Development of a Comprehensive Genotype-to-Fitness Map of Adaptation-Driving Mutations in Yeast.

Adaptive evolution plays a large role in generating the phenotypic diversity observed in nature, yet current methods are impractical for characterizing the molecular basis and fitness effects of large numbers of individual adaptive mutations. Here, we used a DNA barcoding approach to generate the genotype-to-fitness map for adaptation-driving mutations from a Saccharomyces cerevisiae population experimentally evolved by serial transfer under limiting glucose. We isolated and measured the fitness of thousands of independent adaptive clones and sequenced the genomes of hundreds of clones. We found only two major classes of adaptive mutations: self-diploidization and mutations in the nutrient-responsive Ras/PKA and TOR/Sch9 pathways. Our large sample size and precision of measurement allowed us to determine that there are significant differences in fitness between mutations in different genes, between different paralogs, and even between different classes of mutations within the same gene.

A model for the interplay between plastic tradeoffs and evolution in changing environments.

Performance tradeoffs are ubiquitous in both ecological and evolutionary modeling, yet they are usually postulated and built into fitness and ecological landscapes. However, tradeoffs depend on genetic background and evolutionary history and can themselves evolve. We present a simple model capable of capturing the key feedback loop: evolutionary history shapes tradeoff strength, which, in turn, shapes evolutionary future. One consequence of this feedback is that genomes with identical fitness can have different evolutionary properties shaped by prior environmental exposure. Another is that, generically, the best adaptations to one environment may evolve in another. Our simple framework bridges the gap between the phenotypic Fisher's Geometric Model and the genotypic properties, such as modularity and evolvability, and can serve as a rich playground for investigating evolution in multiple or changing environments.

Stabilization of extensive fine-scale diversity by ecologically driven spatiotemporal chaos.

It has recently become apparent that the diversity of microbial life extends far below the species level to the finest scales of genetic differences. Remarkably, extensive fine-scale diversity can coexist spatially. How is this diversity stable on long timescales, despite selective or ecological differences and other evolutionary processes? Most work has focused on stable coexistence or assumed ecological neutrality. We present an alternative: extensive diversity maintained by ecologically driven spatiotemporal chaos, with no assumptions about niches or other specialist differences between strains. We study generalized Lotka-Volterra models with antisymmetric correlations in the interactions inspired by multiple pathogen strains infecting multiple host strains. Generally, these exhibit chaos with increasingly wild population fluctuations driving extinctions. But the simplest spatial structure, many identical islands with migration between them, stabilizes a diverse chaotic state. Some strains (subspecies) go globally extinct, but many persist for times exponentially long in the number of islands. All persistent strains have episodic local blooms to high abundance, crucial for their persistence as, for many, their average population growth rate is negative. Snapshots of the abundance distribution show a power law at intermediate abundances that is essentially indistinguishable from the neutral theory of ecology. But the dynamics of the large populations are much faster than birth-death fluctuations. We argue that this spatiotemporally chaotic "phase" should exist in a wide range of models, and that even in rapidly mixed systems, longer-lived spores could similarly stabilize a diverse chaotic phase.

Quantitative evolutionary dynamics using high-resolution lineage tracking.

Evolution of large asexual cell populations underlies ∼30% of deaths worldwide, including those caused by bacteria, fungi, parasites, and cancer. However, the dynamics underlying these evolutionary processes remain poorly understood because they involve many competing beneficial lineages, most of which never rise above extremely low frequencies in the population. To observe these normally hidden evolutionary dynamics, we constructed a sequencing-based ultra high-resolution lineage tracking system in Saccharomyces cerevisiae that allowed us to monitor the relative frequencies of ∼500,000 lineages simultaneously. In contrast to some expectations, we found that the spectrum of fitness effects of beneficial mutations is neither exponential nor monotonic. Early adaptation is a predictable consequence of this spectrum and is strikingly reproducible, but the initial small-effect mutations are soon outcompeted by rarer large-effect mutations that result in variability between replicates. These results suggest that early evolutionary dynamics may be deterministic for a period of time before stochastic effects become important.

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics.

The dynamics of evolution is intimately shaped by epistasis - interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary history. A key step is thus developing models that enable study of the effects of past evolution on future evolution. In this work, we introduce a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance. Their Gaussian character allows for tractable computational as well as analytic understanding. We study the properties of these landscapes focusing on the simplest evolutionary process: random adaptive (uphill) walks. Conventional measures of "ruggedness" are shown to not much affect such adaptive walks. Instead, the long-distance statistics of epistasis cause all properties to be highly conditional on past evolution, determining the statistics of the local landscape (the distribution of fitness-effects of available mutations and combinations of these), as well as the global geometry of evolutionary trajectories. In order to further explore the effects of conditioning on past evolution, we model the effects of slowly changing environments. At long times, such fitness "seascapes" cause a statistical steady state with highly intermittent evolutionary dynamics: populations undergo bursts of rapid adaptation, interspersed with periods in which adaptive mutations are rare and the population waits for more new directions to be opened up by changes in the environment. Finally, we discuss prospects for studying more complex evolutionary dynamics and on broader classes of high-dimensional landscapes and seascapes.

