The distribution of fitness effects in an uncertain world

The distribution of fitness effects (DFE) among new mutations plays a critical role in adaptive evolution and the maintenance of genetic variation. Although fitness landscape models predict several key features of the DFE, most theory to date focuses on predictable environmental conditions, while ignoring stochastic environmental fluctuations that feature prominently in the ecology of many organisms. Here, we derive an extension of Fisher's geometric model that incorporates two common effects of environmental variation: (1) nonadaptive genotype‐by‐environment interactions (G × E), in which the phenotype of a given genotype varies across environmental contexts; and (2) random fluctuation of the fitness optimum, which generates fluctuating selection. We show that both factors cause a mismatch between the DFE within single generations and the distribution of geometric mean fitness effects (averaged over multiple generations) that governs long‐term evolutionary change. Such mismatches permit strong evolutionary constraints—despite an abundance of beneficial fitness variation within single environmental contexts—and to conflicting DFE estimates from direct versus indirect inference methods. Finally, our results suggest an intriguing parallel between the genetics and ecology of evolutionary constraints, with environmental fluctuations and pleiotropy placing qualitatively similar limits on the availability of adaptive genetic variation.     

Cuckoos versus hosts in insects and birds: adaptations,counter‐adaptations and outcomes

Avian parents and social insect colonies are victimized by interspecific brood parasites—cheats that procure costly care for their dependent offspring by leaving them in another species' nursery. Birds and insects defend themselves from attack by brood parasites; their defences in turn select counter‐strategies in the parasite, thus setting in motion antagonistic co‐evolution between the two parties. Despite their considerable taxonomic disparity, here we show striking parallels in the way that co‐evolution between brood parasites and their hosts proceeds in insects and birds. First, we identify five types of co‐evolutionary arms race from the empirical literature, which are common to both systems. These are: (a) directional co‐evolution of weaponry and armoury; (b) furtiveness in the parasite countered by strategies in the host to expose the parasite; (c) specialist parasites mimicking hosts who escape by diversifying their genetic signatures; (d) generalist parasites mimicking hosts who escape by favouring signatures that force specialization in the parasite; and (e) parasites using crypsis to evade recognition by hosts who then simplify their signatures to make the parasite more detectable. Arms races a and c are well characterized in the theoretical literature on co‐evolution, but the other types have received little or no formal theoretical attention. Empirical work suggests that hosts are doomed to lose arms races b and e to the parasite, in the sense that parasites typically evade host defences and successfully parasitize the nest. Nevertheless hosts may win when the co‐evolutionary trajectory follows arms race a, c or d. Next, we show that there are four common outcomes of the co‐evolutionary arms race for hosts. These are: (1) successful resistance; (2) the evolution of defence portfolios (or multiple lines of resistance); (3) acceptance of the parasite; and (4) tolerance of the parasite. The particular outcome is not determined by the type of preceding arms race but depends more on whether hosts or parasites control the co‐evolutionary trajectory: tolerance is an outcome that parasites inflict on hosts, whereas the other three outcomes are more dependent on properties intrinsic to the host species. Finally, our review highlights considerable interspecific variation in the complexity and depth of host defence portfolios. Whether this variation is adaptive or merely reflects evolutionary lag is unclear. We propose an adaptive explanation, which centres on the relative strength of two opposing processes: strategy‐facilitation, in which one line of host defence promotes the evolution of another form of resistance, and strategy‐blocking, in which one line of defence may relax selection on another so completely that it causes it to decay. We suggest that when strategy‐facilitation outweighs strategy‐blocking, hosts will possess complex defence portfolios and we identify selective conditions in which this is likely to be the case.     

