FISHER'S GEOMETRIC MODEL OF ADAPTATION MEETS THE FUNCTIONAL SYNTHESIS: DATA ON PAIRWISE EPISTASIS FOR FITNESS YIELDS INSIGHTS INTO THE SHAPE AND SIZE OF PHENOTYPE SPACE

The functional synthesis uses experimental methods from molecular biology, biochemistry and structural biology to decompose evolutionarily important mutations into their more proximal mechanistic determinants. However these methods are technically challenging and expensive. Noting strong formal parallels between R.A. Fisher's geometric model of adaptation and a recent model for the phenotypic basis of protein evolution, we sought to use the former to make inferences into the latter using data on pairwise fitness epistasis between mutations. We present an analytic framework for classifying pairs of mutations with respect to similarity of underlying mechanism on this basis, and also show that these data can yield an estimate of the number of mutationally labile phenotypes underlying fitness effects. We use computer simulations to explore the robustness of our approach to violations of analytic assumptions and analyze several recently published datasets. This work provides a theoretical complement to the functional synthesis as well as a novel test of Fisher's geometric model.     

SLOWLY SWITCHING BETWEEN ENVIRONMENTS FACILITATES REVERSE EVOLUTION IN SMALL POPULATIONS

Natural populations must constantly adapt to ever‐changing environmental conditions. A particularly interesting question is whether such adaptations can be reversed by returning the population to an ancestral environment. Such evolutionary reversals have been observed in both natural and laboratory populations. However, the factors that determine the reversibility of evolution are still under debate. The time scales of environmental change vary over a wide range, but little is known about how the rate of environmental change influences the reversibility of evolution. Here, we demonstrate computationally that slowly switching between environments increases the reversibility of evolution for small populations that are subject to only modest clonal interference. For small populations, slow switching reduces the mean number of mutations acquired in a new environment and also increases the probability of reverse evolution at each of these “genetic distances.” As the population size increases, slow switching no longer reduces the genetic distance, thus decreasing the evolutionary reversibility. We confirm this effect using both a phenomenological model of clonal interference and also a Wright–Fisher stochastic simulation that incorporates genetic diversity. Our results suggest that the rate of environmental change is a key determinant of the reversibility of evolution, and provides testable hypotheses for experimental evolution.     

IS LIFE IMPOSSIBLE? INFORMATION,SEX, AND THE ORIGIN OF COMPLEX ORGANISMS

The earliest organisms are thought to have had high mutation rates. It has been asserted that these high mutation rates would have severely limited the information content of early genomes. This has led to a well‐known “paradox” because, in contemporary organisms, the mechanisms that suppress mutations are quite complex and a substantial amount of information is required to construct these mechanisms. The paradox arises because it is not clear how efficient error‐suppressing mechanisms could have evolved, and thus allowed the evolution of complex organisms, at a time when mutation rates were too high to permit the maintenance of very substantial amounts of information within genomes. Here, we use concepts from the formal theory of information to calculate the amount of genomic information that can be maintained. We identify conditions under which much higher levels of genomic information can be maintained than previously considered possible among origin‐of‐life researchers. In particular, we find that the highest levels of information are maintained when many genotypes produce identical phenotypes, and when reproduction occasionally involves recombination between multiple parental genomes. There is a good reason to believe that these conditions are relevant for very early organisms, and thus the results presented may provide a solution to a long‐standing logical problem associated with the early evolution of life.     

The fitness effect of mutations across environments: Fisher's geometrical model with multiple optima

When are mutations beneficial in one environment and deleterious in another? More generally, what is the relationship between mutation effects across environments? These questions are crucial to predict adaptation in heterogeneous conditions in a broad sense. Empirical evidence documents various patterns of fitness effects across environments but we still lack a framework to analyze these multivariate data. In this article, we extend Fisher's geometrical model to multiple environments determining distinct peaks. We derive the fitness distribution, in one environment, among mutants with a given fitness in another and the bivariate distribution of random mutants’ fitnesses across two or more environments. The geometry of the phenotype‐fitness landscape is naturally interpreted in terms of fitness trade‐offs between environments. These results may be used to fit/predict empirical distributions or to predict the pattern of adaptation across heterogeneous conditions. As an example, we derive the genomic rate of substitution and of adaptation in a metapopulation divided into two distinct habitats in a high migration regime and show that they depend critically on the geometry of the phenotype‐fitness landscape.     