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

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

Acceleration of evolutionary spread by long-range dispersal.

The spreading of evolutionary novelties across populations is the central element of adaptation. Unless populations are well mixed (like bacteria in a shaken test tube), the spreading dynamics depend not only on fitness differences but also on the dispersal behavior of the species. Spreading at a constant speed is generally predicted when dispersal is sufficiently short ranged, specifically when the dispersal kernel falls off exponentially or faster. However, the case of long-range dispersal is unresolved: Although it is clear that even rare long-range jumps can lead to a drastic speedup--as air-traffic-mediated epidemics show--it has been difficult to quantify the ensuing stochastic dynamical process. However, such knowledge is indispensable for a predictive understanding of many spreading processes in natural populations. We present a simple iterative scaling approximation supported by simulations and rigorous bounds that accurately predicts evolutionary spread, which is determined by a trade-off between frequency and potential effectiveness of long-distance jumps. In contrast to the exponential laws predicted by deterministic "mean-field" approximations, we show that the asymptotic spatial growth is according to either a power law or a stretched exponential, depending on the tails of the dispersal kernel. More importantly, we provide a full time-dependent description of the convergence to the asymptotic behavior, which can be anomalously slow and is relevant even for long times. Our results also apply to spreading dynamics on networks with a spectrum of long-range links under certain conditions on the probabilities of long-distance travel: These are relevant for the spread of epidemics.

Determinism and stochasticity during maturation of the zebrafish antibody repertoire.

It is thought that the adaptive immune system of immature organisms follows a more deterministic program of antibody creation than is found in adults. We used high-throughput sequencing to characterize the diversifying antibody repertoire in zebrafish over five developmental time points. We found that the immune system begins in a highly stereotyped state with preferential use of a small number of V (variable) D (diverse) J (joining) gene segment combinations, but that this stereotypy decreases dramatically as the zebrafish mature, with many of the top VDJ combinations observed in 2-wk-old zebrafish virtually disappearing by 1 mo. However, we discovered that, in the primary repertoire, there are strong correlations in VDJ use that increase with zebrafish maturity, suggesting that VDJ recombination involves a level of deterministic programming that is unexpected. This stereotypy is masked by the complex diversification processes of antibody maturation; the variation and lack of correlation in full repertoires between individuals appears to be derived from randomness in clonal expansion during the affinity maturation process. These data provide a window into the mechanisms of VDJ recombination and diversity creation and allow us to better understand how the adaptive immune system achieves diversity.

Spatiotemporal ecological chaos enables gradual evolutionary diversification without niches or tradeoffs.

Ecological and evolutionary dynamics are intrinsically entwined. On short timescales, ecological interactions determine the fate and impact of new mutants, while on longer timescales evolution shapes the entire community. Here, we study the evolution of large numbers of closely related strains with generalized Lotka Volterra interactions but no niche structure. Host-pathogen-like interactions drive the community into a spatiotemporally chaotic state characterized by continual, spatially-local, blooms and busts. Upon the slow serial introduction of new strains, the community diversifies indefinitely, accommodating an arbitrarily large number of strains in spite of the absence of stabilizing niche interactions. The diversifying phase persists - albeit with gradually slowing diversification - in the presence of general, nonspecific, fitness differences between strains, which break the assumption of tradeoffs inherent in much previous work. Building on a dynamical-mean field-theory analysis of the ecological dynamics, an approximate effective model captures the evolution of the diversity and distributions of key properties. This work establishes a potential scenario for understanding how the interplay between evolution and ecology - in particular coevolution of a bacterial and a generalist phage species - could give rise to the extensive fine-scale diversity that is ubiquitous in the microbial world.

Hybridization breaks species barriers in long-term coevolution of a cyanobacterial population.

Bacterial species often undergo rampant recombination yet maintain cohesive genomic identity. Ecological differences can generate recombination barriers between species and sustain genomic clusters in the short term. But can these forces prevent genomic mixing during long-term coevolution? Cyanobacteria in Yellowstone hot springs comprise several diverse species that have coevolved for hundreds of thousands of years, providing a rare natural experiment. By analyzing more than 300 single-cell genomes, we show that despite each species forming a distinct genomic cluster, much of the diversity within species is the result of hybridization driven by selection, which has mixed their ancestral genotypes. This widespread mixing is contrary to the prevailing view that ecological barriers can maintain cohesive bacterial species and highlights the importance of hybridization as a source of genomic diversity.

