Exact moment calculations for genetic models with migration,mutation, and drift

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. In addition, we provide closed-form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.     

Differentiation among populations with migration, mutation, and drift: implications for genetic inference

Populations may become differentiated from one another as a result of genetic drift. The amounts and patterns of differentiation at neutral loci are determined by local population sizes, migration rates among populations, and mutation rates. We provide exact analytical expressions for the mean, variance, and covariance of a stochastic model for hierarchically structured populations subject to migration, mutation, and drift. In addition to the expected correlation in allele frequencies among populations in the same geographic region, we demonstrate that there is a substantial correlation in allele frequencies among regions at the top level of the hierarchy. We propose a hierarchical Bayesian model for inference of Wright's F-statistics in a two-level hierarchy in which we estimate the among-region correlation in allele frequencies by substituting replication across loci for replication across time. We illustrate the approach through an analysis of human microsatellite data, and we show that approaches ignoring the among-region correlation in allele frequencies underestimate the amount of genetic differentiation among major geographic population groups by approximately 30%. Finally, we discuss the implications of these results for the use and interpretation of F-statistics in evolutionary studies.     

The coalescent process in models with selection, recombination and geographic subdivision

A population genetic model with a single locus at which balancing selection acts and many linked loci at which neutral mutations can occur is analysed using the coalescent approach. The model incorporates geographic subdivision with migration, as well as mutation, recombination, and genetic drift of neutral variation. It is found that geographic subdivision can affect genetic variation even with high rates of migration, providing that selection is strong enough to maintain different allele frequencies at the selected locus. Published sequence data from the alcohol dehydrogenase locus of Drosophila melanogaster are found to fit the proposed model slightly better than a similar model without subdivision.     

Polymorphism and divergence for island-model species

Estimates of the scaled selection coefficient, gamma of Sawyer and Hartl, are shown to be remarkably robust to population subdivision. Estimates of mutation parameters and divergence times, in contrast, are very sensitive to subdivision. These results follow from an analysis of natural selection and genetic drift in the island model of subdivision in the limit of a very large number of subpopulations, or demes. In particular, a diffusion process is shown to hold for the average allele frequency among demes in which the level of subdivision sets the timescale of drift and selection and determines the dynamic equilibrium of allele frequencies among demes. This provides a framework for inference about mutation, selection, divergence, and migration when data are available from a number of unlinked nucleotide sites. The effects of subdivision on parameter estimates depend on the distribution of samples among demes. If samples are taken singly from different demes, the only effect of subdivision is in the rescaling of mutation and divergence-time parameters. If multiple samples are taken from one or more demes, high levels of within-deme relatedness lead to low levels of intraspecies polymorphism and increase the number of fixed differences between samples from two species. If subdivision is ignored, mutation parameters are underestimated and the species divergence time is overestimated, sometimes quite drastically. Estimates of the strength of selection are much less strongly affected and always in a conservative direction.     

Variation in migratory behavior influences regional genetic diversity and structure among American Kestrel populations (Falco sparverius) in North America

Birds employ numerous strategies to cope with seasonal fluctuations in high-quality habitat availability. Long distance migration is a common tactic; however, partial migration is especially common among broadly distributed species. Under partial migration systems, a portion of a species migrates, whereas the remainder inhabits breeding grounds year round. In this study, we identified effects of migratory behavior variation on genetic structure and diversity of American Kestrels (Falco sparverius), a widespread partial migrant in North America. American Kestrels generally migrate; however, a resident group inhabits the southeastern United States year round. The southeastern group is designated as a separate subspecies (F. s. paulus) from the migratory group (F. s. sparverius). Using mitochondrial DNA and microsatellites from 183 and 211 individuals, respectively, we illustrate that genetic structure is stronger among nonmigratory populations, with differentiation measures ranging from 0.060 to 0.189 depending on genetic marker and analysis approach. In contrast, measures from western North American populations ranged from 0 to 0.032. These findings suggest that seasonal migratory behavior is also associated with natal and breeding dispersal tendencies. We likewise detected significantly lower genetic diversity within nonmigratory populations, reflecting the greater influence of genetic drift in small populations. We identified the signal of population expansion among nonmigratory populations, consistent with the recent establishment of higher latitude breeding locations following Pleistocene glacial retreat. Differentiation of F. s. paulus and F. s. sparverius reflected subtle differences in allele frequencies. Because migratory behavior can evolve quickly, our analyses suggest recent origins of migratory American Kestrel populations in North America.     

