Imperfect genes, Fisherian mutation and the evolution of sex

Direct inference of the distribution of fitness effects of spontaneous mutations from recombinant inbred Caenorhabditis elegans mutation accumulation lines

The distribution of fitness effects of new mutations plays a central role in evolutionary biology. Estimates of the distribution of fitness effect from experimental mutation accumulation lines are compromised by the complete linkage disequilibrium between mutations in different lines. To reduce the linkage disequilibrium, we constructed 2 sets of recombinant inbred lines from a cross of 2 Caenorhabditis elegans mutation accumulation lines. One set of lines ("RIAILs") was intercrossed for 10 generations prior to 10 generations of selfing; the second set of lines ("RILs") omitted the intercrossing. Residual linkage disequilibrium in the RIAILs is much less than in the RILs, which affects the inferred distribution of fitness effect when the sets of lines are analyzed separately. The best-fit model estimated from all lines (RIAILs + RILs) infers a large fraction of mutations with positive effects (∼40%); models that constrain mutations to have negative effects fit much worse. The conclusion is the same using only the RILs. For the RIAILs, however, models that constrain mutations to have negative effects fit nearly as well as models that allow positive effects. When mutations in high linkage disequilibrium are pooled into haplotypes, the inferred distribution of fitness effect becomes increasingly negative-skewed and leptokurtic. We conclude that the conventional wisdom-most mutations have effects near 0, a handful of mutations have effects that are substantially negative, and mutations with positive effects are very rare-is likely correct, and that unless it can be shown otherwise, estimates of the distribution of fitness effect that infer a substantial fraction of mutations with positive effects are likely confounded by linkage disequilibrium.

Fisher's Geometric Model as a Tool to Study Speciation

Interactions between alleles and across environments play an important role in the fitness of hybrids and are at the heart of the speciation process. Fitness landscapes capture these interactions and can be used to model hybrid fitness, helping us to interpret empirical observations and clarify verbal models. Here, we review recent progress in understanding hybridization outcomes through Fisher's geometric model, an intuitive and analytically tractable fitness landscape that captures many fitness patterns observed across taxa. We use case studies to show how the model parameters can be estimated from different types of data and discuss how these estimates can be used to make inferences about the divergence history and genetic architecture. We also highlight some areas where the model's predictions differ from alternative incompatibility-based models, such as the snowball effect and outlier patterns in genome scans.

Changing fitness effects of mutations through long-term bacterial evolution

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

Effects of Parkin on the Mitochondrial Genome in the Heart and Brain of Mitochondrial Mutator Mice

Mitochondrial dysfunction has been implicated in neurodegenerative diseases like Parkinson's disease (PD). This study investigates the role of Parkin, a protein involved in mitochondrial quality control, and strongly linked to PD, in the context of mitochondrial DNA (mtDNA) mutations. Mitochondrial mutator mice (PolgD257A/D257A ) (Polg) are used and bred with Parkin knockout (PKO) mice or mice with disinhibited Parkin (W402A). In the brain, mtDNA mutations are analyzed in synaptosomes, presynaptic neuronal terminals, which are far from neuronal soma, which likely renders mitochondria there more vulnerable compared with brain homogenate. Surprisingly, PKO results in reduced mtDNA mutations in the brain but increased control region multimer (CRM) in synaptosomes. In the heart, both PKO and W402A lead to increased mutations, with W402A showing more mutations in the heart than PKO. Computational analysis reveals many of these mutations are deleterious. These findings suggest that Parkin plays a tissue-dependent role in regulating mtDNA damage response, with differential effects in the brain and heart. Understanding the specific role of Parkin in different tissues may provide insights into the underlying mechanisms of PD and potential therapeutic strategies. Further investigation into these pathways can enhance the understanding of neurodegenerative diseases associated with mitochondrial dysfunction.

The distribution of mutational effects on fitness in Caenorhabditis elegans inferred from standing genetic variation

The distribution of fitness effects (DFE) for new mutations is one of the most theoretically important but difficult to estimate properties in population genetics. A crucial challenge to inferring the DFE from natural genetic variation is the sensitivity of the site frequency spectrum to factors like population size change, population substructure, genome structure, and nonrandom mating. Although inference methods aim to control for population size changes, the influence of nonrandom mating remains incompletely understood, despite being a common feature of many species. We report the DFE estimated from 326 genomes of Caenorhabditis elegans, a nematode roundworm with a high rate of self-fertilization. We evaluate the robustness of DFE inferences using simulated data that mimics the genomic structure and reproductive life history of C. elegans. Our observations demonstrate how the combined influence of self-fertilization, genome structure, and natural selection on linked sites can conspire to compromise estimates of the DFE from extant polymorphisms with existing methods. These factors together tend to bias inferences toward weakly deleterious mutations, making it challenging to have full confidence in the inferred DFE of new mutations as deduced from standing genetic variation in species like C. elegans. Improved methods for inferring the DFE are needed to appropriately handle strong linked selection and selfing. These results highlight the importance of understanding the combined effects of processes that can bias our interpretations of evolution in natural populations.

