Genome sharing in large pedigrees: multiple imputation of ibd for linkage detection

Our objective is the development of robust methods for assessment of evidence for linkage of loci affecting a complex trait to a marker linkage group, using data on extended pedigrees. Using Markov chain Monte Carlo (MCMC) methods, it is possible to sample realizations from the distribution of gene identity by descent (IBD) patterns on a pedigree, conditional on observed data YM at multiple marker loci. Measures of gene IBDW which capture joint genome sharing in extended pedigrees often have unknown and highly skewed distributions, particularly when conditioned on marker data. MCMC provides a direct estimate of the distribution of such measures. Let W be the IBD measure from data YM, and W* the IBD measure from pseudo-data Y*M simulated with the same data availability and genetic marker model as the true data YM, but in the absence of linkage. Then measures of the difference in distributions of W and W* provide evidence for linkage. This approach extracts more information from the data YM than either comparison to the pedigree prior distribution of W or use of statistics that are expectations of W given the data YM. A small example is presented.     

Identity-by-descent estimation and mapping of qualitative traits in large, complex pedigrees

Computing identity-by-descent sharing between individuals connected through a large, complex pedigree is a computationally demanding task that often cannot be done using exact methods. What I present here is a rapid computational method for estimating, in large complex pedigrees, the probability that pairs of alleles are IBD given the single-point genotype data at that marker for all individuals. The method can be used on pedigrees of essentially arbitrary size and complexity without the need to divide the individuals into separate subpedigrees. I apply the method to do qualitative trait linkage mapping using the nonparametric sharing statistic S(pairs). The validity of the method is demonstrated via simulation studies on a 13-generation 3028-person pedigree with 700 genotyped individuals. An analysis of an asthma data set of individuals in this pedigree finds four loci with P-values <10(-3) that were not detected in prior analyses. The mapping method is fast and can complete analyses of approximately 150 affected individuals within this pedigree for thousands of markers in a matter of hours.     

Inherent intractability of the ascertainment problem for pedigree data: a general likelihood framework.

The problem of ascertainment in segregation analysis arises when families are selected for study through ascertainment of affected individuals. In this case, ascertainment must be corrected for in data analysis. However, methods for ascertainment correction are not available for many common sampling schemes, e.g., sequential sampling of extended pedigrees (except in the case of "single" selection). Concerns about whether ascertainment correction is even required for large pedigrees, about whether and how multiple probands in the same pedigree can be taken into account properly, and about how to apply sequential sampling strategies have occupied many investigators in recent years. We address these concerns by reconsidering a central issue, namely, how to handle pedigree structure (including size). We introduce a new distinction, between sampling in such a way that observed pedigree structure does not depend on which pedigree members are probands (proband-independent [PI] sampling) and sampling in such a way that observed pedigree structure does depend on who are the probands (proband-dependent [PD] sampling). This distinction corresponds roughly (but not exactly) to the distinction between fixed-structure and sequential sampling. We show that conditioning on observed pedigree structure in ascertained data sets obtained under PD sampling is not in general correct (with the exception of "single" selection), while PI sampling of pedigree structures larger than simple sibships is generally not possible. Yet, in practice one has little choice but to condition on observed pedigree structure. We conclude that the problem of genetic modeling in ascertained data sets is, in most situations, literally intractable. We recommend that future efforts focus on the development of robust approximate approaches to the problem.     

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.     

Construction of the model for the Genetic Analysis Workshop 14 simulated data: genotype-phenotype relationships,gene interaction,linkage, association,disequilibrium, and ascertainment effects for a complex phenotype

