Genetic variability at neutral markers,quantitative trait land trait in a subdivided population under selection

Genetic variability in a subdivided population under stabilizing and diversifying selection was investigated at three levels: neutral markers, QTL coding for a trait, and the trait itself. A quantitative model with additive effects was used to link genotypes to phenotypes. No physical linkage was introduced. Using an analytical approach, we compared the diversity within deme (H(S)) and the differentiation (F(ST)) at the QTL with the genetic variance within deme (V(W)) and the differentiation (Q(ST)) for the trait. The difference between F(ST) and Q(ST) was shown to depend on the relative amounts of covariance between QTL within and between demes. Simulations were used to study the effect of selection intensity, variance of optima among demes, and migration rate for an allogamous and predominantly selfing species. Contrasting dynamics of the genetic variability at markers, QTL, and trait were observed as a function of the level of gene flow and diversifying selection. The highest discrepancy among the three levels occurred under highly diversifying selection and high gene flow. Furthermore, diversifying selection might cause substantial heterogeneity among QTL, only a few of them showing allelic differentiation, while the others behave as neutral markers.     

Genetic load,inbreeding depression and heterosis in an age‐structured metapopulation

In a metapopulation, the process of recurrent local extinction and recolonization gives rise to an age structure among demes. Recently established demes will tend to differ from older demes in terms of the levels of genetic diversity found within them and the way this diversity is distributed among demes in the same and different ages. The effects of population turnover on average levels of genetic diversity among demes in a metapopulation have been the focus of much attention, both for neutral and nonneutral loci, but much less is known about the distribution of nonneutral genetic diversity among demes of different ages. In this paper, we used computer simulations to study the distribution of genetic load, inbreeding depression and heterosis in an age‐structured metapopulation. We found that, for mildly deleterious mutations, within‐deme inbreeding depression increased, whereas heterosis and genetic load decreased with deme age following severe colonization bottlenecks. In contrast, recessive lethal alleles tended to be purged during colonization, with older populations showing higher genetic load and higher within‐deme inbreeding depression. Heterosis caused by recessive lethal alleles and resulting from gene flow among different demes tended to be greatest for young demes, because the mutations responsible tended to be purged in the first few generations after colonization, but its effects increased again as populations grow older as a result of immigration. Our results point to a need for estimates of genetic diversity, genetic load, within‐deme inbreeding depression and heterosis in demes of different age classes separately.     

Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions

Population structure affects the relative influence of selection and drift on the change in allele frequencies. Several models have been proposed recently, using diffusion approximations to calculate fixation probabilities, fixation times, and equilibrium properties of subdivided populations. We propose here a simple method to construct diffusion approximations in structured populations; it relies on general expressions for the expectation and variance in allele frequency change over one generation, in terms of partial derivatives of a "fitness function" and probabilities of genetic identity evaluated in a neutral model. In the limit of a very large number of demes, these probabilities can be expressed as functions of average allele frequencies in the metapopulation, provided that coalescence occurs on two different timescales, which is the case in the island model. We then use the method to derive expressions for the probability of fixation of new mutations, as a function of their dominance coefficient, the rate of partial selfing, and the rate of deme extinction. We obtain more precise approximations than those derived by recent work, in particular (but not only) when deme sizes are small. Comparisons with simulations show that the method gives good results as long as migration is stronger than selection.     

Population Dynamic and Genetic Consequences of Spatial Density-Dependent Dispersal in Patchy Populations

Predictions about sex-specific, spatial density-dependent dispersal and their demographic and genetic consequences were tested in experimental populations of root voles (Microtus oeconomus). Each population consisted of two demes inhabiting equal-sized habitat patches imbedded in a barren matrix area. We used a neutral two-allele allozyme marker to monitor gene flow. Initially, the two demes were genetically distinct and had different densities so that the size of a high-density deme (genotype bb) was four times larger than that of a low-density deme (genotype aa). The sex-specific dispersal pattern was in accordance with our prediction. Male dispersal was unconditional on deme-specific densities, and the majority of the first-generation males became dispersed from both demes, whereas female dispersal was strongly density dependent, so that dispersal took place exclusively from the high-density to the low-density deme. The demographic implication of this dispersal pattern was that the initial density difference between the demes was quickly canceled out. We built a mathematical model that predicted that the initially rare allele (a) would increase in frequency given the dispersal pattern, and this was supported by our experimental data. This result relies mostly on the density-independent male-dispersal strategy, which presumably stems from inbreeding avoidance. Our study highlights the importance of incorporating sex-specific dispersal strategies in population genetic models. Sex-biased dispersal may act as a deterministic force counteracting the tendency for stochastic loss of alleles in small and fragmented populations.     

