Emerging technologies based on mass spectrometry or nuclear magnetic resonance enable the monitoring of hundreds of small metabolites from tissues or body fluids. Profiling of metabolites can help elucidate causal pathways linking established genetic variants to known disease risk factors such as blood lipid traits.We applied statistical methodology to dissect causal relationships between single nucleotide polymorphisms, metabolite concentrations, and serum lipid traits, focusing on 95 genetic loci reproducibly associated with the four main serum lipids . The dataset used included 2,973 individuals from two independent population-based cohorts with data for 151 small molecule metabolites and four main serum lipids. Three statistical approaches, namely conditional analysis, Mendelian randomization, and structural equation modeling, were compared to investigate causal relationship at sets of a single nucleotide polymorphism, a metabolite, and a lipid trait associated with one another.FADS1, GCKR, and LPA) have a statistically significant association with at least one main lipid and one metabolite concentration in our data, defining a total of 38 cross-associated sets of a single nucleotide polymorphism, a metabolite and a lipid trait. Structural equation modeling provided sufficient discrimination to indicate that the association of a single nucleotide polymorphism with a lipid trait was mediated through a metabolite at 15 of the 38 sets, and involving variants at the FADS1 and GCKR loci.A subset of three lipid-associated loci  in mediating the association between established genetic variants and diseases or traits. Recent technological advances allow for the collection of high-dimensional molecular phenotype datasets in thousands of individuals in a highly standardized manner. Metabolomics technologies based on mass spectrometry (MS) or nuclear magnetic resonance (NMR) enable the monitoring of hundreds of small molecule metabolites in tissues or body fluids -3. MetabAn emerging application of quantitative or semi-quantitative technologies such as LC-MS-based metabolomics is their combination with genome-wide association data to discover genetic loci underlying variation in human metabolism. Genome-wide metabolomics scans based on hundreds of metabolite and lipid species measured using standardized high-throughput assays have to date identified over 100 independent loci for metabolites -14. ImpoThis study explored the application of statistical inference to dissect causal relationships at complex-trait loci where there is a concomitant association with one or more metabolites. The analysis was focused on: (1) a set of SNPs robustly associated with the four main circulating serum lipids in genome-wide association studies at the time of analysis, and including total cholesterol (TC), low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein cholesterol (HDL-C), and triglycerides (TG) ,16; (2) The overarching aim of this study was to apply statistical approaches to interrogate causal relationships using genomic, metabolomic, and circulating lipid biomarker measures as an exemplar model. This provides a framework that can be applied in many other settings both in relation to metabolomics data as well as other -omic measures.The Cooperative Health Research in the Region of Augsburg (KORA) study is a series of independent population-based epidemiological surveys and follow-up studies of participants living in the region of Augsburg, Southern Germany . Blood sFor genotyping, 1,814 KORA F4 samples were randomly selected and genotyped using the Affymetrix Human SNP Array 6.0. After filtering out low call rate SNPs and SNPs violating Hardy-Weinberg Equilibrium (HWE), imputation was conducted using IMPUTE v0.4.2  based onFour serum lipid measurements (in mg/dl) were collected using the Dimension RxL (Dade Behring); total cholesterol was determined by cholesterol-esterase method , HDL-C cholesterol by the AHDL Flex , LDL-C cholesterol by the ALDL Flex  and triglycerides (TG) by the TGL Flex .IDQ Kit p150 across three periods of time . Finally, a total of 1,797 KORA F4 samples were available with genotypes, metabolite, and serum lipid measurements  as described in  and the IDQ Kit p150 under an identical protocol as for the KORA study at the Genome Analysis Center of the Helmholtz Zentrum München. For 1,235 randomly selected TwinsUK samples with genotypes available, the metabolite measurements were conducted in two batches: one for 422 individuals in April 2009 and the other for 813 individuals in November 2009. One reference sample was included in each of the 10 plates run in the second batch, and metabolites were measured five times in each plate. These reference measurements were used for quality control purposes. After further QC (more details below), a total of 1,176 TwinsUK samples were available with metabolite, genotype, and serum-lipids measurements.Metabolite measurements were performed using the metabolomics platform Biocrates AbsoluteAll the participants in both KORA and TwinsUK cohorts have provided informed consent and this study has been approved by Local Research Ethics Committee, Guy’s and St. Thomas’ Hospital Ethics Committee for TwinsUK, and Bayerische Landesärztekammer for KORA. Summary information for all the samples can be found in Additional file The analyzed metabolite panel comprises 163 different metabolites, including 14 amino acids, hexoses (H1), free carnitine (C0), 40 acylcarnitines (Cx:y), hydroxylacylcarnitines (C(OH)x:y), and dicarboxylacylcarnitines (Cx:y-DC), 15 sphingomyelins (SMx:y) and N-hydroxylacyloylsphingosylphosphocholine (SM (OH)x:y), 77 phosphatidylcholines , and 15 lyso-phosphatidylcholines. Quality parameters and quantification procedures were as described by us . After qIDQ Kit p150 (BIOCRATES Life Sciences AG). Sample analyses were done on 4000 Q TRAP LC/MS/MS System (AB Sciex) equipped with a Shimadzu Prominence LC20AD pump and a SIL-20 AC autosampler. The complete analytical process was performed using the MetIQ software package, which is an integral part of the AbsoluteIDQ kit. The MetIQ version 1.2.1r (Lithium), released in April 2010 was used, which incorporates an isotope correction. The experimental targeted metabolomics measurement technique is described in detail by US patent US 2007/0004044 [Liquid handling of serum samples (10 μL) was performed with a Hamilton Star (Hamilton