Single-nucleotide polymorphism versus microsatellite markers in a combined linkage and segregation analysis of a quantitative trait

Increasingly, single-nucleotide polymorphism (SNP) markers are being used in preference to microsatellite markers. However, methods developed for microsatellites may be problematic when applied to SNP markers. We evaluated the results of using SNPs vs. microsatellites in Monte Carlo Markov chain (MCMC) oligogenic combined segregation and linkage analysis methods. These methods were developed with microsatellite markers in mind. We selected chromosome 7 from the Collaborative Study on the Genetics of Alcoholism dataset for analysis because linkage to an electrophysiological trait had been reported there. We found linkage in the same region of chromosome 7 with the Affymetrix SNP data, the Illumina SNP data, and the microsatellite marker data. The MCMC sampler appears to mix with both types of data. The sampler implemented in this MCMC oligogenic combined segregation and linkage analysis appears to handle SNP data as well as microsatellite data and it is possible that the localizations with the SNP data are better.     

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.     

The role of parametric linkage methods in complex trait analyses using microsatellites

Many investigators of complexly inherited familial traits bypass classical segregation analysis to perform model-free genome-wide linkage scans. Because model-based or parametric linkage analysis may be the most powerful means to localize genes when a model can be approximated, model-free statistics may result in a loss of power to detect linkage. We performed limited segregation analyses on the electrophysiological measurements that have been collected for the Collaborative Study on the Genetics of Alcoholism. The resulting models are used in whole-genome scans. Four genomic regions provided a model-based LOD > 2 and only 3 of these were detected (p < 0.05) by a model-free approach. We conclude that parametric methods, using even over-simplified models of complex phenotypes, may complement nonparametric methods and decrease false positives.     

Two-trait-locus linkage analysis: a powerful strategy for mapping complex genetic traits.

Recent advances in molecular biology have provided geneticists with ever-increasing numbers of highly polymorphic genetic markers that have made possible linkage mapping of loci responsible for many human diseases. However, nearly all diseases mapped to date follow clear Mendelian, single-locus segregation patterns. In contrast, many common familial diseases such as diabetes, psoriasis, several forms of cancer, and schizophrenia are familial and appear to have a genetic component but do not exhibit simple Mendelian transmission. More complex models are required to explain the genetics of these important diseases. In this paper, we explore two-trait-locus, two-marker-locus linkage analysis in which two trait loci are mapped simultaneously to separate genetic markers. We compare the utility of this approach to standard one-trait-locus, one-marker-locus linkage analysis with and without allowance for heterogeneity. We also compare the utility of the two-trait-locus, two-marker-locus analysis to two-trait-locus, one-marker-locus linkage analysis. For common diseases, pedigrees are often bilineal, with disease genes entering via two or more unrelated pedigree members. Since such pedigrees often are avoided in linkage studies, we also investigate the relative information content of unilineal and bilineal pedigrees. For the dominant-or-recessive and threshold models that we consider, we find that two-trait-locus, two-marker-locus linkage analysis can provide substantially more linkage information, as measured by expected maximum lod score, than standard one-trait-locus, one-marker-locus methods, even allowing for heterogeneity, while, for a dominant-or-dominant generating model, one-locus models that allow for heterogeneity extract essentially as much information as the two-trait-locus methods. For these three models, we also find that bilineal pedigrees provide sufficient linkage information to warrant their inclusion in such studies. We also discuss strategies for assessing the significance of the two linkages assumed in two-trait-locus, two-marker-locus models.     

Quantifying genomic imprinting in the presence of linkage

Genomic imprinting decreases the power of classical linkage analysis, in which paternal and maternal transmissions of marker alleles are equally weighted. Several methods have been proposed for taking genomic imprinting into account in the model-free linkage analysis of binary traits. However, none of these methods are suitable for the formal identification and quantification of genomic imprinting in the presence of linkage. In addition, the available methods are designed for use with pure sib-pairs, requiring artificial decomposition in cases of larger sibships, leading to a loss of power. We propose here the maximum likelihood binomial method adaptive for imprinting (MLB-I), which is a unified analytic framework giving rise to specific tests in sibships of any size for (i) linkage adaptive to imprinting, (ii) genomic imprinting in the presence of linkage, and (iii) partial versus complete genomic imprinting. In addition, we propose an original measure for quantifying genomic imprinting. We have derived and validated the distribution of the three tests under their respective null hypotheses for various genetic models, and have assessed the power of these tests in simulations. This method can readily be applied to genome-wide scanning, as illustrated here for leprosy sibships. Our approach provides a novel tool for dissecting genomic imprinting in model-free linkage analysis, and will be of considerable value for identifying and evaluating the contribution of imprinted genes to complex diseases.     