SHIFTING FITNESS LANDSCAPES IN RESPONSE TO ALTERED ENVIRONMENTS

The role of adaptation in molecular evolution has been contentious for decades. Here, we shed light on the adaptive potential in Saccharomyces cerevisiae by presenting systematic fitness measurements for all possible point mutations in a region of Hsp90 under four environmental conditions. Under elevated salinity, we observe numerous beneficial mutations with growth advantages up to 7% relative to the wild type. All of these beneficial mutations were observed to be associated with high costs of adaptation. We thus demonstrate that an essential protein can harbor adaptive potential upon an environmental challenge, and report a remarkable fit of the data to a version of Fisher's geometric model that focuses on the fitness trade‐offs between mutations in different environments.     

Properties of selected mutations and genotypic landscapes under Fisher's geometric model

The fitness landscape—the mapping between genotypes and fitness—determines properties of the process of adaptation. Several small genotypic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here, we generate several testable predictions for the properties of these small genotypic landscapes under Fisher's geometric model of adaptation. When the ancestral strain is far from the fitness optimum, we analytically compute the fitness effect of selected mutations and their epistatic interactions. Epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected, or coselected in an adaptive walk. Simulations show that genotypic landscapes built from Fisher's model are very close to an additive landscape when the ancestral strain is far from the optimum. However, when it is close to the optimum, a large diversity of landscape with substantial roughness and sign epistasis emerged. Strikingly, small genotypic landscapes built from several replicate adaptive walks on the same underlying landscape were highly variable, suggesting that several realizations of small genotypic landscapes are needed to gain information about the underlying architecture of the fitness landscape.     

ANTIBIOTIC RESISTANCE AND STRESS IN THE LIGHT OF FISHER'S MODEL

The role of mutations in evolution depends upon the distribution of their effects on fitness. This distribution is likely to depend on the environment. Indeed genotype‐by‐environment interactions are key for the process of local adaptation and ecological specialization. An important trait in bacterial evolution is antibiotic resistance, which presents a clear case of change in the direction of selection between environments with and without antibiotics. Here, we study the distribution of fitness effects of mutations, conferring antibiotic resistance to Escherichia coli, in benign and stressful environments without drugs. We interpret the distributions in the light of a fitness landscape model that assumes a single fitness peak. We find that mutation effects (s) are well described by a shifted gamma distribution, with a shift parameter that reflects the distance to the fitness peak and varies across environments. Consistent with the theoretical predictions of Fisher's geometrical model, with a Gaussian relationship between phenotype and fitness, we find that the main effect of stress is to increase the variance in s. Our findings are in agreement with the results of a recent meta‐analysis, which suggest that a simple fitness landscape model may capture the variation of mutation effects across species and environments.     

Antagonistic Coevolution Under Sexual Conflict

The theory of sexual conflict predicts that sexual coevolution will be very dynamic, with in principle perpetual evolutionary arms races and chases. These arms races are expected to stop once the costs of conflict adaptations become too high. We argue that this prediction is contingent on specific assumptions about the sexual interaction and the adaptations involved in the arms race. More generally, evolutionary arms races stop when the fitness benefit of further escalations is outweighed by the fitness costs. For this it is not necessary that the absolute costs of conflict must be high at the stable state, or that the population fitness must be decreased at equilibrium. We expect the outcome of sexual antagonistic coevolution to be determined by the possibility to reach compromises and by the relative ability of each sex to control the outcome of the interaction. We exemplify with a theoretical conflict model, which leads to population extinction when conflict is settled by armaments with expression-level determined costs. The model predicts a compromise with small conflict costs for the population, if costs are in addition determined by the extent of conflict between the sexes, which may be the case when the cost depends on behavioural antagonism.     

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.     

THE INEVITABILITY OF UNCONDITIONALLY DELETERIOUS SUBSTITUTIONS DURING ADAPTATION

Studies on the genetics of adaptation from new mutations typically neglect the possibility that a deleterious mutation might fix. Nonetheless, here we show that, in many regimes, the first mutation to fix is most often deleterious, even when fitness is expected to increase in the long term. In particular, we prove that this phenomenon occurs under weak mutation for any house‐of‐cards model with an equilibrium distribution. We find that the same qualitative results hold under Fisher's geometric model. We also provide a simple intuition for the surprising prevalence of unconditionally deleterious substitutions during early adaptation. Importantly, the phenomenon we describe occurs on fitness landscapes without any local maxima and is therefore distinct from “valley crossing.” Our results imply that the common practice of ignoring deleterious substitutions leads to qualitatively incorrect predictions in many regimes. Our results also have implications for the substitution process at equilibrium and for the response to a sudden decrease in population size.     

