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The relationship between genotype and phenotype, or the fitness landscape, is the foundation of genetic engineering and evolution. However, mapping fitness landscapes poses a major technical challenge due to the amount of quantifiable data that is required. Catalytic RNA is a special topic in the study of fitness landscapes due to its relatively small sequence space combined with its importance in synthetic biology. The combination of in vitro selection and high-throughput sequencing has recently provided empirical maps of both complete and local RNA fitness landscapes, but the astronomical size of sequence space limits purely experimental investigations. Next steps are likely to involve data-driven interpolation and extrapolation over sequence space using various machine learning techniques. We discuss recent progress in understanding RNA fitness landscapes, particularly with respect to protocells and machine representations of RNA. The confluence of technical advances may significantly impact synthetic biology in the near future.

The herein proposed Python package pflacco provides a set of numerical features to characterize single-objective continuous and constrained optimization problems. Thereby, pflacco addresses two major challenges in the area of optimization. Firstly, it provides the means to develop an understanding of a given problem instance, which is crucial for designing, selecting, or configuring optimization algorithms in general. Secondly, these numerical features can be utilized in the research streams of automated algorithm selection and configuration. While the majority of these landscape features are already available in the R package flacco, our Python implementation offers these tools to an even wider audience and thereby promotes research interests and novel avenues in the area of optimization. [ABSTRACT FROM AUTHOR]

The identification of catalytic RNAs is typically achieved through primarily experimental means. However, only a small fraction of sequence space can be analyzed even with high-throughput techniques. Methods to extrapolate from a limited data set to predict additional ribozyme sequences, particularly in a human-interpretable fashion, could be useful both for designing new functional RNAs and for generating greater understanding about a ribozyme fitness landscape. Using information theory, we express the effects of epistasis (i.e., deviations from additivity) on a ribozyme. This representation was incorporated into a simple model of the epistatic fitness landscape, which identified potentially exploitable combinations of mutations. We used this model to theoretically predict mutants of high activity for a self-aminoacylating ribozyme, identifying potentially active triple and quadruple mutants beyond the experimental data set of single and double mutants. The predictions were validated experimentally, with nine out of nine sequences being accurately predicted to have high activity. This set of sequences included mutants that form a previously unknown evolutionary bridge between two ribozyme families that share a common motif. Individual steps in the method could be examined, understood, and guided by a human, combining interpretability and performance in a simple model to predict ribozyme sequences by extrapolation.

Summary: Climate change is simultaneously increasing carbon dioxide concentrations ([CO2]) and temperature. These factors could interact to influence plant physiology and performance. Alternatively, increased [CO2] may offset costs associated with elevated temperatures. Furthermore, the interaction between elevated temperature and [CO2] may differentially affect populations from along an elevational gradient and disrupt local adaptation.We conducted a multifactorial growth chamber experiment to examine the interactive effects of temperature and [CO2] on fitness and ecophysiology of diverse accessions of Boechera stricta (Brassicaceae) sourced from a broad elevational gradient in Colorado. We tested whether increased [CO2] would enhance photosynthesis across accessions, and whether warmer conditions would depress the fitness of high‐elevation accessions owing to steep reductions in temperature with increasing elevation in this system. Elevational clines in [CO2] are not as evident, making it challenging to predict how locally adapted ecotypes will respond to elevated [CO2].This experiment revealed that elevated [CO2] increased photosynthesis and intrinsic water use efficiency across all accessions. However, these instantaneous responses to treatments did not translate to changes in fitness. Instead, increased temperatures reduced the probability of reproduction for all accessions. Elevated [CO2] and increased temperatures interacted to shift the adaptive landscape, favoring lower elevation accessions for the probability of survival and fecundity.Our results suggest that elevated temperatures and [CO2] associated with climate change could have severe negative consequences, especially for high‐elevation populations. [ABSTRACT FROM AUTHOR]

The role of spontaneous mutations in evolution depends on the distribution of their effects on fitness. Despite a general consensus that new mutations are deleterious on average, a handful of mutation accumulation experiments in diverse organisms instead suggest that beneficial and deleterious mutations can have comparable fitness impacts, i.e. the product of their respective rates and effects can be roughly equal. We currently lack a general framework for predicting when such a pattern will occur. One idea is that beneficial mutations will be more evident in genotypes that are not well adapted to the testing environment. We tested this prediction experimentally in the laboratory yeast Saccharomyces cerevisiae by allowing nine replicate populations to adapt to novel environments with complex sets of stressors. After >1000 asexual generations interspersed with 41 rounds of sexual reproduction, we assessed the mean effect of induced mutations on yeast growth in both the environment to which they had been adapting and the alternative novel environment. The mutations were deleterious on average, with the severity depending on the testing environment. However, we found no evidence that the adaptive match between genotype and environment is predictive of mutational fitness effects. [ABSTRACT FROM AUTHOR]

SARS-CoV-2 employs its spike protein's receptor binding domain (RBD) to enter host cells. The RBD is constantly subjected to immune responses, while requiring efficient binding to host cell receptors for successful infection. However, our understanding of how RBD's biophysical properties contribute to SARS-CoV-2's epidemiological fitness remains largely incomplete. Through a comprehensive approach, comprising large-scale sequence analysis of SARS-CoV-2 variants and the identification of a fitness function based on binding thermodynamics, we unravel the relationship between the biophysical properties of RBD variants and their contribution to viral fitness. We developed a biophysical model that uses statistical mechanics to map the molecular phenotype space, characterized by dissociation constants of RBD to ACE2, LYCoV016, LY-CoV555, REGN10987, and S309, onto an epistatic fitness landscape. We validate our findings through experimentally measured and machine learning (ML) estimated binding affinities, coupled with infectivity data derived from population-level sequencing. Our analysis reveals that this model effectively predicts the fitness of novel RBDvariants and can account for the epistatic interactions among mutations, including explaining the later reversal of Q493R. Our study sheds light on the impact of specific mutations on viral fitness and delivers a tool for predicting the future epidemiological trajectory of previously unseen or emerging low-frequency variants. These insights offer not only greater understanding of viral evolution but also potentially aid in guiding public health decisions in the battle against COVID-19 and future pandemics. [ABSTRACT FROM AUTHOR]

