neutral haplotype networks, in which no haplotype is more or less credibly fit than any other, and for detecting epistasis in fitness landscapes. Our implemented approach, called QuasiFit, is available at http://www.cbg.ethz.ch/software/quasifit.

Multidimensional epistasis and the transitory advantage of sex

Identifying and quantifying the benefits of sex and recombination is a long-standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional fitness landscapes in the presence of sign epistasis. Here we present a comparative numerical study of sexual and asexual evolutionary dynamics of haploids on tunably rugged model landscapes under strong selection, paying special attention to the temporal development of the evolutionary advantage of recombination and the link between population diversity and the rate of adaptation. We show that the adaptive advantage of recombination on static rugged landscapes is strictly transitory. At early times, an advantage of recombination arises through the possibility to combine individually occurring beneficial mutations, but this effect is reversed at longer times by the much more efficient trapping of recombining populations at local fitness peaks. These findings are explained by means of well-established results for a setup with only two loci. In accordance with the Red Queen hypothesis the transitory advantage can be prolonged indefinitely in fluctuating environments, and it is maximal when the environment fluctuates on the same time scale on which trapping at local optima typically occurs.

The rate of adaptation in large sexual populations with linear chromosomes

In large populations, multiple beneficial mutations may be simultaneously spreading. In asexual populations, these mutations must either arise on the same background or compete against each other. In sexual populations, recombination can bring together beneficial alleles from different backgrounds, but tightly linked alleles may still greatly interfere with each other. We show for well-mixed populations that when this interference is strong, the genome can be seen as consisting of many effectively asexual stretches linked together. The rate at which beneficial alleles fix is thus roughly proportional to the rate of recombination and depends only logarithmically on the mutation supply and the strength of selection. Our scaling arguments also allow us to predict, with reasonable accuracy, the fitness distribution of fixed mutations when the mutational effect sizes are broad. We focus on the regime in which crossovers occur more frequently than beneficial mutations, as is likely to be the case for many natural populations.

Universality and predictability in molecular quantitative genetics

Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. We review recent developments in evolutionary theory and experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis, which is often at least partially unknown. We show that universal measurements can be used to infer selection on a quantitative trait, which determines its evolutionary mode of conservation or adaptation. Furthermore, universality is closely linked to predictability of trait evolution across lineages. We argue that universal trait statistics extends over a range of cellular scales and opens new avenues of quantitative evolutionary systems biology.

The impact of recombination on short-term selection gain in plant breeding experiments

Recombination is a requirement for response to selection, but researchers still debate whether increasing recombination beyond normal levels will result in significant gains in short-term selection. We tested this hypothesis, in the context of plant breeding, through a series of simulation experiments comparing short-term selection response (≤20 cycles) between populations with normal levels of recombination and similar populations with unconstrained recombination (i.e., free recombination). We considered additive and epistatic models and examined a wide range of values for key design variables: selection cycles, QTL number, heritability, linkage phase, selection intensity and population size. With few exceptions, going from normal to unconstrained levels of recombination produced only modest gains in response to selection (≈11 % on average). We then asked how breeders might capture some of this theoretical gain by increasing recombination through either (1) extra rounds of mating or (2) selection of highly recombinant individuals via use of molecular markers/maps. All methods tested captured less than half of the potential gain, but our analysis indicates that the most effective method is to select for increased recombination and the trait simultaneously. This recommendation is based on evidence of a favorable interaction between trait selection and the impact of recombination on selection gains. Finally, we examined the relative contributions of the two components of meiotic recombination, chromosome assortment and crossing over, to short-term selection gain. Depending primarily on the presence of trait selection pressure, chromosome assortment alone accounted for 40-75 % of gain in response to short-term selection.

Clonal interference in the evolution of influenza

The seasonal influenza A virus undergoes rapid evolution to escape human immune response. Adaptive changes occur primarily in antigenic epitopes, the antibody-binding domains of the viral hemagglutinin. This process involves recurrent selective sweeps, in which clusters of simultaneous nucleotide fixations in the hemagglutinin coding sequence are observed about every 4 years. Here, we show that influenza A (H3N2) evolves by strong clonal interference. This mode of evolution is a red queen race between viral strains with different beneficial mutations. Clonal interference explains and quantifies the observed sweep pattern: we find an average of at least one strongly beneficial amino acid substitution per year, and a given selective sweep has three to four driving mutations on average. The inference of selection and clonal interference is based on frequency time series of single-nucleotide polymorphisms, which are obtained from a sample of influenza genome sequences over 39 years. Our results imply that mode and speed of influenza evolution are governed not only by positive selection within, but also by background selection outside antigenic epitopes: immune adaptation and conservation of other viral functions interfere with each other. Hence, adapting viral proteins are predicted to be particularly brittle. We conclude that a quantitative understanding of influenza's evolutionary and epidemiological dynamics must be based on all genomic domains and functions coupled by clonal interference.