Genealogy of Neutral Genes and Spreading of Selected Mutations in a Geographically Structured Population

In a geographically structured population, the interplay among gene migration, genetic drift and natural selection raises intriguing evolutionary problems, but the rigorous mathematical treatment is often very difficult. Therefore several approximate formulas were developed concerning the coalescence process of neutral genes and the fixation process of selected mutations in an island model, and their accuracy was examined by computer simulation. When migration is limited, the coalescence (or divergence) time for sampled neutral genes can be described by the convolution of exponential functions, as in a panmictic population, but it is determined mainly by migration rate and the number of demes from which the sample is taken. This time can be much longer than that in a panmictic population with the same number of breeding individuals. For a selected mutation, the spreading over the entire population was formulated as a birth and death process, in which the fixation probability within a deme plays a key role. With limited amounts of migration, even advantageous mutations take a large number of generations to spread. Furthermore, it is likely that these mutations which are temporarily fixed in some demes may be swamped out again by non-mutant immigrants from other demes unless selection is strong enough. These results are potentially useful for testing quantitatively various hypotheses that have been proposed for the origin of modern human populations.     

Analysis of linkage disequilibrium in an island model

Linkage disequilibria for two loci in a finite island model were parameterized. The total linkage disequilibrium was decomposed into three components, gametic, demic, and population, for which corresponding unbiased estimators were established. Other statistics encountered provided measures of differentiation corresponding to the hierarchical structure of the ecological model. Under the assumption of linkage equilibrium, the variances and covariances of these estimators and statistics were formulated in terms of descent measures, functions of gene frequencies, and the numbers of individuals, demes, and populations sampled. The functions of gene frequencies fall into two classes, one representing the differentiation of genes at each locus, and the other representing the association of genes between the loci. For a neutral model with extinction, migration, and linkage, transition equations were derived for the descent measures which also take into account deme size and numbers of dems within the population. With the addition of unequal mutation rates for a finite number of alleles at each locus, the transition equations were solved for the descent measures in the equilibrium state. This permitted the exact numerical evaluation of the effects of the sampling and ecological dimensions and of extinction, migration, and mutation rates in any parameter range. Some numerical results were presented for the effects of linkage, extinction, migration, and sampling on the variances of various measures of linkage disequilibrium and genetic differentiation. Also, some results were compared with the approximate numerical results of Ohta which agreed fairly well in the parameter ranges she considered, but not so well in other ranges.     

Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow

Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few‐locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two‐deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration‐selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual‐based simulations.     

Testing neutrality in subdivided populations

Statistical tests of the neutrality hypothesis that are based on the sampling theory of Ewens (1972) require the assumption of panmixia. It is proposed that for a population comprising numerous local populations with weak gene flow among them, tests based on Ewens' theory can be applied separately to samples from each local population. At low levels of gene flow, migration acts primarily like mutation, introducing new alleles to each local population. It is shown with simulation results that, at low levels of migration, correlations in allele frequencies among demes are sufficiently small that the results from the application of Ewens' theory to each deme are statistically independent. It is also shown that, by combining the results of the tests in different demes, some statistical power to detect deviations from neutrality is gained. The method is illustrated with the application to data on a salamander species. At low levels of gene flow, population subdivision must be taken account of in testing neutrality and the proposed test provides one way to do so.     

PHASE III OF WRIGHT'S SHIFTING BALANCE PROCESS AND THE VARIANCE AMONG DEMES IN MIGRATION RATE

Interdemic selection by the differential migration of individuals out from demes of high fitness and into demes of low fitness (Phase III) is one of the most controversial aspects of Wright's Shifting Balance Theory. I derive a relationship between Phase III migration and the interdemic selection differential, S, and show its potential effect on F_ST. The relationship reveals a diversifying effect of interdemic selection by Phase III migration on the genetic structure of a metapopulation. Using experimental metapopulations, I explored the effect of Phase III migration on F_ST by comparing the genetic variance among demes for two different patterns of migration: (1) island model migration and (2) Wright's Phase III migration. Although mean migration rates were the same, I found that the variance among demes in migration rate was significantly higher with Phase III than with island model migration. As a result, F_ST for the frequency of a neutral marker locus was higher with Phase III than it was with island model migration. By increasing F_ST, Phase III enhanced the genetic differentiation among demes for traits not subject to interdemic selection. This feature makes Wright's process different from individual selection which, by reducing effective population size, decreases the genetic variance within demes for all other traits. I discussed this finding in relation to the efficacy of Phase III and random migration for effecting peak shifts, and the contribution of genes with indirect effects to among‐deme variation.     