It is commonly thought that the long-term advantage of meiotic recombination is to dissipate genetic linkage, allowing natural selection to act independently on different loci. It is thus theoretically expected that genes with higher recombination rates evolve under more effective selection. On the other hand, recombination is often associated with GC-biased gene conversion (gBGC), which theoretically interferes with selection by promoting the fixation of deleterious GC alleles. To test these predictions, several studies assessed whether selection was more effective in highly recombining genes (due to dissipation of genetic linkage) or less effective (due to gBGC), assuming a fixed distribution of fitness effects (DFE) for all genes. In this study, I directly derive the DFE from a gene's evolutionary history (shaped by mutation, selection, drift, and gBGC) under empirical fitness landscapes. I show that genes that have experienced high levels of gBGC are less fit and thus have more opportunities for beneficial mutations. Only a small decrease in the genome-wide intensity of gBGC leads to the fixation of these beneficial mutations, particularly in highly recombining genes. This results in increased positive selection in highly recombining genes that is not caused by more effective selection. Additionally, I show that the death of a recombination hotspot can lead to a higher d N / d S than its birth, but with substitution patterns biased towards AT, and only at selected positions. This shows that controlling for a substitution bias towards GC is therefore not sufficient to rule out the contribution of gBGC to signatures of accelerated evolution. Finally, although gBGC does not affect the fixation probability of GC-conservative mutations, I show that by altering the DFE, gBGC can also significantly affect nonsynonymous GC-conservative substitution patterns. [ABSTRACT FROM AUTHOR]

Assessing whether phenological shifts in response to climate change confer a fitness advantage requires investigating the relationships among phenology, fitness, and environmental drivers of selection. Despite widely documented advancements in phenology with warming climate, we lack empirical estimates of how selection on phenology varies in response to continuous climate drivers or how phenological shifts in response to warming conditions affect fitness. We leverage an unusual long-term dataset with repeated, individual measurements of phenology and reproduction in a long-lived alpine plant. We analyze phenotypic plasticity in flowering phenology in relation to two climate drivers, snowmelt timing and growing degree days (GDDs). Plants flower earlier with increased GDDs and earlier snowmelt, and directional selection also favors earlier flowering under these conditions. However, reproduction still declines with warming and early snowmelt, even when flowering is early. Furthermore, the steepness of this reproductive decline increases dramatically with warming conditions, resulting in very little fruit production regardless of flowering time once GDDs exceed approximately 225 degree days or snowmelt occurs before May 15. Even though advancing phenology confers a fitness advantage relative to stasis, these shifts are insufficient to maintain reproduction under warming, highlighting limits to the potential benefits of phenological plasticity under climate change. [ABSTRACT FROM AUTHOR]

Directed evolution is a powerful tool that can bypass gaps in our understanding of the sequence-function relationship of proteins and still isolate variants with desired activities, properties, and substrate specificities. The rise of directed evolution platforms for polymerase engineering has accelerated the isolation of xenobiotic nucleic acid (XNA) synthetases and reverse transcriptases capable of processing a wide array of unnatural XNAs which have numerous therapeutic and biotechnological applications. Still, the current generation of XNA polymerases functions with significantly lower efficiency than the natural counterparts and retains a significant level of DNA polymerase activity which limits their in vivo applications. Although directed evolution approaches are continuously being developed and implemented to improve XNA polymerase engineering, the field lacks an in-depth analysis of the effect of selection parameters, library construction biases and sampling biases. Focusing on the directed evolution pipeline for DNA and XNA polymerase engineering, this work sets out a method for understanding the impact of selection conditions on selection success and efficiency. We also explore the influence of selection conditions on fidelity at the population and individual mutant level. Additionally, we explore the sequencing coverage requirements in directed evolution experiments, which differ from genome assembly and other -omics approaches. This analysis allowed us to identify the sequencing coverage threshold for the accurate and precise identification of significantly enriched mutants. Overall, this study introduces a robust methodology for optimizing selection protocols, which effectively streamlines selection processes by employing small libraries and cost-effective NGS sequencing. It provides valuable insights into critical considerations, thereby enhancing the overall effectiveness and efficiency of directed evolution strategies applicable to enzymes other than the ones considered here.

Does genetic background contribute to populations following the same or divergent adaptive trajectories? A recent study by Filipow et al. evolved multiple genetically distinct Pseudomonas aeruginosa strains to an artificial cystic fibrosis lung sputum media. The strains adapted at different rates but converged on similar phenotypes despite their initial diversity. [ABSTRACT FROM AUTHOR]

Multiple mutations often have non-additive (epistatic) phenotypic effects. Epistasis is of fundamental biological relevance but is not well understood mechanistically. Adaptive evolution, i.e., the evolution of new biochemical activities, is rich in epistatic interactions. To better understand the principles underlying epistasis during genetic adaptation, we studied the evolution of TEM-1 β-lactamase variants exhibiting cefotaxime resistance. We report the collection of a library of 487 observed evolutionary trajectories for TEM-1 and determine the epistasis status based on cefotaxime resistance phenotype for 206 combinations of 2-3 TEM-1 mutations involving 17 positions under adaptive selective pressure. Gain-of-function (GOF) mutations are gatekeepers for adaptation. To see if GOF phenotypes can be inferred based solely on sequence data, we calculated the enrichment of GOF mutations in the different categories of epistatic pairs. Our results suggest that this is possible because GOF mutations are particularly enriched in sign and reciprocal sign epistasis, which leave a major imprint on the sequence space accessible to evolution. We also used FoldX to explore the relationship between thermodynamic stability and epistasis. We found that mutations in observed evolutionary trajectories tend to destabilize the folded structure of the protein, albeit their cumulative effects are consistently below the protein's free energy of folding. The destabilizing effect is stronger for epistatic pairs, suggesting that modest or local alterations in folding stability can modulate catalysis. Finally, we report a significant relationship between epistasis and the degree to which two protein positions are structurally and dynamically coupled, even in the absence of ligand.

