Multipoint quantitative-trait linkage analysis in general pedigrees.

Multipoint linkage analysis of quantitative-trait loci (QTLs) has previously been restricted to sibships and small pedigrees. In this article, we show how variance-component linkage methods can be used in pedigrees of arbitrary size and complexity, and we develop a general framework for multipoint identity-by-descent (IBD) probability calculations. We extend the sib-pair multipoint mapping approach of Fulker et al. to general relative pairs. This multipoint IBD method uses the proportion of alleles shared identical by descent at genotyped loci to estimate IBD sharing at arbitrary points along a chromosome for each relative pair. We have derived correlations in IBD sharing as a function of chromosomal distance for relative pairs in general pedigrees and provide a simple framework whereby these correlations can be easily obtained for any relative pair related by a single line of descent or by multiple independent lines of descent. Once calculated, the multipoint relative-pair IBDs can be utilized in variance-component linkage analysis, which considers the likelihood of the entire pedigree jointly. Examples are given that use simulated data, demonstrating both the accuracy of QTL localization and the increase in power provided by multipoint analysis with 5-, 10-, and 20-cM marker maps. The general pedigree variance component and IBD estimation methods have been implemented in the SOLAR (Sequential Oligogenic Linkage Analysis Routines) computer package.     

Powerful regression-based quantitative-trait linkage analysis of general pedigrees

We present a new method of quantitative-trait linkage analysis that combines the simplicity and robustness of regression-based methods and the generality and greater power of variance-components models. The new method is based on a regression of estimated identity-by-descent (IBD) sharing between relative pairs on the squared sums and squared differences of trait values of the relative pairs. The method is applicable to pedigrees of arbitrary structure and to pedigrees selected on the basis of trait value, provided that population parameters of the trait distribution can be correctly specified. Ambiguous IBD sharing (due to incomplete marker information) can be accommodated in the method by appropriate specification of the variance-covariance matrix of IBD sharing between relative pairs. We have implemented this regression-based method and have performed simulation studies to assess, under a range of conditions, estimation accuracy, type I error rate, and power. For normally distributed traits and in large samples, the method is found to give the correct type I error rate and an unbiased estimate of the proportion of trait variance accounted for by the additive effects of the locus-although, in cases where asymptotic theory is doubtful, significance levels should be checked by simulations. In large sibships, the new method is slightly more powerful than variance-components models. The proposed method provides a practical and powerful tool for the linkage analysis of quantitative traits.     

Exact genetic linkage computations for general pedigrees

MOTIVATION: Genetic linkage analysis is a useful statistical tool for mapping disease genes and for associating functionality of genes with their location on the chromosome. There is a need for a program that computes multipoint likelihood on general pedigrees with many markers that also deals with two-locus disease models. RESULTS: In this paper we present algorithms for performing exact multipoint likelihood calculations on general pedigrees with a large number of highly polymorphic markers, taking into account a variety of disease models. We have implemented these algorithms in a new computer program called SUPERLINK which outperforms leading linkage software with regards to functionality, speed, memory requirements and extensibility.     

Nonparametric simulation-based statistics for detecting linkage in general pedigrees.

We present here four nonparametric statistics for linkage analysis that test whether pairs of affected relatives share marker alleles more often than expected. These statistics are based on simulating the null distribution of a given statistic conditional on the unaffecteds' marker genotypes. Each statistic uses a different measure of marker sharing: the SimAPM statistic uses the simulation-based affected-pedigree-member measure based on identity-by-state (IBS) sharing. The SimKIN (kinship) measure is 1.0 for identity-by-descent (IBD) sharing, 0.0 for no IBD status sharing, and the kinship coefficient when the IBD status is ambiguous. The simulation-based IBD (SimIBD) statistic uses a recursive algorithm to determine the probability of two affecteds sharing a specific allele IBD. The SimISO statistic is identical to SimIBD, except that it also measures marker similarity between unaffected pairs. We evaluated our statistics on data simulated under different two-locus disease models, comparing our results to those obtained with several other nonparametric statistics. Use of IBD information produces dramatic increases in power over the SimAPM method, which uses only IBS information. The power of our best statistic in most cases meets or exceeds the power of the other nonparametric statistics. Furthermore, our statistics perform comparisons between all affected relative pairs within general pedigrees and are not restricted to sib pairs or nuclear families.     