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.     

Intra-deme molecular diversity in spatially expanding populations

We report here a simulation study examining the effect of a recent spatial expansion on the pattern of molecular diversity within a deme. We first simulate a range expansion in a virtual world consisting in a two-dimensional array of demes exchanging a given proportion of migrants (m) with their neighbors. The recorded demographic and migration histories are then used under a coalescent approach to generate the genetic diversity in a sample of genes. We find that the shape of the gene genealogies and the overall pattern of diversity within demes depend not only on the age of the expansion but also on the level of gene flow between neighboring demes, as measured by the product Nm, where N is the size of a deme. For small Nm values (< approximately 20 migrants sent outwards per generation), a substantial proportion of coalescent events occur early in the genealogy, whereas with larger levels of gene flow, most coalescent events occur around the time of the onset of the spatial expansion. Gene genealogies are star shaped, and mismatch distributions are unimodal after a range expansion for large Nm values. In contrast, gene genealogies present a mixture of both very short and very long branch lengths, and mismatch distributions are multimodal for small Nm values. It follows that statistics used in tests of selective neutrality like Tajima's D statistic or Fu's F(S) statistic will show very significant negative values after a spatial expansion only in demes with high Nm values. In the context of human evolution, this difference could explain very simply the fact that analyses of samples of mitochondrial DNA sequences reveal multimodal mismatch distributions in hunter-gatherers and unimodal distributions in post-Neolithic populations. Indeed, the current simulations show that a recent increase in deme size (resulting in a larger Nm value) is sufficient to prevent recent coalescent events and thus lead to unimodal mismatch distributions, even if deme sizes (and therefore Nm values) were previously much smaller. The fact that molecular diversity within deme is so dependent on recent levels of gene flow suggests that it should be possible to estimate Nm values from samples drawn from a single deme.     

Populational heritability: empirical studies of evolution in metapopulations

Using demes from experimental metapopulations of the flour beetle, Tribolium castaneum, we investigated phase 3 of Wright's shifting balance process. Using parent demes of high, intermediate, and low mean fitness, we experimentally modeled migration of varying amounts from demes of high mean fitness into demes of lower mean fitness (like phase 3) as well as the reciprocal (the opposite of phase 3). In natural populations, some migration among demes occurs independently of deme fitness. In this case, demes of high mean fitness are likely to receive migrants from demes of lower mean fitness; these effects might limit the effectiveness of phase 3 but have not been studied experimentally. We estimated the populational heritability of mean fitness by the regression of offspring deme means on the weighted parental means and found moderate levels of demic heritability one (0.641-0.690) and two (0.518-0.552) generations after migration. We discuss our findings in relation to the role of interdemic migration in "adaptive peak shifts" in metapopulations and the controversies over group selection and the units of inheritance.     

Landscape genetic analyses reveal cryptic population structure and putative selection gradients in a large-scale estuarine environment

Disentangling the relative contributions of selective and neutral processes underlying phenotypic and genetic variation under natural, environmental conditions remains a central challenge in evolutionary ecology. However, much of the variation that could be informative in this area of research is likely to be cryptic in nature; thus, the identification of wild populations suitable for study may be problematic. We use a landscape genetics approach to identify such populations of three-spined stickleback inhabiting the Saint Lawrence River estuary. We sampled 1865 adult fish over multiple years. Individuals were genotyped for nine microsatellite loci, and georeferenced multilocus data were used to infer population groupings, as well as locations of genetic discontinuities, under a Bayesian model framework ( geneland ). We modelled environmental data using nonparametric multiple regression to explain genetic differentiation as a function of spatio-ecological effects. Additionally, we used genotype data to estimate dispersal and gene flow to parameterize a simple model predicting adaptive vs. plastic divergence between demes. We demonstrate a bipartite division of the genetic landscape into freshwater and maritime zones, independent of geographical distance. Moreover, we show that the greatest proportion of genetic variation (31.5%) is explained by environmental differences. However, the potential for either adaptive or plastic divergence between demes is highly dependent upon the strength of migration and selection. Consequently, we highlight the utility of landscape genetics as a tool for hypothesis generation and experimental design, to identify focal populations and putative selection gradients, in order to distinguish between phenotypic plasticity and local adaptation.     

