Individuals with type 2 diabetes are at an increased risk of cardiovascular disease. Alterations in circulating lipid levels, total cholesterol (TC), low-density lipoprotein (LDL), high-density lipoprotein (HDL), and triglycerides (TG) are heritable risk factors for cardiovascular disease. Here we conduct a genome-wide association study (GWAS) of common and rare variants to investigate associations with baseline lipid levels in 7,844 individuals with type 2 diabetes from the ACCORD clinical trial.DNA extracted from stored blood samples from ACCORD participants were genotyped using the Affymetrix Axiom Biobank 1 Genotyping Array. After quality control and genotype imputation, association of common genetic variants (CV), defined as minor allele frequency (MAF) ≥ 3%, with baseline levels of TC, LDL, HDL, and TG was tested using a linear model. Rare variant (RV) associations (MAF < 3%) were conducted using a suite of methods that collapse multiple RV within individual genes.p < 1 × 10−8) replicate findings in large meta-analyses in non-diabetic subjects. RV analyses also confirmed findings in other studies, whereas significant RV associations with CNOT2, HPN-AS1, and SIRPD appear to be novel (q < 0.1).Many statistically significant CV (p < 1 × 10−8) associations of CV with lipid levels in 11 genes or chromosomal regions, all of which were previously identified in meta-analyses of mostly non-diabetic cohorts. We also identified 13 associations in 11 genes based on RV, several of which represent novel findings.Here we present findings for the largest GWAS of lipid levels in people with type 2 diabetes to date. We identified 17 statistically significant ( Cardiovascular diseases (CVD) remain the leading cause of death worldwide . IndividThe Action to Control Cardiovascular Risk in Diabetes (ACCORD) clinical trial was designed to be the definitive clinical trial comparing the risks and benefits of treatment strategies targeting normal glycemic levels, normal blood pressure and intensively managing dyslipidemia with combined statin-fenofibrate therapy versus strategies with standard targets and approaches in patients with type 2 diabetes at high risk for CVD  The clinHere we test >8 million common genetic variants, defined as minor allele frequency (MAF) ≥ 3%, and rare genetic variants (MAF < 3%) covering 16,538 genes in 7,844 subjects with type 2 diabetes. Although large-scale meta-analyses incorporating multiple cohorts of both healthy subjects and subjects with a variety of cardiovascular and metabolic diseases have already identified more than 150 loci affecting blood lipids , the anahttps://clinicaltrials.gov/ct2/show/NCT00000620) had a double 2 × 2 factorial design, consisting of 10,251 recruited subjects with type 2 diabetes mellitus and either a history of cardiovascular disease (CVD) or at least two known risk factors for cardiovascular disease, such as documented atherosclerosis, albuminuria, dyslipidemia, hypertension, smoking, or obesity  were included as controls on each plate. Amplification, fragmentation, and hybridization of DNA to Axiom Biobank 1 genotyping arrays  were carried out using Axiom Reagent Kits, and hybridization, ligation, washing, staining and scanning of the arrays were carried out on the GeneTitan MC instrument (Affymetrix). Initial plate QC was performed using Affymetrix Genotyping Console Software and genotype calling was done using Affymetrix Power Tools (v1.15.0) with the Axiom GT1 algorithm, which is a modified version of the BRLMM-P algorithm that adapts generic prior cluster positions to the data using an EM algorithm.http://www.ncbi.nlm.nih.gov/dbgap).The Axiom Biobank Genotyping Array from Affymetrix includes ∼246,000 common genetic variants selected to optimize genome-wide coverage for association in addition to ∼335,000 variants focused on the coding portion of the genome, and including non-synonymous, frameshift, indel and splice variants as well as other known loss-of-function and disease causing mutations. Most of this second group of variants was identified by exome sequencing in up to 26,000 individuals, and the majority of them are uncommon or rare. Additional variants to cover known eQTLs and pharmacogenomics markers are also included on the array. A total of 628,679 probes were genotyped. After genotype quality control, genotypes were available for 583,613 variants, of which 89,212 were monomorphic. After imputation based on 1,000 genomes haplotype data, an additional 26,862,499 imputed variants with an “info” metric > 0.5 were retained for association testing. The genotype information is available in dbGaP  in at least two of the four main ethnic subgroups were excluded from the imputation process. Values of the cleaned probe set for white samples are shown in Genotypes were subjected to rigorous quality control based on genotyping quality metrics, duplicate concordance, Mendelian segregation (in HapMap trios included on the genotyping plates), Hardy–Weinberg Equilibrium, and predicted gender see . Cryptic: 1,485) . Princip: 1,485) . The fir: 1,485) . Both stAll samples were pre-phased together since this approach was previously found to improve phasing in a cohort with diverse ancestries compared to phasing groups separately . The impr =  − 0.77), systolic and diastolic blood pressure were positively correlated (r = 0.53) and BMI and waist circumference were positively correlated (r = 0.63). See Here, we take a combined approach to variable selection to address potential confounding variables. Some covariates are forced into the model based on the results of previous studies or on expert knowledge related to the phenotype, while variable selection, via backwards selection, is subsequently performed on candidate variables to identify covariates specific to the ACCORD dataset. Covariate names and descriptions can be found in Tables S3 and S4. A substantial proportion of the cohort was taking lipid lowering medications at the time baseline lipid measurments were taken . Lipid lowering concomitant medications were forced into the model to prevent confounding of the baseline lipid measurements. The percentage of the cohort on each of these lipid lowering medications is in The phenotypic variation explained by genome-wide variants is estimated using the software tool genome-wide complex trait analysis  . An estiy is the phenotype, α0 is the intercept, X are the covariates, α are the covariate regression parameters, βg is the regression parameter for the variant, g is the additively coded genotype and ϵ is the error term. Genotyped variants are tested using PLINK, where ith individual. Imputed variants are tested using a linear regression model in the statistical programming language, R, where Aa and aa  into a single variable, which is then tested for association with a phenotype. However, a major limitation of simple burden tests is that they cannot account for the possible direction (positive or negative association) of a rare variant effect . One nona priori that can easily be computed from genotype data. More sophisticated approaches can incorporate variant-specific information and variable thresholds for collapsing. Three burden tests are used here and are based on simple collapsing approaches. These methods first create a collapse score, c, and then test for association using the linear regression model y is the phenotype, α0 is the intercept, X are covariates, α are the covariate regression parameters, βc is the regression parameter for the collapse score and ϵ is the error term. Association p-values are computed under the null hypothesis H0:βc = 0. The selected burden tests differ in how c is computed.Simple collapsing methods use indicator, proportion and weighted approaches chosen ci is simply an indicator function The first two tests are based on RVT1 and RVT2 originally proposed by l method . While bl method . While Sl method . AdditioHere we use both SKAT and SKAT-O in addition to the three burden tests mentioned above. Only those variants <3% MAF were included in the rare variant approaches. The non-burden approaches were implemented using the R package “SKAT” (v0.95) .p values, one for each rare variant test. This complication can be resolved by combining the set of p-values into a single p-value for each gene, while accounting for the dependence of p-values using the “correlated Lancaster procedure” described by Dai et al. to combine the p-values from each test into a single p-value for each gene    approachach gene . Combiniv1.36.0) . AdditioAfter all sample quality control steps a total of 7,844 individuals were included in the association analysis for TC (mg/dL), LDL (mg/dL), HDL (mg/dL) and TG (mg/dL) phenotypes. Heritability for each phenotype was approximated using the set of genotyped variants to construct the genetic relationship matrix (GRM). The phenotype, pruned covariates and GRM were used by GCTA to compute an approximate heritability of 11.7%, 11.3%, 43.7% and 14.0% for TC, LDL, HDL and TG, respectively.p-values versus genomic location for each of the phenotypes are shown in All common genotyped and imputed variants were tested individually for association using PLINK or a linear model in the statistical programing language, R, respectively. A set of LD pruned (VIF < 1.5), genotyped probes was used to compute genomic inflation values for different MAF thresholds, as shown in p < 1 × 10−8) were observed in the TC association. The lead markers in these regions are located 109.82 Mb on Chr1, 126.5 Mb on Chr8, and 45.41 Mb on Chr 19  is not in HWE (p < 1 × 10−5) in all populations combined. These lead SNPs are in the LPL, LIPC, CETP, LIPG, and APOE genes, respectively (rs6982502) on Chr 8 was significantly out of HWE (p < 1 × 10−5) in all populations combined. These SNPs are located in the ANGPTL3, GCKR, MLXIPL, LPL, TRIB1, ZNF259, and APOE genes, respectively  and a MAF < 3% were considered