Selection in a subdivided population with local extinction and recolonization

In a subdivided population, local extinction and subsequent recolonization affect the fate of alleles. Of particular interest is the interaction of this force with natural selection. The effect of selection can be weakened by this additional source of stochastic change in allele frequency. The behavior of a selected allele in such a population is shown to be equivalent to that of an allele with a different selection coefficient in an unstructured population with a different size. This equivalence allows use of established results for panmictic populations to predict such quantities as fixation probabilities and mean times to fixation. The magnitude of the quantity N(e)s(e), which determines fixation probability, is decreased by extinction and recolonization. Thus deleterious alleles are more likely to fix, and advantageous alleles less likely to do so, in the presence of extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

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.     

Conservation corridors affect the fixation of novel alleles

Corridors are a popular tool for conservation of small populations. However, two purported benefits of corridors, increasing gene flow and providing a means for the recolonization of extinct patches of habitat (population rescue), may have unappreciated impacts on the likelihood that a new allele will become incorporated (fixed) within a population. Using a simulation model, I demonstrate that connecting a stable, isolated population with a population that requires periodic rescue (due to extinction via natural or anthropogenic disturbance) can affect fixation of alleles in the stable population, largely by changing the effective population size Ne of the two-patch complex. When disturbance is rare, connecting the two patches with corridors can increase fixation of beneficial alleles and increase loss of harmful alleles. However, the opposite occurs when rates of disturbance are high: corridors can promote fixation of harmful alleles and reduce fixation of beneficial alleles. Because the impact of corridors hinges upon disturbance frequency (i.e. rate of population rescue), population growth rate, movement rates, and habitat quality, different species are likely to have different responses to corridor-mediated fixation, even if the species reside within the same ecological community. By changing fixation, corridors could thus either promote adaptation or extinction.     

The effects of migration and drift on local adaptation to a heterogeneous environment

Local adaptation experiments are widely used to quantify the levels of adaptation within a heterogeneous environment. However, theoretical studies generally focus on the probability of fixation of alleles or the mean fitness of populations, rather than local adaptation as it is commonly measured experimentally or in field studies. Here, we develop mathematical models and use them to generate analytical predictions for the level of local adaptation as a function of selection, migration and genetic drift. First, we contrast mean fitness and local adaptation measures and show that the latter can be expressed in a simple and general way as a function of the spatial covariance between population mean phenotype and local environmental conditions. Second, we develop several approximations of a population genetics model to show that the system exhibits different behaviours depending on the rate of migration. The main insights are the following: with intermediate migration, both genetic drift and migration decrease local adaptation; with low migration, drift decreases local adaptation but migration speeds up adaptation; with high migration, genetic drift has no effect on local adaptation. Third, we extend this analysis to cases where the trait under selection is continuous using classical quantitative genetics theory. Finally, we discuss these results in the light of recent experimental work on local adaptation.     

Fixation probability in a two-locus model by the ancestral recombination-selection graph

We use the ancestral influence graph (AIG) for a two-locus, two-allele selection model in the limit of a large population size to obtain an analytic approximation for the probability of ultimate fixation of a single mutant allele A. We assume that this new mutant is introduced at a given locus into a finite population in which a previous mutant allele B is already segregating with a wild type at another linked locus. We deduce that the fixation probability increases as the recombination rate increases if allele A is either in positive epistatic interaction with B and allele B is beneficial or in no epistatic interaction with B and then allele A itself is beneficial. This holds at least as long as the recombination fraction and the selection intensity are small enough and the population size is large enough. In particular this confirms the Hill-Robertson effect, which predicts that recombination renders more likely the ultimate fixation of beneficial mutants at different loci in a population in the presence of random genetic drift even in the absence of epistasis. More importantly, we show that this is true from weak negative epistasis to positive epistasis, at least under weak selection. In the case of deleterious mutants, the fixation probability decreases as the recombination rate increases. This supports Muller's ratchet mechanism to explain the accumulation of deleterious mutants in a population lacking recombination.     

