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.     

Improved techniques for sampling complex pedigrees with the Gibbs sampler

Markov chain Monte Carlo (MCMC) methods have been widely used to overcome computational problems in linkage and segregation analyses. Many variants of this approach exist and are practiced; among the most popular is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its simplest form) mixing and reducibility problems; furthermore in order to initiate a Gibbs sampling chain we need a starting genotypic or allelic configuration which is consistent with the marker data in the pedigree and which has suitable weight in the joint distribution. We outline a procedure for finding such a configuration in pedigrees which have too many loci to allow for exact peeling. We also explain how this technique could be used to implement a blocking Gibbs sampler.     

Optimal designs for estimating and testing interaction among multiple loci in complex traits by a Gibbs sampler

A simulation study was conducted to provide a practical guideline for experimental designs with the Bayesian approach using Gibbs sampling (BAGS), a recently developed method for estimating interaction among multiple loci. Various data sets were simulated from combinations of number of loci, within-genotype variance, sample size, and balance of design. Mean square prediction error (MSPE) and empirical statistical power were obtained from estimating and testing the posterior mean estimate of combination genotypic effect. Simultaneous use of both MSPE and power was suggested to find an optimal design because their correlation estimate (− 0.8) would not be large enough to ignore either of them. The optimal sample sizes with MSPE > 2.0 and power > 0.8 with the within-genotype variance of 30 were 135, 675, and > 8100 for 2-, 3-, and 4-locus unbalanced data. The BAGS was suggested for interaction effects among limited number (4 or less) of loci in practice. A practical guideline for determining an optimal sample size with a given power or vise versa is provided for BAGS.     

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.     

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.     

An efficient variance component approach implementing an average information REML suitable for combined LD and linkage mapping with a general complex pedigree

Variance component (VC) approaches based on restricted maximum likelihood (REML) have been used as an attractive method for positioning of quantitative trait loci (QTL). Linkage disequilibrium (LD) information can be easily implemented in the covariance structure among QTL effects (e.g. genotype relationship matrix) and mapping resolution appears to be high. Because of the use of LD information, the covariance structure becomes much richer and denser compared to the use of linkage information alone. This makes an average information (AI) REML algorithm based on mixed model equations and sparse matrix techniques less useful. In addition, (near-) singularity problems often occur with high marker densities, which is common in fine-mapping, causing numerical problems in AIREML based on mixed model equations. The present study investigates the direct use of the variance covariance matrix of all observations in AIREML for LD mapping with a general complex pedigree. The method presented is more efficient than the usual approach based on mixed model equations and robust to numerical problems caused by near-singularity due to closely linked markers. It is also feasible to fit multiple QTL simultaneously in the proposed method whereas this would drastically increase computing time when using mixed model equation-based methods.     

Using dominance relationship coefficients based on linkage disequilibrium and linkage with a general complex pedigree to increase mapping resolution

Dominance (intralocus allelic interactions) plays often an important role in quantitative trait variation. However, few studies about dominance in QTL mapping have been reported in outbred animal or human populations. This is because common dominance effects can be predicted mainly for many full sibs, which do not often occur in outbred or natural populations with a general pedigree. Moreover, incomplete genotypes for such a pedigree make it infeasible to estimate dominance relationship coefficients between individuals. In this study, identity-by-descent (IBD) coefficients are estimated on the basis of population-wide linkage disequilibrium (LD), which makes it possible to track dominance relationships between unrelated founders. Therefore, it is possible to use dominance effects in QTL mapping without full sibs. Incomplete genotypes with a complex pedigree and many markers can be efficiently dealt with by a Markov chain Monte Carlo method for estimating IBD and dominance relationship matrices (D(RM)). It is shown by simulation that the use of D(RM) increases the likelihood ratio at the true QTL position and the mapping accuracy and power with complete dominance, overdominance, and recessive inheritance modes when using 200 genotyped and phenotyped individuals.     