for incorporation into the gene-based, rare variant analysis. After QC, a total of 16,480 genes contained at least two variants below the MAF threshold. In total, 146,689 genotyped and 73,295 imputed variants went into the analysis, with median of nine variants per gene. Mean minor allele frequencies for all the rare variants in an individual gene ranged from 6.37e–05 to 2.53e–02. The suite of three burden and two nonburden tests were applied and the resulting q < 0.1), with the number of rare variants in these genes ranging from two to 22  significantly associated with lipid concentrations.p < 5 × 10−8) were found, which included all 36 loci previously reported in GWASs at the time and 59 novel loci. An expanded study was performed on ∼189,000 individuals, primarily of European ancestry, in a 2013 meta-analysis conducted by p < 0.05) with the same phenotypes in ACCORD.Several large meta-analyses have previously investigated genetic variants associated with lipid levels. For example, Some cohorts included in these and other large-scale meta-analyses included subjects with type 2 diabetes, but these only represent a small proportion of the overall subjects studied. One early GWAS comprised of approximately half individuals with type 2 diabetes and half matched controls from Finland and Sweden tested associations with LDL, HDL and TG in ∼2,600 subjects . Associap-value for each peak on the corresponding Manhattan plot  was the only gene found to be associated with LDL in the rare variant analysis, and associations with this gene and LDL levels have been previously reported in PCSK9 to lower LDL have been a high priority in the pharmaceutical industry, and based on promising results in clinical trials, the first drug targeting PCSK9 (Evolocumab) was recently recommended for expedited approval by the US Food and Drug Administration  was significantly associated with an increase in HDL (q = 0.085). HNF1B encodes the transcription factor (HNF1B) that regulates a wide range of target genes and is involved in several pathologies including cancer, renal cysts and diabetes syndrome, an early onset form of diabetes (HNF1B-MODY), impaired glucose metabolism, venous thrombosis, and several others . HDL is higher in blacks than whites overall, so despite efforts to control for population stratification by incorporating PCs as covariates in the analysis, it appears that the apparent association of HNF1B with HDL levels in all subjects combined may be due to confounding by population admixture. Additional research is needed to better understand the role of HNF1B and the other novel associations presented here. Although many genetic associations presented here are similar to previous findings in cohorts not focused on diabetes, these findings shed new light on the relationship of dyslipidemia in both individuals with and without type 2 diabetes and the novel findings presented here may indicate new biomarkers or therapeutic targets to better regulate alterations in lipid levels in high-risk, populations with type 2 diabetes.The individuals in the ACCORD trial have type 2 diabetes and are also at a high risk of CVD; however, many of the significant associations observed here have been previously reported in the literature, indicating that many of the genetic contributions to dyslipidemia are similar between these individuals and individuals without type 2 diabetes. In contrast, the rare-variant analysis produced four significantly associated genes that, to our knowledge, have not been previously reported for either HDL or TG. l others . However10.7717/peerj.3187/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj.3187/supp-2File S1Click here for additional data file.


The prediction error estimated from the optimized threshold may also be subject to an optimistic bias. To improve genomic risk prediction, we proposed new empirical Bayes approaches to recover the underlying effect sizes and used them as weights to construct PRS. We applied the new PRS to twelve cardio-metabolic traits in the Northern Finland Birth Cohort and demonstrated improvements in predictive power (in R2) when compared to standard PRS at the best p-value threshold. Importantly, for eleven out of the twelve traits studied, the predictive performance from the entire set of genome-wide markers outperformed the best R2 from standard PRS at optimal p-value thresholds. Our proposed methodology essentially enables an automatic PRS weighting scheme without the need of choosing tuning parameters. The new method also performed satisfactorily in simulations. It is computationally simple and does not require assumptions on the effect size distributions.Polygenic risk scores (PRS) from genome-wide association studies (GWAS) are increasingly used to predict disease risks. However some included variants could be false positives and the raw estimates of effect sizes from them may be subject to selection bias. In addition, the standard PRS approach requires testing over a range of  Traditionally, for complex diseases with substantial heritability, the prediction of disease risk has been largely based on family history and clinical risk factors. However, with the advent in genotyping technologies, an increasing number of susceptibility variants for complex diseases have been identified. In particular, genome-wide association studies (GWAS), which allow interrogation of more than a million single nucleotide polymorphisms (SNPs) in the genome, has become a very popular and useful tool in deciphering the genetic basis of complex diseases1Polygenic risk scores (PRS) are usually constructed as a weighted sum of allele counts, the weights being given by log odds ratios or linear regression coefficients from univariate regression tests. A simpler approach by weighting each marker by +1 or −1 is also possibleet al.67Traditionally only the top established variants are considered in risk prediction. However, variants with smaller effects may also aid prediction. Purcell et al. proposed a new way of constructing PRS by weighing the estimated effect sizes with the local true discovery ratep-value threshold.To our knowledge, only two previous studies focused on how to improve genomic risk prediction from summary statistics. A Bayesian genomic risk prediction method known as LDpredet al.not require any distributional assumptions of effect sizes. Moreover, both the standard PRS and LDpred necessitate a tuning parameter to be chosen, and require testing over a range of p-value thresholds or fractions of causal variants. The choice of such thresholds is usually arbitrary, and the predictive performance estimated from the optimized threshold may be subject to an optimistic bias. It is therefore desirable to develop a new PRS weighting method such that all markers can potentially be included in the prediction model, obviating the choice of any thresholds. As we will describe later, for 11 out of 12 actual disease traits studied, the predictive performances of our new approach with the entire set of genome-wide markers outperformed the best R2 from standard PRS at the optimal p-value thresholds, which are not known in advance. We also showed that our approach outperformed Mak et al.’s method in actual GWAS datasets.In this study we proposed a different PRS weighting scheme compared to LDpredPolygenic risk scores are usually constructed from a weighted sum of allelic count allelic counts. Without loss of generality, we assume the allelic counts have been standardized, and the PRS can be given by r2 threshold of 0.25 to all SNPs, followed by p-value thresholding in the test set.In practice, due to the presence of linkage disequilibrium (LD) between genetic markers, markers are usually LD-pruned before construction of PRS. It is common to include variable selection in the pruning procedure, such that the more significant makers are preferentially retained. This kind of algorithm is implemented in PLINK, also known as “LD-clumping”. In this study, for standard and the three other PRS weighting methods, we first applied LD-clumping with an true” z-statistic  from a set of observed z-statistics. The z-statistics can then be converted to variance in liability (or heritability) explained as described in So et al.Assume that a GWAS or meta-analysis of GWAS was done and we tested the association of each variant with the phenotype by a regression analysis. We formulated the problem as recovering the “z-statistics are denoted by z. We assume thatIt is useful to consider the following model for our problem. The observed δ is the underlying true effect size. δ = 0 for null variants and is non-zero for the truly associated variants.where δ:Efronf(x) is the is probability density function of x. The same formula was discovered by Tweedie in 1950 s, hence also named the Tweedie’s formulaf(x) as described in So et al.K is given bywhere h is the bandwidth or smoothing parameter. The computation was performed using the R function “density”, with the default settings using a Gaussian kernel. An important advantage of the Tweedie’s formula is that it only involves estimation of the marginal density f(x), hence avoiding the need to derive the distributions of z-statistics under H0 and H1. This approach does not require any particular choice of the prior distribution of δ.where βi 11where The Tweedie’s formula shrinks effect size estimates towards zero, but unlike some other procedures such as LASSOfdr is the local false discovery ratez-statistic. (1-fdr) is hence the local true discovery rate. This method weighs each effect size estimate from Tweedie’s formula by the probability of being non-null. In practice, it will further shrink effect sizes towards zero and a portion of the effect sizes will become zero, as the local fdr equal one for some markers.where et al.10We also include another estimator that was recently developed by Mak locfdr, an R package based