Allen Orr and the genetics of adaptation

Over most of the 20th century, evolutionary biologists predominantly subscribed to a strong form of "micro-mutationism," in which adaptive phenotypic divergence arises from allele frequency changes at many loci, each with a small effect on the phenotype. To be sure, there were well-known examples of large-effect alleles contributing to adaptation, yet such cases were generally regarded as atypical and unrepresentative of evolutionary change in general. In 1998, Allen Orr published a landmark theoretical paper in Evolution, which showed that both small- and large-effect mutations are likely to contribute to "adaptive walks" of a population to an optimum. Coupled with a growing set of empirical examples of large-effect alleles contributing to divergence (e.g., from QTL studies), Orr's paper provided a mathematical formalism that converted many evolutionary biologists from micro-mutationism to a more pluralistic perspective on the genetic basis of evolutionary change. We revisit the theoretical insights emerging from Orr's paper within the historical context leading up to 1998, and track the influence of this paper on the field of evolutionary biology through an examination of its citations over the last two decades and an analysis of the extensive body of theoretical and empirical research that Orr's pioneering paper inspired.

The geometry and genetics of hybridization

When divergent populations form hybrids, hybrid fitness can vary with genome composition, current environmental conditions, and the divergence history of the populations. We develop analytical predictions for hybrid fitness, which incorporate all three factors. The predictions are based on Fisher's geometric model, and apply to a wide range of population genetic parameter regimes and divergence conditions, including allopatry and parapatry, local adaptation, and drift. Results show that hybrid fitness can be decomposed into intrinsic effects of admixture and heterozygosity, and extrinsic effects of the (local) adaptedness of the parental lines. Effect sizes are determined by a handful of geometric distances, which have a simple biological interpretation. These distances also reflect the mode and amount of divergence, such that there is convergence toward a characteristic pattern of intrinsic isolation. We next connect our results to the quantitative genetics of line crosses in variable or patchy environments. This means that the geometrical distances can be estimated from cross data, and provides a simple interpretation of the "composite effects." Finally, we develop extensions to the model, involving selectively induced disequilibria, and variable phenotypic dominance. The geometry of fitness landscapes provides a unifying framework for understanding speciation, and wider patterns of hybrid fitness.

Cultural evolution and prehistoric demography

One prominent feature of human culture is that different populations have different tools, technologies and cultural artefacts, and these unique toolkits can also differ in size and complexity. Over the past few decades, researchers in the fields of prehistoric demography and cultural evolution have addressed a number of questions regarding variation in toolkit size and complexity across prehistoric and modern populations. Several factors have been proposed as possible explanations for this variation: in particular, the mobility of a population, the resources it uses, the volatility of its environment and the number of individuals in the population. Using a variety of methods, including empirical and ethnographic research, computational models and laboratory-based experiments, researchers have found disparate results regarding each hypothesis. These discordant findings have led to debate over the factors that most significantly influence toolkit size and composition. For instance, several computational, empirical and laboratory studies of food-producing populations have found a positive correlation between the number of individuals in a population and toolkit size, whereas similar studies of hunter-gatherer populations have found little evidence of such a link. In this paper, we conduct a comprehensive review of the literature in this field of study and propose corollaries and interdisciplinary approaches with the goal of reconciling dissimilar findings into a more comprehensive view of cultural toolkit variation. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.

The distribution of epistasis on simple fitness landscapes

Fitness interactions between mutations can influence a population's evolution in many different ways. While epistatic effects are difficult to measure precisely, important information is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from a class of simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effect sizes, mutational bias and maladaptation of the wild type. We illustrate our approach by reanalysing a large dataset of mutant effects in a yeast snoRNA (small nucleolar RNA). Though characterized by some large epistatic effects, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have limited influence on the evolutionary dynamics in this system. We also show how the amount of epistasis depends on both the underlying fitness landscape and the distribution of mutations, and so is expected to vary in consistent ways between new mutations, standing variation and fixed mutations.

Model genotype-phenotype mappings and the algorithmic structure of evolution

Cancers are complex dynamic systems that undergo evolution and selection. Personalized medicine approaches in the clinic increasingly rely on predictions of tumour response to one or more therapies; these predictions are complicated by the inevitable evolution of the tumour. Despite enormous amounts of data on the mutational status of cancers and numerous therapies developed in recent decades to target these mutations, many of these treatments fail after a time due to the development of resistance in the tumour. The emergence of these resistant phenotypes is not easily predicted from genomic data, since the relationship between genotypes and phenotypes, termed the genotype-phenotype (GP) mapping, is neither injective nor functional. We present a review of models of this mapping within a generalized evolutionary framework that takes into account the relation between genotype, phenotype, environment and fitness. Different modelling approaches are described and compared, and many evolutionary results are shown to be conserved across studies despite using different underlying model systems. In addition, several areas for future work that remain understudied are identified, including plasticity and bet-hedging. The GP-mapping provides a pathway for understanding the potential routes of evolution taken by cancers, which will be necessary knowledge for improving personalized therapies.

