Adaptive and maladaptive genetic diversity in small populations: Insights from the Brook Charr (Salvelinus fontinalis) case study

Investigating the relative importance of neutral versus selective processes governing the accumulation of genetic variants is a key goal in both evolutionary and conservation biology. This is particularly true in the context of small populations, where genetic drift can counteract the effect of selection. Using Brook Charr (Salvelinus fontinalis) from Québec, Canada, as a case study, we investigated the importance of demographic versus selective processes governing the accumulation of both adaptive and maladaptive mutations in closed versus open and connected populations to assess gene flow effect. This was achieved by using 14,779 high‐quality filtered SNPs genotyped among 1,416 fish representing 50 populations from three life history types: lacustrine (closed populations), riverine and anadromous (connected populations). Using the PROVEAN algorithm, we observed a considerable accumulation of putative deleterious mutations across populations. The absence of correlation between the occurrence of putatively beneficial or deleterious mutations and local recombination rate supports the hypothesis that genetic drift might be the main driver of the accumulation of such variants. However, despite a lower genetic diversity observed in lacustrine than in riverine or anadromous populations, lacustrine populations do not exhibit more deleterious mutations than the two other history types, suggesting that the negative effect of genetic drift in lacustrine populations may be mitigated by that of relaxed purifying selection. Moreover, we also identified genomic regions associated with anadromy, as well as an overrepresentation of transposable elements associated with variation in environmental variables, thus supporting the importance of transposable elements in adaptation.     

Fitness effects of fixed beneficial mutations in microbial populations

Beneficial mutations are intuitively relevant to understanding adaptation, yet not all beneficial mutations are of consequence to the long-term evolutionary outcome of adaptation. Many beneficial mutations-mostly those of small effect-are lost due either to (1) genetic drift or to (2) competition among clones carrying different beneficial mutations, a phenomenon called the "Hill-Robertson effect" for sexual populations and "clonal interference" for asexual populations. Competition among clones becomes more prevalent with increasing genetic linkage and increasing population size, and it is thus generally characteristic of microbial populations. Together, these two phenomena suggest that only those beneficial mutations of large fitness effect should achieve fixation, despite the fact that most beneficial mutations produced are predicted to have very small fitness effects. Here, we confirm this prediction-both empirically and theoretically-by showing that fitness effects of fixed beneficial mutations follow a distribution whose mode is positive.     

Patterns of inbreeding depression and architecture of the load in subdivided populations

Inbreeding depression is a general phenomenon that is due mainly to recessive deleterious mutations, the so-called mutation load. It has been much studied theoretically. However, until very recently, population structure has not been taken into account, even though it can be an important factor in the evolution of populations. Population subdivision modifies the dynamics of deleterious mutations because the outcome of selection depends on processes both within populations (selection and drift) and between populations (migration). Here, we present a general model that permits us to gain insight into patterns of inbreeding depression, heterosis, and the load in subdivided populations. We show that they can be interpreted with reference to single-population theory, using an appropriate local effective population size that integrates the effects of drift, selection, and migration. We term this the "effective population size of selection" (NS(e)). For the infinite island model, for example, it is equal to NS(e) = N1 + m/hs, where N is the local population size, m the migration rate, and h and s the dominance and selection coefficients of deleterious mutation. Our results have implications for the estimation and interpretation of inbreeding depression in subdivided populations, especially regarding conservation issues. We also discuss the possible effects of migration and subdivision on the evolution of mating systems.     