Bonaduz AG) robot, and samples were prepared for quantification using the Absolute/0004044  and in t/0004044 -32, and /0004044 . Briefly/0004044 ,33,34. CThe mean differences of the metabolomics measurements across different measurement batches were compared to assess the influence of possible batch effects due to calibration of the machines at periodical time points. To account for these differences in mean, a batch variable was included in all analyses of metabolomics data. For consistency this batch variable was applied to all metabolites independent of demonstration of significant batch effects.Quality control of the metabolomics datasets was conducted in two steps. In the first step the quality of all metabolites was controlled by their coefficient of variation (CV) and missing value rate. For CV calculation, one reference blood sample was measured five times on each plate across all 10 plates. The CV for each metabolite was calculated as follows:The mean CV for each metabolite was computed from all 10 plates. All metabolites with a mean CV greater than 25% were excluded. In addition to this criterion, a maximal missing value rate of 5% was imposed. The second step of our quality control was removing outlying data points and outlying samples. This step was applied to log-transformed metabolites, which were consistently closer to normality than the untransformed metabolites based on the Anderson Darling test. Outlying data points were defined as values greater than 5 sd away from the mean for each metabolite. For each sample, two outlying data points were claimed to be independent if the correlation of corresponding metabolites was less than 70%. Samples with more than three independent outlying data points were excluded. For samples with less than, or equal to, three independent outlying data points, only the data points were excluded. Finally, all missing values were imputed using the R-package ‘mice’ , which aA total of 163 metabolites were measured in 3,061 samples of KORA F4 and in 1,237 samples of TwinsUK. In the first step of quality control, 11 metabolites were excluded for having a CV higher than 25% and one metabolite for having more than 5% missing values  since our study would not have the same statistical power to detect additional novel lipid-associated loci with even smaller variances explained. Among the 102 SNPs, 52 were associated with TC, 37 with LDL-C, 47 with HDL-C, and 32 with TG in the original study. Many of these loci were associated with multiple lipid traits; for example, 41 were associated with two lipid traits, seven with three lipid traits, and six with all four lipid traits. Summary information for these SNPs measured in KORA and TwinsUK cohorts can be found in Additional file The analysis focused on a total of 102 SNPs at 95 lipid-associated loci reported as primary association signals in a large-scale GWAS  for fourThe Anderson Darling test with and without log-transformation was used to test deviation from normality for metabolite values. The log-transformed metabolites were consistently closer to normality than the untransformed metabolites, and thus all metabolite measurements were log-transformed for analysis. The skewness of metabolites used in our causal analyses is reported in the Additional file For each metabolite, the narrow sense heritability was estimated from 86 monozygotic and 245 dizygotic twin pairs in TwinsUK under the ACE model. The ACE model assumes that the phenotypic variance is influenced by additive genetic variation, common environmental effects, and unique environmental effects (or random effects), and infers the narrow sense heritability as the ratio of the estimated additive genetic variance to the phenotypic variance. The estimation was done by maximum likelihood methods implemented in OpenMx software .P value <8.3 × 10−5 (Bonferroni corrected for 4 lipids and 151 metabolites) and the same direction of Spearman’s rho in both cohorts. We note that this correction over the number of tests may be over-conservative owing to highly correlated metabolite concentrations. Significant covariates  were regressed out from metabolites and lipids prior to the correlation test. The computation of the P value and Spearman’s rho were done using the function ‘cor.test’ in R. Correlations were visualized by a heat map plot combined with a hierarchical clustering using the ‘heatmap.2’ function of the R-package ‘gplots’ [Spearman’s correlation tests were used to identify correlated metabolite-lipid pairs, defined as ‘gplots’  with defP value <3.3 × 10−6 (=0.05 / (102 × 151)) in the meta-analysis and nominal association (P <0.05) in both cohorts were selected. Associations of the 102 candidate SNPs and main lipids were also tested using the same approach, and SNPs with P value <0.05 in the TwinsUK-KORA meta-analysis were retained for analysis.The association of the 102 candidate SNPs with all 151 metabolites was investigated under the linear model adjusting for age, batch, and sex, using SNPTEST and MERLIN (with -fastassoc option) in the KORA and TwinsUK sample, respectively. Summary statistics for the two cohorts were combined based on the inverse of the variance under the fixed effect meta-analysis model, and SNPs with Each metabolite with its statistically significantly associated SNP and lipid trait (defined by the criteria above) was assigned to a unique SNP-MET-LIP dataset, where SNP denotes a genetic variant, MET denotes a metabolite, and LIP denotes a serum lipid trait. Only unrelated samples in TwinsUK (N = 845) were included for analysis. For metabolites and lipid traits, covariates adjustment were performed including age, sex, and batch effect using a linear regression model .For each SNP-MET-LIP set, the association between SNP and LIP was tested under a linear regression model with and without adjustment for MET.P value between SNP and LIP in adjusted model was examined  and the change of the estimated effect size of SNP was measured as follows.To examine the influence of MET on SNP-LIP association, the To estimate the causal effect of a metabolite on a lipid trait, Mendelian randomization (MR) ,38 was aMR studies rest on three assumptions: (1) G is associated with X; (2) G is independent of U; and (3) G is independent of Y given X and U, that is, there is only one path from G to Y which is through X. For the estimation in MR, the Wald ratio, two-stage least squares and