Using an evolutionary algorithm and parallel computing for haplotyping in a general complex pedigree with multiple marker loci

Background  

Haplotype reconstruction is important in linkage mapping and association mapping of quantitative trait loci (QTL). One widely used statistical approach for haplotype reconstruction is simulated annealing (SA), implemented in SimWalk2. However, the algorithm needs a very large number of sequential iterations, and it does not clearly show if convergence of the likelihood is obtained.     

Sample reproducibility of genetic association using different multimarker TDTs in genome-wide association studies: characterization and a new approach

Multimarker Transmission/Disequilibrium Tests (TDTs) are very robust association tests to population admixture and structure which may be used to identify susceptibility loci in genome-wide association studies. Multimarker TDTs using several markers may increase power by capturing high-degree associations. However, there is also a risk of spurious associations and power reduction due to the increase in degrees of freedom. In this study we show that associations found by tests built on simple null hypotheses are highly reproducible in a second independent data set regardless the number of markers. As a test exhibiting this feature to its maximum, we introduce the multimarker 2-Groups TDT (mTDT(2G)), a test which under the hypothesis of no linkage, asymptotically follows a χ2 distribution with 1 degree of freedom regardless the number of markers. The statistic requires the division of parental haplotypes into two groups: disease susceptibility and disease protective haplotype groups. We assessed the test behavior by performing an extensive simulation study as well as a real-data study using several data sets of two complex diseases. We show that mTDT(2G) test is highly efficient and it achieves the highest power among all the tests used, even when the null hypothesis is tested in a second independent data set. Therefore, mTDT(2G) turns out to be a very promising multimarker TDT to perform genome-wide searches for disease susceptibility loci that may be used as a preprocessing step in the construction of more accurate genetic models to predict individual susceptibility to complex diseases.     

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.     

Three novel quantitative trait loci for skin thickness in swine identified by linkage and genome‐wide association studies

Skin is the largest organ in the pig body and plays a key role in protecting the body against pathogens and excessive water loss. Deciphering the genetic basis of swine skin thickness would enrich our knowledge about the skin. To identify the loci for porcine skin thickness, we first performed a genome scan with 194 microsatellite markers in a White Duroc × Erhualian F₂ intercross. We identified three genome‐wide significant QTL on pig chromosomes (SSC) 4, 7 and 15 using linkage analysis. The most significant QTL was found on SSC7 with a small confidence interval of ~5 cM, explaining 23.9 percent of phenotypic variance. Further, we conducted a genome‐wide association study (GWAS) using Illumina PorcineSNP60 Beadchips for the F₂ pedigree and a population of Chinese Sutai pigs. We confirmed significant QTL in the F₂ pedigree and replicated QTL on SSC15 in Chinese Sutai pigs. A meta‐analysis of GWASs on both populations detected a genomic region associated with skin thickness on SSC4. GWAS results were generally consistent with QTL mapping. Identical‐by‐descent analysis defined QTL on SSC7 in a 683‐kb region harboring an interesting candidate gene: HMGA1. On SSC15, the linkage disequilibrium analysis showed a haplotype block of 2.20 Mb that likely harbors the gene responsible for skin thickness. Our findings provide novel insights into the genetic basis of swine skin thickness, which would benefit further understanding of porcine skin function.     

Power for genetic association studies with random allele frequencies and genotype distributions

One of the first and most important steps in planning a genetic association study is the accurate estimation of the statistical power under a proposed study design and sample size. In association studies for candidate genes or in fine-mapping applications, allele and genotype frequencies are often assumed to be known when, in fact, they are unknown (i.e., random variables from some distribution). For example, if we consider a diallelic marker with allele frequencies of 0.5 and 0.5 and Hardy-Weinberg proportions, the three genotype frequencies are often assumed to be 0.25, 0.50, and 0.25, and the statistical power is calculated. Unfortunately, ignoring this source of variation can inflate the estimated power of the study. In the present article, we propose averaging the estimates of power over the distribution of the genotype frequencies to calculate the true estimate of power for a fixed allele frequency. For the usual situation, in which allele frequencies in a population are not known, we propose placing a prior distribution on the allele frequency, taking advantage of any available genotype information. This Bayesian approach provides a more accurate estimate of power. We present examples for quantitative and qualitative traits in cohort studies of unrelated individuals and results from an extensive series of examples that show that ignoring the uncertainty in allele frequencies can inflate the estimated power of the study. We also present the results from case-control studies and show that standard methods may also overestimate power. As discussed in this article, the approach of fixing allele frequencies even if they are not known is the common approach to power calculations. We show that ignoring the sources of variation in allele frequencies tends to result in overestimates of power and, consequently, in studies that are underpowered. Software in C is available at http://www.ambrosius.net/Power/.     

