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The Trans-Omics for Precision Medicine (TOPMed) programme seeks to elucidate the genetic architecture and biology of heart, lung, blood and sleep disorders, with the ultimate goal of improving diagnosis, treatment and prevention of these diseases. The initial phases of the programme focused on whole-genome sequencing of individuals with rich phenotypic data and diverse backgrounds. Here we describe the TOPMed goals and design as well as the available resources and early insights obtained from the sequence data. The resources include a variant browser, a genotype imputation server, and genomic and phenotypic data that are available through dbGaP (Database of Genotypes and Phenotypes)1. In the first 53,831 TOPMed samples, we detected more than 400 million single-nucleotide and insertion or deletion variants after alignment with the reference genome. Additional previously undescribed variants were detected through assembly of unmapped reads and customized analysis in highly variable loci. Among the more than 400 million detected variants, 97% have frequencies of less than 1% and 46% are singletons that are present in only one individual (53% among unrelated individuals). These rare variants provide insights into mutational processes and recent human evolutionary history. The extensive catalogue of genetic variation in TOPMed studies provides unique opportunities for exploring the contributions of rare and noncoding sequence variants to phenotypic variation. Furthermore, combining TOPMed haplotypes with modern imputation methods improves the power and reach of genome-wide association studies to include variants down to a frequency of approximately 0.01%., The goals, resources and design of the NHLBI Trans-Omics for Precision Medicine (TOPMed) programme are described, and analyses of rare variants detected in the first 53,831 samples provide insights into mutational processes and recent human evolutionary history.

The two alleles an individual carries at a locus are identical by descent (ibd) if they have descended from a single ancestral allele in a reference population, and the probability of such identity is the inbreeding coefficient of the individual. Inbreeding coefficients can be predicted from pedigrees with founders constituting the reference population, but estimation from genetic data is not possible without data from the reference population. Most inbreeding estimators that make explicit use of sample allele frequencies as estimates of allele probabilities in the reference population are confounded by average kinships with other individuals. This means that the ranking of those estimates depends on the scope of the study sample and we show the variation in rankings for common estimators applied to different subdivisions of 1000 Genomes data. Allele-sharing estimators of within-population inbreeding relative to average kinship in a study sample, however, do have invariant rankings across all studies including those individuals. They are unbiased with a large number of SNPs. We discuss how allele sharing estimates are the relevant quantities for a range of empirical applications.

A match of HLA loci between patients and donors is critical for successful hematopoietic stem cell transplantation. However, the extreme polymorphism of HLA loci – an outcome of millions of years of natural selection – reduces the chances that two individuals will carry identical combinations of multilocus HLA genotypes. Further, HLA variability is not homogeneously distributed throughout the world: African populations on average have greater variability than non-Africans, reducing the chances that two unrelated African individuals are HLA identical. Here, we explore how self-identification (often equated with “ethnicity” or “race”) and genetic ancestry are related to the chances of finding HLA compatible donors in a large sample from Brazil, a highly admixed country. We query REDOME, Brazil’s Bone Marrow Registry, and investigate how different criteria for identifying ancestry influence the chances of finding a match. We find that individuals who self-identify as “Black” and “Mixed” on average have lower chances of finding matches than those who self-identify as “White” (up to 57% reduction). We next show that an individual’s African genetic ancestry, estimated using molecular markers and quantified as the proportion of an individual’s genome that traces its ancestry to Africa, is strongly associated with reduced chances of finding a match (up to 60% reduction). Finally, we document that the strongest reduction in chances of finding a match is associated with having an MHC region of exclusively African ancestry (up to 75% reduction). We apply our findings to a specific condition, for which there is a clinical indication for transplantation: sickle-cell disease. We show that the increased African ancestry in patients with this disease leads to reduced chances of finding a match, when compared to the remainder of the sample, without the condition. Our results underscore the influence of ancestry on chances of finding compatible HLA matches, and indicate that efforts guided to increasing the African component of registries are necessary.

The concept of kinship permeates many domains of fundamental and applied biology ranging from social evolution to conservation science to quantitative and human genetics. Until recently, pedigrees were the gold standard to infer kinship, but the advent of next‐generation sequencing and the availability of dense genetic markers in many species make it a good time to (re)evaluate the usefulness of genetic markers in this context. Using three published data sets where both pedigrees and markers are available, we evaluate two common and a new genetic estimator of kinship. We show discrepancies between pedigree values and marker estimates of kinship and explore via simulations the possible reasons for these. We find these discrepancies are attributable to two main sources: pedigree errors and heterogeneity in the origin of founders. We also show that our new marker‐based kinship estimator has very good statistical properties and behaviour and is particularly well suited for situations where the source population is of small size, as will often be the case in conservation biology, and where high levels of kinship are expected, as is typical in social evolution studies.

Lipoprotein(a), Lp(a), is a modified low-density lipoprotein particle that contains apolipoprotein(a), encoded by LPA, and is a highly heritable, causal risk factor for cardiovascular diseases that varies in concentrations across ancestries. Here, we use deep-coverage whole genome sequencing in 8392 individuals of European and African ancestry to discover and interpret both single-nucleotide variants and copy number (CN) variation associated with Lp(a). We observe that genetic determinants between Europeans and Africans have several unique determinants. The common variant rs12740374 associated with Lp(a) cholesterol is an eQTL for SORT1 and independent of LDL cholesterol. Observed associations of aggregates of rare non-coding variants are largely explained by LPA structural variation, namely the LPA kringle IV 2 (KIV2)-CN. Finally, we find that LPA risk genotypes confer greater relative risk for incident atherosclerotic cardiovascular diseases compared to directly measured Lp(a), and are significantly associated with measures of subclinical atherosclerosis in African Americans., Circulating lipoprotein(a) is an important risk factor for cardiovascular disease and shows variability between different ethnic groups. Here, Zekavat et al. perform whole-genome sequencing in individuals of European and African ancestries and find ancestry-specific genetic determinants for lipoprotein(a) levels.

