A blocking Gibbs sampling method to detect major genes with phenotypic data from a diallel mating

Diallel mating is a frequently used design for estimating the additive and dominance genetic (polygenic) effects involved in quantitative traits observed in the half- and full-sib progenies generated in plant breeding programmes. Gibbs sampling has been used for making statistical inferences for a mixed-inheritance model (MIM) that includes both major genes and polygenes. However, using this approach it has not been possible to incorporate the genetic properties of major genes with the additive and dominance polygenic effects in a diallel mating population. A parent block Gibbs sampling method was developed in this study to make statistical inferences about the major gene and polygenic effects on quantitative traits for progenies derived from a half-diallel mating design. Using simulated data sets with different major and polygenic effects, the proposed method accurately estimated the major and polygenic effects of quantitative traits, and possible genotypes of parents and progenies. The impact of specifying different prior distributions was examined and was found to have little effect on inference on the posterior distribution. This approach was applied to an experimental data set of Loblolly pine (Pinus taeda L.) derived from a 6-parent half-diallel mating. The result indicated that there might be a recessive major gene affecting height growth in this diallel population.     

Analysis of rabbit doe longevity using a semiparametric log-Normal animal frailty model with time-dependent covariates

Data on doe longevity in a rabbit population were analysed using a semiparametric log-Normal animal frailty model. Longevity was defined as the time from the first positive pregnancy test to death or culling due to pathological problems. Does culled for other reasons had right censored records of longevity. The model included time dependent covariates associated with year by season, the interaction between physiological state and the number of young born alive, and between order of positive pregnancy test and physiological state. The model also included an additive genetic effect and a residual in log frailty. Properties of marginal posterior distributions of specific parameters were inferred from a full Bayesian analysis using Gibbs sampling. All of the fully conditional posterior distributions defining a Gibbs sampler were easy to sample from, either directly or using adaptive rejection sampling. The marginal posterior mean estimates of the additive genetic variance and of the residual variance in log frailty were 0.247 and 0.690.     

Estimation of additive, dominance and epistatic variance components using finite locus models implemented with a single-site Gibbs and a descent graph sampler

In a previous contribution, we implemented a finite locus model (FLM) for estimating additive and dominance genetic variances via a Bayesian method and a single-site Gibbs sampler. We observed a dependency of dominance variance estimates on locus number in the analysis FLM. Here, we extended the FLM to include two-locus epistasis, and implemented the analysis with two genotype samplers (Gibbs and descent graph) and three different priors for genetic effects (uniform and variable across loci, uniform and constant across loci, and normal). Phenotypic data were simulated for two pedigrees with 6300 and 12,300 individuals in closed populations, using several different, non-additive genetic models. Replications of these data were analysed with FLMs differing in the number of loci. Simulation results indicate that the dependency of non-additive genetic variance estimates on locus number persisted in all implementation strategies we investigated. However, this dependency was considerably diminished with normal priors for genetic effects as compared with uniform priors (constant or variable across loci). Descent graph sampling of genotypes modestly improved variance components estimation compared with Gibbs sampling. Moreover, a larger pedigree produced considerably better variance components estimation, suggesting this dependency might originate from data insufficiency. As the FLM represents an appealing alternative to the infinitesimal model for genetic parameter estimation and for inclusion of polygenic background variation in QTL mapping analyses, further improvements are warranted and might be achieved via improvement of the sampler or treatment of the number of loci as an unknown.     

Analysis of single gene multitrait effects in livestock by the use of Gibbs sampling

The paper presents a method of multivariate data analysis described by a model which involves fixed effects, additive polygenic individual effects and the effects of a major gene. To find the estimates of model parameters, the maximization of likelihood function method is applied. The maximum of likelihood function is computed by the use of the Gibbs sampling approach. In this approach, following the conditional posterior distributions, values of all unknown parameters are generated. On the basis of the obtained samples the marginal posterior densities as well as the estimates of fixed effects, gene frequency, genotypic values, major gene, polygenic and error (co)variances are calculated. A numerical example, supplemented to theoretical considerations, deals with data simulated according to the considered model.     