A hierarchical Bayesian network approach for linkage disequilibrium modeling and data-dimensionality reduction prior to genome-wide association studies

Background  

Discovering the genetic basis of common genetic diseases in the human genome represents a public health issue. However, the dimensionality of the genetic data (up to 1 million genetic markers) and its complexity make the statistical analysis a challenging task.     

Dispersal and habitat connectivity in complex heterogeneous landscapes: an analysis with a GIS-based random walk model

A grid-based random walk model has been developed to simulate animal dispersal, taking landscape heterogeneity and linear barriers such as roads and rivers into account The model can be used to estimate connectivity and has been parametenzed for the badger in the central Netherlands The importance of key parameters was evaluated by means of sensitivity analysis Results agree with field observations, and give interesting insight into the isolation of populations and potential populations The model can be applied to obtain knowledge about dispersal processes in complex landscapes     

A general and efficient approach for the construction of RNA oligonucleotides containing a 5'-phosphorothiolate linkage

Oligoribonucleotides containing a 5'-phosphorothiolate linkage have provided effective tools to study the mechanisms of RNA catalysis, allowing resolution of kinetic ambiguity associated with mechanistic dissection and providing a strategy to establish linkage between catalysis and specific functional groups. However, challenges associated with their synthesis have limited wider application of these modified nucleic acids. Here, we describe a general semisynthetic strategy to obtain these oligoribonucleotides reliably and relatively efficiently. The approach begins with the chemical synthesis of an RNA dinucleotide containing the 5'-phosphorothiolate linkage, with the adjacent 2'-hydroxyl group protected as the photolabile 2'-O-o-nitrobenzyl or 2'-O-α-methyl-o-nitrobenzyl derivative. Enzymatic ligation of the 2'-protected dinucleotide to transcribed or chemically synthesized 5' and 3' flanking RNAs yields the full-length oligoribonucleotide. The photolabile protecting group increases the chemical stability of these highly activated oligoribonucleotides during synthesis and long-term storage but is easily removed with UV irradiation under neutral conditions, allowing immediate use of the modified RNA in biochemical experiments.     

Vitiligo: complex segregation and linkage disequilibrium analyses with respect to microsatellite loci spanning the HLA

Familial clustering and linkage disequilibrium studies suggest that genetic factors predispose to vitiligo, although a clear transmission pattern and cosegregation of vitiligo with specific mutations have not been demonstrated. We collected pedigree data on vitiligo from a set of 56 multigeneration families belonging to the Paisa community from Antioquia, Colombia, with the goal of applying the unified model of complex segregation and linkage disequilibrium analyses to test the hypotheses of the existence of a major gene predisposing to vitiligo and that allelic or haplotype polymorphisms of microsatellite loci at 6p21.3-21.4 spanning HLA (D6S276, D6S265, D6S273, and D6S291) are associated with this predisposition. Minimum sibship sample size to discriminate dominant and recessive inheritance models was largely accomplished. Between the 15 models of complex segregation used, the one that best fitted the data was that of a major dominant gene and the existence of strong environmental effects acting on the recessive genotype. The penetrance and risk estimations discriminated two sets of vitiligo patients: those with early onset of vitiligo cosegregating with a dominant mode of inheritance without environmental effects, and those with late onset of vitiligo cosegregating with the recessive genotype and being influenced by environmental effects. After establishing the normal distribution of allelic frequencies and performing multiple comparisons correction, the linkage disequilibrium analysis suggested that a major genetic factor could be located at 6p21.3-21.4, because we detected significant case-control differences for allele 122 at D6S265 ( Pc=0.0264) and significant linkage disequilibrium between loci D6S276 and D6S273 in the cases but not in the controls. We cannot explain these results as a consequence of evolutionary forces or as genetic stratification acting differentially on cases and controls, because there was neither deviation from the Hardy-Weinberg expectations nor genetic subdivision between cases and controls, as theta; (non-biased F(ST)) was not significantly different from 0.     

