Equilibrium Values of Measures of Population Subdivision for Stepwise Mutation Processes

Expected values of WRIGHT's F-statistics are functions of probabilities of identity in state. These values may be quite different under an infinite allele model and under stepwise mutation processes such as those occurring at microsatellite loci. However, a relationship between the probability of identity in state in stepwise mutation models and the distribution of coalescence times can be deduced from the relationship between probabilities of identity by descent and the distribution of coalescence times. The values of F(IS) and F(ST) can be computed using this property. Examination of the conditional probability of identity in state given some coalescence time and of the distribution of coalescence times are also useful for explaining the properties of F(IS) and F(ST) at high mutation rate loci, as shown here in an island model of population structure.     

A Comparison of Isozyme and Quantitative Genetic Variation in Pinus Contorta Ssp. Latifolia by F(st)

We employed F-statistics to analyze quantitative and isozyme variation among five populations of Pinus contorta ssp. latifolia, a wind-pollinated outcrossing conifer with wide and continuous distribution in west North America. Estimates of population differentiation (F(ST)) for six quantitative traits were compared with the overall estimate of the differentiation (F*(ST)) from 19 isozymes that tested neutral to examine whether similar evolutionary processes were involved in morphological and isozyme differentiation. While the F(ST) estimates for specific gravity, stem diameter, stem height and branch length were significantly greater than the F*(ST) estimate, as judged from the 95% confidence intervals by bootstrapping, the F(ST) estimates for branch angle and branch diameter were indistinguishable from the F*(ST) estimate. Differentiation in stem height and stem diameter might reflect the inherent adaptation of the populations for rapid growth to escape suppression by neighboring plants during establishment and to regional differences in photoperiod, precipitation and temperature. In contrast, divergences in wood specific gravity and branch length might be correlated responses to population differentiation in stem growth. Possible bias in the estimation of F(ST) due to Hardy-Weinberg disequilibrium (F(IS) & 0), linkage disequilibrium, maternal effects and nonadditive genetic effects was discussed with special reference to P. contorta ssp. latifolia.     

Detecting Isolation by Distance Using Phylogenies of Genes

We introduce a method for analyzing phylogenies of genes sampled from a geographically structured population. A parsimony method can be used to compute s, the minimum number of migration events between pairs of populations sampled, and the value of s can be used to estimate the effective migration rate M, the value of Nm in an island model with local populations of size N and a migration rate m that would yield the same value of s. Extensive simulations show that there is a simple relationship between M and the geographic distance between pairs of samples in one- and two-dimensional models of isolation by distance. Both stepping-stone and lattice models were simulated. If two demes k steps apart are sampled, then, s, the average value of s, is a function only of k/(Nm) in a one-dimensional model and is a function only of k/(Nm)2 in a two-dimensional model. Furthermore, log(M) is approximately a linear function of log(k). In a one-dimensional model, the regression coefficient is approximately -1 and in a two-dimensional model the regression coefficient is approximately -0.5. Using data from several locations, the regression of log(M) on log(distance) may indicate whether there is isolation by distance in a population at equilibrium and may allow an estimate of the effective migration rate between adjacent sampling locations. Alternative methods for analyzing DNA sequence data from a geographically structured population are discussed. An application of our method to the data of R. L. Cann, M. Stoneking and A. C. Wilson on human mitochondrial DNA is presented.     

A new Bayesian method to identify the environmental factors that influence recent migration

We present a new multilocus genotype method that makes inferences about recent immigration rates and identifies the environmental factors that are more likely to explain observed gene flow patterns. It also estimates population-specific inbreeding coefficients, allele frequencies, and local population F(ST)'s and performs individual assignments. We generate synthetic data sets to determine the region of the parameter space where our method is and is not able to provide accurate estimates. Our simulation study indicates that reliable results can be obtained when the global level of genetic differentiation (F(ST)) is >1%, the number of loci is only 10, and sample sizes are of the order of 50 individuals per population. We illustrate our method by applying it to Pakistani human data, considering altitude and geographic distance as explanatory factors. Our results suggest that altitude explains better the genetic data than geographic distance. Additionally, they show that southern low-altitude populations have higher migration rates than northern high-altitude ones.     