limited information maximum likelihood are commonly used, which are equivalent for a single instrument . The WalThe confidence interval of the unconfounded causal effect was computed using 1,000 bootstrap replicates  using thSEM represents a generalization of the MR model. While MR tests the magnitude of an unconfounded effect under a given hypothesis on a causal relationship , SEM measures the likelihood of each of the possible hypotheses on path model implying a causal relationship, to select the best fitted path model. When a SNP and two traits are cross-associated with one another, 10 path models are suggested to be possible , the expected covariance matrix Σ can be estimated as followswhere S is computed directly from the variable values. Finally, the difference between expected and observed covariance matrices Σ and S is evaluated by Pearson’s chi-squared test (Goodness of Fit Test) under the null hypothesis that the model fits the observation. The test statistic is derived asThe matrix Σ = Σ(θ) is a function of model parameter vector θ which includes model coefficients, measurement errors, and structural disturbances. Next, the observed covariance matrix p is the number of variables included. All SEM analyses were performed by using the R-package ‘sem’ [where ge ‘sem’ .P value ≥0.05 ; (2) 0.9 < Goodness of Fit Index (GoFI) ≤1; (3) Root Mean Squared Error Approximation (RMSEA) ≤0.05; (4) smallest negative Bayesian Information Criterion (BIC). Where multiple models fit to the data, the best fitted model was selected if its BIC was at least two units smaller than the next lowest BIC [Once the fit of all possible path models was evaluated, the best fitted model was required to fit the following four criteria as defined previously -48: (1) Most analyses were carried out using publically available packages in the R environment. SNP-metabolite association analyses were carried out using SNPTEST and MERLIN. Heritability estimation was carried out in OpenMx.et al.[The study design is shown in Figure et al. was exte2 < 50% and 28 with h2 ≥ 50%)  and P value = 6.22 × 10−83), rs1260326 in GCKR was associated with the phosphatidylcholine PC aa C40:5 (Beta = 0.037 (0.008) and P value = 1.26 × 10−6) and rs1564348 in LPA with carnitines C3 (Beta = 0.053 (0.011) and P value = 4.94 × 10−7) and C8:1 (Beta = 0.09 (0.017) and P value = 6.28 × 10−8). Among them, the phosphatidylcholine PC aa C40:5 was associated with both rs174546 in FADS1 and rs1260326 in GCKR.Genetic associations between 151 metabolites and 102 SNPs at 95 known lipid loci  were furBased on the association result, all 38 significant SNP-MET-LIP sets were selected  after adjusting for PC aa C40:5. These observations were compatible with the hypothesis that these metabolites may mediate the lipid pathways.First, the SNP-LIP association was conditioned on MET under a linear regression model in each SNP-MET-LIP set. A total of 19 metabolites associated with loci FADS1 as an instrumental variable, the unconfounded causal effect of PC ae C38:5 onto TG was estimated to be −0.62 ) in KORA, but only −0.53 ) in a set of unrelated TwinsUK individuals  at the 5% significance level, however, none of them were replicated in TwinsUK at the same level of significance   assuming SNP → MET → LIP  and myocardial infarction (MI), and targets for therapeutic intervention. Recent large scale meta-analyses of genome-wide association scans (GWAS) totaling >100,000 individuals has identified a total of 95 independent and common loci statistically significantly associated with at least one of the four main lipid traits  ,16. SomeFADS1 and GCKR .In this study, the potential roles of metabolites as intermediate phenotypes of the four main lipid traits were examined. First, we showed that all 151 small metabolites profiled on the Biocrates metabolite panel were statistically significantly associated with lipid traits in two independent cohorts. Second, we demonstrated that 37 of these metabolites were robustly associated with variants at three different lipid-associated loci, including one metabolite associated with two loci, highlighting both known and potential new biochemical correlates  and metabolic traits  ,25,64-66The advantage of using metabolites as intermediate phenotypes is that they are more proximal to genes and biological pathways than downstream phenotypes or clinical endpoints , ensurinFADS1 predicts that phosphatidylcholines mediate the association between SNP rs174546 and TG. FADS1 encodes a fatty acid desaturase regulating the desaturation of fatty acids by the addition of a fourth double bond between carbons of the fatty acyl chain [GCKR to TC through phosphatidylcholines. GCKR encodes a glucokinase regulatory protein that inhibits glucokinase in liver and pancreatic islet cells by binding non-covalently to form an inactive complex with the enzyme. The locus has been shown to have a pleiotropic effect on multiple cardio-metabolic phenotypes [GCKR SNP rs1260326 affects TC through regulation of phosphatidylcholine metabolism, a hypothesis that needs to be validated in experimental settings.Importantly, we demonstrate that our results are robust in two independent populations and recapitulate a known biological process. For instance, the most plausible path model at yl chain -61, a roenotypes ,24,52-56Conditional analysis is a commonly used approach to show dependencies between the variables of the unadjusted model and the variable being adjusted for. However, the different results between unadjusted and adjusted models might be due to reverse causation or confounding rather than causation. One of the most widely applied causal inference approaches is MR. If the direction of the association is previously known between two variables , MR can measure the extent of the unconfounded causal relationship using genetic variants as instrumental variables. However, in some –omics level studies, the direction of the association among variables cannot be easily assumed. To overcome this limitation of MR, we also applied SEM, which evaluates each hypothesis based upon the directional relationship of variables by comparing it with all possible hypotheses and infers the most likely causal relationship. By applying both SEM and MR to our dataset, we obtained significant support for our hypothesis on the direction and the degree of association in each SNP-MET-LIP set. Our framework suggests the