The century-old debate about the origin and evolution of non-additive effects (dominance and epistasis) and their roles in adaptation and speciation is far from settled. Dominance describes the observed relative difference in fitness or phenotype between heterozygotes and the average of homozygotes at a given polymorphic locus. Emerging empirical evidence supports and illustrates how the observed dominance at a locus can vary as a result of multi-locus interactions. Wade proposed a model that explains variable dominance at a focal locus through the change in the frequency of dominance-modifying alleles at other loci. Fitness landscape models that integrate epistasis and dominance may serve to quantify the consequences of variable dominance for adaptation and speciation. Dominance is usually considered a constant value that describes the relative difference in fitness or phenotype between heterozygotes and the average of homozygotes at a focal polymorphic locus. However, the observed dominance can vary with the genetic background of the focal locus. Here, alleles at other loci modify the observed phenotype through position effects or dominance modifiers that are sometimes associated with pathogen resistance, lineage, sex, or mating type. Theoretical models have illustrated how variable dominance appears in the context of multi-locus interaction (epistasis). Here, we review empirical evidence for variable dominance and how the observed patterns may be captured by proposed epistatic models. We highlight how integrating epistasis and dominance is crucial for comprehensively understanding adaptation and speciation. [ABSTRACT FROM AUTHOR]

Drug resistance is a significant obstacle to effective cancer treatment. To gain insights into how drug resistance develops, we adopted a concept called fitness landscape and employed a phenotype-structured population model by fitting to a set of experimental data on a drug used for ovarian cancer, olaparib. Our modeling approach allowed us to understand how a drug affects the fitness landscape and track the evolution of a population of cancer cells structured with a spectrum of drug resistance. We also incorporated pharmacokinetic (PK) modeling to identify the optimal dosages of the drug that could lead to long-term tumor reduction. We derived a formula that indicates that maximizing variation in plasma drug concentration over a dosing interval could be important in reducing drug resistance. Our findings suggest that it may be possible to achieve better treatment outcomes with a drug dose lower than the levels recommended by the drug label. Acknowledging the current limitations of our work, we believe that our approach, which combines modeling of both PK and drug resistance evolution, could contribute to a new direction for better designing drug treatment regimens to improve cancer treatment. [ABSTRACT FROM AUTHOR]

Seasonal H3N2 influenza evolves rapidly, leading to an extremely poor vaccine efficacy. Substitutions employed during vaccine production using embryonated eggs (i.e., egg passage adaptation) contribute to the poor vaccine efficacy (VE), but the evolutionary mechanism remains elusive. Using an unprecedented number of hemagglutinin sequences (n = 89,853), we found that the fitness landscape of passage adaptation is dominated by pervasive epistasis between two leading residues (186 and 194) and multiple other positions. Convergent evolutionary paths driven by strong epistasis explain most of the variation in VE, which has resulted in extremely poor vaccines for the past decade. Leveraging the unique fitness landscape, we developed a novel machine learning model that can predict egg passage substitutions for any candidate vaccine strain before the passage experiment, providing a unique opportunity for the selection of optimal vaccine viruses. Our study presents one of the most comprehensive characterizations of the fitness landscape of a virus and demonstrates that evolutionary trajectories can be harnessed for improved influenza vaccines.

The emergence of an RNA replicase capable of self-replication is considered an important stage in the origin of life. RNA polymerase ribozymes (PR) -including a variant that uses trinucleotide triphosphates (triplets) as substrates -have been created by in vitro evolution and are the closest functional analogues of the replicase, but the structural basis for their function is poorly understood. Here we use single-particle cryogenic electron microscopy (cryo-EM) and high-throughput mutation analysis to obtain the structure of a triplet polymerase ribozyme (TPR) apoenzyme and map its functional landscape. The cryo-EM structure at 5-Å resolution reveals the TPR as an RNA heterodimer comprising a catalytic subunit and a noncatalytic, auxiliary subunit, resembling the shape of a left hand with thumb and fingers at a 70° angle. The two subunits are connected by two distinct kissing-loop (KL) interactions that are essential for polymerase function. Our combined structural and functional data suggest a model for templated RNA synthesis by the TPR holoenzyme, whereby heterodimer formation and KL interactions preorganize the TPR for optimal primer-template duplex binding, triplet substrate discrimination, and templated RNA synthesis. These results provide a better understanding of TPR structure and function and should aid the engineering of more efficient PRs. [ABSTRACT FROM AUTHOR]

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present, generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g., the rbs locus and pykF) and species (e.g., Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide a method and mathematical justification for exploration of biological networks in higher dimensions. [ABSTRACT FROM AUTHOR]

Simple Summary: A critical environmental factor that affects the growth and development of insect herbivores is food quality, and insect herbivores require the correct blend and balance of different nutrients in order to meet their physiological demands. For the first time, we investigated the nutritional regulation of the oriental armyworm, Mythimna separata (walker), and the association between insect performance (i.e., developmental time, insect mass, and reproductive response) and nutrients. Caterpillars had different intake targets for two macronutrients, proteins and carbohydrates, at two larval stages, and food consumption and nutrient intake were closely correlated with the content of protein and carbohydrate, respectively. Interestingly, we also found that the trade-off between nutritional regulation and fecundity, a phenomenon often seen in this migrating species, may be attributed to food quality and, subsequently, physiological preparation. These results help us better understand the behavior of this economically important pest in the field. In nature, plants can contain variable nutrients depending upon the species, tissue, and developmental stage. Insect herbivores may regulate their nutrient intake behaviorally and physio- logically when encountering different foods. This study examined the nutritional regulation of the oriental armyworm, Mythimna separata, for the first time. In one experiment, we allowed the cater-pillars to choose between two nutritionally balanced but complementary diets. The caterpillars did not randomly consume the paired foods, but instead chose between the nutritionally balanced but complementary diets. This intake behavior was found to change with their developmental stages. Furthermore, the nutrient concentrations in food significantly impacted the insect's performance. In the other experiment, caterpillars were given one of eleven diets that reflected the different nutrient conditions in the field. The results showed that proteins were significantly associated with developmental time and fecundity. For example, by consuming protein-biased food, the caterpillars developed faster and produced more eggs. In contrast, carbohydrates were more strongly linked to lipid accumulation, and caterpillars accumulated more lipids when consuming the carbohydrate-biased food. Moreover, the caterpillars were also found to actively regulate their intake of proteins and carbohydrates based on food quality and to physiologically prepare for subsequent life stages. These findings enhance our understanding of how M. separata feeds and responds to different nutritional environments in the field, which could have implications for managing insect herbivores in agricultural settings. [ABSTRACT FROM AUTHOR]