Interfering waves of adaptation promote spatial mixing

A fundamental problem of asexual adaptation is that beneficial substitutions are not efficiently accumulated in large populations: Beneficial mutations often go extinct because they compete with one another in going to fixation. It has been argued that such clonal interference may have led to the evolution of sex and recombination in well-mixed populations. Here, we study clonal interference, and mechanisms of its mitigation, in an evolutionary model of spatially structured populations with uniform selection pressure. Clonal interference is much more prevalent with spatial structure than without, due to the slow wave-like spread of beneficial mutations through space. We find that the adaptation speed of asexuals saturates when the linear habitat size exceeds a characteristic interference length, which becomes shorter with smaller migration and larger mutation rate. The limiting speed is proportional to μ(1/2) and μ(1/3) in linear and planar habitats, respectively, where the mutational supply μ is the product of mutation rate and local population density. This scaling and the existence of a speed limit should be amenable to experimental tests as they fall far below predicted adaptation speeds for well-mixed populations (that scale as the logarithm of population size). Finally, we show that not only recombination, but also long-range migration is a highly efficient mechanism of relaxing clonal competition in structured populations. Our conservative estimates of the interference length predict prevalent clonal interference in microbial colonies and biofilms, so clonal competition should be a strong driver of both genetic and spatial mixing in those contexts.     

The Population Genetics of Adaptation: Multiple Substitutions on a Smooth Fitness Landscape

Much recent work in the theoretical study of adaptation has focused on the so-called strong selection–weak mutation (SSWM) limit, wherein adaptation is due to new mutations of definite selective advantage. This work, in turn, has focused on the first step (substitution) during adaptive evolution. Here we extend this theory to allow multiple steps during adaptation. We find analytic solutions to the probability that adaptation follows a certain path during evolution as well as the probability that adaptation arrives at a given genotype regardless of the path taken. We also consider the probability of parallel adaptation and the proportion of the total increase in fitness caused by the first substitution. Our key assumption is that there is no epistasis among beneficial mutations.RECENTLY, there has been a great deal of interest in the genetics of adaptation. While much of this interest has focused on experimental studies of adaptive evolution (e.g., Lenski and Travisano 1994; Holder and Bull 2001; Rokyta et al. 2005; Weinreich et al. 2006; Betancourt 2009), there has also been considerable interest in theoretical analyses of adaptation (reviewed in Gillespie 1991; Orr 2005; Joyce et al. 2008), a topic that was, until recently, surprisingly neglected.These theoretical studies have considered a number of questions: What does the distribution of fitness effects among new beneficial mutations look like? What does the distribution of fitness effects among fixed beneficial mutations look like? How does clonal interference among competing mutations distort this distribution? Do early substitutions generally have larger effects on fitness than later ones? And how likely is it that independently evolving populations substitute the same beneficial mutations?A number of approaches have been taken to these and similar questions, including analysis of phenotypic and DNA sequence-based models. Among sequence-based studies, a good deal of attention has focused on the so-called strong selection–weak mutation (SSWM) scenario, introduced by Gillespie (1983, 1984, 1991). Under this scenario, selection is strong enough that mutations are either definitely beneficial or definitely deleterious and neutral mutations are not allowed. Also, mutation is weak enough that the population is, at any point in time, essentially composed of a single wild-type DNA sequence and mutations are rare enough that double mutants and the complications of clonal interference (Gerrish and Lenski 1998) can be ignored. Adaptation in the SSWM domain thus involves the appearance and substitution of new mutations. It is usually assumed that adaptation occurs in response to a sudden change in the environment. Recurrent mutation from the current (and now somewhat maladapted) wild-type allele produces different beneficial mutations. While most of these new mutations are lost accidentally by genetic drift each time they appear, one mutation will ultimately escape stochastic loss and be substituted. At this point, the population arrives at a new wild-type sequence and the process begins anew. Adaptation thus features the stepwise substitution of single mutations.Even in this simple SSWM scenario, mathematical analysis of adaptation has proved difficult. The most important results were derived by Gillespie (1983, 1984, 1991) himself. Given recurrent mutation from a wild-type DNA sequence to m different beneficial mutations, Gillespie calculated the probability that natural selection would, at the next substitution event, fix any particular one of these mutations. His result, as explained in more detail below, revealed that the probability that a particular mutation is fixed at the next event depends on the magnitude of its selective advantage relative to those of all available beneficial mutations. Gillespie was thus able to write down transition probabilities for the next substitution event in adaptation. As empirical studies of adaptation accumulate, it is of interest to examine the predictability of those patterns observed when populations adapt via multiple substitutions.Here we extend Gillespie''s analysis to allow multiple substitution events. Specifically, we show how one can calculate the probability that a population will, after the substitution of several beneficial mutations, arrive at a particular genotype. We also calculate the probability that evolution takes a particular path to this genotype, as well as the probability that two independently evolving populations adapt in parallel, arriving at the same genotype after multiple substitutions. One of our results was derived previously by Weinreich et al. (2006). For completeness and clarity we briefly rederive his result here. As expected, we find that Gillespie''s one-substitution results become special cases of our multiple-substitution results.As emphasized below, our key assumption is that the beneficial effects of mutations are independent; i.e., no epistasis occurs among mutations. As we also emphasize, our analysis proves more difficult mathematically than Gillespie''s because the study of multiple substitutions given independent fitness effects necessarily involves a complex dependence on history: the identity of mutations fixed late during adaptation depends on the identity of mutations fixed earlier.     