Population subdivision in westslope cutthroat trout (Oncorhynchus clarki lewisi) at the northern periphery of its range: evolutionary inferences and conservation implications

Westslope cutthroat trout (Oncorhynchus clarki lewisi, Salmonidae) are native to the upper Columbia, Missouri, and South Saskatchewan river drainages of western North America and are at the northern periphery of their range in southeastern British Columbia, Canada. We examined geographical variation in allele frequencies at eight microsatellite loci in 36 samples of westslope cutthroat trout from British Columbia to assess levels of population subdivision and to test the hypothesis that different habitat types (principally mainstem vs. above migration barrier habitats) would influence levels of genetic diversity, genetic divergence among populations, and attainment of equilibrium between gene flow and genetic drift. Across all samples, the mean number of alleles per locus was 3.9 and mean expected heterozygosity was 0.56. Population subdivision was extensive with an overall Fst (theta) of 0.32. Populations sampled above migration barriers had significantly fewer alleles, lower expected heterozygosity, but greater average pairwise Fst than populations sampled from mainstem localities. We found evidence for isolation-by-distance from a significant correlation between genetic distance and geographical distance (r = 0.31), but the pattern was much stronger (r = 0.51) when above barrier populations and a population that may have been involved in headwater exchanges were removed. By contrast, isolation-by-distance was not observed when only above barrier populations were tested among themselves. Our data support the maintenance of separate demographic management strategies for westslope cutthroat trout inhabiting different river systems and illustrate how differing habitat structure (e.g. presence of migration barriers) may influence patterns of biodiversity and gene flow-drift equilibrium.     

Population amalgamation and genetic variation: observations on artificially agglomerated tribal populations of Central and South America.

The interpretation of data on genetic variation with regard to the relative roles of different evolutionary factors that produce and maintain genetic variation depends critically on our assumptions concerning effective population size and the level of migration between neighboring populations. In humans, recent population growth and movements of specific ethnic groups across wide geographic areas mean that any theory based on assumptions of constant population size and absence of substructure is generally untenable. We examine the effects of population subdivision on the pattern of protein genetic variation in a total sample drawn from an artificial agglomerate of 12 tribal populations of Central and South America, analyzing the pooled sample as though it were a single population. Several striking findings emerge. (1) Mean heterozygosity is not sensitive to agglomeration, but the number of different alleles (allele count) is inflated, relative to neutral mutation/drift/equilibrium expectation. (2) The inflation is most serious for rare alleles, especially those which originally occurred as tribally restricted "private" polymorphisms. (3) The degree of inflation is an increasing function of both the number of populations encompassed by the sample and of the genetic divergence among them. (4) Treating an agglomerated population as though it were a panmictic unit of long standing can lead to serious biases in estimates of mutation rates, selection pressures, and effective population sizes. Current DNA studies indicate the presence of numerous genetic variants in human populations. The findings and conclusions of this paper are all fully applicable to the study of genetic variation at the DNA level as well.     

Behavior and Genetic Variation in Natural Populations

An analysis of allelic variation at genetic loci controllingseveral esterases and hemoglobin, as demonstrated by electrophoresis,indicates that wild populations of the house mouse (Mus musculus)are characterized by fine-scale genetic subdivision, which,through the territorial behavior of family groups (tribes),is achieved even in the absence of physical or ecological barriersto migration. Heterogeneity in allele frequencies among samples from farmsin the same region and from barns on the same farm was demonstrated.Spatial variation in allele frequencies within single barns,involving a clustering of like genotypes, was shown by grid-trapping,thus providing direct evidence of tribal subdivision in continuouslydistributed populations. For two loci, Es-3 and Hbb, an excess of heterozygotes appearedin samples from small populations, while a deficit characterizedsamples from large populations. The evolutionary significance of subdivision and consequentdrift in house mouse populations cannot properly be evaluatedat this time. Although stochastic processes may play the dominantrole in determining, at a given locus, the genotypes of individualsand frequencies of alleles in small populations, geographicpatterns of variation, as studied in Texas, are characterizedby uniformity of allelic frequency in major physiographic orclimatic regions, as would be expected if selection is determiningthe frequencies.     

