This computational simplification may lead to reduced power to identify variants with small effect sizes and requires correcting for multiple hypothesis tests with complex relationships. However, advances in computational methods and increase in computational resources are enabling the computation of models that adhere more closely to the theory of multifactorial inheritance. Here, a Bayesian variable selection and model averaging approach is formulated for searching for additive and dominant genetic effects. The approach considers simultaneously all available variants for inclusion as predictors in a linear genotype-phenotype mapping and averages over the uncertainty in the variable selection. This leads to naturally interpretable summary quantities on the significances of the variants and their contribution to the genetic basis of the studied trait. We first characterize the behavior of the approach in simulations. The results indicate a gain in the causal variant identification performance when additive and dominant variation are simulated, with a negligible loss of power in purely additive case. An application to the analysis of high- and low-density lipoprotein cholesterol levels in a dataset of 3895 Finns is then presented, demonstrating the feasibility of the approach at the current scale of single-nucleotide polymorphism data. We describe a Markov chain Monte Carlo algorithm for the computation and give suggestions on the specification of prior parameters using commonly available prior information. An open-source software implementing the method is available at  In recent years, numerous genome-wide association studies (GWAS) have been successful in locating disease or trait associated variations in the human genome  dominance. As baseline models, we use a purely additive formulation and a pseudo-SNP approach, where the number of variants is naively doubled by introducing an additional pseudo variant with heterozygous coding for each genetic variant. Rationale for the latter is that it allows for the modeling of dominance and any software handling the basic additive formulation could be used for the analysis. The behavior of these models is studied in simulations based on real single-nucleotide polymorphism (SNP) data and the results are compared against conventional single-SNP analysis. An application to the analysis of the genetic basis of variation in key lipid metabolism components in the circulation, high-density (HDL-C) and low-density lipoprotein cholesterol (LDL-C), is then presented. The dataset consists of 3895 Finnish individuals with (imputed) genotypes available on over one million SNPs.The simultaneous identification of trait associated  variants is facilitated by modeling the genotype-phenotype mapping as a sparse multiple linear regression, where only a small proportion of the variants is expected to have non-zero effects. Specifically, our formulation corresponds to a type of spike-and-slab prior An excellent general discussion on Bayesian variable selection in GWAS is provided by Guan and Stephens Let Let M and m be the major and minor alleles at a SNP. The following types of genetic effects may be considered:Additive (A) with 0, 1, 2 coding for the genotypes MM, Mm/mM, mm.Heterozygous  with 0, 1, 0 coding for MM, Mm/mM, mm.Dominant  with 0, 1, 1 coding for MM, Mm/mM, mm.Recessive  with 0, 0, 1 coding for MM, Mm/mM, mm.The model indicator The attention will be restricted to models, which allow 1) additive effects (referred to as BMA A), 2) additive or additive and heterozygous effects (BMA A/AH) and 3) additive effects with pseudo variants (BMA pseudo); see The variable selection is facilitated by placing a prior distribution on the vector A functionally similar prior can be used for the effect types In matrix notation, the regression model in Equation 1 can be written asThe distribution of the residual is assumed normalThe prior for the variable selection coefficients are given the semi-conjugate formFinally, to account for missing data a categorical prior is placed on an element of Often estimates of the heritability of the trait are available from published genome-wide association studies or from some other sources . This prior knowledge can be used to guide the setting of the hyperparameters of the variance distributions in the model.First, note that the proportion of variance explained by the linear modelSimilar derivation can be made for a single effect with heritability contribution A constant term of ones is included to account for non-zero mean of the trait. An improper prior is placed for the corresponding regression coefficient: ar model , step 3 Markov chain Monte Carlo (MCMC) sampling is used to generate samples from the posterior distribution of the model parameters. The sampling of Sample Sample Sample Sample Sample Note that the steps 3–5 can be seen as a draw from a block distribution After proposing an update of Four types of updates are considered:addition of a variant to the model,removal of a variant from the model,switch of two variants (combination of the two above),switch of effect type for a variant,with probabilities 0.4, 0.4, 0.1 and 0.1. For updates 2 and 4, the variant is chosen randomly among the variants in the model (disregarding the effect type). Update 3 is formed as a composition of updates 1 and 2. The proposal distributions for additions and selection of effect types are formed adaptively during an initial sampling period as explained below, after which they are fixed. Samples from the adaptive phase are not used for posterior inference.The proposal distribution for additions is formed according to the marginal association probabilities of the variants  approach behave differently in the estimation of the marginal significances of variants in regions with high linkage disequilibrium (LD): while single-SNP methods report similar significances for the variants in the region, BMA tends to dilute the posterior probability mass among the variants, since only one of them is needed in the model. It is then sensible to compute the posterior probabilities for regions of the genome. Often the actual causal variants cannot anyway be assumed to be among those genotyped. Unfortunately, the Rao-Blackwellization approach is not feasible for this, although summing over the association probabilities within a region can be used as an estimate of the number of associated variants within the region Human data was not collected primarily for this article and was analyzed here anonymously. Primary collection has followed appropriate ethics guidelines.Simulations were used to characterize the behavior of the models and to validate the approach against a single-SNP approach implemented in the popular software PLINK . Specifically, correct values were used to set means and modes, but the distributions were given large variances  Effect type identification accuracies for causal variants were computed on the region level weighted with posterior association probabilities The Bayesian model averaging approach facilitates inferences on heritability  and the number of causal variants. The model size distributions are summarized with 95% central posterior intervals in The Bayesian model averaging (BMA) approach was then applied to real data. BMA A (additive) and A/AH (additive or additive and heterozygous terms) models were used.Data were available from 3895 Finnish individuals from two studies. 2002 of the individuals were from a metabolic syndrome case-control sample Location parameters of the prior distributions were specified based on a recently published large meta-analysis investigating blood concentrations of lipids The posterior association probabilities were computed for regions of the genome using HapMap genetic maps  CETP gene. The two associations (one of which is in region not reported by Teslovich LIPC gene. The previously unreported (to our knowledge) putative association on chromosome 5 is about 14 kbp upstream of CAST gene and is suspect to being a false positive.For HDL-C, there are seven regions with posterior association probability over half, five of which have been identified previously PCSK9, in and near which associations to LDL-C have also been previously reported. The estimate for the number of associations in this region is 1.6 .For LDL-C, there are five regions with posterior association probability over half, four of which are in regions, where LDL-C associated SNPs have been found previously in the large meta-analysis study n is 1.6  with somLDLRAD3 gene.analysis . For LDLanalysis . PLINK AHeritability samples were obtained from the MCMC as the proportion of  variance explained by the included genetic effects . The medOur results demonstrate that Bayesian variable selection and model averaging (BMA) in searching for additive and dominant genetic effects is feasible on genome-wide scale and has several potential benefits over single-SNP analysis. The primary interest in genome-wide association studies (GWAS) often lies in locating causal variants (or variants linked to them), which may provide insight into the underlying biology of the phenotype, indicate new therapeutic targets for diseases and enable personalized risk analytics Notably, even if only additive effects were simulated, there was virtually no decrease in the identification accuracy from allowing AH terms. This behavior can (at least partly) be explained by allowing the data to provide information on the relative numbers of the different types of effects We also compared the BMA A/AH approach to a pseudo-SNP approach, which doubles the number of variants by introducing an additional pseudo SNP with heterozygosity coding for each original SNP. This allows simple modeling of dominance without requiring any special implementation handling different effect types. However, our simulations indicate that an explicit model for the dominance variation may increase the performance of identifying associations. Moreover, the prior specification of model size and effect types are more natural when an explicit model is used. The performance for the identification of the types of effects had mixed results in our simulations.The BMA approach facilitates posterior inference on heritability based on genotype data of unrelated individuals as studied by Guan and Stephens A few issues regarding our modeling choices and computation should be highlighted. First, the distribution for the effect sizes was assumed normal for computational convenience, although a heavier tailed distribution could be more robust and often truer to prior assumptions in GWAS Click here for additional data file.Text S2PLINK analysis options.(PDF)Click here for additional data file.Figure S1True positive rate as a function of false positive rate in simulations with all forty replicate datasets combined within each configuration. sB refers to Bayesian single-SNP analysis. Regions were defined based on HapMap genetic maps with 0.005 cM cutoff. sB A and PLINK A may be difficult to distinguish because of overlap.(TIF)Click here for additional data file.Figure S2True positive rate as a function of false positive rate in simulations with all forty replicate datasets combined within each configuration. sB refers to Bayesian single-SNP analysis. Regions were defined using the default LD block algorithm in the Haploview software (TIF)Click here for additional data file.Figure S3True positive rate as a function of false positive rate in simulations with all forty replicate datasets combined within each configuration. sB refers to Bayesian single-SNP analysis. Regions were defined based on HapMap genetic maps with 0.01 cM cutoff (this figure is the same as in the main article expect for the inclusion of the sB results). sB A and PLINK A may be difficult to distinguish because of overlap.(TIF)Click here for additional data file.Figure S4Comparison of the posterior association probabilities between BMA A/AH MCMC chains for HDL-C and LDL-C (SNP-wise and region-wise with the regions from HapMap genetic maps with 0.01 cM cutoff).(TIF)Click here for additional data file.Figure S5Region-wise BMA A posterior association probabilities for ten permutations of the HDL-C data. The trait (TIF)Click here for additional data file.Figure S6Estimates of the number of associated variants in the regions (using HapMap genetic maps with 0.01 cM cutoff) for HDL-C and LDL-C with BMA A/AH. Calculated for each region as a sum of the Rao-Blackwellized posterior association probabilities of the SNPs within the region (TIF)Click here for additional data file.Figure S7Region-wise BMA A/AH posterior association probabilities (gray) and PLINK AH for HDL-C and LDL-C.(TIF)Click here for additional data file.