The effect of linkage disequilibrium on linkage analysis of incomplete pedigrees

Dense SNP maps can be highly informative for linkage studies. But when parental genotypes are missing, multipoint linkage scores can be inflated in regions with substantial marker-marker linkage disequilibrium (LD). Such regions were observed in the Affymetrix SNP genotypes for the Genetic Analysis Workshop 14 (GAW14) Collaborative Study on the Genetics of Alcoholism (COGA) dataset, providing an opportunity to test a novel simulation strategy for studying this problem. First, an inheritance vector (with or without linkage present) is simulated for each replicate, i.e., locations of recombinations and transmission of parental chromosomes are determined for each meiosis. Then, two sets of founder haplotypes are superimposed onto the inheritance vector: one set that is inferred from the actual data and which contains the pattern of LD; and one set created by randomly selecting parental alleles based on the known allele frequencies, with no correlation (LD) between markers. Applying this strategy to a map of 176 SNPs (66 Mb of chromosome 7) for 100 replicates of 116 sibling pairs, significant inflation of multipoint linkage scores was observed in regions of high LD when parental genotypes were set to missing, with no linkage present. Similar inflation was observed in analyses of the COGA data for these affected sib pairs with parental genotypes set to missing, but not after reducing the marker map until r2 between any pair of markers was 相似文献   

A test for linkage and association in general pedigrees: the pedigree disequilibrium test

Family-based tests of linkage disequilibrium typically are based on nuclear-family data including affected individuals and their parents or their unaffected siblings. A limitation of such tests is that they generally are not valid tests of association when data from related nuclear families from larger pedigrees are used. Standard methods require selection of a single nuclear family from any extended pedigrees when testing for linkage disequilibrium. Often data are available for larger pedigrees, and it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this study, we present the pedigree disequilibrium test (PDT) for analysis of linkage disequilibrium in general pedigrees. The PDT can use data from related nuclear families from extended pedigrees and is valid even when there is population substructure. Using computer simulations, we demonstrated validity of the test when the asymptotic distribution is used to assess the significance, and examined statistical power. Power simulations demonstrate that, when extended pedigree data are available, substantial gains in power can be attained by use of the PDT rather than existing methods that use only a subset of the data. Furthermore, the PDT remains more powerful even when there is misclassification of unaffected individuals. Our simulations suggest that there may be advantages to using the PDT even if the data consist of independent families without extended family information. Thus, the PDT provides a general test of linkage disequilibrium that can be widely applied to different data structures.     

Detecting pleiotropy and epistasis using variance components linkage analysis in jPAP

jPAP (Java Pedigree Analysis Package) performs variance components linkage analysis of either quantitative or discrete traits. Multivariate linkage analysis of two or more traits (all quantitative, all discrete, or any combination) allows the inference of pleiotropy between the traits. The inclusion of multiple quantitative trait loci in linkage analysis allows the inference of epistasis between loci. A user-friendly graphical user interface facilitates the usage of jPAP.     

Exact multipoint quantitative-trait linkage analysis in pedigrees by variance components

Methods based on variance components are powerful tools for linkage analysis of quantitative traits, because they allow simultaneous consideration of all pedigree members. The central idea is to identify loci making a significant contribution to the population variance of a trait, by use of allele-sharing probabilities derived from genotyped marker loci. The technique is only as powerful as the methods used to infer these probabilities, but, to date, no implementation has made full use of the inheritance information in mapping data. Here we present a new implementation that uses an exact multipoint algorithm to extract the full probability distribution of allele sharing at every point in a mapped region. At each locus in the region, the program fits a model that partitions total phenotypic variance into components due to environmental factors, a major gene at the locus, and other unlinked genes. Numerical methods are used to derive maximum-likelihood estimates of the variance components, under the assumption of multivariate normality. A likelihood-ratio test is then applied to detect any significant effect of the hypothesized major gene. Simulations show the method to have greater power than does traditional sib-pair analysis. The method is freely available in a new release of the software package GENEHUNTER.     