Natural selection, larval dispersal, and the geography of phenotype in the sea

Populations evolve generalist, specialist, and plastic strategies in response to environmental heterogeneity. Describing such within-species variation in phenotype and how it arises is central to understanding a variety of ecological and evolutionary topics. The literature on phenotypic differences among populations is highly biased; for every one article published on a marine species, at least 10 articles are published on a terrestrial species and eight focus on terrestrial plants. Here, I outline what we know from the marine literature about geographic variation in phenotype in the sea, with a principal focus on local adaptation. The theory of environmental "grain" predicts that the most likely evolutionary response (e.g., local adaptation, phenotypic plasticity, generalism, and balanced polymorphism) depends on the spatial scale of environmental variation relative to the distance that an organism disperses. Consistent with these predictions, phenotypic plasticity is stronger among invertebrates with geographically broad dispersal versus restricted dispersal (i.e., planktonic-dispersers versus direct-developers). However, contrary to predictions, the relative frequency, and spatial scale of local adaptation is not consistently greater among direct-developers relative to planktonic disperers. This indicates that the likelihood of local adaptation depends on other organismal or environmental traits. Two of the most vexing issues that remain include (1) predicting the extent to which barriers to dispersal are a cause versus consequence of phenotypic differentiation and (2) delineating the relative importance of evolutionary forces that favor or impede local adaptation. Understanding the mechanistic basis of the geography of phenotypic differences, or phenogeography, has gained recent momentum because of a need to predict impacts of global climatic change, anthropogenic disturbances, and dispersal of organisms to non-native habitats.     

The influence of deleterious mutations on adaptation in asexual populations

We study the dynamics of adaptation in asexual populations that undergo both beneficial and deleterious mutations. In particular, how the deleterious mutations affect the fixation of beneficial mutations was investigated. Using extensive Monte Carlo simulations, we find that in the "strong-selection weak mutation (SSWM)" regime or in the "clonal interference (CI)" regime, deleterious mutations rarely influence the distribution of "selection coefficients of the fixed mutations (SCFM)"; while in the "multiple mutations" regime, the accumulation of deleterious mutations would lead to a decrease in fitness significantly. We conclude that the effects of deleterious mutations on adaptation depend largely on the supply of beneficial mutations. And interestingly, the lowest adaptation rate occurs for a moderate value of selection coefficient of deleterious mutations.     

The evolution of mutation rates: separating causes from consequences

Natural selection can adjust the rate of mutation in a population by acting on allelic variation affecting processes of DNA replication and repair. Because mutation is the ultimate source of the genetic variation required for adaptation, it can be appealing to suppose that the genomic mutation rate is adjusted to a level that best promotes adaptation. Most mutations with phenotypic effects are harmful, however, and thus there is relentless selection within populations for lower genomic mutation rates. Selection on beneficial mutations can counter this effect by favoring alleles that raise the mutation rate, but the effect of beneficial mutations on the genomic mutation rate is extremely sensitive to recombination and is unlikely to be important in sexual populations. In contrast, high genomic mutation rates can evolve in asexual populations under the influence of beneficial mutations, but this phenomenon is probably of limited adaptive significance and represents, at best, a temporary reprieve from the continual selection pressure to reduce mutation. The physiological cost of reducing mutation below the low level observed in most populations may be the most important factor in setting the genomic mutation rate in sexual and asexual systems, regardless of the benefits of mutation in producing new adaptive variation. Maintenance of mutation rates higher than the minimum set by this "cost of fidelity" is likely only under special circumstances.     