O. sativa accessions. The phenotyping for 14 traits was conducted in both temperate (Arkansas) and subtropical (Texas) climates and the genotyping used 154 SSRs and an indel marker. Heading, plant height and weight, and panicle length had negative correlations, while seed set and grain weight/panicle had positive correlations with harvest index across both locations. Subsequent genetic diversity and population structure analyses identified five groups in this collection, which corresponded to their geographic origins. Model comparisons revealed that different dimensions of principal components analysis (PCA) affected harvest index traits for mapping accuracy, and kinship did not help. In total, 36 markers in Arkansas and 28 markers in Texas were identified to be significantly associated with harvest index traits. Seven and two markers were consistently associated with two or more harvest index correlated traits in Arkansas and Texas, respectively. Additionally, four markers were constitutively identified at both locations, while 32 and 24 markers were identified specifically in Arkansas and Texas, respectively. Allelic analysis of four constitutive markers demonstrated that allele 253 bp of RM431 had significantly greater effect on decreasing plant height, and 390 bp of RM24011 had the greatest effect on decreasing panicle length across both locations. Many of these identified markers are located either nearby or flanking the regions where the QTLs for harvest index have been reported. Thus, the results from this association mapping study complement and enrich the information from linkage-based QTL studies and will be the basis for improving harvest index directly and indirectly in rice.Harvest index is a measure of success in partitioning assimilated photosynthate. An improvement of harvest index means an increase in the economic portion of the plant. Our objective was to identify genetic markers associated with harvest index traits using 203  Oryza sativa L.) is one of the most important staple foods In food production, optimizing grain yield, reducing production costs, and minimizing risks to the environment have been the primary objectives since the beginning of the twentieth century Crop harvest index is also highly influenced by environmental factors Classical QTL mapping reveals only a portion of the genetic control of a trait because there are only two alleles that can differ at any locus between the two parental lines. More comprehensive analyses of genetic architecture require consideration of a larger sample of the genetic variation in the species. One approach is association mapping, which maps the QTLs either among extant breeding lines with known pedigree relationships or in a diverse germplasm collection. Given pedigree and marker information, the probability for different lines in complex populations to share identity by descent QTLs can be defined, permitting estimation of the effects of each QTL O. sativaRecently, the USDA rice mini-core (URMC) subset was developed and serves as a genetically diversified panel for mining genes of interest to various users sativa URMC accessions with 155 molecular markers and phenotyped 14 traits contributable to harvest index in both temperate  and subtropical  locations. Our objectives were to identify the traits significantly correlated with harvest index per se and the markers significantly associated with component traits of harvest index. To control spurious associations, i.e., Type I error, we analyzed the genetic structure and familial relatedness in the collection. Different mapping models were tested for best fit of each trait. The chosen model was used to map markers associated with harvest index and associated traits phenotyped in two environments.We genotyped 203 O. indel with genome-wide distribution detected a total of 1993 alleles among 203 O. sativa accessions. The average number of alleles per locus was 12.86 ranging from 2 for RM338 to 57 for con673. Polymorphic Information Content (PIC) varied from 0.25 for AP5625-1 to 0.97 for con673 among the 155 markers with an average of 0.71. Nei's (1983) The set of 154 SSRs and an STRUCTURE software with multi-loci genotype data, a five-group model was identified to sufficiently explain genetic structure among 203 accessions. Ancestry of each of these accessions was inferred for assignment into a genetic group  belong to indica (IND), temperate japonica (TEJ), tropical japonica (TRJ), aus (AUS) and aromatic (ARO) (The resultant five groups of ic (ARO) , based oic (ARO) . TEJ accStatistical analysis using a mixed model demonstrated that the differences due to genotypes and genotype×location interactions were highly significant at the 0.001 level of probability for all of the 14 traits . The difSix traits were significantly correlated with harvest index and these correlation directions were the same across the two locations. The correlations with harvest index were negative for heading (−0.46 at Stuttgart and −0.61 at Beaumont), plant height (−0.50 and −0.50), plant weight (−0.36 and −0.30), panicle length (−0.45 and −0.32), while positive for seed set (0.52 and 0.61) and grain weight/panicle (0.32 and 0.40) . In the Dimension determination for PCA indicated that different dimensions should be included for testing associations for these traits. Further, relative performance of the association mapping models was also evaluated based on the criterion BIC . The sma−3 level of probability (the Bonferroni corrected significance level)  . Among 3eviously . AdditioAt Beaumont, we identified 28 markers significantly associated with harvest index traits . Among tAcross two locations, the associations of RM431 with plant height, Rid12 and RM471 with plant weight, and RM24011 with panicle length were consistently true. The four markers that associated with the same trait across both locations are called “constitutive QTL” markers, while others that associated with a certain trait only at one location are called “adaptive QTL” markers The allelic effects of the constitutive markers associated with their traits were estimated using the least square mean (LSMEAN) of phenotypic values and are presented in The average number of alleles per locus was 12.86 among 203 accessions in the URMC genotyped with 155 markers. The allele number per locus is the highest among the rice collections that have been reported to date O. sativa accessions in the URMC were divided into five model-based groups from ancestry analysis , the PCA showed the best fit with the smallest BIC value for harvest index traits. Interestingly, correction of the kinship model was not observed to be better than the naive model. Similarly, the models with Q+kinship or PCA+kinship did not perform better than the ones with only Q or PCA, either. Shao et al. qHID7-1” responsible for harvest index Ghd7” having major effects on grains per panicle, plant height and heading in rice qHID3-2” for control of harvest index sd1” sd1 that is involved in gibberellic acid biosynthesis decreases plant height, thus increases harvest index. The decreased height reduces lodging susceptiblity, is tolerant to heavy applications of nitrogen fertilizer, and can be planted at relatively high density, all contributing to improved grain yield that has resulted in the Green Revolution in cereal crops including rice Harvest index is an integrative trait including the net effect of all physiological processes during the crop cycle and its phenotypic expression is generally affected by genes responsible for non-target traits, such as heading qHID4-1 and qHID4-2 for harvest index qHID8-1qHID8-1hi2.1Other markers were associated with the traits correlated with harvest index, but not with harvest index directly in this study. These markers have been reported either nearby or flanking the QTLs for harvest index. RM5, which was associated with plant height in the Stuttgart study, was close to a reported QTL for harvest index on Chr 1 Quantitative traits show a range of sensitivities to environmental changes Environment-specific QTLs can be used for marker-assisted selection (MAS) at specific environments. For example, RM431 could be used to improve harvest index directly and indirectly through decreasing plant height and increasing seed set in Arkansas because it was co-associated with harvest index, plant height, and seed set. However, the constitutive marker-trait associations over multiple environments can be applied to MAS programs in a wide area. For example, results suggest that the constitutive markers Rid12 and RM471 could be used to improve harvest index indirectly through decreasing plant weight in the southern states of the USA.Comparison of allelic effects of these constitutive markers can classify the alleles within a marker locus into superior or inferior ones, which helps decide which to use for MAS in the southern states. For example, allele 253 bp of RM431 and allele 390 bp of RM24011 had the largest effect on decreasing two traits, plant height and panicle length, negatively associated with harvest index. Thus, these superior alleles can be introduced for improvement of harvest index indirectly through decreasing the negative traits at both locations. Conversely, the allele 411 bp of RM24011 had the largest effect on increasing the panicle length and thus would not be useful for improving harvest index using MAS at either location. Interestingly, the two alleles of Rid12 associated with plant weight had opposite effects at the two locations. Allelic choice for this marker should be dependent on the particular environment targeted for breeding.Results of the present study demonstrated that genome-wide association mapping in the URMC could complement and enrich the information derived from linkage-based QTL studies. After validation or fine mapping of these putative genomic regions, the information will help secure food production through either direct improvement of harvest index or indirect improvement via changes in seed set, grain weight per panicle, heading, plant height and weight, and panicle length using the MAS.sativa whereas the remaining belongs to other species in Oryza. Pure seed of these accessions were provided by the Genetic Stock Oryza Collection (GSOR) (www.ars.usda.gov/spa/dbnrrc/gsor) with cultivar name or designation, accession number, registration year, place of origin, longitude and latitude of origin, pedigree or genetic background (if available), morphological characteristics and references. The GSOR supplies seeds for research purposes to national and international users upon to request. In this study, only 203 O. sativa accessions were used for the following analysis because the wild relatives, O. glaberrima, nivara, rufipogon, glumaepatula and latifolia, contain many rare alleles. Rare alleles are one of the factors that increase the risk of Type I errors or spurious associations Of 217 accessions in the URMC, 203 belong to O. −1 of nitrogen as urea was applied. Weeds were controlled at both pre-planting and pre-flooding stages with locally recommended herbicides.Evaluations were conducted for 14 traits in two field locations, USDA-ARS Dale Bumpers National Rice Research Center near Stuttgart, Arkansas and USDA-ARS Rice Research Unit near Beaumont, Texas during the 2009 growing season. The Stuttgart test site is located at N 34°27′44″ and W 91°24′59″, representing a temperate climate