On the multivariate probit model for exchangeable binary data with covariates

This paper considers the use of a multivariate binomial probit model for the analysis of correlated exchangeable binary data. The model can naturally accommodate both cluster and individual level covariates, while keeping a fairly flexible intracluster association structure. We discuss Bayesian estimation when a sample of independent clusters of varying sizes are available, and show how Gibbs sampling may be used to derive the posterior densities of parameters. The methodology is illustrated with two examples: the first involves epidemiological data from a study of familial disease aggregation; the second uses teratological data from a developmental toxicity application.     

Genetic-based signatures of the latitudinal differences in chronotype

The natural cycles of night and day, and their length, remain stable in near-equatorial African regions but they vary with latitude and season in Eurasia. This new environmental factor might shape the adaptation of circadian rhythms of Eurasians after the out-of-African dispersal of their African ancestors. To identify the genetic-based signatures of this adaptation, geographic variation in allele frequencies of more than 2300 genetic variants was analyzed using data from 5 African and 11 Eurasian populations of the 1000 Genomes Project. The genetic signatures of latitude-dependent polygenic selection were found more frequently within non-coding DNA regions associated with morningness–eveningness in genome-wide association studies (GWASs) than among polymorphisms hinted by GWASs of other traits/diseases and among polymorphisms sampled from pseudogenes and from protein-coding regions in either circadian clock genes or reference genes. Some of such variants were located within the introgressions of the Neanderthal’s genome into the genomes of Eurasians.     

Selecting SNPs for association studies based on population frequencies: a novel interactive tool and its application to polygenic diseases

Common complex polygenic diseases as autoimmune diseases have not been completely understood on a molecular level. While many genes are known to be involved in the pathways responsible for the phenotype, explicit causes for the susceptibility of the disease remain to be elucidated. The susceptibility to disease is thought to be the result of genetic epistatic interactions between common polymorphic genes. This polymorphism is mostly caused by single nucleotide polymorphisms (SNPs). Human subpopulations are known to differ in the susceptibility to the diseases and generally in the distribution of single nucleotide polymorphisms. The here presented approach retrieves SNPs with the most divergent frequencies for selected human subpopulations to help defining properties for the experimental verification of SNPs within defined regions. A web-accessible program implementing this approach was evaluated for multiple sclerosis (MS), a common human polygenic disease. A link to a summary of data from "The SNP Consortium" (TSC) with sex-dependencies of SNPs is available. Associations of SNPs to genes, genetic markers and chromosomal loci are retrieved from the Ensembl project. This tool is recommended to be used in conjunction with microarray analyses or marker association studies that link genes or chromosomal loci to particular diseases.     

Multivariate Bayesian analysis of Gaussian,right censored Gaussian,ordered categorical and binary traits using Gibbs sampling

A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed.     

DNA repair genetic polymorphisms and risk of colorectal cancer in the Czech Republic

Colorectal cancer represents a complex disease where susceptibility may be influenced by genetic polymorphisms in the DNA repair system. In the present study we investigated the role of nine single nucleotide polymorphisms in eight DNA repair genes on the risk of colorectal cancer in a hospital-based case-control population (532 cases and 532 sex- and age-matched controls). Data analysis showed that the variant allele homozygotes for the Asn148Glu polymorphism in the APE1 gene were at a statistically non-significant increased risk of colorectal cancer. The risk was more pronounced for colon cancer (odds ratio, OR: 1.50; 95% confidence interval, CI: 1.01-2.22; p=0.05). The data stratification showed increased risk of colorectal cancer in the age group 64-86 years in both individuals heterozygous (OR: 1.79; 95% CI: 1.04-3.07; p=0.04) and homozygous (OR: 2.57; 95% CI: 1.30-5.06; p=0.007) for the variant allele of the APE1 Asn148Glu polymorphism. Smokers homozygous for the variant allele of the hOGG1 Ser326Cys polymorphism showed increased risk of colorectal cancer (OR: 4.17; 95% CI: 1.17-15.54; p=0.03). The analysis of binary genotype combinations showed increased colorectal cancer risk in individuals simultaneously homozygous for the variant alleles of APE1 Asn148Glu and hOGG1 Ser326Cys (OR: 6.37; 95% CI: 1.40-29.02; p=0.02). Considering the subtle effect of the DNA repair polymorphisms on the risk of colorectal cancer, exploration of gene-gene and gene-environmental interactions with a large sample size with sufficient statistical power are recommended.     

Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects

In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.     

Systematic association mapping identifies NELL1 as a novel IBD disease gene

Crohn disease (CD), a sub-entity of inflammatory bowel disease (IBD), is a complex polygenic disorder. Although recent studies have successfully identified CD-associated genetic variants, these susceptibility loci explain only a fraction of the heritability of the disease. Here, we report on a multi-stage genome-wide scan of 393 German CD cases and 399 controls. Among the 116,161 single-nucleotide polymorphisms tested, an association with the known CD susceptibility gene NOD2, the 5q31 haplotype, and the recently reported CD locus at 5p13.1 was confirmed. In addition, SNP rs1793004 in the gene encoding nel-like 1 precursor (NELL1, chromosome 11p15.1) showed a consistent disease-association in independent German population- and family-based samples (942 cases, 1082 controls, 375 trios). Subsequent fine mapping and replication in an independent sample of 454 French/Canadian CD trios supported the authenticity of the NELL1 association. Further confirmation in a large German ulcerative colitis (UC) sample indicated that NELL1 is a ubiquitous IBD susceptibility locus (combined p<10(-6); OR = 1.66, 95% CI: 1.30-2.11). The novel 5p13.1 locus was also replicated in the French/Canadian sample and in an independent UK CD patient panel (453 cases, 521 controls, combined p<10(-6) for SNP rs1992660). Several associations were replicated in at least one independent sample, point to an involvement of ITGB6 (upstream), GRM8 (downstream), OR5V1 (downstream), PPP3R2 (downstream), NM_152575 (upstream) and HNF4G (intron).     

The immunoglobulin heavy-chain variable region in insulin-dependent diabetes mellitus: affected-sib-pair analysis and association studies.

We have analyzed immunoglobulin heavy-chain variable-region (VH) polymorphisms and genetic susceptibility to insulin-dependent diabetes mellitus (IDDM) by using a set of polymorphic loci that span approximately 1,000 kb of the VH region on chromosome 14q32. One hundred one Finnish families with at least two children affected with IDDM were studied. Conventional RFLPs determined by hybridization were used, since no microsatellite repeat markers have been available for this gene region. No evidence for linkage between the VH genes and IDDM could be obtained from haplotype-sharing analysis among the 133 diabetic sib pairs. The frequencies of various VH genotypes were also compared between 101 familial IDDM cases and 114 controls derived from the Finnish background population. The distribution of the genotypes at the VH2-B5 locus was significantly different between these groups (P=.004), the 3.4/3.4 genotype being less common in the IDDM cases. In addition, a different genotype distribution at the VH5-B2 locus was observed in the diabetic subjects (P = .022). When the IDDM cases were stratified by presence or absence of the high-risk HLA-DQB1*0302 allele, no differences in VH genotype frequencies were observed between the 0302-positive and 0302-negative cases. In the transmission test for linkage disequilibrium (TDT), no differences were found between the expected and observed frequencies of the transmitted alleles at the VH2-B5 or VH5-B2 locus. In conclusion, significant differences in VH genotype distributions were observed between the familial IDDM cases and the controls, but the observed associations could not be confirmed by the TDT. Haplotype sharing analysis provided no evidence for genetic linkage between the VH gene region and IDDM.     

