Epistasis, pleiotropy, and the mutation load in sexual and asexual populations

The divergence of mean phenotypes under persistent Gaussian selection

Although multigenic traits are often assumed to be under some form of stabilizing selection, numerous aspects of the population-genetic environment can cause mean phenotypes to deviate from presumed optima, often in ways that effectively transform the fitness landscape to one of directional selection. Focusing on an asexual population, we consider the ways in which such deviations scale with the relative power of selection and genetic drift, the number of linked genomic sites, the magnitude of mutation bias, and the location of optima with respect to possible genotypic space. Even in the absence of mutation bias, mutation will influence evolved mean phenotypes unless the optimum happens to coincide exactly with the mean expected under neutrality. In the case of directional mutation bias and large numbers of selected sites, effective population sizes (Ne) can be dramatically reduced by selective interference effects, leading to further mismatches between phenotypic means and optima. Situations in which the optimum is outside or near the limits of possible genotypic space (e.g. a half-Gaussian fitness function) can lead to particularly pronounced gradients of phenotypic means with respect to Ne, but such gradients can also occur when optima are well within the bounds of attainable phenotypes. These results help clarify the degree to which mean phenotypes can vary among populations experiencing identical mutation and selection pressures but differing in Ne, and yield insight into how the expected scaling relationships depend on the underlying features of the genetic system.

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.

The evolution of sex along an environmental gradient

Although temporally changing environments generally favor sex and recombination, the effects of spatial environmental heterogeneity have been less explored. In this article, we use a classical model of adaptation along with an environmental gradient to study the selective forces acting on reproductive mode evolution in the central and marginal parts of the distribution range of a species. The model considers a polygenic trait under stabilizing selection (the optimal trait value changing across space) and includes a demographic component imposing range limits. The results show that in the central part of the range (where populations are well adapted), recombination tends to increase the mean fitness of offspring in regimes where drift is sufficiently strong (generating a benefit for sex), while it has the opposite effect when the effect of drift stays negligible. However, these effects remain weak and are easily overwhelmed by slight intrinsic fitness differences between sexuals and asexuals. In agreement with previous results, asexuality may be favored in marginal populations, as it can preserve adaptation to extreme conditions. However, a substantial advantage of asexuality is possible only in conditions maintaining a strong maladaptation of sexuals at range limits (high effective environmental gradient, weak selection at loci coding for the trait).

On Deleterious Mutations in Perennials: Inbreeding Depression, Mutation Load, and Life-History Evolution

AbstractIn angiosperms, perennials typically present much higher levels of inbreeding depression than annuals. One hypothesis to explain this pattern stems from the observation that inbreeding depression is expressed across multiple life stages in angiosperms. It posits that increased inbreeding depression in more long-lived species could be explained by differences in the way mutations affect fitness, through the life stages at which they are expressed. In this study, we investigate this hypothesis. We combine a physiological growth model and multilocus population genetics approaches to describe a full genotype-to-phenotype-to-fitness map. We study the behavior of mutations affecting growth or survival and explore their consequences in terms of inbreeding depression and mutation load. Although our results agree with empirical data only within a narrow range of conditions, we argue that they may point us toward the type of traits capable of generating high inbreeding depression in long-lived species-that is, traits under sufficiently strong selection, on which selection decreases sharply as life expectancy increases. Then we study the role deleterious mutations maintained at mutation-selection balance may play in the joint evolution of growth and survival strategies.

Epistasis, inbreeding depression, and the evolution of self-fertilization

Inbreeding depression resulting from partially recessive deleterious alleles is thought to be the main genetic factor preventing self-fertilizing mutants from spreading in outcrossing hermaphroditic populations. However, deleterious alleles may also generate an advantage to selfers in terms of more efficient purging, while the effects of epistasis among those alleles on inbreeding depression and mating system evolution remain little explored. In this article, we use a general model of selection to disentangle the effects of different forms of epistasis (additive-by-additive, additive-by-dominance, and dominance-by-dominance) on inbreeding depression and on the strength of selection for selfing. Models with fixed epistasis across loci, and models of stabilizing selection acting on quantitative traits (generating distributions of epistasis) are considered as special cases. Besides its effects on inbreeding depression, epistasis may increase the purging advantage associated with selfing (when it is negative on average), while the variance in epistasis favors selfing through the generation of linkage disequilibria that increase mean fitness. Approximations for the strengths of these effects are derived, and compared with individual-based simulation results.