Sexual selection modulates genetic conflicts and patterns of genomic imprinting

Recent years have seen a surge of interest in linking the theories of kin selection and sexual selection. In particular, there is a growing appreciation that kin selection, arising through demographic factors such as sex‐biased dispersal, may modulate sexual conflicts, including in the context of male–female arms races characterized by coevolutionary cycles. However, evolutionary conflicts of interest need not only occur between individuals, but may also occur within individuals, and sex‐specific demography is known to foment such intragenomic conflict in relation to social behavior. Whether and how this logic holds in the context of sexual conflict—and, in particular, in relation to coevolutionary cycles—remains obscure. We develop a kin‐selection model to investigate the interests of different genes involved in sexual and intragenomic conflict, and we show that consideration of these conflicting interests yields novel predictions concerning parent‐of‐origin specific patterns of gene expression and the detrimental effects of different classes of mutation and epimutation at loci underpinning sexually selected phenotypes.     

Modelling the evolution of common cuckoo host‐races: speciation or genetic swamping?

Co‐evolutionary arms races have provided clear evidence for evolutionary change, especially in host–parasite systems. The evolution of host‐specific races in the common cuckoo (Cuculus canorus), however, is also an example where sexual conflict influences the outcome. Cuckoo females benefit from better adaptation to overcome host defences, whereas cuckoo males face a trade‐off between the benefits of better adaptation to a host and the benefits of multiple mating with females from other host‐races. The outcome of this trade‐off might be genetic differentiation or prevention of it by genetic swamping. We use a simulation model to test which outcome is more likely with three sympatric cuckoo host‐races. We assume a cost for cuckoo chicks that express a host adaptation allele not suited to their foster host species and that cuckoo males that switch to another host‐race experience either a fitness benefit or cost. Over most of the parameter space, cuckoo male host‐race fidelity increases significantly with time, and gene flow between host‐races ceases within a few thousand to a hundred thousand generations. Our results hence support the idea that common cuckoo host‐races might be in the incipient stages of speciation.     

An exact steady state solution of Fisher's geometric model and other models

Because nearly neutral substitutions are thought to contribute substantially to molecular evolution, and much of our insight about the workings of nearly neutral evolution relies on theory, solvable models of this process are of particular interest. Here, I present an analytical method for solving models of nearly neutral evolution at steady state. The steady state solution applies to any constant fitness landscape under a dynamic of successive fixations, each of which occurs on the background of the population's most recent common ancestor. Because this dynamic neglects the effects of polymorphism in the population beyond the mutant allele under consideration, the steady state solution provides a decent approximation of evolutionary dynamics when the population mutation rate is low (Nu<1). To demonstrate the method, I apply it to two examples: Fisher's geometric model (FGM), and a simple model of molecular evolution. Since recent papers have studied the steady state behavior of FGM under this dynamic, I analyze its behavior in detail and compare the results with previous work.     

RATES OF FITNESS DECLINE AND REBOUND SUGGEST PERVASIVE EPISTASIS

Unraveling the factors that determine the rate of adaptation is a major question in evolutionary biology. One key parameter is the effect of a new mutation on fitness, which invariably depends on the environment and genetic background. The fate of a mutation also depends on population size, which determines the amount of drift it will experience. Here, we manipulate both population size and genotype composition and follow adaptation of 23 distinct Escherichia coli genotypes. These have previously accumulated mutations under intense genetic drift and encompass a substantial fitness variation. A simple rule is uncovered: the net fitness change is negatively correlated with the fitness of the genotype in which new mutations appear—a signature of epistasis. We find that Fisher's geometrical model can account for the observed patterns of fitness change and infer the parameters of this model that best fit the data, using Approximate Bayesian Computation. We estimate a genomic mutation rate of 0.01 per generation for fitness altering mutations, albeit with a large confidence interval, a mean fitness effect of mutations of ?0.01, and an effective number of traits nine in mutS^? E. coli. This framework can be extended to confront a broader range of models with data and test different classes of fitness landscape models.     