Background and Aims The ability of plants to track shifting fitness optima is crucial within the context of global change, where increasing environmental extremes may have dramatic consequences for life history, fitness, and ultimately population persistence. However, tracking changing conditions relies on the relationship between genetic and environmental variance, where selection may favour plasticity, the evolution of genetic differences, or both depending on the spatial and temporal scale of environmental heterogeneity. Methods Over three years, we compared the genetic and environmental components of phenological and life-history variation in a common environment for the spring perennial Geum triflorum. Populations were sourced from alvar habitats that exhibit extreme but predictable annual flood–desiccation cycles and prairie habitats that exhibit similar but less predictable variation in water availability. Key Results Heritability was generally higher for early life-history (emergence probability) relative to later life-history traits (total seed mass), indicating that traits associated with establishment are under stronger genetic control relative to later life-history fitness expressions, where plasticity may play a larger role. This pattern was particularly notable in seeds sourced from environmentally extreme but predictable alvar habitats relative to less predictable prairie environments. Fitness landscapes based on seed source origin, largely characterized by varying water availability and flower production, described selection as the degree of maladaptation of seed source environment relative to the prairie common garden environment. Plants from alvar populations were consistently closer to the fitness optimum across all years. Annually, the breadth of the fitness optimum expanded primarily along a moisture gradient, with inclusion of more populations onto the expanding optimum. Conclusions These results highlight the importance of temporally and spatially varying selection in life-history evolution, indicating plasticity may become a primary mechanism needed to track fitness for later life-history events within perennial systems. [ABSTRACT FROM AUTHOR]

We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore, we discover within this analogy that the stationary population distribution on the landscape corresponds exactly to the ground-state wavefunction. This mathematical equivalence grants entry to a wide range of analytical tools developed by the quantum mechanics community, such as the Rayleigh–Ritz variational method and the Rayleigh–Schrödinger perturbation theory, allowing us not only the conduct of reasonable quantitative assessments but also exploration of fundamental biological inquiries. We demonstrate the effectiveness of these tools by estimating the population success on landscapes where precise answers are elusive, and unveiling the ecological consequences of stress-induced mutagenesis—a prevalent evolutionary mechanism in pathogenic and neoplastic systems. We show that, even in an unchanging environment, a sharp mutational burst resulting from stress can always be advantageous, while a gradual increase only enhances population size when the number of relevant evolving traits is limited. Our interdisciplinary approach offers novel insights, opening up new avenues for deeper understanding and predictive capability regarding the complex dynamics of evolving populations. [ABSTRACT FROM AUTHOR]

We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore, we discover within this analogy that the stationary population distribution on the landscape corresponds exactly to the ground-state wavefunction. This mathematical equivalence grants entry to a wide range of analytical tools developed by the quantum mechanics community, such as the Rayleigh–Ritz variational method and the Rayleigh–Schrödinger perturbation theory, allowing us not only the conduct of reasonable quantitative assessments but also exploration of fundamental biological inquiries. We demonstrate the effectiveness of these tools by estimating the population success on landscapes where precise answers are elusive, and unveiling the ecological consequences of stress-induced mutagenesis—a prevalent evolutionary mechanism in pathogenic and neoplastic systems. We show that, even in an unchanging environment, a sharp mutational burst resulting from stress can always be advantageous, while a gradual increase only enhances population size when the number of relevant evolving traits is limited. Our interdisciplinary approach offers novel insights, opening up new avenues for deeper understanding and predictive capability regarding the complex dynamics of evolving populations.

Estimating the complex relationship between fitness and genotype or phenotype (i.e. the adaptive landscape) is one of the central goals of evolutionary biology. However, adaptive walks connecting genotypes to organismal fitness, speciation, and novel ecological niches are still poorly understood and processes for surmounting fitness valleys remain controversial. One outstanding system for addressing these connections is a recent adaptive radiation of ecologically and morphologically novel pupfishes (a generalist, molluscivore, and scale-eater) endemic to San Salvador Island, Bahamas. We leveraged whole-genome sequencing of 139 hybrids from two independent field fitness experiments to identify the genomic basis of fitness, estimate genotypic fitness networks, and measure the accessibility of adaptive walks on the fitness landscape. We identified 132 single nucleotide polymorphisms (SNPs) that were significantly associated with fitness in field enclosures. Six out of the 13 regions most strongly associated with fitness contained differentially expressed genes and fixed SNPs between trophic specialists; one gene (mettl21e) was also misexpressed in lab-reared hybrids, suggesting a potential intrinsic genetic incompatibility. We then constructed genotypic fitness networks from adaptive alleles and show that scale-eating specialists are the most isolated of the three species on these networks. Intriguingly, introgressed and de novo variants reduced fitness landscape ruggedness as compared to standing variation, increasing the accessibility of genotypic fitness paths from generalist to specialists. Our results suggest that adaptive introgression and de novo mutations alter the shape of the fitness landscape, providing key connections in adaptive walks circumventing fitness valleys and triggering the evolution of novelty during adaptive radiation.

Species' phenotypic characteristics often remain unchanged over long stretches of geological time. Stabilizing selection--in which fitness is highest for intermediate phenotypes and lowest for the extremes--has been widely invoked as responsible for this pattern. At the community level, such stabilizing selection acting individually on co-occurring species is expected to produce a rugged fitness landscape on which different species occupy distinct fitness peaks. However, even with an explosion of microevolutionary field studies over the past four decades, evidence for persistent stabilizing selection driving long-term stasis is lacking. Nonetheless, biologists continue to invoke stabilizing selection as a major factor explaining macroevolutionary patterns. Here, by directly measuring natural selection in the wild, we identified a complex community-wide fitness surface in which four Anolis lizard species each occupy a distinct fitness peak close to their mean phenotype. The presence of local fitness optima within species, and fitness valleys between species, presents a barrier to adaptive evolutionary change and acts to maintain species differences through time. However, instead of continuously operating stabilizing selection, we found that species were maintained on these peaks by the combination of many independent periods among which selection fluctuated in form, strength, direction, or existence and in which stabilizing selection rarely occurred. Our results suggest that lack of substantial phenotypic evolutionary change through time may be the result of selection, but not persistent stabilizing selection as classically envisioned. [ABSTRACT FROM AUTHOR]

