Mapping genes that underlie ethnic differences in disease risk: methods for detecting linkage in admixed populations, by conditioning on parental admixture.

Genes that underlie ethnic differences in disease risk can be mapped in affected individuals of mixed descent if the ancestry of the alleles at each marker locus can be assigned to one of the two founding populations. Linkage can be detected by testing for association of the disease with the ancestry of alleles at the marker locus, by conditioning on the admixture (defined as the proportion of genes that have ancestry from the high-risk population) of both parents. With regard to exploiting the effects of admixture, this test is more flexible and powerful than the transmission-disequilibrium test. Under the assumption of a multiplicative model, the statistical power for a given sample size depends only on parental admixture and the risk ratio r between populations that is generated by the locus. The most informative families are those in which mean parental admixture is .2-.7 and in which admixture is similar in both parents. The number of markers required for a genome search depends on the number of generations since admixture and on the information content for ancestry (f) of the markers, defined as a function of allele frequencies in the two founding populations. Simulations using a hidden Markov model suggest that, when admixture has occurred 2-10 generations earlier, a multipoint analysis using 2,000 biallelic markers, with f values of 30%, can extract 70%-90% of the ancestry information for each locus. Sets of such markers could be selected from libraries of single-nucleotide polymorphisms, when these become available.     

Design and analysis of admixture mapping studies

Admixture between populations originating on different continents can be exploited to detect disease susceptibility loci at which risk alleles are distributed differentially between these populations. We first examine the statistical power and mapping resolution of this approach in the limiting situation in which gamete admixture and locus ancestry are measured without uncertainty. We show that, for a rare disease, the most efficient design is to study affected individuals only. In a typical African American population (two-way admixture proportions 0.8/0.2, ancestry crossover rate 2 per 100 cM), a study of 800 affected individuals has 90% power to detect at P values <10(-5) a locus that generates a risk ratio of 2 between populations, with an expected mapping resolution (size of 95% confidence region for the position of the locus) of 4 cM. In practice, to infer locus ancestry from marker data requires Bayesian computationally intensive methods, as implemented in the program ADMIXMAP. Affected-only study designs require strong prior information on the frequencies of each allele given locus ancestry. We show how data from unadmixed and admixed populations can be combined to estimate these ancestry-specific allele frequencies within the admixed population under study, allowing for variation between allele frequencies in unadmixed and admixed populations. Using simulated data based on the genetic structure of the African American population, we show that 60% of information can be extracted in a test for linkage using markers with an ancestry information content of 36% at 3-cM spacing. As in classic linkage studies, the most efficient strategy is to use markers at a moderate density for an initial genome search and then to saturate regions of putative linkage with additional markers, to extract nearly all information about locus ancestry.     

Statistical tests for admixture mapping with case-control and cases-only data

Admixture mapping is a promising new tool for discovering genes that contribute to complex traits. This mapping approach uses samples from recently admixed populations to detect susceptibility loci at which the risk alleles have different frequencies in the original contributing populations. Although the idea for admixture mapping has been around for more than a decade, the genomic tools are only now becoming available to make this a feasible and attractive option for complex-trait mapping. In this article, we describe new statistical methods for analyzing multipoint data from admixture-mapping studies to detect "ancestry association." The new test statistics do not assume a particular disease model; instead, they are based simply on the extent to which the sample's ancestry proportions at a locus deviate from the genome average. Our power calculations show that, for loci at which the underlying risk-allele frequencies are substantially different in the ancestral populations, the power of admixture mapping can be comparable to that of association mapping but with a far smaller number of markers. We also show that, although "ancestry informative markers" (AIMs) are superior to random single-nucleotide polymorphisms (SNPs), random SNPs can perform quite well when AIMs are not available. Hence, researchers who study admixed populations in which AIMs are not available can perform admixture mapping with the use of modestly higher densities of random markers. Software to perform the gene-mapping calculations, "MALDsoft," is freely available on the Pritchard Lab Web site.     