F(st) in a Hierarchical Island Model

It is shown that in a hierarchical island model, in which demes within a neighborhood exchange migrants at a much higher rate than do demes in different neighborhoods, hierarchical F statistics introduced by S. Wright can indicate the extent of gene flow within and between neighborhoods. At equilibrium, the within-neighborhood inbreeding coefficient, FSN, is approximately 1/(1 + 4Nm1) where N is the deme size and m1 is the migration rate among demes in the same neighborhood. The between-neighborhood inbreeding coefficient, FNT, is approximately 1/(1 + 4Ndm2) where d is the number of demes in a neighborhood and m2 is the migration rate among demes in different neighborhoods.     

Unequal allelic frequencies at the self‐incompatibility locus within local populations of Prunus avium L.: an effect of population structure?

In this paper, we investigated the genetic structure and distribution of allelic frequencies at the gametophytic self-incompatibility locus in three populations of Prunus avium L. In line with theoretical predictions under balancing selection, genetic structure at the self-incompatibility locus was almost three times lower than at seven unlinked microsatellites. Furthermore, we found that S-allele frequencies in wild cherry populations departed significantly from the expected isoplethic distribution towards which balancing selection is expected to drive allelic frequencies (i.e. identical frequency equal to the inverse of the number of alleles in the population). To assess whether this departure could be caused either by drift alone or by population structure, we used numerical simulations to compare our observations with allelic frequency distributions expected : (1) within a single deme from a subdivided population with various levels of differentiation; and (2) within a finite panmictic population with identical allelic diversity. We also investigated the effects of sample size and degree of population structure on tests of departure from isoplethic equilibrium. Overall, our results showed that the observed allele frequency distributions were consistent with a model of subdivided population with demes linked by moderate migration rate.     

Invasion and fixation of sex-reversal genes

We simulated a meta-population with random dispersal among demes but local mating within demes to investigate conditions under which a dominant female-determining gene W, with no individual selection advantage, can invade and become fixed in females, changing the population from male to female heterogamety. Starting with one mutant W in a single deme, the interaction of sex ratio selection and random genetic drift causes W to be fixed among females more often than a comparable neutral mutation with no influence on sex determination, even when YY males have slightly reduced viability. Meta-population structure and interdeme selection can also favour the fixation of W. The reverse transition from female to male heterogamety can also occur with higher probability than for a comparable neutral mutation. These results help to explain the involvement of sex-determining genes in the evolution of sex chromosomes and in sexual selection and speciation.     

Microhabitat Types Promote the Genetic Structure of a Micro-Endemic and Critically Endangered Mole Salamander (Ambystoma leorae) of Central Mexico

The reduced immigration and emigration rates resulting from the lack of landscape connectivity of patches and the hospitality of the intervening matrix could favor the loss of alleles through genetic drift and an increased chance of inbreeding. In order for isolated populations to maintain sufficient levels of genetic diversity and adapt to environmental changes, one important conservation goal must be to preserve or reestablish connectivity among patches in a fragmented landscape. We studied the last known population of Ambystoma leorae, an endemic and critically threatened species. The aims of this study were: (1) to assess the demographic parameters of A. leorae and to distinguish and characterize the microhabitats in the river, (2) to determine the number of existing genetic groups or demes of A. leorae and to describe possible relationships between microhabitats types and demes, (3) to determine gene flow between demes, and (4) to search for geographic locations of genetic discontinuities that limit gene flow between demes. We found three types of microhabitats and three genetically differentiated subpopulations with a significant level of genetic structure. In addition, we found slight genetic barriers. Our results suggest that mole salamander’s species are very sensitive to microhabitat features and relatively narrow obstacles in their path. The estimates of bidirectional gene flow are consistent with the pattern of a stepping stone model between demes, where migration occurs between adjacent demes, but there is low gene flow between distant demes. We can also conclude that there is a positive correlation between microhabitats and genetic structure in this population.     