Genetic studies among seven endogamous populations of the Koshi Zone, Bihar (India)

The distribution of AB0 and Rhesus blood groups, PTC taste sensitivity and colour blindness was studied among seven endogamous populations (Tharu, Mushar, Santal, Dhobi, Julaha, Kulhaiya and Karan Kayastha) in the Koshi Zone of Bihar (India). The phenotype and allele frequencies of the four gene loci (AB0, RH, PTC and colour blindness) show considerable differences between these populations. The measurement of genetic distances revealed, that the lowest genetic distance is seen between Dhobi and Julaha, the highest between Mushar and Tharu. From the genetic distance analysis there is some evidence for a close genetic relationship among the population groups belonging to the same region, irrespective of their caste, religion, linguistic or any other affinities. It may be concluded that all these populations have arisen through a common ancestor and changed gene frequencies among them is due to evolutionary forces like mutation, selection, migration, temporal variation and genetic drift. However, these populations retain their separate entities by practising endogamy. Gene diversity analysis reveals that these populations are at an early stage of genetic differentiation.     

Differentiation among populations of the Rhodiola iremelica Boriss. (Grassulaceae). in the Southern Urals

Isoenzyme markers and polyacrylamide gel electrophoresis have been used to study the genetic structure of populations of Rhodiola iremelica Boriss. (Grassulaceae), a Southern Ural endemic protected by the state and included in the Red Data Book of Bashkortostan Republic. A relatively large genetic variation at the species level has been found. The subdivision among populations (F(ST) = 0.115) is higher than in most cross-pollination angiosperms. No consistent pattern has been observed in the spatial distribution of its genetic variation. The relatively high differentiation among samples of R. iremelica characterized by small effective population sizes, may be accounted for by genetic drift, inbreeding, and a restricted gene flow. To preserve the population gene pool, in situ protection of the species in nature is insufficient. It seems advisable to create synthetic populations ex situ and reintroduce them into nature.     

Patterns of differentiation and hybridization in North American wolflike canids, revealed by analysis of microsatellite loci

Genetic divergence and gene flow among closely related populations are difficult to measure because mutation rates of most nuclear loci are so low that new mutations have not had sufficient time to appear and become fixed. Microsatellite loci are repeat arrays of simple sequences that have high mutation rates and are abundant in the eukaryotic genome. Large population samples can be screened for variation by using the polymerase chain reaction and polyacrylamide gel electrophoresis to separate alleles. We analyzed 10 microsatellite loci to quantify genetic differentiation and hybridization in three species of North American wolflike canids. We expected to find a pattern of genetic differentiation by distance to exist among wolflike canid populations, because of the finite dispersal distances of individuals. Moreover, we predicted that, because wolflike canids are highly mobile, hybrid zones may be more extensive and show substantial changes in allele frequency, relative to nonhybridizing populations. We demonstrate that wolves and coyotes do not show a pattern of genetic differentiation by distance. Genetic subdivision in coyotes, as measured by theta and Gst, is not significantly different from zero, reflecting persistent gene flow among newly established populations. However, gray wolves show significant subdivision that may be either due to drift in past Ice Age refugia populations or a result of other causes. Finally, in areas where gray wolves and coyotes hybridize, allele frequencies of gray wolves are affected, but those of coyotes are not. Past hybridization between the two species in the south-central United States may account for the origin of the red wolf.      

SNP and haplotype variation in the human genome

We have surveyed and summarized several aspects of DNA variability among humans. The variation described is the result of mutation followed by a combination of drift, migration and selection bringing the frequencies high enough to be observed. This paper describes what we have learned about how DNA variability differs among genes and populations. We sequenced functional regions of a set of 3950 genes. DNA was sampled from 82 unrelated humans: 20 African-Americans, 20 East Asians, 21 Caucasians, 18 Hispanic-Latinos and 3 Native Americans. Different aspects of variability showed a great deal of concordance. In particular, we studied patterns of single nucleotide polymorphism (SNP) allele and haplotype sharing among the four, large sample populations. We also examined how linkage disequilibrium (LD) between SNPs relates to physical distance in the different populations. It is clear from our findings that while many variants are common to all populations, many others have a more restricted distribution. Research that attempts to find genetic variants that explain phenotypic variants must be careful in their choice of study population.     

