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.     

A Bayesian MCMC Approach to Assess the Complete Distribution of Fitness Effects of New Mutations: Uncovering the Potential for Adaptive Walks in Challenging Environments

The role of adaptation in the evolutionary process has been contentious for decades. At the heart of the century-old debate between neutralists and selectionists lies the distribution of fitness effects (DFE)—that is, the selective effect of all mutations. Attempts to describe the DFE have been varied, occupying theoreticians and experimentalists alike. New high-throughput techniques stand to make important contributions to empirical efforts to characterize the DFE, but the usefulness of such approaches depends on the availability of robust statistical methods for their interpretation. We here present and discuss a Bayesian MCMC approach to estimate fitness from deep sequencing data and use it to assess the DFE for the same 560 point mutations in a coding region of Hsp90 in Saccharomyces cerevisiae across six different environmental conditions. Using these estimates, we compare the differences in the DFEs resulting from mutations covering one-, two-, and three-nucleotide steps from the wild type—showing that multiple-step mutations harbor more potential for adaptation in challenging environments, but also tend to be more deleterious in the standard environment. All observations are discussed in the light of expectations arising from Fisher’s geometric model.     

Natural selection and the genetics of adaptation in threespine stickleback

Growing knowledge of the molecular basis of adaptation in wild populations is expanding the study of natural selection. We summarize ongoing efforts to infer three aspects of natural selection—mechanism, form and history—from the genetics of adaptive evolution in threespine stickleback that colonized freshwater after the last ice age. We tested a mechanism of selection for reduced bony armour in freshwater by tracking genotype and allele frequency changes at an underlying major locus (Ectodysplasin) in transplanted stickleback populations. We inferred disruptive selection on genotypes at the same locus in a population polymorphic for bony armour. Finally, we compared the distribution of phenotypic effect sizes of genes underlying changes in body shape with that predicted by models of adaptive peak shifts following colonization of freshwater. Studies of the effects of selection on genes complement efforts to identify the molecular basis of adaptive differences, and improve our understanding of phenotypic evolution.     

The Evolutionarily Stable Distribution of Fitness Effects

The distribution of fitness effects (DFE) of new mutations is a key parameter in determining the course of evolution. This fact has motivated extensive efforts to measure the DFE or to predict it from first principles. However, just as the DFE determines the course of evolution, the evolutionary process itself constrains the DFE. Here, we analyze a simple model of genome evolution in a constant environment in which natural selection drives the population toward a dynamic steady state where beneficial and deleterious substitutions balance. The distribution of fitness effects at this steady state is stable under further evolution and provides a natural null expectation for the DFE in a population that has evolved in a constant environment for a long time. We calculate how the shape of the evolutionarily stable DFE depends on the underlying population genetic parameters. We show that, in the absence of epistasis, the ratio of beneficial to deleterious mutations of a given fitness effect obeys a simple relationship independent of population genetic details. Finally, we analyze how the stable DFE changes in the presence of a simple form of diminishing-returns epistasis.     

Joint inference of the distribution of fitness effects of deleterious mutations and population demography based on nucleotide polymorphism frequencies

The distribution of fitness effects of new mutations (DFE) is important for addressing several questions in genetics, including the nature of quantitative variation and the evolutionary fate of small populations. Properties of the DFE can be inferred by comparing the distributions of the frequencies of segregating nucleotide polymorphisms at selected and neutral sites in a population sample, but demographic changes alter the spectrum of allele frequencies at both neutral and selected sites, so can bias estimates of the DFE if not accounted for. We have developed a maximum-likelihood approach, based on the expected allele-frequency distribution generated by transition matrix methods, to estimate parameters of the DFE while simultaneously estimating parameters of a demographic model that allows a population size change at some time in the past. We tested the method using simulations and found that it accurately recovers simulated parameter values, even if the simulated demography differs substantially from that assumed in our analysis. We use our method to estimate parameters of the DFE for amino acid-changing mutations in humans and Drosophila melanogaster. For a model of unconditionally deleterious mutations, with effects sampled from a gamma distribution, the mean estimate for the distribution shape parameter is approximately 0.2 for human populations, which implies that the DFE is strongly leptokurtic. For Drosophila populations, we estimate that the shape parameter is approximately 0.35. Differences in the shape of the distribution and the mean selection coefficient between humans and Drosophila result in significantly more strongly deleterious mutations in Drosophila than in humans, and, conversely, nearly neutral mutations are significantly less frequent.     

