Estimation of Allele Frequencies in Ethnically Heterogeneous Populations

A method for reconstructing allele frequencies characteristic of an original ethnically homogeneous population before the start of migration processes is described. Information on both the ethnic group studied and offspring of interethnic marriages is used to estimate the allele frequencies. This makes it possible to increase the informativeness of the sample, which, in the case of ethnic heterogeneity, depends not only on allele frequencies and the total sample size, but also on the ethnic structure of the sample. The problem of estimating allele frequency in an ethnically heterogeneous sample has been solved analytically for diallelic loci. It has been demonstrated that, if offspring of interethnic marriages with the same degree of outbreeding is added to a sample of the ethnic group studied, the sample informativeness does not change. To utilize the information contained in the phenotypes of the offspring of interethnic marriages, representatives of the population from which migration occurs should be included into the sample. The size of the sample ensuring the preassigned accuracy of estimation is minimized at a certain ratio between the numbers of the offspring of interethnic marriages and the “immigrants.” To analyze polyallelic loci, a software package has been developed that allows estimating allele frequencies, determining the errors of these estimates, and planning the sample ensuring the preassigned accuracy of estimation. The package is available free at http://mga.bionet.nsc.ru/PopMixed/PopMixed.html.__________Translated from Genetika, Vol. 41, No. 7, 2005, pp. 990–996.Original Russian Text Copyright © 2005 by Axenovich, Kirichenko.     

Genetic-demographic processes in urban populations of the Ukraine in the 90's. The marital structure of the Poltava population

Analysis of records of the marriages that were contracted in the city of Poltava revealed an increase in outbreeding between 1960 and 1985 in the Poltava population. This was expressed in increased ethnic diversity, proportion of interethnic marriages, migration range, and the parent-offspring and average marital distances, whereas the proportion of the indigenous ethnic group (Ukrainians) decreased. By 1995, outbreeding decreased: the ethnic composition of the population became more homogeneous (98% Slavic), the proportion of Ukrainians and the frequency of monoethnic marriages increased, and the migration range decreased. During the period studied, the population became more panmictic with respect to ethnicity and birthplace, with the social and professional subdivisions of the population remaining unchanged.     

Genetic subdivision of Dagestan ethnic populations

Relationships between ethnic and genetic differentiation with respect to 54 microsatellites have been analyzed in five Daghestan ethnic groups. To detect the microsatellites, human chromosomes 3, 17, and 18 were screened with a step of 10 cM (Weber/CHLC 9.0 markers) at the Mammalian Genotyping Service (National Institute of Health, United States). Comparison of the polymorphism of these loci in Daghestan populations with average worldwide data has revealed generally low heterozygosity in Daghestan populations, which is accounted for by traditional endogamous and consanguineous marriages throughout the history of these populations. The inbreeding coefficient in Daghestan ethnic groups varies from 0.005 to 0.0134 and is close to the worldwide maximum known to date. For some DNA loci, significant differences between the offsprings of consanguineous and exogamous marriages with respect to allele sizes and their variance have been found. The Daghestan ethnic populations studied differ from one another in both the frequencies of common alleles and the presence of rare alleles that are unique for each ethnic group of Daghestan and have not been found in any other population in the world.     

Genetic demographic processes in Ukrainian population in 1990. The marriage structure of the Donetsk population

Analysis of records of the marriages that were contracted in the city of Donetsk revealed that, between 1960 and 1992, the marriage rate in the city decreased from 14.8 to 4.7 per 1000 people, the migration rate (m) decreased from 0.71 to 0.34, and the endogamy index increased from 0.123 to 0.458. Between 1960 and 1985, outbreeding in the Donetsk population increased, which was expressed in an increase in the frequency of interethnic marriages, migration range, and the average marital distance, as well as a decrease in the proportion of the indigenous ethnic group (Ukrainians). By 1992, outbreeding decreased: the population became more homogeneous ethnically (93% Slavic), the proportion of Ukrainians and the frequency of monoethnic marriages increased, and the average marital distance decreased. In 1960 and 1992, the coefficients of marriage contingency (K) with respect to ethnicity were 0.34 and 0.22, respectively. Regarding birthplaces, the population became almost panmictic (in 1960 and 1992, the K values were 0.15 and 0.10, respectively). Marriage structure with respect to occupation remained almost unchanged (the K values were 0.22 and 0.23, respectively). Throughout the entire period studied, the most pronounced population subdivision was that with respect to the education level (the K values were 0.36 and 0.39, respectively).     

