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Bayesian modelling of multivariate quantitative traits using seemingly unrelated regressions.

We investigate a Bayesian approach to modelling the statistical association between markers at multiple loci and multivariate quantitative traits. In particular, we describe the use of Bayesian Seemingly Unrelated Regressions (SUR) whereby genotypes at the different loci are allowed to have non-simultaneous effects on the phenotypes considered with residuals from each regression assumed correlated. We present results from simulations showing that, under rather general conditions that are likely to hold in real situations, the Bayesian SUR approach has increased probability of selecting the true model compared to univariate analyses. Finally, we apply our methods to data from subjects genotyped for 12 SNPs in the apolipoprotein E (APOE) gene. Phenotypes relate to response to treatment with atorvastatin and include changes in total cholesterol, low-density lipoprotein cholesterol, and triglycerides. Missing genotype data are naturally accommodated in our Bayesian framework by imputing them using a nested haplotype phasing algorithm.

Algorithms↗

Mapping quantitative trait loci using multiple phenotypes in general pedigrees.

The use of correlated phenotypes may dramatically increase the power to detect the underlying quantitative trait loci (QTLs). Current approaches for multiple phenotypes include regression-based methods, the multivariate variance of components method, factor analysis and structural equations. Issues with these methods include: 1) They are computation intensive and are subject to problems of optimization algorithms; 2) Existing claims on the asymptotic distribution of the likelihood ratio statistic for the multivariate variance of components method are contradictory and erroneous; 3) The dimension reduction of the parameter space under the null hypothesis, a phenomenon that is unique to multivariate analyses, makes the asymptotic distribution of the likelihood ratio statistic more complicated than expected. In this article, three cases of varying complexity are considered. For each case, the efficient score statistic, which is asympotically equivalent to the likelihood ratio statistic, is derived, so is its asymptotic distribution [correction]. These methods are straightforward to calculate. Finite-sample properties of these score statistics are studied through extensive simulations. These score statistics are for use with general pedigrees.

Algorithms↗

Cold sweetening in diploid potato: mapping quantitative trait loci and candidate genes.

A candidate gene approach has been used as a first step to identify the molecular basis of quantitative trait variation in potato. Sugar content of tubers upon cold storage was the model trait chosen because the metabolic pathways involved in starch and sugar metabolism are well known and many of the genes have been cloned. Tubers of two F(1) populations of diploid potato grown in six environments were evaluated for sugar content after cold storage. The populations were genotyped with RFLP, AFLP, and candidate gene markers. QTL analysis revealed that QTL for glucose, fructose, and sucrose content were located on all potato chromosomes. Most QTL for glucose content mapped to the same positions as QTL for fructose content. QTL explaining >10% of the variability for reducing sugars were located on linkage groups I, III, VII, VIII, IX, and XI. QTL consistent across populations and/or environments were identified. QTL were linked to genes encoding invertase, sucrose synthase 3, sucrose phosphate synthase, ADP-glucose pyrophosphorylase, sucrose transporter 1, and a putative sucrose sensor. The results suggest that allelic variants of enzymes operating in carbohydrate metabolic pathways contribute to the genetic variation in cold sweetening.

Carbohydrate Metabolism↗

A unified framework for mapping quantitative trait loci in bivalent tetraploids using single-dose restriction fragments: a case study from alfalfa.

The development of statistical methodologies for quantitative trait locus (QTL) mapping in polyploids is complicated by complex polysomic inheritance. In this article, we propose a statistical method for mapping QTL in tetraploids undergoing bivalent formation at meiosis by using single-dose restriction fragments. Our method is based on a unified framework, one that uses chromosome bivalent pairing configuration and gametic recombination to discern different mechanisms of gamete formation. Our bivalent polyploid model can not only provide a simultaneous estimation of the linkage and chromosome pairing configuration-a cytological parameter of evolutionary and systematic interest-but also enhances the precision of estimating QTL effects and position by correctly characterizing gene segregation during polyploid meiosis. By using our method and a linkage map constructed in a previous study, we successfully identify several QTL affecting winter hardiness in bivalent tetraploid alfalfa. Moreover, our results reveal significant preferential chromosome pairing at meiosis in an F1 hybrid population, which indicates the importance of reassessing the traditional view of random chromosome segregation in alfalfa.

Chromosome Pairing↗

Confirmation of quantitative trait loci affecting fatness in chickens.