Inferring Genome-Wide Correlations of Mutation Fitness Effects between Populations

The effect of a mutation on fitness may differ between populations depending on environmental and genetic context, but little is known about the factors that underlie such differences. To quantify genome-wide correlations in mutation fitness effects, we developed a novel concept called a joint distribution of fitness effects (DFE) between populations. We then proposed a new statistic w to measure the DFE correlation between populations. Using simulation, we showed that inferring the DFE correlation from the joint allele frequency spectrum is statistically precise and robust. Using population genomic data, we inferred DFE correlations of populations in humans, Drosophila melanogaster, and wild tomatoes. In these species, we found that the overall correlation of the joint DFE was inversely related to genetic differentiation. In humans and D. melanogaster, deleterious mutations had a lower DFE correlation than tolerated mutations, indicating a complex joint DFE. Altogether, the DFE correlation can be reliably inferred, and it offers extensive insight into the genetics of population divergence.     

A Comparison of Models to Infer the Distribution of Fitness Effects of New Mutations

Knowing the distribution of fitness effects (DFE) of new mutations is important for several topics in evolutionary genetics. Existing computational methods with which to infer the DFE based on DNA polymorphism data have frequently assumed that the DFE can be approximated by a unimodal distribution, such as a lognormal or a gamma distribution. However, if the true DFE departs substantially from the assumed distribution (e.g., if the DFE is multimodal), this could lead to misleading inferences about its properties. We conducted simulations to test the performance of parametric and nonparametric discretized distribution models to infer the properties of the DFE for cases in which the true DFE is unimodal, bimodal, or multimodal. We found that lognormal and gamma distribution models can perform poorly in recovering the properties of the distribution if the true DFE is bimodal or multimodal, whereas discretized distribution models perform better. If there is a sufficient amount of data, the discretized models can detect a multimodal DFE and can accurately infer the mean effect and the average fixation probability of a new deleterious mutation. We fitted several models for the DFE of amino acid-changing mutations using whole-genome polymorphism data from Drosophila melanogaster and the house mouse subspecies Mus musculus castaneus. A lognormal DFE best explains the data for D. melanogaster, whereas we find evidence for a bimodal DFE in M. m. castaneus.     

Genetic Variation in Heterogeneous Environments

A model of population structure in heterogeneous environments is described and conditions sufficient for maintaining a polymorphism are derived.

The absolute fitness of any genotype is regarded as a function of location in the niche space and the population density at that location. Two modes of habitat selection are examined: (1) organisms are distributed uniformly over the environment; and (2) each organism selects to occupy that habitat in which it is most fit ("optimal habitant selection").—Sufficient conditions for maintenance of genetic polymorphisms are derived for both models. In populations which do not practice habitat selection heterozygote superiority averaged over the environment is sufficient to guarantee the existence of polymorphisms. Comparable conditions for populations which practice optimal habitat selection are much less restrictive. If the heterozygotes are superior to one homozygote in any one part of the niche and to the other homozygote in any other part of the niche then a polymorphism will be defined.—A positive correlation between genetic and environmental variation follows from the model with habitat selection, but not from the other. The adaptive significance of polymorphisms thus depends on how animals behave.

     

Functional diversity buffers the effects of a pulse perturbation on the dynamics of tritrophic food webs

Biodiversity decline causes a loss of functional diversity, which threatens ecosystems through a dangerous feedback loop: This loss may hamper ecosystems’ ability to buffer environmental changes, leading to further biodiversity losses. In this context, the increasing frequency of human‐induced excessive loading of nutrients causes major problems in aquatic systems. Previous studies investigating how functional diversity influences the response of food webs to disturbances have mainly considered systems with at most two functionally diverse trophic levels. We investigated the effects of functional diversity on the robustness, that is, resistance, resilience, and elasticity, using a tritrophic—and thus more realistic—plankton food web model. We compared a non‐adaptive food chain with no diversity within the individual trophic levels to a more diverse food web with three adaptive trophic levels. The species fitness differences were balanced through trade‐offs between defense/growth rate for prey and selectivity/half‐saturation constant for predators. We showed that the resistance, resilience, and elasticity of tritrophic food webs decreased with larger perturbation sizes and depended on the state of the system when the perturbation occurred. Importantly, we found that a more diverse food web was generally more resistant and resilient but its elasticity was context‐dependent. Particularly, functional diversity reduced the probability of a regime shift toward a non‐desirable alternative state. The basal‐intermediate interaction consistently determined the robustness against a nutrient pulse despite the complex influence of the shape and type of the dynamical attractors. This relationship was strongly influenced by the diversity present and the third trophic level. Overall, using a food web model of realistic complexity, this study confirms the destructive potential of the positive feedback loop between biodiversity loss and robustness, by uncovering mechanisms leading to a decrease in resistance, resilience, and potentially elasticity as functional diversity declines.     