Old Trade, New Tricks: Insights into the Spontaneous Mutation Process from the Partnering of Classical Mutation Accumulation Experiments with High-Throughput Genomic Approaches

Mutations spawn genetic variation which, in turn, fuels evolution. Hence, experimental investigations into the rate and fitness effects of spontaneous mutations are central to the study of evolution. Mutation accumulation (MA) experiments have served as a cornerstone for furthering our understanding of spontaneous mutations for four decades. In the pregenomic era, phenotypic measurements of fitness-related traits in MA lines were used to indirectly estimate key mutational parameters, such as the genomic mutation rate, new mutational variance per generation, and the average fitness effect of mutations. Rapidly emerging next-generating sequencing technology has supplanted this phenotype-dependent approach, enabling direct empirical estimates of the mutation rate and a more nuanced understanding of the relative contributions of different classes of mutations to the standing genetic variation. Whole-genome sequencing of MA lines bears immense potential to provide a unified account of the evolutionary process at multiple levels-the genetic basis of variation, and the evolutionary dynamics of mutations under the forces of selection and drift. In this review, we have attempted to synthesize key insights into the spontaneous mutation process that are rapidly emerging from the partnering of classical MA experiments with high-throughput sequencing, with particular emphasis on the spontaneous rates and molecular properties of different mutational classes in nuclear and mitochondrial genomes of diverse taxa, the contribution of mutations to the evolution of gene expression, and the rate and stability of transgenerational epigenetic modifications. Future advances in sequencing technologies will enable greater species representation to further refine our understanding of mutational parameters and their functional consequences.

Robustness and evolvability of heterogeneous cell populations

Biological systems are endowed with two fundamental but seemingly contradictory properties: robustness, the ability to withstand environmental fluctuations and genetic variability; and evolvability, the ability to acquire selectable and heritable phenotypic changes. Cell populations with heterogeneous genetic makeup, such as those of infectious microbial organisms or cancer, rely on their inherent robustness to maintain viability and fitness, but when encountering environmental insults, such as drug treatment, these populations are also poised for rapid adaptation through evolutionary selection. In this study, we develop a general mathematical model that allows us to explain and quantify this fundamental relationship between robustness and evolvability of heterogeneous cell populations. Our model predicts that robustness is, in fact, essential for evolvability, especially for more adverse environments, a trend we observe in aneuploid budding yeast and breast cancer cells. Robustness also compensates for the negative impact of the systems' complexity on their evolvability. Our model also provides a mathematical means to estimate the number of independent processes underlying a system's performance and identify the most generally adapted subpopulation, which may resemble the multi-drug-resistant "persister" cells observed in cancer.

The empirical case against the 'demographic turn' in Palaeolithic archaeology

Recently, it has become commonplace to interpret major transitions and other patterns in the Palaeolithic archaeological record in terms of population size. Increases in cultural complexity are claimed to result from increases in population size; decreases in cultural complexity are suggested to be due to decreases in population size; and periods of no change are attributed to low numbers or frequent extirpation. In this paper, we argue that this approach is not defensible. We show that the available empirical evidence does not support the idea that cultural complexity in hunter-gatherers is governed by population size. Instead, ethnographic and archaeological data suggest that hunter-gatherer cultural complexity is most strongly influenced by environmental factors. Because all hominins were hunter-gatherers until the Holocene, this means using population size to interpret patterns in the Palaeolithic archaeological record is problematic. In future, the population size hypothesis should be viewed as one of several competing hypotheses and its predictions formally tested alongside those of its competitors.This article is part of the themed issue 'Major transitions in human evolution'.

Fisher's geometrical model and the mutational patterns of antibiotic resistance across dose gradients

Fisher's geometrical model (FGM) has been widely used to depict the fitness effects of mutations. It is a general model with few underlying assumptions that gives a large and comprehensive view of adaptive processes. It is thus attractive in several situations, for example adaptation to antibiotics, but comes with limitations, so that more mechanistic approaches are often preferred to interpret experimental data. It might be possible however to extend FGM assumptions to better account for mutational data. This is theoretically challenging in the context of antibiotic resistance because resistance mutations are assumed to be rare. In this article, we show with Escherichia coli how the fitness effects of resistance mutations screened at different doses of nalidixic acid vary across a dose-gradient. We found experimental patterns qualitatively consistent with the basic FGM (rate of resistance across doses, gamma distributed costs) but also unexpected patterns such as a decreasing mean cost of resistance with increasing screen dose. We show how different extensions involving mutational modules and variations in trait covariance across environments, can be discriminated based on these data. Overall, simple extensions of the FGM accounted well for complex mutational effects of resistance mutations across antibiotic doses.

