Genetic drift in an infinite population. The pseudohitchhiking model

Selected substitutions at one locus can induce stochastic dynamics that resemble genetic drift at a closely linked neutral locus. The pseudohitchhiking model is a one-locus model that approximates these effects and can be used to describe the major consequences of linked selection. As the changes in neutral allele frequencies when hitchhiking are rapid, diffusion theory is not appropriate for studying neutral dynamics. A stationary distribution and some results on substitution processes are presented that use the theory of continuous-time Markov processes with discontinuous sample paths. The coalescent of the pseudohitchhiking model is shown to have a random number of branches at each node, which leads to a frequency spectrum that is different from that of the equilibrium neutral model. If genetic draft, the name given to these induced stochastic effects, is a more important stochastic force than genetic drift, then a number of paradoxes that have plagued population genetics disappear.     

IS THE POPULATION SIZE OF A SPECIES RELEVANT TO ITS EVOLUTION?

Abstract This paper examines aspects of genetic draft, the stochastic force induced by substitutions at one locus on the dynamics of a closely linked locus. Of particular interest is the role of population size on genetic draft. Remarkably, the rate of substitution of weakly selected advantageous mutations decreases with increasing population size, whereas that for deleterious mutations increases with population size. This dependency on population size is the opposite of that for genetic drift. Moreover, these rates are only weakly dependent on population size, again contrary to the strong dependency of drift‐based dynamics. Four models of the strongly selected loci responsible for genetic draft are examined. Three of these exhibit a very weak dependency on population size, which implies that their induced effects will also be weakly dependent on population size. Together, these results suggest that population size and binomial sampling may not be relevant to a species' evolution. If this is the case, then a number of evolutionary conundrums are resolved.     

Selection and drift influence genetic differentiation of insular Canada lynx (Lynx canadensis) on Newfoundland and Cape Breton Island

Island populations have long been important for understanding the dynamics and mechanisms of evolution in natural systems. While genetic drift is often strong on islands due to founder events and population bottlenecks, the strength of selection can also be strong enough to counteract the effects of drift. Here, we used several analyses to identify the roles of genetic drift and selection on genetic differentiation and diversity of Canada lynx (Lynx canadensis) across eastern Canada, including the islands of Cape Breton and Newfoundland. Specifically, we assessed whether we could identify a genetic component to the observed morphological differentiation that has been reported across insular and mainland lynx. We used a dinucleotide repeat within the promoter region of a functional gene that has been linked to mammalian body size, insulin‐like growth factor‐1 (IGF‐1). We found high genetic differentiation at neutral molecular markers but convergence of allele frequencies at the IGF‐1 locus. Thus, we showed that while genetic drift has influenced the observed genetic structure of lynx at neutral molecular markers, natural selection has also played a role in the observed patterns of genetic diversity at the IGF‐1 locus of insular lynx.     

Selection maintains MHC diversity through a natural population bottleneck

A perceived consequence of a population bottleneck is the erosion of genetic diversity and concomitant reduction in individual fitness and evolutionary potential. Although reduced genetic variation associated with demographic perturbation has been amply demonstrated for neutral molecular markers, the effective management of genetic resources in natural populations is hindered by a lack of understanding of how adaptive genetic variation will respond to population fluctuations, given these are affected by selection as well as drift. Here, we demonstrate that selection counters drift to maintain polymorphism at a major histocompatibility complex (MHC) locus through a population bottleneck in an inbred island population of water voles. Before and after the bottleneck, MHC allele frequencies were close to balancing selection equilibrium but became skewed by drift when the population size was critically low. MHC heterozygosity generally conformed to Hardy-Weinberg expectations except in one generation during the population recovery where there was a significant excess of heterozygous genotypes, which simulations ascribed to strong differential MHC-dependent survival. Low allelic diversity and highly skewed frequency distributions at microsatellite loci indicated potent genetic drift due to a strong founder affect and/or previous population bottlenecks. This study is a real-time examination of the predictions of fundamental evolutionary theory in low genetic diversity situations. The findings highlight that conservation efforts to maintain the genetic health and evolutionary potential of natural populations should consider the genetic basis for fitness-related traits, and how such adaptive genetic diversity will vary in response to both the demographic fluctuations and the effects of selection.     