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.

Digest: How mutational bias could explain the maintenance of sex

How does mutational bias affect the fitness of populations under different reproductive strategies? Vanhoenacker et al. (2018) found that mutational bias can greatly reduce the mean fitness of asexual populations, offering a new hypothesis for the maintenance of sex.

The Nonstationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation

Various models describe asexual evolution by mutation, selection, and drift. Some focus directly on fitness, typically modeling drift but ignoring or simplifying both epistasis and the distribution of mutation effects (traveling wave models). Others follow the dynamics of quantitative traits determining fitness (Fisher's geometric model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift. In all cases, predictions are typically obtained in high or low mutation rate limits and for long-term stationary regimes, thus losing information on transient behaviors and the effect of initial conditions. Here, we connect fitness-based and trait-based models into a single framework, and seek explicit solutions even away from stationarity. The expected fitness distribution is followed over time via its cumulant generating function, using a deterministic approximation that neglects drift. In several cases, explicit trajectories for the full fitness distribution are obtained for arbitrary mutation rates and standing variance. For nonepistatic mutations, especially with beneficial mutations, this approximation fails over the long term but captures the early dynamics, thus complementing stationary stochastic predictions. The approximation also handles several diminishing returns epistasis models (e.g., with an optimal genotype); it can be applied at and away from equilibrium. General results arise at equilibrium, where fitness distributions display a "phase transition" with mutation rate. Beyond this phase transition, in Fisher's geometric model, the full trajectory of fitness and trait distributions takes a simple form; robust to the details of the mutant phenotype distribution. Analytical arguments are explored regarding why and when the deterministic approximation applies.

The Fitness Effects of Spontaneous Mutations Nearly Unseen by Selection in a Bacterium with Multiple Chromosomes

Mutation accumulation (MA) experiments employ the strategy of minimizing the population size of evolving lineages to greatly reduce effects of selection on newly arising mutations. Thus, most mutations fix within MA lines independently of their fitness effects. This approach, more recently combined with genome sequencing, has detailed the rates, spectra, and biases of different mutational processes. However, a quantitative understanding of the fitness effects of mutations virtually unseen by selection has remained an untapped opportunity. Here, we analyzed the fitness of 43 sequenced MA lines of the multi-chromosome bacterium Burkholderia cenocepacia that had each undergone 5554 generations of MA and accumulated an average of 6.73 spontaneous mutations. Most lineages exhibited either neutral or deleterious fitness in three different environments in comparison with their common ancestor. The only mutational class that was significantly overrepresented in lineages with reduced fitness was the loss of the plasmid, though nonsense mutations, missense mutations, and coding insertion-deletions were also overrepresented in MA lineages whose fitness had significantly declined. Although the overall distribution of fitness effects was similar between the three environments, the magnitude and even the sign of the fitness of a number of lineages changed with the environment, demonstrating that the fitness of some genotypes was environmentally dependent. These results present an unprecedented picture of the fitness effects of spontaneous mutations in a bacterium with multiple chromosomes and provide greater quantitative support for the theory that the vast majority of spontaneous mutations are neutral or deleterious.

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.

Accelerating Mutational Load Is Not Due to Synergistic Epistasis or Mutator Alleles in Mutation Accumulation Lines of Yeast