on the methodology described by Efronlocfdr algorithm failed to converge in the presence of more extreme z-statistics. We hence assumed a local fdr of zero for genetic variants with p-value of 1.97 × 10−9). For simplicity, we will also use in which the regression coefficients are weighted by the local true discovery rates. For the estimation of fdr, we employed Following the previous derivations, we wish to test if PRS directly constructed from the corrected effect size estimates improve prediction. The new PRS can be expressed as M is the total number of markers and h2 is the total heritability explained by the panel markers. The algorithm also allows for a non-infinitesimal model, in which only a fraction p of all makers are causal. A Gaussian mixture prior is assumed in this case in which p and p).LDpred is a recently developed algorithm which takes into account the LD among genetic markers for polygenic risk prediction. The effects of markers are assumed to follow a Gaussian distribution. In an infinitesimal model, all markers are assumed to be causal and the marker effects follow the distribution p. An approximate MCMC Gibbs sampler is used to estimate the posterior mean for the non-infinitesimal case while an analytic solution is available for the infinitesimal case. In this study, we followed all the recommended parameters set by the authors of LDpred. The LDpred program was downloaded from https://github.com/bvilhjal/ldpred.LDpred computes the posterior mean effects of markers, taking into account the LD structure. The effect sizes can be computed for different proportion of causal markers M is the total number of causal markers. Liability  was simulated as x denotes the standardized genotype counts. To reduce memory and computational costs, the prevalence was set at 0.45 with people exceeding the liability threshold assuming to be affected. An equal number of cases and controls were then sampled.We first performed simulations with independent SNPs. A liability threshold model was assumed in the simulations. A panel of 20,000 independent SNPs was simulated, and 2.5% of the SNPs were set to be causal. The total heritabilities explained were set at 0.15, 0.35 or 0.55. The training sample sizes were set at 5000, 10000, 15000 or 20000 respectively. The test sets were of equal size to the train sets. We assumed a minor allele frequency (MAF) of at least 0.05 and uniform MAF. The true regression coefficients were assumed to follow a normal distribution with mean zero and variance equal to the average heritability per marker, i.e. PRS were computed from the training set, using the uncorrected and each of the corrected coefficient estimates (3), (4) and (5). Predictive performances were assessed in the testing set in terms of prediction R-squared and area under the receiver operating characteristic curve (AUC). Simulations were repeated for 20 times.p < 1e-5) were excluded. Individuals with genotyping rates <90% are excluded from analyses. In each training set, linear regression was carried out with the top 10 principal components as covariates. After quality control procedures, 334458 variants and 5402 individuals were retained for further analyses.Next we performed larger scale simulations using real genotype data. Raw genotype data was obtained from a GWAS of cardio-metabolic traits from the Northern Finland Birth Cohort (NFBC) 1966h2 was set at 0.1, 0.2, 0.3 or 0.4. This model matches exactly with the prior assumed in LDpred when all markers are causal.An infinitesimal model. All markers were assumed to be causal. The effect sizes were simulated by A model with only a limited number of large-effect variants. We simulated 5, 10, 20, and 25 large-effect markers each with heritability explained = 0.6%. All other markers were null.A model in which both small and larger effects were present. Two sets of casual varaints were simulated and then combined as described below.We simulated phenotypes under three gross categories of genetic architecture:i.e. Laplace) model by μ and b are the location and scale parameters respectively. Different fractions of causal markers  were assumed. The effects θ were further scaled by N denotes the corresponding number of variants. This is to ensure that the total variance explained summed up to the desired level of heritability.The first set of causal variants were simulated under a double exponential  was used as the reference LD panel.Prediction was performed using the standard PRS, three other corrected effect size estimates [p-value thresholds at 1e-5, 1e-4, 5e-4, 1e-3, 5e-3, 1e-2, 0.03, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.For methods other than LDpred, we performed LD-clumping using the following PLINK command: –clump-p1 1 –clump-p2 1 –clump-r2 0.25 –clump-kb 250. Note that the algorithm preferentially selects the most significant markers. On average around 110,000 variants were retained after clumping. We set We employed 5-fold cross-validation (CV) to estimate the predictive performance of polygenic scores, using the uncorrected and corrected effect size estimates. Summary statistics were derived from the train sets. Cross-validation was repeated 4 times, producing a total of 20 pairs of train sets and test sets.We also applied the five different PRS weighting methods to twelve anthropometric and metabolic traits in the NFBC. The traits included triglycerides (TG), high-density lipoprotein (HDL), low-density lipoprotein (LDL), insulin (INS), glucose (FG), C-reactive protein (CRP), body mass index (BMI), waist-hip ratio (WHR), systolic blood pressure (SBP), diastolic blood pressure (DBP) and body height and weight. Five-fold CV (repeated 4 times) was used to assess predictive performance of different polygenic scoring methods.https://sites.google.com/site/honcheongso/).Quality control and basic GWAS association analyses were performed using PLINK 1.9p-value threshold, The results of simulations with independent SNPs are shown in When all the SNPs were included in the PRS, all three estimators performed very well and they outperformed the standard PRS method by a large margin. In addition, their performances were highly comparable to and sometimes outperformed the standard PRS at the optimal thresholds .h2 = 0.1. Interestingly, p , LDpred slightly outperformed the other methods when the number of causal variants  was 5, 15 or 20. Nevertheless, other methods especially Ncausual was 10. However, when we consider prediction from all markers, Ncausual.Under another model in which only few large-effect variants were present, the predictive performances of the five methods considered were much closer . When cop thresholds, there is no clear winner across all scenarios. However, compared to the standard PRS, methods using corrected effect sizes , R2 at the optimal p threshold.The third type of genetic architecture involves a mixture of variants with small and larger effects, and is probably a more realistic model. If we consider the predictive performance at the optimal d better . When thR2 from 5 × 4 CV are shown in R2 improved from 1.23% to 1.82%  but generally better at higher h2. A likely explanation is that the effect sizes may be too small in relation to the sampling error of the PRS at low heritability levels. As LDpred includes all markers in prediction, the sampling error may be larger than the pruned PRS derived from fewer markers.We then simulated a wider range of genetic architecture with real genotype data. As expected, LDpred performed well under an infinitesimal model with a matching Gaussian prior. The empirical Bayes methods may over-correct the effect sizes under a non-sparse scenario, leading to worse performances. Under another model where there were only a few large effects, all correction methods outperformed standard PRS and the results were quite close. Nevertheless these two kinds of genetic architecture might be less likely than a mixture of small and larger effects. Under this third model, we observed mixed results of different estimators. LDpred tends to perform worse at lower levels of heritability  which are associated with HLA variants. Multiple large-effect variants in LD are likely to be present within the HLA region for these diseases. For other traits, there may not be multiple strong effects within a LD region; hence the improvement by joint modeling may be less marked.A recent study by Dudbridge et al.The applications of the PRS methodologies to actual cardio-metabolic traits showed superior performances of It is also noteworthy that for methods that rely on an external LD reference panel, there is a certain level of approximation which may affect the predictive performance. In this study, the LD reference data was derived from the original sample by CV, hence LD mismatch should not be a problem; however it may not be true for other studies using other reference datasets. LD pruning or clumping methods may be advantageous when there is insufficient sample size to derive a reference LD matrix, because inaccurate LD information may degrade the performance of LD-dependent methods. For example, authors of LDpred suggest the reference panel should contain at least 1000 unrelated individuals with the same ancestry make-up as the people from which the summary statistics are derived. This may not always be feasible depending on the population under study. In addition, it may be difficult to find genotype data that matches very well with the LD pattern of the original study population (from which summary statistics are derived). In spite of the above arguments, joint modelling methods such as LDpred may become more useful when sample sizes of studies continue to rise. Our proposed methodology does not fully account for LD, and may be improved by modelling LD structure for the whole panel of markers.p-value thresholds, and essentially a single threshold of one can be chosen. In other