Nonneutral admixture of immigrant genotypes in African Drosophila melanogaster populations from Zimbabwe

Drosophila melanogaster originated in Africa and colonized the rest of the world only recently (approximately 10,000 to 15,000 years ago). Using 151 microsatellite loci, we investigated patterns of gene flow between African D. melanogaster populations representing presumptive ancestral variation and recently colonized European populations. Although we detected almost no evidence for alleles of non-African ancestry in a rural D. melanogaster population from Zimbabwe, an urban population from Zimbabwe showed evidence for admixture. Interestingly, the degree of admixture differed among chromosomes. X chromosomes of both rural and urban populations showed almost no non-African ancestry, but the third chromosome in the urban population showed up to 70% of non-African alleles. When chromosomes were broken into contingent microsatellite blocks, even higher estimates of admixture and significant heterogeneity in admixture was observed among these blocks. The discrepancy between the X chromosome and the third chromosome is not consistent with a neutral admixture hypothesis. The higher number of European alleles on the third chromosome could be due to stronger selection against foreign alleles on the X chromosome or to more introgression of (beneficial) alleles on the third chromosome.     

Assessing the role of HLA-linked and unlinked determinants of disease.

The relationship between increased risk in relatives over population prevalence (lambda R = KR/K) and probability of sharing zero marker alleles identical by descent (ibd) at a linked locus (such as HLA) by an affected relative pair is examined. For a model assuming a single disease-susceptibility locus or group of loci tightly linked to a marker locus, the relationship is remarkably simple and general. Namely, if phi R is the prior probability for the relative pair to share zero marker alleles identical by descent, then P (sharing 0 markers/both relatives are affected) is just phi R/lambda R. Alternatively, lambda AR, the increased risk over population prevalence to a relative R due to a disease locus tightly linked to marker locus A, equals the prior probability that the relative pair share zero A alleles ibd divided by the posterior probability that they share zero alleles ibd, given that they are both affected. For example, for affected sib pairs, P (sharing 0 markers/both sibs are affected) = .25/lambda S. This formula holds true for any number of alleles at the disease locus and for their frequencies, penetrances, and population prevalence. Similar formulas are derived for sharing one and two markers. Application of these formulas to several well-studied HLA-associated diseases yields the following results: For multiple sclerosis, insulin-dependent diabetes mellitus, and coeliac disease, a single-locus model of disease susceptibility is rejected, implying the existence of additional unlinked familial determinants. For all three diseases, the effect of the HLA-linked locus on familiality is minor: for multiple sclerosis, it accounts for only a 2.5-fold increased risk to sibs over the population prevalence, compared to an observed value of 20; for coeliac disease, it accounts for approximately a 5.25-fold increased risk to sibs, while the observed value is on the order of 60; for insulin-dependent diabetes mellitus, it accounts for a 3.42-fold increased risk in sibs, while the observed value is 15. In all cases, the secondary determinants must be outside the HLA region. For tuberculoid leprosy, an unlinked familial determinant is also implicated (increased risk to sibs due to HLA = 1.49; observed value = 2.38). For hemochromatosis and Hodgkin's disease, there is little evidence for HLA-unlinked familial determinants. With this formula, it is also possible to examine the hypothesis of pleiotropy versus linkage dis-equilibrium by comparing lambda AS with the increased risk to sibs due to the associated allele(s).(ABSTRACT TRUNCATED AT 400 WORDS)     

Relation of risk of systemic lupus erythematosus to west African admixture in a Caribbean population