with a 243 d frost free period and average temperature of 23.9 C during the growing season. The Beaumont test site is located at N 30°03′47″ and W 94°17′45″, representing a subtropical climate with a 253 d frost free period and an average temperature of 26.1 C during the growing season. The experiments at both locations utilized a randomized complete block design having three replications with nine plants spaced 0.3×0.6 m in each plot. Three seeds were sown in each of nine hills in a plot using a Hege 1000 grain drill planter on April 23 and May 6 of 2009 at Stuttgart and Beaumont, respectively. Each hill was thinned to a single plant right after the permanent flood was applied at five leaf stage. Before flooding, fertilizer at 55 kg haData collection followed procedures described by Yan et al. http://www.gramene.org/), and five SSRs  were amplified in house indel at the Rc locus, named Rid 12 and is responsible for rice pericarp color. Polymerase chain reaction (PCR) marker amplifications were performed as described in Agrama et al. http://www.gramene.org/). Markers labeled with different colored fluorescence and that amplified products with size differences of 20 bp or more were multiplexed together post PCR.Bulk tissue from five plants was collected from each accession as described by Brondani et al. PowerMarker version 3.25 PowerMarker was also used to calculate the average number of alleles, gene diversity, and polymorphism information content (PIC) values. The tree to visualize the phylogenetic distribution of accessions and ancestry groups was constructed using MEGA version 4 Genetic distance was calculated from the 155 molecular markers using Nei distance 2 = σg2/(σg2+σe2/n), where σg2 as the genotypic variance, σe2 as the environmental variance and n as the number of replications NTSYSpc software version 2.11 Each of the 14 phenotypic traits was modeled independently with the MIXED procedure in SASv.9.2, where genotype, location and interaction of location with genotype were defined as fixed effects while replication within a location (block effect) was a random effect. Broad-sense heritability was calculated using formula HSTRUCTURED(K), assisted with L(K), L′(K) and (L″K). The D(K) perceives the rate of change in log probability of the data between successive (K) values rather than just the log probability of the data. Determination of mixed ancestry (an accession unable to be clearly assigned to only one group) was based on 60% (Q) as a threshold to consider an individual with its inferred ancestry from one single group. Principal component analysis (PCA), that summarizes the major patterns of variation in a multi-locus data set, was performed with NTSYSpc software version 2.11 STRUCTURE for the following linkage disequilibrium analysis.The model-based program P values were compared to the Bonferroni threshold (1/155 = 6.45×10−3) to identify statistically significant loci. Allelic effects at marker loci were compared using the LSMEANS and pdiff option in the MIXED procedure, using Saxton's PDMIX800 SAS macro Following the procedures previously recommended Table S1A. Spearman correlation for each pair of 14 traits evaluated at Stuttgart, Arkansas in 2009. B. Spearman correlation for each pair of 14 traits evaluated at Beaumont, Texas in 2009.(DOC)Click here for additional data file.Table S2Fitness analysis of mapping model for harvest index traits using Bayesian information criterion (BIC) in both Arkansas and Texas.(DOC)Click here for additional data file.Table S3The marker loci associated with harvest index traits at Stuttgart, Arkansas and Beaumont, Texas in 2009.(DOC)Click here for additional data file.Table S4Comparison of allelic effect of four constitutive marker loci at two locations, Stuttgart, Arkansas and Beaumont, Texas. RM431 for Plant height, RM471 and Rid12 for Plant weight, and RM24011 for Panicle length.(DOC)Click here for additional data file.


Because subjective responses to drugs may predict drug addiction, identifying alleles that influence acute response may also provide insight into the genetic risk factors for drug abuse. We performed a Genome Wide Association Study (GWAS) for the subjective responses to amphetamine in 381 non-drug abusing healthy volunteers. Responses to amphetamine were measured using a double-blind, placebo-controlled, within-subjects design. We used sparse factor analysis to reduce the dimensionality of the data to ten factors. We identified several putative associations; the strongest was between a positive subjective drug-response factor and a SNP (rs3784943) in the 8th intron of cadherin 13 , a gene previously associated with a number of psychiatric traits including methamphetamine dependence. Additionally, we observed a putative association between a factor representing the degree of positive affect at baseline and a SNP (rs472402) in the 1st intron of steroid-5-alpha-reductase-α-polypeptide-1 , a gene whose protein product catalyzes the rate-limiting step in synthesis of the neurosteroid allopregnanolone. This SNP belongs to an LD-block that has been previously associated with the expression of SRD5A1 and differences in SRD5A1 enzymatic activity. The purpose of this study was to begin to explore the genetic basis of subjective responses to stimulant drugs using a GWAS approach in a modestly sized sample. Our approach provides a case study for analysis of high-dimensional intermediate pharmacogenomic phenotypes, which may be more tractable than clinical diagnoses.Both the subjective response to  We obtained responses on three questionnaires, administered over six time points, in three sessions, after placebo or one of two doses of drug. Such multi-dimensional “intermediate phenotypes” have many advantages over binary diagnoses. Drug abuse is a heterogeneous phenotype that consists of a series of stages, each influenced by a variety of environmental and genetic factors Despite the potential advantages noted above, high-dimensional intermediate phenotypes pose considerable analytic challenges. Here we describe the results of an innovative strategy for analyzing these data, which includes methods to normalize phenotypes and application of sparse factor analysis (SFA) Healthy young adults  aged 18–35 years old were recruited and screened through a physical examination, electrocardiogram, modified Structured Clinical Interview for DSM-IV, psychiatric symptom checklist (SCL90) and self-reported health and drug use history. Exclusion criteria were: past year Axis I Disorder, history of mania or psychosis, less than a high-school education, smoking more than ten cigarettes per week, drinking more than three cups of coffee per day, lack of English fluency, or medical contraindication to amphetamine administration. Participants were inexperienced stimulant users: only 24% reported any previous use of stimulants and less than 2% reported 50 or more lifetime uses. Participants were asked to abstain from drugs and alcohol for 24 hours, nicotine for 12 hours and to fast for 12 hours prior to each session. At the start of each session, participants provided urine  and breath samples  to confirm drug, alcohol and nicotine abstinence, and female participants were tested for pregnancy.d-amphetamine (10 or 20 mg) under double-blind conditions. They completed questionnaires measuring subjective effects before and 30, 60, 90, 150 and 180 minutes after ingesting the capsule; heart rate and blood pressure were also measured at these times; these procedures have been described previously Participants completed three randomized 4-hour study sessions, separated by at least 72 hours, during which they received placebo or First we imputed missing phenotype values using probabilistic principal components analysis In addition to the primary outcome phenotypes, several demographic measures were collected . We exambaseline measure; and (ii) the mean of the last four time points  controlling for the first time point (0 min), which we refer to as the response measure. Note that, by construction, these two summary values are uncorrelated.Amphetamine treatment significantly affected most of the phenotypes . ExploraAn alternative that we considered but rejected was to combine the first two time points to form the baseline measure. Factor loadings were quite similar using this approach; however, we observed some evidence of early drug effects for some measures in a subset of participants at the 30 minute time point, and thus we chose to omit the 30 minute time point to avoid controlling for drug response.dimension reduction. Combining data across correlated measurements reduces environmental noise and measurement error. We chose to perform dimension reduction using sparse factor analysis (SFA) The above process yielded a baseline and response measure for each of the 22 phenotypes in each session . Next we sought to combine information across sessions and phenotypes to yield a small number of phenotypes that efficiently captured the primary patterns in the whole data; this process is commonly referred to as DNA was extracted from blood at the General Clinical Research Center at the University of Chicago. Genotyping was performed using the Affymetrix 6.0 array at the Functional Genomics Core Facility . The arrays were passed through the Affymetrix apt-geno-qc package, and DM call rate, contrast QC metric, and genotypic gender were computed. Genotypes were called with the Birdseed quantile normalized). We then corrected for potential population stratification by controlling each factor for the first two principal components computed by applying SmartPCA We performed association mapping separately for each of the ten factors in 381 individuals. First, to reduce potential problems due to non-normality, each factor was quantile-quantile transformed to a standard normal distribution  were conducted with genotype as the grouping factor and dose and time as the two within-subjects factors; age, sex, BMI, and the first two principal components from SmartPCA were included as covariates.Because 325 of the 381 participants were Caucasians (based on both self-report and clustering with SmartPCA), we also performed association mapping on this Caucasian-only subset for those SNPs highlighted in the Results section without controlling for population stratification  involved genes that, on the basis of prior biological evidence, are good candidates for being associated with these phenotypes. We view these results as generating credible hypotheses that can be evaluated in future studies.We performed a GWAS on 381 participants for ten phenotypes at 5,476,100 SNPs; results are shown in P = 4.58×10−8; log10BF = 5.26). The frequency of this SNP did not show marked differences among populations in 1000 Genomes, and an analysis of the Caucasian-only subset yielded consistent results . The factor loadings show that this factor consists primarily of responses in participants in the 10 mg session. Friendliness, Elation, Vigor, Feel, High, More, Like, Amphetamine, Benzedrine, Marijuana and MBG have positive loadings on this factor, while Depression, Fatigue, Confusion and PCAG have negative loadings (th intron of the gene cadherin 13 (CDH13) which codes for a cell adhesion molecule that is highly expressed in the brain P-value was 0.231. The genome-wide P-values for this factor are shown in We identified a potential association between rs3784943 and factor