Modularity, noise, and natural selection

Most biological systems are formed by component parts that are to some degree interrelated. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of modularity is that biological systems usually present an unequal distribution of the genetic variation among traits. Estimating the covariance matrix that describes these systems is a difficult problem due to a number of factors such as poor sample sizes and measurement errors. We show that this problem will be exacerbated whenever matrix inversion is required, as in directional selection reconstruction analysis. We explore the consequences of varying degrees of modularity and signal-to-noise ratio on selection reconstruction. We then present and test the efficiency of available methods for controlling noise in matrix estimates. In our simulations, controlling matrices for noise vastly improves the reconstruction of selection gradients. We also perform an analysis of selection gradients reconstruction over a New World Monkeys skull database to illustrate the impact of noise on such analyses. Noise-controlled estimates render far more plausible interpretations that are in full agreement with previous results.     

MULTIDIMENSIONAL ADAPTIVE EVOLUTION OF A FEED‐FORWARD NETWORK AND THE ILLUSION OF COMPENSATION

When multiple substitutions affect a trait in opposing ways, they are often assumed to be compensatory, not only with respect to the trait, but also with respect to fitness. This type of compensatory evolution has been suggested to underlie the evolution of protein structures and interactions, RNA secondary structures, and gene regulatory modules and networks. The possibility for compensatory evolution results from epistasis. Yet if epistasis is widespread, then it is also possible that the opposing substitutions are individually adaptive. I term this possibility an adaptive reversal. Although possible for arbitrary phenotype‐fitness mappings, it has not yet been investigated whether such epistasis is prevalent in a biologically realistic setting. I investigate a particular regulatory circuit, the type I coherent feed‐forward loop, which is ubiquitous in natural systems and is accurately described by a simple mathematical model. I show that such reversals are common during adaptive evolution, can result solely from the topology of the fitness landscape, and can occur even when adaptation follows a modest environmental change and the network was well adapted to the original environment. The possibility of adaptive reversals warrants a systems perspective when interpreting substitution patterns in gene regulatory networks.     

SELECTION BIASES THE PREVALENCE AND TYPE OF EPISTASIS ALONG ADAPTIVE TRAJECTORIES

The contribution to an organism's phenotype from one genetic locus may depend upon the status of other loci. Such epistatic interactions among loci are now recognized as fundamental to shaping the process of adaptation in evolving populations. Although little is known about the structure of epistasis in most organisms, recent experiments with bacterial populations have concluded that antagonistic interactions abound and tend to deaccelerate the pace of adaptation over time. Here, we use the NK model of fitness landscapes to examine how natural selection biases the mutations that substitute during evolution based on their epistatic interactions. We find that, even when beneficial mutations are rare, these biases are strong and change substantially throughout the course of adaptation. In particular, epistasis is less prevalent than the neutral expectation early in adaptation and much more prevalent later, with a concomitant shift from predominantly antagonistic interactions early in adaptation to synergistic and sign epistasis later in adaptation. We observe the same patterns when reanalyzing data from a recent microbial evolution experiment. These results show that when the order of substitutions is not known, standard methods of analysis may suggest that epistasis retards adaptation when in fact it accelerates it.     

The evolution of cooperation by the Hankshaw effect

The evolution of cooperation—costly behavior that benefits others—faces one clear obstacle. Namely, cooperators are always at a competitive disadvantage relative to defectors, individuals that reap the benefits, but evade the cost of cooperation. One solution to this problem involves genetic hitchhiking, where the allele encoding cooperation becomes linked to a beneficial mutation, allowing cooperation to rise in abundance. Here, we explore hitchhiking in the context of adaptation to a stressful environment by cooperators and defectors with spatially limited dispersal. Under such conditions, clustered cooperators reach higher local densities, thereby experiencing more mutational opportunities than defectors. Thus, the allele encoding cooperation has a greater probability of hitchhiking with alleles conferring stress adaptation. We label this probabilistic enhancement the “Hankshaw effect” after the character Sissy Hankshaw, whose anomalously large thumbs made her a singularly effective hitchhiker. Using an agent‐based model, we reveal a broad set of conditions that allow the evolution of cooperation through this effect. Additionally, we show that spite, a costly behavior that harms others, can evolve by the Hankshaw effect. While in an unchanging environment these costly social behaviors have transient success, in a dynamic environment, cooperation and spite can persist indefinitely.     

Antibody‐mediated crosslinking of gut bacteria hinders the spread of antibiotic resistance

The body is home to a diverse microbiota, mainly in the gut. Resistant bacteria are selected by antibiotic treatments, and once resistance becomes widespread in a population of hosts, antibiotics become useless. Here, we develop a multiscale model of the interaction between antibiotic use and resistance spread in a host population, focusing on an important aspect of within‐host immunity. Antibodies secreted in the gut enchain bacteria upon division, yielding clonal clusters of bacteria. We demonstrate that immunity‐driven bacteria clustering can hinder the spread of a novel resistant bacterial strain in a host population. We quantify this effect both in the case where resistance preexists and in the case where acquiring a new resistance mutation is necessary for the bacteria to spread. We further show that the reduction of spread by clustering can be countered when immune hosts are silent carriers, and are less likely to get treated, and/or have more contacts. We demonstrate the robustness of our findings to including stochastic within‐host bacterial growth, a fitness cost of resistance, and its compensation. Our results highlight the importance of interactions between immunity and the spread of antibiotic resistance, and argue in the favor of vaccine‐based strategies to combat antibiotic resistance.     