words, the new estimator p-value thresholds or fraction of causal variants). This is a unique feature among all PRS weighting methods.A remarkable feature we wish to highlight is that the predictive performance of the empirical Bayes method not require the choice of tuning parameters? Firstly, it avoids a potential bias in the estimation of the true prediction errors. Varma and Simonp; the same approach was taken in the study on LDpredet al.e.g. to assess if a PRS can be used in clinical practice to predict future disease risks), then this potential bias should preferably be corrected by a nested CV or estimating the prediction error in an independent sample. The former however is not possible if only summary statistics are available while the latter may not be practical if the study involves an uncommon disease phenotype or treatment side effect for example. Designating a portion of the testing sample for tuning will impair the precision of prediction error estimates. Clearly an automatic PRS weighting scheme avoids the above complications. Essentially such a weighting scheme saves a portion of the sample size that is required for parameter tuning.What are the advantages for having a method that does p thresholds is usually arbitrary. A diligent search across many thresholds will increase computational cost while the optimal threshold may be missed if too few thresholds are tried. When only summary statistics are available, the automatic weighting scheme is also directly applicable to a single new patient. This is not true for the other methods in general as parameter tuning requires a certain sample size. While one can choose a pre-determined threshold, using an non-optimized threshold might lead to inferior predictive performance.The second advantage is that computational load can be reduced when no parameters need to be tuned. Also, the choice of Another important feature of the proposed methodology is that it is computationally simple and conceptually relatively straightforward. Compared to LDpred, it does not require MCMC procedures. As only summary statistics are required, it can be readily applied to a wide variety of traits and take advantage of the large sample sizes in GWAS meta-analyses. The empirical Bayes approach also does not require any particular priors to be specified or assumptions about the genetic architecture of the trait, such as the proportion of causal markers or distribution of effect sizes. On the other hand, LDpred requires the assumption of a point-normal mixture prior.p-value threshold. Nevertheless, for fasting insulin, which has a very low prediction R2, the performance of The key limitation of our proposed methodology, as already discussed earlier, is that we do not fully account for the LD structure of all markers. It is also worth mentioning that if raw genotype data is available, other methods such as those based on a mixed effects modelsIn summary, we have developed a new empirical Bayes framework to improve risk prediction from polygenic scores, using summary statistics. We hope the presented methodology will be a useful new way to improve genomic risk prediction, with the potential for translation to better personalized medical care in the future.How to cite this article: So, H.-C. and Sham, P. C. Improving polygenic risk prediction from summary statistics by an empirical Bayes approach. Sci. Rep.7, 41262; doi: 10.1038/srep41262 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Methods for inference and interpretation of evolutionary quantitative genetic parameters, and for prediction of the response to selection, are best developed for traits with normal distributions. Many traits of evolutionary interest, including many life history and behavioral traits, have inherently nonnormal distributions. The generalized linear mixed model (GLMM) framework has become a widely used tool for estimating quantitative genetic parameters for nonnormal traits. However, whereas GLMMs provide inference on a statistically convenient latent scale, it is often desirable to express quantitative genetic parameters on the scale upon which traits are measured. The parameters of fitted GLMMs, despite being on a latent scale, fully determine all quantities of potential interest on the scale on which traits are expressed. We provide expressions for deriving each of such quantities, including population means, phenotypic (co)variances, variance components including additive genetic (co)variances, and parameters such as heritability. We demonstrate that fixed effects have a strong impact on those parameters and show how to deal with this by averaging or integrating over fixed effects. The expressions require integration of quantities determined by the link function, over distributions of latent values. In general cases, the required integrals must be solved numerically, but efficient methods are available and we provide an implementation in an R package, QGglmm. We show that known formulas for quantities such as heritability of traits with binomial and Poisson distributions are special cases of our expressions. Additionally, we show how fitted GLMM can be incorporated into existing methods for predicting evolutionary trajectories. We demonstrate the accuracy of the resulting method for evolutionary prediction by simulation and apply our approach to data from a wild pedigreed vertebrate population. Comprehensive systems for estimating genetic parameters and predicting evolutionary trajectories of non-Gaussian traits will hence be very useful for quantitative genetic studies of adaptation.ADDITIVE genetic variances and covariances of phenotypic traits determine the response to selection and so are key determinants of the processes of adaptation in response to natural selection and of genetic improvement in response to artificial selection  is very ribution ]. Furtheribution . Conseque.g., et al. 2013; Villemereuil et al. 2013). Whereas LMM analysis directly estimates additive genetic parameters on the scale on which traits are expressed and selected, and upon which we may most naturally consider their evolution, this is not the case for GLMMs. In this article, we offer a comprehensive description of the assumptions of GLMMs and their consequences in terms of quantitative genetics and a framework to infer quantitative genetic parameters from GLMMs output. This work applies and extends theory in For the analysis of Gaussian traits, linear mixed model (LMM)-based inferences of genetic parameters, using the “animal model,” have become common practice in animal and plant breeding , but alsWhile it will undoubtedly be desirable to develop a comprehensive method for making data-scale inferences of quantitative genetic parameters with GLMMs, such an endeavor will not yield a system for predicting evolution in response to natural or artificial selection, even if a particular empirical system is very well served by the assumptions of a GLMM. This is because systems for evolutionary prediction, specifically the breeder’s equation  and the Ovis aries) and how our framework can help to overcome them. Fourth, we outline a system of evolutionary prediction for non-Gaussian traits that capitalizes on the fact that the latent scale in a GLMM satisfies the assumptions of available equations for the prediction of evolution. We show in a simulation study that (i) evolutionary predictions using additive genetic variances on the observed data scale represent approximations and can, in fact, give substantial errors, and (ii) making inferences via the latent scale provides unbiased predictions, insofar as a GLMM may provide a pragmatic model of variation in non-Gaussian traits. The framework introduced here (including both quantitative genetic parameter inference and evolutionary prediction) has been implemented in an R package  LMM and especially to the Gaussian animal model , residual variation may include both inherently stochastic components and components that correspond to unmodeled systematic differences among observations. In an LMM, such differences are not distinguished, but contribute to residual variance. However, for many non-Gaussian traits it may be desirable to treat the former as arising from some known statistical distribution, such as the binomial or Poisson distribution, and to deal with additional variation via a latent-scale residual . Separation of these two kinds of variation in residuals may be very generally useful in evolutionary quantitative genetic studies.In addition to inherent nonadditivity, many non-Gaussian traits will have complex patterns of variation. Over and above sources of variation that can be modeled with fixed and random effects, as in an LMM  is required to model the “noise” of observed values around the expected value , but this intrinsic value can be studied only through random realizations. As we will see, because breeding values are intrinsic individual values, the additive genetic variance is the same for both scales, but, due to the added noise in observed data, the heritabilities are not. The choice of which scale to calculate heritability depends on the underlying biological question. For example, individuals  might have an intrinsic annual reproductive success of 3.4, but can produce only an integer number of offspring each year : Heritabilities of both intrinsic expectations and observed numbers can be computed, but their values and interpretations will differ.The distinction we make between the expected and observed data scales is one of convenience as they are not different scales i.e., combinations of link functions and distribution functions): for a binomial model with a probit link function [i.e., the “threshold model”  were included in the GLMM model.i.e., applying to both the mean expected value and the mean observed value) is given byμ and variance The expected mean phenotype Phenotypic variance on the