Confidence Intervals for Population Allele Frequencies: The General Case of Sampling from a Finite Diploid Population of Any Size

The estimation of population allele frequencies using sample data forms a central component of studies in population genetics. These estimates can be used to test hypotheses on the evolutionary processes governing changes in genetic variation among populations. However, existing studies frequently do not account for sampling uncertainty in these estimates, thus compromising their utility. Incorporation of this uncertainty has been hindered by the lack of a method for constructing confidence intervals containing the population allele frequencies, for the general case of sampling from a finite diploid population of any size. In this study, we address this important knowledge gap by presenting a rigorous mathematical method to construct such confidence intervals. For a range of scenarios, the method is used to demonstrate that for a particular allele, in order to obtain accurate estimates within 0.05 of the population allele frequency with high probability (%), a sample size of is often required. This analysis is augmented by an application of the method to empirical sample allele frequency data for two populations of the checkerspot butterfly (Melitaea cinxia L.), occupying meadows in Finland. For each population, the method is used to derive % confidence intervals for the population frequencies of three alleles. These intervals are then used to construct two joint % confidence regions, one for the set of three frequencies for each population. These regions are then used to derive a % confidence interval for Jost''s D, a measure of genetic differentiation between the two populations. Overall, the results demonstrate the practical utility of the method with respect to informing sampling design and accounting for sampling uncertainty in studies of population genetics, important for scientific hypothesis-testing and also for risk-based natural resource management.     

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.     

Simple allelic-phenotype diversity and differentiation statistics for allopolyploids

The analysis of genetic diversity within and between populations is a routine task in the study of diploid organisms. However, population genetic studies of polyploid organisms have been hampered by difficulties associated with scoring and interpreting molecular data. This occurs because the presence of multiple alleles at each locus often precludes the measurement of genotype or allele frequencies. In allopolyploids, the problem is compounded because genetically distinct isoloci frequently share alleles. As a result, analysis of genetic diversity patterns in allopolyploids has tended to rely on the interpretation of phenotype frequencies, which loses information available from allele composition. Here, we propose the use of a simple allelic-phenotype diversity statistic (H') that measures diversity as the average number of alleles by which pairs of individuals differ. This statistic can be extended to a population differentiation measure (F'ST), which is analogous to FST. We illustrate the behaviour of these statistics using coalescent computer simulations that show that F'ST behaves in a qualitatively similar way to FST, thus providing a useful way to quantify population differentiation in allopolyploid species.     

Further data on the microsatellite locus D12S67 in worldwide populations: an unusual distribution of D12S67 alleles in Native Americans

We report the frequencies of alleles at the microsatellite locus D12S67 in 2 widely separated ethnic groups of the world: 2 populations from Sulawesi, an island in the Indonesian archipelago, and 5 Native American tribes of Colombia, South America. The allele frequencies in the Minihasans and Torajans of Sulawesi are similar to each other (but the modal class allele is different) and in general agreement with those reported in mainland Asian groups, but different from both Europeans and Chinese Han of Taiwan. The 5 Native American tribes (Arsario, Kogui, Ijka, Wayuu, and Coreguaje) display different allele frequencies from those seen in Sulawesi populations, in other groups from Europe and mainland Asia, and in Chinese Han of Taiwan. Native Americans exhibit a bimodal distribution of alleles, unlike other groups, with significant differences among the tribes. The Arsario and Kogui have no admixture with Europeans or Africans and are the most distinctive, while the Wayuu have the most admixture and show most similarity to other groups. The data suggest that nonadmixed Native Americans may be quite distinctive with respect to this marker. The most common allele varies across the 5 tribes, from 249 base pairs to 261 base pairs. All samples exhibit Hardy-Weinberg genotype proportions; heterozygosities are lowest in the 2 nonadmixed Native American tribes. Examination of all the available data indicates that some east Asian and southeast Asian groups are characterized by a high frequency of smaller sized D12S67 alleles, while other populations have a greater proportion of the larger sized alleles. The cumulative, though still highly restricted, population data on locus D12S67 demonstrate that it may be of considerable value in anthropological genetic studies of ethnic groups. Data are required on Native Americans outside Colombia before this marker can be used in admixture studies of this group.     