Genetic Subdivision of Daghestan Ethnic Populations

Relationships between ethnic and genetic differentiation with respect to 54 microsatellites have been analyzed in five Daghestan ethnic groups. To detect the microsatellites, human chromosomes 3, 17, and 18 were screened with a step of 10 cM (Weber/CHLC 9.0 markers) at the Mammalian Genotyping Service (National Institute of Health, United States). Comparison of the polymorphism of these loci in Daghestan populations with average worldwide data has revealed generally low heterozygosity in Daghestan populations, which is accounted for by traditional endogamous and consanguineous marriages throughout the history of these populations. The inbreeding coefficient in Daghestan ethnic groups varies from 0.005 to 0.0134 and is close to the worldwide maximum known to date. For some DNA loci, significant differences between the offsprings of consanguineous and exogamous marriages with respect to allele sizes and their variance have been found. The Daghestan ethnic populations studied differ from one another in both the frequencies of common alleles and the presence of rare alleles that are unique for each ethnic group of Daghestan and have not been found in any other population in the world.     

Analysis and Optimization of Bulk DNA Sampling with Binary Scoring for Germplasm Characterization

The strategy of bulk DNA sampling has been a valuable method for studying large numbers of individuals through genetic markers. The application of this strategy for discrimination among germplasm sources was analyzed through information theory, considering the case of polymorphic alleles scored binarily for their presence or absence in DNA pools. We defined the informativeness of a set of marker loci in bulks as the mutual information between genotype and population identity, composed by two terms: diversity and noise. The first term is the entropy of bulk genotypes, whereas the noise term is measured through the conditional entropy of bulk genotypes given germplasm sources. Thus, optimizing marker information implies increasing diversity and reducing noise. Simple formulas were devised to estimate marker information per allele from a set of estimated allele frequencies across populations. As an example, they allowed optimization of bulk size for SSR genotyping in maize, from allele frequencies estimated in a sample of 56 maize populations. It was found that a sample of 30 plants from a random mating population is adequate for maize germplasm SSR characterization. We analyzed the use of divided bulks to overcome the allele dilution problem in DNA pools, and concluded that samples of 30 plants divided into three bulks of 10 plants are efficient to characterize maize germplasm sources through SSR with a good control of the dilution problem. We estimated the informativeness of 30 SSR loci from the estimated allele frequencies in maize populations, and found a wide variation of marker informativeness, which positively correlated with the number of alleles per locus.     

Accuracy of haplotype frequency estimation for biallelic loci, via the expectation-maximization algorithm for unphased diploid genotype data

Haplotype analyses have become increasingly common in genetic studies of human disease because of their ability to identify unique chromosomal segments likely to harbor disease-predisposing genes. The study of haplotypes is also used to investigate many population processes, such as migration and immigration rates, linkage-disequilibrium strength, and the relatedness of populations. Unfortunately, many haplotype-analysis methods require phase information that can be difficult to obtain from samples of nonhaploid species. There are, however, strategies for estimating haplotype frequencies from unphased diploid genotype data collected on a sample of individuals that make use of the expectation-maximization (EM) algorithm to overcome the missing phase information. The accuracy of such strategies, compared with other phase-determination methods, must be assessed before their use can be advocated. In this study, we consider and explore sources of error between EM-derived haplotype frequency estimates and their population parameters, noting that much of this error is due to sampling error, which is inherent in all studies, even when phase can be determined. In light of this, we focus on the additional error between haplotype frequencies within a sample data set and EM-derived haplotype frequency estimates incurred by the estimation procedure. We assess the accuracy of haplotype frequency estimation as a function of a number of factors, including sample size, number of loci studied, allele frequencies, and locus-specific allelic departures from Hardy-Weinberg and linkage equilibrium. We point out the relative impacts of sampling error and estimation error, calling attention to the pronounced accuracy of EM estimates once sampling error has been accounted for. We also suggest that many factors that may influence accuracy can be assessed empirically within a data set-a fact that can be used to create "diagnostics" that a user can turn to for assessing potential inaccuracies in estimation.     