F1, which we labeled “10 mg response” . Similar to the previous example, this SNP did not show marked differences among populations in 1000 Genomes, and an analysis of the Caucasian-only subset yielded consistent results . Several other SNPs in strong linkage disequilibrium (LD) with rs472402 (r2 = 0.77–0.98) were also associated with the baseline positive affect factor  is shown in We also identified a potential association between rs472402 and factor F2, which we labeled “positive affect at baseline”  at multiple SNPs CDH13 (16q21–16q24) CDH13 and ADHD was performed that found a gene-wide significant association at one SNP (rs11150556) CDH13 has also been implicated by GWAS in depression (rs10514585) CDH13 have also been significantly associated with adiponectin levels in two GWAS CDH13 knockout mice show decreases in conditioned place preference to cocaine , which is highly consistent with a difference in the subjective response to amphetamine that we observed.Our strongest genetic association with a drug response factor was between rs3784943 and factor F1 . This SNCDH13 and sensitivity to the subjective effects of amphetamine may provide insight into the mechanism by which an allele influences the risk for drug dependence. Drug dependence develops through many stages, including initial experimentation with drugs, continued use, dependence, withdrawal and relapse The association between SRD5A1, which is expressed in the brain A agonist. Allopregnanolone has been shown to have anxiolytic effects in animals 2 = 0.73) has been identified as a cis-eQTL for the SRD5A1 gene in human monocytes P = 6×10−19) and is also in moderate LD (r2 = 0.3–0.7) with several SNPs that have been identified as cis-eQTLs for SRD5A1 in post-mortem samples from cerebellum and parietal cortex 2 = 0.89), which has been associated with differences in SRD5A1 activity SRD5A1 has also been suggested as a positional candidate gene based on a linkage study for cocaine dependence and major depressive episode SRD5A1 could influence subjective positive affect by modulating both expression and enzymatic activity of SRD5A1 and thereby altering allopregnanolone levels in the brain.Our strongest association with a baseline factor was between rs472402 and factor F2 . This SNWhile techniques that aggregate information using dimension reduction are attractive, the results must be both interpretable and biologically meaningful. Our results here illustrate how SFA can yield more interpretable data summaries than other methods, such as PCA, facilitating the systematic aggregation of a large collection of phenotypic information without sacrificing interpretability. Regardless of the dimension reduction technique used to identify putative associations, it is important to examine the raw phenotypes to determine how a given SNP correlates with the underlying phenotypic data . In bothThis study has several strengths and limitations. One limitation is that we used a relatively small number of participants to test a large number of putative predictors (genotypes). Despite the small sample, there is credible evidence that intermediate pharmacogenomic phenotypes might be more likely to have larger effect alleles CDH13 and positive subjective response. Replication of this result was challenging because a suitable study would have included administration of a stimulant drug, under similar conditions and corresponding dosage, and would have had to collect the same or related measurements of subjective response. In addition, the associated SNP had a fairly low minor allele frequency and only a moderate effect on the phenotype, so a relatively large dataset would be needed to have sufficient power for replication. Alternatively, our results can be viewed as replicating prior associations with CDH13, however the lack of convergence on a single SNP or haplotype across studies is a cause for concern. Because of these limitations, the results from Cdh13 knockout mice and other biologically based studies of CDH13 function may be the best route for further investigation and replication of our results.While intermediate phenotypes have many advantages, a major limitation is that replication samples are seldom available. We were unable to identify any suitable replication dataset for the association between the SNP (rs3784943) in SRD5A1 and baseline positive affect appeared to be a more tractable problem because multiple GWAS datasets that include measurements of personality traits are available. Although our questionnaires were designed to detect differences in mood state, the effect persisted regardless of session or time point, which is consistent with a difference in trait independent of drug or session effects. We examined SNPs in strong LD with rs472402 in subjects from the National Institutes of Health/National Institute of Mental Health (NIH/NIMH) bipolar genetics studies with personality trait data consisting of the ZKPQ (n = 1007) and TCI (n = 944) subscales Replication of the association between the SNP (rs472402) in CDH13 has previously been associated with a number of substance abuse and other psychiatric phenotypes and is also supported by data from knock-out mice. Replication in independent datasets will be important to establish the role of CDH13 in drug addiction, and to determine the extent to which initial drug responses are related to the etiology of addiction. SRD5A1 is similarly supported by prior evidence including corroborating genetic studies, gene expression and enzymatic activity data, but the lack of replication of this result is a cause for concern. We were motivated to perform this study using a relatively modest sample size because we believed that intermediate pharmacogenomic phenotypes might be influenced by alleles that contribute a larger fraction of the genetic variance. This study reflects both the utility and challenges of such phenotypes for discovery and enrichment of our understanding of complex psychiatric constructs such as drug abuse.In conclusion we have performed the first GWAS of the subjective response to a drug of abuse and identified two interesting associations. Figure S1Correlation between putative demographic and other covariates and raw phenotype data. The putative covariates are on the x-axis; the raw data for each subscale for each time point and session are on the y-axis. Abbreviations on the x-axis are as follows: body mass index (BMI), alcoholic drinks per week (AlcWeek), cigarettes smoked per week (CigWeek), cups of caffeinated beverages per week (CaffWeek), times smoking marijuana per month (MarijMonth), ever used sedatives (SedEver), ever used stimulants (StimEver), ever used opiates (OpiatEver), ever used hallucinogens , ever used inhalants , ever used marijuana (MarijEver). Abbreviations on the y-axis are defined in the text with the following exceptions: Physiological phenotypes (Phys), heart rate (HR), diastolic blood pressure (DiastolicBP), systolic blood pressure (SystolicBP). The Pearson correlation coefficient is indicated according to the scale bar on the right. Based on these data, Age, Gender and BMI were regressed from the phenotypic data.(PDF)Click here for additional data file.Figure S2Factor loadings and GWAS results for all 10 factors. Panel A shows the factor loadings; abbreviations of outcome measures are defined in the text. Percentage of variance explained (PVE), or the contribution to the variance in the survey data by each factor, is shown in the top left hand corner. Note that the PVE does not sum, because there is correlation among the factors. Panel B shows the raw phenotype scores as a function of dose  and time (x-axis within each panel) for individuals in the upper and lower deciles of this factor. Panel C shows the Manhattan plot of observed −log10P for each chromosome; the red horizontal line indicates 5×10−8, which is often used as a threshold for significance. The blue horizontal line indicates 1×10−5, which could be considered a threshold for suggestive evidence. Panel D shows a Q-Q plot of observed −log10P versus the average −log10P from then random permutations. Factor descriptions are as follows (defined by Panels A and B): F1) responses during the 10 mg and 20 mg sessions, with highest scores on the 10 mg session; F2) positive affect at baseline for all three sessions; F3) responses during the 10 mg and 20 mg sessions, with highest scores on the 20 mg session; F4) responses during the 10 mg and 20 mg sessions; F5) negative affect at baseline for all three sessions; F6) blood pressure baseline measurements for all sessions; F7) responses primarily during the placebo session; F8) baseline measurements for the placebo session; F9) baseline measurements for the 10 mg session; F10) baseline measurements for the 20 mg session.(PDF)Click here for additional data file.Figure S3Summary of genotyping quality control results. Panel A shows observed HWE P-values plotted against expected P-values as computed by PLINK in the Caucasian-only sample. A cutoff of 10−4 was used and 149 SNPs were removed. Panel B shows the first two genetic principal components computed with SmartPCA on the full sample of 381 individuals. Individuals are color coded according to self-reported ancestry.(PDF)Click here for additional data file.Table S1Demographic characteristics of the participant sample. Mean values are expressed as mean ± SEM.(DOC)Click here for additional data file.Table S2Amphetamine effects on individual scales. POMS is Profile of Mood States questionnaire; DEQ is Drug Effect Questionnaire; ARCI is Addiction Research Center Inventory questionnaire. LSD is Lysergic acid; MBG is Morphine-Benzedrine Group; PCAG is Pentobarbitol-Chlorpromazine-Alcohol Group.(DOC)Click here for additional data file.Table S3Description of factors obtained from Sparse Factor Analysis. Interpretations based on factor loading plots (ng plots  and decing plots  are give(DOC)Click here for additional data file.Table S4Association results for all SNPs with P−5.<1×10 Factor designations are given in column 1: F1) responses during the 10 mg and 20 mg sessions, with highest scores on the 10 mg session; F2) positive affect at baseline for all three sessions; F3) responses during the 10 mg and 20 mg sessions, with highest scores on the 20 mg session; F4) responses during the 10 mg and 20 mg sessions; F5) negative affect at baseline for all three sessions; F6) blood pressure baseline measurements for all sessions; F7) responses primarily during the placebo session; F8) baseline measurements for the placebo session; F9) baseline measurements for the 10 mg session; F10) baseline measurements for the 20 mg session. P-values and log10BF are shown for SNPs highlighted in the Results section.(XLS)Click here for additional data file.Table S5Association of a linkage disequilibrium block within SRD5A1 and F2, the positive affect at baseline factor. The post-re-genotyping association P-value, log10BF, and HWE P-value are given. SNPs with direct eQTL evidence in the eqtl.uchicago.edu database are noted.(XLS)Click here for additional data file.Supporting Information S1Combined Supporting Materials and Methods and Supporting Results file. Additional details of the methods are provided in the Supporting Materials and Methods section. Alternative dimensionality methods are detailed in the Supporting Materials and Methods and Results sections.(DOC)Click here for additional data file.