We study a discrete-time multi-type Wright–Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic behavior of the model, focusing on the impact of the mean-field dynamics on it. One of the results is a limit theorem that describes sufficient conditions for an almost certain path to extinction, first eliminating the type which is the least fit at the mean-field equilibrium. The effect is explained by the metastability of the stochastic system, which under the conditions of the theorem spends almost all time before the extinction event in a neighborhood of the equilibrium. In addition to the limit theorems, we propose a maximization principle for a general deterministic replicator dynamics and study its implications for the stochastic model. [ABSTRACT FROM AUTHOR]

As an effective tool to solve continuous optimization problems, differential evolution (DE) algorithm has been widely used in numerous fields. To enhance the performance, in recent years, many DE variants have been developed based on the idea of multiple strategies. However, there still exists an issue for them that the strategy selection method relies on the historical search experience. The experience may be suitable for the problems with smooth fitness landscapes, but not for the problems with rugged fitness landscapes. To alleviate this issue, in this work, a new multiple strategies-based DE variant with dual information guidance is proposed, called DIGDE. In the DIGDE, to avoid the unreliable historical search experience, the fitness information and spatial information are utilized simultaneously as a guidance to estimate the evolutionary states for each individual, and then the most appropriate strategy can be chosen correspondingly. To verify the effectiveness of the DIGDE, 52 test functions are included in the experiments, and three well-established DE variants and four other evolutionary algorithms are involved in the performance comparison. The results show that the DIGDE achieves competitive performance on not only the result accuracy but also the convergence rate. [ABSTRACT FROM AUTHOR]

Recent work has shown that evaluating functional trait distinctiveness, the average trait distance of a species to other species in a community offers promising insights into biodiversity dynamics and ecosystem functioning. However, the ecological mechanisms underlying the emergence and persistence of functionally distinct species are poorly understood. Here, we address the issue by considering a heterogeneous fitness landscape whereby functional dimensions encompass peaks representing trait combinations yielding positive population growth rates in a community. We identify four ecological cases contributing to the emergence and persistence of functionally distinct species. First, environmental heterogeneity or alternative phenotypic designs can drive positive population growth of functionally distinct species. Second, sink populations with negative population growth can deviate from local fitness peaks and be functionally distinct. Third, species found at the margin of the fitness landscape can persist but be functionally distinct. Fourth, biotic interactions (positive or negative) can dynamically alter the fitness landscape. We offer examples of these four cases and guidelines to distinguish between them. In addition to these deterministic processes, we explore how stochastic dispersal limitation can yield functional distinctiveness. Our framework offers a novel perspective on the relationship between fitness landscape heterogeneity and the functional composition of ecological assemblages. [ABSTRACT FROM AUTHOR]

RNA viruses, such as hepatitis C virus (HCV), influenza virus, and SARS-CoV-2, are notorious for their ability to evolve rapidly under selection in novel environments. It is known that the high mutation rate of RNA viruses can generate huge genetic diversity to facilitate viral adaptation. However, less attention has been paid to the underlying fitness landscape that represents the selection forces on viral genomes, especially under different selection conditions. Here, we systematically quantified the distribution of fitness effects of about 1,600 single amino acid substitutions in the drug-targeted region of NS5A protein of HCV. We found that the majority of nonsynonymous substitutions incur large fitness costs, suggesting that NS5A protein is highly optimized. The replication fitness of viruses is correlated with the pattern of sequence conservation in nature, and viral evolution is constrained by the need to maintain protein stability. We characterized the adaptive potential of HCV by subjecting the mutant viruses to selection by the antiviral drug daclatasvir at multiple concentrations. Both the relative fitness values and the number of beneficial mutations were found to increase with the increasing concentrations of daclatasvir. The changes in the spectrum of beneficial mutations in NS5A protein can be explained by a pharmacodynamics model describing viral fitness as a function of drug concentration. Overall, our results show that the distribution of fitness effects of mutations is modulated by both the constraints on the biophysical properties of proteins (i.e., selection pressure for protein stability) and the level of environmental stress (i.e., selection pressure for drug resistance).IMPORTANCE Many viruses adapt rapidly to novel selection pressures, such as antiviral drugs. Understanding how pathogens evolve under drug selection is critical for the success of antiviral therapy against human pathogens. By combining deep sequencing with selection experiments in cell culture, we have quantified the distribution of fitness effects of mutations in hepatitis C virus (HCV) NS5A protein. Our results indicate that the majority of single amino acid substitutions in NS5A protein incur large fitness costs. Simulation of protein stability suggests viral evolution is constrained by the need to maintain protein stability. By subjecting the mutant viruses to selection under an antiviral drug, we find that the adaptive potential of viral proteins in a novel environment is modulated by the level of environmental stress, which can be explained by a pharmacodynamics model. Our comprehensive characterization of the fitness landscapes of NS5A can potentially guide the design of effective strategies to limit viral evolution.

An effective vaccine that can protect against HIV infection does not exist. A major reason why a vaccine is not available is the high mutability of the virus, which enables it to evolve mutations that can evade human immune responses. This challenge is exacerbated by the ability of the virus to evolve compensatory mutations that can partially restore the fitness cost of immune-evading mutations. Based on the fitness landscapes of HIV proteins that account for the effects of coupled mutations, we designed a single long peptide immunogen comprising parts of the HIV proteome wherein mutations are likely to be deleterious regardless of the sequence of the rest of the viral protein. This immunogen was then stably expressed in adenovirus vectors that are currently in clinical development. Macaques immunized with these vaccine constructs exhibited T-cell responses that were comparable in magnitude to animals immunized with adenovirus vectors with whole HIV protein inserts. Moreover, the T-cell responses in immunized macaques strongly targeted regions contained in our immunogen. These results suggest that further studies aimed toward using our vaccine construct for HIV prophylaxis and cure are warranted.