Risk of systemic lupus erythematosus (SLE) is higher in people of west African descent than in Europeans. The objective of this study was to distinguish between genetic and environmental explanations for this ethnic difference by examining the relationship of disease risk to individual admixture (defined as the proportion of the genome that is of west African ancestry); 124 cases of SLE and 219 matched controls resident in Trinidad were studied. Analysis of admixture was restricted to 52 cases and 107 controls who reported no Indian or Chinese ancestry. These individuals were typed with a panel of 26 single-nucleotide polymorphisms and five insertion/deletion polymorphisms chosen to have large allele frequency differentials between west African, European and Native American populations. A Bayesian model for population admixture, individual admixture and locus ancestry was fitted by Markov chain simulation. Mean west African admixture (M) was 0.81 in cases and 0.74 in controls (P=0.01). The risk ratio for SLE associated with unit change in M was estimated as 32.5 with a 95% confidence interval (CI) of 2.0-518. Adjustment for measures of socioeconomic status (household amenities in childhood and years of education) altered this risk ratio only slightly (adjusted risk ratio: 28.4, 95% CI 1.7-485). These results support an additive genetic model for the ethnic difference in risk of SLE between west Africans and Europeans, rather than an environmental explanation or an "overdominant" model in which risk is higher in heterozygous than in homozygous individuals. This conclusion lays a basis for localizing the genes underlying this ethnic difference in risk of SLE by admixture mapping.     

Estimates of African, European and Native American ancestry in Afro-Caribbean men on the island of Tobago

BACKGROUND/AIMS: The Tobago Afro-Caribbean population is a valuable resource for studying the genetics of diseases that show significant differences in prevalence between populations of African descent and populations of other ancestries. Empirical confirmation of low European and Native American admixture may help in clarifying the ethnic variation in risk for such diseases. We hypothesize that the degree of European and Native American admixture in the Tobago population is low. METHODS: Admixture was estimated in a random sample of 220 men, from a population-based prostate cancer screening survey of 3,082 Tobago males, aged 40 to 79 years. We used a set of six autosomal markers with large allele frequency differences between the major ethnic populations involved in the admixture process, Europeans, Native Americans and West Africans. RESULTS: The ancestral proportions of Tobago population are estimated as 94.0+/-1.2% African, 4.6+/-3.4% European and 1.4+/-3.6% Native American. CONCLUSIONS: We conclude that Tobago Afro-Caribbean men are predominantly of West African ancestry, with minimal European and Native American admixture. The Tobago population, thus, may carry a higher burden of high-risk alleles of African origin for certain diseases than the more admixed African-American population. Conversely, this population may benefit from a higher prevalence of protective alleles of African origin.     

Enhanced statistical tests for GWAS in admixed populations: assessment using African Americans from CARe and a Breast Cancer Consortium

While genome-wide association studies (GWAS) have primarily examined populations of European ancestry, more recent studies often involve additional populations, including admixed populations such as African Americans and Latinos. In admixed populations, linkage disequilibrium (LD) exists both at a fine scale in ancestral populations and at a coarse scale (admixture-LD) due to chromosomal segments of distinct ancestry. Disease association statistics in admixed populations have previously considered SNP association (LD mapping) or admixture association (mapping by admixture-LD), but not both. Here, we introduce a new statistical framework for combining SNP and admixture association in case-control studies, as well as methods for local ancestry-aware imputation. We illustrate the gain in statistical power achieved by these methods by analyzing data of 6,209 unrelated African Americans from the CARe project genotyped on the Affymetrix 6.0 chip, in conjunction with both simulated and real phenotypes, as well as by analyzing the FGFR2 locus using breast cancer GWAS data from 5,761 African-American women. We show that, at typed SNPs, our method yields an 8% increase in statistical power for finding disease risk loci compared to the power achieved by standard methods in case-control studies. At imputed SNPs, we observe an 11% increase in statistical power for mapping disease loci when our local ancestry-aware imputation framework and the new scoring statistic are jointly employed. Finally, we show that our method increases statistical power in regions harboring the causal SNP in the case when the causal SNP is untyped and cannot be imputed. Our methods and our publicly available software are broadly applicable to GWAS in admixed populations.     

Admixture mapping as a tool in gene discovery

Admixture mapping is a rapidly developing method to map susceptibility alleles in complex genetic disease associated with continental ancestry. Theoretically, when admixture between continental populations has occurred relatively recently, the chromosomal segments derived from the parental populations can be deduced from the differences in genotype allele frequencies. Progress in computational algorithms, in identification of ancestry informative single nucleotide polymorphisms, and in recent studies applying these tools suggests that this approach will complement other strategies for identifying the variation that underlies many complex diseases.     

