The evolutionarily stable distribution of fitness effects

Changing fitness effects of mutations through long-term bacterial evolution

The distribution of fitness effects of new mutations shapes evolution, but it is challenging to observe how it changes as organisms adapt. Using Escherichia coli lineages spanning 50,000 generations of evolution, we quantify the fitness effects of insertion mutations in every gene. Macroscopically, the fraction of deleterious mutations changed little over time whereas the beneficial tail declined sharply, approaching an exponential distribution. Microscopically, changes in individual gene essentiality and deleterious effects often occurred in parallel; altered essentiality is only partly explained by structural variation. The identity and effect sizes of beneficial mutations changed rapidly over time, but many targets of selection remained predictable because of the importance of loss-of-function mutations. Taken together, these results reveal the dynamic-but statistically predictable-nature of mutational fitness effects.

A dynamical limit to evolutionary adaptation

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

Inferring the distributions of fitness effects and proportions of strongly deleterious mutations

The distribution of fitness effects is a key property in evolutionary genetics as it has implications for several evolutionary phenomena including the evolution of sex and mating systems, the rate of adaptive evolution, and the prevalence of deleterious mutations. Despite the distribution of fitness effects being extensively studied, the effects of strongly deleterious mutations are difficult to infer since such mutations are unlikely to be present in a sample of haplotypes, so genetic data may contain very little information about them. Recent work has attempted to correct for this issue by expanding the classic gamma-distributed model to explicitly account for strongly deleterious mutations. Here, we use simulations to investigate one such method, adding a parameter (plth) to capture the proportion of strongly deleterious mutations. We show that plth can improve the model fit when applied to individual species but underestimates the true proportion of strongly deleterious mutations. The parameter can also artificially maximize the likelihood when used to jointly infer a distribution of fitness effects from multiple species. As plth and related parameters are used in current inference algorithms, our results are relevant with respect to avoiding model artifacts and improving future tools for inferring the distribution of fitness effects.

A dynamical limit to evolutionary adaptation

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

Digest: Few new mutations are recessive lethal

When a new mutation arises, what is the probability that it is recessive lethal? Wade et al. find that fewer than 1% of nonsynonymous mutations in humans and Drosophila melanogaster are recessive lethal. The authors show that methods based on site frequency spectrum (SFS) analyses, though generally robust in their estimations of the nonlethal distribution of fitness effects (DFE), are unable to accurately estimate the fraction of recessive lethal mutations.

Quantifying the local adaptive landscape of a nascent bacterial community

The fitness effects of all possible mutations available to an organism largely shape the dynamics of evolutionary adaptation. Yet, whether and how this adaptive landscape changes over evolutionary times, especially upon ecological diversification and changes in community composition, remains poorly understood. We sought to fill this gap by analyzing a stable community of two closely related ecotypes ("L" and "S") shortly after they emerged within the E. coli Long-Term Evolution Experiment (LTEE). We engineered genome-wide barcoded transposon libraries to measure the invasion fitness effects of all possible gene knockouts in the coexisting strains as well as their ancestor, for many different, ecologically relevant conditions. We find consistent statistical patterns of fitness effect variation across both genetic background and community composition, despite the idiosyncratic behavior of individual knockouts. Additionally, fitness effects are correlated with evolutionary outcomes for a number of conditions, possibly revealing shifting patterns of adaptation. Together, our results reveal how ecological and epistatic effects combine to shape the adaptive landscape in a nascent ecological community.

Evolutionary scaling of maximum growth rate with organism size

Data from nearly 1000 species reveal the upper bound to rates of biomass production achievable by natural selection across the Tree of Life. For heterotrophs, maximum growth rates scale positively with organism size in bacteria but negatively in eukaryotes, whereas for phototrophs, the scaling is negligible for cyanobacteria and weakly negative for eukaryotes. These results have significant implications for understanding the bioenergetic consequences of the transition from prokaryotes to eukaryotes, and of the expansion of some groups of the latter into multicellularity. The magnitudes of the scaling coefficients for eukaryotes are significantly lower than expected under any proposed physical-constraint model. Supported by genomic, bioenergetic, and population-genetic data and theory, an alternative hypothesis for the observed negative scaling in eukaryotes postulates that growth-diminishing mutations with small effects passively accumulate with increasing organism size as a consequence of associated increases in the power of random genetic drift. In contrast, conditional on the structural and functional features of ribosomes, natural selection has been able to promote bacteria with the fastest possible growth rates, implying minimal conflicts with both bioenergetic constraints and random genetic drift. If this extension of the drift-barrier hypothesis is correct, the interpretations of comparative studies of biological traits that have traditionally ignored differences in population-genetic environments will require revisiting.