Statistical tests for Hardy–Weinberg equilibrium are important elementary tools in genetic data analysis. X-chromosomal variants have long been tested by applying autosomal test procedures to females only, and gender is usually not considered when testing autosomal variants for equilibrium. Recently, we proposed specific Xchromosomal exact test procedures for bi-allelic variants that include the hemizygous males, as well as autosomal tests that consider gender. In this study, we present the extension of the previous work for variants with multiple alleles. A full enumeration algorithm is used for the exact calculations of tri-allelic variants. For variants with many alternate alleles, we use a permutation test. Some empirical examples with data from the 1,000 genomes project are discussed.

The Elizabeth W. Jones Award for Excellence in Education recognizes an individual or group that has had significant, sustained impact on genetics education at any level, from K-12 through graduate school and beyond. Bruce Weir (University of Washington) is the 2019 recipient in recognition of his work training thousands of researchers in the rigorous use of statistical analysis methods for genetic and genomic data. His contributions fall into three categories: the acclaimed Summer Institute in Statistical Genetics, which has been held continuously for 23 years and has trained > 10,000 researchers worldwide; the popular graduate-level textbook Genetic Data Analysis; and the training of a growing number of forensic geneticists during the rise of DNA evidence in courts around the world.

Quantifying the effects of inbreeding is critical to characterizing the genetic architecture of complex traits. This study highlights through theory and simulations the strengths and shortcomings of three SNP-based inbreeding measures commonly used to estimate inbreeding depression (ID). We demonstrate that heterogeneity in linkage disequilibrium (LD) between causal variants and SNPs biases ID estimates, and we develop an approach to correct this bias using LD and minor allele frequency stratified inference (LDMS). We quantified ID in 25 traits measured in [Formula: see text] participants of the UK Biobank, using LDMS, and confirmed previously published ID for 4 traits. We find unique evidence of ID for handgrip strength, waist/hip ratio, and visual and auditory acuity (ID between -2.3 and -5.2 phenotypic SDs for complete inbreeding; [Formula: see text]). Our results illustrate that a careful choice of the measure of inbreeding combined with LDMS stratification improves both detection and quantification of ID using SNP data.

Heritability, the proportion of phenotypic variance explained by genetic factors, can be estimated from pedigree data 1, but such estimates are uninformative with respect to the underlying genetic architecture. Analyses of data from genome-wide association studies (GWAS) on unrelated individuals have shown that for human traits and disease, approximately one-third to two-thirds of heritability is captured by common SNPs 2–5. It is not known whether the remaining heritability is due to the imperfect tagging of causal variants by common SNPs, in particular if the causal variants are rare, or other reasons such as overestimation of heritability from pedigree data. Here we show that pedigree heritability for height and body mass index (BMI) appears to be largely recovered from whole-genome sequence (WGS) data on 25,465 unrelated individuals of European ancestry. We assigned 33.7 million genetic variants to groups based upon their minor allele frequencies (MAF) and linkage disequilibrium (LD) with variants nearby, and estimated and partitioned genetic variance accordingly. The estimated heritability was 0.68 (SE 0.10) for height and 0.30 (SE 0.10) for BMI, with a range of ~0.60 – 0.71 for height and ~0.25 – 0.35 for BMI, depending on quality control and analysis strategies. Low-MAF variants in low LD with neighbouring variants were enriched for heritability, to a greater extent for protein-altering variants, consistent with negative selection thereon. Cumulatively variants with 0.0001 < MAF < 0.1 explained 0.47 (SE 0.07) and 0.30 (SE 0.10) of heritability for height and BMI, respectively. Our results imply that rare variants, in particular those in regions of low LD, is a major source of the still missing heritability of complex traits and disease.

Summary paragraphThe Trans-Omics for Precision Medicine (TOPMed) program seeks to elucidate the genetic architecture and disease biology of heart, lung, blood, and sleep disorders, with the ultimate goal of improving diagnosis, treatment, and prevention. The initial phases of the program focus on whole genome sequencing of individuals with rich phenotypic data and diverse backgrounds. Here, we describe TOPMed goals and design as well as resources and early insights from the sequence data. The resources include a variant browser, a genotype imputation panel, and sharing of genomic and phenotypic data via dbGaP. In 53,581 TOPMed samples, >400 million single-nucleotide and insertion/deletion variants were detected by alignment with the reference genome. Additional novel variants are detectable through assembly of unmapped reads and customized analysis in highly variable loci. Among the >400 million variants detected, 97% have frequency

Principal component analysis (PCA) is widely used in genome-wide association studies (GWAS), and the principal component axes often represent perpendicular gradients in geographic space. The explanation of PCA results is of major interest for geneticists to understand fundamental demographic parameters. Here, we provide an interpretation of PCA based on relatedness measures, which are described by the probability that sets of genes are identical-by-descent (IBD). An approximately linear transformation between ancestral proportions (AP) of individuals with multiple ancestries and their projections onto the principal components is found.In addition, a new method of eigenanalysis “EIGMIX” is proposed to estimate individual ancestries. EIGMIX is a method of moments with computational efficiency suitable for millions of SNP data, and it is not subject to the assumption of linkage equilibrium. With the assumptions of multiple ancestries and their surrogate ancestral samples, EIGMIX is able to infer ancestral proportions (APs) of individuals. The methods were applied to the SNP data from the HapMap Phase 3 project and the Human Genome Diversity Panel. The APs of individuals inferred by EIGMIX are consistent with the findings of the program ADMIXTURE.In conclusion, EIGMIX can be used to detect population structure and estimate genome-wide ancestral proportions with a relatively high accuracy.