expected data scale can be obtained analogously to the data scale population mean. Having obtained v,Phenotypic variance of observed values is the sum of the variance in expected values and variance arising from the distribution function. Since these variances are independent by construction in a GLMM, they can be summed. This distribution variance is influenced by the latent trait value, but might also depend on additional distribution parameters included in a, i.e., its genotypic value on the data scales Because the link function is nonlinear, additive genetic variance on the latent scale is manifested as a combination of additive and nonadditive variance on the data scales. Following i.e., z that depends linearly on the latent breeding values. The breeding values on the data scale can then be defined as the predictions of a least-squares regression of the observed data on the latent breeding values,z predicted by the regression, a is the latent breeding value, and m and b are the parameters of the regression. Thus, we have z [i.e., the expected data scale X and Y are bivariate normally distributed random variables, then the covariance of Y and some function of X, X and Y, sob as other forms of regression coefficients, and for consistency with The additive variance on the data scales is the variance of breeding values computed on the data scales. Following , breedini.e., directly based on GLMM assumptions).Because of the nonlinearity introduced by the link function in a GLMM, all quantitative genetic parameters are directly influenced by the presence of fixed effects. Hence, when fixed effects are included in the model, it will often be important to marginalize over them to compute accurate population parameters. There are different approaches to do so. We first describe the simplest approach  and others are not . In such cases it may be desirable to integrate over those fixed effects that are biologically interesting and fix others at some sensible value . From this estimate of In a GLMM, no assumption is made about the distribution of covariates in the fixed effects. Given this, we can marginalize over fixed effects by averaging over predicted values  may be useful. A first approach is to predict values according to a new set of covariates constructed to be representative of the population . Given these new predicted values, the above approach can readily be used to compute quantitative genetic parameters of interest. A drawback of this approach is that it requires one to create a finite sample of predicted values instead of a full distribution of the covariates. A second approach requires one to specify such a distribution for fixed covariates, here noted The distribution of covariate values in i.e., Equations 5–16 give the values of different parameters that are useful for deriving other evolutionary quantitative genetic parameters on the observed data scale. Hence, from them, other parameters can be computed. The narrow-sense heritability on the observed data scale can be written asvability  can be jFigure S1). However, it can be shown  that a GLMM with a binomial distribution and a probit-link function is exactly equivalent to such a model, only with slightly differently defined scales. For threshold models, heritability can be computed on this liability scale by adding a so-called “link variance” Heritabilities of binary traits have a long history of analysis with a threshold model , wherebyp is the probability of occurrence of the minor phenotype and t is the density of a standard normal distribution at the pth quantile  that this formula is an exact analytical solution to Equations 5–21 in the case of a GLMM with binomial distribution and a probit link. When fixed effects are included in the model, it is still possible to use these formulas by integration over the marginalized predictions . Note that Equation 25 applies only to analyses conducted with a probit link; it does not apply to a binomial model with a logit-link function.When the heritability is computed using the threshold model, see also . It can λ is the data scale phenotypic mean, computed analytically asFile S1, section B) that these formulas are exact solutions to Equation 5–21 when assuming a Poisson distribution with a log link. The inclusion of fixed effects in the model makes the expression slightly more complicated . These results can also be extended to the negative-binomial distribution with log link with slight modifications of the analytical expressions .For a log-link function and a Poisson distribution, both the derivative of the inverse link function and the variance of the distribution are equal to the expected value. Consequently, analytical results are obtainable for a log/Poisson model for quantities such as broad- and narrow-sense heritabilities. i.e., repeatability) for this kind of model , they should be added to The component of the broad-sense heritability on the observed data scale that arises from additive genetic effects on the latent scale can be computed as an intraclass correlation coefficient (of model :Hobs2=V(O. aries) lambs on St. Kilda, Outer Hebrides, Scotland. We analyzed records of 3814 individuals born between 1985 and 2001 that are known to either have died in their first year, defined operationally as having died before the first of April in the year following their birth, or have survived beyond their first year. Months of mortality for sheep of all ages are generally known from direct observation, and day of mortality is typically known. Furthermore, every lamb included in this analysis had a known sex and twin status (whether or not it had a twin) and a mother of a known age.We modeled the first-year survival of Soay sheep  lamb with an average-aged (4.8 years) mother. Males have lower survival than females, and twins have lower survival than singletons. There were also substantial effects of maternal age, corresponding to a rapid increase in lamb survival with maternal age among relatively young mothers and a negative curvature, such that the maximum survival probabilities occur among offspring of mothers aged 6 or 7 years. The trajectories of maternal age effects in the cubic model are similar to those obtained when maternal age is fitted as a multilevel effect.We identified important effects on individual survival probability; variance . The modTo illustrate the consequences of accounting for different fixed effects on expected and observed data scale inferences, we calculated several parameters under a series of different treatments of the latent scale parameters of the GLMM. We calculated the phenotypic mean, the additive genetic variance, the total variance of expected values, the total variance of observed values, and the heritability of survival on the expected and observed scales.μ in Equations 1 and 3a). This intercept, under default settings, is arbitrarily defined by the linear modeling software implementation and is thus software dependent. In the current case, due to the details of how the data were coded, the intercept is the latent scale prediction for female singletons with average-aged (4.8 years) mothers. In an average year, singleton females with average-aged mothers have a probability of survival of ∼80%. The additive genetic variance First, we calculated parameters using only the model intercept  intercept, corresponding to twin males, we would obtain a mean survival rate of 0.37 and an additive genetic variance that is approximately twice as large, but similar heritabilities . Note thi.e., no difference in explained variance): female singletons vs. male twins, in both cases, assuming focal groups of individuals are all born to average-aged mothers. Again these differences in phenotypic variances and heritabilities arise from differences in intercepts, not from any differences in variance explained by fixed effects. All parameters on the expected and observed value scales are dependent on the intercept, including the mean, the additive genetic variance, and the total variance generated from random effects. Heritability is modestly affected by the intercept, because additive genetic and total variances are similarly, but not identically, influenced by the model intercept.This first comparison has illustrated a major way in which the fixed effects in a GLMM influence inferences on the expected and observed data scales. For linear mixed models, it has been noted that variance in the response is explained by the fixed predictors and that this may inappropriately reduce the phenotypic variance and inflate heritability estimates for some purposes . HoweverAdditive genetic effects are those arising from the average effect of alleles on phenotype, integrated over all background genetic and environmental circumstances in which alternate alleles might occur. Fixed effects, where they represent biologically relevant variation, are part of this background. Following our framework (see Equation 17), we can solve the issue of the influence of the intercept by integrating our calculation of Given this, which estimates should be reported or interpreted? We have seen that when fixed effects are included in a GLMM, the quantitative genetic parameters calculated without integration are sensitive to an arbitrary parameter: the intercept. Hence integration over fixed effects may often be the best strategy for obtaining parameters that are not arbitrary. In the case of survival analyzed here, The data analyzed  in this example are archived and available via the following DOI: 10.17605/OSF.IO/SCZPR.Systems for predicting adaptive evolution in response to phenotypic selection assume that the distribution of breeding values is multivariate normal and, in most applications, that the joint distribution of phenotypes and breeding values is multivariate normal . The disμ (from 0 to 3). We simulated 10,000 replicates of each scenario, each composed of