Investigation of the genetic association between quantitative measures of psychosis and schizophrenia: a polygenic risk score analysis

The presence of subclinical levels of psychosis in the general population may imply that schizophrenia is the extreme expression of more or less continuously distributed traits in the population. In a previous study, we identified five quantitative measures of schizophrenia (positive, negative, disorganisation, mania, and depression scores). The aim of this study is to examine the association between a direct measure of genetic risk of schizophrenia and the five quantitative measures of psychosis. Estimates of the log of the odds ratios of case/control allelic association tests were obtained from the Psychiatric GWAS Consortium (PGC) (minus our sample) which included genome-wide genotype data of 8,690 schizophrenia cases and 11,831 controls. These data were used to calculate genetic risk scores in 314 schizophrenia cases and 148 controls from the Netherlands for whom genotype data and quantitative symptom scores were available. The genetic risk score of schizophrenia was significantly associated with case-control status (p<0.0001). In the case-control sample, the five psychosis dimensions were found to be significantly associated with genetic risk scores; the correlations ranged between.15 and.27 (all p<.001). However, these correlations were not significant in schizophrenia cases or controls separately. While this study confirms the presence of a genetic risk for schizophrenia as categorical diagnostic trait, we did not find evidence for the genetic risk underlying quantitative schizophrenia symptom dimensions. This does not necessarily imply that a genetic basis is nonexistent, but does suggest that it is distinct from the polygenic risk score for schizophrenia.     

High frequency of HLA-DQB1 non-Asp(57) alleles in Kuwaiti children with insulin-dependent diabetes mellitus

The prevalence of polymorphic amino acids at position 57 of the HLA DQB1 in Kuwaiti children with insulin-dependent diabetes mellitus (IDDM) and nondiabetic controls has been determined using a polymerase chain reaction-sequence-specific primers (PCR-SSP) method. Using this approach, 34/55 (62%) IDDM children were found to be homozygous Ala/Ala and 19/55 (35%) were heterozygous with various combinations. Amongst the IDDM children with heterozygous genotype at codon 57 of HLA DQB1, 6/55 (11%) had Asp/Ala, 8/55 (15%) had Ala/Val, 4/55 (7%) had Ala/Ser and 1/55 had Asp/Val allelic combinations. When considered collectively, the nonaspartate (NA) alleles were represented in 87% of the IDDM cases and only 13% cases had Asp(57) allele in different heterozygous combinations, while none of the IDDM subjects had a homozygous Asp genotype. In nondiabetic controls, homozygous non-Asp (NA) alleles were represented in 44% subjects, 37% of the controls were heterozygous (NA/A) and 19% had a homozygous (A/A) genotype. These differences between the IDDM group and the control group were found to be statistically significant. Our data report one of the highest frequency of NA/NA residues at this locus compared with that from different world populations (Sardinians, Norwegians, US Caucasians, US Blacks and Chinese).     

Two genetic loci regulate T cell-dependent islet inflammation and drive autoimmune diabetes pathogenesis

Insulin-dependent diabetes mellitus (IDDM) is a polygenic disease caused by progressive autoimmune infiltration (insulitis) of the pancreatic islets of Langerhan, culminating in the destruction of insulin-producing beta cells. Genome scans of families with diabetes suggest that multiple loci make incremental contributions to disease susceptibility. However, only the IDDM1 locus is well characterized, at a molecular and functional level, as alleleic variants of the major histocompatibility complex (MHC) class II HLA-DQB1, DRB1, and DPB1 genes that mediate antigen presentation to T cells. In the nonobese diabetic (NOD) mouse model, the Idd1 locus was shown to be the orthologous MHC gene I-Ab. Inheritance of susceptibility alleles at IDDM1/Idd1 is insufficient for disease development in humans and NOD mice. However, the identities and functions of the remaining diabetes loci (Idd2-Idd19 in NOD mice) are largely undefined. A crucial limitation in previous genetic linkage studies of this disease has been reliance on a single complex phenotype-diabetes that displays low penetrance and is of limited utility for high-resolution genetic mapping. Using the NOD model, we have identified an early step in diabetes pathogenesis that behaves as a highly penetrant trait. We report that NOD-derived alleles at both the Idd5 and Idd13 loci regulate a T lymphocyte-dependent progression from a benign to a destructive stage of insulitis. Human chromosomal regions orthologous to the Idd5 and -13 intervals are also linked to diabetes risk, suggesting that conserved genes encoded at these loci are central regulators of disease pathogenesis. These data are the first to reveal a role for individual non-MHC Idd loci in a specific, critical step in diabetes pathogenesis-T cell recruitment to islet lesions driving destructive inflammation. Importantly, identification of intermediate phenotypes in complex disease pathogenesis provides the tools required to progress toward gene identification at these loci.     