Hitchhiking of Deleterious Alleles and the Cost of Adaptation in Partially Selfing Species

Self-fertilization is generally seen to be disadvantageous in the long term. It increases genetic drift, which subsequently reduces polymorphism and the efficiency of selection, which also challenges adaptation. However, high selfing rates can increase the fixation probability of recessive beneficial mutations, but existing theory has generally not accounted for the effect of linked sites. Here, we analyze a model for the fixation probability of deleterious mutants that hitchhike with selective sweeps in diploid, partially selfing populations. Approximate analytical solutions show that, conditional on the sweep not being lost by drift, higher inbreeding rates increase the fixation probability of the deleterious allele, due to the resulting reduction in polymorphism and effective recombination. When extending the analysis to consider a distribution of deleterious alleles, as well as the average fitness increase after a sweep, we find that beneficial alleles generally need to be more recessive than the previously assumed dominance threshold (h < 1/2) for selfing to be beneficial from one-locus theory. Our results highlight that recombination aiding the efficiency of selection on multiple loci amplifies the fitness benefits of outcrossing over selfing, compared to results obtained from one-locus theory. This effect additionally increases the parameter range under which obligate outcrossing is beneficial over partial selfing.     

Disease swamps molecular signatures of genetic-environmental associations to abiotic factors in Tasmanian devil (Sarcophilus harrisii) populations

Landscape genomics studies focus on identifying candidate genes under selection via spatial variation in abiotic environmental variables, but rarely by biotic factors (i.e., disease). The Tasmanian devil (Sarcophilus harrisii) is found only on the environmentally heterogeneous island of Tasmania and is threatened with extinction by a transmissible cancer, devil facial tumor disease (DFTD). Devils persist in regions of long-term infection despite epidemiological model predictions of species’ extinction, suggesting possible adaptation to DFTD. Here, we test the extent to which spatial variation and genetic diversity are associated with the abiotic environment (i.e., climatic variables, elevation, vegetation cover) and/or DFTD. We employ genetic-environment association analyses using 6886 SNPs from 3287 individuals sampled pre- and post-disease arrival across the devil's geographic range. Pre-disease, we find significant correlations of allele frequencies with environmental variables, including 365 unique loci linked to 71 genes, suggesting local adaptation to abiotic environment. The majority of candidate loci detected pre-DFTD are not detected post-DFTD arrival. Several post-DFTD candidate loci are associated with disease prevalence and were in linkage disequilibrium with genes involved in tumor suppression and immune response. Loss of apparent signal of abiotic local adaptation post-disease suggests swamping by strong selection resulting from the rapid onset of DFTD.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

Adaptation from standing genetic variation

Populations adapt to novel environments in two distinct ways: selection on pre-existing genetic variation and selection on new mutations. These alternative sources of beneficial alleles can result in different evolutionary dynamics and distinct genetic outcomes. Compared with new mutations, adaptation from standing genetic variation is likely to lead to faster evolution, the fixation of more alleles of small effect and the spread of more recessive alleles. There is potential to distinguish between adaptation from standing variation and that from new mutations by differences in the genomic signature of selection. Here we review these approaches and possible examples of adaptation from standing variation in natural populations. Understanding how the source of genetic variation affects adaptation will be integral for predicting how populations will respond to changing environments.     

Determinants of Genetic Structure in a Nonequilibrium Metapopulation of the Plant Silene latifolia

Population genetic differentiation will be influenced by the demographic history of populations, opportunities for migration among neighboring demes and founder effects associated with repeated extinction and recolonization. In natural populations, these factors are expected to interact with each other and their magnitudes will vary depending on the spatial distribution and age structure of local demes. Although each of these effects has been individually identified as important in structuring genetic variance, their relative magnitude is seldom estimated in nature. We conducted a population genetic analysis in a metapopulation of the angiosperm, Silene latifolia, from which we had more than 20 years of data on the spatial distribution, demographic history, and extinction and colonization of demes. We used hierarchical Bayesian methods to disentangle which features of the populations contributed to among population variation in allele frequencies, including the magnitude and direction of their effects. We show that population age, long-term size and degree of connectivity all combine to affect the distribution of genetic variance; small, recently-founded, isolated populations contributed most to increase F _ST in the metapopulation. However, the effects of population size and population age are best understood as being modulated through the effects of connectivity to other extant populations, i.e. F _ST diminishes as populations age, but at a rate that depends how isolated the population is. These spatial and temporal correlates of population structure give insight into how migration, founder effect and within-deme genetic drift have combined to enhance and restrict genetic divergence in a natural metapopulation.     