usefulness of combined statistical methods as an exploratory tool to infer causal relationship from high-dimensional molecular data.Although our approach helps to infer causation statistically, it has limitations. In MR, the validation for all of the assumptions is not always feasible, although its violation could increase the bias . MR alsoIntervention-calculus when the DAG is Absent) estimates total causal effects from all the observed variables using PC algorithm and intervention calculus [Recent papers based on Gaussian graphical models or Bayesian networks ,43,70-72calculus . AlthougBiological systems are clearly far more complex than relatively simple sets of equations. However, new insights on underlying biological processes can be obtained from the analysis of data generated in a highly standardized manner and the careful choice of model variables. We showed that, with the use of appropriate statistical instruments, we could dissect the contribution of metabolites assessed through high-throughput molecular profiling to complex biological pathways. The application of these methods to loci identified in large-scale associations of genome-wide SNP data will provide powerful tools for dissecting metabolic pathways at a wide range of complex trait loci. Preliminary studies exploring metabolic signatures associated with hypertension ,74, myocThe authors declare that they have no competing interests.Data analysis: SYS, AKP, CG, and NS. Manuscript preparation: SYS, AKP, CG, and NS. Provision of data or materials: SW, GZ, WRM, KSS, AD, AP, EG, CP, RWS, H-EW, MHdeA, TI, JA, PD, TDS, and KS. All authors read and approved the final manuscript.Table S2. Characteristics of metabolites analyzed in this study. Table S3. SNP quality metrics in KORA and TwinsUK. Table S4. Metabolite-lipid correlation metrics. Table S5. Results of conditional analysis. Table S6. Results of Mendelian randomization. Table S7. Results of structural equation modeling. Table S8. Skewness of metabolites in 38 significant SNP-MET-LIP sets tested.Description of study samples. Click here for fileMetabolite-lipid correlation heat maps. Heat map plot of metabolite-lipid correlation combined with a hierarchical clustering to show six main groups of metabolites showing similar patterns of correlation with main lipids. The groups are separated by the heavy black line in the heat map and labeled 1 to 6 from top to bottom. The metabolites in each group can be found in the table below.Click here for file


Dense SNP genotypes are often combined with complex trait phenotypes to map causal variants, study genetic architecture and provide genomic predictions for individuals with genotypes but no phenotype. A single method of analysis that jointly fits all genotypes in a Bayesian mixture model (BayesR) has been shown to competitively address all 3 purposes simultaneously. However, BayesR and other similar methods ignore prior biological knowledge and assume all genotypes are equally likely to affect the trait. While this assumption is reasonable for SNP array genotypes, it is less sensible if genotypes are whole-genome sequence variants which should include causal variants.We introduce a new method (BayesRC) based on BayesR that incorporates prior biological information in the analysis by defining classes of variants likely to be enriched for causal mutations. The information can be derived from a range of sources, including variant annotation, candidate gene lists and known causal variants. This information is then incorporated objectively in the analysis based on evidence of enrichment in the data. We demonstrate the increased power of BayesRC compared to BayesR using real dairy cattle genotypes with simulated phenotypes. The genotypes were imputed whole-genome sequence variants in coding regions combined with dense SNP markers. BayesRC increased the power to detect causal variants and increased the accuracy of genomic prediction. The relative improvement for genomic prediction was most apparent in validation populations that were not closely related to the reference population. We also applied BayesRC to real milk production phenotypes in dairy cattle using independent biological priors from gene expression analyses. Although current biological knowledge of which genes and variants affect milk production is still very incomplete, our results suggest that the new BayesRC method was equal to or more powerful than BayesR for detecting candidate causal variants and for genomic prediction of milk traits.BayesRC provides a novel and flexible approach to simultaneously improving the accuracy of QTL discovery and genomic prediction by taking advantage of prior biological knowledge. Approaches such as BayesRC will become increasing useful as biological knowledge accumulates regarding functional regions of the genome for a range of traits and species.The online version of this article (doi:10.1186/s12864-016-2443-6) contains supplementary material, which is available to authorized users. In humans, plants and livestock, data on genome-wide SNP markers and complex trait phenotypes have been used for 3 purposes: to identify SNP associated with the trait, to study the genetic architecture of the trait, and to predict the genetic value or future phenotype of individuals. Although different statistical methods are commonly used for these three purposes, the Bayesian “genomic selection” or “genomic prediction” approach of Meuwissen et al  can be eTo date, methods such as BayesR, GBLUP and traditional GWAS (genome wide association studies) assume that each variant is equally likely to affect the trait: that is, no prior biological knowledge is included in the model. Instead, the available biological knowledge is often applied post-analysis, in a somewhat arbitrary and potentially biased manner to confirm candidate genes and mutations. When analysing dense SNP array genotypes it is reasonable to assume a model in which each marker may equally affect the trait. However, this assumption is less sensible when analysing whole-genome sequence variants, some of which may be known to cause non-synonymous coding changes or affect regulatory regions of candidate genes. In humans, as well as some livestock it is now possible to impute sequence variants for many thousands of individuals, so there is a need to develop methods that objectively include independent biological information in the analytical