Environmental robustness and the adaptability of populations

Recent work has shown that genetic robustness can either facilitate or impede adaptation. But the impact of environmental robustness on adaptation remains unclear. Environmental robustness helps ensure that organisms consistently develop the same phenotype in the face of "environmental noise" during development. Under purifying selection, those genotypes that express the optimal phenotype most reliably will be selectively favored. The resulting reduction in genetic variation tends to slow adaptation when the population is faced with a novel target phenotype. However, environmental noise sometimes induces the expression of an alternative advantageous phenotype, which may speed adaptation by genetic assimilation. Here, we use a population-genetic model to explore how these two opposing effects of environmental noise influence the capacity of a population to adapt. We analyze how the rate of adaptation depends on the frequency of environmental noise, the degree of environmental robustness in the population, the distribution of environmental robustness across genotypes, the population size, and the strength of selection for a newly adaptive phenotype. Over a broad regime, we find that environmental noise can either facilitate or impede adaptation. Our analysis uncovers several surprising insights about the relationship between environmental noise and adaptation, and it provides a general framework for interpreting empirical studies of both genetic and environmental robustness.     

Invasion of gene duplication through masking for maladaptive gene flow

Gene duplication can increase an organism's ability to mask the effect of deleterious alleles present in the population, but this is typically a small effect when the source of the genetic variation is mutation. Migration can introduce orders of magnitude more deleterious alleles per generation and may therefore be an important force acting on the structure of genomes. Using formal analytical methods, we study the invasion of haplotypes containing two copies of the resident allele, assuming that a single-locus equilibrium is already established in a continent-island model of migration. Provided that the immigrant allele can be completely masked by multiple functional gene copies, a new duplication will deterministically spread so long as duplicate haplotypes are, on average, fitter than single-copy haplotypes. When fitness depends on the number of immigrant allele copies and their masking ability then the threshold for invasion depends on the rate of immigration and the rate of recombination between the gene copies. Results from several special cases, including formation of protein dimers and Dobzhansky-Muller incompatibilities, suggest that duplications can invade in a wide range of selection regimes. We hypothesize that duplication in response to gene flow may provide an explanation for the high levels of polymorphism in gene copy number observed in natural populations.     

Hitchhiking in space: Ancestry in adapting,spatially extended populations*

Selective sweeps reduce neutral genetic diversity. In sexual populations, this “hitchhiking” effect is thought to be limited to the local genomic region of the sweeping allele. While this is true in panmictic populations, we find that in spatially extended populations the combined effects of many unlinked sweeps can affect patterns of ancestry (and therefore neutral genetic diversity) across the whole genome. Even low rates of sweeps can be enough to skew the spatial locations of ancestors such that neutral mutations that occur in an individual living outside a small region in the center of the range have virtually no chance of fixing in the population. The fact that nearly all ancestry rapidly traces back to a small spatial region also means that relatedness between individuals falls off very slowly as a function of the spatial distance between them.     

Populations adapt to fluctuating selection using derived and ancestral allelic diversity

Populations can adapt to changing environments by using allelic diversity, yet whether diversity is recently derived or ancestral is often debated. Although evolution could productively use both types of diversity in a changing environment, their relative frequency has not been quantified. We address this question experimentally using budding yeast strains that harbor a tandem repeat containing URA3 gene, which we expose to cyclical selection and counterselection. We characterize and quantify the dynamics of frameshift events in the URA3 gene in eight populations over 12 cycles of selection and find that ancestral alleles account for 10–20% of all adaptive events. Using a general model of fluctuating selection, we determine how these results depend on mutation rates, population sizes, and fluctuation timescales. We quantify the contribution of derived alleles to the adaptation process using the de novo mutation rate along the population's ancestral lineage, a novel measure that is applicable in a wide range of settings. We find that the adaptive dynamics undergoes a sharp transition from selection on ancestral alleles to selection on derived alleles as fluctuation timescales increase. Our results demonstrate that fluctuations can select between different modes of adaptation over evolutionary timescales.     