Evolution by small steps and rugged landscapes in the RNA virus phi6

Fisher's geometric model of adaptive evolution argues that adaptive evolution should generally result from the substitution of many mutations of small effect because advantageous mutations of small effect should be more common than those of large effect. However, evidence for both evolution by small steps and for Fisher's model has been mixed. Here we report supporting results from a new experimental test of the model. We subjected the bacteriophage phi6 to intensified genetic drift in small populations and caused viral fitness to decline through the accumulation of a deleterious mutation. We then propagated the mutated virus at a range of larger population sizes and allowed fitness to recover by natural selection. Although fitness declined in one large step, it was usually recovered in smaller steps. More importantly, step size during recovery was smaller with decreasing size of the recovery population. These results confirm Fisher's main prediction that advantageous mutations of small effect should be more common. We also show that the advantageous mutations of small effect are compensatory mutations whose advantage is conditional (epistatic) on the presence of the deleterious mutation, in which case the adaptive landscape of phi6 is likely to be very rugged.     

Mutating away from your enemies: The evolution of mutation rate in a host–parasite system

The rate at which mutations occur in nature is itself under natural selection. While a general reduction of mutation rates is advantageous for species inhabiting constant environments, higher mutation rates can be advantageous for those inhabiting fluctuating environments that impose on-going directional selection. Analogously, species involved in antagonistic co-evolutionary arms races, such as hosts and parasites, can also benefit from higher mutation rates. We use modifier theory, combined with simulations, to investigate the evolution of mutation rate in such a host–parasite system. We derive an expression for the evolutionary stable mutation rate between two alleles, each of whose fitness depends on the current genetic composition of the other species. Recombination has been shown to weaken the strength of selection acting on mutation modifiers, and accordingly, we find that the evolutionarily attracting mutation rate is lower when recombination between the selected and the modifier locus is high. Cyclical dynamics are potentially commonplace for loci governing antagonistic species interactions. We characterize the parameter space where such cyclical dynamics occur and show that the evolution of large mutation rates tends to inhibit cycling and thus eliminates further selection on modifiers of the mutation rate. We then find using computer simulations that stochastic fluctuations in finite populations can increase the size of the region where cycles occur, creating selection for higher mutation rates. We finally use simulations to investigate the model behaviour when there are more than two alleles, finding that the region where cycling occurs becomes smaller and the evolutionarily attracting mutation rate lower when there are more alleles.     

FISHER'S GEOMETRIC MODEL WITH A MOVING OPTIMUM

Fisher's geometric model has been widely used to study the effects of pleiotropy and organismic complexity on phenotypic adaptation. Here, we study a version of Fisher's model in which a population adapts to a gradually moving optimum. Key parameters are the rate of environmental change, the dimensionality of phenotype space, and the patterns of mutational and selectional correlations. We focus on the distribution of adaptive substitutions, that is, the multivariate distribution of the phenotypic effects of fixed beneficial mutations. Our main results are based on an “adaptive‐walk approximation,” which is checked against individual‐based simulations. We find that (1) the distribution of adaptive substitutions is strongly affected by the ecological dynamics and largely depends on a single composite parameter γ, which scales the rate of environmental change by the “adaptive potential” of the population; (2) the distribution of adaptive substitution reflects the shape of the fitness landscape if the environment changes slowly, whereas it mirrors the distribution of new mutations if the environment changes fast; (3) in contrast to classical models of adaptation assuming a constant optimum, with a moving optimum, more complex organisms evolve via larger adaptive steps.     