The genetics of speciation: Insights from Fisher's geometric model

Research in speciation genetics has uncovered many robust patterns in intrinsic reproductive isolation, and fitness landscape models have been useful in interpreting these patterns. Here, we examine fitness landscapes based on Fisher's geometric model. Such landscapes are analogous to models of optimizing selection acting on quantitative traits, and have been widely used to study adaptation and the distribution of mutational effects. We show that, with a few modifications, Fisher's model can generate all of the major findings of introgression studies (including "speciation genes" with strong deleterious effects, complex epistasis and asymmetry), and the major patterns in overall hybrid fitnesses (including Haldane's Rule, the speciation clock, heterosis, hybrid breakdown, and male-female asymmetry in the F1). We compare our approach to alternative modeling frameworks that assign fitnesses to genotypes by identifying combinations of incompatible alleles. In some cases, the predictions are importantly different. For example, Fisher's model can explain conflicting empirical results about the rate at which incompatibilities accumulate with genetic divergence. In other cases, the predictions are identical. For example, the quality of reproductive isolation is little affected by the manner in which populations diverge.

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.

The Utility of Fisher's Geometric Model in Evolutionary Genetics

The accumulation of data on the genomic bases of adaptation has triggered renewed interest in theoretical models of adaptation. Among these models, Fisher Geometric Model (FGM) has received a lot of attention over the last two decades. FGM is based on a continuous multidimensional phenotypic landscape, but it is for the emerging properties of individual mutation effects that it is mostly used. Despite an apparent simplicity and a limited number of parameters, FGM integrates a full model of mutation and epistatic interactions that allows the study of both beneficial and deleterious mutations, and subsequently the fate of evolving populations. In this review, I present the different properties of FGM and the qualitative and quantitative support they have received from experimental evolution data. I later discuss how to estimate the different parameters of the model and outline some future directions to connect FGM and the molecular determinants of adaptation.

Environment determines epistatic patterns for a ssDNA virus

Despite the accumulation of substantial quantities of information about epistatic interactions among both deleterious and beneficial mutations in a wide array of experimental systems, neither consistent patterns nor causal explanations for these interactions have yet emerged. Furthermore, the effects of mutations depend on the environment in which they are characterized, implying that the environment may also influence epistatic interactions. Recent work with beneficial mutations for the single-stranded DNA bacteriophage ID11 demonstrated that interactions between pairs of mutations could be understood by means of a simple model that assumes that mutations have additive phenotypic effects and that epistasis arises through a nonlinear phenotype-fitness map with a single intermediate optimum. To determine whether such a model could also explain changes in epistatic patterns associated with changes in environment, we measured epistatic interactions for these same mutations under conditions for which we expected to find the wild-type ID11 at different distances from its phenotypic optimum by assaying fitnesses at three different temperatures: 33°, 37°, and 41°. Epistasis was present and negative under all conditions, but became more pronounced as temperature increased. We found that the additive-phenotypes model explained these patterns as changes in the parameters of the phenotype-fitness map, but that a model that additionally allows the phenotypes to vary across temperatures performed significantly better. Our results show that ostensibly complex patterns of fitness effects and epistasis across environments can be explained by assuming a simple structure for the genotype-phenotype relationship.

Current hypotheses for the evolution of sex and recombination

The evolution of sex is one of the most important and controversial problems in evolutionary biology. Although sex is almost universal in higher animals and plants, its inherent costs have made its maintenance difficult to explain. The most famous of these is the twofold cost of males, which can greatly reduce the fecundity of a sexual population, compared to a population of asexual females. Over the past century, multiple hypotheses, along with experimental evidence to support these, have been put forward to explain widespread costly sex. In this review, we outline some of the most prominent theories, along with the experimental and observational evidence supporting these. Historically, there have been 4 classes of theories: the ability of sex to fix multiple novel advantageous mutants (Fisher-Muller hypothesis); sex as a mechanism to stop the build-up of deleterious mutations in finite populations (Muller's ratchet); recombination creating novel genotypes that can resist infection by parasites (Red Queen hypothesis); and the ability of sex to purge bad genomes if deleterious mutations act synergistically (mutational deterministic hypothesis). Current theoretical and experimental evidence seems to favor the hypothesis that sex breaks down selection interference between new mutants, or it acts as a mechanism to shuffle genotypes in order to repel parasitic invasion. However, there is still a need to collect more data from natural populations and experimental studies, which can be used to test different hypotheses.

Hidden epistastic interactions can favour the evolution of sex and recombination

Deleterious mutations can have a strong influence on the outcome of evolution. The nature of this influence depends on how mutations combine together to affect fitness. “Negative epistasis” occurs when a new deleterious mutation causes the greatest loss in fitness in a genome that already contains many deleterious mutations. Negative epistasis is a key ingredient for some of the leading hypotheses regarding the evolution of recombination, the evolution of sex, and a variety of other phenomena. In general, laboratory studies have not supported the idea that negative epistasis is ubiquitous, and this has led to doubts about its importance in biological evolution. Here, we show that these experimental results may be misleading, because negative epistasis can produce evolutionary advantages for sex and recombination while simultaneously being almost impossible to detect using current experimental methods. Under asexual reproduction, such hidden epistasis influences evolutionary outcomes only if the fittest individuals are present in substantial numbers, while also forming a very small proportion of the population as a whole. This implies that our results for asexuals will apply only for very large populations, and also limits the extent of the fitness benefits that hidden epistasis can provide. Despite these caveats, our results show that the fitness consequences of sex and recombination cannot always be inferred from observable epistasis alone.