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.     

On the size distribution of private microsatellite alleles

Private microsatellite alleles tend to be found in the tails rather than in the interior of the allele size distribution. To explain this phenomenon, we have investigated the size distribution of private alleles in a coalescent model of two populations, assuming the symmetric stepwise mutation model as the mode of microsatellite mutation. For the case in which four alleles are sampled, two from each population, we condition on the configuration in which three distinct allele sizes are present, one of which is common to both populations, one of which is private to one population, and the third of which is private to the other population. Conditional on this configuration, we calculate the probability that the two private alleles occupy the two tails of the size distribution. This probability, which increases as a function of mutation rate and divergence time between the two populations, is seen to be greater than the value that would be predicted if there was no relationship between privacy and location in the allele size distribution. In accordance with the prediction of the model, we find that in pairs of human populations, the frequency with which private microsatellite alleles occur in the tails of the allele size distribution increases as a function of genetic differentiation between populations.     

Drawing inferences about the coancestry coefficient

The coancestry coefficient, also known as the population structure parameter, is of great interest in population genetics. It can be thought of as the intraclass correlation of pairs of alleles within populations and it can serve as a measure of genetic distance between populations. For a general class of evolutionary models it determines the distribution of allele frequencies among populations. Under more restrictive models it can be regarded as the probability of identity by descent of any pair of alleles at a locus within a random mating population. In this paper we review estimation procedures that use the method of moments or are maximum likelihood under the assumption of normally distributed allele frequencies. We then consider the problem of testing hypotheses about this parameter. In addition to parametric and non-parametric bootstrap tests we present an asymptotically-distributed chi-square test. This test reduces to the contingency-table test for equal sample sizes across populations. Our new test appears to be more powerful than previous tests, especially for loci with multiple alleles. We apply our methods to HapMap SNP data to confirm that the coancestry coefficient for humans is strictly positive.     

孔雀微卫星引物筛选及其遗传多样性分析

利用29对鸡微卫星标记对孔雀基因组DNA进行种间扩增, 发现14对引物能扩增出特异性条带, 每对引物扩增的平均等位基因数为1.71, 有7对引物具有较丰富的多态性, 其中MCW0080和MCW0098最为理想。蓝孔雀和绿孔雀群体间和群体内的遗传分析结果表明, 绿孔雀和蓝孔雀两个群体的期望杂合度分别为0.7422和0.6943, 群体间的遗传分化系数为0.078, Reynolds’遗传距离和基因流分别为0.0603和3.896, 结果显示这两个孔雀群体的杂合度和遗传多样性水平都很低, 且有相互混杂的趋势。     

A likelihood ratio approach for identifying three-quarter siblings in genetic databases

The detection of family relationships in genetic databases is of interest in various scientific disciplines such as genetic epidemiology, population and conservation genetics, forensic science, and genealogical research. Nowadays, screening genetic databases for related individuals forms an important aspect of standard quality control procedures. Relatedness research is usually based on an allele sharing analysis of identity by state (IBS) or identity by descent (IBD) alleles. Existing IBS/IBD methods mainly aim to identify first-degree relationships (parent–offspring or full siblings) and second degree (half-siblings, avuncular, or grandparent–grandchild) pairs. Little attention has been paid to the detection of in-between first and second-degree relationships such as three-quarter siblings (3/4S) who share fewer alleles than first-degree relationships but more alleles than second-degree relationships. With the progressively increasing sample sizes used in genetic research, it becomes more likely that such relationships are present in the database under study. In this paper, we extend existing likelihood ratio (LR) methodology to accurately infer the existence of 3/4S, distinguishing them from full siblings and second-degree relatives. We use bootstrap confidence intervals to express uncertainty in the LRs. Our proposal accounts for linkage disequilibrium (LD) by using marker pruning, and we validate our methodology with a pedigree-based simulation study accounting for both LD and recombination. An empirical genome-wide array data set from the GCAT Genomes for Life cohort project is used to illustrate the method.Subject terms: Genetic markers, Population genetics     