Denoising PCR-amplified metagenome data.

BACKGROUND: PCR amplification and high-throughput sequencing theoretically enable the characterization of the finest-scale diversity in natural microbial and viral populations, but each of these methods introduces random errors that are difficult to distinguish from genuine biological diversity. Several approaches have been proposed to denoise these data but lack either speed or accuracy. RESULTS: We introduce a new denoising algorithm that we call DADA (Divisive Amplicon Denoising Algorithm). Without training data, DADA infers both the sample genotypes and error parameters that produced a metagenome data set. We demonstrate performance on control data sequenced on Roche's 454 platform, and compare the results to the most accurate denoising software currently available, AmpliconNoise. CONCLUSIONS: DADA is more accurate and over an order of magnitude faster than AmpliconNoise. It eliminates the need for training data to establish error parameters, fully utilizes sequence-abundance information, and enables inclusion of context-dependent PCR error rates. It should be readily extensible to other sequencing platforms such as Illumina.

Population genetics of polymorphism and divergence in rapidly evolving populations.

In rapidly evolving populations, numerous beneficial and deleterious mutations can arise and segregate within a population at the same time. In this regime, evolutionary dynamics cannot be analyzed using traditional population genetic approaches that assume that sites evolve independently. Instead, the dynamics of many loci must be analyzed simultaneously. Recent work has made progress by first analyzing the fitness variation within a population, and then studying how individual lineages interact with this traveling fitness wave. However, these "traveling wave" models have previously been restricted to extreme cases where selection on individual mutations is either much faster or much slower than the typical coalescent timescale Tc. In this work, we show how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (Tcs) are neither large nor small compared to one. This enables us to describe the dynamics of populations subject to a wide range of fitness effects, and in particular, in cases where it is not immediately clear which mutations are most important in shaping the dynamics and statistics of genetic diversity. We use this approach to derive new expressions for the fixation probabilities and site frequency spectra of mutations as a function of their scaled fitness effects, along with related results for the coalescent timescale Tc and the rate of adaptation or Muller's ratchet. We find that competition between linked mutations can have a dramatic impact on the proportions of neutral and selected polymorphisms, which is not simply summarized by the scaled selection coefficient Tcs. We conclude by discussing the implications of these results for population genetic inferences.

A new method reveals microtubule minus ends throughout the meiotic spindle.

Anastral meiotic spindles are thought to be organized differently from astral mitotic spindles, but the field lacks the basic structural information required to describe and model them, including the location of microtubule-nucleating sites and minus ends. We measured the distributions of oriented microtubules in metaphase anastral spindles in Xenopus laevis extracts by fluorescence speckle microscopy and cross-correlation analysis. We localized plus ends by tubulin incorporation and combined this with the orientation data to infer the localization of minus ends. We found that minus ends are localized throughout the spindle, sparsely at the equator and at higher concentrations near the poles. Based on these data, we propose a model for maintenance of the metaphase steady-state that depends on continuous nucleation of microtubules near chromatin, followed by sorting and outward transport of stabilized minus ends, and, eventually, their loss near poles.

Synonymous mutations reveal genome-wide levels of positive selection in healthy tissues.

Genetic alterations under positive selection in healthy tissues have implications for cancer risk. However, total levels of positive selection across the genome remain unknown. Passenger mutations are influenced by all driver mutations, regardless of type or location in the genome. Therefore, the total number of passengers can be used to estimate the total number of drivers-including unidentified drivers outside of cancer genes that are traditionally missed. Here we analyze the variant allele frequency spectrum of synonymous mutations from healthy blood and esophagus to quantify levels of missing positive selection. In blood, we find that only 30% of passengers can be explained by single-nucleotide variants in driver genes, suggesting high levels of positive selection for mutations elsewhere in the genome. In contrast, more than half of all passengers in the esophagus can be explained by just the two driver genes NOTCH1 and TP53, suggesting little positive selection elsewhere.

Fundamental limits on the rate of bacterial growth and their influence on proteomic composition.

Despite abundant measurements of bacterial growth rate, cell size, and protein content, we lack a rigorous understanding of what sets the scale of these quantities and when protein abundances should (or should not) depend on growth rate. Here, we estimate the basic requirements and physical constraints on steady-state growth by considering key processes in cellular physiology across a collection of Escherichia coli proteomic data covering ≈4,000 proteins and 36 growth rates. Our analysis suggests that cells are predominantly tuned for the task of cell doubling across a continuum of growth rates; specific processes do not limit growth rate or dictate cell size. We present a model of proteomic regulation as a function of nutrient supply that reconciles observed interdependences between protein synthesis, cell size, and growth rate and propose that a theoretical inability to parallelize ribosomal synthesis places a firm limit on the achievable growth rate. A record of this paper's transparent peer review process is included in the supplemental information.

