Identification of a new candidate locus for uric acid nephrolithiasis

Renal stone formation is a common multifactorial disorder, of unknown etiology, with an established genetic contribution. Lifetime risk for nephrolithiasis is approximately 10% in Western populations, and uric acid stones account for 5%-10% of all stones, depending on climatic, dietary, and ethnic differences. We studied a small, isolated founder population in Sardinia, characterized by an increased prevalence of uric acid stones, and performed a genomewide search in a deep-rooted pedigree comprising many members who formed uric acid renal stones. The pedigree was created by tracing common ancestors of affected individuals through a genealogical database based on archival records kept by the parish church since 1640. This genealogical information was used as the basis for the study strategy, involving screening for alleles shared among affected individuals, originating from common ancestors, and utilization of large pedigrees to obtain greater power for linkage detection. We performed multistep linkage and allele-sharing analyses. In the initial stage, 382 markers were typed in 14 closely related affected subjects; interesting regions were subsequently investigated in the whole sample. We identified two chromosomal regions that may harbor loci with susceptibility genes for uric acid stones. The strongest evidence was observed on 10q21-q22, where a LOD score of 3.07 was obtained for D10S1652 under an affected-only dominant model, and a LOD score of 3.90 was obtained using a dominant pseudomarker assignment. The localization was supported also by multipoint allele-sharing statistics and by haplotype analysis of familial cases and of unrelated affected subjects collected from the isolate. In the second region on 20q13.1-13.3, multipoint nonparametric scores yielded suggestive evidence in a approximately 20-cM region, and further analysis is needed to confirm and fine-map this putative locus. Replication studies are required to investigate the involvement of these regions in the genetic contribution to uric acid stone formation.     

A Novel Test for Gene-Ancestry Interactions in Genome-Wide Association Data

Genome-wide association study (GWAS) data on a disease are increasingly available from multiple related populations. In this scenario, meta-analyses can improve power to detect homogeneous genetic associations, but if there exist ancestry-specific effects, via interactions on genetic background or with a causal effect that co-varies with genetic background, then these will typically be obscured. To address this issue, we have developed a robust statistical method for detecting susceptibility gene-ancestry interactions in multi-cohort GWAS based on closely-related populations. We use the leading principal components of the empirical genotype matrix to cluster individuals into “ancestry groups” and then look for evidence of heterogeneous genetic associations with disease or other trait across these clusters. Robustness is improved when there are multiple cohorts, as the signal from true gene-ancestry interactions can then be distinguished from gene-collection artefacts by comparing the observed interaction effect sizes in collection groups relative to ancestry groups. When applied to colorectal cancer, we identified a missense polymorphism in iron-absorption gene CYBRD1 that associated with disease in individuals of English, but not Scottish, ancestry. The association replicated in two additional, independently-collected data sets. Our method can be used to detect associations between genetic variants and disease that have been obscured by population genetic heterogeneity. It can be readily extended to the identification of genetic interactions on other covariates such as measured environmental exposures. We envisage our methodology being of particular interest to researchers with existing GWAS data, as ancestry groups can be easily defined and thus tested for interactions.     

Matrilineal fertility inheritance detected in hunter-gatherer populations using the imbalance of gene genealogies

Fertility inheritance, a phenomenon in which an individual's number of offspring is positively correlated with his or her number of siblings, is a cultural process that can have a strong impact on genetic diversity. Until now, fertility inheritance has been detected primarily using genealogical databases. In this study, we develop a new method to infer fertility inheritance from genetic data in human populations. The method is based on the reconstruction of the gene genealogy of a sample of sequences from a given population and on the computation of the degree of imbalance in this genealogy. We show indeed that this level of imbalance increases with the level of fertility inheritance, and that other phenomena such as hidden population structure are unlikely to generate a signal of imbalance in the genealogy that would be confounded with fertility inheritance. By applying our method to mtDNA samples from 37 human populations, we show that matrilineal fertility inheritance is more frequent in hunter-gatherer populations than in food-producer populations. One possible explanation for this result is that in hunter-gatherer populations, individuals belonging to large kin networks may benefit from stronger social support and may be more likely to have a large number of offspring.     