Extent of linkage disequilibrium between the androgen receptor gene CAG and GGC repeats in human populations: implications for prostate cancer risk

While studies have implicated alleles at the CAG and GGC trinucleotide repeats of the androgen receptor gene with high-grade, aggressive prostate cancer disease, little is known about the normal range of variation for these two loci, which are separated by about 1.1 kb. More importantly, few data exist on the extent of linkage disequilibrium (LD) between the two loci in different human populations. Here we present data on CAG and GGC allelic variation and LD in six diverse populations. Alleles at the CAG and GGC repeat loci of the androgen receptor were typed in over 1000 chromosomes from Africa, Asia, and North America. Levels of linkage disequilibrium between the two loci were compared between populations. Haplotype variation and diversity were estimated for each population. Our results reveal that populations of African descent possess significantly shorter alleles for the two loci than non-African populations (P<0.0001). Allelic diversity for both markers was higher among African Americans than any other population, including indigenous Africans from Sierra Leone and Nigeria. Analysis of molecular variance revealed that approx. 20% of CAG and GGC repeat variance could be attributed to differences between the populations. All non-African populations possessed the same common haplotype while the three populations of African descent possessed three divergent common haplotypes. Significant LD was observed in our sample of healthy African Americans. The LD observed in the African American population may be due to several reasons; recent migration of African Americans from diverse rural communities following urbanization, recurrent gene flow from diverse West African populations, and admixture with European Americans. This study represents the largest genotyping effort to be performed on the two androgen receptor trinucleotide repeat loci in diverse human populations.     

Multiethnic Genetic Association Studies Improve Power for Locus Discovery

To date, genome-wide association studies have focused almost exclusively on populations of European ancestry. These studies continue with the advent of next-generation sequencing, designed to systematically catalog and test low-frequency variation for a role in disease. A complementary approach would be to focus further efforts on cohorts of multiple ethnicities. This leverages the idea that population genetic drift may have elevated some variants to higher allele frequency in different populations, boosting statistical power to detect an association. Based on empirical allele frequency distributions from eleven populations represented in HapMap Phase 3 and the 1000 Genomes Project, we simulate a range of genetic models to quantify the power of association studies in multiple ethnicities relative to studies that exclusively focus on samples of European ancestry. In each of these simulations, a first phase of GWAS in exclusively European samples is followed by a second GWAS phase in any of the other populations (including a multiethnic design). We find that nontrivial power gains can be achieved by conducting future whole-genome studies in worldwide populations, where, in particular, African populations contribute the largest relative power gains for low-frequency alleles (<5%) of moderate effect that suffer from low power in samples of European descent. Our results emphasize the importance of broadening genetic studies to worldwide populations to ensure efficient discovery of genetic loci contributing to phenotypic trait variability, especially for those traits for which large numbers of samples of European ancestry have already been collected and tested.     

A genome-wide analysis of admixture in Uyghurs and a high-density admixture map for disease-gene discovery

Following up on our previous study, we conducted a genome-wide analysis of admixture for two Uyghur population samples (HGDP-UG and PanAsia-UG), collected from the northern and southern regions of Xinjiang in China, respectively. Both HGDP-UG and PanAsia-UG showed a substantial admixture of East-Asian (EAS) and European (EUR) ancestries, with an empirical estimation of ancestry contribution of 53:47 (EAS:EUR) and 48:52 for HGDP-UG and PanAsia-UG, respectively. The effective admixture time under a model with a single pulse of admixture was estimated as 110 generations and 129 generations, or admixture events occurred about 2200 and 2580 years ago for HGDP-UG and PanAsia-UG, respectively, assuming an average of 20 yr per generation. Despite Uyghurs' earlier history compared to other admixture populations, admixture mapping, holds promise for this population, because of its large size and its mixture of ancestry from different continents. We screened multiple databases and identified a genome-wide single-nucleotide polymorphism panel that can distinguish EAS and EUR ancestry of chromosomal segments in Uyghurs. The panel contains 8150 ancestry-informative markers (AIMs) showing large frequency differences between EAS and EUR populations (F_ST > 0.25, mean F_ST = 0.43) but small frequency differences (7999 AIMs validated) within both populations (F_ST < 0.05, mean F_ST < 0.01). We evaluated the effectiveness of this admixture map for localizing disease genes in two Uyghur populations. To our knowledge, our map constitutes the first practical resource for admixture mapping in Uyghurs, and it will enable studies of diseases showing differences in genetic risk between EUR and EAS populations.     