Much of our knowledge about the fitness effects of new mutations has been gained from mutation accumulation (MA) experiments. Yet the fitness effect of single mutations is rarely measured in MA experiments. This raises several issues, notably for inferring epistasis for fitness. The acceleration of fitness decline in MA lines has been taken as evidence for synergistic epistasis, but establishing the role of epistasis requires measuring the fitness of genotypes carrying known numbers of mutations. Otherwise, accelerating fitness loss could be explained by increased genetic mutation rates. Here we segregated mutations accumulated over 4800 generations in haploid and diploid MA lines of the yeast Saccharomyces cerevisiae. We found no correspondence between an accelerated fitness decline and synergistic epistasis among deleterious mutations in haploid lines. Pairs of mutations showed no overall epistasis. Furthermore, several lines of evidence indicate that genetic mutation rates did not increase in the MA lines. Crucially, segregant fitness analyses revealed that MA accelerated in both haploid and diploid lines, even though the fitness of diploid lines was nearly constant during the MA experiment. This suggests that the accelerated fitness decline in haploids was caused by cryptic environmental factors that increased mutation rates in all lines during the last third of the lines' transfers. In addition, we provide new estimates of deleterious mutation rates, including lethal mutations, and highlight that nearly all the mutational load we observed was due to one or two mutations having a large effect on fitness.

What happens after inbreeding avoidance? Inbreeding by rejected relatives and the inclusive fitness benefit of inbreeding avoidance

Avoiding inbreeding, and therefore avoiding inbreeding depression in offspring fitness, is widely assumed to be adaptive in systems with biparental reproduction. However, inbreeding can also confer an inclusive fitness benefit stemming from increased relatedness between parents and inbred offspring. Whether or not inbreeding or avoiding inbreeding is adaptive therefore depends on a balance between inbreeding depression and increased parent-offspring relatedness. Existing models of biparental inbreeding predict threshold values of inbreeding depression above which males and females should avoid inbreeding, and predict sexual conflict over inbreeding because these thresholds diverge. However, these models implicitly assume that if a focal individual avoids inbreeding, then both it and its rejected relative will subsequently outbreed. We show that relaxing this assumption of reciprocal outbreeding, and the assumption that focal individuals are themselves outbred, can substantially alter the predicted thresholds for inbreeding avoidance for focal males. Specifically, the magnitude of inbreeding depression below which inbreeding increases a focal male’s inclusive fitness increases with increasing depression in the offspring of a focal female and her alternative mate, and it decreases with increasing relatedness between a focal male and a focal female’s alternative mate, thereby altering the predicted zone of sexual conflict. Furthermore, a focal male’s inclusive fitness gain from avoiding inbreeding is reduced by indirect opportunity costs if his rejected relative breeds with another relative of his. By demonstrating that variation in relatedness and inbreeding can affect intra- and inter-sexual conflict over inbreeding, our models lead to novel predictions for family dynamics. Specifically, parent-offspring conflict over inbreeding might depend on the alternative mates of rejected relatives, and male-male competition over inbreeding might lead to mixed inbreeding strategies. Making testable quantitative predictions regarding inbreeding strategies occurring in nature will therefore require new models that explicitly capture variation in relatedness and inbreeding among interacting population members.

The efficiency of close inbreeding to reduce genetic adaptation to captivity

Although ex situ conservation is indispensable for thousands of species, captive breeding is associated with negative genetic changes: loss of genetic variance and genetic adaptation to captivity that is deleterious in the wild. We used quantitative genetic individual-based simulations to model the effect of genetic management on the evolution of a quantitative trait and the associated fitness of wild-born individuals that are brought to captivity. We also examined the feasibility of the breeding strategies under a scenario of a large number of loci subject to deleterious mutations. We compared two breeding strategies: repeated half-sib mating and a method of minimizing mean coancestry (referred to as gc/mc). Our major finding was that half-sib mating is more effective in reducing genetic adaptation to captivity than the gc/mc method. Moreover, half-sib mating retains larger allelic and adaptive genetic variance. Relative to initial standing variation, the additive variance of the quantitative trait increased under half-sib mating during the sojourn in captivity. Although fragmentation into smaller populations improves the efficiency of the gc/mc method, half-sib mating still performs better in the scenarios tested. Half-sib mating shows two caveats that could mitigate its beneficial effects: low heterozygosity and high risk of extinction when populations are of low fecundity and size and one of the following conditions are met: (i) the strength of selection in captivity is comparable with that in the wild, (ii) deleterious mutations are numerous and only slightly deleterious. Experimental validation of half-sib mating is therefore needed for the advancement of captive breeding programs.

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.