New methods for inference of local tree topologies with recombinant SNP sequences in populations

Large amount of population-scale genetic variation data are being collected in populations. One potentially important biological problem is to infer the population genealogical history from these genetic variation data. Partly due to recombination, genealogical history of a set of DNA sequences in a population usually cannot be represented by a single tree. Instead, genealogy is better represented by a genealogical network, which is a compact representation of a set of correlated local genealogical trees, each for a short region of genome and possibly with different topology. Inference of genealogical history for a set of DNA sequences under recombination has many potential applications, including association mapping of complex diseases. In this paper, we present two new methods for reconstructing local tree topologies with the presence of recombination, which extend and improve the previous work in. We first show that the "tree scan" method can be converted to a probabilistic inference method based on a hidden Markov model. We then focus on developing a novel local tree inference method called RENT that is both accurate and scalable to larger data. Through simulation, we demonstrate the usefulness of our methods by showing that the hidden-Markov-model-based method is comparable with the original method in terms of accuracy. We also show that RENT is competitive with other methods in terms of inference accuracy, and its inference error rate is often lower and can handle large data.     

Matrilineal Fertility Inheritance Detected in Hunter–Gatherer Populations Using the Imbalance of Gene Genealogies

Fertility inheritance, a phenomenon in which an individual's number of offspring is positively correlated with his or her number of siblings, is a cultural process that can have a strong impact on genetic diversity. Until now, fertility inheritance has been detected primarily using genealogical databases. In this study, we develop a new method to infer fertility inheritance from genetic data in human populations. The method is based on the reconstruction of the gene genealogy of a sample of sequences from a given population and on the computation of the degree of imbalance in this genealogy. We show indeed that this level of imbalance increases with the level of fertility inheritance, and that other phenomena such as hidden population structure are unlikely to generate a signal of imbalance in the genealogy that would be confounded with fertility inheritance. By applying our method to mtDNA samples from 37 human populations, we show that matrilineal fertility inheritance is more frequent in hunter–gatherer populations than in food-producer populations. One possible explanation for this result is that in hunter–gatherer populations, individuals belonging to large kin networks may benefit from stronger social support and may be more likely to have a large number of offspring.     

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.     

MicroRNA-34a modulates genes involved in cellular motility and oxidative phosphorylation in neural precursors derived from human umbilical cord mesenchymal stem cells

Background

Uric acid is the primary byproduct of purine metabolism. Hyperuricemia is associated with body mass index (BMI), sex, and multiple complex diseases including gout, hypertension (HTN), renal disease, and type 2 diabetes (T2D). Multiple genome-wide association studies (GWAS) in individuals of European ancestry (EA) have reported associations between serum uric acid levels (SUAL) and specific genomic loci. The purposes of this study were: 1) to replicate major signals reported in EA populations; and 2) to use the weak LD pattern in African ancestry population to better localize (fine-map) reported loci and 3) to explore the identification of novel findings cognizant of the moderate sample size.

Methods

African American (AA) participants (n = 1,017) from the Howard University Family Study were included in this study. Genotyping was performed using the Affymetrix^® Genome-wide Human SNP Array 6.0. Imputation was performed using MACH and the HapMap reference panels for CEU and YRI. A total of 2,400,542 single nucleotide polymorphisms (SNPs) were assessed for association with serum uric acid under the additive genetic model with adjustment for age, sex, BMI, glomerular filtration rate, HTN, T2D, and the top two principal components identified in the assessment of admixture and population stratification.

Results

Four variants in the gene SLC2A9 achieved genome-wide significance for association with SUAL (p-values ranging from 8.88 × 10^-9 to 1.38 × 10^-9). Fine-mapping of the SLC2A9 signals identified a 263 kb interval of linkage disequilibrium in the HapMap CEU sample. This interval was reduced to 37 kb in our AA and the HapMap YRI samples.