Fine-scale spatial genetic structure and dispersal among spotted salamander (Ambystoma maculatum) breeding populations

We examined fine-scale genetic variation among breeding aggregations of the spotted salamander (Ambystoma maculatum) to quantify dispersal, interpopulation connectivity and population genetic structure. Spotted salamanders rely on temporary ponds or wetlands for aggregate breeding. Adequate breeding sites are relatively isolated from one another and field studies suggest considerable adult site fidelity; therefore, we expected to find population structure and differentiation at small spatial scales. We used microsatellites to estimate population structure and dispersal among 29 breeding aggregations in Tompkins County, New York, USA, an area encompassing 1272 km(2). Bayesian and frequency-based analyses revealed fine-scale genetic structure with two genetically defined demes: the North deme included seven breeding ponds, and the South deme included 13 ponds. Nine ponds showed evidence of admixture between these two genetic pools. Bayesian assignment tests for detection of interpopulation dispersal indicate that immigration among ponds is common within demes, and that certain populations serve as sources of immigrants to neighbouring ponds. Likewise, spatial genetic correlation analyses showed that populations < or = 4.8 km distant from each other show significant genetic correlation that is not evident at higher scales. Within-population levels of relatedness are consistently larger than expected if mating were completely random across ponds, and in the case of a few ponds, within-population processes such as inbreeding or reproductive skew contribute significantly to differentiation from neighbouring ponds. Our data underscore the importance of these within-population processes as a source of genetic diversity across the landscape, despite considerable population connectivity. Our data further suggest that spotted salamander breeding groups behave as metapopulations, with population clusters as functional units, but sufficient migration among demes to allow for potential rescue and recolonization. Amphibian habitats are becoming increasingly fragmented and a clear understanding of dispersal and patterns of population connectivity for taxa with different ecologies and life histories is crucial for their conservation.     

Demographic and genetic factors shaping contemporary metapopulation effective size and its empirical estimation in salmonid fish

The preservation of biodiversity requires an understanding of the maintenance of its components, including genetic diversity. Effective population size determines the amount of genetic variance maintained in populations, but its estimation can be complex, especially when populations are interconnected in a metapopulation. Theory predicts that the effective size of a metapopulation (meta-N(e)) can be decreased or increased by population subdivision, but little empirical work has evaluated these predictions. Here, we use neutral genetic markers and simulations to estimate the effective size of a putative metapopulation in Atlantic salmon (Salmo salar). For a weakly structured set of rivers, we find that meta-N(e) is similar to the sum of local deme sizes, whereas higher genetic differentiation among demes dramatically reduces meta-N(e) estimates. Interdemic demographic processes, such as asymmetrical gene flow, may explain this pattern. However, simulations also suggest that unrecognized population subdivision can also introduce downward bias into empirical estimation, emphasizing the importance of identifying the proper scale of distinct demographic and genetic processes. Under natural patterns of connectivity, evolutionary potential may generally be maintained at higher levels than the local population, with implications for conservation given ongoing species declines and habitat fragmentation.     

Plasticity and heritability of morphological variation within and between parapatric stickleback demes

The threespine stickleback (Gasterosteus aculeatus) has emerged as an important model organism in evolutionary ecology, largely due to the repeated, parallel evolution of divergent morphotypes found in populations having colonized freshwater habitats. However, morphological divergence following colonization is not a universal phenomenon. We explore this in a large-scale estuarine ecosystem inhabited by two parapatric stickleback demes, each physiologically adapted to divergent osmoregulatory environments (fresh vs. saline waters). Using geometric morphometric analyses of wild-caught individuals, we detected significant differences between demes, in addition to sexual dimorphism, in body shape. However, rearing full-sib families from each deme under controlled, reciprocal salinity conditions revealed no differences between genotypes and highly significant environmental effects. It is also noteworthy that fish from both demes were fully plated, whether found in the wild or reared under reciprocal salinity conditions. Although we found significant heritability for body shape, we also noted significant direct environmental effects for many latent shape variables. Moreover, we found little evidence for diversifying selection acting on body size and shape (Q(ST) ). Nevertheless, uniform compressive variation did exceed neutral expectations, yet despite evidence of both allometry and genetic correlation with body length, we detected no correlated signatures of selection. Taken together, these results suggest that much of the morphological divergence observed in this system is the result of plastic responses to environmental variation rather than adaptive differentiation.