Temporal changes in allele frequencies in two reciprocally selected maize populations

The effects of breeding on allele frequency changes at 82 restriction fragment length polymorphism (RFLP) loci were examined in two maize (Zea mays L.) populations undergoing reciprocal recurrent selection, Iowa Stiff Stalk Synthetic and Iowa Corn Borer Synthetic #1. After 12 cycles of selection, approximately 30% of the alleles were extinct and 10% near fixation in each population. A test of selective neutrality identified several loci in each population whose allele frequency changes cannot be explained by genetic drift; interpopulation mean expected heterozygosity increased for that subset of 28 loci but not for the remaining 54 loci. Mean expected heterozygosity within the two subpopulations decreased 39%, while the between-population component of genetic variation increased from 0.5% to 33.4% of the total. Effective population size is a key parameter for discerning allele frequency changes due to genetic drift versus those resulting from selection and genetic hitchhiking. Empirical estimates of effective population size for each population were within the range predicted by the breeding method. Received: 10 June 1998 / Accepted: 29 April 1999     

湘江野鲤养殖群体和自然群体遗传多样性的微卫星分析

采用微卫星技术,用17对微卫星引物对湘江野鲤养殖群体和自然群体的的遗传多样性进行分析.结果表明:有15对引物扩增出清晰的条带,其中13对引物在群体间呈现多态性;2个群体中,13对多态性引物分别扩增等位基因2～12个,共90个,其中35个等位基因为2群体共有,55个等位基因具有群体特异性,引物平均等位基因数为6.92个,等位基因频率为0.0667～0.8333;养殖群体和自然群体的平均遗传杂合度和平均多态信息含量分别为0.5688、0.5152,0.5860、0.5347;2个群体间遗传相似性指数为0.6762,遗传距离为0.3238,表明湘江野鲤养殖和自然群体遗传多样性均较为丰富,2个群体间遗传变异程度较高.     

Evolutionary and statistical properties of three genetic distances

Many genetic distances have been developed to summarize allele frequency differences between populations. I review the evolutionary and statistical properties of three popular genetic distances: DS, DA, and theta;, using computer simulation of two simple evolutionary histories: an isolation model of population divergence and an equilibrium migration model. The effect of effective population size, mutation rate, and mutation mechanism upon the parametric value between pairs of populations in these models explored, and the unique properties of each distance are described. The effect of these evolutionary parameters on study design is also investigated and similar results are found for each genetic distance in each model of evolution: large sample sizes are warranted when populations are relatively genetically similar; and loci with more alleles produce better estimates of genetic distance.     

Population genetic analysis of 15 autosomal STR loci in the Russian population of northeastern Inner-Mongolia, China

In the present study, we investigated the genetic polymorphisms of 15 autosomal STR loci in the Russian population of northeastern Inner-Mongolia, China as well as its genetic relationships with other populations. DNA typing for 15 autosomal STR loci was performed on 148 randomly selected healthy individuals from the Russian population living in Eerguna, northeastern Inner-Mongolia. Allelic frequencies of these loci were calculated by direct counting. The genotype data of this Russian population was moreover compared to other populations using neighbor-joining method, as such constructing a phylogenic tree. A total of 143 alleles were found in the Russian population with corresponding allele frequencies in the range from 0.0034 to 0.5372. Among all the 15 loci, D18S51 had the highest polymorphism (PIC = 0.8632), whereas TPOX had the lowest (PIC = 0.5179). In the phylogenic tree, this Russian population has a close relationship with the populations of South Siberia and northeastern Asia. This study may increase our understanding of the genetic background of the Russian population in Eerguna, China as such providing useful information for anthropological research, forensic sciences as well as disease-association studies.     