Inbreeding coefficients and coalescence times.

This paper describes the relationship between probabilities of identity by descent and the distribution of coalescence times. By using the relationship between coalescence times and identity probabilities, it is possible to extend existing results for inbreeding coefficients in regular systems of mating to find the distribution of coalescence times and the mean coalescence times. It is also possible to express Sewall Wright's FST as the ratio of average coalescence times of different pairs of genes. That simplifies the analysis of models of subdivided populations because the average coalescence time can be found by computing separately the time it takes for two genes to enter a single subpopulation and time it takes for two genes in the same subpopulation to coalesce. The first time depends only on the migration matrix and the second time depends only on the total number of individuals in the population. This approach is used to find FST in the finite island model and in one- and two-dimensional stepping-stone models. It is also used to find the rate of approach of FST to its equilibrium value. These results are discussed in terms of different measures of genetic distance. It is proposed that, for the purposes of describing the amount of gene flow among local populations, the effective migration rate between pairs of local populations, M, which is the migration rate that would be estimated for those two populations if they were actually in an island model, provides a simple and useful measure of genetic similarity that can be defined for either allozyme or DNA sequence data.     

Random amplified polymorphic DNA diversity of marginal and central populations in Pinus contorta subsp. latifolia.

Fifteen populations of lodgepole pine (Pinus contorta subsp. latifolia) were surveyed for diversity across 52 random amplified polymorphic DNAs (RAPDs). The objective was to compare single-locus and multilocus structures in four marginal, three intermediate, and eight central populations. Single-locus estimates indicated average observed and expected heterozygosity to be 0.19 and 0.17, respectively. When these estimates were split into population categories, a clear trend of increasing diversity was detected in the direction of marginal to central populations. F-statistics indicated an excess of heterozygotes, with F(IS) ranging from -0.08 for marginal populations to -0.15 for central populations and averaging -0.12 over 15 populations. The estimates of F(ST) decreased towards the margins of the species range, indicating increased population differentiation. Forty-nine of 52 RAPDs tested neutral in the Ewens-Watterson analysis. Multilocus analysis showed significant two-locus and high-order gametic disequilibria in all 15 populations. The most prominent components of the two-locus analysis were the variance of disequilibrium (VD, 46.2%) and the multilocus Wahlund effect (31.9%). This high value for VD indicated that founder effects could explain much of the observed multilocus associations. When analyzed by population categories, the VD showed a decreasing trend indicating that variation due to founder effects was more prominent in marginal populations. The two-locus Wahlund effect (WC) that is characteristic of strong population subdivision was highest in the central populations. This indicated significant levels of gene flow between populations with different allelic combinations.     

Population structure of the large Japanese field mouse, Apodemus speciosus (Rodentia: Muridae), in suburban landscape, based on mitochondrial D-loop sequences

Genetic structure of the large Japanese field mouse populations in suburban landscape of West Tokyo, Japan was determined using mitochondrial DNA control region sequence. Samples were collected from six habitats linked by forests and green tract along the Tama River, and from two forests segregated by urban areas from those continuous habitats. Thirty-five haplotypes were detected in 221 animals. Four to eight haplotypes were found within each local population belonging to the continuous landscape. Some haplotypes were shared by two or three adjacent local populations. On the other hand, two isolated habitats were occupied by one or two indigenous haplotypes. Significant genetic differentiation between all pairs of local populations, except for one pair in the continuous habitats, was found by analysis of molecular variance (amova). The geographical distance between habitats did not explain the large variance of pairwise F(ST)-values among local populations. F(ST)-values between local populations segregated by urban areas were higher than those between local populations in the continuous habitat, regardless of geographical distance. The results of this study demonstrated quantitatively that urban areas inhibit the migration of Apodemus speciosus, whereas a linear green tract along a river functions as a corridor. Moreover, it preserves the metapopulation structure of A. speciosus as well as the corridors in suburban landscape.     