How does adaptation sweep through the genome? Insights from long-term selection experiments

A major goal in evolutionary biology is to understand the origins and fates of adaptive mutations. Natural selection may act to increase the frequency of de novo beneficial mutations, or those already present in the population as standing genetic variation. These beneficial mutations may ultimately reach fixation in a population, or they may stop increasing in frequency once a particular phenotypic state has been achieved. It is not yet well understood how different features of population biology, and/or different environmental circumstances affect these adaptive processes. Experimental evolution is a promising technique for studying the dynamics of beneficial alleles, as populations evolving in the laboratory experience natural selection in a replicated, controlled manner. Whole-genome sequencing, regularly obtained over the course of sustained laboratory selection, could potentially reveal insights into the mutational dynamics that most likely occur in natural populations under similar circumstances. To date, only a few evolution experiments for which whole-genome data are available exist. This review describes results from these resequenced laboratory-selected populations, in systems with and without sexual recombination. In asexual systems, adaptation from new mutations can be studied, and results to date suggest that the complete, unimpeded fixation of these mutations is not always observed. In sexual systems, adaptation from standing genetic variation can be studied, and in the admittedly few examples we have, the complete fixation of standing variants is not always observed. To date, the relative frequency of adaptation from new mutations versus standing variation has not been tested using a single experimental system, but recent studies using Caenorhabditis elegans and Saccharomyces cerevisiae suggest that this a realistic future goal.     

Diminishing returns of population size in the rate of RNA virus adaptation

Whenever an asexual viral population evolves by adapting to new environmental conditions, beneficial mutations, the ultimate cause of adaptation, are randomly produced and then fixed in the population. The larger the population size and the higher the mutation rate, the more beneficial mutations can be produced per unit time. With the usually high mutation rate of RNA viruses and in a large enough population, several beneficial mutations could arise at the same time but in different genetic backgrounds, and if the virus is asexual, they will never be brought together through recombination. Thus, the best of these genotypes must outcompete each other on their way to fixation. This competition among beneficial mutations has the effect of slowing the overall rate of adaptation. This phenomenon is known as clonal interference. Clonal interference predicts a speed limit for adaptation as the population size increases. In the present report, by varying the size of evolving vesicular stomatitis virus populations, we found evidence clearly demonstrating this speed limit and thus indicating that clonal interference might be an important factor modulating the rate of adaptation to an in vitro cell system. Several evolutionary and epidemiological implications of the clonal interference model applied to RNA viruses are discussed.     

Beneficial fitness effects are not exponential for two viruses

The distribution of fitness effects for beneficial mutations is of paramount importance in determining the outcome of adaptation. It is generally assumed that fitness effects of beneficial mutations follow an exponential distribution, for example, in theoretical treatments of quantitative genetics, clonal interference, experimental evolution, and the adaptation of DNA sequences. This assumption has been justified by the statistical theory of extreme values, because the fitnesses conferred by beneficial mutations should represent samples from the extreme right tail of the fitness distribution. Yet in extreme value theory, there are three different limiting forms for right tails of distributions, and the exponential describes only those of distributions in the Gumbel domain of attraction. Using beneficial mutations from two viruses, we show for the first time that the Gumbel domain can be rejected in favor of a distribution with a right-truncated tail, thus providing evidence for an upper bound on fitness effects. Our data also violate the common assumption that small-effect beneficial mutations greatly outnumber those of large effect, as they are consistent with a uniform distribution of beneficial effects.     

