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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.

Likelihood ratios are necessary to properly interpret mixed stain DNA evidence. They can flexibly consider alternate hypotheses and can account for population substructure. The likelihood ratio should be seen as an estimate and not a fixed value, because the calculations are functions of allelic frequency estimates that were estimated from a small portion of the population. Current methods do not account for uncertainty in the likelihood ratio estimates and are therefore an incomplete picture of the strength of the evidence. We propose the use of a confidence interval to report the consequent variation of likelihood ratios. The confidence interval is calculated using the standard forensic likelihood ratio formulae and a variance estimate derived using the Taylor expansion. The formula is explained, and a computer program has been made available. Numeric work shows that the evidential strength of DNA profiles decreases as the variation among populations increases.

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

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.

Characterizing the genetic structure of populations is of importance to evolutionary biology, to human disease gene mapping, and to forensic science. Sewall Wright introduced a set of F-statistics to describe population structure in 1951, and he emphasized that these quantities were ratios of variances. Responding to uncertainty over the best way to estimate F-statistics, Weir and Cockerham published a method-of-moments set of estimators in 1984. This paper continues to be widely cited, with over 7,000 citations to date. Some background to the publishing history of the Weir and Cockerham paper is given here, along with subsequent developments and a discussion of current uses of Wright's F-statistics.

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.

Adrenergic receptor beta(2) (ADRB2) is a primary target for epinephrine. It plays a critical role in mediating physiological and psychological responses to environmental stressors. Thus, functional genetic variants of ADRB2 will be associated with a complex array of psychological and physiological phenotypes. These genetic variants should also interact with environmental factors such as physical or emotional stress to produce a phenotype vulnerable to pathological states. In this study, we determined whether common genetic variants of ADRB2 contribute to the development of a common chronic pain condition that is associated with increased levels of psychological distress and low blood pressure, factors which are strongly influenced by the adrenergic system. We genotyped 202 female subjects and examined the relationships between three major ADRB2 haplotypes and psychological factors, resting blood pressure, and the risk of developing a chronic musculoskeletal pain condition-Temporomandibular Joint Disorder (TMD). We propose that the first haplotype codes for lower levels of ADRB2 expression, the second haplotype codes for higher ADRB2 expression, and the third haplotype codes for higher receptor expression and rapid agonist-induced internalization. Individuals who carried one haplotype coding for high and one coding for low ADRB2 expression displayed the highest positive psychological traits, had higher levels of resting arterial pressure, and were about 10 times less likely to develop TMD. Thus, our data suggest that either positive or negative imbalances in ADRB2 function increase the vulnerability to chronic pain conditions such as TMD through different etiological pathways that imply the need for tailored treatment options.

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.

The DNA profiles of two individuals can have 0, 1, or 2 pairs of alleles that are the same at each locus. These events may be called mismatches, partial matches or matches, respectively, and they have probabilities that depend on the population proportions of alleles as well as the population structure parameter theta. The observed and expected numbers of pairs of individuals with various numbers of matching or partially matching loci in FBI and Australian databases are found to be in good agreement provided theta is set equal to some small value greater than zero. The likelihood ratios for two individuals having a specified degree of relationship versus being unrelated also depend on the numbers of matching and partially matching loci, but even unrelated pairs of individuals can have likelihood ratios that support hypotheses of relatedness. Matching probabilities allow predictions to be made for the sizes of databases that are expected to contain a pair of individuals with high numbers of matching loci. It is very likely that two individuals with at least 9 matching loci among the 13 CODIS loci have already been typed.

Summary: GWASTools is an R/Bioconductor package for quality control and analysis of genome-wide association studies (GWAS). GWASTools brings the interactive capability and extensive statistical libraries of R to GWAS. Data are stored in NetCDF format to accommodate extremely large datasets that cannot fit within R’s memory limits. The documentation includes instructions for converting data from multiple formats, including variants called from sequencing. GWASTools provides a convenient interface for linking genotypes and intensity data with sample and single nucleotide polymorphism annotation. Availability and implementation: GWASTools is implemented in R and is available from Bioconductor (http://www.bioconductor.org). An extensive vignette detailing a recommended work flow is included. Contact: sdmorris@uw.edu

▪ 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.

(2000). Challenges Facing Statistical Genetics. Journal of the American Statistical Association: Vol. 95, No. 449, pp. 319-322.

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.

This volume contains a selection of chapters base on papers presented at the Fourth Seattle Symposium in Biostatistics: Clinical Trials. The symposium was held in 2010 to celebrate the 40th anniversary of the University of Washington School of Public Health and Community Medicine. It featured keynote lectures by David DeMets and Susan Ellenberg and 16 invited presentations by other prominent researchers. The papers contained in this volume encompass recent methodological advances in several important clinical trials research, such as biomarkers, meta-analyses, sequential and adaptive clinical trials, and various genetic bioinformatic techniques. This volume will be a valuable reference for researchers and practitioners in the field of clinical trials.

Genetic risk factors are believed to combine with environmental exposures and contribute to the risk of developing temporomandibular disorder (TMD). In this prospective cohort study, 2,737 people without TMD were assessed for common genetic variation in 358 genes known to contribute to nociceptive pathways, inflammation, and affective distress. During a median follow-up period of 2.8 years, 260 people developed first-onset TMD. Hazard ratios were computed as measures of association between 2,924 single-nucleotide polymorphisms and TMD incidence. After correction for multiple testing, no single single-nucleotide polymorphism was significantly associated with risk of onset TMD. However, several single-nucleotide polymorphisms exceeded Bonferroni correction for multiple comparison or false discovery rate thresholds (.05, .1, or .2) for association with intermediate phenotypes shown to be predictive of TMD onset. Nonspecific orofacial symptoms were associated with voltage-gated sodium channel, type I, alpha subunit ( SCN1A , rs6432860, P = 2.77 × 10 −5 ) and angiotensin I–converting enzyme 2 ( ACE2 , rs1514280, P = 4.86 × 10 −5 ); global psychological symptoms with prostaglandin-endoperoxide synthase 1 ( PTGS1 , rs3842803, P = 2.79 × 10 −6 ); stress and negative affectivity with amyloid-β (A4) precursor protein ( APP , rs466448, P = 4.29 × 10 −5 ); and heat pain temporal summation with multiple PDZ domain protein ( MPDZ , rs10809907, P = 3.05 × 10 −5 ). The use of intermediate phenotypes for complex pain diseases revealed new genetic pathways influencing risk of TMD. Perspective This article reports the findings of a large candidate gene association study of first-onset TMD and related intermediate phenotypes in the OPPERA Study. Although no genetic markers predicted TMD onset, several genetic risk factors for clinical, psychological, and sensory phenotypes associated with TMD onset were observed.

SummaryA MINQUE(l) procedure, which is minimum norm quadratic unbiased estimation (MINQUE) method with 1 for all the prior values, is suggested for estimating variance and covariance components in a bio-model for diallel crosses. Unbiasedness and efficiency of estimation were compared for MINQUE(l), restricted maximum likelihood (REML) and MINQUE(θ) which has parameter values for the prior values. MINQUE(l) is almost as efficient as MINQUE(θ) for unbiased estimation of genetic variance and covariance components. The bio-model is efficient and robust for estimating variance and covariance components for maternal and paternal effects as well as for nuclear effects. A procedure of adjusted unbiased prediction (AUP) is proposed for predicting random genetic effects in the bio-model. The jack-knife procedure is suggested for estimation of sampling variances of estimated variance and covariance components and of predicted genetic effects. Worked examples are given for estimation of variance and covariance components and for prediction of genetic merits.

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.

Summary: Genome-wide association studies are widely used to investigate the genetic basis of diseases and traits, but they pose many computational challenges. We developed gdsfmt and SNPRelate (R packages for multi-core symmetric multiprocessing computer architectures) to accelerate two key computations on SNP data: principal component analysis (PCA) and relatedness analysis using identity-by-descent measures. The kernels of our algorithms are written in C/C++ and highly optimized. Benchmarks show the uniprocessor implementations of PCA and identity-by-descent are ∼8–50 times faster than the implementations provided in the popular EIGENSTRAT (v3.0) and PLINK (v1.07) programs, respectively, and can be sped up to 30–300-fold by using eight cores. SNPRelate can analyse tens of thousands of samples with millions of SNPs. For example, our package was used to perform PCA on 55 324 subjects from the ‘Gene-Environment Association Studies’ consortium studies. Availability and implementation: gdsfmt and SNPRelate are available from R CRAN (http://cran.r-project.org), including a vignette. A tutorial can be found at https://www.genevastudy.org/Accomplishments/software. Contact: zhengx@u.washington.edu

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.

DNA profiling of biological material from scenes of crimes is often complicated because the amount of DNA is limited and the quality of the DNA may be compromised. Furthermore, the sensitivity of STR typing kits has been continuously improved to detect low level DNA traces. This may lead to (1) partial DNA profiles and (2) detection of additional alleles. There are two key phenomena to consider: allelic or locus ‘drop-out’, i.e. ‘missing’ alleles at one or more genetic loci, while ‘drop-in’ may explain alleles in the DNA profile that are additional to the assumed main contributor(s). The drop-in phenomenon is restricted to 1 or 2 alleles per profile. If multiple alleles are observed at more than two loci then these are considered as alleles from an extra contributor and analysis can proceed as a mixture of two or more contributors. Here, we give recommendations on how to estimate probabilities considering drop-out, Pr(D), and drop-in, Pr(C). For reasons of clarity, we have deliberately restricted the current recommendations considering drop-out and/or drop-in at only one locus. Furthermore, we offer recommendations on how to use Pr(D) and Pr(C) with the likelihood ratio principles that are generally recommended by the International Society of Forensic Genetics (ISFG) as measure of the weight of the evidence in forensic genetics. Examples of calculations are included. An Excel spreadsheet is provided so that scientists and laboratories may explore the models and input their own data.

With the expansion of offender/arrestee DNA profile databases, genetic forensic identification has become commonplace in the United States criminal justice system. Implementation of familial searching has been proposed to extend forensic identification to family members of individuals with profiles in offender/arrestee DNA databases. In familial searching, a partial genetic profile match between a database entrant and a crime scene sample is used to implicate genetic relatives of the database entrant as potential sources of the crime scene sample. In addition to concerns regarding civil liberties, familial searching poses unanswered statistical questions. In this study, we define confidence intervals on estimated likelihood ratios for familial identification. Using these confidence intervals, we consider familial searching in a structured population. We show that relatives and unrelated individuals from population samples with lower gene diversity over the loci considered are less distinguishable. We also consider cases where the most appropriate population sample for individuals considered is unknown. We find that as a less appropriate population sample, and thus allele frequency distribution, is assumed, relatives and unrelated individuals become more difficult to distinguish. In addition, we show that relationship distinguishability increases with the number of markers considered, but decreases for more distant genetic familial relationships. All of these results indicate that caution is warranted in the application of familial searching in structured populations, such as in the United States., Author Summary The forensic identification of criminal suspects through DNA profiling is now common in the United States. Indirect identification by familial DNA profiling is increasingly proposed to extend the utility of DNA databases. In familial searching, a DNA profile from a crime scene partially matches a database profile entry, implicating close relatives of the partial match. While the basic principles behind familial searching methods are simple and elegant, statistical confidence that a partially matched profile belongs to a true genetic relative has not been fully explored. Here, we derive relative identification likelihood ratio statistics and consider how the ability of familial searching to distinguish relatives from unrelated individuals varies over population samples and is affected by inaccurately assumed population background. We observe lower relationship distinguishability for population samples with less identifying information in the genetic loci considered. Additionally, we show that relationship distinguishability decreases with discordance between true and assumed population samples. These results indicate that, if an inappropriate genetic population group is assumed, individuals from certain marginalized groups may be disproportionately more often subject to false familial identification. Our results suggest that care is warranted in the use and interpretation of familial searching forensic techniques.

A simple tandem repeat (STR) PCR-based typing system developed for the genetic individualization of domestic cat samples has been used to generate a population genetic database of domestic cat breeds. A panel of 10 tetranucleotide STR loci and a gender-identifying sequence tagged site (STS) were co-amplified in genomic DNA of 1043 individuals representing 38 cat breeds. The STR panel exhibits relatively high heterozygosity in cat breeds, with an average 10-locus heterozygosity of 0.71, which represents an average of 38 breed-specific heterozygosities for the 10-member panel. When the entire set of breed individuals was analyzed as a single population, a heterozygosity of 0.87 was observed. Heterozygosities obtained for the 10 loci range from 0.72 to 0.96. The power for genetic individualization of domestic cat samples of the multiplex is high, with a probability of match (p(m)) of 6.2E-14, using a conservative θ = 0.05.

Recently, we reported a method to estimate the proportion of phenotypic variance explained by all SNPs from genome-wide association studies, and estimated that half of the heritability for human height was captured by common SNPs. Here we partition genetic variation for height, body mass index (BMI), von Willebrand factor (vWF) and QT interval (QTi) onto chromosomes and chromosome segments, using 586,898 SNPs genotyped on 11,586 unrelated individuals. We estimate that ~45%, ~17%, ~25% and ~21% of variance in height, BMI, vWF and QTi, respectively, can be explained by considering all autosomal SNPs simultaneously, and a further ~0.5–1% by X-chromosome SNPs for height, BMI and vWF. We show that variance explained by each chromosome for height and QTi is proportional to the total gene length on that chromosome. In genome-wide analyses, common SNPs in or near genes explain more variation than SNPs between genes. We propose a novel approach to estimate variation due to cryptic relatedness and population stratification. Our results provide further evidence that a substantial proportion of heritability is accounted for by causal variants in linkage disequilibrium with common SNPs; that height, BMI and QTi are highly polygenic traits; and that the additive variation explained by a part of the genome is approximately proportional to the total length of DNA contained within genes therein.

Genetic factors play a role in the etiology of persistent pain conditions, putatively by modulating underlying processes such as nociceptive sensitivity, psychological well-being, inflammation, and autonomic response. However, to date, only a few genes have been associated with temporomandibular disorders (TMD). This study evaluated 358 genes involved in pain processes, comparing allelic frequencies between 166 cases with chronic TMD and 1,442 controls enrolled in the OPPERA (Orofacial Pain: Prospective Evaluation and Risk Assessment) study cooperative agreement. To enhance statistical power, 182 TMD cases and 170 controls from a similar study were included in the analysis. Genotyping was performed using the Pain Research Panel, an Affymetrix gene chip representing 3,295 single nucleotide polymorphisms, including ancestry-informative markers that were used to adjust for population stratification. Adjusted associations between genetic markers and TMD case status were evaluated using logistic regression. The OPPERA findings provided evidence supporting previously reported associations between TMD and 2 genes: HTR2A and COMT. Other genes were revealed as potential new genetic risk factors for TMD, including NR3C1, CAMK4, CHRM2, IFRD1, and GRK5. While these findings need to be replicated in independent cohorts, the genes potentially represent important markers of risk for TMD, and they identify potential targets for therapeutic intervention. Perspective Genetic risk factors for TMD pain were explored in the case-control component of the OPPERA cooperative agreement, a large population-based prospective cohort study. Over 350 candidate pain genes were assessed using a candidate gene panel, with several genes displaying preliminary evidence for association with TMD status.

Mitochondrial DNA (mtDNA) and the non-recombining portion of the Y-chromosome are inherited matrilinealy and patrilinealy, respectively, and without recombination. Collectively they are termed 'lineage markers'. Lineage markers may be used in forensic testing of an item, such as a hair from a crime scene, against a hypothesised source, or in relationship testing. An estimate of the evidential weight of a match is usually provided by a count of the occurrence in some database of the mtDNA or Y-STR haplotype under consideration. When the factual statement of a count in the database is applied to a case, issues of relevance of the database and sampling uncertainty may arise. In this paper, we re-examine the issues of sampling uncertainty, the relevance of the database, and the combination of autosomal and lineage marker evidence. We also review the recent developments by C.H. Brenner. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

SummaryAlthough the expected relationship or proportion of genome shared by pairs of relatives can be obtained from their pedigrees, the actual quantities deviate as a consequence of Mendelian sampling and depend on the number of chromosomes and map length. Formulae have been published previously for the variance of actual relationship for a number of specific types of relatives but no general formula for non-inbred individuals is available. We provide here a unified framework that enables the variances for distant relatives to be easily computed, showing, for example, how the variance of sharing for great grandparent–great grandchild, great uncle–great nephew, half uncle–nephew and first cousins differ, even though they have the same expected relationship. Results are extended in order to include differences in map length between sexes, no recombination in males and sex linkage. We derive the magnitude of skew in the proportion shared, showing the skew becomes increasingly large the more distant the relationship. The results obtained for variation in actual relationship apply directly to the variation in actual inbreeding as both are functions of genomic coancestry, and we show how to partition the variation in actual inbreeding between and within families. Although the variance of actual relationship falls as individuals become more distant, its coefficient of variation rises, and so, exacerbated by the skewness, it becomes increasingly difficult to distinguish different pedigree relationships from the actual fraction of the genome shared.

Phylogenetic trees may be constructed from pairwise distances among the taxonomic units. When the data consist of DNA sequences, appropriate distances can be defined to reflect the mutation model and to have expected values proportional to the time of divergence of the sequences. With the growing amount of sequence data, it is also necessary to incorporate within-species sequence variation into measures of distance between sequences. This additional feature requires attention to be paid to drift and recombination as well as mutation, and greatly increases the difficulty of estimating variances of estimated distances. Numerical resampling seems appropriate. These concepts are illustrated with some sequence data from the Adhl gene from maize and pearl millet.

We propose a multilocus version of FST and a measure of haplotype diversity using localized haplotype clusters. Specifically, we use haplotype clusters identified with BEAGLE, which is a program implementing a hidden Markov model for localized haplotype clustering and performing several functions including inference of haplotype phase. We apply this methodology to HapMap phase 3 data. With this haplotype-cluster approach, African populations have highest diversity and lowest divergence from the ancestral population, East Asian populations have lowest diversity and highest divergence, and other populations (European, Indian, and Mexican) have intermediate levels of diversity and divergence. These relationships accord with expectation based on other studies and accepted models of human history. In contrast, the population-specific FST estimates obtained directly from single-nucleotide polymorphisms (SNPs) do not reflect such expected relationships. We show that ascertainment bias of SNPs has less impact on the proposed haplotype-cluster-based FST than on the SNP-based version, which provides a potential explanation for these results. Thus, these new measures of FST and haplotype-cluster diversity provide an important new tool for population genetic analysis of high-density SNP data.