A study of Y-chromosome microsatellite variation in sub-Saharan Africa: a comparison between F(ST) and R(ST) genetic distances

Seven Y-chromosome microsatellite loci (DYS19, DYS389I, DYS389II, DYS390, DYS391, DYS392, and DYS393) were analyzed in three populations from sub-Saharan Africa: the Bamileke and Ewondo populations from Cameroon and the Hutu from Rwanda. Complete typing was obtained for 112 individuals, and a total of 53 different haplotypes was observed. The single-locus gene diversity, averaged across populations, ranges from 0.100 for the DYS392 locus to 0.610 for the DYS389I locus. The haplotype diversity ranges from 0.832 (Ewondo) to 0.965 (Hutu), with an intermediate value of 0.918 in the Bamileke. The diversity among Bamileke, Ewondo, Hutu, and other sub-Saharan populations selected from the literature was analyzed using both a classical (F(ST)) and a stepwise-based (R(ST)) genetic distance method. The pattern of interpopulational diversity based on F(ST) was congruent with anthropological knowledge, while that based on R(ST) revealed unexpected and unconvincing population affinities. From a practical point of view, our study indicates that Y-chromosome microsatellite data may provide useful information for analyses of interpopulational diversity among sub-Saharan populations if an adequate number of loci and individuals along with an appropriate genetic distance method are used. On a theoretical ground, we propose that the lesser performance of R(ST) compared to F(ST) could be explained by the important role played by genetic drift in shaping the relationships among examined populations.     

Joint estimation of migration rate and effective population size using the island model

Using the island model of population demography, I report that the demographic parameters migration rate and effective population size can be jointly estimated with equilibrium probabilities of identity in state calculated using a sample of genotypes collected at a single point in time from a single generation. The method, which uses moment-type estimators, applies to dioecious populations in which females and males have identical demography and monoecious populations with no selfing and requires that offspring genotypes are sampled following reproduction and prior to migration. I illustrate the estimation procedure using the infinite-island model with no mutation and the finite-island model with three kinds of mutation models. In the infinite-island model with no mutation, the estimators can be expressed as simple functions of estimates of the F-statistic parameters F(IT) and F(ST). In the finite-island model with mutation among k alleles, mutation rate, migration rate, and effective population size can be simultaneously estimated. The estimates of migration rate and effective population size are somewhat robust to violations in assumptions that may arise in empirical applications such as different kinds of mutation models and deviations from temporal equilibrium.     

Hierarchical analysis of colony and population genetic structure of the eastern subterranean termite, Reticulitermes flavipes, using two classes of molecular markers

Termites (Isoptera) comprise a large and important group of eusocial insects, yet, in contrast to the eusocial Hymenoptera (ants, bees, wasps), the breeding systems of termites remain poorly understood. In this study, I inferred the breeding system of the subterranean termite Reticulitermes flavipes based on colony and population genetic structure as determined from microsatellite and mitochondrial DNA markers. Termites were sampled from natural wood debris from three undisturbed, forested sites in central North Carolina. In each site, two transects separated by 1 km were sampled at approximately 15-m intervals. A total of 1272 workers collected from 57 collection points were genotyped at six microsatellite loci, and mitochondrial DNA haplotype was determined for a subset of these individuals using either restriction fragment length polymorphism or sequence variation in the AT-rich region. Colonies appeared to be localized: workers from the 57 collection points represented 56 genetically distinct colonies with only a single colony occupying two collection points located 15 m apart. Genetic analysis of family structure and comparisons of estimates of F-statistics (F(IT), F(IC), F(CT)) and coefficients of relatedness (r) among nestmate workers with results of computer simulations of potential breeding systems suggested that 77% of all colonies were simple families headed by outbred monogamous pairs, whereas the remaining colonies were extended (inbred) families headed by low numbers of neotenics (about two females and one male) who were the direct offspring of the colony founders. There was no detectable isolation by distance among colonies along transects, suggesting that colony reproduction by budding is not common and that dispersal of reproductives during mating flights is not limited over this distance. Higher-level analysis of the microsatellite loci indicated weak but significant differentiation among sites (F(ST) = 0.06), a distance of 16-38 km, and between transects within sites (F(ST) = 0.06), a distance of 1 km. No significant differentiation at either the transect or site level was detected in the mitochondrial DNA sequence data. These results indicate that the study populations of R. flavipes have a breeding system characterized by monogamous pairs of outbred reproductives and relatively low levels of inbreeding because most colonies do not live long enough to produce neotenics, and those colonies that do generate neotenics contain an effectively small number of them.     