The consistency of beneficial fitness effects of mutations across diverse genetic backgrounds

Parallel and convergent evolution have been remarkably common observations in molecular adaptation but primarily in the context of the same genotype adapting to the same conditions. These phenomena therefore tell us about the stochasticity and limitations of adaptation. The limited data on convergence and parallelism in the adaptation of different genotypes conflict as to the importance of such events. If the effects of beneficial mutations are highly context dependent (i.e., if they are epistatic), different genotypes should adapt through different mutations. Epistasis for beneficial mutations has been investigated but mainly through measurement of interactions between individually beneficial mutations for the same genotype. We examine epistasis for beneficial mutations at a broader genetic scale by measuring the fitness effects of two mutations beneficial for the ssDNA bacteriophage ID11 in eight different, related genotypes showing 0.3-3.7% nucleotide divergence from ID11. We found no evidence for sign epistasis, but the mutations tended to have much smaller or no effects on fitness in the new genotypes. We found evidence for diminishing-returns epistasis; the effects were more beneficial for lower-fitness genotypes. The patterns of epistasis were not determined by phylogenetic relationships to the original genotype. To improve our understanding of the patterns of epistasis, we fit the data to a model in which each mutation had a constant, nonepistatic phenotypic effect across genotypes and the phenotype-fitness map had a single optimum. This model fit the data well, suggesting that epistasis for these mutations was due to nonlinearity in the phenotype-fitness mapping and that the likelihood of parallel evolution depends more on phenotype than on genotype.

What drives the evolution of hunter-gatherer subsistence technology? A reanalysis of the risk hypothesis with data from the Pacific Northwest

Recent studies have suggested that the decisions that hunter-gatherers make about the diversity and complexity of their subsistence toolkits are strongly affected by risk of resource failure. However, the risk proxies and samples employed in these studies are potentially problematic. With this in mind, we retested the risk hypothesis with data from hunter-gatherer populations who lived in the northwest coast and plateau regions of the Pacific Northwest during the early contact period. We focused on these populations partly because the northwest coast and plateau differ in ways that can be expected to lead to differences in risk, and partly because of the availability of data for a wide range of risk-relevant variables. Our analyses suggest that the plateau was a more risky environment than the northwest coast. However, the predicted differences in the number and complexity of the populations' subsistence tools were not observed. The discrepancy between our results and those of previous tests of the risk hypothesis is not due to methodological differences. Rather, it seems to reflect an important but hitherto unappreciated feature of the relationship between risk and toolkit structure, namely that the impact of risk is dependent on the scale of the risk differences among populations.

Descent with modification and the archaeological record

Recent years have seen major advances in our understanding of the way in which cultural transmission takes place and the factors that affect it. The theoretical foundations of those advances have been built by postulating the existence of a variety of different processes and deriving their consequences mathematically or by simulation. The operation of these processes in the real world can be studied through experiment and naturalistic observation. In contrast, archaeologists have an 'inverse problem'. For them the object of study is the residues of different behaviours represented by the archaeological record and the problem is to infer the microscale processes that produced them, a vital task for cultural evolution since this is the only direct record of past cultural patterns. The situation is analogous to that faced by population geneticists scanning large number of genes and looking for evidence of selection as opposed to drift, but more complicated for many reasons, not least the enormous variety of different forces that affect cultural transmission. This paper reviews the progress that has been made in inferring processes from patterns and the role of demography in those processes, together with the problems that have arisen.

A biophysical protein folding model accounts for most mutational fitness effects in viruses

Fitness effects of mutations fall on a continuum ranging from lethal to deleterious to beneficial. The distribution of fitness effects (DFE) among random mutations is an essential component of every evolutionary model and a mathematical portrait of robustness. Recent experiments on five viral species all revealed a characteristic bimodal-shaped DFE featuring peaks at neutrality and lethality. However, the phenotypic causes underlying observed fitness effects are still unknown and presumably, are thought to vary unpredictably from one mutation to another. By combining population genetics simulations with a simple biophysical protein folding model, we show that protein thermodynamic stability accounts for a large fraction of observed mutational effects. We assume that moderately destabilizing mutations inflict a fitness penalty proportional to the reduction in folded protein, which depends continuously on folding free energy (ΔG). Most mutations in our model affect fitness by altering ΔG, whereas based on simple estimates, ~10% abolish activity and are unconditionally lethal. Mutations pushing ΔG > 0 are also considered lethal. Contrary to neutral network theory, we find that, in mutation/selection/drift steady state, high mutation rates (m) lead to less stable proteins and a more dispersed DFE (i.e., less mutational robustness). Small population size (N) also decreases stability and robustness. In our model, a continuum of nonlethal mutations reduces fitness by ~2% on average, whereas ~10-35% of mutations are lethal depending on N and m. Compensatory mutations are common in small populations with high mutation rates. More broadly, we conclude that interplay between biophysical and population genetic forces shapes the DFE.