In this report we describe the analysis of an advanced intercross line (AIL) to confirm the quantitative trait locus (QTL) regions found for fatness traits in a previous study. QTL analysis was performed on chromosomes 1, 3, 4, 15, 18, and 27. The AIL was created by random intercrossing in each generation from generation 2 (G(2)) onwards until generation 9 (G(9)) was reached. QTL for abdominal fat weight (AFW) and/or percentage abdominal fat (AF%) on chromosomes 1, 3 and 27 were confirmed in the G(9) population. In addition, evidence for QTL for body weight at the age of 5 (BW5) and 7 (BW7) weeks and for the percentage of intramuscular fat (IF%) were found on chromosomes 1, 3, 15, and 27. Significant evidence for QTL was detected on chromosome 1 for BW5 and BW7. Suggestive evidence was found on chromosome 1 for AFW, AF% and IF%, on chromosome 15 for BW5, and on chromosome 27 for AF% and IF%. Furthermore, evidence on the chromosome-wise level was found on chromosome 3 for AFW, AF%, and BW7 and on chromosome 27 for BW5. For chromosomes 4 and 18, test statistics did not exceed the significance threshold.

Animals↗

Expressionview: visualization of quantitative trait loci and gene-expression data in Ensembl.

We present here a software tool for combined visualization of gene-expression data and quantitative trait loci (QTL). The application is implemented as an extension to the Ensembl project and caters for a direct transition from microarray experiments of gene or protein expression levels to the genomic context of individual genes and QTL. It supports the visualization of gene clusters and the selection of functional candidate genes in the context of research on complex traits.

Animals↗

A quantitative trait locus for oleic fatty acid content on Sus scrofa chromosome 7.

A partial genome scan using microsatellite markers was conducted to detect quantitative trait loci (QTLs) for 10 fatty acid contents of backfat on 15 chromosomes in a porcine resource population. Two QTLs were discovered on Sus scrofa chromosome 4 (SSC4) and SSC7. The QTL on SSC4 was located between marker loci sw1336 and sw512, and this QTL was detected (P < 0.05) only for linoleic acid. Its position was in proximity of those mapped for linoleic acid content in previous studies. The QTL on SSC7 was mapped between markers swr1343 and sw2155, and it was significant (P < 0.05) only for oleic acid. A novelty of the QTL for oleic acid was suggested because the QTL was located far from any other QTLs previously mapped for fatness traits. The QTL on SSC7 explained 19% of phenotypic variation for oleic acid content. Further studies on fine mapping and positional comparative candidate gene analysis would be the next step toward better understanding of the genetic architecture of fatty acid contents.

Animals↗

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.

Alleles↗

Linkage disequilibrium mapping of quantitative-trait Loci by selective genotyping.

The principles of linkage disequilibrium mapping of dichotomous diseases can be well applied to the mapping of quantitative-trait loci through the method of selective genotyping. In 1999, M. Slatkin considered a truncation selection (TS) approach. We propose in this report an extended TS approach and an extreme-rank-selection (ERS) approach. The properties of these selection approaches are studied analytically. By using a simulation study, we demonstrate that both the extended TS approach and the ERS approach provide remarkable improvements over Slatkin's original TS approach.

Genotype↗

Quantitative trait loci affecting components of wing shape in Drosophila melanogaster.

Two composite multiple regression-interval mapping analyses were performed to identify candidate quantitative trait loci (QTL) affecting components of wing shape in Drosophila melanogaster defined by eight relative warp-based measures. A recombinant inbred line design was used to map QTL for the shape of two intervein regions in the anterior compartment of the wing, using a high resolution map of retrotransposon insertion sites between Oregon-R and Russian 2b. A total of 35 QTL representing up to 23 different loci were identified, many of which are located near components of the epidermal growth factor-Ras signal transduction pathway that regulates vein vs. intervein decision making and vein placement. Over one-half of the loci were detected in both sexes, and just under one-half were detected at two different growth temperatures. Different loci were found to affect aspects of shape in each intervein region, confirming that the shape of the whole wing should be regarded as a compound trait composed of several developmental units. In addition, a reciprocal backcross design was used to map QTL affecting shape in the posterior compartment of the wings of 831 flies, using a molecular map of 16 allele-specific oligohybridization single nucleotide polymorphism (SNP) markers between two divergent inbred lines. A total of 13 QTL were detected and shown to have generally additive effects on separable components of shape, in both sexes. By contrast, 8 QTL that affected wing size in these backcrosses were nearly dominant in their effects. The results confirm at the genetic level that wing shape is regulated independent of wing size and set up the hypothesis that wing shape is regulated in part through the regulation of the length and positioning of wing veins, involving quantitative regulation of the activity of secreted growth factors.

Animals↗

[Identification of quantitative trait loci controlling F2 sterility and heading date in rice].

Ninety-six F2 lines derived from a cross between a japonica cultivar Taichung 65 and an indica cultivar Bhadua were developed. At the first step, an RFLP linkage map based on the F2 lines was constructed. The RFLP map contained 94 RFLP makers. F2 sterility and heading date are important agronomic traits of rice; meanwhile heading date is related to many characters of agronomic importance including sterility. Quantitative trait locus (QTL) analysis was carried out to identify genes controlling F2 sterility and heading date. Both single factor analysis and interval analysis were applied for QTL analysis. Two QTLs for F2 spikelet sterility were newly detected on Chromosome 1 and 8. Five QTLs for heading date were detected on Chromosome 1, 4, 6, 8 and 10. Two of them on chromosome 1 and 10 were newly detected. Near-isogenic lines are now under construction for further QTL analysis and gene mapping of these QTLs newly identified in this paper.