Standard linkage and association methods identify the mechanism of four susceptibility genes for a simulated complex disease

The simulated dataset of the Genetic Analysis Workshop 14 provided affection status and the presence or absence of 12 traits. It was determined that all affected individuals must have traits E, F and H (EFH phenotype) and they must also have either trait B (B subtype) or traits C, D, and G (CDG subtype). A genome screen was performed, and linkage peaks were identified on chromosomes 1, 3, 5, and 9 using microsatellite markers. Dense panels of single-nucleotide polymorphism (SNP) markers were ordered for each of the four linkage peaks. In each case, association analyses identified a single SNP that accounted for the linkage evidence. The SNP on chromosome 1 appeared to primarily influence the B subtype, while the SNPs on chromosomes 5 and 9 primarily influenced the CDG subtype. The chromosome 3 SNP had the strongest effect and influenced both subtypes, as well as the requisite EFH phenotype. Recognizing the two subtypes prior to linkage analysis was key to identifying these loci using only a single replicate. This highlights the need in real life situations for careful examination of the phenotypic data prior to genetic analysis.     

Genome-wide linkage scan of a pedigree with familial hypercholesterolemia suggests susceptibility loci on chromosomes 3q25-26 and 21q22

Background

Familial hypercholesterolemia (FH) is a heritable disorder that can increase the risk of premature coronary heart disease. Studies suggest there are substantial genetic heterogeneities for different populations. Here we tried to identify novel susceptibility loci for FH in a Chinese pedigree.

Methodology/Principal Findings

We performed a SNP-based genome-wide linkage scan with the Chinese FH pedigree. Two suggestive linkage loci not previously reported were identified on chromosomes 3q25.1-26.1 (NPL = 9.01, nominal P<0.00001, and simulated occurrence per genome scan = 1.08) and 21q22.3 (NPL = 8.95, nominal P<0.00001, and simulated occurrence per genome scan = 1.26). In the interaction analysis with a trimmed version of the pedigree, we obtained a significantly increased joint LOD score (2.70) compared with that obtained when assuming the two loci uncorrelated, suggesting that more than one locus was involved in this pedigree. Exon screening of two candidate genes ABCG1 and LSS from one of the suggestive region 21q22 didn''t report any causative mutations.

Conclusions/Significances

These results confirm complex etiologies and suggest new genetic casual factors for the FH disorder. Further study of the two candidate regions is advocated.     

Power calculations for a general class of tests of linkage and association that use nuclear families with affected and unaffected sibs

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

Likelihood approach for detecting imprinting and in utero maternal effects using general pedigrees from prospective family-based association studies

Genetic imprinting and in utero maternal effects are causes of parent-of-origin effect but they are confounded with each other. Tests attempting to detect only one of these effects would have a severely inflated type I error rate if the assumption of the absence of the other effect is violated. Some existing methods avoid the potential confounding by modeling imprinting and in utero maternal effect simultaneously. However, these methods are not amendable to extended families, which are commonly recruited in family-based studies. In this article, we propose a likelihood approach for detecting imprinting and maternal effects (LIME) using general pedigrees from prospective family-based association studies. LIME formulates the probability of familial genotypes without the Hardy-Weinberg equilibrium assumption by introducing a novel concept called conditional mating type between marry-in founders and their nonfounder spouses. Further, a logit link is used to model the penetrance. To deal with the issue of incomplete pedigree genotypic data, LIME imputes the unobserved genotypes implicitly by considering all compatible ones conditional on the observed genotypes. We carried out a simulation study to evaluate the relative power and type I error of LIME and two existing methods. The results show that the use of extended pedigree data, even with incomplete information, can achieve much greater power than using nuclear families for detecting imprinting and in utero maternal effects without leading to inflated type I error rates.