Genetic isolation of fragmented populations is exacerbated by drift and selection

Reduced genetic variation at marker loci in small populations has been well documented, whereas the relationship between quantitative genetic variation and population size has attracted little empirical investigation. Here we demonstrate that both neutral and quantitative genetic variation are reduced in small populations of a fragmented plant metapopulation, and that both drift and selective change are enhanced in small populations. Measures of neutral genetic differentiation (F(ST)) and quantitative genetic differentiation (Q(ST)) in two traits were higher among small demes, and Q(ST) between small populations exceeded that expected from drift alone. This suggests that fragmented populations experience both enhanced genetic drift and divergent selection on phenotypic traits, and that drift affects variation in both neutral markers and quantitative traits. These results highlight the need to integrate natural selection into conservation genetic theory, and suggests that small populations may represent reservoirs of genetic variation adaptive within a wide range of environments.     

The influence of stochastic and selective forces in the population divergence of female colour polymorphism in damselflies of the genus Ischnura

Disentangling the relative importance and potential interactions of selection and genetic drift in driving phenotypic divergence of species is a classical research topic in population genetics and evolutionary biology. Here, we evaluate the role of stochastic and selective forces on population divergence of a colour polymorphism in seven damselfly species of the genus Ischnura, with a particular focus on I. elegans and I. graellsii. Colour-morph frequencies in Spanish I. elegans populations varied greatly, even at a local scale, whereas more similar frequencies were found among populations in eastern Europe. In contrast, I. graellsii and the other five Ischnura species showed little variation in colour-morph frequencies between populations. F(ST)-outlier analyses revealed that the colour locus deviated strongly from neutral expectations in Spanish populations of I. elegans, contrasting the pattern found in eastern European populations, and in I. graellsii, where no such discrepancy between morph divergence and neutral divergence could be detected. This suggests that divergent selection has been operating on the colour locus in Spanish populations of I. elegans, whereas processes such as genetic drift, possibly in combination with other forms of selection (such as negative frequency-dependent selection), appear to have been present in other regions, such as eastern Europe. Overall, the results indicate that both selective and stochastic processes operate on these colour polymorphisms, and suggest that the relative importance of factors varies between geographical regions.     

Genetic Drift of HIV Populations in Culture

Populations of Human Immunodeficiency Virus type 1 (HIV-1) undergo a surprisingly large amount of genetic drift in infected patients despite very large population sizes, which are predicted to be mostly deterministic. Several models have been proposed to explain this phenomenon, but all of them implicitly assume that the process of virus replication itself does not contribute to genetic drift. We developed an assay to measure the amount of genetic drift for HIV populations replicating in cell culture. The assay relies on creation of HIV populations of known size and measurements of variation in frequency of a neutral allele. Using this assay, we show that HIV undergoes approximately ten times more genetic drift than would be expected from its population size, which we defined as the number of infected cells in the culture. We showed that a large portion of the increase in genetic drift is due to non-synchronous infection of target cells. When infections are synchronized, genetic drift for the virus is only 3-fold higher than expected from its population size. Thus, the stochastic nature of biological processes involved in viral replication contributes to increased genetic drift in HIV populations. We propose that appreciation of these effects will allow better understanding of the evolutionary forces acting on HIV in infected patients.     

Dynamics of inbreeding depression due to deleterious mutations in small populations: mutation parameters and inbreeding rate

A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation-selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.     