Adaptation in sexuals vs. asexuals: clonal interference and the Fisher-Muller model

Fisher and Muller's theory that recombination speeds adaptation by eliminating competition among beneficial mutations has proved a popular explanation for the advantage of sex. Recent theoretical studies have attempted to quantify the speed of adaptation under the Fisher-Muller model, partly in an attempt to understand the role of "clonal interference" in microbial experimental evolution. We reexamine adaptation in sexuals vs. asexuals, using a model of DNA sequence evolution. In this model, a modest number of sites can mutate to beneficial alleles and the fitness effects of these mutations are unequal. We study (1) transition probabilities to different beneficial mutations; (2) waiting times to the first and the last substitutions of beneficial mutations; and (3) trajectories of mean fitness through time. We find that some of these statistics are surprisingly similar between sexuals and asexuals. These results highlight the importance of the choice of substitution model in assessing the Fisher-Muller advantage of sex.     

Genetic load in subdivided populations: interactions between the migration rate, the size and the number of subpopulations

We assess the relative importance of migration rate, size and number of subpopulations on the genetic load of subdivided populations. Using diffusion approximations, we show that in most cases subdivision has detrimental effects on fitness. Moreover, our results suggest that fitness increases with subpopulation size, so that for the same total population size, genetic load is relatively lower when there are a small number of large subpopulations. Using elasticity analysis, we show that the size of the subpopulations appears to be the parameter that most strongly determines genetic load. interconnecting subpopulations via migration would also be of importance for population fitness when subpopulations are small and gene flow is low. Interestingly, the number of subpopulations has minor influence on genetic load except for the case of both very slightly deleterious mutations and small subpopulations. Elasticities decrease as the magnitude of deleterious effects increases. In other words, population structure does not matter for very deleterious alleles, but strongly affects fitness for slightly deleterious alleles.     

Clonal interference and the periodic selection of new beneficial mutations in Escherichia coli

The conventional model of adaptation in asexual populations implies sequential fixation of new beneficial mutations via rare selective sweeps that purge all variation and preserve the clonal genotype. However, in large populations multiple beneficial mutations may co-occur, causing competition among them, a phenomenon called "clonal interference." Clonal interference is thus expected to lead to longer fixation times and larger fitness effects of mutations that ultimately become fixed, as well as to a genetically more diverse population. Here, we study the significance of clonal interference in populations consisting of mixtures of differently marked wild-type and mutator strains of Escherichia coli that adapt to a minimal-glucose environment for 400 generations. We monitored marker frequencies during evolution and measured the competitive fitness of random clones from each marker state after evolution. The results demonstrate the presence of multiple beneficial mutations in these populations and slower and more erratic invasion of mutants than expected by the conventional model, showing the signature of clonal interference. We found that a consequence of clonal interference is that fitness estimates derived from invasion trajectories were less than half the magnitude of direct estimates from competition experiments, thus revealing fundamental problems with this fitness measure. These results force a reevaluation of the conventional model of periodic selection for asexual microbes.     

The rate of fitness-valley crossing in sexual populations

Biological traits result in part from interactions between different genetic loci. This can lead to sign epistasis, in which a beneficial adaptation involves a combination of individually deleterious or neutral mutations; in this case, a population must cross a "fitness valley" to adapt. Recombination can assist this process by combining mutations from different individuals or retard it by breaking up the adaptive combination. Here, we analyze the simplest fitness valley, in which an adaptation requires one mutation at each of two loci to provide a fitness benefit. We present a theoretical analysis of the effect of recombination on the valley-crossing process across the full spectrum of possible parameter regimes. We find that low recombination rates can speed up valley crossing relative to the asexual case, while higher recombination rates slow down valley crossing, with the transition between the two regimes occurring when the recombination rate between the loci is approximately equal to the selective advantage provided by the adaptation. In large populations, if the recombination rate is high and selection against single mutants is substantial, the time to cross the valley grows exponentially with population size, effectively meaning that the population cannot acquire the adaptation. Recombination at the optimal (low) rate can reduce the valley-crossing time by up to several orders of magnitude relative to that in an asexual population.     