Mitochondrial DNA under siege in avian phylogeography

Mitochondrial DNA (mtDNA) has been the workhorse of research in phylogeography for almost two decades. However, concerns with basing evolutionary interpretations on mtDNA results alone have been voiced since the inception of such studies. Recently, some authors have suggested that the potential problems with mtDNA are so great that inferences about population structure and species limits are unwarranted unless corroborated by other evidence, usually in the form of nuclear gene data. Here we review the relative merits of mitochondrial and nuclear phylogeographical studies, using birds as an exemplar class of organisms. A review of population demographic and genetic theory indicates that mitochondrial and nuclear phylogeographical results ought to concur for both geographically unstructured populations and for populations that have long histories of isolation. However, a relatively common occurrence will be shallow, but geographically structured mtDNA trees--without nuclear gene corroboration--for populations with relatively shorter periods of isolation. This is expected because of the longer coalescence times of nuclear genes (approximately four times that of mtDNA); such cases do not contradict the mtDNA inference of recent isolation and evolutionary divergence. Rather, the nuclear markers are more lagging indicators of changes in population structure. A review of the recent literature on birds reveals the existence of relatively few cases in which nuclear markers contradict mitochondrial markers in a fashion not consistent with coalescent theory. Preliminary information from nuclear genes suggests that mtDNA patterns will prove to be robust indicators of patterns of population history and species limits. At equilibrium, mitochondrial loci are generally a more sensitive indicator of population structure than are nuclear loci, and mitochondrial estimates of F(ST)-like statistics are generally expected to exceed nuclear ones. Hence, invoking behavioural or ecological explanations of such differences is not parsimonious. Nuclear genes will prove important for quantitative estimates of the depths of haplotype trees, rates of population growth and values of gene flow.     

Genetic variability in East Asian dogs using microsatellite loci analysis.

An analysis of eight microsatellite loci in 213 animals was performed to define the genetic structure and variability of 11 East Asian native dog populations. Allele diversity, observed heterozygosities, expected heterozygosities, F-statistics, G(ST) estimates, number of migrants per generation (Nm), and Nei's DA distance were calculated. Expected mean heterozygosities of Asian native dogs varied within a range of 0.310-0.718 with a mean value of 0.580. In a sample of 11 Asian dogs, the highest genetic diversity was exhibited in the Korean native dogs and the lowest in the Shiba, the Japanese native dog. All populations except the Kishu and Akita showed statistically significant deviation from Hardy-Weinberg equilibrium at more than one locus. After corrections for multiple significance tests, deviations over all loci were statistically significant in 7 of 11 dog populations, meaning that Asian dogs are genetically subdivided (global F(ST) = 0.154). Despite the locus-specific deviations, statistically significant departures from the Hardy-Weinberg equilibrium reflect deviations in the direction of heterozygote deficit, the global F(IS) being 0.072. In the neighbor-joining and unweighted pair group method with arithmetic mean (UPGMA) dendrograms based on Nei's DA distance, the Korean native breeds (the Sapsaree and the Jindo) were grouped together, then with the Eskimo dog. The two Japanese native dogs (the Hokkaido and the Akita) also clustered together, with moderate bootstrap support. In spite of some deviation, the three-dimensional scattergram based on principal components supported the conclusions suggested by the dendrograms based on Nei's DA distance. From these two analyses, the Korean native dogs formed the closest groups and then showed a close relationship to the Eskimo dogs, reflecting the fact that the Korean native dogs might be originated from dogs in the northern part of Far East Asia.     