Microevolution in island forms: the roles of drift and directional selection in morphological divergence of a passerine bird

Abstract.— Theory predicts that in small isolated populations random genetic drift can lead to phenotypic divergence; however this prediction has rarely been tested quantitatively in natural populations. Here we utilize natural repeated island colonization events by members of the avian species complex, Zosterops lateralis , to assess whether or not genetic drift alone is an adequate explanation for the observed patterns of microevolutionary divergence in morphology. Morphological and molecular genetic characteristics of island and mainland populations are compared to test three predictions of drift theory: (1) that the pattern of morphological change is idiosyncratic to each island; (2) that there is concordance between morphological and neutral genetic shifts across island populations; and (3) for populations whose time of colonization is known, that the rate of morphological change is sufficiently slow to be accounted for solely by genetic drift. Our results are not consistent with these predictions. First, the direction of size shifts was consistently towards larger size, suggesting the action of a nonrandom process. Second, patterns of morphological divergence among recently colonized populations showed little concordance with divergence in neutral genetic characters. Third, rate tests of morphological change showed that effective population sizes were not small enough for random processes alone to account for the magnitude of microevolutionary change. Altogether, these three lines of evidence suggest that drift alone is not an adequate explanation of morphological differentiation in recently colonized island Zosterops and therefore we suggest that the observed microevolutionary changes are largely a result of directional natural selection.     

Local selection and population structure in a deep‐sea fish,the roundnose grenadier (Coryphaenoides rupestris)

Local populations within a species can become isolated by stochastic or adaptive processes, though it is most commonly the former that we quantify. Using presumably neutral markers we can assess the time‐dependent process of genetic drift, and thereby quantify patterns of differentiation in support of the effective management of diversity. However, adaptive differences can be overlooked in these studies, and these are the very characteristics that we hope to conserve by managing neutral diversity. In this study, we used 16 hypothetically neutral microsatellite markers to investigate the genetic structure of the roundnose grenadier in the North Atlantic. We found that one locus was a clear outlier under directional selection, with F_ST values much greater than at the remaining loci. Differentiation between populations at this locus was related to depth, suggesting directional selection, presumably acting on a linked locus. Considering only the loci identified as neutral, there remained significant population structure over the region of the North Atlantic studied. In addition to a weak pattern of isolation by distance, we identified a putative barrier to gene flow between sample sites either side of the Charlie‐Gibbs Fracture Zone, which marks the location where the sub‐polar front crosses the Mid‐Atlantic Ridge. This may reflect a boundary across which larvae are differentially distributed in separate current systems to some extent, promoting differentiation by drift. Structure due to both drift and apparent selection should be considered in management policy.     

DOES MATE LIMITATION IN SELF‐INCOMPATIBLE SPECIES PROMOTE THE EVOLUTION OF SELFING? THE CASE OF LEAVENWORTHIA ALABAMICA

Genetic diversity at the S‐locus controlling self‐incompatibility (SI) is often high because of negative frequency‐dependent selection. In species with highly patchy spatial distributions, genetic drift can overwhelm balancing selection and cause stochastic loss of S‐alleles. Natural selection may favor the breakdown of SI in populations with few S‐alleles because low S‐allele diversity constrains the seed production of self‐incompatible plants. We estimated S‐allele diversity, effective population sizes, and migration rates in Leavenworthia alabamica, a self‐incompatible mustard species restricted to discrete habitat patches in rocky glades. Patterns of polymorphism were investigated at the S‐locus and 15 neutral microsatellites in three large and three small populations with 100‐fold variation in glade size. Populations on larger glades maintained more S‐alleles, but all populations were estimated to harbor at least 20 S‐alleles, and mate availabilities typically exceeded 0.80, which is consistent with little mate limitation in nature. Estimates of the effective size (N_e) in each population ranged from 600 to 1600, and estimated rates of migration (m) ranged from 3 × 10⁻⁴ to nearly 1 × 10⁻³. According to theoretical models, there is limited opportunity for genetic drift to reduce S‐allele diversity in populations with these attributes. Although pollinators or resources limit seed production in small glades, limited S‐allele diversity does not appear to be a factor promoting the incipient breakdown of SI in populations of this species that were studied.     