US Hispanic/Latino individuals are diverse in genetic ancestry, culture, and environmental exposures. Here, we characterized and controlled for this diversity in genome-wide association studies (GWASs) for the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). We simultaneously estimated population-structure principal components (PCs) robust to familial relatedness and pairwise kinship coefficients (KCs) robust to population structure, admixture, and Hardy-Weinberg departures. The PCs revealed substantial genetic differentiation within and among six self-identified background groups (Cuban, Dominican, Puerto Rican, Mexican, and Central and South American). To control for variation among groups, we developed a multi-dimensional clustering method to define a “genetic-analysis group” variable that retains many properties of self-identified background while achieving substantially greater genetic homogeneity within groups and including participants with non-specific self-identification. In GWASs of 22 biomedical traits, we used a linear mixed model (LMM) including pairwise empirical KCs to account for familial relatedness, PCs for ancestry, and genetic-analysis groups for additional group-associated effects. Including the genetic-analysis group as a covariate accounted for significant trait variation in 8 of 22 traits, even after we fit 20 PCs. Additionally, genetic-analysis groups had significant heterogeneity of residual variance for 20 of 22 traits, and modeling this heteroscedasticity within the LMM reduced genomic inflation for 19 traits. Furthermore, fitting an LMM that utilized a genetic-analysis group rather than a self-identified background group achieved higher power to detect previously reported associations. We expect that the methods applied here will be useful in other studies with multiple ethnic groups, admixture, and relatedness.

Genealogical inference from genetic data is essential for a variety of applications in human genetics. In genome-wide and sequencing association studies, for example, accurate inference on both recent genetic relatedness, such as family structure, and more distant genetic relatedness, such as population structure, is necessary for protection against spurious associations. Distinguishing familial relatedness from population structure with genotype data, however, is difficult because both manifest as genetic similarity through the sharing of alleles. Existing approaches for inference on recent genetic relatedness have limitations in the presence of population structure, where they either (1) make strong and simplifying assumptions about population structure, which are often untenable, or (2) require correct specification of and appropriate reference population panels for the ancestries in the sample, which might be unknown or not well defined. Here, we propose PC-Relate, a model-free approach for estimating commonly used measures of recent genetic relatedness, such as kinship coefficients and IBD sharing probabilities, in the presence of unspecified structure. PC-Relate uses principal components calculated from genome-screen data to partition genetic correlations among sampled individuals due to the sharing of recent ancestors and more distant common ancestry into two separate components, without requiring specification of the ancestral populations or reference population panels. In simulation studies with population structure, including admixture, we demonstrate that PC-Relate provides accurate estimates of genetic relatedness and improved relationship classification over widely used approaches. We further demonstrate the utility of PC-Relate in applications to three ancestrally diverse samples that vary in both size and genealogical complexity.

Microarray single-nucleotide polymorphism genotyping, combined with imputation of untyped variants, has been widely adopted as an efficient means to interrogate variation across the human genome. “Genomic coverage” is the total proportion of genomic variation captured by an array, either by direct observation or through an indirect means such as linkage disequilibrium or imputation. We have performed imputation-based genomic coverage assessments of eight current genotyping arrays that assay from ~0.3 to ~5 million variants. Coverage was determined separately in each of the four continental ancestry groups in the 1000 Genomes Project phase 1 release. We used the subset of 1000 Genomes variants present on each array to impute the remaining variants and assessed coverage based on correlation between imputed and observed allelic dosages. More than 75% of common variants (minor allele frequency > 0.05) are covered by all arrays in all groups except for African ancestry, and up to ~90% in all ancestries for the highest density arrays. In contrast, less than 40% of less common variants (0.01 < minor allele frequency < 0.05) are covered by low density arrays in all ancestries and 50–80% in high density arrays, depending on ancestry. We also calculated genome-wide power to detect variant-trait association in a case-control design, across varying sample sizes, effect sizes, and minor allele frequency ranges, and compare these array-based power estimates with a hypothetical array that would type all variants in 1000 Genomes. These imputation-based genomic coverage and power analyses are intended as a practical guide to researchers planning genetic studies.