a different array of 10,000 individuals. For each simulation, we simulated 10,000 offspring. For each offspring, a breeding value was simulated according to To explore the predictions of the breeder’s equation applied at the level of observed phenotype, we conducted a simulation in which phenotypes were generated according to a Poisson GLMM  and then selected the largest observed count values (positive selection) with a range of proportions of selected individuals , a range of latent-scale heritabilities , and a range of latent means e.g., this is not the case when using negative instead of positive selection; data not shown). In particular, evolutionary predictions are poorest in absolute terms for large μ and large (latent) heritabilities. However, because we were analyzing simulation data, we could track the selection differential of latent values . We can also calculate the mean latent breeding value after selection. Across all simulation scenarios, the ratio of the change in mean breeding value after selection to the change in breeding value before selection was equal to the latent heritability  values are, of course, not measured. However, given an estimate of the effect of traits on fitness, say via regression analysis, we can derive the parameters necessary to predict evolution on the latent scale. The idea is thus to relate measured fitness on the observed data scale to the latent scale, compute the evolutionary response on the latent scale, and finally compute the evolutionary response on the observed data scale.kth data scale category . Population mean fitness can then be calculated in an analogous way to Equation 5:To relate the measured fitness on the observed scale to the latent scale, we need to compute the expected fitness i.e., The change in the mean genetic value of any character due to selection is equal to the covariance of breeding value with relative fitness , 1968. Ui.e., the expressionIf fixed effects need to be considered, the approach can be modified in the same way as integration over fixed effects is accomplished for calculating other quantities; Phenotypic change caused by changes in allele frequencies in response to selection is calculated asFile S1 (section C).Another derivation of the expected evolutionary response using the Price–Robertson identity  is givenUsing the same replicates as in the simulation study above, we used Equations 29–34 to predict phenotypic evolution. This procedure provides greatly improved predictions of evolutionary change on the observed scale . Howeverhttps://cran.r-project.org/. The package does not perform any GLMM inference but rather implements the hereby introduced framework for analysis posterior to a GLMM inference. While the calculations we provide will often  be more computationally demanding than calculations on the latent scale, they will be direct ascertainments of specific parameters of interest, since the scale of evolutionary interest is likely to be the observed data scale, rather than the latent scale . Most applications should not be onerous. Computations of means and (additive genetic) variances took <1 sec on a 1.7-GHz processor when using our R functions on the Soay sheep data set. Summation over fixed effects and integration over 1000 posterior samples of the fitted model took several minutes. When analytical expressions are available , these computations are considerably accelerated.The framework developed here  is implemented in the R package QGglmm available via the R comprehensive archive network, The general approach outlined here for quantitative genetic inference with GLMMs has several desirable features: (i) It is a general framework, which should work with any given GLMM and especially any link and distribution function; (ii) it provides mechanisms for rigorously handling fixed effects, which can be especially important in GLMMs; and (iii) it can be used for evolutionary prediction under standard GLMM assumptions about the genetic architecture of traits.Currently, with the increasing application of GLMMs, investigators seem eager to convert to the observed data scale. It seems clear that conversions between scales are generally useful. However, it is of note that the underlying assumption when using GLMMs for evolutionary prediction is that predictions hold on the latent scale. Hence, some properties of heritabilities for additive Gaussian traits, particularly the manner in which they can be used to predict evolution, do not hold on the data scale for non-Gaussian traits, even when expressed on the data scale. Yet, given an estimate of a fitness function, no further assumptions are necessary to predict evolution on the data scale, via the latent scale , over and above those that are made in the first place upon deciding to pursue GLMM-based quantitative genetic analysis. Hence we recommend using this framework to produce accurate predictions about evolutionary scenarios.e.g., because they represent experimental rather than natural variability). In such cases, it will be important to work with a biologically meaningful intercept, which can be achieved for example by centering covariates on relevant values  while some other fixed effects  would be left aside.We have highlighted important ways in which fixed effects influence quantitative genetic inferences with GLMMs and developed an approach for handling these complexities. In LMMs, the main consideration pertaining to fixed effects is that they explain variance, and some or all of this variance might be inappropriate to exclude from an assessment of bilities . This ast values . Finallyi.e., whether we should compute One of the most difficult concepts in GLMMs seen as a nonlinear developmental model  is that i.e., intraclass correlations) on an underlying scale provides only a value of the broad-sense heritability .The expressions given here for quantitative genetic parameters on the expected and observed data scales are exact, given the GLMM model assumptions, in two senses. First, they are not approximations, such as might be obtained by linear approximations (


Hypothesising underlying non‐additive genetic variation, we present an approach using genome‐wide high density markers to identify genomic loci with dominance effects on bTB resistance and to test previously published regions with heterozygote advantage in bTB. Our data comprised 1151 Holstein–Friesian cows from Northern Ireland, confirmed bTB cases and controls, genotyped with the 700K Illumina BeadChip. Genome‐wide markers were tested for associations between heterozygosity and bTB status using marker‐based relationships. Results were tested for robustness against genetic structure, and the genotypic frequencies of a significant locus were tested for departures from Hardy‐Weinberg equilibrium. Genomic regions identified in our study and in previous publications were tested for dominance effects. Genotypic effects were estimated through ASReml mixed models. A SNP (rs43032684) on chromosome 6 was significant at the chromosome‐wide level, explaining 1.7% of the phenotypic variance. In the controls, there were fewer heterozygotes for rs43032684 (P < 0.01) with the genotypic values suggesting that heterozygosity confers a heterozygote disadvantage. The region surrounding rs43032684 had a significant dominance effect (P < 0.01). SNP rs43032684 resides within a pseudogene with a parental gene involved in macrophage response to infection and within a copy‐number‐variation region previously associated with nematode resistance. No dominance effect was found for the region on chromosome 11, as indicated by a previous candidate region bTB study. These findings require further validation with large‐scale data.Genetic selection of cattle more resistant to bovine tuberculosis ( Mycobacterium bovis and has devastating consequences for the UK cattle industry. Previous studies have demonstrated genetic variation in resistance to bTB  is an infectious zoonotic disease caused by . et al. . Selecti. et al.  and resiet al. Such studies typically assume that the QTL have additive effects. However, some of the phenotypic variation in disease resistance could also be explained by QTL with dominance effects. The increasing and decreasing expression of dominance is commonly assumed to underlie hybrid vigour and inbreeding depression respectively . This method has been widely used in human and animal studies to identify associations between genetic polymorphisms and traits through the use of large‐scale SNP data ; see Tsairidou et al.  for furt. et al. . Control. et al. .genabel package (r/2.15.2)  based upon pairwise distances between individuals calculated from the genome‐wide IBS information using the dij = 1 if individual i was a heterozygote at locus j and dij = 0 otherwise. The ‘polygenic’ function of genabel was used to obtain residuals under a polygenic model ; m is the overall mean and 1 a vector of 1's; b is the vector of fixed effects with incidence matrix X, comprising the age of the individual as a covariate, year of testing, season of testing, the reason for testing and the two principal components calculated from the CMDS analysis on the genomic relationship matrix G (where data from the secondary cluster was included); a is the vector of polygenic breeding values with a assumed to follow a multivariate normal distribution, a~MVN , where σa2 is the additive genetic variance; and e is the residual error, assumed to be distributed MVN .An adaptation of the GWAS was developed to identify non‐additive genetic variation. Firstly, genotypes were recoded as a binary heterozygosity indicator: so genabel, which calculates G following Amin et al.  of individual i at SNP locus k, coded as 0, 1 and 2, where the reference allele is arbitrarily chosen; pk is the frequency of the reference allele in the data; HE,k is the expected heterozygosity at locus k assuming Hardy‐Weinberg