Combining the meiosis Gibbs sampler with the random walk approach for linkage and association studies with a general complex pedigree and multimarker loci

A linkage analysis for finding inheritance states and haplotype configurations is an essential process for linkage and association mapping. The linkage analysis is routinely based upon observed pedigree information and marker genotypes for individuals in the pedigree. It is not feasible for exact methods to use all such information for a large complex pedigree especially when there are many missing genotypic data. Proposed Markov chain Monte Carlo approaches such as a single-site Gibbs sampler or the meiosis Gibbs sampler are able to handle a complex pedigree with sparse genotypic data; however, they often have reducibility problems, causing biased estimates. We present a combined method, applying the random walk approach to the reducible sites in the meiosis sampler. Therefore, one can efficiently obtain reliable estimates such as identity-by-descent coefficients between individuals based on inheritance states or haplotype configurations, and a wider range of data can be used for mapping of quantitative trait loci within a reasonable time.     

Simulation of pedigree genotypes by random walks.

A random walk method, based on the Metropolis algorithm, is developed for simulating the distribution of trait and linkage marker genotypes in pedigrees where trait phenotypes are already known. The method complements techniques suggested by Ploughman and Boehnke and by Ott that are based on sequential sampling of genotypes within a pedigree. These methods are useful for estimating the power of linkage analysis before complete study of a pedigree is undertaken. We apply the random walk technique to a partially penetrant disease, schizophrenia, and to a recessive disease, ataxia-telangiectasia. In the first case we show that accessory phenotypes with higher penetrance than that of schizophrenia itself may be crucial for effective linkage analysis, and in the second case we show that impressionistic selection of informative pedigrees may be misleading.     

Markov chain Monte Carlo segregation and linkage analysis for oligogenic models.

A new method for segregation and linkage analysis, with pedigree data, is described. Reversible jump Markov chain Monte Carlo methods are used to implement a sampling scheme in which the Markov chain can jump between parameter subspaces corresponding to models with different numbers of quantitative-trait loci (QTL's). Joint estimation of QTL number, position, and effects is possible, avoiding the problems that can arise from misspecification of the number of QTL's in a linkage analysis. The method is illustrated by use of a data set simulated for the 9th Genetic Analysis Workshop; this data set had several oligogenic traits, generated by use of a 1,497-member pedigree. The mixing characteristics of the method appear to be good, and the method correctly recovers the simulated model from the test data set. The approach appears to have great potential both for robust linkage analysis and for the answering of more general questions regarding the genetic control of complex traits.     

Genetic counseling in rare syndromes: a resampling method for determining an approximate confidence interval for gene location with linkage data from a single pedigree.

Multipoint linkage analysis is a powerful method for mapping a rare disease gene on the human gene map despite limited genotype and pedigree data. However, there is no standard procedure for determining a confidence interval for gene location by using multipoint linkage analysis. A genetic counselor needs to know the confidence interval for gene location in order to determine the uncertainty of risk estimates provided to a consultant on the basis of DNA studies. We describe a resampling, or "bootstrap," method for deriving an approximate confidence interval for gene location on the basis of data from a single pedigree. This method was used to define an approximate confidence interval for the location of a gene causing nonsyndromal X-linked mental retardation in a single pedigree. The approach seemed robust in that similar confidence intervals were derived by using different resampling protocols. Quantitative bounds for the confidence interval were dependent on the genetic map chosen. Once an approximate confidence interval for gene location was determined for this pedigree, it was possible to use multipoint risk analysis to estimate risk intervals for women of unknown carrier status. Despite the limited genotype data, the combination of the resampling method and multipoint risk analysis had a dramatic impact on the genetic advice available to consultants.     

A Genome Scan Conducted in a Multigenerational Pedigree with Convergent Strabismus Supports a Complex Genetic Determinism

A genome-wide linkage scan was conducted in a Northern-European multigenerational pedigree with nine of 40 related members affected with concomitant strabismus. Twenty-seven members of the pedigree including all affected individuals were genotyped using a SNP array interrogating > 300,000 common SNPs. We conducted parametric and non-parametric linkage analyses assuming segregation of an autosomal dominant mutation, yet allowing for incomplete penetrance and phenocopies. We detected two chromosome regions with near-suggestive evidence for linkage, respectively on chromosomes 8 and 18. The chromosome 8 linkage implied a penetrance of 0.80 and a rate of phenocopy of 0.11, while the chromosome 18 linkage implied a penetrance of 0.64 and a rate of phenocopy of 0. Our analysis excludes a simple genetic determinism of strabismus in this pedigree.     