Genotyping of classical human leukocyte antigen (HLA) alleles is an essential tool in the analysis of diseases and adverse drug reactions with associations mapping to the major histocompatibility complex (MHC). However, deriving high-resolution HLA types subsequent to whole-genome single-nucleotide polymorphism (SNP) typing or sequencing is often cost prohibitive for large samples. An alternative approach takes advantage of the extended haplotype structure within the MHC to predict HLA alleles using dense SNP genotypes, such as those available from genome-wide SNP panels. Current methods for HLA imputation are difficult to apply or may require the user to have access to large training data sets with SNP and HLA types. We propose HIBAG, HLA Imputation using attribute BAGging, that makes predictions by averaging HLA-type posterior probabilities over an ensemble of classifiers built on bootstrap samples. We assess the performance of HIBAG using our study data (n=2668 subjects of European ancestry) as a training set and HLA data from the British 1958 birth cohort study (n≈1000 subjects) as independent validation samples. Prediction accuracies for HLA-A, B, C, DRB1 and DQB1 range from 92.2% to 98.1% using a set of SNP markers common to the Illumina 1M Duo, OmniQuad, OmniExpress, 660K and 550K platforms. HIBAG performed well compared with the other two leading methods, HLA*IMP and BEAGLE. This method is implemented in a freely available HIBAG R package that includes pre-fit classifiers for European, Asian, Hispanic and African ancestries, providing a readily available imputation approach without the need to have access to large training data sets.

Many population genetic activities, ranging from evolutionary studies to association mapping, to forensic identification, rely on appropriate estimates of population structure or relatedness. All applications require recognition that quantities with an underlying meaning of allelic dependence are not defined in an absolute sense, but instead are made “relative to” some set of alleles other than the target set. The 1984 Weir and Cockerham FST estimate made explicit that the reference set of alleles was across populations, whereas standard kinship estimates do not make the reference explicit. Weir and Cockerham stated that their FST estimates were for independent populations, and standard kinship estimates have an implicit assumption that pairs of individuals in a study sample, other than the target pair, are unrelated or are not inbred. However, populations lose independence when there is migration between them, and dependencies between pairs of individuals in a population exist for more than one target pair. We have therefore recast our treatments of population structure, relatedness, and inbreeding to make explicit that the parameters of interest involve the differences in degrees of allelic dependence between the target and the reference sets of alleles, and so can be negative. We take the reference set to be the population from which study individuals have been sampled. We provide simple moment estimates of these parameters, phrased in terms of allelic matching within and between individuals for relatedness and inbreeding, or within and between populations for population structure. A multi-level hierarchy of alleles within individuals, alleles between individuals within populations, and alleles between populations, allows a unified treatment of relatedness and population structure. We expect our new measures to have a wide range of applications, but we note that their estimates are sensitive to rare or private variants: some population-characterization applications suggest exploiting those sensitivities, whereas estimation of relatedness may best use all genetic markers without filtering on minor allele frequency.

The goal of the International HapMap Project is to determine the common patterns of DNA sequence variation in the human genome and to make this information freely available in the public domain. An international consortium is developing a map of these patterns across the genome by determining the genotypes of one million or more sequence variants, their frequencies and the degree of association between them, in DNA samples from populations with ancestry from parts of Africa, Asia and Europe. The HapMap will allow the discovery of sequence variants that affect common disease, will facilitate development of diagnostic tools, and will enhance our ability to choose targets for therapeutic intervention. © 2003 Nature Publishing Group.

Platelets play an essential role in hemostasis and thrombosis. We performed a genome-wide association study of platelet count in 12,491 participants of the Hispanic Community Health Study/Study of Latinos by using a mixed-model method that accounts for admixture and family relationships. We discovered and replicated associations with five genes (ACTN1, ETV7, GABBR1-MOG, MEF2C, and ZBTB9-BAK1). Our strongest association was with Amerindian-specific variant rs117672662 (p value = 1.16× 10(-28)) in ACTN1, agene implicated in congenital macrothrombocytopenia. rs117672662 exhibited allelic differences in transcriptional activity and protein binding in hematopoietic cells. Our results underscore the value of diverse populations to extend insights into the allelic architecture of complex traits.

Clonal mosaicism for large chromosomal anomalies (duplications, deletions and uniparental disomy) was detected using SNP microarray data from over 50,000 subjects recruited for genome-wide association studies. This detection method requires a relatively high frequency of cells (>5–10%) with the same abnormal karyotype (presumably of clonal origin) in the presence of normal cells. The frequency of detectable clonal mosaicism in peripheral blood is low (

The use of DNA markers to identify sources of crime scene evidence has revolutionized forensic science. The routine use of simple tandem repeat (STR) markers applied to genetic individualization of human samples has become the realization of the potential of samples of nonhuman origin. The identification of an individual pet or other animal may provide the critical piece of information in a criminal investigation and prosecution. With the majority of American households (55%) housing at least one cat or dog (73 million cats, 68 million dogs) (1), it is not unusual for animal specimens, particularly hair specimens, to be part of the physical evidence associated with a crime scene (2–7). A study on the transfer and persistence of animal hair has demonstrated that it is almost impossible to enter a house where a domestic animal lives without becoming a “carrier” of its hair (8). Hairs from a pet can be indicative of a perpetrator’s presence at a crime scene or provide evidence of a connection between victim and perpetrator. Since 1996, DNA extracted from cat hair and dog blood, hair, and saliva from crime scene evidence has contributed to physical evidence leading to conviction of defendants in Canada and numerous states (2,4,5,9,10). While the genetic individualization of animal specimens is in its infancy, a set of guidelines has been proposed for animal genetic identity testing (11). We have developed an STR typing system for genetic individualization of domestic cat (Felis catus) samples. Previously, we reported on the characterization of a panel of 22 tetranucleotide STR loci in 213 domestic cats representing 28 breeds, from which 11 loci were selected for a forensic typing panel (12). A multiplex amplification protocol was generated and optimized for the 11 loci (12,13) and a gender-identifying sequence tagged site (STS) from the cat Y-chromosome Sex determining Region-Y gene (SRY) (14). We report on a population genetic database for the multiplex, with which to compute composite match probabilities, that was generated from a panel of 1043 domestic cat samples representing 38 cat breeds recognized by the two largest domestic cat registries in the United States, the Cat Fanciers’ Association (CFA) and The International Cat Association (TICA).