To examine more closely whether the common variants have the expected effects, we calculated a weighted allele score (WAS), which is a weighted prediction of height for each individual based on the previously estimated effect sizes of the common variants in the overall population. The average WAS is consistent with expectation in the tall individuals, but was not as extreme as expected in the shortest individuals (p<0.006), indicating that some of the short stature is explained by factors other than common genetic variation. The discrepancy was more pronounced (p<10−6) in the most extreme individuals (height<0.25 percentile). The results at the extreme short tails are consistent with a large number of models incorporating either rare genetic non-additive or rare non-genetic factors that decrease height. We conclude that common genetic variants are associated with height at the extremes as well as across the population, but that additional factors become more prominent at the shorter extreme.Common genetic variants have been shown to explain a fraction of the inherited variation for many common diseases and quantitative traits, including height, a classic polygenic trait. The extent to which common variation determines the phenotype of highly heritable traits such as height is uncertain, as is the extent to which common variation is relevant to individuals with more extreme phenotypes. To address these questions, we studied 1,214 individuals from the top and bottom extremes of the height distribution , drawn from ∼78,000 individuals from the HUNT and FINRISK cohorts. We found that common variants still influence height at the extremes of the distribution: common variants (49/141) were nominally associated with height in the expected direction more often than is expected by chance ( Although there are many loci in the human genome that have been discovered to be significantly associated with height, it is unclear if these loci have similar effects in extremely tall and short individuals. Here, we examine hundreds of extremely tall and short individuals in two population-based cohorts to see if these known height determining loci are as predictive as expected in these individuals. We found that these loci are generally as predictive of height as expected in these individuals but that they begin to be less predictive in the most extremely short individuals. We showed that this result is consistent with models that not only include the common variants but also multiple low frequency genetic variants that substantially decrease height. However, this result is also consistent with non-additive genetic effects or rare non-genetic factors that substantially decrease height. This finding suggests the possibility of a major role of low frequency variants, particularly in individuals with extreme phenotypes, and has implications on whole-genome or whole-exome sequencing efforts to discover rare genetic variation associated with complex traits. Height is a highly heritable trait, with estimates of heritability as high as 90% In this paper, we describe our approach to determine whether common alleles known to be associated with height in the general population have the expected distribution in individuals from the extremes of the height distribution. We used DNA samples from individuals with extreme heights from two population-based cohorts of Finnish (FINRISK) and Norwegian (HUNT) ancestry and genotyped them for common variants known to be associated with height. Under a polygenic model in which there are many variants and each variant additively contributes a small effect to the phenotype, we found that for individuals within ∼2.81 standard deviations of the mean, the common variants have the predicted associations with height, consistent with their effect sizes estimated from the previous population study p<0.0001; FINRISK 122/155, p<0.0001) and there was a significant enrichment in SNPs reaching nominal significance for association with height (p<0.0001) had directions of effect consistent with previously published results p<5×10−28). This result confirms that, as a group, SNPs found to be associated with height in the general population are also associated with height at the extremes of the phenotypic spectrum.We attempted to genotype SNPs at the 180 loci previously associated with height in individuals from the short and tall extremes of the FINRISK and HUNT cohorts and then performed association analyses for each SNP with height using the Cochran-Mantel-Haenszel test and logistic regression respectively. In FINRISK, SNPs at 158 of the height loci were successfully genotyped in 181 short and 192 tall individuals from the 1% tails of the height distribution. In the HUNT study, SNPs at 160 of the height loci were successfully genotyped in 385 short and 456 tall individuals from the ∼1.5% tails of height. Here we focus on the 279 short and 309 tall individuals from the 1% tails of the HUNT study, so as to provide consistency with the FINRISK study. In both cohorts, the majority of SNPs had effect directions consistent with the published results h height . We thenh height . Ninety-p = 0.94; FINRISK 75/155 SNPs, p = 0.48 and combined 75/141, p = 0.45); (We next tested whether the observed odds ratios (OR) are consistent with the expected odds ratios, based on the previously estimated effect sizes from the GIANT study = 0.45); . Next, f= 0.45); . This reWAS) for each individual using the height-associated SNPs previously described. The WAS is the cumulative effect of all of the SNPs on height weighted by each SNP's estimated effect size (β). In WAS based on the 143 loci genotyped in both cohorts versus the individual height Z-scores. As expected, the WAS are significantly different between the tall extremes and the short extremes (p<3×10−86), with individuals in the tall extreme having higher WAS on average than individuals in the short extremes.After determining that the individual SNPs have similar effects at the extremes of the height distribution as in the general population, we then performed additional analyses on the combined set of height-associated variants. We asked whether extremely short and extremely tall individuals show overall enrichment of height-decreasing and height-increasing alleles, respectively, to the extent expected under a purely polygenic additive model. If the enrichment is less than expected, this result would suggest that the common variants are not explaining as much of the phenotypic variation in the extremes as in the general population. To test this possibility, we first calculated the weighted allele score . These results suggest that the collective effect of the common variants in the short extremes do not account for as much of the phenotypic variation in height as predicted from the effects seen in the general population.We then tested whether the ions see . For eaced model . For theed model . Finallyed model . In eachWAS in the short extremes was no longer significantly different than expected (p = 0.526), indicating that the shift in WAS is driven by the most extremely short individuals. To further explore this hypothesis, we then selected more extreme individuals at two thresholds, including only the top and bottom 0.5% or 0.25% of the population (See WAS in the short extremes (p = 7.12×10−6 and p = 9.88×10−7 for the 0.5% and 0.25% extremes respectively), but again no deviation in the tall extremes. Similar observations occurred when we analyzed the cohorts separately using the same stratification procedure  of the SNPS have an observed effect size smaller than expected (p = 0.02)  . This anWAS distribution did not change, indicating that adding additional common variants of similar effect sizes cannot explain the phenotypic variation in the short extremes. We then modeled a single rare variant of very large effect: frequency 0.005 and effect size of −4 SD. In this model, the mean WAS distribution in the extremely short individuals shifts more than we observed in our population. This simulation essentially excludes the possibility of a 0.5% variant of very large effect within our cohort. Such a variant would also be likely to be discovered in linkage studies of several thousand sib-pairs We hypothesized that lower frequency and rare genetic variants with larger effect sizes than the common variants may explain the phenotypic variation in the short extremes. To test this hypothesis, we performed population simulations with rare-variants of various allele frequencies and effect sizes, and asked if our observed data were consistent with these simulated scenarios . As a neWAS consistent with our observed data . We then performed this same analysis for the 0.25% to 1.5% tails individuals and there was no significant difference in z-scores of siblings between the short  and tall  groups . So the differential regression to the mean appears to be limited to the shortest ∼0.25% of individuals with this group regressing more quickly than the tall extreme group. This is consistent with the results we observe with the weighted allele score (WAS) approach.To provide further support for a different genetic architecture in individuals in the extreme short tails we performed an analysis in siblings from the HUNT study. We queried the entire HUNT database  and identified 21,365 siblings pairs. The correlation of age and gender adjusted height between siblings was high (r = 0.466). We then identified 98 individuals (aged between 20–70 yrs) with a Z-score<−2.81 (∼0.25% tails) and 80 with a Z-score>2.81 who also had at least one sibling in the database . The average height Z-score for the siblings of the extreme short group was −0.97 ; the average Z-score for the full siblings of the extreme tall group was 1.29  which are significantly different  are consistent with our observed data, as is a single variant with a 2SD effect. The sibling analysis also suggests a role for WAS) method developed here could be used to select individuals to sequence in the search for these types of rarer variants, not only for height but also for other