From nature to the laboratory: the impact of founder effects on adaptation

Most founding events entail a reduction in population size, which in turn leads to genetic drift effects that can deplete alleles. Besides reducing neutral genetic variability, founder effects can in principle shift additive genetic variance for phenotypes that underlie fitness. This could then lead to different rates of adaptation among populations that have undergone a population size bottleneck as well as an environmental change, even when these populations have a common evolutionary history. Thus, theory suggests that there should be an association between observable genetic variability for both neutral markers and phenotypes related to fitness. Here, we test this scenario by monitoring the early evolutionary dynamics of six laboratory foundations derived from founders taken from the same source natural population of Drosophila subobscura. Each foundation was in turn three‐fold replicated. During their first few generations, these six foundations showed an abrupt increase in their genetic differentiation, within and between foundations. The eighteen populations that were monitored also differed in their patterns of phenotypic adaptation according to their immediately ancestral founding sample. Differences in early genetic variability and in effective population size were found to predict differences in the rate of adaptation during the first 21 generations of laboratory evolution. We show that evolution in a novel environment is strongly contingent not only on the initial composition of a newly founded population but also on the stochastic changes that occur during the first generations of colonization. Such effects make laboratory populations poor guides to the evolutionary genetic properties of their ancestral wild populations.     

Sex ratio and gamete size across eastern North America in Dictyostelium discoideum,a social amoeba with three sexes

Theory indicates that numbers of mating types should tend towards infinity or remain at two. The social amoeba, Dictyostelium discoideum, however, has three mating types. It is therefore a mystery how this species has broken the threshold of two mating types, but has not increased towards a much higher number. Frequency‐dependent selection on rare types in combination with isogamy, a form of reproduction involving gametes similar in size, could explain the evolution of multiple mating types in this system. Other factors, such as drift, may be preventing the evolution of more than three. We first looked for evidence of isogamy by measuring gamete size associated with each type. We found no evidence of size dissimilarities between gametes. We then looked for evidence of balancing selection, by examining mating type distributions in natural populations and comparing genetic differentiation at the mating type locus to that at more neutral loci. We found that mating type frequency varied among the three populations we examined, with only one of the three showing an even sex ratio, which does not support balancing selection. However, we found more population structure at neutral loci than the mating type locus, suggesting that the three mating types are indeed maintained at intermediate frequencies by balancing selection. Overall, the data are consistent with balancing selection acting on D. discoideum mating types, but with a sufficiently weak rare sex advantage to allow for drift, a potential explanation for why these amoebae have only three mating types.     

Selection and genetic drift in captive versus wild populations: an assessment of neutral and adaptive (MHC-linked) genetic variation in wild and hatchery brown trout (<Emphasis Type="Italic">Salmo trutta</Emphasis>) populations

Captive bred individuals are often released into natural environments to supplement resident populations. Captive bred salmonid fishes often exhibit lower survival rates than their wild brethren and stocking measures may have a negative influence on the overall fitness of natural populations. Stocked fish often stem from a different evolutionary lineage than the resident population and thus may be maladapted for life in the wild, but this phenomenon has also been linked to genetic changes that occur in captivity. In addition to overall loss of genetic diversity via captive breeding, adaptation to captivity has become a major concern. Altered selection pressure in captivity may favour alleles at adaptive loci like the Major Histocompatibility Complex (MHC) that are maladaptive in natural environments. We investigated neutral and MHC-linked genetic variation in three autochthonous and three hatchery populations of Austrian brown trout (Salmo trutta). We confirm a positive selection pressure acting on the MHC II β locus, whereby the signal for positive selection was stronger in hatchery versus wild populations. Additionally, diversity at the MHC II β locus was higher, and more uniform among hatchery samples compared to wild populations, despite equal levels of diversity at neutral loci. We postulate that this stems from a combination of stronger genetic drift and a weakening of positive selection at this locus in wild populations that already have well adapted alleles for their specific environments.     