Chromosome Mapping↗

Minor quantitative trait loci underlie floral traits associated with mating system divergence in Mimulus.

The genetic basis of species differences provides insight into the mode and tempo of phenotypic divergence. We investigate the genetic basis of floral differences between two closely related plant taxa with highly divergent mating systems, Mimulus guttatus (large-flowered outcrosser) and M. nasutus (small-flowered selfer). We had previously constructed a framework genetic linkage map of the hybrid genome containing 174 markers spanning approximately 1800 cM on 14 linkage groups. In this study, we analyze the genetics of 16 floral, reproductive, and vegetative characters measured in a large segregating M. nasutus x M. guttatus F2 population (N = 526) and in replicates of the parental lines and F1 hybrids. Phenotypic analyses reveal strong genetic correlations among floral traits and epistatic breakdown of male and female fertility traits in the F2 hybrids. We use multitrait composite interval mapping to jointly locate and characterize quantitative trait loci (QTLs) underlying interspecific differences in seven floral traits. We identified 24 floral QTLs, most of which affected multiple traits. The large number of QTLs affecting each trait (mean = 13, range = 11-15) indicates a strikingly polygenic basis for floral divergence in this system. In general, QTL effects are small relative to both interspecific differences and environmental variation within genotypes, ruling out QTLs of major effect as contributors to floral divergence between M. guttatus and M. nasutus. QTLs show no pattern of directional dominance. Floral characters associated with pollinator attraction (corolla width) and self-pollen deposition (stigma-anther distance) share several pleiotropic or linked QTLs, but unshared QTLs may have allowed selfing to evolve independently from flower size. We discuss the polygenic nature of divergence between M. nasutus and M. guttatus in light of theoretical work on the evolution of selfing, genetics of adaptation, and maintenance of variation within populations.

Biological Evolution↗

Genetic linkage methods for quantitative traits.

We discuss methods for detecting genetic linkage for quantitative data. The usual LOD score method uses a pseudolikelihood formulation and has optimal power provided all parameters are correctly specified, but can lead to erroneous estimates of the location for the locus influencing a trait under misspecification of parameters describing the variance of the trait. Alternative methods, in which attention focuses upon modelling covariation among relatives as a function of genetic marker, similarity lead to unbiased estimates of the location and major gene heritability of the trait influencing locus. The Haseman-Elston approach uses a regression method to perform linkage analysis and its properties have been widely studied. This method is generally less powerful than variance components procedures, but the maximum likelihood-based variance components procedures require normality of the trait to ensure robustness of the genetic linkage tests (i.e. a correct false positive rate). When samples are non-randomly selected an ascertainment correction is generally required in order to obtain unbiased parameter estimates when applying variance components methods. For quantitative traits, ascertainment corrections usually condition either on the proband exceeding a threshold, or on the trait value of the proband. We summarize simulations that show that both approaches lead to similar efficiencies for estimating genetic effects. Finally, we discuss methods for analysing diseases that include time-to-onset information. A variety of methods are available for the linkage analysis of quantitative traits. Here, we have reviewed the most commonly used methods.

Biometry↗

Controlling the type I and type II errors in mapping quantitative trait loci.

Although the interval mapping method is widely used for mapping quantitative trait loci (QTLs), it is not very well suited for mapping multiple QTLs. Here, we present the results of a computer simulation to study the application of exact and approximate models for multiple QTLs. In particular, we focus on an automatic two-stage procedure in which in the first stage "important" markers are selected in multiple regression on markers. In the second stage a QTL is moved along the chromosomes by using the preselected markers as cofactors, except for the markers flanking the interval under study. A refined procedure for cases with large numbers of marker cofactors is described. Our approach will be called MQM mapping, where MQM is an acronym for "multiple-QTL models" as well as for "marker-QTL-marker." Our simulation work demonstrates the great advantage of MQM mapping compared to interval mapping in reducing the chance of a type I error (i.e., a QTL is indicated at a location where actually no QTL is present) and in reducing the chance of a type II error (i.e., a QTL is not detected).

Chromosome Mapping↗

Mapping quantitative trait loci affecting life history traits in the nematode Caenorhabditis elegans.