A consensus linkage map for sugi (Cryptomeria japonica) from two pedigrees, based on microsatellites and expressed sequence tags

A consensus map for sugi (Cryptomeria japonica) was constructed by integrating linkage data from two unrelated third-generation pedigrees, one derived from a full-sib cross and the other by self-pollination of F1 individuals. The progeny segregation data of the first pedigree were derived from cleaved amplified polymorphic sequences, microsatellites, restriction fragment length polymorphisms, and single nucleotide polymorphisms. The data of the second pedigree were derived from cleaved amplified polymorphic sequences, isozyme markers, morphological traits, random amplified polymorphic DNA markers, and restriction fragment length polymorphisms. Linkage analyses were done for the first pedigree with JoinMap 3.0, using its parameter set for progeny derived by cross-pollination, and for the second pedigree with the parameter set for progeny derived from selfing of F1 individuals. The 11 chromosomes of C. japonica are represented in the consensus map. A total of 438 markers were assigned to 11 large linkage groups, 1 small linkage group, and 1 nonintegrated linkage group from the second pedigree; their total length was 1372.2 cM. On average, the consensus map showed 1 marker every 3.0 cM. PCR-based codominant DNA markers such as cleaved amplified polymorphic sequences and microsatellite markers were distributed in all linkage groups and occupied about half of mapped loci. These markers are very useful for integration of different linkage maps, QTL mapping, and comparative mapping for evolutional study, especially for species with a large genome size such as conifers.     

Linkage analysis and the inheritance of arches in a Habbanite isolate.

A pedigree and linkage analysis was performed on a corrected version of the Habbanite pedigree 2 of Slatis et al. [1]. The trait "arch on any digit" was examined for major gene inheritance and possible linkage to several blood and serum group markers. The results confirm the proposed dominant major gene inheritance of this trait with almost complete penetrance. In addition, the analysis suggests linkage with the haptoglobin locus with evidence against linkage with Pl and Rhesus. These results are of particular interest in view of recently reported dermatoglyphic associations with haptoglobin.     

Fast computation of genetic likelihoods on human pedigree data.

Gene mapping and genetic epidemiology require large-scale computation of likelihoods based on human pedigree data. Although computation of such likelihoods has become increasingly sophisticated, fast calculations are still impeded by complex pedigree structures, by models with many underlying loci and by missing observations on key family members. The current paper 'introduces' a new method of array factorization that substantially accelerates linkage calculations with large numbers of markers. This method is not limited to nuclear families or to families with complete phenotyping. Vectorization and parallelization are two general-purpose hardware techniques for accelerating computations. These techniques can assist in the rapid calculation of genetic likelihoods. We describe our experience using both of these methods with the existing program MENDEL. A vectorized version of MENDEL was run on an IBM 3090 supercomputer. A parallelized version of MENDEL was run on parallel machines of different architectures and on a network of workstations. Applying these revised versions of MENDEL to two challenging linkage problems yields substantial improvements in computational speed.     

Increasing the efficiency of variance component quantitative trait loci analysis by using reduced-rank identity-by-descent matrices

Recent technological development in genetics has made large-scale marker genotyping fast and practicable, facilitating studies for detection of QTL in large general pedigrees. We developed a method that speeds up restricted maximum-likelihood (REML) algorithms for QTL analysis by simplifying the inversion of the variance-covariance matrix of the trait vector. The method was tested in an experimental chicken pedigree including 767 phenotyped individuals and 14 genotyped markers on chicken chromosome 1. The computation time in a chromosome scan covering 475 cM was reduced by 43% when the analysis was based on linkage only and by 72% when linkage disequilibrium information was included. The relative advantage of using our method increases with pedigree size, marker density, and linkage disequilibrium, indicating even greater improvements in the future.     

Comparison of longitudinal variance components and regression-based approaches for linkage detection on chromosome 17 for systolic blood pressure

We compare two methods to detect genetic linkage by using serial observations of systolic blood pressure in pedigree data from the Framingham Heart Study focusing on chromosome 17. The first method is a variance components (VC) approach that incorporates longitudinal pedigree data, and the second method is a regression-based approach that summarizes all longitudinal measures in one single measure. No evidence of linkage was found either using the VC longitudinal approach or the regression-based approach, except when all time points were used from Cohorts 1 and 2 and only subjects aged 25 and 75 years were included.     

A new test for linkage in the presence of locus heterogeneity.