An estimator for pairwise relatedness using molecular markers

I propose a new estimator for jointly estimating two-gene and four-gene coefficients of relatedness between individuals from an outbreeding population with data on codominant genetic markers and compare it, by Monte Carlo simulations, to previous ones in precision and accuracy for different distributions of population allele frequencies, numbers of alleles per locus, actual relationships, sample sizes, and proportions of relatives included in samples. In contrast to several previous estimators, the new estimator is well behaved and applies to any number of alleles per locus and any allele frequency distribution. The estimates for two- and four-gene coefficients of relatedness from the new estimator are unbiased irrespective of the sample size and have sampling variances decreasing consistently with an increasing number of alleles per locus to the minimum asymptotic values determined by the variation in identity-by-descent among loci per se, regardless of the actual relationship. The new estimator is also robust for small sample sizes and for unknown relatives being included in samples for estimating allele frequencies. Compared to previous estimators, the new one is generally advantageous, especially for highly polymorphic loci and/or small sample sizes.     

Marriage structure of Yakut populations: Ethnic composition and isonymy inbreeding

Marriage structure has been analyzed in the populations of the administrative centers of five uluses of the Republic of Sakha (Yakutia). The populations studied differ from one another with respect to ethnic composition, namely in the ratio between the indigenous and immigrant populations (the indigenous populations are larger in three uluses), in the proportions of representatives of indigenous ethnic groups among men and women contracting marriages, and in the frequencies of monoethnic and interethnic marriages. Positive assortative marriage among persons of the same ethnic group has been demonstrated. The total inbreeding estimated by isonymy (Fit) varies from 0 to 0.007576.     

Use of microsatellite loci to classify individuals by relatedness

This study investigates the use of microsatellite loci for estimating relatedness between individuals in wild, outbred, vertebrate populations. We measured allele frequencies at 20 unlinked, dinucleotide-repeat microsatellite loci in a population of wild mice ( Mus musculus ), and used these observed frequencies to generate the expected distributions of pairwise relatedness among full sib, half sib, and unrelated pairs of individuals, as would be estimated from the microsatellite data. In this population one should be able to discriminate between unrelated and full-sib dyads with at least 97% accuracy, and to discriminate half-sib pairs from unrelated pairs or from full-sib pairs with better than 80% accuracy. If one uses the criterion that parent-offspring pairs must share at least one allele per locus, then only 15% of full-sib pairs, 2% of half-sib pairs, and 0% of unrelated pairs in this population would qualify as potential parent-offspring pairs. We verified that the simulation results (which assume a random mating population in Hardy-Weinberg and linkage equilibrium) accurately predict results one would obtain from this population in real life by scoring laboratory-bred full- and half-sib families whose parents were wild-caught mice from the study population. We also investigated the effects of using different numbers of loci, or loci of different average heterozygosities ( He ), on misclassification frequencies. Both variables have strong effects on misclassification rate. For example, it requires almost twice as many loci of He = 0.62 to achieve the same accuracy as a given number of loci of He = 0.75. Finally, we tested the ability of UPGMA clustering to identify family groups in our population. Clustering of allele matching scores among the offspring of four sets of independent maternal half sibships (four females, each mated to two different males) perfectly recovered the true family relationships.     

Allelic frequencies and statistical data obtained from 12 codis STR loci in an admixed population of the Brazilian Amazon

The allelic frequencies of 12 short tandem repeat loci were obtained from a sample of 307 unrelated individuals living in Macapá, a city in the northern Amazon region, Brazil. These loci are the most commonly used in forensics and paternity testing. Based on the allele frequency obtained for the population of Macapá, we estimated an interethnic admixture for the three parental groups (European, Native American and African) of, respectively, 46%, 35% and 19%. Comparing these allele frequencies with those of other Brazilian populations and of the Iberian Peninsula population, no significant distances were observed. The interpopulation genetic distances (F(ST) coefficients) to the present database ranged from F(ST) = 0.0016 between Macapá and Belém to F(ST) = 0.0036 between Macapá and the Iberian Peninsula.     