Genetic architecture and the evolution of sex

Theoretical investigations of the advantages of sex have tended to treat the genetic architecture of organisms as static and have not considered that genetic architecture might coevolve with reproductive mode. As a result, some potential advantages of sex may have been missed. Using a gene network model, we recently showed that recombination imposes selection for robustness to mutation and that negative epistasis can evolve as a by-product of this selection. These results motivated a detailed exploration of the mutational deterministic hypothesis, a hypothesis in which the advantage of sex depends critically on epistasis. We found that sexual populations do evolve higher mean fitness and lower genetic load than asexual populations at equilibrium, and, under moderate stabilizing selection and large population size, these equilibrium sexual populations resist invasion by asexuals. However, we found no evidence that these long- and short-term advantages to sex were explained by the negative epistasis that evolved in our experiments. The long-term advantage of sex was that sexual populations evolved a lower deleterious mutation rate, but this property was not sufficient to account for the ability of sexual populations to resist invasion by asexuals. The ability to resist asexual invasion was acquired simultaneously with an increase in recombinational robustness that minimized the cost of sex. These observations provide the first direct evidence that sexual reproduction does indeed select for conditions that favor its own maintenance. Furthermore, our results highlight the importance of considering a dynamic view of the genetic architecture to understand the evolution of sex and recombination.

What can we learn about the distribution of fitness effects of new mutations from DNA sequence data?

We investigate several questions concerning the inference of the distribution of fitness effects (DFE) of new mutations from the distribution of nucleotide frequencies in a population sample. If a fixed sequencing effort is available, we find that the optimum strategy is to sequence a modest number of alleles (approx. 10). If full genome information is available, the accuracy of parameter estimates increases as the number of alleles sequenced increases, but with diminishing returns. It is unlikely that the DFE for single genes can be reliably estimated in organisms such as humans and Drosophila, unless genes are very large and we sequence hundreds or perhaps thousands of alleles. We consider models involving several discrete classes of mutations in which the selection strength and density apportioned to each class can vary. Models with three classes fit almost as well as four class models unless many hundreds of alleles are sequenced. Large numbers of alleles need to be sequenced to accurately estimate the distribution's mean and variance. Estimating complex DFEs may therefore be difficult. Finally, we examine models involving slightly advantageous mutations. We show that the distribution of the absolute strength of selection is well estimated if mutations are assumed to be unconditionally deleterious.

Distribution of fitness effects caused by single-nucleotide substitutions in bacteriophage f1

Empirical knowledge of the fitness effects of mutations is important for understanding many evolutionary processes, yet this knowledge is often hampered by several sources of measurement error and bias. Most of these problems can be solved using site-directed mutagenesis to engineer single mutations, an approach particularly suited for viruses due to their small genomes. Here, we used this technique to measure the fitness effect of 100 single-nucleotide substitutions in the bacteriophage f1, a filamentous single-strand DNA virus. We found that approximately one-fifth of all mutations are lethal. Viable ones reduced fitness by 11% on average and were accurately described by a log-normal distribution. More than 90% of synonymous substitutions were selectively neutral, while those affecting intergenic regions reduced fitness by 14% on average. Mutations leading to amino acid substitutions had an overall mean deleterious effect of 37%, which increased to 45% for those changing the amino acid polarity. Interestingly, mutations affecting early steps of the infection cycle tended to be more deleterious than those affecting late steps. Finally, we observed at least two beneficial mutations. Our results confirm that high mutational sensitivity is a general property of viruses with small genomes, including RNA and single-strand DNA viruses infecting animals, plants, and bacteria.

The fitness effects of random mutations in single-stranded DNA and RNA bacteriophages

Mutational fitness effects can be measured with relatively high accuracy in viruses due to their small genome size, which facilitates full-length sequencing and genetic manipulation. Previous work has shown that animal and plant RNA viruses are very sensitive to mutation. Here, we characterize mutational fitness effects in single-stranded (ss) DNA and ssRNA bacterial viruses. First, we performed a mutation-accumulation experiment in which we subjected three ssDNA (ΦX174, G4, F1) and three ssRNA phages (Qβ, MS2, and SP) to plaque-to-plaque transfers and chemical mutagenesis. Genome sequencing and growth assays indicated that the average fitness effect of the accumulated mutations was similar in the two groups. Second, we used site-directed mutagenesis to obtain 45 clones of ΦX174 and 42 clones of Qβ carrying random single-nucleotide substitutions and assayed them for fitness. In ΦX174, 20% of such mutations were lethal, whereas viable ones reduced fitness by 13% on average. In Qβ, these figures were 29% and 10%, respectively. It seems therefore that high mutational sensitivity is a general property of viruses with small genomes, including those infecting animals, plants, and bacteria. Mutational fitness effects are important for understanding processes of fitness decline, but also of neutral evolution and adaptation. As such, these findings can contribute to explain the evolution of ssDNA and ssRNA viruses.