Genetic ancestry,population sub-structure,and cardiovascular disease-related traits among African-American participants in the CARDIA Study

African-American populations are genetically admixed. Studies performed among unrelated individuals from ethnically admixed populations may be both vulnerable to confounding by population stratification, but offer an opportunity for efficiently mapping complex traits through admixture linkage disequilibrium. By typing 42 ancestry-informative markers and estimating genetic ancestry, we assessed genetic admixture and heterogeneity among African-American participants in the Coronary Artery Risk Development in Young Adults (CARDIA) cohort. We also assessed associations between individual genetic ancestry and several quantitative and binary traits related to cardiovascular risk. We found evidence of population sub-structure and excess inter-marker linkage disequilibrium, consistent with recent admixture. The estimated group admixture proportions were 78.1% African and 22.9% European, but differed according to geographic region. In multiple regression models, African ancestry was significantly associated with decreased total cholesterol, decreased LDL-cholesterol, and decreased triglycerides, and also with increased risk of insulin resistance. These observed associations between African ancestry and several lipid traits are consistent with the general tendency of individuals of African descent to have healthier lipid profiles compared to European-Americans. There was no association between genetic ancestry and hypertension, BMI, waist circumference, CRP level, or coronary artery calcification. These results demonstrate the potential for confounding of genetic associations with some cardiovascular disease-related traits in large studies involving US African-Americans.     

Methods for high-density admixture mapping of disease genes

Admixture mapping (also known as "mapping by admixture linkage disequilibrium," or MALD) has been proposed as an efficient approach to localizing disease-causing variants that differ in frequency (because of either drift or selection) between two historically separated populations. Near a disease gene, patient populations descended from the recent mixing of two or more ethnic groups should have an increased probability of inheriting the alleles derived from the ethnic group that carries more disease-susceptibility alleles. The central attraction of admixture mapping is that, since gene flow has occurred recently in modern populations (e.g., in African and Hispanic Americans in the past 20 generations), it is expected that admixture-generated linkage disequilibrium should extend for many centimorgans. High-resolution marker sets are now becoming available to test this approach, but progress will require (a). computational methods to infer ancestral origin at each point in the genome and (b). empirical characterization of the general properties of linkage disequilibrium due to admixture. Here we describe statistical methods to estimate the ancestral origin of a locus on the basis of the composite genotypes of linked markers, and we show that this approach accurately estimates states of ancestral origin along the genome. We apply this approach to show that strong admixture linkage disequilibrium extends, on average, for 17 cM in African Americans. Finally, we present power calculations under varying models of disease risk, sample size, and proportions of ancestry. Studying approximately 2500 markers in approximately 2500 patients should provide power to detect many regions contributing to common disease. A particularly important result is that the power of an admixture mapping study to detect a locus will be nearly the same for a wide range of mixture scenarios: the mixture proportion should be 10%-90% from both ancestral populations.     