The Genetic Analysis Workshop 14 simulated dataset was designed 1) To test the ability to find genes related to a complex disease (such as alcoholism). Such a disease may be given a variety of definitions by different investigators, have associated endophenotypes that are common in the general population, and is likely to be not one disease but a heterogeneous collection of clinically similar, but genetically distinct, entities. 2) To observe the effect on genetic analysis and gene discovery of a complex set of gene x gene interactions. 3) To allow comparison of microsatellite vs. large-scale single-nucleotide polymorphism (SNP) data. 4) To allow testing of association to identify the disease gene and the effect of moderate marker x marker linkage disequilibrium. 5) To observe the effect of different ascertainment/disease definition schemes on the analysis. Data was distributed in two forms. Data distributed to participants contained about 1,000 SNPs and 400 microsatellite markers. Internet-obtainable data consisted of a finer 10,000 SNP map, which also contained data on controls. While disease characteristics and parameters were constant, four "studies" used varying ascertainment schemes based on differing beliefs about disease characteristics. One of the studies contained multiplex two- and three-generation pedigrees with at least four affected members. The simulated disease was a psychiatric condition with many associated behaviors (endophenotypes), almost all of which were genetic in origin. The underlying disease model contained four major genes and two modifier genes. The four major genes interacted with each other to produce three different phenotypes, which were themselves heterogeneous. The population parameters were calibrated so that the major genes could be discovered by linkage analysis in most datasets. The association evidence was more difficult to calibrate but was designed to find statistically significant association in 50% of datasets. We also simulated some marker x marker linkage disequilibrium around some of the genes and also in areas without disease genes. We tried two different methods to simulate the linkage disequilibrium.     

Gametogenesis processes and multilocus gene identity by descent.

With few exceptions, the determination of unconditional probability of genes shared identical by descent (IBD) by relatives can be very difficult, especially if the relationship is complex or if multiple loci are involved. It is particularly difficult if one needs the IBD probability in a explicit form, expressed in terms of interlocus recombination fractions. In this paper, I will further extend the concept of gametogenesis process introduced elsewhere and indicate that it completely determines the gene IBD events of interest in pedigrees. I will demonstrate that the gametogenesis process not only serves as a convenient conceptual framework in considering IBD events in pedigrees but also provides a simple yet powerful tool to solve a wide range of seemingly difficult problems. In particular, I consider the problem of multilocus IBD probability for relative pairs, k siblings, and a group of pedigree members. In addition, I consider the problem of multilocus autozygosity probability and the problem of gene preservation in close relatives.     

Mapping by admixture linkage disequilibrium in human populations: limits and guidelines.

Certain human hereditary conditions, notably those with low penetrance and those which require an environmental event such as infectious disease exposure, are difficult to localize in pedigree analysis, because of uncertainty in the phenotype of an affected patient's relatives. An approach to locating these genes in human cohort studies would be to use association analysis, which depends on linkage disequilibrium of flanking polymorphic DNA markers. In theory, a high degree of linkage disequilibrium between genes separated by 10-20 cM will be generated and persist in populations that have a history of recent (3-20 generations ago) admixture between genetically differentiated racial groups, such as has occurred in African Americans and Hispanic populations. We have conducted analytic and computer simulations to quantify the effect of genetic, genomic, and population parameters that affect the amount and ascertainment of linkage disequilibrium in populations with a history of genetic admixture. Our goal is to thoroughly explore the ranges of all relevant parameters or factors (e.g., sample size and degree of genetic differentiation between populations) that may be involved in gene localization studies, in hopes of prescribing guidelines for an efficient mapping strategy. The results provide reasonable limits on sample size (200-300 patients), marker number (200-300 in 20-cM intervals), and allele differentiation (loci with allele frequency difference of > or = .3 between admixed parent populations) to produce an efficient approach (> 95% ascertainment) for locating genes not easily tracked in human pedigrees.     

Identification of genetic loci for basal cell nevus syndrome and inflammatory bowel disease in a single large pedigree