Genome-wide linkage analysis of systolic blood pressure: a comparison of two approaches to phenotype definition

Problem 1 of the Genetic Analysis Workshop 13(GAW13) contains longitudinal data of cardiovascular measurements from 330 pedigrees. The longitudinal data complicates the phenotype definition because multiple measurements are taken on each individual. To address this complication, we propose an approach that uses generalized estimating equations to obtain residuals for each time point for each person. The mean residual is then taken as the new phenotype with which to use in a variance components linkage analysis. We compare our phenotype definition approach to an approach that first reduces the multiple measurements to a single measurement and then models these summary statistics as regression terms in a variance components analysis. For each approach, multipoint linkage analysis was performed using the residuals and the SOLAR computer program. Our results show little difference between the methods based on the LOD scores.     

Simultaneous fine mapping of multiple closely linked quantitative trait Loci using combined linkage disequilibrium and linkage with a general pedigree

Within a small region (e.g., <10 cM), there can be multiple quantitative trait loci (QTL) underlying phenotypes of a trait. Simultaneous fine mapping of closely linked QTL needs an efficient tool to remove confounded shade effects among QTL within such a small region. We propose a variance component method using combined linkage disequilibrium (LD) and linkage information and a reversible jump Markov chain Monte Carlo (MCMC) sampling for model selection. QTL identity-by-descent (IBD) coefficients between individuals are estimated by a hybrid MCMC combining the random walk and the meiosis Gibbs sampler. These coefficients are used in a mixed linear model and an empirical Bayesian procedure combines residual maximum likelihood (REML) to estimate QTL effects and a reversible jump MCMC that samples the number of QTL and the posterior QTL intensities across the tested region. Note that two MCMC processes are used, i.e., an (internal) MCMC for IBD estimation and an (external) MCMC for model selection. In a simulation study, the use of the multiple-QTL model clearly removes the shade effects between three closely linked QTL located at 1.125, 3.875, and 7.875 cM across the region of 10 cM, using 40 markers at 0.25-cM intervals. It is shown that the use of combined LD and linkage information gives much more useful information compared to using linkage information alone for both single- and multiple-QTL analyses. When using a lower marker density (11 markers at 1-cM intervals), the signal of the second QTL can disappear. Extreme values of past effective size (resulting in extreme levels of LD) decrease the mapping accuracy.     

The potential of probabilistic graphical models in linkage map construction

Key message

Probabilistic graphical models show great potential for robust and reliable construction of linkage maps. We show how to use probabilistic graphical models to construct high-quality linkage maps in the face of data perturbations caused by genotyping errors and reciprocal translocations.

Abstract

It has been shown that linkage map construction can be hampered by the presence of genotyping errors and chromosomal rearrangements such as inversions and translocations. Here, we report a novel method for linkage map construction using probabilistic graphical models. The method is proven, both theoretically and practically, to be effective in filtering out markers that contain genotyping errors. In particular, it carries out marker filtering and ordering simultaneously, and is therefore superior to the standard post hoc filtering using nearest-neighbour stress. Furthermore, we demonstrate empirically that the proposed method offers a promising solution to linkage map construction in the case of a reciprocal translocation.