Genetic diversity and linkage disequilibrium in the Polynesian population of Niue Island

Isolated populations that recently have been derived from small homogeneous groups of founders should have low genetic diversity and high levels of linkage disequilibrium and should be ideal for mapping ancestral polymorphisms that influence complex genetic disease susceptibility. Populations that fulfill these criteria have been difficult to identify. We have been looking for Polynesian populations with these characteristics, because Polynesians have high rates of complex genetic diseases. In Niue Islanders all ancestral female (mitochondrial HSVI sequence) and 90.4% of ancestral male (Y-chromosome haplogroup) lineages are of Southeast Asian origin. The frequency of European Y-chromosome haplogroups is 7.2%. The diversities of mitochondrial HSV1 sequences (h = 0.18 +/- 0.05) and Y-chromosome haplo-groups (h = 0.18 +/- 0.05) are lower than values published for any other population. Ten autosomal microsatellites spaced over 5.8 cM show low allele numbers in Niue Islanders relative to Europeans (55 vs. 88 total alleles, respectively) and a modest reduction in heterozygous loci (0.71 +/- 0.02 vs. 0.78 +/- 0.02, p = 0.04). The higher linkage disequilibrium (d2) between these loci in Niue Islanders relative to Europeans (p = 0.001) is negatively correlated (r = -0.47, p = 0.01) with genetic distance. In summary, Niue Islanders are genetically isolated and have a homogeneous Southeast Asian ancestry. They have reduced autosomal genetic diversity and high levels of linkage disequilibrium that are consistent with the influence of genetic drift mechanisms, such as a founder effect or bottlenecks. High-powered linkage disequilibrium studies designed to map ancestral polymorphisms that influence complex genetic disease susceptibility may be feasible in this population.     

Intrahepatic Cholestasis of Pregnancy (ICP) in U.S. Latinas and Chileans: Clinical features,Ancestry Analysis,and Admixture Mapping

In the Americas, women with Indigenous American ancestry are at increased risk of intrahepatic cholestasis of pregnancy (ICP), relative to women of other ethnicities. We hypothesized that ancestry-related genetic factors contribute to this increased risk. We collected clinical and laboratory data, and performed biochemical assays on samples from U.S. Latinas and Chilean women, with and without ICP. The study sample included 198 women with ICP (90 from California, U.S., and 108 from Chile) and 174 pregnant control women (69 from California, U.S., and 105 from Chile). SNP genotyping was performed using Affymetrix arrays. We compared overall genetic ancestry between cases and controls, and used a genome-wide admixture mapping approach to screen for ICP susceptibility loci. We identified commonalities and differences in features of ICP between the 2 countries and determined that cases had a greater proportion of Indigenous American ancestry than did controls (p = 0.034). We performed admixture mapping, taking country of origin into account, and identified one locus for which Native American ancestry was associated with increased risk of ICP at a genome-wide level of significance (P = 3.1 x 10^-5, P_corrected = 0.035). This locus has an odds ratio of 4.48 (95% CI: 2.21-9.06) for 2 versus zero Indigenous American chromosomes. This locus lies on chromosome 2, with a 10 Mb 95% confidence interval which does not contain any previously identified hereditary ‘cholestasis genes.’ Our results indicate that genetic factors contribute to the risk of developing ICP in the Americas, and support the utility of clinical and genetic studies of ethnically mixed populations for increasing our understanding of ICP.     

Admixture in Mexico City: implications for admixture mapping of Type 2 diabetes genetic risk factors

Admixture mapping is a recently developed method for identifying genetic risk factors involved in complex traits or diseases showing prevalence differences between major continental groups. Type 2 diabetes (T2D) is at least twice as prevalent in Native American populations as in populations of European ancestry, so admixture mapping is well suited to study the genetic basis of this complex disease. We have characterized the admixture proportions in a sample of 286 unrelated T2D patients and 275 controls from Mexico City and we discuss the implications of the results for admixture mapping studies. Admixture proportions were estimated using 69 autosomal ancestry-informative markers (AIMs). Maternal and paternal contributions were estimated from geographically informative mtDNA and Y-specific polymorphisms. The average proportions of Native American, European and, West African admixture were estimated as 65, 30, and 5%, respectively. The contributions of Native American ancestors to maternal and paternal lineages were estimated as 90 and 40%, respectively. In a logistic model with higher educational status as dependent variable, the odds ratio for higher educational status associated with an increase from 0 to 1 in European admixture proportions was 9.4 (95%, credible interval 3.8–22.6). This association of socioeconomic status with individual admixture proportion shows that genetic stratification in this population is paralleled, and possibly maintained, by socioeconomic stratification. The effective number of generations back to unadmixed ancestors was 6.7 (95% CI 5.7–8.0), from which we can estimate that genome-wide admixture mapping will require typing about 1,400 evenly distributed AIMs to localize genes underlying disease risk between populations of European and Native American ancestry. Sample sizes of about 2,000 cases will be required to detect any locus that contributes an ancestry risk ratio of at least 1.5.     