APOE ɛ4 allele and TOMM40‐APOC1 variants jointly contribute to survival to older ages

Age‐related diseases characteristic of post‐reproductive life, aging, and life span are the examples of polygenic non‐Mendelian traits with intricate genetic architectures. Polygenicity of these traits implies that multiple variants can impact their risks independently or jointly as combinations of specific variants. Here, we examined chances to live to older ages, 85 years and older, for carriers of compound genotypes comprised of combinations of genotypes of rs429358 (APOE ɛ4 encoding polymorphism), rs2075650 (TOMM40), and rs12721046 (APOC1) polymorphisms using data from four human studies. The choice of these polymorphisms was motivated by our prior results showing that the ɛ4 carriers having minor alleles of the other two polymorphisms were at exceptionally high risk of Alzheimer''s disease (AD), compared with non‐carriers of the minor alleles. Consistent with our prior findings for AD, we show here that the adverse effect of the ɛ4 allele on survival to older ages is significantly higher in carriers of minor alleles of rs2075650 and/or rs12721046 polymorphisms compared with their non‐carriers. The exclusion of AD cases made this effect stronger. Our results provide compelling evidence that AD does not mediate the associations of the same compound genotypes with chances to survive until older ages, indicating the existence of genetically heterogeneous mechanisms. The survival chances can be mainly associated with lipid‐ and immunity‐related mechanisms, whereas the AD risk, can be driven by the AD‐biomarker‐related mechanism, among others. Targeting heterogeneous polygenic profiles of individuals at high risks of complex traits is promising for the translation of genetic discoveries to health care.     

Gallbladder cancer predisposition: a multigenic approach to DNA-repair, apoptotic and inflammatory pathway genes

Gallbladder cancer (GBC) is a multifactorial disease with complex interplay between multiple genetic variants. We performed Classification and Regression Tree Analysis (CART) and Grade of Membership (GoM) analysis to identify combinations of alleles among the DNA repair, inflammatory and apoptotic pathway genetic variants in modifying the risk for GBC. We analyzed 16 polymorphisms in 8 genes involved in DNA repair, apoptotic and inflammatory pathways to find out combinations of genetic variants contributing to GBC risk. The genes included in the study were XRCC1, OGG1, ERCC2, MSH2, CASP8, TLR2, TLR4 and PTGS2. Single locus analysis by logistic regression showed association of MSH2 IVS1+9G>C (rs2303426), ERCC2 Asp312Asn (rs1799793), OGG1 Ser326Cys (rs1052133), OGG1 IVS4-15C>G (rs2072668), CASP8 -652 6N ins/del (rs3834129), PTGS2 -1195G>A (rs689466), PTGS2 -765G>C (rs20417), TLR4 Ex4+936C>T (rs4986791) and TLR2 -196 to -174del polymorphisms with GBC risk. The CART analysis revealed OGG1 Ser326Cys, and OGG1 IVS4-15C>G polymorphisms as the best polymorphic signature for discriminating between cases and controls. In the GoM analysis, the data was categorized into six sets representing risk for GBC with respect to the investigated polymorphisms. Sets I, II and III described low intrinsic risk (controls) characterized by multiple protective alleles while sets IV, V and VI represented high intrinsic risk groups (GBC cases) characterized by the presence of multiple risk alleles. The CART and GoM analyses also showed the importance of PTGS2 -1195G>A polymorphism in susceptibility to GBC risk. In conclusion, the present multigenic approach can be used to define individual risk profiles for gallbladder cancer in North Indian population.     