Analytical estimation of the power of linkage analysis in large pedigrees

Different approaches to analytical calculation of the power in linkage analysis whose efficiencies have been demonstrated in small pedigrees are described. The possibility of applying them to large pedigrees has been estimated. Equivalence of the analytical estimates of power obtained using different approaches based on analysis of individual pairs of relatives has been shown. The accuracy of the resultant analytical estimation of the power has been analyzed for three large pedigrees and a wide range of quantitative trait inheritance models; the accuracy has been demonstrated to be sufficiently high and equal to the accuracy in the case of small pedigrees.     

Blocking Gibbs sampling for linkage analysis in large pedigrees with many loops.

We apply the method of "blocking Gibbs" sampling to a problem of great importance and complexity-linkage analysis. Blocking Gibbs sampling combines exact local computations with Gibbs sampling, in a way that complements the strengths of both. The method is able to handle problems with very high complexity, such as linkage analysis in large pedigrees with many loops, a task that no other known method is able to handle. New developments of the method are outlined, and it is applied to a highly complex linkage problem in a human pedigree.     

Effects of epistasis on tests for linkage in self-pollinated species

Summary Tests for linkage based on covariances among relatives in self-pollinated species are usually based upon an assumption that epistasis is not important. This study was conducted to determine the impact of epistasis on, and to investigate the sensitivity of, such tests. Thirty covariances were calculated for each of ten non-epistatic and ten epistatic genetic models with varying probabilities of recombination between two coupling or repulsion loci. Each set of covariances was tested for linkage by comparing covariances calculated for the model with those expected for an additive-dominance model with no linkage. Results showed that the test for linkage is quite insensitive to the effects of linkage due to the disproportionate influence of inbreeding. Repulsion linkages should be easier to detect than coupling linkages for all models. Epistasis was found to mimic or counteract the effects of linkage. Tests for linkage based on covariances within a hierarchical mating design appear to be insensitive to linkage and may confuse the effects of linkage and epistasis.     

Accounting for expected linkage in biometric analysis of quantitative traits

Russian Journal of Genetics - The problem of accounting for a genetic estimation of expected linkage in the disposition of random loci was solved for the additive-dominant model. The...     

A two-stage linkage analysis of Chinese schizophrenia pedigrees in 10 target chromosomes

We performed a two-stage linkage scan involving 25 Chinese schizophrenia families, focusing on 10 target chromosomes which have already been the subject of considerable research. We initially genotyped 237 individuals with 186 markers, five candidate regions were then chosen for fine mapping and 49 additional markers were genotyped. In region 1q21-23, a maximum multipoint HLOD (HLOD=2.38) was observed between D1S484 and D1S2705, under the dominant model. In region 5q35, dominant HOLD of 2.36, 2.04, and 2.31 were found at marker D5S2030, D5S408, and D5S2006, respectively. Consistent multipoint results also supported linkage to this region under the same dominant model, with a highest HOLD of 2.47. Furthermore, single-point HLODs (HLOD=1.95 at D22S274, and HLOD=1.91 at D22S1157) were found in region 22q13, under the dominant model. Evidence from these three regions satisfied the criteria for suggestive linkage and should help in identifying schizophrenia susceptibility genes.     

Maximum likelihood haplotyping for general pedigrees

Haplotype data is valuable in mapping disease-susceptibility genes in the study of Mendelian and complex diseases. We present algorithms for inferring a most likely haplotype configuration for general pedigrees, implemented in the newest version of the genetic linkage analysis system SUPERLINK. In SUPERLINK, genetic linkage analysis problems are represented internally using Bayesian networks. The use of Bayesian networks enables efficient maximum likelihood haplotyping for more complex pedigrees than was previously possible. Furthermore, to support efficient haplotyping for larger pedigrees, we have also incorporated a novel algorithm for determining a better elimination order for the variables of the Bayesian network. The presented optimization algorithm also improves likelihood computations. We present experimental results for the new algorithms on a variety of real and semiartificial data sets, and use our software to evaluate MCMC approximations for haplotyping.     