model.A priori we allocate all genotyped variants into classes, where each class of variants is believed to potentially differ in the probability that they contain causal variants for the trait. For example, one class could contain all non-synonymous coding variants within previously reported candidate genes such that this class may be enriched for causal variants compared to a random selection of variants. We call the method BayesRC. Previously Brondum et al. . Each iteration this was updated by sampling:Variant effects were assumed to belong to one of four normal distributions: β was a vector with the number of variants in each of the four distributions as currently estimated from the data. Each iteration, P was used in updating the conditional posterior probability that variant i belongs distribution d (details in . This was updated each iteration within each class:BayesRC used the same approach as BayesR except that βc was the current number of variants in each of the four distributions within class c, as estimated from the data. Thus, we used a relatively uninformative prior for all classes, but within a class the posterior proportion of variants in each distribution was informed by the data and could vary from one class to the next. If a class is found to be enriched for QTL this increases the probability that a true QTL effect in this class will be included in the model. The prior of αc = 1 can be argued to have little influence on the posterior distribution provided that there is a reasonably large number of variants per class. The updating of all other parameters was carried out as described for BayesR [where r BayesR .We consider three versions of BayesRC  defined by how the prior allocated SNP to one of three classes, as described in Table Wv) with a single SNP regression of phenotype on genotype, one SNP at a time. That is, as well as the SNP regression, the model included the overall mean, fixed effects, a polygenic term and phenotypes were weighted for heterogeneous error variance [An association study was conducted in the AUS dataset using ‘SNP Snappy’ . This prvariance .A traditional GBLUP method was implemented for the simulated data as described in  using ASŷv) and the simulated true genetic value. In AUS-Sim we assessed the bias of the predictions using the regression coefficient of the true genetic value on the predicted genetic value. Accuracies and regression coefficients were calculated within each of five MCMC chains and the reported value is the mean.The accuracy of genomic prediction was estimated from the correlation between the predicted genetic value The allele frequency spectrum of the 994,019 imputed SEQ variants was similar for all three cattle breeds used in this study . A larger proportion of NSC and REG variants had MAF < 0.1 (55 % and 49 % respectively) compared to CHIP variants (21 %)  and class II (REG). However, the QTL represented only 3 % of class I variants and 0.5 % of all class II variants: that is enrichment for QTL in these two classes was weak.QTL simulated on random variants genome-wide, including NSC, REG and CHIP variants. This trait represents a null model with QTL randomly dispersed across all classes, therefore none of the BayesRC priors were biologically informative: that is there was no class enrichment for QTL.The AUS-Sim data Table  used reaFigure For Trait 1, accuracy was highest for the BayesRC Lact model Fig.  where clFor Trait 2, although all QTL were contained in classes I and II of the BayesRC Seq model, this did not lead to an increase in accuracy, probably because the QTL represented only 3 % and 0.5 % of all variants in the two classes respectively. That is, enrichment for QTL in these classes was too low. For the BayesRC RLact  and all BayesRC models tested on Trait 3 (no enrichment of QTL in classes I or II) there was no difference in accuracy compared to the BayesR SEQ model Fig. . ImportaThe genetic architecture of the simulated traits was relatively accurately recovered in BayesR and BayesRC models with SEQ genotypes. For instance, in Trait 1 the proportions of QTL in each of the four distributions within each class of the BayesRC Lact model approximated the true proportions Table . AlthougIn the Bayesian framework, the observed posterior probability of a variant having a non-zero effect should provide a direct measure of the relative likelihood that a variant is causal or is in very high LD with a real QTL. For all three simulated traits, the posterior probability generally reflected close to the true probability that a variant was a QTL Fig. . That isThe power to detect the 4000 QTL from approximately 900,000 variants was highest for Trait 1 with the BayesRC Lact model Fig. . For exaIn the DANZ analysis, there was generally a consistent trend for accuracy of prediction to increase with variant density moving from 800 K to SEQ Table . OverallFor the DANZ analysis, there was a trend for slightly increased accuracy with the BayesRC Lact model compared to the BayesR SEQ model in both validation sets except in the Australian Red validation for Fat Yield. The Lact genes were expected to be most highly associated with Milk Yield because of the experimental design used to identify these genes  were similar for all models with SEQ data  using the variant effects estimated from BayesRC Lact (DANZ), for each of the five replicated MCMC chains. We then randomly selected 790 gene regions and allocated equivalent numbers of SEQ variants to class I, II and III as in BayesRC Lact. Prediction equations for these random variant sets were derived from the BayesR SEQ estimated variant effects. This was replicated 10 times by sampling a new set of 790 genes with replacement, giving a total of 50 replicates (because prediction equations were derived for each of the five BayesR SEQ chains). The accuracy of all prediction equations for each class was estimated in the Red Holstein validation set and averaged across replicates. We repeated the same procedure for Fat and Protein Yield.For Milk Yield there was higher prediction accuracy from BayesRC Lact class I and II equations compared to those from the random gene classes I and II, confirming enrichment of Milk Yield QTL in class I and II Fig. . For ProUse of SEQ compared to CHIP genotypes was expected to improve QTL discovery, particularly if a causal variant was rare and/or present in the SEQ data. We detected a number