     

Comparison of marker types and map assumptions using Markov chain Monte Carlo-based linkage analysis of COGA data

We performed multipoint linkage analysis of the electrophysiological trait ECB21 on chromosome 4 in the full pedigrees provided by the Collaborative Study on the Genetics of Alcoholism (COGA). Three Markov chain Monte Carlo (MCMC)-based approaches were applied to the provided and re-estimated genetic maps and to five different marker panels consisting of microsatellite (STRP) and/or SNP markers at various densities. We found evidence of linkage near the GABRB1 STRP using all methods, maps, and marker panels. Difficulties encountered with SNP panels included convergence problems and demanding computations.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

Quantitative trait loci (QTL) affecting the phenotype of interest can be detected using linkage analysis (LA), linkage disequilibrium (LD) mapping or a combination of both (LDLA). The LA approach uses information from recombination events within the observed pedigree and LD mapping from the historical recombinations within the unobserved pedigree. We propose the Bayesian variable selection approach for combined LDLA analysis for single-nucleotide polymorphism (SNP) data. The novel approach uses both sources of information simultaneously as is commonly done in plant and animal genetics, but it makes fewer assumptions about population demography than previous LDLA methods. This differs from approaches in human genetics, where LDLA methods use LA information conditional on LD information or the other way round. We argue that the multilocus LDLA model is more powerful for the detection of phenotype–genotype associations than single-locus LDLA analysis. To illustrate the performance of the Bayesian multilocus LDLA method, we analyzed simulation replicates based on real SNP genotype data from small three-generational CEPH families and compared the results with commonly used quantitative transmission disequilibrium test (QTDT). This paper is intended to be conceptual in the sense that it is not meant to be a practical method for analyzing high-density SNP data, which is more common. Our aim was to test whether this approach can function in principle.     

Pelican: pedigree editor for linkage computer analysis

SUMMARY: Linkage analysis software requires an input text file that describes the structure of the pedigrees to be analysed. Manual creation of these files is tedious and error-prone, and a graphical input tool is desirable. This is currently only available in commercial packages that include much greater functionality. We have therefore developed Pelican, a lightweight graphical pedigree editor for rapid construction of linkage pedigree files and diagrams. AVAILABILITY: The software runs on any Java-enabled machine (version 1.2 or higher). A Java Web Start launch, class files, a demonstration applet, source code and documentation are freely available at http://www.rfcgr.mrc.ac.uk/Software/PELICAN/     

Evidence of linkage of HDL level variation to<Emphasis Type="Italic"> APOC3</Emphasis> in two samples with different ascertainment

The APOA1-C3-A4-A5 gene complex encodes genes whose products are implicated in the metabolism of HDL and/or triglycerides. Although the relationship between polymorphisms in this gene cluster and dyslipidemias was first reported more than 15 years ago, association and linkage results have remained inconclusive. This is due, in part, to the oligogenic and multivariate nature of dyslipidemic phenotypes. Therefore, we investigate evidence of linkage of APOC3 and HDL using two samples of dyslipidemic pedigrees: familial combined hyperlipidemia (FCHL) and isolated low-HDL (ILHDL). We used a strategy that deals with several difficulties inherent in the study of complex traits: by using a Bayesian Markov Chain Monte Carlo (MCMC) approach we allow for oligogenic trait models, as well as simultaneous incorporation of covariates, in the context of multipoint analysis. By using this approach on extended pedigrees we provide evidence of linkage of APOC3 and HDL level variation in two samples with different ascertainment. In addition to APOC3, we estimate that two to three genes, each with a substantial effect on total variance, are responsible for HDL variation in both data sets. We also provide evidence, using the FCHL data set, for a pleiotropic effect between HDL, HDL3 and triglycerides at the APOC3 locus.     

GOLD--graphical overview of linkage disequilibrium

SUMMARY: We describe a software package that provides a graphical summary of linkage disequilibrium in human genetic data. It allows for the analysis of family data and is well suited to the analysis of dense genetic maps. AVAILABILITY: http://www.well.ox.ac.uk/asthma/GOLD CONTACT: goncalo@well.ox.ac.uk     

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. I. Methodology

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameter estimators were marginal posterior means computed using a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage, and the parameters (allele frequency, QTL substitution effect, recombination rate, polygenic and residual variances). Several MCMC algorithms were derived for computing Bayesian tests of linkage, which consisted of the marginal posterior probability of linkage and the marginal likelihood of the QTL variance associated with the marker.     