Population-based resequencing of experimentally evolved populations reveals the genetic basis of body size variation in Drosophila melanogaster

Body size is a classic quantitative trait with evolutionarily significant variation within many species. Locating the alleles responsible for this variation would help understand the maintenance of variation in body size in particular, as well as quantitative traits in general. However, successful genome-wide association of genotype and phenotype may require very large sample sizes if alleles have low population frequencies or modest effects. As a complementary approach, we propose that population-based resequencing of experimentally evolved populations allows for considerable power to map functional variation. Here, we use this technique to investigate the genetic basis of natural variation in body size in Drosophila melanogaster. Significant differentiation of hundreds of loci in replicate selection populations supports the hypothesis that the genetic basis of body size variation is very polygenic in D. melanogaster. Significantly differentiated variants are limited to single genes at some loci, allowing precise hypotheses to be formed regarding causal polymorphisms, while other significant regions are large and contain many genes. By using significantly associated polymorphisms as a priori candidates in follow-up studies, these data are expected to provide considerable power to determine the genetic basis of natural variation in body size.     

A bivariate quantitative genetic model for a linear Gaussian trait and a survival trait

With the increasing use of survival models in animal breeding to address the genetic aspects of mainly longevity of livestock but also disease traits, the need for methods to infer genetic correlations and to do multivariate evaluations of survival traits and other types of traits has become increasingly important. In this study we derived and implemented a bivariate quantitative genetic model for a linear Gaussian and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted. Model parameters were inferred from their marginal posterior distributions. The required fully conditional posterior distributions were derived and issues on implementation are discussed. The two Weibull baseline parameters were updated jointly using a Metropolis-Hasting step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. Simulation results showed that the estimated marginal posterior distributions covered well and placed high density to the true parameter values used in the simulation of data. In conclusion, the proposed method allows inferring additive genetic and environmental correlations, and doing multivariate genetic evaluation of a linear Gaussian trait and a survival trait.     

High-resolution linkage mapping for susceptibility genes in human polygenic disease: Insulin-dependent diabetes mellitus and chromosome 11q

Insulin-dependent diabetes mellitus (IDDM) has a complex pattern of genetic inheritance. In addition to genes mapping to the major histocompatibility complex (MHC), several lines of evidence point to the existence of other genetic susceptibility factors. Recent studies of the nonobese diabetic mouse (NOD) model of IDDM have suggested the presence, on mouse chromosome 9, of a susceptibility gene linked to the locus encoding the T-cell antigen, Thy-1. A region on human chromosome 11q is syntenic to this region on mouse chromosome 9. We have used a set of polymorphic DNA markers from chromosome 11q to investigate this region for linkage to a susceptibility gene in 81 multiplex diabetic pedigrees. The data were investigated by maximization of lod scores over genetic models and by multiple-locus affected-sib-pair analysis. We were able to exclude the presence of a susceptibility gene (location scores less than -2) throughout greater than 90% of the chromosome 11q homology region, under the assumption that the susceptibility factor would cause greater than 50% of affected sib pairs to share two alleles identical by descent. Theoretical estimates of the power to map susceptibility genes with a high-resolution map of linked markers in a candidate region were made, using HLA as a model locus. This result illustrates the feasibility that IDDM linkage studies using mapped sets of polymorphic DNA markers have, both for other areas of the genome in IDDM and for other polygenic diseases. The analytic approaches introduced here will be useful for affected-sib-pair studies of other complex phenotypes.