Abstract Functional traits affect the demographic performance of individuals in their environment, leading to fitness differences that scale up to drive population dynamics and community assembly. Understanding the links between traits and fitness is, therefore, critical for predicting how populations and communities respond to environmental change. However, the net effects of traits on species fitness are largely unknown because we have lacked a framework for estimating fitness across multiple species and environments. We present a modelling framework that integrates trait effects on demographic performance over the life cycles of individuals to estimate the net effect of traits on species fitness. This approach involves (1) modelling trait effects on individual demographic rates (growth, survival and recruitment) as multidimensional performance surfaces that vary with individual size and environment and (2) integrating these effects into a population model to project population growth rates (i.e., fitness) as a function of traits and environment. We illustrate our approach by estimating performance surfaces and fitness landscapes for trees across a temperature gradient in the eastern United States. Functional traits (wood density, specific leaf area and maximum height) interacted with individual size and temperature to influence tree growth, survival and recruitment rates, generating demographic trade‐offs and shaping the contours of fitness landscapes. Tall tree species had high survival, growth and fitness across the temperature gradient. Wood density and specific leaf area had interactive effects on demographic performance, resulting in fitness landscapes with multiple peaks. With this approach it is now possible to empirically estimate the net effect of traits on fitness, leading to an improved understanding of the selective forces that drive community assembly and permitting generalizable predictions of population and community dynamics in changing environments.

The Hepatitis C virus (HCV) envelope glycoprotein E1 forms a non-covalent heterodimer with E2, the main target of neutralizing antibodies. How E1–E2 interactions influence viral fitness and contribute to resistance to E2-specific antibodies remain largely unknown. We investigate this problem using a combination of fitness landscape and evolutionary modeling. Our analysis indicates that E1 and E2 proteins collectively mediate viral fitness and suggests that fitness-compensating E1 mutations may accelerate escape from E2-targeting antibodies. Our analysis also identifies a set of E2-specific human monoclonal antibodies that are predicted to be especially resilient to escape via genetic variation in both E1 and E2, providing directions for robust HCV vaccine development. [ABSTRACT FROM AUTHOR]

The distribution of fitness effects (DFE) of new mutations is key to our understanding of many evolutionary processes. Theoreticians have developed several models to help understand the patterns seen in empirical DFEs. Many such models reproduce the broad patterns seen in empirical DFEs but these models often rely on structural assumptions that cannot be tested empirically. Here, we investigate how much of the underlying "microscopic" biological processes involved in the mapping of new mutations to fitness can be inferred from "macroscopic" observations of the DFE. We develop a null model by generating random genotype-to-fitness maps and show that the null DFE is that with the largest possible information entropy. We further show that, subject to one simple constraint, this null DFE is a Gompertz distribution. Finally, we illustrate how the predictions of this null DFE match empirically measured DFEs from several datasets, as well as DFEs simulated from Fisher's geometric model. This suggests that a match between models and empirical data is often not a very strong indication of the mechanisms underlying the mapping of mutation to fitness. [ABSTRACT FROM AUTHOR]

Rapid adaptive radiation poses a distinct question apart from speciation and adaptation: what happens after one speciation event? That is, how are some lineages able to continue speciating through a rapid burst? This question connects global macroevolutionary patterns to microevolutionary processes. Here we review major features of rapid radiations in nature and their mismatch with theoretical models and what is currently known about speciation mechanisms. Rapid radiations occur on three major diversification axes - species richness, phenotypic disparity, and ecological diversity - with exceptional outliers on each axis. The paradox is that the hallmark early stage of adaptive radiation, a rapid burst of speciation and niche diversification, is contradicted by most existing speciation models which instead predict continuously decelerating speciation rates and niche subdivision through time. Furthermore, while speciation mechanisms such as magic traits, phenotype matching, and physical linkage of co-adapted alleles promote speciation, it is often not discussed how these mechanisms could promote multiple speciation events in rapid succession. Additional mechanisms beyond ecological opportunity are needed to understand how rapid radiations occur. We review the evidence for five emerging theories: 1) the 'transporter' hypothesis: introgression and the ancient origins of adaptive alleles, 2) the 'signal complexity' hypothesis: the dimensionality of sexual traits, 3) the connectivity of fitness landscapes, 4) 'diversity begets diversity', and 5) flexible stem/'plasticity first'. We propose new questions and predictions to guide future work on the mechanisms underlying the rare origins of rapid radiation.

Darwinian evolution is driven by random mutations, genetic recombination (gene shuffling) and selection that favors genotypes with high fitness. For systems where each genotype can be represented as a bitstring of length L, an overview of possible evolutionary trajectories is provided by the L-cube graph with nodes labeled by genotypes and edges directed toward the genotype with higher fitness. Peaks (sinks in the graphs) are important since a population can get stranded at a suboptimal peak. The fitness landscape is defined by the fitness values of all genotypes in the system. Some notion of curvature is necessary for a more complete analysis of the landscapes, including the effect of recombination. The shape approach uses triangulations (shapes) induced by fitness landscapes. The main topic for this work is the interplay between peak patterns and shapes. Because of constraints on the shapes for L = 3 imposed by peaks, there are in total 25 possible combinations of peak patterns and shapes. Similar constraints exist for higher L. Specifically, we show that the constraints induced by the staircase triangulation can be formulated as a condition of universal positive epistasis, an order relation on the fitness effects of arbitrary sets of mutations that respects the inclusion relation between the corresponding genetic backgrounds. We apply the concept to a large protein fitness landscape for an immunoglobulin-binding protein expressed in Streptococcal bacteria. [ABSTRACT FROM AUTHOR]

Functional traits affect the demographic performance of individuals in their environment, leading to fitness differences that scale up to drive population dynamics and community assembly. Understanding the links between traits and fitness is, therefore, critical for predicting how populations and communities respond to environmental change. However, the net effects of traits on species fitness are largely unknown because we have lacked a framework for estimating fitness across multiple species and environments.We present a modelling framework that integrates trait effects on demographic performance over the life cycles of individuals to estimate the net effect of traits on species fitness. This approach involves (1) modelling trait effects on individual demographic rates (growth, survival and recruitment) as multidimensional performance surfaces that vary with individual size and environment and (2) integrating these effects into a population model to project population growth rates (i.e., fitness) as a function of traits and environment. We illustrate our approach by estimating performance surfaces and fitness landscapes for trees across a temperature gradient in the eastern United States.Functional traits (wood density, specific leaf area and maximum height) interacted with individual size and temperature to influence tree growth, survival and recruitment rates, generating demographic trade‐offs and shaping the contours of fitness landscapes. Tall tree species had high survival, growth and fitness across the temperature gradient. Wood density and specific leaf area had interactive effects on demographic performance, resulting in fitness landscapes with multiple peaks.With this approach it is now possible to empirically estimate the net effect of traits on fitness, leading to an improved understanding of the selective forces that drive community assembly and permitting generalizable predictions of population and community dynamics in changing environments. [ABSTRACT FROM AUTHOR]