Distinct evolutionary strategies of human leucocyte antigen loci in pathogen-rich environments

Human leucocyte antigen (HLA) loci have a complex evolution where both stochastic (e.g. genetic drift) and deterministic (natural selection) forces are involved. Owing to their extraordinary level of polymorphism, HLA genes are useful markers for reconstructing human settlement history. However, HLA variation often deviates significantly from neutral expectations towards an excess of genetic diversity. Because HLA molecules play a crucial role in immunity, this observation is generally explained by pathogen-driven-balancing selection (PDBS). In this study, we investigate the PDBS model by analysing HLA allelic diversity on a large database of 535 populations in relation to pathogen richness. Our results confirm that geographical distances are excellent predictors of HLA genetic differentiation worldwide. We also find a significant positive correlation between genetic diversity and pathogen richness at two HLA class I loci (HLA-A and -B), as predicted by PDBS, and a significant negative correlation at one HLA class II locus (HLA-DQB1). Although these effects are weak, as shown by a loss of significance when populations submitted to rapid genetic drift are removed from the analysis, the inverse relationship between genetic diversity and pathogen richness at different loci indicates that HLA genes have adopted distinct evolutionary strategies to provide immune protection in pathogen-rich environments.     

Genetic drift vs. natural selection in a long-term small isolated population: major histocompatibility complex class II variation in the Gulf of California endemic porpoise (Phocoena sinus)

Although many studies confirm long-term small isolated populations (e.g. island endemics) commonly sustain low neutral genetic variation as a result of genetic drift, it is less clear how selection on adaptive or detrimental genes interplay with random forces. We investigated sequence variation at two major histocompatibility complex (Mhc) class II loci on a porpoise endemic to the upper Gulf of California, México (Phocoena sinus, or vaquita). Its unique declining population is estimated around 500 individuals. Single-strand conformation polymorphism analysis revealed one putative functional allele fixed at the locus DQB (n = 25). At the DRB locus, we found two presumed functional alleles (n = 29), differing by a single nonsynonymous nucleotide substitution that could increase the stability at the dimer interface of alphabeta-heterodimers on heterozygous individuals. Identical trans-specific DQB1 and DRB1 alleles were identified between P. sinus and its closest relative, the Burmeister's porpoise (Phocoena spinipinnis). Comparison with studies on four island endemic mammals suggests fixation of one allele, due to genetic drift, commonly occurs at the DQA or DQB loci (effectively neutral). Similarly, deleterious alleles of small effect are also effectively neutral and can become fixed; a high frequency of anatomical malformations on vaquita gave empirical support to this prediction. In contrast, retention of low but functional polymorphism at the DRB locus was consistent with higher selection intensity. These observations indicated natural selection could maintain (and likely also purge) some crucial alleles even in the face of strong and prolonged genetic drift and inbreeding, suggesting long-term small populations should display low inbreeding depression. Low levels of Mhc variation warn about a high susceptibility to novel pathogens and diseases in vaquita.     

Contrasting patterns of body shape and neutral genetic divergence in marine and lake populations of threespine sticklebacks

Comparisons of neutral marker and quantitative trait divergence can provide important insights into the relative roles of natural selection and neutral genetic drift in population differentiation. We investigated phenotypic and genetic differentiation among Fennoscandian threespine stickleback (Gasterosteus aculeatus) populations, and found that the highest degree of differentiation occurred between sea and freshwater habitats. Within habitats, morphological divergence was highest among the different freshwater populations. Pairwise phenotypic and neutral genetic distances among populations were positively correlated, suggesting that genetic drift may have contributed to the morphological differentiation among habitats. On the other hand, the degree of phenotypic differentiation (PST) clearly surpassed the neutral expectation set by FST, suggesting a predominant role for natural selection over genetic drift as an explanation for the observed differentiation. However, separate PST/FST comparisons by habitats revealed that body shape divergence between lake and marine populations, and even among marine populations, can be strongly influenced by natural selection. On the other hand, genetic drift can play an important role in the differentiation among lake populations.     