Dispersal and genetic structure in the American marten, Martes americana

Natal dispersal in a vagile carnivore, the American marten (Martes americana), was studied by comparing radio-tracking data and microsatellite genetic structure in two populations occupying contrasting habitats. The genetic differentiation determined among groups of individuals using F(ST) indices appeared to be weak in both landscapes, and showed no increase with geographical distance. Genetic structure investigated using pairwise genetic distances between individuals conversely showed a pattern of isolation by distance (IBD), but only in the population occurring in a homogeneous high-quality habitat, therefore showing the advantage of individual-based analyses in detecting within-population processes and local landscape effects. The telemetry study of juveniles revealed a leptokurtic distribution of dispersal distances in both populations, and estimates of the mean squared parent-offspring axial distance (sigma2) inferred both from the genetic pattern of IBD and from the radio-tracking survey showed that most juveniles make little contribution to gene flow.     

Genetic Differentiation in Populations with Different Classes of Individuals

I formulate and analyse a model of population structure with different classes of individuals. These different classes may be age classes, other demographic classes, or different types of habitats homogeneously distributed over a geographical area. The value of population differentiation under an island model of dispersal and the increase of differentiation with geographical distance in one- and two-dimensional "isolation by distance" models are then obtained for a generalization of the FST measure of population structure, as a function of "effective" mutation, migration, and population size parameters. The relevant effective subpopulation size is related to the "mutation effective population size" of a single isolated subpopulation and, in models of age-structured populations, to the inbreeding effective population size.     

Microsatellite null alleles and estimation of population differentiation

Microsatellite null alleles are commonly encountered in population genetics studies, yet little is known about their impact on the estimation of population differentiation. Computer simulations based on the coalescent were used to investigate the evolutionary dynamics of null alleles, their impact on F(ST) and genetic distances, and the efficiency of estimators of null allele frequency. Further, we explored how the existing method for correcting genotype data for null alleles performed in estimating F(ST) and genetic distances, and we compared this method with a new method proposed here (for F(ST) only). Null alleles were likely to be encountered in populations with a large effective size, with an unusually high mutation rate in the flanking regions, and that have diverged from the population from which the cloned allele state was drawn and the primers designed. When populations were significantly differentiated, F(ST) and genetic distances were overestimated in the presence of null alleles. Frequency of null alleles was estimated precisely with the algorithm presented in Dempster et al. (1977). The conventional method for correcting genotype data for null alleles did not provide an accurate estimate of F(ST) and genetic distances. However, the use of the genetic distance of Cavalli-Sforza and Edwards (1967) corrected by the conventional method gave better estimates than those obtained without correction. F(ST) estimation from corrected genotype frequencies performed well when restricted to visible allele sizes. Both the proposed method and the traditional correction method have been implemented in a program that is available free of charge at http://www.montpellier.inra.fr/URLB/. We used 2 published microsatellite data sets based on original and redesigned pairs of primers to empirically confirm our simulation results.     

Genetic structure in the coral-reef-associated Banggai cardinalfish, Pterapogon kauderni

In this study, we used 11 polymorphic microsatellite loci to show that oceanic distances as small as 2-5 km are sufficient to produce high levels of population genetic structure (multilocus F(ST) as high as 0.22) in the Banggai cardinalfish (Pterapogon kauderni), a heavily exploited reef fish lacking a pelagic larval dispersal phase. Global F(ST) among all populations, separated by a maximum distance of 203 km, was 0.18 (R(ST) = 0.35). Moreover, two lines of evidence suggest that estimates of F(ST) may actually underestimate the true level of genetic structure. First, within-locus F(ST) values were consistently close to the theoretical maximum set by the average within-population heterozygosity. Second, the allele size permutation test showed that R(ST) values were significantly larger than F(ST) values, indicating that populations have been isolated long enough for mutation to have played a role in generating allelic variation among populations. The high level of microspatial structure observed in this marine fish indicates that life history traits such as lack of pelagic larval phase and a good homing ability do indeed play a role in shaping population genetic structure in the marine realm.     