Long-term experimental evolution in Escherichia coli. XII. DNA topology as a key target of selection

The genetic bases of adaptation are being investigated in 12 populations of Escherichia coli, founded from a common ancestor and serially propagated for 20,000 generations, during which time they achieved substantial fitness gains. Each day, populations alternated between active growth and nutrient exhaustion. DNA supercoiling in bacteria is influenced by nutritional state, and DNA topology helps coordinate the overall pattern of gene expression in response to environmental changes. We therefore examined whether the genetic controls over supercoiling might have changed during the evolution experiment. Parallel changes in topology occurred in most populations, with the level of DNA supercoiling increasing, usually in the first 2000 generations. Two mutations in the topA and fis genes that control supercoiling were discovered in a population that served as the focus for further investigation. Moving the mutations, alone and in combination, into the ancestral background had an additive effect on supercoiling, and together they reproduced the net change in DNA topology observed in this population. Moreover, both mutations were beneficial in competition experiments. Clonal interference involving other beneficial DNA topology mutations was also detected. These findings define a new class of fitness-enhancing mutations and indicate that the control of DNA supercoiling can be a key target of selection in evolving bacterial populations.     

Genetic variation and the fate of beneficial mutations in asexual populations

The fate of a newly arising beneficial mutation depends on many factors, such as the population size and the availability and fitness effects of other mutations that accumulate in the population. It has proved difficult to understand how these factors influence the trajectories of particular mutations, since experiments have primarily focused on characterizing successful clones emerging from a small number of evolving populations. Here, we present the results of a massively parallel experiment designed to measure the full spectrum of possible fates of new beneficial mutations in hundreds of experimental yeast populations, whether these mutations are ultimately successful or not. Using strains in which a particular class of beneficial mutation is detectable by fluorescence, we followed the trajectories of these beneficial mutations across 592 independent populations for 1000 generations. We find that the fitness advantage provided by individual mutations plays a surprisingly small role. Rather, underlying "background" genetic variation is quickly generated in our initially clonal populations and plays a crucial role in determining the fate of each individual beneficial mutation in the evolving population.     

Hitchhiking effect of a beneficial mutation spreading in a subdivided population

A central problem in population genetics is to detect and analyze positive natural selection by which beneficial mutations are driven to fixation. The hitchhiking effect of a rapidly spreading beneficial mutation, which results in local removal of standing genetic variation, allows such an analysis using DNA sequence polymorphism. However, the current mathematical theory that predicts the pattern of genetic hitchhiking relies on the assumption that a beneficial mutation increases to a high frequency in a single random-mating population, which is certainly violated in reality. Individuals in natural populations are distributed over a geographic space. The spread of a beneficial allele can be delayed by limited migration of individuals over the space and its hitchhiking effect can also be affected. To study this effect of geographic structure on genetic hitchhiking, we analyze a simple model of directional selection in a subdivided population. In contrast to previous studies on hitchhiking in subdivided populations, we mainly investigate the range of sufficiently high migration rates that would homogenize genetic variation at neutral loci. We provide a heuristic mathematical analysis that describes how the genealogical structure at a neutral locus linked to the locus under selection is expected to change in a population divided into two demes. Our results indicate that the overall strength of genetic hitchhiking--the degree to which expected heterozygosity decreases--is diminished by population subdivision, mainly because opportunity for the breakdown of hitchhiking by recombination increases as the spread of the beneficial mutation across demes is delayed when migration rate is much smaller than the strength of selection. Furthermore, the amount of genetic variation after a selective sweep is expected to be unequal over demes: a greater reduction in expected heterozygosity occurs in the subpopulation from which the beneficial mutation originates than in its neighboring subpopulations. This raises a possibility of detecting a "hidden" geographic structure of population by carefully analyzing the pattern of a selective sweep.     

The Hill-Robertson effect and the evolution of recombination

In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This "Hill-Robertson effect" generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles.