Search

Family-based tests of association are now often used when trying to fine-map a disease susceptibility locus. Recently, several tests of linkage and association have been proposed that use nuclear families with multiple affected and unaffected sibs rather than just case-parent triads. In this paper we propose a test that generalizes these previous tests. Formulae are derived to calculate the power of the test for a randomly mating population. These power calculations are used to determine conditions under which it is advantageous to include unaffected sibs in the analysis.

Summary One strategy for localization of a quantitative-trait locus (QTL) is to test whether the distribution of a quantitative trait depends on the number of copies of a specific genetic-marker allele that an individual possesses. This approach tests for association between alleles at the marker and the QTL, and it assumes that association is a consequence of the marker being physically close to the QTL. However, problems can occur when data are not from a homogeneous population, since associations can arise irrespective of a genetic marker being in physical proximity to the QTL—that is, no information is gained regarding localization. Methods to address this problem have recently been proposed. These proposed methods use family data for indirect stratification of a population, thereby removing the effect of associations that are due to unknown population substructure. They are, however, restricted in terms of the number of children per family that can be used in the analysis. Here we introduce tests that can be used on family data with parent and child genotypes, with child genotypes only, or with a combination of these types of families, without size restrictions. Furthermore, equations that allow one to determine the sample size needed to achieve desired power are derived. By means of simulation, we demonstrate that the existing tests have an elevated false-positive rate when the size restrictions are not followed and that a good deal of information is lost as a result of adherence to the size restrictions. Finally, we introduce permutation procedures that are recommended for small samples but that can also be used for extensions of the tests to multiallelic markers and to the simultaneous use of more than one marker.

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.

Family-based tests of linkage disequilibrium are usually based on nuclear family data including affected individuals and their parents or their unaffected siblings. A problem with these tests is that they are not valid tests of association when data from related nuclear families from larger pedigrees are used. One way to ensure validity when testing for association is to select a single nuclear family from each extended pedigree in the sample. When data are available for larger pedigrees, it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this paper we present such a test: the Pedigree Disequilibrium Test (PDT). The PDT can use data from related nuclear families from extended pedigrees and remains valid when there is population substructure. Power simulations demonstrate that, when extended pedigree data are available, gains in power can be obtained by using the PDT rather than existing methods that only use a subset of the data. The PDT can also be more powerful than current methods when the data consist of a sample of independent nuclear families or sibships.

One of the goals of the International HapMap Project is the identification of common haplotypes in genes. However, HapMap uses an incomplete catalogue of single nucleotide polymorphisms (SNPs) and might miss some common haplotypes. We examined this issue using data from the Environmental Genome Project (EGP) which resequenced 335 genes in 90 people, and thus, has a nearly complete catalogue of gene SNPs. The EGP identified a total of 45,243 SNPs, of which 10,780 were common SNPs (minor allele frequency ≥0.1). Using EGP common SNP genotype data, we identified 1,459 haplotypes with frequency ≥0.05 and we use these as “benchmark” haplotypes. HapMap release 16 had genotype information for 1,573 of 10,780 (15%) EGP common SNPs. Using these SNPs, we identified common HapMap haplotypes (frequency ≥0.05) in each of the four HapMap ethnic groups. To compare common HapMap haplotypes to EGP benchmark haplotypes, we collapsed benchmark haplotypes to the set of 1,573 SNPs. Ninety-eight percent of the collapsed benchmark haplotypes could be found as common HapMap haplotypes in one or more of the four HapMap ethnic groups. However, collapsing benchmark haplotypes to the set of SNPs available in HapMap resulted in a loss of haplotype information: 545 of 1,459 (37%) benchmark haplotypes were uniquely identified, and only 25% of genes had all their benchmark haplotypes uniquely identified. We resampled the EGP data to examine the effect of increasing the number of HapMap SNPs to 5 million, and estimate that ∼40% of common SNPs in genes will be sampled and that half of the genes will have sufficient SNPs to identify all common haplotypes. This inability to distinguish common haplotypes of genes may result in loss of power when examining haplotype-disease association. (Cancer Epidemiol Biomarkers Prev 2006;15(1):133–7)

The pedigree disequilibrium test (PDT) has been proposed recently as a test for association in general pedigrees [Martin et al., Am J Hum Genet 67:146-54, 2000]. The Genetic Analysis Workshop (GAW) 12 simulated data, with many extended pedigrees, is an example the type of data to which the PDT is ideally suited. In replicate 42 from the general population the PDT correctly identifies candidate genes 1, 2, and 6 as containing single nucleotide polymorphisms (SNPs) that are significantly associated with the disease. We also applied the truncated product method (TPM) [Zaykin et al., Genet Epidemiol, in press] to combine p-values in overlapping windows across the genes. Our results show that the TPM is helpful in identifying significant SNPs as well as removing spurious false positives. Our results indicate that, using the PDT, functional disease-associated SNPs can be successfully identified with a dense map of moderately polymorphic SNPs.

Summary: Genetic association studies increasingly rely on the use of linkage disequilibrium (LD) tag SNPs to reduce genotyping costs. We developed a software package TAGster to select, evaluate and visualize LD tag SNPs both for single and multiple populations. We implement several strategies to improve the efficiency of current LD tag SNP selection algorithms: (1) we modify the tag SNP selection procedure of Carlson et al. to improve selection efficiency and further generalize it to multiple populations. (2) We propose a redundant SNP elimination step to speed up the exhaustive tag SNP search algorithm proposed by Qin et al. (3) We present an additional multiple population tag SNP selection algorithm based on the framework of Howie et al., but using our modified exhaustive search procedure. We evaluate these methods using resequenced candidate gene data from the Environmental Genome Project and show improvements in both computational and tagging efficiency.Availability: The software Package TAGster is freely available at http://www.niehs.nih.gov/research/resources/software/tagster/Contact: taylor@niehs.nih.govSupplementary information: Additional information, including a tutorial, detailed algorithm and detailed evaluation results, is also available from TAGster web site (see above).

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

A statistical test for detecting genetic differentiation of subpopulations is described that uses molecular variation in samples of DNA sequences from two or more localities. The statistical significance of the test is determined with Monte Carlo simulations. The power of the test to detect genetic differentiation in a selectively neutral Wright-Fisher island model depends on both sample size and the rates of migration, mutation, and recombination. It is found that the power of the test is substantial with samples of size 50, when 4Nm less than 10, where N is the subpopulation size and m is the fraction of migrants in each subpopulation each generation. More powerful tests are obtained with genes with recombination than with genes without recombination.

A numerical method is developed for solving a nonstandard singular system of second-order differential equations arising from a problem in population genetics concerning the coalescent process for a sample from a population undergoing selection. The nonstandard feature of the system is that there are terms in the equations that approach infinity as one approaches the boundary. The numerical recipe is patterned after the LU decomposition for tridiagonal matrices. Although there is no analytic proof that this method leads to the correct solution, various examples are presented that suggest that the method works. This method allows one to calculate the expected number of segregating sites in a random sample of n genes from a population whose evolution is described by a model which is not selectively neutral.

The statistical properties of the process describing the genealogical history of a random sample of genes at a selectively neutral locus which is linked to a locus at which natural selection operates are investigated. It is found that the equations describing this process are simple modifications of the equations describing the process assuming that the two loci are completely linked. Thus, the statistical properties of the genealogical process for a random sample at a neutral locus linked to a locus with selection follow from the results obtained for the selected locus. Sequence data from the alcohol dehydrogenase (Adh) region of Drosophila melanogaster are examined and compared to predictions based on the theory. It is found that the spatial distribution of nucleotide differences between Fast and Slow alleles of Adh is very similar to the spatial distribution predicted if balancing selection operates to maintain the allozyme variation at the Adh locus. The spatial distribution of nucleotide differences between different Slow alleles of Adh do not match the predictions of this simple model very well.

A model of the evolution of a transposable element family in a Mendelian host population is proposed that incorporates heritable phenotypic mutations in the elements. The temporal behavior of the numbers of mutant and wild-type elements is studied, and the expected extinction time of the transposable element family is examined. Our results indicate that, if the mutant can be transposed equally well in the presence of the wild type, then it can be expected to be found in preponderance, whereas elements, such as retroviruses, where the transposing genome and its phenotypic expression are coupled, may be characterized by a low mutant frequency.

Statistical properties of the amount of divergence of members of a transposable element family are studied. The analysis is based on the model proposed by Langley et al. [5], describing the evolution of a family of selectively neutral transposable elements in a finite haploid population of size 2N. By considering the time back to the most recent common ancestor of two copies, both the probability of identity and the moments of the number of sites that differ between two sampled copies are obtained. Our analytic results are consistent with the numerical results of Ohta [8] for a similar model. The effects of gene conversion are also examined. In agreement with Slatkin [9], we find that gene conversion has a minimal effect on the probability of identity providing that the rate of deletion is sufficiently large.

SummaryA population genetics model of the role of asymmetric pairing and unequal exchange in the stabilization of transposable element copy number in natural populations is proposed and analysed. Monte Carlo simulations indicate that the approximations incorporated into the analysis are robust in the relevant parameter ranges. Given several simple assumptions concerning transposition and excision, equal and unequal exchange, and chromosome structure, predictions of the relative numbers of transposable elements in various regions of theDrosophila melanogastergenome are compared to the observed distribution ofroo/B104elements across chromosomal regions with differing rates of exchange, and betweenXchromosomes and autosomes. There is no indication of an accumulation of elements in the distal regions of chromosomes, which is expected if unequal exchange is reduced concomitantly with normal crossing over in the distal regions. There is, however, an indication of an excess of elements relative to physical length in the proximal regions of the chromosomes, which also have restricted crossing over. This observation is qualitatively consistent with the model's predictions. The observed distribution of elements between the mid-sections of theXchromosomes and autosomes is consistent with the predictions of one of two models of unequal exchange.

Methods are proposed for estimating the parameters in the frequency spectrum derived from the model of Langley, Brookfield and Kaplan for the evolution of a transposable element in a finite Mendelian population. Statistical properties of these estimates are studied, and the results are supported with simulation data. The effects on the estimates caused by possible insensitivities of the experimental technique are also discussed. To illustrate the proposed methodology, the data of Montgomery and Langley are analyzed.