Coalescence-time distributions in a serial founder model of human evolutionary history

Simulation studies have demonstrated that a variety of patterns in worldwide genetic variation are compatible with the trends predicted by a serial founder model, in which populations expand outward from an initial source via a process in which new populations contain only subsets of the genetic diversity present in their parental populations. Here, we provide analytical results for key quantities under the serial founder model, deriving distributions of coalescence times for pairs of lineages sampled either from the same population or from different populations. We use these distributions to obtain expectations for coalescence times and for homozygosity and heterozygosity values. A predicted approximate linear decline in expected heterozygosity with increasing distance from the source population reproduces a pattern that has been observed both in human genetic data and in simulations. Our formulas predict that populations close to the source location have lower between-population gene identity than populations far from the source, also mirroring results obtained from data and simulations. We show that different models that produce similar declining patterns in heterozygosity generate quite distinct patterns in coalescence-time distributions and gene identity measures, thereby providing a basis for distinguishing these models. We interpret the theoretical results in relation to their implications for human population genetics.     

SNP-based analysis of genetic substructure in the German population

OBJECTIVE: To evaluate the relevance and necessity to account for the effects of population substructure on association studies under a case-control design in central Europe, we analysed three samples drawn from different geographic areas of Germany. Two of the three samples, POPGEN (n = 720) and SHIP (n = 709), are from north and north-east Germany, respectively, and one sample, KORA (n = 730), is from southern Germany. METHODS: Population genetic differentiation was measured by classical F-statistics for different marker sets, either consisting of genome-wide selected coding SNPs located in functional genes, or consisting of selectively neutral SNPs from 'genomic deserts'. Quantitative estimates of the degree of stratification were performed comparing the genomic control approach [Devlin B, Roeder K: Biometrics 1999;55:997-1004], structured association [Pritchard JK, Stephens M, Donnelly P: Genetics 2000;155:945-959] and sophisticated methods like random forests [Breiman L: Machine Learning 2001;45:5-32]. RESULTS: F-statistics showed that there exists a low genetic differentiation between the samples along a north-south gradient within Germany (F(ST)(KORA/POPGEN): 1.7 . 10(-4); F(ST)(KORA/SHIP): 5.4 . 10(-4); F(ST)(POPGEN/SHIP): -1.3 . 10(-5)). CONCLUSION: Although the F(ST )-values are very small, indicating a minor degree of population structure, and are too low to be detectable from methods without using prior information of subpopulation membership, such as STRUCTURE [Pritchard JK, Stephens M, Donnelly P: Genetics 2000;155:945-959], they may be a possible source for confounding due to population stratification.     

Allozymic diversity of Allium tricoccum (Ait.) Solander var. burdickii Hanes in isolated populations of Nova Scotia (Canada)

 Allium tricoccumvar. burdickii is a rare species in Nova Scotia, growing in isolated populations. Genetic variation was investigated in three populations using cellulose acetate gel electrophoresis. The results showed that all 13 enzyme loci were polymorphic. An excess of heterozygotes was found in all populations. A total of 29 genotypes were detected in the populations. Very few genotypes were common to two populations and none to the three populations. Genetic diversity among populations was compared with geographic distance and previous work. The comparison of the genetic distance matrix to the geographic distance matrix indicated no relationship. F-statistics suggested that the populations are predominantly maintained through vegetative propagation. Occasional sexual reproduction and gene flow might occur in order to maintain high level of variation among populations. Environmental conditions could also influence population genetic structure as they occur in highly different habitats. Received November 13, 2000 Accepted February 26, 2001