Environmental heterogeneity enhances clonal interference

Clonal interference (CI) is a phenomenon that may be important in several asexual microbes. It occurs when population sizes are large and mutation rates to new beneficial alleles are of significant magnitude. Here we explore the role of gene flow and spatial heterogeneity in selection strength in the adaptation of asexuals. We consider a subdivided population of individuals that are adapting, through new beneficial mutations, and that migrate between different patches. The fitness effect of each mutation depends on the patch and all mutations considered are assumed to be unconditionally beneficial. We find that spatial variation in selection pressure affects the rate of adaptive evolution and its qualitative effects depend on the level of gene flow. In particular, we find that both low migration and high levels of heterogeneity lead to enhanced CI. In contrast, for high levels of migration the rate of fixation of adaptive mutations is higher when environmental heterogeneity is present. In addition, we observe that the level of fitness variation is higher and simultaneous fixation of multiple mutations tends to occur in the regime of low migration rates and high heterogeneity.     

Soft sweeps: molecular population genetics of adaptation from standing genetic variation

A population can adapt to a rapid environmental change or habitat expansion in two ways. It may adapt either through new beneficial mutations that subsequently sweep through the population or by using alleles from the standing genetic variation. We use diffusion theory to calculate the probabilities for selective adaptations and find a large increase in the fixation probability for weak substitutions, if alleles originate from the standing genetic variation. We then determine the parameter regions where each scenario-standing variation vs. new mutations-is more likely. Adaptations from the standing genetic variation are favored if either the selective advantage is weak or the selection coefficient and the mutation rate are both high. Finally, we analyze the probability of "soft sweeps," where multiple copies of the selected allele contribute to a substitution, and discuss the consequences for the footprint of selection on linked neutral variation. We find that soft sweeps with weaker selective footprints are likely under both scenarios if the mutation rate and/or the selection coefficient is high.     

Effects of environmental heterogeneity on victim-exploiter coevolution

We study victim-exploiter coevolution in a spatially heterogeneous island model. In each species, fitness consequences of between-species interactions are controlled by a single haploid diallelic locus. Our emphasis is on the conditions for the maintenance of genetic variation, the dynamic patterns observed, the extent of local adaptation and genetic differentiation between different demes, and on how different parameters (such as the strength and heterogeneity in selection, migration rates, and the number of sites) affect the dynamic and static behavior of the system. We show that under spatially homogeneous selection the maintenance of genetic variation is possible through asynchronous nonlinear dynamics where the allele frequencies in a majority of demes quickly synchronize but the rest do not. Spatially heterogeneous selection can maintain genetic variation even if migration rates are maximal. This happens in an oscillatory way. Genetic variation is most likely to be maintained at high levels if the heterogeneity in selection is large. If there are some restrictions on migration, genetic variation can be maintained at a stable equilibrium. This behavior is most likely at intermediate migration rates. In this case, the system can exhibit high spatial subdivision as measured by F(ST) values but relatively low local adaptation.     

Melanic through nature or nurture: genetic polymorphism and phenotypic plasticity in Harmonia axyridis

Abstract Individuals can adapt to heterogeneity in their environment through either local adaptation or phenotypic plasticity. Colour forms of the ladybird Harmonia axyridis are a classic example of local adaptation, in which the frequency of melanic forms varies greatly between populations. In some populations, there are also large seasonal changes in allele frequency, with melanism being costly in summer and beneficial in winter. We report that the non‐melanic morph of H. axyridis dramatically increases its degree of melanization at cold temperatures. Furthermore, there is genetic variation in reaction norms, with different families responding to temperature in different ways. Variation at different spatial and temporal scales appears to have selected for either genetic or phenotypically plastic adaptations, which may be important in thermoregulation. As melanism is known to have a large effect on fitness in H. axyridis, this plasticity of melanization may have hastened its spread as an invasive species.     