The fitness effects of mutations are the raw material for natural selection. It has been shown that point mutations typically have strongly deleterious effects in plant and animal RNA viruses, whereas cellular organisms are comparatively more robust. Here, we characterize the fitness effects of random mutations in DNA viruses and compare them with those found in RNA viruses, using six phage species of similar genome sizes. To achieve this goal, we introduced mutations by chemical and site-directed mutagenesis, identified the genetic changes by sequencing, and quantified their fitness effects using growth-rate assays. In all cases, mutations had a strong average impact on fitness. We conclude that mutational sensitivity is a general property of viruses with small genomes and discuss the evolutionary implications of these findings.

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.

The distribution of fitness effects of new mutations

The distribution of fitness effects (DFE) of new mutations is a fundamental entity in genetics that has implications ranging from the genetic basis of complex disease to the stability of the molecular clock. It has been studied by two different approaches: mutation accumulation and mutagenesis experiments, and the analysis of DNA sequence data. The proportion of mutations that are advantageous, effectively neutral and deleterious varies between species, and the DFE differs between coding and non-coding DNA. Despite these differences between species and genomic regions, some general principles have emerged: advantageous mutations are rare, and those that are strongly selected are exponentially distributed; and the DFE of deleterious mutations is complex and multi-modal.

The evolution of condition-dependent sex in the face of high costs

Facultatively sexual organisms often engage in sex more often when in poor condition. We show that such condition-dependent sex carries evolutionary advantages and can explain the evolution of sexual reproduction even when sex entails high costs. Specifically, we show that alleles promoting individuals of low fitness to have sex more often than individuals of high fitness spread through a population. Such alleles are more likely to segregate out of bad genetic backgrounds and onto good genetic backgrounds, where they tend to remain. This "abandon-ship" mechanism provides a plausible model for the evolution and maintenance of facultative sex.

Mean curvature versus normality: a comparison of two approximations of Fisher's geometrical model

Fisher's geometrical model amounts to a description of mutation and selection for individuals characterised by a number of quantitative traits. In the present work the fitness landscape is not assumed to be spherically symmetric, hence different points, i.e. phenotypes, on a surface of constant fitness generally have different curvatures. We investigate two different approximations of Fisher's geometrical model that have appeared in the literature. One approximation uses the average curvature of the fitness surface at the parental phenotype. The other approach is based on a normal approximation of a distribution associated with new mutations. Analytical results and simulations are used to compare the accuracy of the two approximations.

Fisher's geometrical model of evolutionary adaptation--beyond spherical geometry

Fisher's geometrical model of evolutionary adaptation has recently been used in a variety of contexts of interest to evolutionary biologists. The renewed interest in this model strongly motivates generalizations that make it a more realistic description of evolutionary adaptation. Previously, the distribution of mutant effects has, for analytical tractability, rather than biological realism, been taken as spherically symmetric. Here we substantially extend Fisher's model, by allowing a wider class of mutational distributions that incorporate mutational bias and more general deviations from spherical symmetry such as correlations between mutant effects. We also incorporate work on generalized fitness landscapes, thereby reducing the number of artificial assumptions underlying the model. The generalized model exhibits a substantially increased flexibility and a far richer underlying geometry. We find that the distribution characterizing selection coefficients of new mutations is expressed in terms of a number of geometrical invariants associated with mutation, selection and the parental phenotype.

Fisher's microscope and Haldane's ellipse

Fisher's geometrical model was introduced to study the phenotypic size of mutations contributing to adaptation. However, as pointed out by Haldane, the model involves a simplified picture of the action of natural selection, and this calls into question its generality. In particular, Fisher's model assumes that each trait contributes independently to fitness. Here, we show that Haldane's concerns may be incorporated into Fisher's model solely by allowing the intensity of selection to vary between traits. We further show that this generalization may be achieved by introducing a single, intuitively defined quantity that describes the phenotype prior to adaptation. Comparing the process of adaptation under the original and generalized models, we show that the generalization may bias results toward either larger or smaller mutations. The applicability of Fisher's model is then discussed.

The genetic theory of adaptation: a brief history

Theoretical studies of adaptation have exploded over the past decade. This work has been inspired by recent, surprising findings in the experimental study of adaptation. For example, morphological evolution sometimes involves a modest number of genetic changes, with some individual changes having a large effect on the phenotype or fitness. Here I survey the history of adaptation theory, focusing on the rise and fall of various views over the past century and the reasons for the slow development of a mature theory of adaptation. I also discuss the challenges that face contemporary theories of adaptation.