Conclusions

The most strongly associated locus for SUAL in EA populations was also the most strongly associated locus in this AA sample. This finding provides evidence for the role of SLC2A9 in uric acid metabolism across human populations. Additionally, our findings demonstrate the utility of following-up EA populations GWAS signals in African-ancestry populations with weaker linkage disequilibrium.     

Breakdown of Methods for Phasing and Imputation in the Presence of Double Genotype Sharing

In genome-wide association studies, results have been improved through imputation of a denser marker set based on reference haplotypes and phasing of the genotype data. To better handle very large sets of reference haplotypes, pre-phasing with only study individuals has been suggested. We present a possible problem which is aggravated when pre-phasing strategies are used, and suggest a modification avoiding the resulting issues with application to the MaCH tool, although the underlying problem is not specific to that tool.We evaluate the effectiveness of our remedy to a subset of Hapmap data, comparing the original version of MaCH and our modified approach. Improvements are demonstrated on the original data (phase switch error rate decreasing by 10%), but the differences are more pronounced in cases where the data is augmented to represent the presence of closely related individuals, especially when siblings are present (30% reduction in switch error rate in the presence of children, 47% reduction in the presence of siblings).The main conclusion of this investigation is that existing statistical methods for phasing and imputation of unrelated individuals might give results of sub-par quality if a subset of study individuals nonetheless are related. As the populations collected for general genome-wide association studies grow in size, including relatives might become more common. If a general GWAS framework for unrelated individuals would be employed on datasets with some related individuals, such as including familial data or material from domesticated animals, caution should also be taken regarding the quality of haplotypes.Our modification to MaCH is available on request and straightforward to implement. We hope that this mode, if found to be of use, could be integrated as an option in future standard distributions of MaCH.     

Prioritization of SNPs for genome-wide association studies using an interaction model of genetic variation,gene expression,and trait variation

The identification of true causal loci to unravel the statistical evidence of genotype-phenotype correlations and the biological relevance of selected single-nucleotide polymorphisms (SNPs) is a challenging issue in genome-wide association studies (GWAS). Here, we introduced a novel method for the prioritization of SNPs based on p-values from GWAS. The method uses functional evidence from populations, including phenotype-associated gene expressions. Based on the concept of genetic interactions, such as perturbation of gene expression by genetic variation, phenotype and gene expression related SNPs were prioritized by adjusting the p-values of SNPs. We applied our method to GWAS data related to drug-induced cytotoxicity. Then, we prioritized loci that potentially play a role in druginduced cytotoxicity. By generating an interaction model, our approach allowed us not only to identify causal loci, but also to find intermediate nodes that regulate the flow of information among causal loci, perturbed gene expression, and resulting phenotypic variation.     

Leveraging Multi-ethnic Evidence for Mapping Complex Traits in Minority Populations: An Empirical Bayes Approach

Elucidating the genetic basis of complex traits and diseases in non-European populations is particularly challenging because US minority populations have been under-represented in genetic association studies. We developed an empirical Bayes approach named XPEB (cross-population empirical Bayes), designed to improve the power for mapping complex-trait-associated loci in a minority population by exploiting information from genome-wide association studies (GWASs) from another ethnic population. Taking as input summary statistics from two GWASs—a target GWAS from an ethnic minority population of primary interest and an auxiliary base GWAS (such as a larger GWAS in Europeans)—our XPEB approach reprioritizes SNPs in the target population to compute local false-discovery rates. We demonstrated, through simulations, that whenever the base GWAS harbors relevant information, XPEB gains efficiency. Moreover, XPEB has the ability to discard irrelevant auxiliary information, providing a safeguard against inflated false-discovery rates due to genetic heterogeneity between populations. Applied to a blood-lipids study in African Americans, XPEB more than quadrupled the discoveries from the conventional approach, which used a target GWAS alone, bringing the number of significant loci from 14 to 65. Thus, XPEB offers a flexible framework for mapping complex traits in minority populations.     