of strong QTL signals in the SEQ analyses in regions where no QTL were detected in the 800 K analyses (ie. variants with a posterior probability > 0.25 of being a QTL effect). One such example was a rare REG variant  that lies 2777 bp upstream of the SMEK1 (suppressor of mek1) gene coding region  gene arise due to LD with one or more causal variants in the nearby casein gene cluster. However, the BayesRC Protein Yield analysis indicates good evidence for an additional causal mutation near the GC gene because the most probable variant in this region is not in strong LD with the highest probability variant in the Casein cluster . Therefore we compared the power and precision of QTL discovery using single SNP regression (“GWAS”), BayesR and BayesRC in several previously documented candidate gene regions. Figure 762 Fig. . In the ter Fig. . Furtherter Fig. . Thus thA second comparison of GWAS and BayesRC Lact is given in Fig. http://www.ncbi.nlm.nih.gov/gene/) as a duplicated PAEP-like protein coding gene (RefSeq status “MODEL”).We also found evidence of improved power of QTL discovery in BayesRC Lact compared to the BayesR SEQ model in a number of QTL regions. An example of this is provided by the PAEP gene  that was included in our Lact gene set. This is an important milk whey protein and mutations in and close to this gene have previously been shown to be associated with milk protein traits –21. FiguTable a priori biological information. We provided evidence that BayesRC can increase the accuracy of genomic prediction and QTL discovery compared to BayesR and GBLUP with informative prior biological information. We also showed that using imputed sequence data in coding regions increased prediction accuracy and power to detect rare causal variants compared to dense SNP array genotypes.This study demonstrates that the BayesRC method can simultaneously be used to map causal variants, to study genetic architecture and to predict future phenotypes as did Moser et al  and Kempa priori. This leads to an objective estimate of the enrichment of effects within a class of variants. This enrichment is then used by the analysis in estimating the probability that any individual variant in the class has a non-zero effect.A desirable feature of Bayes RC is that the prior knowledge is incorporated objectively. In the case of GWAS for example, prior knowledge is only used post-analysis to confirm candidate genes. However, it is often possible to make a plausible case for many genes potentially affecting a trait. In Bayes RC, classes of sequence variants expected to differ in the proportion of variants having an effect on the trait are defined BayesRC is somewhat similar to BayesRS  which usIn real dairy cattle data the increase in accuracy of genomic prediction with BayesRC was only modest at best. This is probably because the class I and II enrichment for non-zero effects was low (similar to the BayesRC Seq model for simulated Trait 2) and most of the genetic variance was explained by class III variants. For instance, for Milk Yield the proportion of variance explained by each class was approximately 6 % for class I, 13 % for class II and 81 % for class III. Thus to increase the accuracy of prediction, we need better prior biological information about the genes and sites in the genome that are likely to affect a particular trait. In human genetics the ENCODE annotations may well provide this . Also, wAnother factor limiting prediction accuracy with Bayes RC in the real data is imperfect imputation of sequence and/or missing causal variants. In addition to imperfect imputation, we did not attempt to analyse full genome sequence but concentrated on gene coding regions, so undoubtedly a proportion of causal variants are missed. However, the use of imputed sequence variants in coding regions did generally increase the accuracy of genomic prediction in simulated and real data compared to high density SNP genotypes Tables  and 5. I2 > 0.75) with an NSC variant in SMEK1 which is predicted to have a deleterious effect on the protein .CSH2 codes for a chorionic somatomammotropin hormone  which has been demonstrated to play a role in bovine mammogenesis and milk production  possiblyThe candidate GC gene (Group-specific Component) in Fig. The candidate gene MYH9 Fig.  codes foThe two NSC variants identified with the highest BayesRC Lact posterior probability in the PAEP  gene Fig.  are the A number of the other candidate genes listed in Table Some other genes in Table In theory it is possible to use many more classes in BayesRC than the three used here. However, although the biological priors are relatively uninformative, it is likely that the Dirichlet prior distribution may still have a moderately strong influence on the posteriors when the number of variants in one class is relatively low. When priors carry much uncertainty, such as our Lact classes, we recommend maintaining reasonable class sizes (more than 1000 variants) to ensure that the data has a strong influence on the posterior parameters. The main motivation for creating more than two classes should be the expectation that enrichment for QTL may differ between classes of variants.A drawback of the BayesR and BayesRC methods is that they are computationally demanding, so it is important to develop faster Bayesian analytical approaches . For 10,If LD is very high across extended regions of the genome, and QTL effects are many and small, there is likely to be little difference between Bayesian and GBLUP genomic prediction when very dense markers are used . We arguOur new BayesRC method provides a flexible approach to improving the accuracy of genomic prediction and QTL discovery, by taking advantage of prior biological knowledge that is already available for a range of traits and species. The approach used in BayesRC to incorporate biological priors is appealing because it is straightforward to apply and is incorporated objectively based on evidence from the data being analysed. Further research on discovering functional regions of the genome, as well as improving sequence and imputation accuracy of rare variant prediction are critical to realising the full potential of this and other similar methods.http://www.cnsgenomics.com/software/. The BayesRC compiled program is available on request for non-commercial research.The 1000 Bull Genomes Project Run 2) has published the sequences of 129 Holstein and 15 Jersey bulls  that wer has publNo experimental animal studies were conducted for the work detailed in this manuscript. References have been provided where animal data was used.