Post‐conflict third‐party affiliation in chimpanzees: what's in it for the third party?

Affiliative behavior after conflicts between conflict participants and other group members is common in many primate species. The proposed functions for such triadic interactions are numerous, mostly concerning the benefit for the former conflict opponents. We investigated post‐conflict third‐party affiliation (TPA) in captive chimpanzees (Pan troglodytes) with the aim of assessing what the affiliating third parties may gain from affiliation. Specifically, we tested whether third‐party‐initiated affiliation protects the third parties from further aggression by conflict opponents. We found support for this “self‐protection hypothesis,” in that third parties selectively directed affiliation to those opponents who more often gave further aggression to them, and affiliation effectively decreased their chance of receiving aggression from these opponents. However, a subset of affiliation, provided to conflict victims by their own kin, appeared to not be self‐protective and the function of it remained open. We conclude that chimpanzee third‐party‐initiated affiliation is a more heterogeneous behavior than thus far assumed. Am. J. Primatol. 71:409–418, 2009. © 2009 Wiley‐Liss, Inc.     

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.     

Population persistence under high mutation rate: From evolutionary rescue to lethal mutagenesis

Populations may genetically adapt to severe stress that would otherwise cause their extirpation. Recent theoretical work, combining stochastic demography with Fisher's geometric model of adaptation, has shown how evolutionary rescue becomes unlikely beyond some critical intensity of stress. Increasing mutation rates may however allow adaptation to more intense stress, raising concerns about the effectiveness of treatments against pathogens. This previous work assumes that populations are rescued by the rise of a single resistance mutation. However, even in asexual organisms, rescue can also stem from the accumulation of multiple mutations in a single genome. Here, we extend previous work to study the rescue process in an asexual population where the mutation rate is sufficiently high so that such events may be common. We predict both the ultimate extinction probability of the population and the distribution of extinction times. We compare the accuracy of different approximations covering a large range of mutation rates. Moderate increase in mutation rates favors evolutionary rescue. However, larger increase leads to extinction by the accumulation of a large mutation load, a process called lethal mutagenesis. We discuss how these results could help design “evolution‐proof” antipathogen treatments that even highly mutable strains could not overcome.     

From bad to good: Fitness reversals and the ascent of deleterious mutations

Deleterious mutations are considered a major impediment to adaptation, and there are straightforward expectations for the rate at which they accumulate as a function of population size and mutation rate. In a simulation model of an evolving population of asexually replicating RNA molecules, initially deleterious mutations accumulated at rates nearly equal to that of initially beneficial mutations, without impeding evolutionary progress. As the mutation rate was increased within a moderate range, deleterious mutation accumulation and mean fitness improvement both increased. The fixation rates were higher than predicted by many population-genetic models. This seemingly paradoxical result was resolved in part by the observation that, during the time to fixation, the selection coefficient (s) of initially deleterious mutations reversed to confer a selective advantage. Significantly, more than half of the fixations of initially deleterious mutations involved fitness reversals. These fitness reversals had a substantial effect on the total fitness of the genome and thus contributed to its success in the population. Despite the relative importance of fitness reversals, however, the probabilities of fixation for both initially beneficial and initially deleterious mutations were exceedingly small (on the order of 10⁻⁵ of all mutations).     

THE EVOLUTION OF COSTLY MATE PREFERENCES I. FISHER AND BIASED MUTATION

Fisher's runaway process is the standard explanation of the evolution of exaggerated female preferences. But mathematical formulations of Fisher's process (haploid and additive diploid) show it cannot cause stable exaggeration if female preference carries a cost. At equilibrium female fitness must be maximized. Our analysis shows that evolutionary stable exaggeration of female preference can be achieved if mutation pressure on the male character is biased, that is, mutation has a directional effect. At this equilibrium female fitness is not maximized. We discuss the reasons and evidence for believing that mutation pressure is typically biased. Our analysis highlights the previously unacknowledged importance of biased mutation for sexual selection.