随机SNP在全基因组关联研究人群分层分析中的应用

在复杂疾病的全基因组关联研究中,人群分层现象会增加结果的假阳性率,因此考虑人群遗传结构、控制人群分层是很有必要的。而在人群分层研究中,使用随机选择的SNP的效果还有待进一步探讨。文章利用HapMap Phase2人群中无关个体的Affymetrix SNP 6.0芯片分型数据,在全基因组上随机均匀选择不同数量的SNP,同时利用f值和Fisher精确检验方法筛选祖先信息标记（Ancestry Informative Markers,AIMs）。然后利用HapMap Phase3中的无关个体的数据,以F-statistics和STRUCTURE分析两种方法评估所选出的不同SNP组合对人群的区分效果。研究发现,随机均匀分布于全基因组的SNP可用于识别人群内部存在的遗传结构。文章进一步提示,在全基因组关联研究中,当没有针对特定人群的AIMs时,可在全基因组上随机选择3000以上均匀分布的SNP来控制人群分层。     

Concept, design and implementation of a cardiovascular gene-centric 50 k SNP array for large-scale genomic association studies

A wealth of genetic associations for cardiovascular and metabolic phenotypes in humans has been accumulating over the last decade, in particular a large number of loci derived from recent genome wide association studies (GWAS). True complex disease-associated loci often exert modest effects, so their delineation currently requires integration of diverse phenotypic data from large studies to ensure robust meta-analyses. We have designed a gene-centric 50 K single nucleotide polymorphism (SNP) array to assess potentially relevant loci across a range of cardiovascular, metabolic and inflammatory syndromes. The array utilizes a "cosmopolitan" tagging approach to capture the genetic diversity across approximately 2,000 loci in populations represented in the HapMap and SeattleSNPs projects. The array content is informed by GWAS of vascular and inflammatory disease, expression quantitative trait loci implicated in atherosclerosis, pathway based approaches and comprehensive literature searching. The custom flexibility of the array platform facilitated interrogation of loci at differing stringencies, according to a gene prioritization strategy that allows saturation of high priority loci with a greater density of markers than the existing GWAS tools, particularly in African HapMap samples. We also demonstrate that the IBC array can be used to complement GWAS, increasing coverage in high priority CVD-related loci across all major HapMap populations. DNA from over 200,000 extensively phenotyped individuals will be genotyped with this array with a significant portion of the generated data being released into the academic domain facilitating in silico replication attempts, analyses of rare variants and cross-cohort meta-analyses in diverse populations. These datasets will also facilitate more robust secondary analyses, such as explorations with alternative genetic models, epistasis and gene-environment interactions.     

Case-Control Association Testing of Common Variants from Sequencing of DNA Pools

While genome-wide association studies (GWAS) have been successful in identifying a large number of variants associated with disease, the challenge of locating the underlying causal loci remains. Sequencing of case and control DNA pools provides an inexpensive method for assessing all variation in a genomic region surrounding a significant GWAS result. However, individual variants need to be ranked in terms of the strength of their association to disease in order to prioritise follow-up by individual genotyping. A simple method for testing for case-control association in sequence data from DNA pools is presented that allows the partitioning of the variance in allele frequency estimates into components due to the sampling of chromosomes from the pool during sequencing, sampling individuals from the population and unequal contribution from individuals during pool construction. The utility of this method is demonstrated on a sequence from the alcohol dehydrogenase (ADH) gene cluster on a case-control sample for heavy alcohol consumption.     

A rapid generalized least squares model for a genome-wide quantitative trait association analysis in families

Genome-wide association studies (GWAS) using family data involve association analyses between hundreds of thousands of markers and a trait for a large number of related individuals. The correlations among relatives bring statistical and computational challenges when performing these large-scale association analyses. Recently, several rapid methods accounting for both within- and between-family variation have been proposed. However, these techniques mostly model the phenotypic similarities in terms of genetic relatedness. The familial resemblances in many family-based studies such as twin studies are not only due to the genetic relatedness, but also derive from shared environmental effects and assortative mating. In this paper, we propose 2 generalized least squares (GLS) models for rapid association analysis of family-based GWAS, which accommodate both genetic and environmental contributions to familial resemblance. In our first model, we estimated the joint genetic and environmental variations. In our second model, we estimated the genetic and environmental components separately. Through simulation studies, we demonstrated that our proposed approaches are more powerful and computationally efficient than a number of existing methods are. We show that estimating the residual variance-covariance matrix in the GLS models without SNP effects does not lead to an appreciable bias in the p values as long as the SNP effect is small (i.e. accounting for no more than 1% of trait variance).     