Differentiation among populations of the Rhodiola iremelica Boriss. (Grassulaceae) in the Southern Urals

Isoenzyme markers and polyacrylamide gel electrophoresis have been used to study the genetic structure of populations of Rhodiola iremelica Boriss. (Grassulaceae), a southern Ural endemic protected by the state and included in the Red Data Book of Bashkortostan Republic. A relatively large genetic variation at the species level has been found. The subdivision among populations (F _ST = 0.115) is higher than in most cross-pollination angiosperms. No consistent pattern has been observed in the spatial distribution of its genetic variation. The relatively high differentiation among samples of R. iremelica characterized by small effective population sizes, may be accounted for by genetic drift, inbreeding, and a restricted gene flow. To preserve the population gene pool, in situ protection of the species in nature is insufficient. It seems advisable to create synthetic populations ex situ and reintroduce them into nature.     

MACRO- AND MICROGEOGRAPHIC STRUCTURE OF A SPATIALLY SUBDIVIDED BEETLE SPECIES IN NATURE

Spatial subdivision of species can affect their population structure by allowing processes such as limited dispersal, spatial heterogeneity in selective pressures, small population sizes, and random events to operate. By studying species restricted to islands or “island” habitats, one can attempt to determine which of these factors have affected the current structure of the population. Collops georgianus (Coleoptera: Melyridae), a beetle species endemic to the “island” habitat of granitic rock outcrops, was chosen to see how its spatially subdivided distribution has affected its genetic structure. Its genetic structure was examined on both a macrogeographic and a microgeographic level using protein electrophoresis. Macrogeographically, 12 populations throughout its range were sampled. The discontinuous distribution of outcrops, and thus populations, throughout its range, has determined the connectivity of the populations. Significant variation in allele frequencies and substructuring (F_ST = 0.192) was found throughout the range, but there was no spatial autocorrelation. Microgeographically, in the central part of the range, where outcrops are denser and more continuously distributed in space, there was evidence of isolation by distance. Very little variation in allele frequencies was found, but a low but significant level of substructuring occurred among the populations. Comparison of disjunct and continuous populations microgeographically revealed no effect of disjunct distributions, although a significant effect of distance was detected. Effective population size variation among populations and between years, compounded with the effects of local extinctions, suggest that random processes such as drift and founder effects are important determinants of the population's genetic structure.     

Genetic variation at nine short tandem repeat loci among islanders of the eastern Adriatic coast of Croatia

We have analyzed the extent of genetic variation at nine autosomal short tandem repeat loci (D3S1358, VWA, FGA, TH01, TPOX, CSF1PO, D5S818, D13S317, D7S820) among six populations from Croatia: five distributed in the islands of the eastern Adriatic coast and one from the mainland. The purpose is to investigate the usefulness of these loci in detecting regional genetic differentiation in the studied populations. Significant heterogeneity among the island and mainland populations is revealed in the distributions of allele frequencies; however, the absolute magnitude of the coefficient of gene differentiation is small but significant. The summary measures of genetic variation, namely, heterozygosity, number of alleles, and allele size variance, do not indicate reduced genetic variation in the island populations compared to the mainland population. In contrast to the two measures of genetic variation, allele size variance and within-locus heterozygosity, the imbalance index (beta) indicates evidence of recent expansion of population sizes in all islands and in the mainland. High mutation rates of the studied loci together with local drift effects are likely explanations for interisland genetic variation and the observed lack of reduced genetic diversity among the island populations.     

The coalescent in an island model of population subdivision with variation among demes

A simple genealogical structure is found for a general finite island model of population subdivision. The model allows for variation in the sizes of demes, in contributions to the migrant pool, and in the fraction of each deme that is replaced by migrants every generation. The ancestry of a sample of non-recombining DNA sequences has a simple structure when the sample size is much smaller than the total number of demes in the population. This allows an expression for the probability distribution of the number of segregating sites in the sample to be derived under the infinite-sites mutation model. It also yields easily computed estimators of the migration parameter for each deme in a multi-deme sample. The genealogical process is such that the lineages ancestral to the sample tend to accumulate in demes with low migration rates and/or which contribute disproportionately to the migrant pool. In addition, common ancestor or coalescent events tend to occur in demes of small size. This provides a framework for understanding the determinants of the effective size of the population, and leads to an expression for the probability that the root of a genealogy occurs in a particular geographic region, or among a particular set of demes.     