The self-incompatibility locus (S -locus) of flowering plants displays a striking allelic diversity. How such a diversity has emerged remains unclear. In this article, we performed numerical simulations in a finite island population genetics model to investigate how population subdivision affects the diversification process at a S -locus, given that the two-gene architecture typical of S -loci involves the crossing of a fitness valley. We show that population structure slightly reduces the parameter range allowing for the diversification of self-incompatibility haplotypes (S -haplotypes), but at the same time also increases the number of these haplotypes maintained in the whole metapopulation. This increase is partly due to a higher rate of diversification and replacement of S -haplotypes within and among demes. We also show that the two-gene architecture leads to a higher diversity in structured populations compared with a simpler genetic architecture, where new S -haplotypes appear in a single mutation step. Overall, our results suggest that population subdivision can act in two opposite directions: it renders S -haplotypes diversification easier, although it also increases the risk that the self-incompatibility system is lost. [ABSTRACT FROM AUTHOR]

A fitness landscape is a mapping from a space of discrete genotypes to the real numbers. A path in a fitness landscape is a sequence of genotypes connected by single mutational steps. Such a path is said to be accessible if the fitness values of the genotypes encountered along the path increase monotonically. We study accessible paths on random fitness landscapes of the House-of-Cards type, on which fitness values are independent, identically and continuously distributed random variables. The genotype space is taken to be a Cartesian power graph A L , where L is the number of genetic loci and the allele graph A encodes the possible allelic states and mutational transitions on one locus. The probability of existence of accessible paths between two genotypes at a distance linear in L displays a transition from 0 to a positive value at a threshold β c for the fitness difference between the initial and final genotype. We derive a lower bound on β c for general A and show that this bound is tight for a large class of allele graphs. Our results generalize previous results for accessibility percolation on the biallelic hypercube, and compare favorably to published numerical results for multiallelic Hamming graphs. [ABSTRACT FROM AUTHOR]

Mutations can have deleterious fitness effects when they decrease protein specific activity or decrease active protein abundance. Mutations will also be deleterious when they cause misfolding or misinteractions that are toxic to the cell (i.e. independent of whether the mutations affect specific activity and abundance). The extent to which protein evolution is shaped by these and other collateral fitness effects is unclear in part because little is known of their frequency and magnitude. Using deep mutational scanning (DMS), we previously found at least 42% of missense mutations in the TEM-1 β-lactamase antibiotic resistance gene cause deleterious collateral fitness effects. Here, we used DMS to comprehensively determine the collateral fitness effects of missense mutations in three genes encoding the antibiotic resistance proteins New Delhi metallo-β-lactamase (NDM-1), chloramphenicol acetyltransferase I (CAT-I), and 2″-aminoglycoside nucleotidyltransferase (AadB). AadB (20%), CAT-I (0.9%), and NDM-1 (0.2%) were less susceptible to deleterious collateral fitness effects than TEM-1 (42%) indicating that genes have different propensities for these effects. As was observed with TEM-1 , all the studied deleterious aadB mutants increased aggregation. However, aggregation did not correlate with collateral fitness effects for many of the deleterious mutants of CAT-I and NDM-1. Select deleterious mutants caused unexpected phenotypes to emerge. The introduction of internal start codons in CAT-1 caused loss of the episome and a mutation in aadB made its cognate antibiotic essential for growth. Our study illustrates how the complexity of the cell provides a rich environment for collateral fitness effects and new phenotypes to emerge. [ABSTRACT FROM AUTHOR]

How protein properties such as protein activity and protein essentiality affect the distribution of fitness effects (DFE) of mutations are important questions in protein evolution. Deep mutational scanning studies typically measure the effects of a comprehensive set of mutations on either protein activity or fitness. Our understanding of the underpinnings of the DFE would be enhanced by a comprehensive study of both for the same gene. Here, we compared the fitness effects and in vivo protein activity effects of ∼4,500 missense mutations in the E. coli rnc gene. This gene encodes RNase III, a global regulator enzyme that cleaves diverse RNA substrates including precursor ribosomal RNA and various mRNAs including its own 5′ untranslated region (5′UTR). We find that RNase III's ability to cleave dsRNA is the most important determinant of the fitness effects of rnc mutations. The DFE of RNase III was bimodal, with mutations centered around neutral and deleterious effects, consistent with previously reported DFE's of enzymes with a singular physiological role. Fitness was buffered to small effects on RNase III activity. The enzyme's RNase III domain, which contains the RNase III signature motif and all active site residues, was more sensitive to mutation than its dsRNA binding domain, which is responsible for recognition and binding to dsRNA. Differential effects on fitness and functional scores for mutations at highly conserved residues G97, G99, and F188 suggest that these positions may be important for RNase III cleavage specificity. [ABSTRACT FROM AUTHOR]

Driven by host–pathogen coevolution, cell surface antigens are often the fastest evolving parts of a microbial pathogen. The persistent evolutionary impetus for novel antigen variants suggests the utility of novelty-seeking algorithms in predicting antigen diversification in microbial pathogens. In contrast to traditional genetic algorithms maximizing variant fitness, novelty-seeking algorithms optimize variant novelty. Here, we designed and implemented three evolutionary algorithms (fitness-seeking, novelty-seeking, and hybrid) and evaluated their performances in 10 simulated and 2 empirically derived antigen fitness landscapes. The hybrid walks combining fitness- and novelty-seeking strategies overcame the limitations of each algorithm alone, and consistently reached global fitness peaks. Thus, hybrid walks provide a model for microbial pathogens escaping host immunity without compromising variant fitness. Biological processes facilitating novelty-seeking evolution in natural pathogen populations include hypermutability, recombination, wide dispersal, and immune-compromised hosts. The high efficiency of the hybrid algorithm improves the evolutionary predictability of novel antigen variants. We propose the design of escape-proof vaccines based on high-fitness variants covering a majority of the basins of attraction on the fitness landscape representing all potential variants of a microbial antigen. [ABSTRACT FROM AUTHOR]