SummaryWhole genome data are allowing the estimation of population genetic parameters with an accuracy not imagined 50 years ago. Variation in these parameters along the genome is being found empirically where once only approximate theoretical values were available. Along with increased information, however, has come the issue of multiple testing and the realization that high values of the coefficients of variation of quantities such as relatedness measures may make it difficult to draw inferences. This review concentrates on measures of allelic association within and between individuals and within and between populations.

Genome-wide scans of nucleotide variation in human subjects are providing an increasing number of replicated associations with complex disease traits. Most of the variants detected have small effects and, collectively, they account for a small fraction of the total genetic variance. Very large sample sizes are required to identify and validate findings. In this situation, even small sources of systematic or random error can cause spurious results or obscure real effects. The need for careful attention to data quality has been appreciated for some time in this field, and a number of strategies for quality control and quality assurance (QC/QA) have been developed. Here we extend these methods and describe a system of QC/QA for genotypic data in genome-wide association studies. This system includes some new approaches that (1) combine analysis of allelic probe intensities and called genotypes to distinguish gender misidentification from sex chromosome aberrations, (2) detect autosomal chromosome aberrations that may affect genotype calling accuracy, (3) infer DNA sample quality from relatedness and allelic intensities, (4) use duplicate concordance to infer SNP quality, (5) detect genotyping artifacts from dependence of Hardy-Weinberg equilibrium (HWE) test p-values on allelic frequency, and (6) demonstrate sensitivity of principal components analysis (PCA) to SNP selection. The methods are illustrated with examples from the ‘Gene Environment Association Studies’ (GENEVA) program. The results suggest several recommendations for QC/QA in the design and execution of genome-wide association studies.

Coevolving interacting genes undergo complementary mutations to maintain their interaction. Distinct combinations of alleles in coevolving genes interact differently, conferring varying degrees of fitness. If this fitness differential is adequately large, the resulting selection for allele matching could maintain allelic association, even between physically unlinked loci. Allelic association is often observed in a population with the use of gametic linkage disequilibrium. However, because the coevolving genes are not necessarily in physical linkage, this is not an appropriate measure of coevolution-induced allelic association. Instead, we propose using both composite linkage disequilibrium (CLD) and a measure of association between genotypes, which we call genotype association (GA). Using a simple selective model, we simulated loci and calculated power for tests of CLD and GA, showing that the tests can detect the allelic association expected under realistic selective pressure. We apply CLD and GA tests to the polymorphic, physically unlinked, and putatively coevolving human gamete-recognition genes ZP3 and ZP3R. We observe unusual allelic association, not attributable to population structure, between ZP3 and ZP3R. This study shows that selection for allele matching can drive allelic association between unlinked loci in a contemporary human population, and that selection can be detected with the use of CLD and GA tests. The observation of this selection is surprising, but reasonable in the highly selected system of fertilization. If confirmed, this sort of selection provides an exception to the paradigm of chromosomal independent assortment.

Genome-wide association studies result in inflated false positive results when unrecognized cryptic relatedness exists. A number of methods have been proposed for testing association between markers and disease with a correction for known pedigree-based relationships. However, in most case-control studies, relationships are generally unknown, yet the design is predicated on the assumption of at least ancestral relatedness among cases. Here, we focus on adjusting cryptic relatedness when the genealogy of the sample is unknown, particularly in the context of samples from isolated populations where cryptic relatedness may be problematic. We estimate cryptic relatedness using maximum-likelihood methods and use a corrected chi-square test with estimated kinship coefficients for testing in the context of unknown cryptic relatedness. Estimated kinship coefficients characterize precisely the relatedness between truly related people, but are biased for unrelated pairs. The proposed test substantially reduces spurious positive results, producing a uniform null distribution of p-values. Especially with missing pedigree information, estimated kinship coefficients can still be used to correct non-independence among individuals. The corrected test was applied to real data sets from genetic isolates and created a distribution of p-value that was close to uniform. Thus the proposed test corrects the non-uniform distribution of p-values obtained with the uncorrected test and illustrates the advantage of the approach on real data.

Wright's F-statistics, and especially F(ST), provide important insights into the evolutionary processes that influence the structure of genetic variation within and among populations, and they are among the most widely used descriptive statistics in population and evolutionary genetics. Estimates of F(ST) can identify regions of the genome that have been the target of selection, and comparisons of F(ST) from different parts of the genome can provide insights into the demographic history of populations. For these reasons and others, F(ST) has a central role in population and evolutionary genetics and has wide applications in fields that range from disease association mapping to forensic science. This Review clarifies how F(ST) is defined, how it should be estimated, how it is related to similar statistics and how estimates of F(ST) should be interpreted.