ADAPTATION AND MALADAPTATION IN SELFING AND OUTCROSSING SPECIES: NEW MUTATIONS VERSUS STANDING VARIATION

Evolution of selfing from outcrossing recurrently occurred in many lineages, especially in flowering plants. Evolution of selfing induces dramatic changes in the population genetics functioning but its consequences on the dynamics of adaptation have been overlooked. We studied a simple one‐locus model of adaptation where a population experiences an environmental change at a given time. We first determined the effect of the mating system on the genetic bases and the speed of adaptation, focusing on the dominance of beneficial mutations and the respective part of standing variation and new mutations. Then, we assumed that the environmental change is associated with population decline to determine the effect of the mating system on the probability of population extinction. Extending previous results, we found that adaptation is more efficient and extinction less likely in outcrossers when beneficial mutations are dominant and codominant and when standing variation plays a significant role in adaptation. However, given adaptation does occur, it is usually more rapid in selfers than in outcrossers. Our results bear implications for the evolution of the selfing syndrome, the dynamics of the domestication process, and the dead‐end hypothesis that posits that selfing lineages are doomed to extinction on the long run.     

The effect of deleterious alleles on adaptation in asexual populations

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.     

Fixation probability and time in subdivided populations

New alleles arising in a population by mutation ultimately are either fixed or lost. Either is possible, for both beneficial and deleterious alleles, because of stochastic changes in allele frequency due to genetic drift. Spatially structured populations differ from unstructured populations in the probability of fixation and the time that this fixation takes. Previous results have generally made many assumptions: that all demes contribute to the next generation in exact proportion to their current sizes, that new mutations are beneficial, and that new alleles have additive effects. In this article these assumptions are relaxed, allowing for an arbitrary distribution among demes of reproductive success, both beneficial and deleterious effects, and arbitrary dominance. The effects of population structure can be expressed with two summary statistics: the effective population size and a variant of Wright's F(ST). In general, the probability of fixation is strongly affected by population structure, as is the expected time to fixation or loss. Population structure changes the effective size of the species, often strongly downward; smaller effective size increases the probability of fixing deleterious alleles and decreases the probability of fixing beneficial alleles. On the other hand, population structure causes an increase in the homozygosity of alleles, which increases the probability of fixing beneficial alleles but somewhat decreases the probability of fixing deleterious alleles. The probability of fixing new beneficial alleles can be simply described by 2hs(1 - F(ST))N(e)/N(tot), where hs is the change in fitness of heterozygotes relative to the ancestral homozygote, F(ST) is a weighted version of Wright's measure of population subdivision, and N(e) and N(tot) are the effective and census sizes, respectively. These results are verified by simulation for a broad range of population structures, including the island model, the stepping-stone model, and a model with extinction and recolonization.     

Microevolution in time and space: SNP analysis of historical DNA reveals dynamic signatures of selection in Atlantic cod

Little is known about how quickly natural populations adapt to changes in their environment and how temporal and spatial variation in selection pressures interact to shape patterns of genetic diversity. We here address these issues with a series of genome scans in four overfished populations of Atlantic cod (Gadus morhua) studied over an 80‐year period. Screening of >1000 gene‐associated single‐nucleotide polymorphisms (SNPs) identified 77 loci that showed highly elevated levels of differentiation, likely as an effect of directional selection, in either time, space or both. Exploratory analysis suggested that temporal allele frequency shifts at certain loci may correlate with local temperature variation and with life history changes suggested to be fisheries induced. Interestingly, however, largely nonoverlapping sets of loci were temporal outliers in the different populations and outliers from the 1928 to 1960 period showed almost complete stability during later decades. The contrasting microevolutionary trajectories among populations resulted in sequential shifts in spatial outliers, with no locus maintaining elevated spatial differentiation throughout the study period. Simulations of migration coupled with observations of temporally stable spatial structure at neutral loci suggest that population replacement or gene flow alone could not explain all the observed allele frequency variation. Thus, the genetic changes are likely to at least partly be driven by highly dynamic temporally and spatially varying selection. These findings have important implications for our understanding of local adaptation and evolutionary potential in high gene flow organisms and underscore the need to carefully consider all dimensions of biocomplexity for evolutionarily sustainable management.     

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.