ABSTRACT Adaptive evolutionary processes are constrained by the availability of mutations which cause a fitness benefit and together make up the fitness landscape, which maps genotype space onto fitness under specified conditions. Experimentally derived fitness landscapes have demonstrated a predictability to evolution by identifying limited “mutational routes” that evolution by natural selection may take between low and high-fitness genotypes. However, such studies often utilize indirect measures to determine fitness. We estimated the competitive fitness of mutants relative to all single-mutation neighbors to describe the fitness landscape of three mutations in a β-lactamase enzyme. Fitness assays were performed at sublethal concentrations of the antibiotic cefotaxime in a structured and unstructured environment. In the unstructured environment, the antibiotic selected for higher-resistance types—but with an equivalent fitness for a subset of mutants, despite substantial variation in resistance—resulting in a stratified fitness landscape. In contrast, in a structured environment with a low antibiotic concentration, antibiotic-susceptible genotypes had a relative fitness advantage, which was associated with antibiotic-induced filamentation. These results cast doubt that highly resistant genotypes have a unique selective advantage in environments with subinhibitory concentrations of antibiotics and demonstrate that direct fitness measures are required for meaningful predictions of the accessibility of evolutionary routes. IMPORTANCE The evolution of antibiotic-resistant bacterial populations underpins the ongoing antibiotic resistance crisis. We aim to understand how antibiotic-degrading enzymes can evolve to cause increased resistance, how this process is constrained, and whether it can be predictable. To this end, competition experiments were performed with a combinatorially complete set of mutants of a β-lactamase gene subject to subinhibitory concentrations of the antibiotic cefotaxime. While some mutations confer on their hosts high resistance to cefotaxime, in competition these mutations do not always confer a selective advantage. Specifically, high-resistance mutants had equivalent fitnesses despite different resistance levels and even had selective disadvantages under conditions involving spatial structure. Together, our findings suggest that the relationship between resistance level and fitness at subinhibitory concentrations is complex; predicting the evolution of antibiotic resistance requires knowledge of the conditions that select for resistant genotypes and the selective advantage evolved types have over their predecessors.

In nature, plants can contain variable nutrients depending upon the species, tissue, and developmental stage. Insect herbivores may regulate their nutrient intake behaviorally and physio- logically when encountering different foods. This study examined the nutritional regulation of the oriental armyworm, Mythimna separata, for the first time. In one experiment, we allowed the cater-pillars to choose between two nutritionally balanced but complementary diets. The caterpillars did not randomly consume the paired foods, but instead chose between the nutritionally balanced but complementary diets. This intake behavior was found to change with their developmental stages. Furthermore, the nutrient concentrations in food significantly impacted the insect’s performance. In the other experiment, caterpillars were given one of eleven diets that reflected the different nutrient conditions in the field. The results showed that proteins were significantly associated with developmental time and fecundity. For example, by consuming protein-biased food, the caterpillars developed faster and produced more eggs. In contrast, carbohydrates were more strongly linked to lipid accumulation, and caterpillars accumulated more lipids when consuming the carbohydrate-biased food. Moreover, the caterpillars were also found to actively regulate their intake of proteins and carbohydrates based on food quality and to physiologically prepare for subsequent life stages. These findings enhance our understanding of how M. separata feeds and responds to different nutritional environments in the field, which could have implications for managing insect herbivores in agricultural settings.

Contrary to previous assumptions that most mutations are deleterious, there is increasing evidence for persistence of large-effect mutations in natural populations. A possible explanation for these observations is that mutant phenotypes and fitness may depend upon the specific environmental conditions to which a mutant is exposed. Here, we tested this hypothesis by growing large-effect flowering time mutants of Arabidopsis thaliana in multiple field sites and seasons to quantify their fitness effects in realistic natural conditions. By constructing environment-specific fitness landscapes based on flowering time and branching architecture, we observed that a subset of mutations increased fitness, but only in specific environments. These mutations increased fitness via different paths: through shifting flowering time, branching, or both. Branching was under stronger selection, but flowering time was more genetically variable, pointing to the importance of indirect selection on mutations through their pleiotropic effects on multiple phenotypes. Finally, mutations in hub genes with greater connectedness in their regulatory networks had greater effects on both phenotypes and fitness. Together, these findings indicate that large-effect mutations may persist in populations because they influence traits that are adaptive only under specific environmental conditions. Understanding their evolutionary dynamics therefore requires measuring their effects in multiple natural environments.

An effective vaccine is urgently required to curb the HIV-1 epidemic. We have previously described an approach to model the fitness landscape of several HIV-1 proteins, and have validated the results against experimental and clinical data. The fitness landscape may be used to identify mutation patterns harmful to virus viability, and consequently inform the design of immunogens that can target such regions for immunological control. Here we apply such an analysis and complementary experiments to HIV-1 Nef, a multifunctional protein which plays a key role in HIV-1 pathogenesis. We measured Nef-driven replication capacities as well as Nef-mediated CD4 and HLA-I down-modulation capacities of thirty-two different Nef mutants, and tested model predictions against these results. Furthermore, we evaluated the models using 448 patient-derived Nef sequences for which several Nef activities were previously measured. Model predictions correlated significantly with Nef-driven replication and CD4 down-modulation capacities, but not HLA-I down-modulation capacities, of the various Nef mutants. Similarly, in our analysis of patient-derived Nef sequences, CD4 down-modulation capacity correlated the most significantly with model predictions, suggesting that of the tested Nef functions, this is the most important in vivo. Overall, our results highlight how the fitness landscape inferred from patient-derived sequences captures, at least in part, the in vivo functional effects of mutations to Nef. However, the correlation between predictions of the fitness landscape and measured parameters of Nef function is not as accurate as the correlation observed in past studies for other proteins. This may be because of the additional complexity associated with inferring the cost of mutations on the diverse functions of Nef.