Evidence for shared ancestral polymorphism rather than recurrent gene flow at microsatellite loci differentiating two hybridizing oaks (Quercus spp.)

Quercus petraea and Quercus robur are two closely related oak species, considered to hybridize. Genetic markers, however, indicate that despite sharing most alleles, the two species remain separate genetic units. Analysis of 20 microsatellite loci in multiple populations from both species suggested a genome-wide differentiation. Thus, the allele sharing between both species could be explained either by low rates of gene flow or shared ancestral variation. We performed further analyses of population differentiation in a biogeographical setting and an admixture analysis in mixed oak stands to distinguish between both hypotheses. Based on our results we propose that the low genetic differentiation among these species results from shared ancestry rather than high rates of gene flow.     

Marker selection for the transmission/disequilibrium test, in recently admixed populations.

Recent admixture between genetically differentiated populations can result in high levels of association between alleles at loci that are <=10 cM apart. The transmission/disequilibrium test (TDT) proposed by Spielman et al. (1993) can be a powerful test of linkage between disease and marker loci in the presence of association and therefore could be a useful test of linkage in admixed populations. The degree of association between alleles at two loci depends on the differences in allele frequencies, at the two loci, in the founding populations; therefore, the choice of marker is important. For a multiallelic marker, one strategy that may improve the power of the TDT is to group marker alleles within a locus, on the basis of information about the founding populations and the admixed population, thereby collapsing the marker into one with fewer alleles. We have examined the consequences of collapsing a microsatellite into a two-allele marker, when two founding populations are assumed for the admixed population, and have found that if there is random mating in the admixed population, then typically there is a collapsing for which the power of the TDT is greater than that for the original microsatellite marker. A method is presented for finding the optimal collapsing that has minimal dependence on the disease and that uses estimates either of marker allele frequencies in the two founding populations or of marker allele frequencies in the current, admixed population and in one of the founding populations. Furthermore, this optimal collapsing is not always the collapsing with the largest difference in allele frequencies in the founding populations. To demonstrate this strategy, we considered a recent data set, published previously, that provides frequency estimates for 30 microsatellites in 13 populations.     

A general mechanistic model for admixture histories of hybrid populations

Admixed populations have been used for inferring migrations, detecting natural selection, and finding disease genes. These applications often use a simple statistical model of admixture rather than a modeling perspective that incorporates a more realistic history of the admixture process. Here, we develop a general model of admixture that mechanistically accounts for complex historical admixture processes. We consider two source populations contributing to the ancestry of a hybrid population, potentially with variable contributions across generations. For a random individual in the hybrid population at a given point in time, we study the fraction of genetic admixture originating from a specific one of the source populations by computing its moments as functions of time and of introgression parameters. We show that very different admixture processes can produce identical mean admixture proportions, but that such processes produce different values for the variance of the admixture proportion. When introgression parameters from each source population are constant over time, the long-term limit of the expectation of the admixture proportion depends only on the ratio of the introgression parameters. The variance of admixture decreases quickly over time after the source populations stop contributing to the hybrid population, but remains substantial when the contributions are ongoing. Our approach will facilitate the understanding of admixture mechanisms, illustrating how the moments of the distribution of admixture proportions can be informative about the historical admixture processes contributing to the genetic diversity of hybrid populations.