Mutation and selection in a large population

In this paper we study a large, but finite population, in which mutation and selection occur at a single genetic locus in a diploid organism. We provide theoretical results for the equilibrium allele frequencies, their variances and covariances and their equilibrium distribution, when the population size is larger than the reciprocal of the mean allelic mutation rate. We are also able to infer that the equilibrium distribution of allele frequencies takes the form of a constrained multivariate Gaussian distribution. Our results provide a rapid way of obtaining useful information in the case of complex mutation and selection schemes when the population size is large. We present numerical simulations to test the applicability of our theoretical formulations. The results of these simulations are in very reasonable agreement with the theoretical predictions.

The accumulation of deleterious mutations within the frozen niche variation hypothesis

The frozen niche variation hypothesis proposes that asexual clones exploit a fraction of a total resource niche available to the sexual population from which they arise. Differences in niche breadth may allow a period of coexistence between a sexual population and the faster reproducing asexual clones. Here, we model the longer term threat to the persistence of the sexual population from an accumulation of clonal diversity, balanced by the cost to the asexual population resulting from a faster rate of accumulation of deleterious mutations. We use Monte-Carlo simulations to quantify the interaction of niche breadth with accumulating deleterious mutations. These two mechanisms may act synergistically to prevent the extinction of the sexual population, given: (1) sufficient genetic variation, and consequently niche breadth, in the sexual population; (2) a relatively slow rate of accumulation of genetic diversity in the clonal population; (3) synergistic epistasis in the accumulation of deleterious mutations.

Modularity and the cost of complexity

In this work we consider the geometrical model of R. A. Fisher, in which individuals are characterized by a number of phenotypic characters under optimizing selection. Recent work on this model by H. A. Orr has demonstrated that as the number of characters increases, there is a significant reduction in the rate of adaptation. Orr has dubbed this a "cost of complexity." Although there is little evidence as to whether such a cost applies in the natural world, we suggest that the prediction is surprising, at least naively. With this in mind, we examine the robustness of Orr's prediction by modifiying the model in various ways that might reduce or remove the cost. In particular, we explore the suggestion that modular pleiotropy, in which mutations affect only a subset of the traits, could play an important role. We conclude that although modifications of the model can mitigate the cost to a limited extent, Orr's finding is robust.

Patterns of epistasis in RNA viruses: a review of the evidence from vaccine design

Epistasis results when the fitness effects of a mutation change depending on the presence or absence of other mutations in the genome. The predictions of many influential evolutionary hypotheses are determined by the existence and form of epistasis. One rich source of data on the interactions among deleterious mutations that has gone untapped by evolutionary biologists is the literature on the design of live, attenuated vaccine viruses. Rational vaccine design depends upon the measurement of individual and combined effects of deleterious mutations. In the current study, we have reviewed data from 29 vaccine-oriented studies using 14 different RNA viruses. Our analyses indicate that (1) no consistent tendency towards a particular form of epistasis exists across RNA viruses and (2) significant interactions among groups of mutations within individual viruses occur but are not common. RNA viruses are significant pathogens of human disease, and are tractable model systems for evolutionary studies--we discuss the relevance of our findings in both contexts.

Facultative sexual reproduction under frequency-dependent selection on a single locus

The evolution of a facultative sexual strategy that simultaneously produced sexual and asexual individuals was studied theoretically, under negative frequency-dependence of fitness. The organism was considered to be diploid, characterized by two loci concerning fitness and determining sexual strategy, between which a certain degree of linkage existed. The locus concerning fitness was assumed to involve two alleles, resulting in three genotypes, the relative fitness of an individual being defined by a decreasing function of frequency of its own genotype on this locus in the population. The sexual reproductive strategy was considered to be determined by three alleles; asexual, obligate sexual and facultative sexual. Simulations under various linkages between loci and level of frequency dependence of fitness showed that a facultative sexual strategy was generally able to invade and increase in the population. In particular, when the level of frequency dependence was high to some degree, the facultative strain producing many sexual individuals tended to exclusively occupy the population. Namely, the frequency-dependent selection resulted in a predominance of obligate sexual strategy over asexual strategy, simultaneously causing a subordination of the former to the facultative sexual strategy. This indicated that the evolution of sex should be considered carefully with respect to the possibility of invasion of facultative sex.

Gene flow between arrhenotokous and thelytokous populations of Venturia canescens (Hymenoptera)

In the solitary parasitoid wasp Venturia canescens both arrhenotokously (sexual) and thelytokously (parthenogenetical) reproducing individuals occur sympatrically. We found in the laboratory that thelytokous wasps are able to mate, receive and use sperm of arrhenotokous males. Using nuclear (amplified fragment length polymorphism, virus-like protein) and mitochondrial (restriction fragment length polymorphism) markers, we show the occurrence of gene flow from the arrhenotokous to the thelytokous mode in the field. Our results reinforce the paradox of sex in this species.