INTERGENERATIONAL PHENOTYPIC MIXING IN VIRAL EVOLUTION

Viral particles (virions) are made of genomic material packaged with proteins, drawn from the pool of proteins in the parent cell. It is well known that when virion concentrations are high, cells can be coinfected with multiple viral strains that can complement each other. Viral genomes can then interact with proteins derived from different strains, in a phenomenon known as phenotypic mixing. But phenotypic mixing is actually far more common: viruses mutate very often, and each time a mutation occurs, the parent cell contains different types of viral genomes. Due to phenotypic mixing, changes in viral phenotypes can be shifted by a generation from the mutations that cause them. In the regime of evolutionary invasion and escape, when mutations are crucial for the virus to survive, this timing can have a large influence on the probability of emergence of an adapted strain. Modeling the dynamics of viral evolution in these contexts thus requires attention to the mutational mechanism and the determinants of fitness.     

Population genetics, pleiotropy, and the preferential fixation of mutations during adaptive evolution

Ongoing debate centers on whether certain types of mutations are fixed preferentially during adaptive evolution. Although there has been much discussion, no quantitative framework currently exists to test for these biases. Here, we describe a method for distinguishing between the two processes that likely account for biased rates of substitution: variation in mutation rates and variation in the probability that a mutation becomes fixed once it arises. We then use this approach to examine the type and magnitude of these biases during evolutionary transitions across multiple scales: those involving repeated origins of individual traits (flower color change), and transitions involving broad suites of traits (morphological and physiological trait evolution in plants and animals). We show that fixation biases can be strong at both levels of comparison, likely due to differences in the magnitude of deleterious pleiotropy associated with alternative mutation categories. However, we also show that the scale at which these comparisons are made greatly influences the results, as broad comparisons that simultaneously analyze multiple traits obscure heterogeneity in the direction and magnitude of these biases. We conclude that preferential fixation of mutations likely is common in nature, but should be studied on a trait-by-trait basis.     

The double edged sword: The demographic consequences of the evolution of self‐fertilization

Phylogenies indicate that the transition from outcrossing to selfing is frequent, with selfing populations being more prone to extinction. The rates of transition to selfing and extinction, acting on different timescales, could explain the observed distributions of extant selfing species among taxa. However, phylogenetic and theoretical studies consider these mechanisms independently, that is transitions do not cause extinction. Here, we theoretically explore the demographic consequences of the evolution of self‐fertilization. Deleterious mutations and mutations modifying the selfing rate are recurrently introduced and the number of offspring depends on individual fitness, allowing for a demographic feedback. We show that mutational meltdowns can be triggered in populations evolving near strict selfing. Populations having survived a demographic crash are more stable than ancestral outcrossing populations once deleterious mutations are purged. The relatively rapid time‐scales at which extinctions occur indicate that during evolutionary transitions the accumulation of deleterious mutations may not be the cause of extinctions observed on longer time scales, but could lead to the underestimation of transition rates from outcrossing to selfing.     

Domestication and fitness in the wild: A multivariate view

Domesticated species continually escaping and interbreeding with wild relatives impose a migration load on wild populations. As domesticated stocks become increasingly different as a result of artificial and natural selection in captivity, fitness of escapees in the wild is expected to decline, reducing the effective rate of migration into wild populations. Recent theory suggest that this may alleviate and eventually eliminate the resulting migration load. I develop a multivariate model of trait and wild fitness evolution resulting from the joint effects of artificial and natural selection in the captive environment. Initially, the evolutionary trajectory is dominated by the effects of artificial selection causing a fast initial decline in fitness of escapees in the wild. In later phases, through the counteracting effects of correlational multivariate natural selection in captivity, the mean phenotype is pushed in directions of weak stabilizing selection, allowing a sustained response in the trait subject to artificial selection. Provided that there is some alignment between the adaptive landscapes in the wild and in captivity, these phases are associated with slower rates of decline in wild fitness of the domesticated stock, suggesting that detrimental effects on wild populations are likely to remain a concern in the foreseeable future.     

When maladaptive gene flow does not increase selection

Populations receiving high maladaptive gene flow are expected to experience strong directional selection—because gene flow pulls mean phenotypes away from local fitness peaks. We tested this prediction by means of a large and replicated mark‐recapture study of threespine stickleback (Gasterosteus aculeatus) in two stream populations. One of the populations (outlet) experiences high gene flow from the lake population and its morphology is correspondingly poorly adapted. The other population (inlet) experiences very low gene flow from the lake population and its morphology is correspondingly well adapted. Contrary to the above prediction, selection was not stronger in the outlet than in the inlet, a result that forced us to consider potential reasons for why maladaptive gene flow might not increase selection. Of particular interest, we show by means of a simple population genetic model that maladaptive gene flow can—under reasonable conditions—decrease the strength of directional selection. This outcome occurs when immigrants decrease mean fitness in the resident population, which decreases the strength of selection against maladapted phenotypes. We argue that this previously unrecognized effect of gene flow deserves further attention in theoretical and empirical studies.