Two modes of evolution shape bacterial strain diversity in the mammalian gut for thousands of generations

How and at what pace bacteria evolve when colonizing healthy hosts remains unclear. Here, by monitoring evolution for more than six thousand generations in the mouse gut, we show that the successful colonization of an invader Escherichia coli depends on the diversity of the existing microbiota and the presence of a closely related strain. Following colonization, two modes of evolution were observed: one in which diversifying selection leads to long-term coexistence of ecotypes and a second in which directional selection propels selective sweeps. These modes can be quantitatively distinguished by the statistics of mutation trajectories. In our experiments, diversifying selection was marked by the emergence of metabolic mutations, and directional selection by acquisition of prophages, which bring their own benefits and costs. In both modes, we observed parallel evolution, with mutation accumulation rates comparable to those typically observed in vitro on similar time scales. Our results show how rapid ecotype formation and phage domestication can be in the mammalian gut.

Here, the authors show that a colonizing bacterial strain evolves in the gut by either generating ecotypes or continuously fixing beneficial mutations. They associate the first mode to metabolic mutations and the second to domestication of bacteriophages that are incorporated into the bacterial genome.

Haplotype-based inference of the distribution of fitness effects

Recent genome sequencing studies with large sample sizes in humans have discovered a vast quantity of low-frequency variants, providing an important source of information to analyze how selection is acting on human genetic variation. In order to estimate the strength of natural selection acting on low-frequency variants, we have developed a likelihood-based method that uses the lengths of pairwise identity-by-state between haplotypes carrying low-frequency variants. We show that in some non-equilibrium populations (such as those that have had recent population expansions) it is possible to distinguish between positive or negative selection acting on a set of variants. With our new framework, one can infer a fixed selection intensity acting on a set of variants at a particular frequency, or a distribution of selection coefficients for standing variants and new mutations. We show an application of our method to the UK10K phased haplotype dataset of individuals.

Improve it or lose it: Evolvability cost of competition for expression

Expression level is known to be a strong determinant of a protein's rate of evolution. But the converse can also be true: evolutionary dynamics can affect expression levels of proteins. Having implications in both directions fosters the possibility of an "improve it or lose it" feedback loop, where higher expressed systems are more likely to improve and be expressed even higher, while those that are expressed less are eventually lost to drift. Using a minimal model to study this in the context of a changing environment, we demonstrate that one unexpected consequence of such a feedback loop is that a slow switch to a new environment can allow genotypes to reach higher fitness sooner than a direct exposure to it.

Global epistasis emerges from a generic model of a complex trait

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

The evolutionary origin of the universal distribution of mutation fitness effect

An intriguing fact long defying explanation is the observation of a universal exponential distribution of beneficial mutations in fitness effect for different microorganisms. To explain this effect, we use a population model including mutation, directional selection, linkage, and genetic drift. The multiple-mutation regime of adaptation at large population sizes (traveling wave regime) is considered. We demonstrate analytically and by simulation that, regardless of the inherent distribution of mutation fitness effect across genomic sites, an exponential distribution of fitness effects emerges in the long term. This result follows from the exponential statistics of the frequency of the less-fit alleles, f, that we predict to evolve, in the long term, for both polymorphic and monomorphic sites. We map the logarithmic slope of the distribution onto the previously derived fixation probability and demonstrate that it increases linearly in time. Our results demonstrate a striking difference between the distribution of fitness effects observed experimentally for naturally occurring mutations, and the "inherent" distribution obtained in a directed-mutagenesis experiment, which can have any shape depending on the organism. Based on these results, we develop a new method to measure the fitness effect of mutations for each variable residue using DNA sequences sampled from adapting populations. This new method is not sensitive to linkage effects and does not require the one-site model assumptions.

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.