Biased estimation of the recombination fraction using half-sib families and informative offspring

A maximum-likelihood method to estimate the recombination fraction and its sampling variance using informative and noninformative half-sib offspring is derived. Estimates of the recombination fraction are biased up to 20 cM when noninformative offspring are discarded. In certain scenarios, the sampling variance can be increased or reduced up to fivefold due to the bias in estimating the recombination fraction and the LOD score can be reduced up to 5 units when discarding noninformative offspring. Comparison of the estimates of recombination fraction, map distance, and LOD score when constructing a genetic map with 251 two-point linkage analyses and six families of Norwegian cattle was carried out to evaluate the implications of discarding noninformative offspring in practical situations. The average discrepancies in absolute value (average difference when using and neglecting noninformative offspring) were 0.0146, 1.64 cM, and 2.61 for the recombination fraction, map distance, and the LOD score, respectively. A method for simultaneous estimation of allele frequencies in the dam population and a transmission disequilibrium parameter is proposed. This method might account for the bias in estimating allele frequencies in the dam population when the half-sib offspring is selected for production traits.     

Sample size requirements for addressing the population genetic issues of forensic use of DNA typing.

DNA typing offers a unique opportunity to identify individuals for medical and forensic purposes. Probabilistic inference regarding the chance occurrence of a match between the DNA type of an evidentiary sample and that of an accused suspect, however, requires reliable estimation of genotype and allele frequencies in the population. Although population-based data on DNA typing at several hypervariable loci are being accumulated at various laboratories, a rigorous treatment of the sample size needed for such purposes has not been made from population genetic considerations. It is shown here that the loci that are potentially most useful for forensic identification of individuals have the intrinsic property that they involve a large number of segregating alleles, and a great majority of these alleles are rare. As a consequence, because of the large number of possible genotypes at the hypervariable loci that offer the maximum potential for individualization, the sample size needed to observe all possible genotypes in a sample is large. In fact, the size is so large that even if such a huge number of individuals could be sampled, it could not be guaranteed that such a sample was drawn from a single homogeneous population. Therefore adequate estimation of genotypic probabilities must be based on allele frequencies, and the sample size needed to represent all possible alleles is far more reasonable. Further economization of sample size is possible if one wants to have representation of only the frequent alleles in the sample, so that the rare allele frequencies can be approximated by an upper bound for forensic applications.     

Pedigree analysis in evaluating gene frequency in aboriginal populations of Siberia]

Procedure is described to estimate allele frequencies in indigenous populations of Siberia using phenotype data not only for "pure-blood" representatives of the ethnic groups examined, but also for the descendants of mixed marriages. Implementation of the method requires reconstruction of the data on relatives for the sample examined. Inclusion of the data on descendants of mixed marriages into the analysis increases the sample information content and decreases variance of the estimates obtained. The advantages of the method are illustrated using an example of Tundra Nentsy, for whom it was shown that variance of estimates at the analysis of the blood groups allele frequencies can be diminished approximately by a factor of 1.5.     

Dynamic of marriage structure in three cities of Ukraine from 1960 to 1992

Marriage structure was studied in the city of Kiev and in two cities of the Sumy oblast, Shostka and Trostyanets. Ethnic affiliations and birthplaces of persons contracting marriage were analyzed as the main characteristics of population genetic diversity. The ethnic composition of persons contracting marriage and the proportions of mono- and interethnic marriages remained almost unchanged during one generation. The majority of the persons contracting marriage were Ukrainians (66-91%); among other ethnic groups, only Russians considerably contributed to ethnic diversity (up to 26%). During the period studied, coefficients of marital migration substantially decreased in Kiev (from 0.66-0.82 to 0.34) and Shostka (from 0.72 to 0.52) and changed only insignificantly in Trostyanets. Outbreeding was estimated based on the migration parameters, exogamy level, and marital migration distances. The outbreeding level in the Shostka population (100,000 people) was comparable with that for the considerably larger Kiev population (two million people); however, it was significantly higher than that for the Trostyanets population, the size of which was close to the size of the Shostka population. It is supposed that "migration stress" may unfavorably affect the adaptive genetic structure of the Shostka population.     