The detection of linkage in complex traits, although potentially of the greatest value, has proved very difficult. One reason may be the drastic effect that locus heterogeneity has on statistical power. We propose a new test for linkage in the presence of heterogeneity, based upon the sum of individual pedigree maximum lod scores, combined with a bootstrap method for estimating the null-hypothesis distribution. The technique is designed to exploit modern computer capability and to avoid reliance on asymptotic-distribution theory. Numerical comparisons indicate that for small pedigrees this new test can detect linkage with 30%-50% less data than are required by standard methods. A computer program for simulating the distribution and for performing the test of linkage is available from the authors.     

The role of pedigree information in combined linkage disequilibrium and linkage mapping of quantitative trait loci in a general complex pedigree

Combined linkage disequilibrium and linkage (LDL) mapping can exploit historical as well as recent and observed recombinations in a recorded pedigree. We investigated the role of pedigree information in LDL mapping and the performance of LDL mapping in general complex pedigrees. We compared using complete and incomplete genotypic data, spanning 5 or 10 generations of known pedigree, and we used bi- or multiallelic markers that were positioned at 1- or 5-cM intervals. Analyses carried out with or without pedigree information were compared. Results were compared with linkage mapping in some of the data sets. Linkage mapping or LDL mapping with sparse marker spacing ( approximately 5 cM) gave a poorer mapping resolution without considering pedigree information compared to that with considering pedigree information. The difference was bigger in a pedigree of more generations. However, LDL mapping with closely linked markers ( approximately 1 cM) gave a much higher mapping resolution regardless of using pedigree information. This study shows that when marker spacing is dense and there is considerable linkage disequilibrium generated from historical recombinations between flanking markers and QTL, the loss of power due to ignoring pedigree information is negligible and mapping resolution is very high.     

An autosomal genetic linkage map of the domestic cat,Felis silvestris catus

We report on the completion of an autosomal genetic linkage (GL) map of the domestic cat (Felis silvestris catus). Unlike two previous linkage maps of the cat constructed with a hybrid pedigree between the domestic cat and the Asian leopard cat, this map was generated entirely with domestic cats, using a large multi-generational pedigree (n = 256) maintained by the Nestlé Purina PetCare Company. Four hundred eighty-three simple tandem repeat (STR) loci have been assigned to linkage groups on the cat's 18 autosomes. A single linkage group spans each autosome. The length of the cat map, estimated at 4370 cM, is long relative to most reported mammalian maps. A high degree of concordance in marker order was observed between the third-generation map and the 1.5 Mb-resolution radiation hybrid (RH) map of the cat. Using the cat 1.9 × whole-genome sequence, we identified map coordinates for 85% of the loci in the cat assembly, with high concordance observed in marker order between the linkage map and the cat sequence assembly. The present version represents a marked improvement over previous cat linkage maps as it (i) nearly doubles the number of markers that were present in the second-generation linkage map in the cat, (ii) provides a linkage map generated in a domestic cat pedigree which will more accurately reflect recombination distances than previous maps generated in a hybrid pedigree, and (iii) provides single linkage groups spanning each autosome. Marker order was largely consistent between this and the previous maps, though the use of a hybrid pedigree in the earlier versions appears to have contributed to some suppression of recombination. The improved linkage map will provide an added resource for the mapping of phenotypic variation in the domestic cat and the use of this species as a model system for biological research.     

Breaking loops in large complex pedigrees

For pedigrees with multiple loops, exact likelihoods could not be computed in an acceptable time frame and thus, approximate methods are used. Some of these methods are based on breaking loops and approximations of complex pedigree likelihoods using the exact likelihood of the corresponding zero-loop pedigree. Due to ignoring loops, this method results in a loss of genetic information and a decrease in the power to detect linkage. To minimize this loss, an optimal set of loop breakers has to be selected. In this paper, we present a graph theory based algorithm for automatic selection of an optimal set of loop breakers. We propose using a total relationship between measured pedigree members as a proxy to power. To minimize the loss of genetic information, we suggest selection of such breakers whose duplication in a pedigree would be accompanied by a minimal loss of total relationship between measured pedigree members. We show that our algorithm compares favorably with other existing loop-breaker selection algorithms in terms of conservation of genetic information, statistical power and CPU time of subsequent linkage analysis. We implemented our method in a software package LOOP_EDGE, which is available at http://mga.bionet.nsc.ru/nlru/.     