Basal Cell Nevus Syndrome (BCNS) is an autosomal dominant disease. PTCH1 gene mutations have been found responsible in many but not all pedigrees. Inflammatory Bowel Disease (IBD) is a complex genetic disorder, disproportionate in Ashkenazim, and characterized by chronic intestinal inflammation. We revisited a large Ashkenazim pedigree, first reported in 1968, with multiple diagnoses of BCNS and IBD, and with a common genetic cause for both disorders proposed. We expanded the pedigree to four generations and performed a genome-wide linkage study for BCNS and IBD traits. Twelve members with BCNS, seven with IBD, five with both diagnoses and eight unaffected were genotyped. Both non-parametric (GENEHUNTER 2.1) and parametric (FASTLINK) linkage analyses were performed and a validation through simulation was performed. BCNS linked to chromosome 9q22 (D9S1120) just proximal to the PTCH1 gene (NPL=3.26, P=0.003; parametric two-point LOD=2.4, parametric multipoint LOD=3.7). Novel IBD linkage evidence was observed at chromosome 1p13 (D1S420, NPL 3.92, P=0.0047; parametric two-point LOD=1.9). Linkage evidence was also observed to previously reported IBD loci on 4q, (D4S2623, NPL 3.02, P=0.012; parametric two-point LOD=2.15), 10q23 (D10S1225 near DLG5, NPL 3.33, P=0.0085; parametric two-point LOD=1.3), 12 overlapping the IBD2 locus (D12S313, NPL 2.6, P=0.018; parametric two-point LOD=1.52), and 7q (D7S510 and D7S3046, NPL 4.06, P=0.0035; parametric two-point LOD=2.18). In this pedigree affected by both BCNS and IBD, the two traits and their respective candidate genetic loci segregate independently; BCNS maps to the PTCH1 gene and IBD maps to several candidate regions, mostly overlapping previously observed IBD loci.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.Carolien I. Panhuysen and Amir Karban contributed equally to this work     

Efficient multipoint linkage analysis through reduction of inheritance space

Computational constraints currently limit exact multipoint linkage analysis to pedigrees of moderate size. We introduce new algorithms that allow analysis of larger pedigrees by reducing the time and memory requirements of the computation. We use the observed pedigree genotypes to reduce the number of inheritance patterns that need to be considered. The algorithms are implemented in a new version (version 2.1) of the software package GENEHUNTER. Performance gains depend on marker heterozygosity and on the number of pedigree members available for genotyping, but typically are 10-1,000-fold, compared with the performance of the previous release (version 2.0). As a result, families with up to 30 bits of inheritance information have been analyzed, and further increases in family size are feasible. In addition to computation of linkage statistics and haplotype determination, GENEHUNTER can also perform single-locus and multilocus transmission/disequilibrium tests. We describe and implement a set of permutation tests that allow determination of empirical significance levels in the presence of linkage disequilibrium among marker loci.     

Powerful allele sharing statistics for nonparametric linkage analysis

Nonparametric linkage analysis is widely used to map susceptibility genes for complex diseases. This paper introduces six nonparametric statistics for measuring marker allele sharing among the affected members of a pedigree. We compare the power of these new statistics and three previous statistics to detect linkage with Mendelian diseases having recessive, additive, and dominant modes of inheritance. The nine statistics represent all possible combinations of three different IBD scoring functions and three different schemes for sampling genes among affecteds. Our results strongly suggest that the statistic T(rec)(blocks) is best for recessive traits, while the two statistics T(kin)(pairs) and T(all)(kin) vie for best for an additive trait. The best statistic for a dominant trait is less clear. The statistics T(kin)(pairs) and T(all)(kin) are equally promising for small sibships, but in extended pedigrees the statistics T(dom)(blocks) and T(dom)(pairs) appear best. For a complex trait, we advocate computing several of these statistics.     

Linkage analysis of von Recklinghausen neurofibromatosis to DNA markers on chromosome 17

Several recent studies indicate that the von Recklinghausen neurofibromatosis (NF1) gene is located near the centromere of chromosome 17 in some families. However, variable expressivity and a very high mutation rate suggest that defects at several different loci could result in phenotypes categorized as NF1. In order to assess this possibility and to map the NF1 gene more precisely, we have used two polymorphic DNA markers from chromosome 17 to screen several pedigrees for linkage to NF1. We ascertained a large Caucasian pedigree (33 individuals sampled, 17 NF1 affected) as well as eight smaller pedigrees and nuclear families (50 individuals sampled, 30 NF1 affected). Here, we report strong evidence of linkage of NF1 to the centromeric marker D17Z1 (maximum lod = 4.42) and a weaker suggestion of linkage to the ERBA1 oncogene (maximum lod = 0.57), both at a recombination fraction of zero. Since obligate cross-overs with NF1 were not observed for either marker in any of the informative families tested, the possibility of NF1 locus heterogeneity is not supported.     