Genetic demography of the Kuznetsk Basin population: changes in marriage assortativeness with respect to ethnicity and age in the Belovo city population with time

A genetic demographic study has been performed in the city of Belovo with the use of the data on marriages contracted there in 1970 and 1994-1999. Marriage assortativeness with respect to age has been found to be the strongest and remain unchanged during the lifetime of one generation (r = 0.730 in 1970 and r = 0.801 in 1994-1999). Monoethnic marriages were substantially more frequent than interethnic ones in the Belovo population during the period studied, although the ethnic marriage assortativeness considerably decreased (K = 0.386 in 1970 and K = 0.141 in 1994-1999). Panmixia has been observed in the Russian population of Belovo. Other Eastern Slavs (Ukrainians and Belarussians) are characterized by negative marriage assortativeness and panmixia; positive marriage assortativeness has been found in other ethnic groups.     

Interethnic Interaction,Strategic Bargaining Power,and the Dynamics of Cultural Norms

Ethnic groups are universal and unique to human societies. Such groups sometimes have norms of behavior that are adaptively linked to their social and ecological circumstances, and ethnic boundaries may function to protect that variation from erosion by interethnic interaction. However, such interaction is often frequent and voluntary, suggesting that individuals may be able to strategically reduce its costs, allowing adaptive cultural variation to persist in spite of interaction with out-groups with different norms. We examine five mechanisms influencing the dynamics of ethnically distinct cultural norms, each focused on strategic individual-level choices in interethnic interaction: bargaining, interaction-frequency-biased norm adoption, assortment on norms, success-biased interethnic social learning, and childhood socialization. We use Bayesian item response models to analyze patterns of norm variation and interethnic interaction in an ethnically structured Amazonian population. We show that, among indigenous Matsigenka, interethnic education with colonial Mestizos is more strongly associated with Mestizo-typical norms than even extensive interethnic experience in commerce and wage labor is. Using ethnographic observations, we show that all five of the proposed mechanisms of norm adoption may contribute to this effect. However, of these mechanisms, we argue that changes in relative bargaining power are particularly important for ethnic minorities wishing to preserve distinctive norms while engaging in interethnic interaction in domains such as education. If this mechanism proves applicable in a range of other ethnographic contexts, it would constitute one cogent explanation for when and why ethnically structured cultural variation can either persist or erode given frequent, and often mutually beneficial, interethnic interaction.     

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Allele frequency and genotype distribution of polymorphisms within disease-related genes is influenced by ethnic population sub-structuring in Sudan

Four single nucleotide polymorphisms (SNPs) and a variable number of tandem repeats (VNTR) polymorphism located within disease associated/causing genes were typed in four populations of different tribal and ethnic affiliation from the Sudan. The genotype and allele frequencies were compared with those of other groups from published and unpublished data of world populations. The combined Sudanese sample conformed with Hardy–Weinberg equilibrium (HWE) expectation. However, population sub-structuring according to ethnic/linguistic group indicated at least two SNPs in departure from HWE. Differences in allele frequencies and genotype distribution between groups was also noted in three of the four SNPs. The other loci were distributed homogeneously within the populations studied with genotype frequencies in agreement with HWE expectation. These results highlight the importance of inter-population stratification for polymorphic markers, as well as the potential influence of evolutionary history and ethnic variation of loci, in the general distribution of SNPs and other polymorphisms.     

Genetic demography of populations of three megalopolises in relation to the problem of creating genetic databases

Based on data collected from urban residents by questionnaire, the basic parameters of the genetic-demographic structure of populations of the three megalopolises, i.e., Moscow, Kharkov, and Minsk, have been calculated, including the migration coefficients and their dynamics in generations, the radius of the cities migration attraction, the parameters of marriage structure (the proportion of interethnic marriages, the level of intraethnic assortative mating the marital distances), and the gene flow between the ethnic groups. Representatives of the most numerous ethnic group of each megalopolis show significant amount of admixture. For Russians of Moscow, Ukrainians of Kharkov, and Belarusians of Minsk, the proportion of individuals whose ancestors were all born in the given city for at least three generations and belonged to the same nationality turned out to be very low (4.75% in Moscow, 1.83% in Kharkov, and 3.13% in Minsk). This finding questions the formation of a reference population in the megalopolis as a sampling of aboriginals of certain ethnic origins. In the paper, we justify principles of creating genetic databases for the population of the megalopolis taking into account the complexity and dynamism of its population structure.