The evolutionary scaling of cellular traits imposed by the drift barrier

Owing to internal homeostatic mechanisms, cellular traits may experience long periods of stable selective pressures, during which the stochastic forces of drift and mutation conspire to generate variation. However, even in the face of invariant selection, the drift barrier defined by the genetic effective population size, which is negatively associated with organism size, can have a substantial influence on the location and dispersion of the long-term steady-state distribution of mean phenotypes. In addition, for multilocus traits, the multiplicity of alternative, functionally equivalent states can draw mean phenotypes away from selective optima, even in the absence of mutation bias. Using a framework for traits with an additive genetic basis, it is shown that 1) optimal phenotypic states may be only rarely achieved; 2) gradients of mean phenotypes with respect to organism size (i.e., allometric relationships) are likely to be molded by differences in the power of random genetic drift across the tree of life; and 3) for any particular set of population-genetic conditions, significant variation in mean phenotypes may exist among lineages exposed to identical selection pressures. These results provide a potentially useful framework for understanding numerous aspects of cellular diversification and illustrate the risks of interpreting such variation in a purely adaptive framework.

A percolation model of natural selection

A new approach has been proposed and developed: the selection of optimal variants in the evolutionary mutation flow is considered as an analogue of a percolation filter. Interaction of mutations in a series of generations and random processes of drift determine the collective behavior of nodes (individuals - carriers and converters of mutations) and bonds (mutations) in the space of percolation lattice. It is shown that the choice of the development trajectory at the population level depends on the spectrum of supporting and prohibiting mutations under the influence of conjugate deterministic and random factors. From the point of view of the fluctuation-bifurcation process, new concepts of the lower and upper thresholds of the percolation selection grid are defined in the hierarchical structure of speciation. The upper threshold determines the state of self-organized criticality, which, when overcome, leads to irreversible self-organization processes in the population caused by the accumulation of mutations.

Higher-fitness yeast genotypes are less robust to deleterious mutations

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

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.

Molecular Origins of Complex Heritability in Natural Genotype-to-Phenotype Relationships

The statistical complexity of heredity has long been evident, but its molecular origins remain elusive. To investigate, we charted 90 comprehensive genotype-to-phenotype maps in a large population of wild diploid yeast. In contrast to long-standing assumptions, all types of genetic variation contributed similarly to phenotype. Causal synonymous and regulatory variants exhibited distinct molecular signatures, as did nonlinearities in heterozygote fitness that likely contribute to hybrid vigor. Highly pleiotropic variants altered disordered sequences within signaling hubs, and their effects correlated across environments-even when antagonistic-suggesting that large fitness gains bring concomitant costs. Natural genetic networks defined by the causal loci differed from those determined by precise gene deletions or protein-protein interactions. Finally, we found that traits that would appear omnigenic in less powered studies do in fact have finite genetic determinants. Integrating these molecular principles will be crucial as genome reading and writing become routine in research, industry, and medicine.

Experimental Design, Population Dynamics, and Diversity in Microbial Experimental Evolution

In experimental evolution, laboratory-controlled conditions select for the adaptation of species, which can be monitored in real time. Despite the current popularity of such experiments, nature's most pervasive biological force was long believed to be observable only on time scales that transcend a researcher's life-span, and studying evolution by natural selection was therefore carried out solely by comparative means. Eventually, microorganisms' propensity for fast evolutionary changes proved us wrong, displaying strong evolutionary adaptations over a limited time, nowadays massively exploited in laboratory evolution experiments. Here, we formulate a guide to experimental evolution with microorganisms, explaining experimental design and discussing evolutionary dynamics and outcomes and how it is used to assess ecoevolutionary theories, improve industrially important traits, and untangle complex phenotypes. Specifically, we give a comprehensive overview of the setups used in experimental evolution. Additionally, we address population dynamics and genetic or phenotypic diversity during evolution experiments and expand upon contributing factors, such as epistasis and the consequences of (a)sexual reproduction. Dynamics and outcomes of evolution are most profoundly affected by the spatiotemporal nature of the selective environment, where changing environments might lead to generalists and structured environments could foster diversity, aided by, for example, clonal interference and negative frequency-dependent selection. We conclude with future perspectives, with an emphasis on possibilities offered by fast-paced technological progress. This work is meant to serve as an introduction to those new to the field of experimental evolution, as a guide to the budding experimentalist, and as a reference work to the seasoned expert.