Slide-and-cluster models for spindle assembly.

BACKGROUND: Mitotic and meiotic spindles are assemblies of microtubules (MTs) that form during cell division to physically separate sister chromosomes. How the various components of spindles act together to establish and maintain the dynamic bipolar structure of spindles is not understood. Interactions between MTs and motors have been studied both experimentally and theoretically in many contexts, including the self-organization of arrays of MTs by motors and the competition between different classes of motors to move a single load. This work demonstrates how the interplay between two types of motors together with continual nucleation of MTs by chromosomes could organize the MTs into spindles. RESULTS: We propose a slide-and-cluster model based on four known molecular activities: MT nucleation near chromosomes, the sliding of MTs by a plus-end-directed motor, the clustering of their minus ends by a minus-end-directed motor, and the loss of MTs by dynamic instability. Our model applies to overlapping, nonkinetochore MTs in anastral spindles, and perhaps also to interpolar MTs in astral spindles. We show mathematically that the slide-and-cluster mechanism robustly forms bipolar spindles with sharp poles and a stable steady-state length. This model accounts for several experimental observations that were difficult to explain with existing models. Three new predictions of the model were tested and verified in Xenopus egg extracts. CONCLUSIONS: We show that a simple two-motor model could create stable, bipolar spindles under a wide range of physical parameters. Our model is the first self-contained model for anastral spindle assembly and MT sliding (known as poleward flux). Our experimental results support the slide-and-cluster scenario; most significantly, we find that MT sliding slows near spindle poles, confirming the model's primary prediction.

The speed of evolution and maintenance of variation in asexual populations.

BACKGROUND: The rate at which beneficial mutations accumulate determines how fast asexual populations evolve, but this is only partially understood. Some recent clonal-interference models suggest that evolution in large asexual populations is limited because smaller beneficial mutations are outcompeted by larger beneficial mutations that occur in different lineages within the same population. This analysis assumes that the important mutations fix one at a time; it ignores multiple beneficial mutations that occur in the lineage of an earlier beneficial mutation, before the first mutation in the series can fix. We focus on the effects of such multiple mutations. RESULTS: Our analysis predicts that the variation in fitness maintained by a continuously evolving population increases as the logarithm of the population size and logarithm of the mutation rate and thus yields a similar logarithmic increase in the speed of evolution. To test these predictions, we evolved asexual budding yeast in glucose-limited media at a range of population sizes and mutation rates. CONCLUSIONS: We find that their evolution is dominated by the accumulation of multiple mutations of moderate effect. Our results agree with our theoretical predictions and are inconsistent with the one-by-one fixation of mutants assumed by recent clonal-interference analysis.

The evolutionary dynamics and fitness landscape of clonal hematopoiesis.

Somatic mutations acquired in healthy tissues as we age are major determinants of cancer risk. Whether variants confer a fitness advantage or rise to detectable frequencies by chance remains largely unknown. Blood sequencing data from ~50,000 individuals reveal how mutation, genetic drift, and fitness shape the genetic diversity of healthy blood (clonal hematopoiesis). We show that positive selection, not drift, is the major force shaping clonal hematopoiesis, provide bounds on the number of hematopoietic stem cells, and quantify the fitness advantages of key pathogenic variants, at single-nucleotide resolution, as well as the distribution of fitness effects (fitness landscape) within commonly mutated driver genes. These data are consistent with clonal hematopoiesis being driven by a continuing risk of mutations and clonal expansions that become increasingly detectable with age.

The rate at which asexual populations cross fitness valleys.

Complex traits often involve interactions between different genetic loci. This can lead to sign epistasis, whereby mutations that are individually deleterious or neutral combine to confer a fitness benefit. In order to acquire the beneficial genotype, an asexual population must cross a fitness valley or plateau by first acquiring the deleterious or neutral intermediates. Here, we present a complete, intuitive theoretical description of the valley-crossing process across the full spectrum of possible parameter regimes. We calculate the rate at which a population crosses a fitness valley or plateau of arbitrary width, as a function of the mutation rates, the population size, and the fitnesses of the intermediates. We find that when intermediates are close to neutral, a large population can cross even wide fitness valleys remarkably quickly, so that valley-crossing dynamics may be common even when mutations that directly increase fitness are also possible. Thus the evolutionary dynamics of large populations can be sensitive to the structure of an extended region of the fitness landscape - the population may not take directly uphill paths in favor of paths across valleys and plateaus that lead eventually to fitter genotypes. In smaller populations, we find that below a threshold size, which depends on the width of the fitness valley and the strength of selection against intermediate genotypes, valley-crossing is much less likely and hence the evolutionary dynamics are less influenced by distant regions of the fitness landscape.