The correlation between alleles at a pair of genetic loci is a measure of linkage disequilibrium. The square of the sample correlation multiplied by sample size provides the usual test statistic for the hypothesis of no disequilibrium for loci with two alleles and this relation has proved useful for study design and marker selection. Nevertheless, this relation holds only in a diallelic case, and an extension to multiple alleles has not been made. Here we introduce a similar statistic, R2, which leads to a correlation-based test for loci with multiple alleles: for a pair of loci with k and m alleles, and a sample of n individuals, the approximate distribution of n(k – 1)(m – 1)/(km)R2 under independence between loci is \documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}{\mathrm{{\chi}}}_{(k-1)(m-1)}^{2}\end{equation*}\end{document}. One advantage of this statistic is that it can be interpreted as the total correlation between a pair of loci. When the phase of two-locus genotypes is known, the approach is equivalent to a test for the overall correlation between rows and columns in a contingency table. In the phase-known case, R2 is the sum of the squared sample correlations for all km 2 × 2 subtables formed by collapsing to one allele vs. the rest at each locus. We examine the approximate distribution under the null of independence for R2 and report its close agreement with the exact distribution obtained by permutation. The test for independence using R2 is a strong competitor to approaches such as Pearson's chi square, Fisher's exact test, and a test based on Cressie and Read's power divergence statistic. We combine this approach with our previous composite-disequilibrium measures to address the case when the genotypic phase is unknown. Calculation of the new multiallele test statistic and its P-value is very simple and utilizes the approximate distribution of R2. We provide a computer program that evaluates approximate as well as “exact” permutational P-values.

A maximum-likelihood estimator for pairwise relatedness is presented for the situation in which the individuals under consideration come from a large outbred subpopulation of the population for which allele frequencies are known. We demonstrate via simulations that a variety of commonly used estimators that do not take this kind of misspecification of allele frequencies into account will systematically overestimate the degree of relatedness between two individuals from a subpopulation. A maximum-likelihood estimator that includes FST as a parameter is introduced with the goal of producing the relatedness estimates that would have been obtained if the subpopulation allele frequencies had been known. This estimator is shown to work quite well, even when the value of FST is misspecified. Bootstrap confidence intervals are also examined and shown to exhibit close to nominal coverage when FST is correctly specified.

This paper addresses the issue of exact-test based statistical inference for Hardy−Weinberg equilibrium in the presence of missing genotype data. Missing genotypes often are discarded when markers are tested for Hardy−Weinberg equilibrium, which can lead to bias in the statistical inference about equilibrium. Single and multiple imputation can improve inference on equilibrium. We develop tests for equilibrium in the presence of missingness by using both inbreeding coefficients (or, equivalently, χ2 statistics) and exact p-values. The analysis of a set of markers with a high missing rate from the GENEVA project on prematurity shows that exact inference on equilibrium can be altered considerably when missingness is taken into account. For markers with a high missing rate (>5%), we found that both single and multiple imputation tend to diminish evidence for Hardy−Weinberg disequilibrium. Depending on the imputation method used, 6−13% of the test results changed qualitatively at the 5% level.

Testing genetic markers for Hardy–Weinberg equilibrium (HWE) is an important tool for detecting genotyping errors in large-scale genotyping studies. For markers at the X chromosome, typically the ¿2 or exact test is applied to the females only, and the hemizygous males are considered to be uninformative. In this paper we show that the males are relevant, because a difference in allele frequency between males and females may indicate HWE not to hold. The testing of markers on the X chromosome has received little attention, and in this paper we lay down the foundation for testing biallelic X-chromosomal markers for HWE. We develop four frequentist statistical test procedures for X-linked markers that take both males and females into account: the ¿2 test, likelihood ratio test, exact test and permutation test. Exact tests that include males are shown to have a better Type I error rate. Empirical data from the GENEVA project on venous thromboembolism is used to illustrate the proposed tests. Results obtained with the new tests differ substantially from tests that are based on female genotype counts only. The new tests detect differences in allele frequencies and seem able to uncover additional genotyping error that would have gone unnoticed in HWE tests based on females only

Recent work and publications in human population genetics involving very dense SNP datasets suggest that the use of these markers will become common in plant breeding. The experience of human geneticists futher suggests that attention will need to be paid to the very high degree of genomic heterogeneity of population genetic measures such as genetic diversity. Dense marker sets will also allow more precision of estimates of relatedness between individual plants or pure-breeding lines.

Inherited genetic variation has a critical but as yet largely uncharacterized role in human disease. Here we report a public database of common variation in the human genome: more than one million single nucleotide polymorphisms (SNPs) for which accurate and complete genotypes have been obtained in 269 DNA samples from four populations, including ten 500-kilobase regions in which essentially all information about common DNA variation has been extracted. These data document the generality of recombination hotspots, a block-like structure of linkage disequilibrium and low haplotype diversity, leading to substantial correlations of SNPs with many of their neighbours. We show how the HapMap resource can guide the design and analysis of genetic association studies, shed light on structural variation and recombination, and identify loci that may have been subject to natural selection during human evolution. © 2005 Nature Publishing Group., link_to_OA_fulltext

Expressions for the joint genotypic probabilities of two related individuals are used in many population and quantitative genetic analyses. These expressions, resting on a set of 15 probabilities of patterns of identity by descent among the four alleles at a locus carried by the relatives, are generally well known. There has been recent interest in special cases where the two individuals are both related and inbred, although there have been differences among published results. Here, we return to the original 15-probability treatment and show appropriate reductions for relatives when they are drawn from a population that itself is inbred or when the relatives have parents who are related. These results have application in affected-relative tests for linkage, and in methods for interpreting forensic genetic profiles.