We have identified chromosomal regions containing quantitative trait loci (QTLs) specifying life history traits in recombinant-inbred strains of the nematode Caenorhabditis elegans. This approach also allows us to examine epistatic interactions between loci and pleiotropic effects on different traits at specific loci. QTLs for mean life span were identified on chromosomes II (near stP101), IV (stP5) and the X (stP61), and QTLs for fertility were identified on II (maPI), III (stP19) and IV (stP51). The QTLs for mean life span accounted for 90% of the genetic component of variance. The loci for mean fertility accounted for 88% of the genetic component of variance. Additional QTLs for temperature-sensitive fertility [II (stP36) and V (stP6)] and internal hatching [IV (stP5)] were also mapped in these crosses. We found evidence for epistatic effects on mean life span between maP1 and bP1 (V), and for epistatic effects on mean fertility between stP36 and stP6, between stP98 (II) and stP192 (V), between maP1 and stP127 (III), between maP1 and stP103 (X), and between stP5 and stP6. Negatively correlated, pleiotropic effects on mean life span and internal hatching were found linked to stP5.

Animals↗

Comparison of a multipoint identity-by-descent method with parametric multipoint linkage analysis for mapping quantitative traits.

We previously developed a method of partitioning genetic variance of a quantitative trait to loci in specific chromosomal regions. In this paper, we compare this method--multipoint IBD (identical by descent) method (MIM)--with parametric multipoint linkage analysis (MLINK). A simulation study was performed comparing the methods for the major-locus, mixed, and two-locus models. The criterion for comparisons between MIM and MLINK was the average lod score from multiple replicates of simulated data sets. The effect of gene frequency, dominance, model misspecification, marker spacing, and informativeness are also considered in a smaller set of simulations. Within the context of the models examined, the MIM approach was found to be comparable in power with parametric multipoint linkage analysis when (a) parental data are unknown, (b) the effect of the major locus is small and there is additional genetic variation, or (c) the parameters of the major-locus model are misspecified. The performance of the MIM method relative to MLINK was markedly lower when the allele frequency at the trait locus was .2 versus .5, particularly for the case when parental data were assumed to be known. Dominance at the trait major locus, as well as marker spacing and heterozygosity, did not appear to have a large effect on the ELOD comparisons.

Chromosome Mapping↗

Mapping multiple quantitative trait Loci for ordinal traits.

Many complex traits in humans and other organisms show ordinal phenotypic variation but do not follow a simple Mendelian pattern of inheritance. These ordinal traits are presumably determined by many factors, including genetic and environmental components. Several statistical approaches to mapping quantitative trait loci (QTL) for such traits have been developed based on a single-QTL model. However, statistical methods for mapping multiple QTL are not well studied as continuous traits. In this paper, we propose a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to map multiple QTL for ordinal traits in experimental crosses. We model the ordinal traits under the multiple threshold model, which assumes a latent continuous variable underlying the ordinal phenotypes. The ordinal phenotype and the latent continuous variable are linked through some fixed but unknown thresholds. We adopt a standardized threshold model, which has several attractive features. An efficient sampling scheme is developed to jointly generate the threshold values and the values of latent variable. With the simulated latent variable, the posterior distributions of other unknowns, for example, the number, locations, genetic effects, and genotypes of QTL, can be computed using existing algorithms for normally distributed traits. To this end, we provide a unified approach to mapping multiple QTL for continuous, binary, and ordinal traits. Utility and flexibility of the method are demonstrated using simulated data.

Algorithms↗

Genome annotation of a 1.5 Mb region of human chromosome 6q23 encompassing a quantitative trait locus for fetal hemoglobin expression in adults.

BACKGROUND: Heterocellular hereditary persistence of fetal hemoglobin (HPFH) is a common multifactorial trait characterized by a modest increase of fetal hemoglobin levels in adults. We previously localized a Quantitative Trait Locus for HPFH in an extensive Asian-Indian kindred to chromosome 6q23. As part of the strategy of positional cloning and a means towards identification of the specific genetic alteration in this family, a thorough annotation of the candidate interval based on a strategy of in silico / wet biology approach with comparative genomics was conducted. RESULTS: The ~1.5 Mb candidate region was shown to contain five protein-coding genes. We discovered a very large uncharacterized gene containing WD40 and SH3 domains (AHI1), and extended the annotation of four previously characterized genes (MYB, ALDH8A1, HBS1L and PDE7B). We also identified several genes that do not appear to be protein coding, and generated 17 kb of novel transcript sequence data from re-sequencing 97 EST clones. CONCLUSION: Detailed and thorough annotation of this 1.5 Mb interval in 6q confirms a high level of aberrant transcripts in testicular tissue. The candidate interval was shown to exhibit an extraordinary level of alternate splicing - 19 transcripts were identified for the 5 protein coding genes, but it appears that a significant portion (14/19) of these alternate transcripts did not have an open reading frame, hence their functional role is questionable. These transcripts may result from aberrant rather than regulated splicing.

3',5'-Cyclic-AMP Phosphodiesterases↗