A novel Markov chain monte carlo approach for constructing accurate meiotic maps

Mapping markers from linkage data continues to be a task performed in many genetic epidemiological studies. Data collected in a study may be used to refine published map estimates and a study may use markers that do not appear in any published map. Furthermore, inaccuracies in meiotic maps can seriously bias linkage findings. To make best use of the available marker information, multilocus linkage analyses are performed. However, two computational issues greatly limit the number of markers currently mapped jointly; the number of candidate marker orders increases exponentially with marker number and computing exact multilocus likelihoods on general pedigrees is computationally demanding. In this article, a new Markov chain Monte Carlo (MCMC) approach that solves both these computational problems is presented. The MCMC approach allows many markers to be mapped jointly, using data observed on general pedigrees with unobserved individuals. The performance of the new mapping procedure is demonstrated through the analysis of simulated and real data. The MCMC procedure performs extremely well, even when there are millions of candidate orders, and gives results superior to those of CRI-MAP.     

Approaches to mapping genetically correlated complex traits

Our Markov chain Monte Carlo (MCMC) methods were used in linkage analyses of the Framingham Heart Study data using all available pedigrees. Our goal was to detect and map loci associated with covariate-adjusted traits log triglyceride (lnTG) and high-density lipoprotein cholesterol (HDL) using multipoint LOD score analysis, Bayesian oligogenic linkage analysis and identity-by-descent (IBD) scoring methods. Each method used all marker data for all markers on a chromosome. Bayesian linkage analysis detected a linkage signal on chromosome 7 for lnTG and HDL, corroborating previously published results. However, these results were not replicated in a classical linkage analysis of the data or by using IBD scoring methods.We conclude that Bayesian linkage analysis provides a powerful paradigm for mapping trait loci but interpretation of the Bayesian linkage signals is subjective. In the absence of a LOD score method accommodating genetically complex traits and linkage heterogeneity, validation of these signals remains elusive.     

Simultaneous fine mapping of closely linked epistatic quantitative trait loci using combined linkage disequilibrium and linkage with a general pedigree

Causal mutations and their intra- and inter-locus interactions play a critical role in complex trait variation. It is often not easy to detect epistatic quantitative trait loci (QTL) due to complicated population structure requirements for detecting epistatic effects in linkage analysis studies and due to main effects often being hidden by interaction effects. Mapping their positions is even harder when they are closely linked. The data structure requirement may be overcome when information on linkage disequilibrium is used. We present an approach using a mixed linear model nested in an empirical Bayesian approach, which simultaneously takes into account additive, dominance and epistatic effects due to multiple QTL. The covariance structure used in the mixed linear model is based on combined linkage disequilibrium and linkage information. In a simulation study where there are complex epistatic interactions between QTL, it is possible to simultaneously map interacting QTL into a small region using the proposed approach. The estimated variance components are accurate and less biased with the proposed approach compared with traditional models.     

QTL analysis in arbitrary pedigrees with incomplete marker information

Mapping quantitative trait loci (QTL) in arbitrary outbred pedigrees is complicated by the combinatorial possibilities of allele flow relationships and of the founder allelic configurations. Exact methods are only available for rather short and simple pedigrees. Stochastic simulation using Markov chain Monte Carlo (MCMC) integration offers more flexibility. MCMC methods are less natural in a frequentist than in a Bayesian context, which we therefore adopt. Among the MCMC algorithms for updating marker locus genotypes, we implement the descent-graph algorithm. It can be used to update marker locus allele flow relationships and can handle arbitrarily complex pedigrees and missing marker information. Compared with updating marker genotypic information, updating QTL parameters, such as position, effects, and the allele flow relationships is relatively easy with MCMC. We treat the effect of each diploid combination of founder alleles as a random variable and only estimate the variance of these effects, ie, we model diploid genotypic effects instead of the usual partition in additive and dominance effects. This is a variant of the random model approach. The number of QTL alleles is generally unknown. In the Bayesian context, the number of QTL present on a linkage group can be treated as variable. Computer simulations suggest that the algorithm can indeed handle complex pedigrees and detect two QTL on a linkage group, but that the number of individuals in a single extended family is limited to about 50 to 100 individuals.