Summary The affected-sib-pair (ASP) method for detecting linkage between a disease locus and marker loci was first established 50 years ago, and since then numerous modifications have been made. We modify two identity-by-state (IBS) test statistics of Lange (Lange, 1986a, 1986b) to allow for inbreeding in the population. We evaluate the power and false positive rates of the modified tests under three disease models, using simulated data. Before estimating false positive rates, we demonstrate that IBS tests are tests of both linkage and linkage disequilibrium between marker and disease loci. Therefore, the null hypothesis of IBS tests should be no linkage and no LD. When the population inbreeding coefficient is large, the false positive rates of Lange's tests become much larger than the nominal value, while those of our modified tests remain close to the nominal value. To estimate power with a controlled false positive rate, we choose the cutoff values based on simulated datasets under the null hypothesis, so that both Lange's tests and the modified tests generate same false positive rate. The powers of Lange's z-test and our modified z-test are very close and do not change much with increasing inbreeding. The power of the modified chi-square test also stays stable when the inbreeding coefficient increases. However, the power of Lange's chi-square test increases with increasing inbreeding, and is larger than that of our modified chi-square test for large inbreeding coefficients. The power is high under a recessive disease model for both Lange's tests and the modified tests, though the power is low for additive and dominant disease models. Allowing for inbreeding is therefore appropriate, at least for diseases known to be recessive.

Summary. Disease genes can be mapped on the basis of associations between genetic markers and disease status, with the case–control design having the advantage of not requiring individuals from different generations. When the marker loci have multiple alleles, there has been debate on whether the power of tests for association increases or decreases. We show here that the multiple-allele version of Armitage's trend test has increased power over the two-allele version under the requirement of equifrequent alleles, but not in general. The trend test has the advantage of remaining valid even when the sampled population is not in Hardy–Weinberg equilibrium. A departure from Hardy–Weinberg means that association tests depend on gametic and nongametic linkage disequilibrium between marker and disease loci, and we illustrate the magnitude of these effects with simulated data.

A dense set of 5,000 SNPs on a 10-Mb region of human chromosome 20 has been typed on samples of African Americans, East Asians, and United Kingdom Caucasians. There are departures from Hardy-Weinberg equilibrium beyond the level at which markers are often discarded because of possible genotyping errors. The observation that markers showing such departures are often close together on the chromosome confirms the result that Hardy-Weinberg tests at two loci are correlated to an extent that depends on the linkage disequilibrium between those two markers. Linkage disequilibrium can be described by the composite linkage disequilibrium coefficient, the parameter that determines the behavior of case-control allelic tests of association. A useful preliminary investigation of datasets of this type is provided by counting the numbers of distinct multi-locus genotypes in windows of a few markers.

▪ Abstract A moment estimator of θ, the coancestry coefficient for alleles within a population, was described by Weir & Cockerham in 1984 ( 100 ) and is still widely cited. The estimate is used by population geneticists to characterize population structure, by ecologists to estimate migration rates, by animal breeders to describe genetic variation, and by forensic scientists to quantify the strength of matching DNA profiles. This review extends the work of Weir & Cockerham by allowing different levels of coancestry for different populations, and by allowing non-zero coancestries between pairs of populations. All estimates are relative to the average value of θ between pairs of populations. Moment estimates for within- and between-population θ values are likely to have large sampling variances, although these may be reduced by combining information over loci. Variances also decrease with the numbers of alleles at a locus, and with the numbers of populations sampled. This review also extends the work of Weir & Cockerham by employing maximum likelihood methods under the assumption that allele frequencies follow the normal distribution over populations. For the case of equal θ values within populations and zero θ values between populations, the maximum likelihood estimate is the same as that given by Robertson & Hill in 1984 ( 70 ). The review concludes by relating functions of θ values to times of population divergence under a pure drift model.

There is great expectation that the levels of association found between genetic markers and disease status will play a role in the location of disease genes. This expectation follows from regarding association as being proportional to linkage disequilibrium and therefore inversely related to recombination value. For disease genes with more than two alleles, the association measure is instead a weighted average of linkage disequilibria, with the weights depending on allele frequencies and genotype susceptibilities at the disease loci. There is no longer a simple relationship, even in expectation, with recombination. We adopt a general framework to examine association mapping methods which helps to clarify the nature of case-control and transmission/disequilibrium-type tests and reveals the relationship between measures of association and coefficients of linkage disequilibrium. In particular, we can show the consequences of additive and nonadditive effects at the trait locus on the behavior of these tests. These concepts have a natural extension to marker haplotypes. The association of two-locus marker haplotypes with disease phenotype depends on a weighted average of three-locus disequilibria (two markers with each disease locus). It is likely that these two-marker analyses will provide additional information in association mapping studies.

SummaryPopulation-based tests of association have used data from either case-control studies or studies based on trios (affected child and parents). Case-control studies are more prone to false-positive results caused by inappropriate controls, which can occur if, for example, there is population admixture or stratification. An advantage of family-based tests is that cases and controls are well matched, but parental data may not always be available, especially for late-onset diseases. Three recent family-based tests of association and linkage utilize unaffected siblings as surrogates for untyped parents. In this paper, we propose an extension of one of these tests. We describe and compare the four tests in the context of a complex disease for both biallelic and multiallelic markers, as well as for sibships of different sizes. We also examine the consequences of having some parental data in the sample.

Estimation of allelic and genotypic distributions for continuous data using kernel density estimation is discussed and illustrated for some variable number of tandem repeat data. These kernel density estimates provide a useful representation of data when only some of the many variants at a locus are present in a sample. Two Hardy-Weinberg test procedures are introduced for continuous data: a continuous chi-square test with test statistic TCCS and a test based on Hellinger's distance with test statistic TCCS. Simulations are used to compare the powers of these tests to each other and to the powers of a test of intraclass correlation TIC, as well as to the power of Fisher's exact test TFET applied to discretized data. Results indicate that the power of TCCS is better than that of THD but neither is as powerful as TFET. The intraclass correlation test does not perform as well as the other tests examined in this article.