High levels of allozyme variation within populations and low allozyme divergence within and among species of Hemerocallis (Liliaceae)

Thirty populations from five species of Hemerocallis in Korea were analyzed by starch gel electrophoresis to measure genetic diversity and to determine genetic population structure and the amount of genetic divergence within and between species at 12 isozyme loci. In addition, Moran's I spatial autocorrelation statistics were used to examine the spatial distribution of allozyme polymorphisms in populations of H. thunbergii and H. hakuunensis. Populations of five Korean species maintain high levels of genetic variation and little differentiation among populations and species. Mean expected heterozygosities range from 0.165 in H. hongdoensis, an island endemic, to 0.265 in H. taeanensis, and a total of 81 alleles across the 12 loci were detected in the five species. G(ST) values for each of the five species were low, ranging from 0.051 in H. taeanensis to 0.078 in H. hakuunensis. Mean intraspecific Nei's genetic identities (I) between populations of the five species were all above 0.97. However, a considerable level of heterozygote deficiencies within populations was detected, ranging from 0.242 to 0.411 measured as F(IS) statistics. This deficiencies may be due to inbreeding, limited pollen and seed dispersal, or from the pooling of subpopulations that differ in allele frequencies. A small spatial scale population substructuring (<12 m) was found in H. thunbergii and H. hakuunensis. A group of populations from each of the five previously designated Hemerocallis species (based on their morphology, ecology, and phenology) agrees with our allozyme data, though pairwise comparisons among species had high I values (from 0.862, H. middendorffii vs. H. hongdoensis, to 0.969, H. thunbergii vs. H. taeanensis). This is attributed to the presence of the same high-frequency alleles in different species at seven loci. In addition, no "diagnostic allele" that appears in all populations of one species, but is absent in other species, was detected at the 12 isozyme loci. These all suggest that species of Hemerocallis in Korea may have recently derived from an ancestor or progenitor harboring high levels of genetic diversity.     

Molecular and genetic characterization of the allelic variants of Du215, Du281, Du323, and Du47G microsatellite loci in parthenogenetic lizard <Emphasis Type="Italic">Darevskia armeniaca</Emphasis> (Lacertidae)

A key issue in the study of unisexual (parthenogenetic) vertebrate species is the determination of their genetic and clonal diversity. In pursuing this aim, various markers of nuclear and mitochondrial genomes can be used. The most effective genetic markers include microsatellite DNA, characterized by high variability. The development and characterization of such markers is a necessary step in the genetic studies of parthenogenetic species. In the present study, using locus-specific PCR, for the first time, an analysis of allelic polymorphism of four microsatellite loci is performed in the populations of parthenogenetic species Darevskia armeniaca. In the studied populations, allelic variants of each locus are identified, and the nucleotide sequences of each allele are determined. It is demonstrated that allele differences are associated with the variation in the structure of microsatellite clusters and single nucleotide substitutions at fixed distances in flanking DNA regions. Structural allele variations form haplotype markers that are specific to each allele and are inherited from their parental bisexual species. It is established which of the parental alleles of each locus were inherited by the parthenogenetic species. The characteristics of the distribution and frequency of the alleles of microsatellite loci in the populations of D. armeniaca determining specific features of each population are obtained. The observed heterozygosity of the populations at the studied loci and the mutation rates in genome regions, as well as Nei’s genetic distances between the studied populations, are determined, and the phylogenetic relationships between them are established.     

C8A and C8B polymorphisms in Norwegians and Norwegian lapps

C8 inheritance patterns in 364 mother-child pairs formed the basis for evaluation of the existence of silent alleles (null alleles) in the genes determining the two known polymorphic C8 systems. While evidence for such alleles was not found in C8A (alpha-gamma complex), two observations of null allele segregation in C8B (beta chain) indicate a C8BQ*0 allele frequency of about 0.07. Two population samples comprising 150 Lappish and 1,264 non-Lappish Norwegians were examined for phenotype distributions in C8A and C8B. The phenotype distributions were mainly in accordance with the expected Hardy-Weinberg distribution. The results for C8A indicated simple, codominant inheritance of two frequent and several rare alleles. Allele frequencies were similar in the two populations. The C8A B gene frequency in Norwegians was significantly lower than that in FRG and higher than that in Negroes. C8B allele frequencies were also calculated from gene counts in the population material, but with due corrections for the C8BQ*0 frequency observed in the mother-child material.     