FecL was first described in the Lacaune sheep meat breed Ovi-Test in 1998. A few studies estimated the effect of this gene on prolificacy but little data is available. In 2010, the Ovi-Test cooperative started genotyping FecL in all of their replacement ewe lambs. Thanks to the large amount of genotyping data that is available now, gene effects on litter size and other relevant traits can be estimated more accurately.The major prolificacy gene Our study included 5775 ewes genotyped since 2010 and 1025 sires genotyped since 2002. Performances and pedigrees were extracted from the French national database for genetic evaluation and research. Analysis of the effect of the gene on different traits was based on linear or threshold genetic animal models using the ASReml software.FecL mutation (L+) and 2% homozygous mutant (LL) ewes. On average, L + ewes produced 0.5 more lambs per lambing than ++ ewes. The FecL gene not only affected the mean litter size but also its variability, which was lower for ++ than for L + ewes. Fertility after insemination was higher for L + ewes than for ++ ewes. Lambs from ++ dams were heavier (+300 g) than the lambs of L + dams and the mortality of twin lambs born from ++ dams was lower than those from L + dams. In addition, bias in estimated breeding values for prolificacy when ignoring the existence of this major gene was quantified.The female population was composed of 71% homozygous wild type ewes (++), 27% heterozygous ewes for the FecL gene on prolificacy was estimated more accurately and we show that this gene affects both the mean and the variability of litter size and other traits. This paper also shows that ignoring the existence of this major gene in genetic evaluation of prolificacy can lead to a large overestimation of polygenic breeding values.The effect of the  The Lacaune sheep breed is the main breed raised in France, with approximately 1.2 million ewes. There are different strains of this breed, depending on the production purpose (dairy or meat). In 1975, the artificial insemination (AI) cooperative Ovi-Test designed a selection program to increase prolificacy of sheep bred for meat production [FecXL mutation (C53Y) of the BMP15 gene, which is located on the X chromosome and results in a high ovulation rate  in heterozygous ewes and sterility in homozygous mutated ewes [FecL gene that is located on chromosome 11 and for which two SNPs (single nucleotide polymorphisms) close or within the B4GALNT2 gene are candidate causal mutations [FecL gene has two alleles and each copy of the mutant allele (designated L) increases ovulation rate by approximately 1.5 additional ova compared to the wild allele (designated +). In 2006, allele frequencies of both genes were estimated in the Lacaune sheep population by genotyping the males at the AI centre [FecXL and 45% for FecL.Since 1982 and the first evidence of a major gene for prolificacy in Booroola Merinos ,4, varioted ewes  and (2) FecXL homozygous ewes and excessive prolificacy of FecL homozygous ewes. Moreover, some on-farm observations and experimental data [FecL animals. Because of the relative frequencies of each of these genes, the sterility induced by the FecXL mutation in the BMP15 gene, the excessive prolificacy of homozygous FecL ewes, and the poor prolificacy of wild type ewes, the Ovi-Test cooperative chose to remove animals that carried the FecXL mutation from its population and to manage the FecL gene at the heterozygous state. Thus, since 2002 all sires are genotyped for both genes and, since 2010 every replacement ewe lamb is genotyped for the FecL gene.Homozygous mutant animals for either of these genes are not adapted to breeders’ needs because of the sterility of tal data  showed tFecL mutation on prolificacy was reported [FecL mutation on prolificacy in a large and unselected sample. Potential effects on fertility after AI, lamb growth and mortality were also analysed to check if the mutation affects these traits directly, since they are important traits for the breeders. In addition, we quantified the bias in estimates of the additive polygenic values since, currently the evaluation process of estimated breeding values (EBV) considers that genetic effects are transmitted according to Fisher's infinitesimal model [In 2006, the first estimate of the effect of the reported , but onlal model .The cooperative nucleus consisted of 26 breeder flocks, with 430 ewes per flock on average (from around 150 to 1000), and a total of 11 201 ewes in June 2013. Most flocks perform three lambings every two years. This breeding program is on-going.FecL when they enter the central testing station for own performance test. Then, they are selected on their own performances for growth, fatness and conformation. Those with less favourable performances (about 50%) are used for natural mating in the nucleus, sold or slaughtered, while the best males continue on in the selection process and undergo a progeny test set up on-farm by AI. The females used as replacement ewes are chosen among the AI-born lambs (about 40% of the lambs result from AI in the nucleus). The first mating for these replacement ewes is a natural mating .Male candidates used in the nucleus are preselected when they are about 45 days old and are genotyped for FecL gene within the population to address the breeder’s goal of optimal prolificacy, the Ovi-Test cooperative imposed various mating rules. The objective is to obtain a nucleus consisting of 50% heterozygous ewes (designated L+) and 50% homozygous wild-type ewes (designated ++), and to minimize the production of homozygous mutant ewes (designated LL). When AI is used, L + and LL ewes must be mated to ++ rams, and ++ females to L + rams. Only ++ rams can be used for natural mating.In order to manage the FecL mutation was predicted by a combination of alleles at three microsatellite loci that determine an L-haplotype that was never detected on wild-type chromosomes [FecL genotyping is based on SNP DLX3:c.