Density- and Frequency-Dependent Selection at the Mdh-2 Locus in DROSOPHILA PSEUDOOBSCURA

We have studied differences in the number of Drosophila pseudoobscura produced in a culture when the flies differ with respect to two alleles (F and S) at the Mdh-2 locus, which codes for a malate dehydrogenase enzyme. The studies were done at low and at high density in two- and three-genotype combinations (S/S, F/F and S/F), with one-genotype cultures as controls.——Density affects the fitness of the Mdh-2 genotypes. Different genotypes are differently affected, and the genotype of the competitors also makes a difference on the fitness of a given genotype. When three genotypes are present in a culture, particularly at high density, intergenotypic competition is less intense than intragenotypic competition at several frequency combinations. That is, there is "overcompensation": the three genotypes together exploit the environmental resources better than one genotype alone.—The fitness of the genotypes is frequency dependent in both two-genotype and three-genotype combinations. An inverse relationship between frequency and fitness is observed at high density. This may lead to a stable polymorphism, because the fitness of a genotype increases as its frequency decreases.—Forty independent strains, sampled from a natural population, were used in the experiments. This ensures that more than 95% of the variation present in the genome in the natural population is also present is the experimental cultures. It also ensures that the genetic background of the Mdh-2 alleles is randomized in the same way as it is in nature. However, the possibility remains that Mdh-2 alleles in nature are nonrandomly associated with alleles at closely linked loci. If linkage disequilibrium is present in the experiments because it exists in nature, then the observed effects (such as frequency-dependent selection) would affect the Mdh-2 locus in nature as well.     

A Bayesian Mutation–Selection Framework for Detecting Site-Specific Adaptive Evolution in Protein-Coding Genes

In recent years, codon substitution models based on the mutation–selection principle have been extended for the purpose of detecting signatures of adaptive evolution in protein-coding genes. However, the approaches used to date have either focused on detecting global signals of adaptive regimes—across the entire gene—or on contexts where experimentally derived, site-specific amino acid fitness profiles are available. Here, we present a Bayesian site-heterogeneous mutation–selection framework for site-specific detection of adaptive substitution regimes given a protein-coding DNA alignment. We offer implementations, briefly present simulation results, and apply the approach on a few real data sets. Our analyses suggest that the new approach shows greater sensitivity than traditional methods. However, more study is required to assess the impact of potential model violations on the method, and gain a greater empirical sense its behavior on a broader range of real data sets. We propose an outline of such a research program.     

An inclusive fitness analysis of synergistic interactions in structured populations

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner''s dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p. We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.     

Properties of adaptive walks on uncorrelated landscapes under strong selection and weak mutation

We examine properties of adaptive walks on uncorrelated (i.e. random) fitness landscapes starting from moderately fit genotypes under strong selection weak mutation. As an extension of Orr's model for a single step in an adaptive walk under these conditions, we show that the fitness rank of the dominant genotype in a population after the fixation of a beneficial mutation is, on average, (i+6)/4, where i is the fitness rank of the starting genotype. This accounts for the change in rank due to acquiring a new set of single-mutation neighbors after fixing a new allele through natural selection. Under this scenario, adaptive walks can be modeled as a simple Markov chain on the space of possible fitness ranks with an absorbing state at i = 1, from which no beneficial mutations are accessible. We find that these walks are typically short and are often completed in a single step when starting from a moderately fit genotype. As in Orr's original model, these results are insensitive to both the distribution of fitness effects and most biological details of the system under consideration.     

The effects of sex-biased gene expression and X-linkage on rates of adaptive protein sequence evolution in Drosophila

A faster rate of adaptive evolution of X-linked genes compared with autosomal genes may be caused by the fixation of new recessive or partially recessive advantageous mutations (the Faster-X effect). This effect is expected to be largest for mutations that affect only male fitness and absent for mutations that affect only female fitness. We tested these predictions in Drosophila melanogaster by using genes with different levels of sex-biased expression and by estimating the extent of adaptive evolution of non-synonymous mutations from polymorphism and divergence data. We detected both a Faster-X effect and an effect of male-biased gene expression. There was no evidence for a strong association between the two effects—modest levels of male-biased gene expression increased the rate of adaptive evolution on both the autosomes and the X chromosome, but a Faster-X effect occurred for both unbiased genes and female-biased genes. The rate of genetic recombination did not influence the magnitude of the Faster-X effect, ruling out the possibility that it reflects less Hill–Robertson interference for X-linked genes.     