polygenic traits and diseases. Specifically, individuals in the extreme tails of a trait distribution who have an unexpectedly high or low weighted allele score may be particularly useful to sequence, especially if multiple relatives with these characteristics were present in the extreme tails.This result also suggests that these families would be good candidates to investigate in sequencing studies, as they may be enriched for rare or de novo, higher penetrance alleles. More generally, the weighted allele score (p<0.0001), and 35% (49/141) of SNPS had p<0.05 in the consistent direction. Our analyses also demonstrate that, outside of the 0.25% tails, this level of association is entirely consistent with that expected given the extreme tail ascertainment of our samples and the individual SNP continuous distribution effect sizes. Given this result, the ascertainment of our 923 samples from the ∼1% to 0.25% tails provides equivalent power to approximately 6000 samples randomly selected from the general population for a variant explaining approximately 0.1% of the variation in height. Indeed, the ability to detect associations in samples ascertained for extreme phenotypes has been recently demonstrated in studies of bone mineral density Our study also demonstrates empirically that selecting individuals from the extreme tails of a complex trait distribution is an efficient approach for genetic studies, as was proposed both for linkage studies In conclusion, we have shown that common genetic variants associated with height in the general population are also associated with height at the ∼1% tails of the height distribution. Our data suggest that common variants play less of a role, and the effect of rarer larger-effect alleles and/or strong environmental factors start to predominate around the 0.25% extreme. This finding may also have broader implications for studies of disease, in that the polygenic model may apply well to those diseases that represent the tails of an underlying normal distribution, but perhaps less well to diseases that correspond to more extreme phenotypes.Both studies were conducted according to the principles expressed in the Declaration of Helsinki. Attendance was voluntary, and each participant signed a written informed consent including information on genetic analyses. Local institutional review boards approved study protocols.www.ntnu.edu/hunt) with personal and family medical histories on approximately 120,000 people from Nord-Trøndelag County, Norway, collected during three intensive studies . Inviting all citizens aged 20 and over, information was collected from self-reported questionnaires consisting of >200 health-related questions, standardized clinical examinations, urine and non-fasting venous blood sample. The population in Nord-Trøndelag County is ethnically homogeneous, <3% of non-Caucasian ethnicity, making it especially suitable for epidemiological genetic research. Height was measured by trained personnel to the nearest 1.0 cm with the participants wearing light clothes without shoes according to standardized methods The Nord-Trøndelag Health Study (HUNT) is a comprehensive population based health study (For this study we sourced data from HUNT 2 (1995–97) in which 65,258 individuals participated (71.2% of invited). We generated age and gender standardized height for the whole population, and selected the shortest 1000 individuals and the tallest 1000 individuals from the 54,909 participants aged between 18 and 70 yrs. We removed known 1st degree relatives based on information from the Medical Birth Registry of Norway, those reporting to be living outside of Norway their first year of life, and those with low DNA concentrations. We then genotyped the remaining shortest 471 individuals (<−2.14 SDs) and the tallest 479 individuals (>2.14 SDs) from the cohort. Mean height and age of the extreme tails are given in FINRISK is a Finnish national survey on risk factors of chronic and non-communicable diseases. It is carried out every five years since 1972 using independent, random and representative population samples from different parts of Finland Blood sampling was done whenever subjects attended HUNT 2. DNA was extracted from peripheral blood leukocytes from whole blood or blood clots stored in the HUNT Biobank, using the Puregene kit  manually or with an Autopure LS (Gentra Systems). Laboratory technicians were blinded to the results of the height measurements. Details on the DNA extraction and the HUNT Biobank are described elsewhere Genotyping of short and tall individuals were done at the Norwegian University of Science and Techonology, Norway using the iSelect Metabochip  and the Infinium HD ultra protocol. Each 96-well plate included both tall and short individuals and one sample of identical reference DNA. Genotype calling was done using GenTrain version 2.0 in GenomeStudio V2010.3 . Genotyping of the middle group was done on the Metabochip at the Center for Inherited Disease Research  and called with BeadStudio 3.3.7 with Gentrain version 1.0 .Samples that did not meet a 99% completion threshold were excluded from further analysis . Additional post-genotyping exclusions based on gender discrepancy (N = 11) and first-degree relatedness  were done using PLINK 106 SNPs of the 180 GIANT height hits were directly typed on the Metabochip. In addition, we used the SNP Annotation and Proxy Search to map 54 of the remaining 74 SNPs with a HapMap r2>0.8 linkage disequilibrium proxy result We directly genotyped the samples for the 180 previously identified height SNPs. The genotyping was done at Children's Hospital Boston using Sequenom iPLEX genotyping . In total, 186 short individuals and 192 tall individuals were successfully genotyped for 158 SNPs. All 158 SNPs had a genotyping success rate ≥90% and the overall genotyping rate was 97.85% . One of We genotyped an additional 49 ancestry informative markers (AIMs) to identify ethnic outliers For FINRISK, we calculated the observed odds ratio for each of our 158 SNPs using the Cochran-Manzel-Hansel test, which is a stratified chi-square test. We stratified the individuals into 4 sub-cohorts based on geography and gender  and perfNormal. For a given SNP, we defined the height-increasing effect size as β and the height-increasing allele frequency as p. The mean height for the height-increasing allele would be iM = β p and the mean height for the height-decreasing allele would be dM = −β (1−p). The variance of height for the both alleles would be V = 1−2 p (1−p)β. We then calculated the odds of observing the height-increasing allele versus the height-decreasing allele for both the tall extremes (cases) and the short extremes (controls) by taking the ratio of the probabilities of each allele being seen in the cases and the controls respectively. These are calculated as:N denotes the density function at x of a Normal distribution with mean M and variance V. We use a cut-off of +/−2.326 to denote the approximate 1% tails. We then calculated the expected odds-ratio by taking the ratio between casesOdds over controlsOdds, i.e.For both cohorts, we calculated the expected odds ratio for each SNP by estimating the odds of the height-increasing versus the height-decreasing allele in both the tall extremes (cases) and the short extremes (controls) assuming a standard normal distribution for standardized height, i.e. height∼2>0.8 HapMap proxies with a genotyped FINRISK SNPs  for each individual, we took the sum of the effective allele dosages of the height SNPs multiplied by their respective estimated effect sizes (βs) using the Stage 1 betas from the GIANT study, as shown in the formula below.β and SNP are the effect size and effective allele dosage  of the height SNPs and WAS is the weighted allele score. N is the total number of SNPs available to calculate the weighted allele score. α is the mean of the sum such that the expected WAS is 0 as shown by the formula below.Frequency is the allele frequency of the effect allele obtained from the Finnish or HUNT estimates.To calculate the Weighted Allele Score  is a normally distributed random variable with mean 0 and variance σ2remaining. σ2remaining is calculated such that the variance of Zscore is 1, i.e. σ2remaining is 1−var(WAS). The variance of WAS can be calculated with the formula below,N = 2 and p being the allele frequencies of each SNP. The simulated effective allele dosages can then be used to calculate each individual's WAS. The simulation approach for each cohort was modeled to mirror the methods of subject selection.The null model assumes that the only factors determining height (Z-score) are the cumulative additive effects of the GIANT height SNPs and noise. We modeled the Z-score with the formula below.WAS) for each simulated individual. This simulation process was repeated 10,000 times. For the stratified analyses of various height cut-offs, we adjusted the numbers of selected individuals in each strata by taking the floor of the expected number of individuals in that strata. In our cohort, the top 0.5% extremes included 21, 32, 25 and 38 individuals from each tail of the 4 sub-populations respectively, and for the top 0.25% extremes included 10, 16, 12 and 19 individuals from each tail of the 4 sub-populations. For the top ∼1% to 0.25% extremes, we included all our extremes but excluded the top 10, 16, 12 and 19 individuals from each tail of the 4 sub-populations.For the FINRISK study, the simulations were performed using the following steps. We first generated the effective allele dosages for each SNP for 200,000 individuals by random sampling. We then randomly sampled 4271, 6582, 5025 and 7610 individuals to represent the 4 sub-populations and obtained their Z-scores using the previously described modeling. For each subgroup, we picked the appropriate number of the most extreme individuals to mimic the actual sample selection. We then pooled the short and tall extremes together and randomly dropped individuals to obtain exactly 181 short extremes and 192 tall extremes. We then randomly drop SNPs from the simulated individuals to mimic the missing genotype rate in FINRISK and then calculate the Weighted Allele Score  where μsimulation is the mean of the mean WAS and σ2simulation is the variance of the mean WAS from the simulations.We evaluated the significance of the mean observed WAS as shown in the equation below.n is the number of independent rare-variants, B represents the effect size of the rare-variants, and V is the allele dosage of the rare-variant. αrv is the mean of the rare-variants score such that the rare-variants do not change the expected Z-score, i.e. the expected Z-score is still 0. Similarly, αrv can be calculated by the following formula,2remaining in this case will have to be adjusted for the rare-variants such that the variance of the Z-score remains at 1, i.e. σ2remaining is 1−var(WAS)−var(Σ B V). F is the allele frequency of the rare-variants. Simulations done with modeling rare-variants are identical to the prior simulations of FINRISK or HUNT except that the new terms are used for calculating the Z-score.Modeling the rare-variant effect into the simulation is accomplished by adding an additional rare-variant term into the calculation of the height Z-score without changing the definition of Figure S1QQ Plot of p-values for individual SNPs based on the meta-analysis of HUNT and FINRISK. The figure shows a Q-Q plot of the p-values of the difference between the observed odd-ratios and the expected odd-ratios.