Including additional controls from public databases improves the power of a genome-wide association study

Though genome-wide association studies (GWAS) have identified numerous susceptibility loci for common diseases, their use is limited due to the expense of genotyping large cohorts of individuals. One potential solution is to use 'additional controls', or genotype data from control individuals deposited in public repositories. While this approach has been used by several groups, the genetically heterogeneous nature of the population of the United States makes this approach potentially problematic. We empirically investigated the utility of this approach in a US-based GWAS. In a small GWAS of pancreatic cancer in New York, we observed clear population structure differences relative to controls from the database of Genotypes and Phenotypes (dbGaP). When we conduct the GWAS using these additional controls, we find large inflation of the test statistic that is properly corrected by using eigenvectors from principal components analysis as covariates. To deal with errors introduced due to different sources, we propose simultaneously genotyping a small number of controls along with cases and then comparing this group to the additional controls. We show that removing SNPs that show differences between these control groups reduces false-positive findings. Thus, through an empirical approach, this report provides practical guidance for using additional controls from publicly available datasets.     

Genome-Wide Prediction Methods in Highly Diverse and Heterozygous Species: Proof-of-Concept through Simulation in Grapevine

Nowadays, genome-wide association studies (GWAS) and genomic selection (GS) methods which use genome-wide marker data for phenotype prediction are of much potential interest in plant breeding. However, to our knowledge, no studies have been performed yet on the predictive ability of these methods for structured traits when using training populations with high levels of genetic diversity. Such an example of a highly heterozygous, perennial species is grapevine. The present study compares the accuracy of models based on GWAS or GS alone, or in combination, for predicting simple or complex traits, linked or not with population structure. In order to explore the relevance of these methods in this context, we performed simulations using approx 90,000 SNPs on a population of 3,000 individuals structured into three groups and corresponding to published diversity grapevine data. To estimate the parameters of the prediction models, we defined four training populations of 1,000 individuals, corresponding to these three groups and a core collection. Finally, to estimate the accuracy of the models, we also simulated four breeding populations of 200 individuals. Although prediction accuracy was low when breeding populations were too distant from the training populations, high accuracy levels were obtained using the sole core-collection as training population. The highest prediction accuracy was obtained (up to 0.9) using the combined GWAS-GS model. We thus recommend using the combined prediction model and a core-collection as training population for grapevine breeding or for other important economic crops with the same characteristics.     

A Population Genetic Signal of Polygenic Adaptation

Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed knowledge about the specific loci underlying polygenic traits has begun to emerge from genome-wide association studies (GWAS). Here we combine this knowledge from GWAS with robust population genetic modeling to identify traits that may have been influenced by local adaptation. We exploit the fact that GWAS provide an estimate of the additive effect size of many loci to estimate the mean additive genetic value for a given phenotype across many populations as simple weighted sums of allele frequencies. We use a general model of neutral genetic value drift for an arbitrary number of populations with an arbitrary relatedness structure. Based on this model, we develop methods for detecting unusually strong correlations between genetic values and specific environmental variables, as well as a generalization of comparisons to test for over-dispersion of genetic values among populations. Finally we lay out a framework to identify the individual populations or groups of populations that contribute to the signal of overdispersion. These tests have considerably greater power than their single locus equivalents due to the fact that they look for positive covariance between like effect alleles, and also significantly outperform methods that do not account for population structure. We apply our tests to the Human Genome Diversity Panel (HGDP) dataset using GWAS data for height, skin pigmentation, type 2 diabetes, body mass index, and two inflammatory bowel disease datasets. This analysis uncovers a number of putative signals of local adaptation, and we discuss the biological interpretation and caveats of these results.     