Effect of population size and selection on Toll-like receptor diversity in populations of Galápagos mockingbirds

The interactions of evolutionary forces are difficult to analyse in free-living populations. However, when properly understood, they provide valuable insights into evolutionary biology and conservation genetics. This is particularly important for the interplay of genetic drift and natural selection in immune genes that confer resistance to disease. The Galápagos Islands are inhabited by four closely related species of mockingbirds (Mimus spp.). We used 12 different-sized populations of Galápagos mockingbirds and one population of their continental relative northern mockingbird (Mimus polyglottos) to study the effects of genetic drift on the molecular evolution of immune genes, the Toll-like receptors (TLRs: TLR1B, TLR4 and TLR15). We found that neutral genetic diversity was positively correlated with island size, indicating an important effect of genetic drift. However, for TLR1B and TLR4, there was little correlation between functional (e.g., protein) diversity and island size, and protein structural properties were largely conserved, indicating only a limited effect of genetic drift on molecular phenotype. By contrast, TLR15 was less conserved and even its putative functional polymorphism correlated with island size. The patterns observed for the three genes suggest that genetic drift does not necessarily dominate selection even in relatively small populations, but that the final outcome depends on the degree of selection constraint that is specific for each TLR locus.     

Can balancing selection on MHC loci counteract genetic drift in small fragmented populations of black grouse?

The ability of natural populations to adapt to new environmental conditions is crucial for their survival and partly determined by the standing genetic variation in each population. Populations with higher genetic diversity are more likely to contain individuals that are better adapted to new circumstances than populations with lower genetic diversity. Here, we use both neutral and major histocompatibility complex (MHC) markers to test whether small and highly fragmented populations hold lower genetic diversity than large ones. We use black grouse as it is distributed across Europe and found in populations with varying degrees of isolation and size. We sampled 11 different populations; five continuous, three isolated, and three small and isolated. We tested patterns of genetic variation in these populations using three different types of genetic markers: nine microsatellites and 21 single nucleotide polymorphisms (SNPs) which both were found to be neutral, and two functional MHC genes that are presumably under selection. The small isolated populations displayed significantly lower neutral genetic diversity compared to continuous populations. A similar trend, but not as pronounced, was found for genotypes at MHC class II loci. Populations were less divergent at MHC genes compared to neutral markers. Measures of genetic diversity and population genetic structure were positively correlated among microsatellites and SNPs, but none of them were correlated to MHC when comparing all populations. Our results suggest that balancing selection at MHC loci does not counteract the power of genetic drift when populations get small and fragmented.     

Gene flow and melanism in garter snakes revisited: a comparison of molecular markers and island vs. coalescent models

Within populations, the stochastic effect of genetic drift and deterministic effect of natural selection are potentially weakened or altered by gene flow among populations. The influence of gene flow on Lake Erie populations of the common garter snake has been of particular interest because of a discontinuous colour pattern polymorphism (striped vs. melanistic) that is a target of natural selection. We reassessed the relative contributions of gene flow and genetic drift using genetic data and population size estimates. We compared all combinations of two marker systems and two analytical approaches to the estimation of gene flow rates: allozymes (data previously published), microsatellite DNA (new data), the island model ( F _ST-based approach), and a coalescence-based approach. For the coalescence approach, mutation rates and sampling effects were also investigated. While the two markers produced similar results, gene flow based on F _ST was considerably higher (Nm > 4) than that from the coalescence-based method (Nm < 1). Estimates of gene flow are likely to be inflated by lack of migration-drift equilibrium and changing population size. Potentially low rates of gene flow (Nm < 1), small population size at some sites, and positive correlations of number of microsatellite DNA alleles and island size and between M , mean ratio of number of alleles to range in allele size, and island size suggest that in addition to selection, random genetic drift may influence colour pattern frequencies. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 79, 389–399.