(TIF)Click here for additional data file.Figure S2WAS) in the HUNT study. The plot shows the result of comparing the mean WAS of the short and tall individuals observed in the HUNT cohort against that obtained from simulation. Each row represents a different stratification of the extremes identical to those defined in WAS of 1224 non-extreme individuals taken from the middle of the height distribution. There is no difference between the mean WAS of the non-extreme individuals from that obtained from simulation (p = 0.56).Comparison of the observed versus simulated mean weighted allele score ((TIF)Click here for additional data file.Figure S3WAS) in the FINRISK study The plot shows the result of comparing the mean WAS of the short and tall individuals observed in the FINRISK cohort against that obtained from simulation. Each row represents a different stratification of the extremes identical to those defined in Comparison of the observed versus simulated mean weighted allele score ((TIF)Click here for additional data file.Figure S4WAS by incorporating additional variants (HUNT only). The plot shows the result of comparing the mean WAS of the short and tall individuals observed from only the HUNT cohort against that obtained from simulation with different scenarios of additional variants. Each row represents a different scenario identical to those defined in Comparison of the observed versus simulated mean (TIF)Click here for additional data file.Figure S5WAS by incorporating additional variants (FINRISK only). The plot shows the result of comparing the mean WAS of the short and tall individuals observed from only the FINRISK cohort against that obtained from simulation with different scenarios of additional variants. Each row represents a different scenario identical to those defined in Comparison of the observed versus simulated mean (TIF)Click here for additional data file.Figure S6Principal component plots from the HUNT study for the 0.25% short individuals versus all tall individuals. The first two principal components obtained from Eigenstrat analysis for the samples in the HUNT study are plotted. There is no significant difference in principal components between the short and tall groups.(TIF)Click here for additional data file.Figure S7Principal component plots from the HUNT study for the 0.25% short vs. the 0.25% tall individuals. The first two principal components obtained from Eigenstrat analysis for the samples in the HUNT study are plotted. There is no significant difference in principal components between the short and tall groups.(TIF)Click here for additional data file.Table S1Individual SNP analysis for HUNT cohort. The table shows the results for the SNPs used in the individual association analysis in the HUNT cohort.(XLS)Click here for additional data file.Table S2Individual SNP analysis for FINRISK cohort. The table shows the results for the SNPs used in the individual association analysis in the FINRISK cohort.(XLS)Click here for additional data file.Table S3Meta-analysis of individual SNPs for HUNT and FINRISK cohort. The table shows the results for the SNPs used in the meta-analysis of the HUNT and FINRISK cohorts.(XLS)Click here for additional data file.Table S4Meta-analysis of individual SNPs for HUNT and FINRISK cohort using only the top 0.25% tails. The table shows the results for the SNPs used in the meta-analysis of the HUNT and FINRISK cohorts using only the top 0.25% tails as extremes.(XLS)Click here for additional data file.Table S5Mean height and age of the individuals in the extreme tails of HUNT. Table of various stratification of extremes, the number of individuals in each strata separated by gender with their corresponding mean height (cm) and age (years) for the HUNT cohort.(XLS)Click here for additional data file.Table S6The FINRISK cohort divided into 4 sub-populations. The table shows the number of individuals used for each of the FINRISK sub-populations. The FINRISK cohort is sub-divided between male and female as well as individuals from east and west Finland.(XLS)Click here for additional data file.Table S7The genotyping rate of FINRISK. The table shows the number of SNPs genotyped in FINRISK and the genotyping rate for the short and tall extremes. The rate is calculated based on having 181 short individuals and 192 tall individuals.(XLS)Click here for additional data file.


Tree breeding is logistically complex and expensive, and breeders have long sought to use molecular markers to accelerate breeding. A candidate gene approach based on testing for association between the presence of DNA sequence variation in or near candidate genes, and phenotypic variation in a population has long been explored ,2. Howevhttp://dendrome.ucdavis.edu/ctgn/) were used for genotyping. A population of 149 cloned full-sib offspring of loblolly pine (Pinus taeda L.) was phenotyped. Fitting 3406 informative SNP markers simultaneously, we estimated genome-wide breeding values and compared them with breeding values based on pedigree model. Variances explained by the marker additive and dominant effects were obtained.Biallelic SNP markers provided by the CTGN project (The accuracy of the genomic estimated breeding values ranged from 0.30 to 0.83 for growth and wood quality traits. Lignin and cellulose content had great accuracy values from GS compared to growth traits. The accuracies were comparable with breeding values that were calculated based on the traditional pedigree model. If we take into account time needed to complete progeny testing, GS would be more efficient than classical progeny testing for some traits. The marker additive effects explained 18% and 23% for lignin and cellulose, respectively. Variances could not be determined for height and volume, because the Gibbs sampler failed to converge, even after five million iterations. We speculate that observed accuracies in this study trace familial linkage rather than historical LD with trait loci, because of small population size and relatively deep pedigrees. The markers are sampling the haplotypes and thus constructing the pedigrees rather than explaining phenotypic variance. Nevertheless, the results are promising, and we expect that with decreases in genotyping cost, GS has a potential to fundamentally change tree breeding in the near future.2=0.25 within 2000 bp [Despite promising results from some early work based on empirical data, there some challenges to overcome to routinely use GS in tree breeding. Conifers have genome size with a range between 18,000 and 40,000 Mbp . Their p 2000 bp . Low LD Another challenge is the lack of genetic maps in forest trees. With a few exceptions, the genomes of forest trees have not been sequenced, and thus precise locations of SNP markers are lacking, which hinders the use of haplotypes. Using haplotypes reduces the dimensions of the data and thus requires much smaller computing resources to analyze. More importantly, with haplotypes, larger variation between trees can be obtained using allelic combinations, although larger training populations are required to adequately sample the effects of all the haplotypes.High marker genotyping cost is the major obstacle in applications of GS in forest trees. More cost efficient genotyping technologies, such as genotyping-by-sequencing and restriction digestion are being explored to reduce cost of markers. On the other hand, advances in computer power have made it possible to analyze large amount of complex data, but bioinformatics challenges still remain to analyze sequence data and SNP marker calling.Further research is needed in development of training models and calibration of prediction model. The number of generations that statistical models can be used before losing accuracy remains to be determined in forest trees. Another question is the validity of models across different populations. In cattle breeding, lower accuracies of GS for dairy versus beef cattle remains a challenge. For some tree species, GxE interaction could be an issue to be addressed; observed marker-trait association observed in one population may not hold in another environment.We are currently working on construction of realized genomic relationship matrix based on SNP markers to use in predictions of breeding values. This method provides flexibility in terms of fitting common environmental effects in mixed models. We expect that decreases in marker genotyping costs will make GS in pine breeding feasible in the near future. Our group will work on pilot projects with forestry companies in the southern US, and plans are underway to revise breeding strategies to incorporate genomic selection.