Genetic diversity of Chinese giant salamander (Andrias davidianus) based on the novel microsatellite markers

Chinese giant salamander (Andrias davidianus) is a rare amphibian species in the world. Microsatellite markers are a promising tool for accurate estimation population structure and genetic diversity. In this paper, we isolated novel microsatellite marker for Chinese giant salamander using fast isolation by AFLP of sequences containing repeats (FIASCO) method. More than 50% sequences in 132 clones had repeat number over ten times with di or trinucleeotide repeat except of (GA)₁₂. Seventy pairs of primers were designed and eleven polymorphic microsatellite loci were characterized for wild and cultivated Chinese giant salamander populations. The allele number was from 3 to 9 in different loci. Polymorphism information content was from 0.544 to 0.702 in cultivated population. The results implied more alleles and PIC were in the wild population than cultivated population. The observed heterozygosities in two populations were higher than 0.553. The data analysis suggested that the cultivated population has lower genetic diversity than wild population, which it??s perhaps owing to inbreeding in artificial breeding. To our knowledge, it??s the first time to isolated microsatellite markers for Chinese giant salamander. The result indicated that the markers were suitable for the population genetic analysis of Chinese giant salamander.     

Joint estimation of contemporary seed and pollen dispersal rates among plant populations

There are few statistical methods for estimating contemporary dispersal among plant populations. A maximum-likelihood procedure is introduced here that uses pre- and post-dispersal population samples of biparentally inherited genetic markers to jointly estimate contemporary seed and pollen immigration rates from a set of discrete external sources into a target population. Monte Carlo simulations indicate that accurate estimates and reliable confidence intervals can be obtained using this method for both pollen and seed migration rates at modest sample sizes (100 parents/population and 100 offspring) when population differentiation is moderate (F(ST) ≥ 0.1), or by increasing pre-dispersal samples (to about 500 parents/population) when genetic divergence is weak (F(ST) = 0.01). The method exhibited low sensitivity to the number of source populations and achieved good accuracy at affordable genetic resolution (10 loci with 10 equifrequent alleles each). Unsampled source populations introduced positive biases in migration rate estimates from sampled sources, although they were minor when the proportion of immigration from the latter was comparatively low. A practical application of the method to a metapopulation of the Australian resprouter shrub Banksia attenuata revealed comparable levels of directional seed and pollen migration among dune groups, and the estimate of seed dispersal was higher than a previous estimate based on conservative assignment tests. The method should be of interest to researchers and managers assessing broad-scale nonequilibrium seed and pollen gene flow dynamics in plants.     

Phylogenetic relationship analysis of Iranians and other world populations using allele frequencies at 12 polymorphic markers

The estimation of genetic distance between populations could improve our viewpoint about human migration and its genetic origin. In this study, we used allele frequency data of 12 polymorphic markers on 250 individuals (500 alleles) from the Iranian population to estimate genetic distance between the Iranians and other world populations. The phylogenetic trees for three different sets of allele frequency data were constructed. Our results revealed the genetic similarity between the Iranians and European populations. The lowest genetic distance was observed between the Iranians and some populations reside in Russia. Furthermore, the high genetic distance was observed between the Iranians and East Asian populations. The data suggested that the Iranians might have relatively close evolutionary history with Europeans, but historically independent from East Asian populations. The evaluation of genetic distance between Indians populations and Iranians was also performed. The Indian groups showed low genetic distance with others, but high genetic distance with the Iranians. This study could provide a new insight into the evolutionary history of the Iranian population.     

广东省猴耳环遗传多样性研究

为了解猴耳环(Archidendron clypearia)种质资源的遗传多样性,以广东省12个野生猴耳环群体的146份种质资源为材料,采用SSR分子标记技术对其遗传多样性和亲缘关系进行分析.结果表明,21对SSR引物共检测到249个等位基因,平均每对SSR引物检测的等位基因数(Na)为11.857,有效等位基因数(N...