Summary The transmission/disequilibrium test (TDT) originally was introduced to test for linkage between a genetic marker and a disease-susceptibility locus, in the presence of association. Recently, the TDT has been used to test for association in the presence of linkage. The motivation for this is that linkage analysis typically identifies large candidate regions, and further refinement is necessary before a search for the disease gene is begun, on the molecular level. Evidence of association and linkage may indicate which markers in the region are closest to a disease locus. As a test of linkage, transmissions from heterozygous parents to all of their affected children can be included in the TDT; however, the TDT is a valid x 2 test of association only if transmissions to unrelated affected children are used in the analysis. If the sample contains independent nuclear families with multiple affected children, then one procedure that has been used to test for association is to select randomly a single affected child from each sibship and to apply the TDT to those data. As an alternative, we propose two statistics that use data from all of the affected children. The statistics give valid x 2 tests of the null hypothesis of no association or no linkage and generally are more powerful than the TDT with a single, randomly chosen, affected child from each family.

The challenges of whole-genome data, when genotypes are available from hundreds of thousands of genetic markers, are explored for four topics in statistical genetics: Hardy-Weinberg testing, estimating linkage disequilibrium from unphased genotypic data, association mapping and characterizing population structure.

Databases were developed for three New Zealand ethnic groups (Caucasian, Maori and Polynesian), at five VNTR loci (D1S7, D2S44, D4S139, D5S110 and D12S11), and validated for interpretation of forensic identity tests. A +/-2.8% sliding window was used to define the alleles at each locus and allelic frequency distributions were obtained for each locus. The conservative nature of the sliding window approach for forensic casework was demonstrated. Tests for independence of alleles within and between loci showed good agreement with the expectation of independence. Although Polynesians are known to have reduced genetic diversity at some VNTR loci, this was found not to be a concern for the present methodology. Procedures for the analysis and reporting of DNA profile results used by New Zealand forensic scientists are therefore appropriate.

In hybrids between Drosophila simulans and D. mauritiana, males are sterile and females are fertile, in compliance with Haldane's rule. The genetic basis of this phenomenon was investigated by introgression of segments of the mauritiana genome into a simulans background. A total of 87 positions throughout the mauritiana genome were marked with P-element insertions and replicate introgressions were made by repeated backcrossing to simulans for 15 generations. The fraction of hemizgyous X chromosomal introgressions that are male sterile is ~50% greater than the fraction of homozygous autosomal segments. This result suggests that male sterility factors have evolved at a higher rate on the X, but chromosomal differences in segment length cannot be ruled out. The fraction of homozygous autosomal introgressions that are male sterile is several times greater than the fraction that are either female sterile or inviable. This observation strongly indicates that male sterility factors have evolved more rapidly than either female sterility or inviability factors. These results, combined with previous work on these and other species, suggest that Haldane> 's rule has at least two causes: recessivity of incompatibility factors and differential accumulation of sterility factors affecting males and females.

On 3 October 1995, O.J. Simpson was acquitted of two murders in spite of very strong DNA evidence linking his blood to the crime. Although numerical statements describing the strength of this evidence were made, the DNA profiles included so many loci that the need for presenting numbers in this case, and in others using similarly high numbers of loci, is probably unnecessary. If numbers are to be presented, however, they should be given in the form of likelihood ratios. One thing the verdict in the Simpson case makes clear is that it is essential that the integrity of DNA evidence (with regard to collection, potential contamination or tampering) be beyond doubt.

Several tests of independence of allelic frequencies within and between loci have been compared, and it has been found that Fisher's exact test is the best test to use. When this test is applied to RFLP databases established by the FBI, paying no attention to the single-band problem, there is generally evidence for independence at one locus but not at two loci. When the test is restricted to double-banded entries in the databases; there is overall evidence for independence.

The current availability of dense sets of marker SNPs for the human genome is having a large impact on genetic studies and offers new possibilities for clinical trials. This chapter offers a unified basis for the analysis of marker and response data, emphasizing the central importance of the correlation, or linkage disequilibrium, between SNP markers and the genes that affect response. It is convenient to phrase the development of association mapping in the language of quantitative genetics, using additive and non-additive components of variance. A novel feature of dense SNP data is that good estimates can be made of actual inbreeding and relatedness. These estimates are more relevant than values predicted from family pedigree, and are all that are available in the absence of family data.The dimensionality of SNP marker datasets has required the development of new methods that are appropriate for a large number of statistical comparisons, and the development of computational methods that allow high-dimensional regression. These methods are reviewed here, as is the use of biological annotation for both viewing the relevance of empirical associations, and to structure analysis in order to focus on those markers with the highest expectation for association with the outcomes under study.

SummaryIn previous analyses, the variation in actual, or realized, relationship has been derived as a function of map length of chromosomes and type of relationship, the variation being greater the shorter the total chromosome length and the coefficient of variation being greater the more distant the relationship. Here, the results are extended to allow for the relatives’ ancestor being inbred. Inbreeding of a parent reduces variation in actual relationship among its offspring, by an amount that depends on the inbreeding level and the type of mating that led to that level. For descendants of full-sibs, the variation is reduced in later generations, but for descendants of half-sibs, it is increased.