A novel class of tests for the detection of mitochondrial DNA-mutation involvement in diseases

We develop a novel class of tests to detect mitochondrial DNA (mtDNA)-mutation involvement in complex diseases by the study of affected pedigree members. For a pedigree, affected individuals are first considered and are then connected through their relatives. We construct a reduced pedigree from an original pedigree. Each configuration of a reduced pedigree is given a score, with high scores given to configurations that are consistent with mtDNA-mutation involvement and low scores given to configurations that are not consistent with mtDNA-mutation involvement. For many pedigrees, the weighted sum of scores of the pedigrees is calculated. The tests are formed by comparing the observed score with the expected score under the null hypothesis that only nuclear autosomal mutations are involved. We study the optimality of score functions and weights under the heterogeneity model without phenocopies. We also develop a method to estimate the contribution that mtDNA mutations make if they are involved under a heterogeneity model. Finally, we apply our methods to three data sets: Leber hereditary optic neuropathy, a disease that has been proved to be caused by mtDNA mutations; non-insulin-dependent diabetes mellitus (NIDDM); and hypertension (HTN). We find evidence of mtDNA-mutation involvement in all three diseases. The estimated fraction of patients with NIDDM due to mtDNA-mutation involvement is 22% (95% confidence interval [CI] 6%-38%). The fraction of patients with HTN potentially due to mtDNA-mutation involvement is estimated at 55% (95% CI 45%-65%).     

DNA "fingerprints" and segregation analysis of multiple markers in human pedigrees

Tandem-repetitive DNA hybridization probes based on a putative human recombination signal detect multiple polymorphic minisatellite fragments in human DNA. The genetic complexity of the resulting individual-specific DNA "fingerprints" was investigated by studying a large sibship affected by neurofibromatosis and a more extensive pedigree segregating for two different hemoglobinopathies. The segregation of up to 41 different heterozygous DNA fragments from each parent could be analyzed in a single sibship, using two different repeat probes. Most of these variable DNA fragments could not be paired as alleles, to an extent which suggests that the DNA fingerprints are together derived from approximately 60 heterozygous loci (approximately 120 variable fragments), only a proportion of which can be scored in a given individual. Two or three of the DNA fragments detected by one probe showed tight linkage and may be derived from long minisatellite(s) that are cleaved to produce more than one polymorphic DNA fragment. Excluding allelic and linked DNA fragments, almost all remaining scorable fragments segregated independently, allowing up to 34 unlinked loci to be examined simultaneously. These loci are scattered over most or all of the human autosomes. Minisatellite probes are therefore suitable for rapid marker generation and can be applied to linkage analysis in human pedigrees.     

Prediction of identity by descent probabilities from marker-haplotypes

The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.     

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.     

Conditional probability methods for haplotyping in pedigrees

Efficient haplotyping in pedigrees is important for the fine mapping of quantitative trait locus (QTL) or complex disease genes. To reconstruct haplotypes efficiently for a large pedigree with a large number of linked loci, two algorithms based on conditional probabilities and likelihood computations are presented. The first algorithm (the conditional probability method) produces a single, approximately optimal haplotype configuration, with computing time increasing linearly in the number of linked loci and the pedigree size. The other algorithm (the conditional enumeration method) identifies a set of haplotype configurations with high probabilities conditional on the observed genotype data for a pedigree. Its computing time increases less than exponentially with the size of a subset of the set of person-loci with unordered genotypes and linearly with its complement. The size of the subset is controlled by a threshold parameter. The set of identified haplotype configurations can be used to estimate the identity-by-descent (IBD) matrix at a map position for a pedigree. The algorithms have been tested on published and simulated data sets. The new haplotyping methods are much faster and provide more information than several existing stochastic and rule-based methods. The accuracies of the new methods are equivalent to or better than those of these existing methods.     

The comparison of RFLP,RAPD, AFLP and SSR (microsatellite) markers for germplasm analysis