Experimental Studies of Evolutionary Dynamics in Microbes

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

Determining the factors driving selective effects of new nonsynonymous mutations

The distribution of fitness effects (DFE) of new mutations plays a fundamental role in evolutionary genetics. However, the extent to which the DFE differs across species has yet to be systematically investigated. Furthermore, the biological mechanisms determining the DFE in natural populations remain unclear. Here, we show that theoretical models emphasizing different biological factors at determining the DFE, such as protein stability, back-mutations, species complexity, and mutational robustness make distinct predictions about how the DFE will differ between species. Analyzing amino acid-changing variants from natural populations in a comparative population genomic framework, we find that humans have a higher proportion of strongly deleterious mutations than Drosophila melanogaster. Furthermore, when comparing the DFE across yeast, Drosophila, mice, and humans, the average selection coefficient becomes more deleterious with increasing species complexity. Last, pleiotropic genes have a DFE that is less variable than that of nonpleiotropic genes. Comparing four categories of theoretical models, only Fisher's geometrical model (FGM) is consistent with our findings. FGM assumes that multiple phenotypes are under stabilizing selection, with the number of phenotypes defining the complexity of the organism. Our results suggest that long-term population size and cost of complexity drive the evolution of the DFE, with many implications for evolutionary and medical genomics.

Disentangling genetic and epigenetic determinants of ultrafast adaptation

A major rationale for the advocacy of epigenetically mediated adaptive responses is that they facilitate faster adaptation to environmental challenges. This motivated us to develop a theoretical-experimental framework for disclosing the presence of such adaptation-speeding mechanisms in an experimental evolution setting circumventing the need for pursuing costly mutation-accumulation experiments. To this end, we exposed clonal populations of budding yeast to a whole range of stressors. By growth phenotyping, we found that almost complete adaptation to arsenic emerged after a few mitotic cell divisions without involving any phenotypic plasticity. Causative mutations were identified by deep sequencing of the arsenic-adapted populations and reconstructed for validation. Mutation effects on growth phenotypes, and the associated mutational target sizes were quantified and embedded in data-driven individual-based evolutionary population models. We found that the experimentally observed homogeneity of adaptation speed and heterogeneity of molecular solutions could only be accounted for if the mutation rate had been near estimates of the basal mutation rate. The ultrafast adaptation could be fully explained by extensive positive pleiotropy such that all beneficial mutations dramatically enhanced multiple fitness components in concert. As our approach can be exploited across a range of model organisms exposed to a variety of environmental challenges, it may be used for determining the importance of epigenetic adaptation-speeding mechanisms in general.

A Statistical Guide to the Design of Deep Mutational Scanning Experiments

The characterization of the distribution of mutational effects is a key goal in evolutionary biology. Recently developed deep-sequencing approaches allow for accurate and simultaneous estimation of the fitness effects of hundreds of engineered mutations by monitoring their relative abundance across time points in a single bulk competition. Naturally, the achievable resolution of the estimated fitness effects depends on the specific experimental setup, the organism and type of mutations studied, and the sequencing technology utilized, among other factors. By means of analytical approximations and simulations, we provide guidelines for optimizing time-sampled deep-sequencing bulk competition experiments, focusing on the number of mutants, the sequencing depth, and the number of sampled time points. Our analytical results show that sampling more time points together with extending the duration of the experiment improves the achievable precision disproportionately compared with increasing the sequencing depth or reducing the number of competing mutants. Even if the duration of the experiment is fixed, sampling more time points and clustering these at the beginning and the end of the experiment increase experimental power and allow for efficient and precise assessment of the entire range of selection coefficients. Finally, we provide a formula for calculating the 95%-confidence interval for the measurement error estimate, which we implement as an interactive web tool. This allows for quantification of the maximum expected a priori precision of the experimental setup, as well as for a statistical threshold for determining deviations from neutrality for specific selection coefficient estimates.

Diverse phenotypic and genetic responses to short-term selection in evolving Escherichia coli populations

Beneficial mutations fuel adaptation by altering phenotypes that enhance the fit of organisms to their environment. However, the phenotypic effects of mutations often depend on ecological context, making the distribution of effects across multiple environments essential to understanding the true nature of beneficial mutations. Studies that address both the genetic basis and ecological consequences of adaptive mutations remain rare. Here, we characterize the direct and pleiotropic fitness effects of a collection of 21 first-step beneficial mutants derived from naïve and adapted genotypes used in a long-term experimental evolution of Escherichia coli. Whole-genome sequencing was able to identify the majority of beneficial mutations. In contrast to previous studies, we find diverse fitness effects of mutations selected in a simple environment and few cases of genetic parallelism. The pleiotropic effects of these mutations were predominantly positive but some mutants were highly antagonistic in alternative environments. Further, the fitness effects of mutations derived from the adapted genotypes were dramatically reduced in nearly all environments. These findings suggest that many beneficial variants are accessible from a single point on the fitness landscape, and the fixation of alternative beneficial mutations may have dramatic consequences for niche breadth reduction via metabolic erosion.