GENETIC DIVERSITY AND POPULATION STRUCTURE IN CAMELLIA JAPONICA L. (THEACEAE)

Camellia japonica is a widespread and morphologically diverse tree native to parts of Japan and adjacent islands. Starch gel electrophoresis was used to score allelic variation at 20 loci in seeds collected from 60 populations distributed throughout the species range. In comparison with other plant species, the level of genetic diversity within C. japonica populations is very high: 66.2% of loci were polymorphic on average per population, with a mean number of 2.16 alleles per locus; the mean observed and panmictic heterozygosities were 0.230 and 0.265, respectively. Genotypic proportions at most loci in most populations fit Hardy-Weinberg expectations. However, small heterozygote deficiencies were commonly observed (mean population fixation index = 0.129). It is suggested that the most likely cause of the observed deficiencies is population subdivision into genetically divergent subpopulations. The overall level of population differentiation is greater than is typically observed in out-breeders: The mean genetic distance and identity (Nei's D and I) between pairs of populations were 0.073 and 0.930, respectively, and Wright's Fst was 0.144. Differences among populations appeared to be manifested as variation in gene frequencies at many loci rather than variation in allelic composition per se. However, the patterns of variation were not random. Reciprocal clinal variation of gene frequencies was observed for allele pairs at six loci. In addition, principal components analysis revealed that populations tended to genetically cluster into four regions representing the geographic areas Kyushu, Shikoku, western Honshu, and eastern Honshu. There was a significant relationship between genetic and geographic distance (r = 0.61; P < 0.01). Analysis of variance on allozyme frequencies showed that there was approximately four times as much differentiation among populations within regions, as among regions. It is likely that the observed patterns of population relationships result from the balance between genetic drift in small subpopulations and gene flow between them.     

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

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

Spatiotemporal genetic differentiation of Cuban natural populations of the pink shrimp <Emphasis Type="Italic">Farfantepenaeus notialis</Emphasis>

We analyzed the spatiotemporal genetic structure of Farfantepenaeus notialis populations using five microsatellites loci in order to understand the influence of natural events such as hurricanes on the genetic drift/migration balance as the main cause for the variation of allele frequencies over time. The results were compared with the previous ones obtained from allozymes and mtDNA. High and stable genetic diversity levels (He=0.879+/-0.0015) were found over eight years for the populations that inhabit the south Cuban platform, however significant changes of allele frequencies were detected over time. The F(ST) estimates, albeit low, revealed significant differences among populations inside the Ana Maria Gulf for 1995 but not for the 1999 and 2003 samples. The F(ST), AMOVA and the genetic distance analysis revealed the instability of the genetic structure over time in accordance with allozymes results. The correspondence of the microsatellite results with those obtained from allozymes confirm the effects of migration enhanced by natural events as the main cause of the temporal variation of allele frequencies. The genetic drift effect was discarded through the evaluation of Ne and the M ratio, while natural selection effects were rejected because of the lowest probability of microsatellite loci being under selective pressures. The microsatellite data are also consistent with the results obtained with mtDNA in detecting significant and persistent genetic differences between the Gulfs of Ana María and Batabanó for the years 1995 and 2003.     

Genetic profile of cosmopolitan populations: effects of hidden subdivision

Natural populations of many organisms exhibit excess of rare alleles in comparison with the predictions of the neutral mutation hypothesis. It has been shown before that either a population bottleneck or the presence of slightly deleterious mutations can explain this phenomenon. A third explanation is presented in this work, showing that hidden subdivision within a population can also lead to an excess of rare alleles in the total population when the expectations of the neutral model are based on the allele frequency profile of the entire population data. With two examples (mitochondrial DNA-morph distribution and isozyme allele frequency distributions), it is shown that most cosmopolitan human populations exhibit excess of rare as well as total allele counts, when these are compared with the expectations of the neutral mutation hypothesis. The mitochondrial data demonstrate that such excesses can be detected from genetic variation at a single locus as well, and this is not due to stochastic error of allele frequency distributions. Contrast of the present observations with the allele frequency profiles in agglomerated tribal populations from South and Central America shows that even when the neutral expectations hold for individual subpopulations, if all subpopulations are grouped into a single population, the pooled data exhibit an excess of total number of alleles that is mainly due to the excess of rare alleles. Therefore, a primary cause of the excess number of rare alleles could be the hidden subdivision, and the magnitude of the excess indicates the extent of substructuring. The two components of hidden subdivision are: 1) Number of subpopulations, and 2) the average genetic distance among them. The implications of this observation in estimating mutation rate are discussed indicating the difficulties of comparing mutation rates from different population surveys.