Adaptive and nonadaptive plasticity in changing environments: Implications for sexual species with different life history strategies

Populations adapt to novel environmental conditions by genetic changes or phenotypic plasticity. Plastic responses are generally faster and can buffer fitness losses under variable conditions. Plasticity is typically modeled as random noise and linear reaction norms that assume simple one‐to‐one genotype–phenotype maps and no limits to the phenotypic response. Most studies on plasticity have focused on its effect on population viability. However, it is not clear, whether the advantage of plasticity depends solely on environmental fluctuations or also on the genetic and demographic properties (life histories) of populations. Here we present an individual‐based model and study the relative importance of adaptive and nonadaptive plasticity for populations of sexual species with different life histories experiencing directional stochastic climate change. Environmental fluctuations were simulated using differentially autocorrelated climatic stochasticity or noise color, and scenarios of directional climate change. Nonadaptive plasticity was simulated as a random environmental effect on trait development, while adaptive plasticity as a linear, saturating, or sinusoidal reaction norm. The last two imposed limits to the plastic response and emphasized flexible interactions of the genotype with the environment. Interestingly, this assumption led to (a) smaller phenotypic than genotypic variance in the population (many‐to‐one genotype–phenotype map) and the coexistence of polymorphisms, and (b) the maintenance of higher genetic variation—compared to linear reaction norms and genetic determinism—even when the population was exposed to a constant environment for several generations. Limits to plasticity led to genetic accommodation, when costs were negligible, and to the appearance of cryptic variation when limits were exceeded. We found that adaptive plasticity promoted population persistence under red environmental noise and was particularly important for life histories with low fecundity. Populations producing more offspring could cope with environmental fluctuations solely by genetic changes or random plasticity, unless environmental change was too fast.     

Naturally segregating loci exhibit epistasis for fitness

The extent to which gene interaction or epistasis contributes to fitness variation within populations remains poorly understood, despite its importance to a myriad of evolutionary questions. Here, we report a multi-year field study estimating fitness of Mimulus guttatus genetic lines in which pairs of naturally segregating loci exist in an otherwise uniform background. An allele at QTL x5b—a locus originally mapped for its effect on flower size—positively affects survival if combined with one genotype at quantitative trait locus x10a (aa) but has negative effects when combined with the other genotypes (Aa and AA). The viability differences between genotypes parallel phenotypic differences for the time and node at which a plant flowers. Viability is negatively correlated with fecundity across genotypes, indicating antagonistic pleiotropy for fitness components. This trade-off reduces the genetic variance for total fitness relative to the individual fitness components and thus may serve to maintain variation. Additionally, we find that the effects of each locus and their interaction often vary with the environment.     

Inference of the distribution of fitness effects of mutations is affected by single nucleotide polymorphism filtering methods,sample size and population structure

The distribution of fitness effects (DFE) of new mutations has been of interest to evolutionary biologists since the concept of mutations arose. Modern population genomic data enable us to quantify the DFE empirically, but few studies have examined how data processing, sample size and cryptic population structure might affect the accuracy of DFE inference. We used simulated and empirical data (from Arabidopsis lyrata) to show the effects of missing data filtering, sample size, number of single nucleotide polymorphisms (SNPs) and population structure on the accuracy and variance of DFE estimates. Our analyses focus on three filtering methods—downsampling, imputation and subsampling—with sample sizes of 4–100 individuals. We show that (1) the choice of missing-data treatment directly affects the estimated DFE, with downsampling performing better than imputation and subsampling; (2) the estimated DFE is less reliable in small samples (<8 individuals), and becomes unpredictable with too few SNPs (<5000, the sum of 0- and 4-fold SNPs); and (3) population structure may skew the inferred DFE towards more strongly deleterious mutations. We suggest that future studies should consider downsampling for small data sets, and use samples larger than 4 (ideally larger than 8) individuals, with more than 5000 SNPs in order to improve the robustness of DFE inference and enable comparative analyses.     

A method for inferring the rate of occurrence and fitness effects of advantageous mutations

The distribution of fitness effects (DFE) of new mutations is of fundamental importance in evolutionary genetics. Recently, methods have been developed for inferring the DFE that use information from the allele frequency distributions of putatively neutral and selected nucleotide polymorphic variants in a population sample. Here, we extend an existing maximum-likelihood method that estimates the DFE under the assumption that mutational effects are unconditionally deleterious, by including a fraction of positively selected mutations. We allow one or more classes of positive selection coefficients in the model and estimate both the fraction of mutations that are advantageous and the strength of selection acting on them. We show by simulations that the method is capable of recovering the parameters of the DFE under a range of conditions. We apply the method to two data sets on multiple protein-coding genes from African populations of Drosophila melanogaster. We use a probabilistic reconstruction of the ancestral states of the polymorphic sites to distinguish between derived and ancestral states at polymorphic nucleotide sites. In both data sets, we see a significant improvement in the fit when a category of positively selected amino acid mutations is included, but no further improvement if additional categories are added. We estimate that between 1% and 2% of new nonsynonymous mutations in D. melanogaster are positively selected, with a scaled selection coefficient representing the product of the effective population size, N(e), and the strength of selection on heterozygous carriers of ～2.5.