The utility of RFLP (restriction fragment length polymorphism), RAPD (random-amplified polymorphic DNA), AFLP (amplified fragment length polymorphism) and SSR (simple sequence repeat, microsatellite) markers in soybean germplasm analysis was determined by evaluating information content (expected heterozygosity), number of loci simultaneously analyzed per experiment (multiplex ratio) and effectiveness in assessing relationships between accessions. SSR markers have the highest expected heterozygosity (0.60), while AFLP markers have the highest effective multiplex ratio (19). A single parameter, defined as the marker index, which is the product of expected heterozygosity and multiplex ratio, may be used to evaluate overall utility of a marker system. A comparison of genetic similarity matrices revealed that, if the comparison involved both cultivated (Glycine max) and wild soybean (Glycine soja) accessions, estimates based on RFLPs, AFLPs and SSRs are highly correlated, indicating congruence between these assays. However, correlations of RAPD marker data with those obtained using other marker systems were lower. This is because RAPDs produce higher estimates of interspecific similarities. If the comparisons involvedG. max only, then overall correlations between marker systems are significantly lower. WithinG. max, RAPD and AFLP similarity estimates are more closely correlated than those involving other marker systems.Abbreviations RFLP restriction fragment length plymorphism - RAPD random-amplified polymorphic DNA - AFLP amplified fragment length polymorphism - SSR simple sequence repeat - PCR polymerase chain reaction - TBE Tris-borate-EDTA buffer - MI marker index - SENA sum of effective numbers of alleles     

Eighteen microsatellite loci for endemic African weakly electric fish (Campylomormyrus,Mormyridae) and their cross species applicability among related taxa

We describe isolation and characterization of the first microsatellite loci specifically developed for African weakly electric fish (Mormyridae), for the genus Campylomormyrus. Seventeen of our 18 loci are polymorphic within the Campylomormyrus numenius species complex. The polymorphic loci showed four to 15 alleles per locus, an expected heterozygosity between 0.46 and 0.94, and an observed heterozygosity between 0.31 and 1.00. Most primers also yield reproducible results in several other mormyrid species. These loci comprise a set of molecular markers for various applications, from moderately polymorphic loci suitable for population studies to highly polymorphic loci for pedigree analysis in mormyrids.     

Genomewide Scan of Multiple Sclerosis in Finnish Multiplex Families

Multiple sclerosis (MS) is a neurological, demyelinating disorder with a putative autoimmune etiology. It is thought to be a multifactorial disease with a complex mode of inheritance. Here we report the results of a two-stage genomewide scan for loci predisposing to MS. The first stage of the screen, with a low-resolution map, was performed in a selection of 16 pedigrees collected from an isolated Finnish population. Multipoint, non-parametric linkage analysis of the 328 markers did not reveal statistically significant results. However, 10 slightly interesting regions (P = .1-.15) emerged, including our previous findings of the HLA complex on 6p21 and a putative locus on 5p14-p12. Eight of these novel regions were further analyzed by use of denser marker maps, in the second stage of the scan. For the chromosomal regions 4cen, 11tel, and 17q, the statistical significance increased, but not conclusively; for 2q32 and 10q21, the statistical significance did not change. Accordingly, genotyping of the high-density markers in these regions was performed, and the data were analyzed by use of two-point, parametric linkage analysis using the complete pedigree information of the 21 Finnish multiplex families. We detected suggestive evidence for a predisposing locus on chromosomal region 17q22-q24. Several markers on 17q22-q24 yielded positive LOD scores, with the maximum LOD score (Zmax) occurring with D17S807 (Zmax = 2.8, theta = .04; dominant model). Interestingly, a suggestive linkage between MS and the markers on 17q22-q24 was also revealed by a recent genomewide scan in MS families from the United Kingdom.     

The affected-pedigree-member method of linkage analysis.

This paper describes a generalization of the affected-sib-pair method of linkage analysis to pedigrees. By substituting identity-by-state relations for identity-by-descent relations, we develop a test statistic for detecting departures from independent segregation of disease and marker phenotypes. The statistic is based on the marker phenotypes of affected pedigree members only. Since it is more striking for distantly affected relatives to share a rare marker allele than a common marker allele, the statistic also includes a weighting factor based on allele frequency. The distributional properties of the statistic are investigated theoretically and by simulation. Part of the theoretical treatment entails generalizing Karigl's multiple-person kinship coefficients. When the test statistic is applied to pedigree data on Huntington disease, the null hypothesis of independent segregation between the marker locus and the disease locus is firmly rejected. In this case, as expected, there is a loss of power when compared with standard lod-score analysis. However, our statistic possesses the advantage of requiring no explicit assumptions about the mode of inheritance of the disease. This point is illustrated by application of the test statistic to data on rheumatoid arthritis.