Genome‐wide SNP analysis reveals a genetic basis for sea‐age variation in a wild population of Atlantic salmon (Salmo salar)

Delaying sexual maturation can lead to larger body size and higher reproductive success, but carries an increased risk of death before reproducing. Classical life history theory predicts that trade‐offs between reproductive success and survival should lead to the evolution of an optimal strategy in a given population. However, variation in mating strategies generally persists, and in general, there remains a poor understanding of genetic and physiological mechanisms underlying this variation. One extreme case of this is in the Atlantic salmon (Salmo salar), which can show variation in the age at which they return from their marine migration to spawn (i.e. their ‘sea age’). This results in large size differences between strategies, with direct implications for individual fitness. Here, we used an Illumina Infinium SNP array to identify regions of the genome associated with variation in sea age in a large population of Atlantic salmon in Northern Europe, implementing individual‐based genome‐wide association studies (GWAS) and population‐based F_ST outlier analyses. We identified several regions of the genome which vary in association with phenotype and/or selection between sea ages, with nearby genes having functions related to muscle development, metabolism, immune response and mate choice. In addition, we found that individuals of different sea ages belong to different, yet sympatric populations in this system, indicating that reproductive isolation may be driven by divergence between stable strategies. Overall, this study demonstrates how genome‐wide methodologies can be integrated with samples collected from wild, structured populations to understand their ecology and evolution in a natural context.     

Extreme‐phenotype genome‐wide association study (XP‐GWAS): a method for identifying trait‐associated variants by sequencing pools of individuals selected from a diversity panel

Although approaches for performing genome‐wide association studies (GWAS) are well developed, conventional GWAS requires high‐density genotyping of large numbers of individuals from a diversity panel. Here we report a method for performing GWAS that does not require genotyping of large numbers of individuals. Instead XP‐GWAS (extreme‐phenotype GWAS) relies on genotyping pools of individuals from a diversity panel that have extreme phenotypes. This analysis measures allele frequencies in the extreme pools, enabling discovery of associations between genetic variants and traits of interest. This method was evaluated in maize (Zea mays) using the well‐characterized kernel row number trait, which was selected to enable comparisons between the results of XP‐GWAS and conventional GWAS. An exome‐sequencing strategy was used to focus sequencing resources on genes and their flanking regions. A total of 0.94 million variants were identified and served as evaluation markers; comparisons among pools showed that 145 of these variants were statistically associated with the kernel row number phenotype. These trait‐associated variants were significantly enriched in regions identified by conventional GWAS. XP‐GWAS was able to resolve several linked QTL and detect trait‐associated variants within a single gene under a QTL peak. XP‐GWAS is expected to be particularly valuable for detecting genes or alleles responsible for quantitative variation in species for which extensive genotyping resources are not available, such as wild progenitors of crops, orphan crops, and other poorly characterized species such as those of ecological interest.     

Mapping trait loci by use of inferred ancestral recombination graphs

Large-scale association studies are being undertaken with the hope of uncovering the genetic determinants of complex disease. We describe a computationally efficient method for inferring genealogies from population genotype data and show how these genealogies can be used to fine map disease loci and interpret association signals. These genealogies take the form of the ancestral recombination graph (ARG). The ARG defines a genealogical tree for each locus, and, as one moves along the chromosome, the topologies of consecutive trees shift according to the impact of historical recombination events. There are two stages to our analysis. First, we infer plausible ARGs, using a heuristic algorithm, which can handle unphased and missing data and is fast enough to be applied to large-scale studies. Second, we test the genealogical tree at each locus for a clustering of the disease cases beneath a branch, suggesting that a causative mutation occurred on that branch. Since the true ARG is unknown, we average this analysis over an ensemble of inferred ARGs. We have characterized the performance of our method across a wide range of simulated disease models. Compared with simpler tests, our method gives increased accuracy in positioning untyped causative loci and can also be used to estimate the frequencies of untyped causative alleles. We have applied our method to Ueda et al.'s association study of CTLA4 and Graves disease, showing how it can be used to dissect the association signal, giving potentially interesting results of allelic heterogeneity and interaction. Similar approaches analyzing an ensemble of ARGs inferred using our method may be applicable to many other problems of inference from population genotype data.