Stable linkage disequilibrium without epistasis in subdivided populations

In a large random mating population stable linkage disequilibrium occurs only when there is epistasis. However if a population is divided into a number of subpopulations among which migration occurs, stable linkage disequilibrium in each subpopulation may be produced without epistasis. In the case of two subpopulations a necessary condition for linkage equilibrium in the absence of epistasis is that at least at one of the two loci under consideration the gene frequency must be the same for the two populations. This condition is rather severe and any violation of this will lead to stable linkage disequilibrium. A similar conclusion can be made with more than two populations. In general the presence of linkage disequilibrium does not necessarily imply the existence of epistasis even in equilibrium populations.     

Robust variance-components approach for assessing genetic linkage in pedigrees.

To assess evidence for genetic linkage from pedigrees, I developed a limited variance-components approach. In this method, variability among trait observations from individuals within pedigrees is expressed in terms of fixed effects from covariates and effects due to an unobservable trait-affecting major locus, random polygenic effects, and residual nongenetic variance. The effect attributable to a locus linked to a marker is a function of the additive and dominance components of variance of the locus, the recombination fraction, and the proportion of genes identical by descent at the marker locus for each pair of sibs. For unlinked loci, the polygenic variance component depends only on the relationship between the relative pair. Parameters can be estimated by either maximum-likelihood methods or quasi-likelihood methods. The forms of quasi-likelihood estimators are provided. Hypothesis tests derived from the maximum-likelihood approach are constructed by appeal to asymptotic theory. A simulation study showed that the size of likelihood-ratio tests was appropriate but that the monogenic component of variance was generally underestimated by the likelihood approach.     

A general framework for statistical linkage analysis in multivalent tetraploids

In multivalent polyploids, simultaneous pairings among homologous chromosomes at meiosis result in a unique cytological phenomenon-double reduction. Double reduction casts an impact on chromosome evolution in higher plants, but because of its confounded effect on the pattern of gene cosegregation, it complicates linkage analysis and map construction with polymorphic molecular markers. In this article, we have proposed a general statistical model for simultaneously estimating the frequencies of double reduction, the recombination fraction, and optimal parental linkage phases between any types of markers, both fully and partially informative, or dominant and codominant, for a tetraploid species that undergoes only multivalent pairing. This model provides an in-depth extension of our earlier linkage model that was built upon Fisher's classifications for different gamete formation modes during the polysomic inheritance of a multivalent polyploid. By implementing a two-stage hierarchical EM algorithm, we derived a closed-form solution for estimating the frequencies of double reduction through the estimation of gamete mode frequencies and the recombination fraction. We performed different settings of simulation studies to demonstrate the statistical properties of our model for estimating and testing double reduction and the linkage in multivalent tetraploids. As shown by a comparative analysis, our model provides a general framework that covers existing statistical approaches for linkage mapping in polyploids that are predominantly multivalent. The model will have great implications for understanding the genome structure and organization of polyploid species.     

MOD-score analysis with simple pedigrees: an overview of likelihood-based linkage methods

A MOD-score analysis, in which the parametric LOD score is maximized with respect to the trait-model parameters, can be a powerful method for the mapping of complex traits. With affected sib pairs, it has been shown before that MOD scores asymptotically follow a mixture of chi(2) distributions with 2, 1 and 0 degrees of freedom under the null hypothesis of no linkage. In that context, a MOD-score analysis yields some (albeit limited) information regarding the trait-model parameters, and there is a chance for an increased power compared to a simple LOD-score analysis. Here, it is shown that with unilineal affected relative pairs, MOD scores asymptotically follow a mixture of chi(2) distributions with 1 and 0 degrees of freedom under the null hypothesis, that is, the same distribution as followed by simple LOD scores. No information regarding the trait model can be obtained in this setting, and no power is gained when compared to a LOD-score analysis. An outlook to larger pedigrees is given. The number of degrees of freedom underlying the null distribution of MOD scores, that depends on the type of pedigrees studied, corresponds to the number of explored dimensions related to power and to the number of parameters that can jointly be estimated.