equilibrium (HWE); and Hik is the observed heterozygosity for animal i (0 or 1).The model was fitted within n et al. : gij=n−1k by the ‘mmscore’ function was: m is the overall mean with 1 a vector of 1's; dk is the vector of heterozygosity indicators for locus k and bk is the associated regression coefficient; and ek* are residuals assumed to be distributed MVN . To provide a check on consistency with the additive screen published by Bermingham et al.  for Model dk was 1.00 (SE = 1.02 × 10−5), indicating no serious inflation due to hidden structure in the data, although accounted for in significances quoted. Bonferroni corrections were applied to obtain genome‐ and chromosome‐wide significance thresholds, derived as −log10(0.05/n) and −log10(0.05/nc) respectively (where nc is the number of SNPs on chromosome c). Particular attention was given to regions identified by Driscoll et al.  and BMS2753 (BTA9: 76 800 661–76 800 769 bp). Here, the 20 SNPs on each side of the two microsatellites were assessed using a significance threshold of −log10(0.05/80) = 3.2.The genome‐wide degree of inflation ; m is the overall mean; β is the vector of fixed effects as described in (1) with incidence matrix X; a is the vector of additive polygenic effects with a~MVN; d is the vector of polygenic dominance effects with d~MVN; α is the vector of regional additive effects with α~MVN, δ is the vector of regional dominance effects with δ~MVN; and e is the vector of residual errors with e ~ MVN . The incidence matrices for all the random effects was I in this data. The (co)variance matrix G was as described above for Model GR was obtained using the same procedure using only the 40 SNPs defining the window. The (co)variance matrices of dominance effects D and DR were calculated as: dij is the genomic relationship between individuals i and j; m is the number of SNPs included, m = n for D and 40 for DR; zik is the heterozygosity indicator for locus k of individual i; pk is the frequency of the reference allele of locus k in the data; and qk is frequency of the alternative allele. Likelihood ratio tests were conducted to identify significant regional effects with the genome‐wide terms a and d assumed to be nuisance factors and included in all models. In addition, alternative models were tested for the region containing the SNP with heterozygote disadvantage after excluding this SNP from the calculation of the local matrices.The significance of the SNPs identified using Model et al.  was furtet al. .The GWAS for heterozygote advantage identified a SNP on BTA6 (rs43032684) which was significant at the chromosome‐wide level with −loget al.  and comparatively fewer heterozygotes, even after accounting for differences in pA  , whereas the controls showed excess homozygosity compared to HWE .The genotypic frequencies for rs43032684 on BTA6 are shown in Table 01) Fig. . The casP < 0.01) (Table P < 0.01), suggesting that the result was not due to SNP‐specific genotyping errors. No dominance variance was detected for either of the regions of microsatellites INRA111 and BMS2753  was detected in this region.The region containing rs43032684, with apparent heterozygote disadvantage, contributed significant dominance variance . A closer look at the surrounding region revealed that the SNP resides within two partly overlapping copy number variation (CNV) regions which were previously associated with resistance to gastrointestinal nematodes in cattle   was found to be adjacent to several candidate genes including the peroxiredoxin‐6 pseudogene . The pseudogene contains two exons, and the SNP resides downstream of exon 1. Pseudogenes are homologues of functional parental genes, from which they have been derived through reverse mRNA transcription (processed pseudogenes) or through gene duplication (non‐processed pseudogenes) (Gerstein & Zheng peroxiredoxin‐6‐like pseudogene against that of the peroxiredoxin‐6 gene (BTA16) confirmed that peroxiredoxin‐6 is the parental gene of peroxiredoxin‐6‐like pseudogene and that the latter is likely to be a processed pseudogene, as the parental gene resides on a different chromosome  and resides within the et al. advantage and a role for dominance in genetic resistance to bTB, which was proposed by Amos et al. , and use , previously published by Driscoll et al.  in the cases and α = 0.005 (SE = 0.0014) in controls and a mean difference between cases and controls of 0.0007 (SE = 0.0018). Therefore, the evidence presented for this region requires interpretation with caution and undoubtedly requires further validation.The region of the rs43032684 SNP on BTA6 was shown to harbour dominance variance in this study, but in contrast to the hypothesis of Driscoll et al.  and Amos , and the degree of departure from Hardy‐Weinberg equilibrium (α) for cases and controls with different constraints.Figure S2 Contour plots for the cases and controls showing departures from HWE.Click here for additional data file.Appendix S2 Standard GWAS.Table S2 Chromosome‐wide significant SNPs identified from standard GWAS and corresponding P‐values.Figure S3 Manhattan plot from standard GWAS showing significance of SNP associations based on their P‐values.Figure S4 Q‐Q plot showing observed compared to expected x2 values under the null hypothesis of no association.Click here for additional data file.


Hordeum vulgare L.) is a major cereal crop, which is cultivated under variable environmental conditions and abiotic stresses in marginal areas around the globe. In this study, we evaluated 150 Jordanian landraces obtained from ICARDA Gene Bank and four local checks for yield and yield components related-traits in two locations across Jordan for three growing seasons under rainfed conditions. The study aims to identify superior Jordanian barley genotypes under dry conditions, to understand the genotype × environment (G × E) interactions, to analyze stability parameters and to identify markers associated with yield and yield components under rainfed conditions.Barley  with three significant QTLs located at 1H, 2H and 7H, which seem important for dry environments.Utilizing Jordanian barley landraces can effectively improve and adapt the current barley cultivars for cultivation under environmental stresses in dry regions. Utilization of markers associated with important agronomical traits and their incorporation in breeding using marker assisted selection can improve barley tolerance to drought stress.The online version of this article (10.1186/s12870-017-1140-1) contains supplementary material, which is available to authorized users. Hordeum vulgare L.) took place prior to 10,000 B.C in the Near East region known as the “Fertile Crescent”, which extends from the southern parts of Jordan to southeastern Turkey to western Iran [The domestication of barley (ern Iran . Landracern Iran . In the ern Iran . In addiern Iran . In JordEbmac415 (chromosome 2H) and GMS21 (chromosome 1H) were associated with increased GY by 19% and 13%, respectively, in most favorable environments for H. spontaneum [acat466 and acag135 on chromosome 3H, acag273 on chromosome 4H, TB2122 on chromosome 5H, and acgc132 and acgt517 on chromosome 6H that appear to be related with nitrogen metabolism in barley.Molecular markers technology offers the possibility to increasing the efficiency and precision of selection in plant breeding program, especially in QTL identification, which determines the location of genes on chromosomes. Therefore, the identification of markers closely linked to important agronomic traits will allow their utilization in marker-assisted selection and thus increase the efficiency of selection in breeding programs , 7. A geontaneum . MickelsAntirrhinum CENTRORADIALIS (HvCEN) was identified in a diverse set of barley germplasm and was found to control flowering and environmental adaptation [The emergence of new high throughput genotyping platforms enabled the implementation of GWAS in barley , 15). Usaptation . In anotaptation . GWAS inaptation . GWAS waThe main objectives of this study were to evaluate the performance of a sample of Jordanian barley landraces accessions under rainfed and drought-prone conditions in Jordan and to identify molecular markers associated with their performance under such conditions. In addition, the tested landraces were evaluated for major agronomic traits in order to identify superior and stable lines with improved adaptation to rainfed conditions. Molecular analysis was carried out to study genetic diversity and population structure and to identify genetic markers associated with high grain yield and yield components under dry conditions by using 9 k Illumina iSelect SNP assay and the GWAS approach.The material used in this study consists of 150 accessions of barley landraces collected in Jordan and held in the Gene Bank of the International Center for Agricultural Research in the Dry Areas (ICARDA)  in farmers’ fields at Madaba  and Ramtha . The field trial locations are described further in Additional file 2 (6 rows × 6.5 m length × 0.25 m distance between rows) planted at a seeding rate of 100 kg ha−1. The PRDiGGer software (http://nswdpibiom.org/austatgen/software/) was used to randomize the entries and a different randomization was used for each of the six year x location combinations. The software uses a user’s specified blocking sequence to distribute replicated treatments in a balanced way across the design to provide an unbiased estimate of the error variance.The experimental design was a partially replicated (p-rep) row-column design with 20 columns and 10 rows. The 150 accessions were replicated once, while the four checks  were replicated 13, 13, 12 and 12 times, respectively, which resulted in 200 plots for each field trial. Plot size was 9.75 mThe materials were sown on the 1st week of December in each growing season and grown under rainfed conditions. At each location, experimental