SimPed: a simulation program to generate haplotype and genotype data for pedigree structures

With the widespread availability of SNP genotype data, there is great interest in analyzing pedigree haplotype data. Intermarker linkage disequilibrium for microsatellite markers is usually low due to their physical distance; however, for dense maps of SNP markers, there can be strong linkage disequilibrium between marker loci. Linkage analysis (parametric and nonparametric) and family-based association studies are currently being carried out using dense maps of SNP marker loci. Monte Carlo methods are often used for both linkage and association studies; however, to date there are no programs available which can generate haplotype and/or genotype data consisting of a large number of loci for pedigree structures. SimPed is a program that quickly generates haplotype and/or genotype data for pedigrees of virtually any size and complexity. Marker data either in linkage disequilibrium or equilibrium can be generated for greater than 20,000 diallelic or multiallelic marker loci. Haplotypes and/or genotypes are generated for pedigree structures using specified genetic map distances and haplotype and/or allele frequencies. The simulated data generated by SimPed is useful for a variety of purposes, including evaluating methods that estimate haplotype frequencies for pedigree data, evaluating type I error due to intermarker linkage disequilibrium and estimating empirical p values for linkage and family-based association studies.     

A Monte Carlo method for combined segregation and linkage analysis.

We introduce a Monte Carlo approach to combined segregation and linkage analysis of a quantitative trait observed in an extended pedigree. In conjunction with the Monte Carlo method of likelihood-ratio evaluation proposed by Thompson and Guo, the method provides for estimation and hypothesis testing. The greatest attraction of this approach is its ability to handle complex genetic models and large pedigrees. Two examples illustrate the practicality of the method. One is of simulated data on a large pedigree; the other is a reanalysis of published data previously analyzed by other methods.     

Association between a genetic trait and a marker: Discrimination between epistasis and gametic disequilibrium

Summary We reconsider the method of Ott and Falk (1982) for the analysis of genetic linkage and of epistasis in the presence of phenotypic association. Their approach is extended to allow for gametic disequilibrium between marker and trait loci. We show that epistasis and tight linkage with gametic disequilibrium may be indistinguishable as explanations of association even in a very large pedigree.     

Parametric and nonparametric linkage analysis: a unified multipoint approach.

In complex disease studies, it is crucial to perform multipoint linkage analysis with many markers and to use robust nonparametric methods that take account of all pedigree information. Currently available methods fall short in both regards. In this paper, we describe how to extract complete multipoint inheritance information from general pedigrees of moderate size. This information is captured in the multipoint inheritance distribution, which provides a framework for a unified approach to both parametric and nonparametric methods of linkage analysis. Specifically, the approach includes the following: (1) Rapid exact computation of multipoint LOD scores involving dozens of highly polymorphic markers, even in the presence of loops and missing data. (2) Non-parametric linkage (NPL) analysis, a powerful new approach to pedigree analysis. We show that NPL is robust to uncertainty about mode of inheritance, is much more powerful than commonly used nonparametric methods, and loses little power relative to parametric linkage analysis. NPL thus appears to be the method of choice for pedigree studies of complex traits. (3) Information-content mapping, which measures the fraction of the total inheritance information extracted by the available marker data and points out the regions in which typing additional markers is most useful. (4) Maximum-likelihood reconstruction of many-marker haplotypes, even in pedigrees with missing data. We have implemented NPL analysis, LOD-score computation, information-content mapping, and haplotype reconstruction in a new computer package, GENEHUNTER. The package allows efficient multipoint analysis of pedigree data to be performed rapidly in a single user-friendly environment.     

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.     

Genetic linkage analysis of bipolar affective disorder in an Old Order Amish pedigree

Summary We have used genetic linkage analysis in an effort to identify a gene responsible for bipolar affective disorder (BAD) in an Old Order Amish pedigree. The initial study of this pedigree showed strong evidence for linkage of the chromosome 11p15 markers HRAS1 and the insulin gene (INS) to BAD, whereas a second report found no evidence for linkage. We have independently determined the INS and HRAS1 genotypes from 81 individuals in this pedigree. A polymerase chain reaction (PCR) assay was used to score INS alleles that are difficult to distinguish from one another by conventional agarose gel electrophoresis. In addition, we used four separate diagnostic models to score individuals with psychiatric illness as either affected or unaffected. No evidence of significant linkage between BAD and the markers was found with either two-point or multipoint analysis regardless of which diagnostic model was used. However, exclusion of the region of chromosome 11 between INS and RAS1 as a possible location for the BAD gene in this family depended on the diagnostic model. Further genetic linkage studies with additional DNA markers that span the genome are necessary to determine the chromosomal location of the BAD gene in this family.