Genome-wide association studies have successfully identified numerous loci at which common variants influence disease risks or quantitative traits of interest. Despite these successes, the variants identified by these studies have generally explained only a small fraction of the variations in the phenotype. One explanation may be that many rare variants that are not included in the common genotyping platforms may contribute substantially to the genetic variations of the diseases. Next-generation sequencing, which would better allow for the analysis of rare variants, is now becoming available and affordable; however, the presence of a large number of rare variants challenges the statistical endeavor to stably identify these disease-causing genetic variants. We conduct a genome-wide association study of Genetic Analysis Workshop 17 case-control data produced by the next-generation sequencing technique and propose that collapsing rare variants within each genetic region through a supervised dimension reduction algorithm leads to several macrovariants constructed for rare variants within each genetic region. A simultaneous association of the phenotype to all common variants and macrovariants is undertaken using a linear discriminant analysis using the penalized orthogonal-components regression algorithm. The results suggest that the proposed analysis strategy shows promise but needs further development. Although genome-wide association studies (GWAS) are becoming a powerful tool to discover causal genes of common diseases, it has been hotly debated whether common diseases are caused by common variants or multiple rare variants. Nowadays, more evidence supporting the role of rare variants in disease association  can be found in the literature. Through the advances in next-generation sequencing techniques, it is possible to incorporate rare variants into association studies. In GWAS, the ability to detect an association at a particular single-nucleotide polymorphism (SNP) decreases with the minor allele frequency (MAF) of that SNP; as a result, studies have so far been underpowered to detect associations with rare variants, and so alternative approaches are required.A natural approach is a collapsing strategy in which rare variants within a defined group are collapsed into a single variant. Individually, low-frequency variants are rare, but within aggregates they may be common enough to account for variations in common traits, which is the basic idea behind the collapsing methods . Li and A simultaneous study of the phenotypic association of all common variants and macrovariants will generate robust hypotheses for subsequent biological investigations.p and small n data, as shown by Zhang et al. [With the available common variants and macrovariants, we conduct the genome-wide case-control study by using a linear discriminant analysis (LDA). The LDA is implemented using the penalized orthogonal-components regression (POCRE) algorithm, which sequentially constructs sparsely loaded orthogonal components with proper regularization. The superior performance of the POCRE algorithm in fitting regression models with large g et al. , allows Here, we use the PLS regression, which is a supervised dimension reduction approach, to help collapse the rare variants within each genetic region. Consider the following model for each gene:Y is the phenotype vector and {X1, …, kX} are the genotypes of k rare variants within the gene. The PLS regression is used to find a set of components that are linear combinations of the jX with the constraint that these components explain as much as possible the covariance between Y and X. Cross validation is used to determine the optimal number of components for each gene.where As shown by Zhang et al. , the POCConsider the following multiple linear regression:Y is the phenotype vector of length n, X is an n × p genotype matrix, jβ is the additive effect of that genetic variant, j = 1, …, p, n is the number of individuals, and p is the number of SNPs. We then further assume that Y and X are centered at 0 and that the POCRE algorithm sequentially constructs the orthogonal components i ≥ 2, is iteratively built to be orthogonal to iw, i ≥ 1, is calculated as γ/||γ||, which minimizes:where α|| = 1, where γg(γ) is a penalty function defined by a proper regularization on γ with tuning parameter λ. Zhang et al. [γg(γ).subject to ||g et al.  used empg et al. , to intriY = 1 if individual i is from the case population, and iY = −1 otherwise. Second, the LDA is implemented with the threshold c = 0 by regressing the phenotype vector Y = T against X using the POCRE algorithm. The design matrix X here contains the genotypic values of both common variants and macrovariants constructed by the PLS regression. The tuning parameter λ is elicited by using a testing data set with candidates from 0.8 to 0.9, with a step size of 0.01.In this case-control genome-wide association study, the LDA is implemented with the POCRE algorithm. First, we define To prevent using the same data twice, a process that results in overfitting, we selected one out of 200 phenotype replicates and applied the PLS regression to collapse rare variants to obtain the macrovariants for each gene. We then used results from the PLS regression to analyze another phenotype replicate using the POCRE algorithm. This is not the case in real data analysis, and we suggest taking a traditional approach to splitting the data into training and testing sets, even though we may suffer a reduction in power by reducing sample size. When the sample size is a concern, we recommend using the whole data set twice, the first time for collapsing rare variants and the second time for association study, even though it may magnify the type I error.Finally, we applied the proposed methods to the binary trait in the GAW17 data. All 697 individuals were kept for our analysis after preprocessing the data using PLINK .We used LDA with the POCRE algorithm to analyze each of the 200 replicates, and we report the SNPs and genes that appeared frequently across all 200 replicates. In our association study, we have two types of genetic variants: the SNPs and the macrovariants. If a SNP is found to be significant, it is reported as a significant SNP; alternately, if any macrovariants representing that gene are found to be significant, then a significant gene is reported. The frequency of nonzero estimated effects out of the 200 replicates is calculated for both SNPs and genes.FLT1), C8S890 (PTK2B), and C6S5380 (VNN1). However, we noticed that only C13S523 and C6S5380 are true disease-related SNPs; C13S523 has a moderate MAF (0.066714) and a large effect size (0.64997), whereas C6S5380 has a large MAF (0.170732) but a moderate effect size (0.24437). Surprisingly, SNP C8S890, which is not in the simulation model, guides us to disease gene PTK2B; this finding might be due to the linkage disequilibrium between SNPs within the gene.In Table FLT1, PTK2B, VNN1, and PIK3C3 are the true casual genetic variants along with two significant environmental factors, Age and Smoke. We have noticed that FLT1 is detected twice, once through the common SNP C13S523 and once through the macrovariants constructed by rare variants within the gene.Out of the 200 replicates, a handful of genes found through macrovariants have a high frequency of nonzero estimated effects. Both the genes and the environmental covariates detected in 10 or more replicates are listed in Table PIK3C3 by collapsing rare variants within genes using PLS regression, and the proposed strategy may gain power through collapsing. Even though we had some success in this study, we are still concerned about the possible low power when applying this method. In fact, association studies become even more difficult when most of the causal genetic effects are due to rare variants, especially when some of them are extremely rare variants . Compared to phenotype Q1 and Q2 in the GAW17 data, the binary trait has relatively low effect size, which makes it even more difficult to detect its signals through this research. Therefore more powerful strategies need to be further investigated in order to effectively associate rare variants with binary traits.Using our developed approach for GWAS, we were able to find a few true associations, but our results still suffer from limited power and a high false-positive rate. We detected the disease gene The authors declare that they have no competing interests.MZ and DZ both conceived the study and drafted the manuscript. LW performed statistical analysis and helped to draft the manuscript. VP participated in the design of the study and preprocessing of the data. YL participated in the design of the study. All authors read and approved the final manuscript.


Both family- and population-based samples are used to identify genetic variants associated with phenotypes. Each strategy has demonstrated advantages, but their ability to identify rare variants and genes containing rare variants is unclear. To compare these two study designs in the identification of rare causal variants, we applied various methods to the population- and family-based data simulated by the Genetic Analysis Workshop 17 with knowledge of the simulated model. Our results suggest that different variants can be identified by different study designs. Family-based and population-based study designs can be complementary in the identification of rare causal variants and should be considered in future studies. Missing heritability is a major challenge in the discovery of genetic variants responsible for complex disease . One posBoth family-based and population-based samples have been used to identify variants associated with phenotypes. In recent years, population-based association studies have gained favor because increased power may be obtained ,6. On thIt is not clear how family- and population-based analyses behave on rare variants. By applying various methods to the population- and family-based data simulated by Genetic Analysis Workshop 17 (GAW17), we compared the power of different designs in the identification of rare  causal variants.Two data sets were analyzed . One conWe analyzed the family-based data with a two-point linkage analysis using Sequential Oligogenic Linkage Analysis Routines (SOLAR) 4.10, with identity-by-descent (IBD) matrices from fully informative markers provided by GAW17.iS = ir/in, where in denotes the number of rare variants successfully genotyped for subject i and ir denotes the number of these variants that carry at least one copy of the minor allele. The third method was weighted-sum collapsing. This method assumes an additive allelic effect by recoding the genotypes into 0, 1, or 2 based on the copy number of the minor allele. Then the single-SNP effect for each of the rare nonsynonymous SNPs was examined using univariate regression. For SNPs with significant (α ≤ 0.1) negative effect, the genotypes were converted to 2, 1, and 0 from 0, 1, and 2, respectively. The genetic information of one particular gene was then summarized as the sum of the numeric genotypes of all rare nonsynonymous SNPs on the gene. The gene-Q1 association was then tested using linear regression.For the population-based data, we collapsed single-nucleotide polymorphism (SNP) information on each of the nine Q1 related genes using three methods. The first method was indicator coding, in which genetic information of a particular gene was dichotomized according to the presence or absence of at least one rare nonsynonymous variant. The second method was percent coding, in which genetic information of a particular gene was calculated as In the population-based data, single-SNP association with Q1 was tested using linear regression. In the family-based data, single-SNP association was assessed using a measured genotype approach that compared polygenic models with or without each of the SNPs as a covariate . The quaAnalyses were performed with knowledge of the simulated model.VEGFA and VEGFC genes  to Q1 phenotype was detected in all Q1-related genes, suggestive linkage (LOD ≥ 2) was detected in five genes, and strong linkage (LOD ≥ 3) was detected in only the  to Q1 phFLT1 and KDR showed high power in all three SNP collapsing methods, followed by the VEGFC and VEGFA genes. Power to detect the ARNT, ELAVL4, HIF1A, FLT4, and HIF3A genes was low . In the family-based data, both KDR and FLT1 have five polymorphic causal variants, whereas VEGFA and VEGFC included only a single causal variant each. Based on the expected performance of linkage, one might expect linkage to work better in genes with multiple variants. However, VEGFA and VEGFC show larger effects ; thus the ability to detect the VEGF gene may be more reflective of the effect than of the number of variants. On the other hand, the methods we used to identify gene-Q1 association in the population-based data rely largely on the probability to capture rare variants; thus a higher power for genes with more rare variants (KDR and FLT1) is not surprising.By comparing the identified and unidentified causal genes Tables  and 2, wWhen comparing SNP association and the measured genotype approach, we found that power is related to MAF  that cannot be used for unrelated individuals and that may enrich rare variants, the family-based design may also be valuable for genome-wide SNP scanning for novel causal variants. Population- and family-based designs can be complementary and should both be considered in future genome-wide association studies.The authors declare that there are no competing interests.XZ carried out the design of the study, analyses using the family-based data and drafted the manuscript. HH carried out analyses using the population-based data. LD, TMB and BGK participated in the discussion, and helped to edit the manuscript. LJM conceived of and oversaw the study. All authors read and approved the final manuscript.Power of the association test in population and family-based data Power% is the number of replicates detected divided by the number of replicates analyzed multiplied by 100. The QTDT was performed with 100 replicates; other analyses were performed with 200 replicates. No result was generated by the QTDT for C1S3181 and C4S1890. SNPs with MAF > 0.01 are shaded. na, not applicable.Click here for file