plots were managed following the standard agricultural practices including weed control (hand weeding and herbicides against broad-leaved weeds) and pesticide use against main pathogens. Data on precipitation during the growing seasons were obtained from meteorological stations nearby the experimental sites , as average grain weight of two one m2 sample randomly taken from each plot, measured after threshing and cleaning; biomass yield (BY in g/m2), as average straw and grain weight of two “one-m2” sample randomly taken from each plot; straw yield (StY in g/m2) obtained by subtracting GY from BY; harvest index (HI as %) calculated by dividing GY by multiplied by 100; thousand kernel weight (TKW in g), as the weight of 200 kernels taken from the bulk seed of the plot and multiplied by 5; spike weight (SW in g), as the weight of five randomly selected spikes in the plot; kernels per spike (K/S): as the number of kernels/spike counted on five randomly selected spikes in the plot; spike length (SL in cm), as the length measured from the base to the top of the spike excluding the awns. The following traits were recorded as an average of three plants randomly selected within each plot: plant height (PH in cm): measured at maturity from the ground level to the top of the spike excluding awns; awn length (AL in cm), as the length from the top of the spike to the longest awn; peduncle extrusion (PEX in cm), as the length of the section of the last internode from the ligule of the flag leaf to the base of spike. Negative values of PEX indicate that the spike, is at least partially, inside the boot; peduncle length (PL in cm), as the length from last node to the base of spike.The traits recorded on plot basis were: grain yield  of the genotype means were obtained for each environment and the trait as the spatial pattern are unique for a field in a given year, and used for assessing the genotypes performance specific to locations and stability over years. For each trial, the field heterogeneity was assessed by coefficient of variation as experimental error standard deviation divided by trial mean × 100, and statistical significance of genotypes effects was assessed by a chi-square based test, called Wald-test, when the genotypes effects were assumed fixed. For each individual trail, heritability in broad sense for each field trial was computed as genotypic variance component estimate divided by sum of genotypic variance component estimate and experimental error variance estimate, in which case the genotypes effects were assumed random as is the usual procedure.BLUEs were used to examine the distribution of genotypes performance at individual trials using boxplots and using means and stability across location and overall the environments. The static stability of a genotype was obtained as coefficient of variation (CV) of its means (BLUEs) across the environments  for GY.The GGE biplot software  was usedFor genomic DNA (gDNA) extraction, barley plants were grown in a growth chamber under controlled conditions with temperature range between 22 and 24 °C and short-day photoperiod (12 h light). Total gDNA was extracted from leaf tissue collected from three-week-old plant of each accession using the CTAB (cetyltrimethylammonium bromide) method as described in Winnepenninckx et al. [For genotyping, a set of 7864 independent, high confidence and gene-based SNPs markers, which are incorporated into the Illumina Infinium iSelect 9 k SNP barley array were used to genotype the accessions as described previously [http://web.stanford.edu/group/pritchardlab/structure.html) was employed to determine population structure. Both the length of burn-in period and the number of iterations were set at 100,000 iterations with k value in the range of 1–12. To reach the appropriate k value, the estimated delta k value was calculated for each estimated k according to Evanno et al. [For genetic diversity assessment, SNP marker data was used to generate an un-rooted tree by using a neighbor-joining (NJ) algorithm implemented in DARwin software . The geno et al. .2) as described by Hedrick [2 against the distance (cM) between markers and fitting a decay curve using the square root transformation of the equation described by Andreescu et al. [2 values between pairs of unlinked loci was 0.197. The 2nd degree-loess  smoothing was calculated and plotted using SigmaPlot V.11 software (http://www.sigmaplot.co.uk/products/sigmaplot/produpdates/prod-updates1.php).The LD between markers was estimated using a squared allele frequency correlation . The analysis was performed with and without taking into account the first three principle components as a covariate (Q matrix) [P-value using the method described in Li et al. [P < 0.001 between SNP markers and traits were also considered as suggestive QTL. The map positions of the associated markers were based on previously described map reported in Comadran et al. [https://triticeaetoolbox.org/barley.Association between SNP markers and yield and yield components traits from selected individual environments, two locations and overall environments with heritability values ≥5 was analyzed using a mixed-model approach (MLM) to control type I errors, accounting for genetic relatedness or kinship (K). The K matrix is a measure of relative kinship and quantifies the probability that two homologous genes are identical by descent  and it w matrix) , 34) in i et al. . The metn et al. . PhysicaThe rainfall data during the three growing seasons were collected from the nearest meteorological stations. The rainfall amounts received in the six field trials were below the long-term average of the respective locations  except for Ramtha 2008/2009 (P = 0.10). However, when genotype effects were assumed random, the broad sense heritability estimates varied from 5 to 45% in four trials while zero in the remaining trials  and at Madaba (389 g/m2). Based on the cultivar superiority index (SCCS), G69 is also ranking first in overall and Madaba  correlation with BY and StY in both locations (Madaba and Ramtha) and overall environment  including the four checks with Fst value of 0.29. Using DARwin software, an unrooted NJ tree was built describing the relatedness between Jordanian accessions , while chromosome 4H carried the smallest number with 253 SNPs. Those SNPs spanned a total genetic distance of 989.9 cM with an average of one marker every 0.3 cM (data not shown). The population structure resulted in two distinct sub-populations  significantly associated with yield and yield components across the tested environments with heritability values ≥5  showed association with GY in Madaba 2008/2009  methods can lead to false negative outcomes as those methods were designed for independent tests while SNPs are dependent due to genetic linkage [P-value cutoff [2 values >0.95 as dependent and can be represented by one marker [To further elaborate on the assumptions extracted from the phenotypic and genotypic data of the tested Jordanian accessions, GWAS was carried out in order to identify QTLs associated with yield and yield components under rainfed conditions. Selecting the best  linkage . To avoie cutoff –50; FDR e cutoff , 52; or e marker , 54. In e marker  followedThe GWAS analysis detected eleven significant SNP-trait associations for yield and it components Table , while aNevertheless, QTLs identified in this study did not show clear consistency across the tested environments. This is in general agreement with the results of Varshney et al.  and MaccIn conclusion, we observed a high level of variation for all of the agro-morphological traits measured in a collection of Jordanian barley landraces evaluated for three years in drought prone locations. Such variation was further confirmed at the molecular level using SNP markers analysis, which demonstrates the existence of considerable genetic variability among these accessions. Marker trait association identified highly significant and suggestive major QTLs for yield and yield components under dry environments located at 1H (position: 133 cM), 2H (position: 106 cM) and 5H (position: 44.2 cM). Finally, the superior accessions identified in this study and their respective QTLs can be used in barley breeding programs and marker assisted approach to improve productivity and stability under dry field conditions in specific locations in marginal areas of Jordan and across arid region in the world.Additional file 1:ICARDA Gene bank information of 154 Jordanian barley genotypes used in this study. (XLSX 21 kb)Additional file 2:Characteristics of field locations, actual total rainfall (mm on monthly basis), number of rainy days and long-term rainfall average in the tested sites over three growing seasons. (XLSX 10 kb)Additional file 3:Combined analysis of variance for grain yield of barley landraces accessions and Restricted Maximum Likelihood Method estimated variances for locations and overall environments. (XLSX 14 kb)Additional file 4;P-value for grain yield of barley accessions evaluated in eight environments. (XLSX 9 kb)Genotypic coefficient of variation, heritability, coefficient of variation and Additional file 5:Means, coefficient of variations (CV%) and standardized cultivar superiority over applicable years of the best linear unbiased estimates (BLUEs) of GY (g/m2) of all tested genotypes. (XLSX 32 kb)Additional file 6:Correlation heat maps between selected triats of all tested genotypes for each indvidual field trial. (XLSX 166 kb)Additional file 7:Population structure of 154 Jordanian barley genotypes used in this study. (XLSX 34 kb)Additional file 8:2) against the genetic distance (in cM). (XLSX 109 kb)Decline of Genome-wide LD Additional file 10:QQ plots for all tested triats in this study. (PDF 360 kb)Additional file 11:Genotypic data of Jordanian barley landraces and four local checks used in this study. (XLSX 2582 kb)