*803A > G (GenBank accession number FJ654646), which is in high linkage disequilibrium with the FecL mutation (<1% recombination) and located in the 3′ UTR sequence of the DLX3 gene [From 2004 to 2009, the presence of the omosomes . Since 2All data  were extracted from the national database for genetic evaluation and research managed by the Institut de l’Elevage (French Livestock Production Institute) and the CTIG . Only females born after 2010 (when consistent genotyping of replacement ewes began) and sires genotyped since 2002 and used in the nucleus were retained . However, too few LL ewes were available to calculate accurate estimates for this genotype and they were removed; thus only ++ and L + genotypes were compared.Allele and genotype frequencies were estimated separately for female and male populations. Potential changes in frequencies between years, as well as Hardy-Weinberg equilibrium, were tested with a Chi-squared test.® V9.2, while final analyses were performed using the ASReml software [In addition to the genotype of the ewe, many factors can affect the four traits analysed and they were defined as similar as possible to those of the national genetic evaluation system. However, not all factors were tested for each model due to the structure of the data. The list of factors tested for each trait and included in the final analysis is in Table software .Litter size The distribution of raw litter size (LS) per genotype is in Table jth category for genotype i was computed for an underlying variable N as: , setting lificacy , the comη as:Then, mean and variance were estimated for a given and η. Another more illustrative method is proposed in the Appendix. It consists in a transformation of the threshold sets estimated for ++ and L + ewes into a common set for both genotypes and instead of fixed parameters  for the underlying variable to give specific values for each genotype. In this case, the variance of the underlying variable is higher for L + than for ++ ewes. Both methods provide similar evidence that the FecL gene affects both the mean and the variability of litter size. Polygenic heritability was estimated by the ratio of the animal variance component to the total variance on the underlying scale, which was equal to the sum of the animal variance component and the residual variance; that last variance was set to 1 in this threshold model.These calculations were done for several values of Artificial insemination fertility Since the mutation affects the number of ovulations, it was relevant to investigate whether it also affects their quality, which can be assessed indirectly by female fertility. Since conditions of natural mating are not well documented in our database, in this study we focused on the effect of the gene on AI fertility. Because ewe lambs were not artificially inseminated in the nucleus, the data used to evaluate the effect of genotype on the success of AI included only a particular sub-sample of ewes. These ewes were more than 14 months old and were primiparous or multiparous when inseminated. Because the number of inseminated ewes that had suckled three or more lambs during their last litter was very small, they were discarded from the analysis. The fixed effects considered for this trait are shown in Table Lamb weight at 30 days of age The aim of this analysis was to observe the effect of dam genotype on the weight of lambs at 30 days of age (30dLW), which is used as a maternal capacity selection criterion in the Ovi-Test breeding program. It was carried out only in 17 flocks in which all lambs were weighed at about 30 days of age. Because some lambs were not weighed at exactly 30 days, the 30dLW was calculated by linear regression using the actual weight at the given age and a fixed birth weight for each lamb category . The variable 30dLW was analysed for 3829 lambs using a linear animal mixed model, with fixed effects as described in Table Mortality from birth to 30 days of age The effect of dam genotype on lamb survival was studied by measuring lamb mortality from birth to 30 days of age. Sex could not be included as a fixed effect because the gender of stillborn lambs was unknown. The rearing type was discarded for similar reasons. This binary trait was analysed for 8338 lambs using a threshold animal mixed model.FecL) or did not (EBV) include the genotype effect as a fixed effect. Comparison of these EBV between ++ and L + ewes was done by a simple ANOVA. Bias due to ignoring the genotype effect in the evaluation of breeding values were assessed within genotypes by comparing the difference between EBVand EBV|FecL with a paired Student's t-test and the slopes of the regressions of EBVon EBV|FecL.Bias in estimates of additive polygenic values for prolificacy of the 2711 genotyped females with lambing records was estimated by comparing BLUP (best linear unbiased prediction) of their breeding values from a threshold animal mixed model which did , compared considering a common set of thresholds {τc} and an effect of genotype on the mean of the underlying variable. As expected, estimates of the thresholds were lower for the prolific L + ewes than for the ++ ewes , the variance on the observable scale was always higher for the L + than for the ++ genotype. In particular, an underlying variable N associated with the thresholds {FecL gene has an effect on both the mean and variance of the trait is presented in the Appendix.The linear model run to select the significant effects showed highly significant effects for genotype P < 0.001), oestrus type (P < 0.01), flock (P < 0.001), month of lambing (P < 0.001) and the composite effect or physiological status of the dam at lambing (P < 0.001). In the threshold animal mixed model, the interaction between thresholds and genotypes was significant (P < 0.01) and the likelihood ratio test showed a better data fit when a separate set of thresholds was considered for each genotype . As expected, estimates of additive genetic variance and heritability were higher when the model did not include the effect of genotype ).Genotype of the ewe (P = 0.016), flock (P < 0.0001), rearing mode (P = 0.05), interval since the last lambing (P = 0.04), and number of lambs suckled in the previous litter (P < 0.0001) had a significant effect on the AI fertility. The average fertility observed following AI was high (0.74) and higher for L + ewes (0.79) than for ++ ewes (0.72). Based on results of the model, L + ewes were significantly more fertile than ++ ewes (P = 0.016) and fertility decreased as the number of lambs suckled in the previous litter increased (P < 0.0001). The difference between genotypes was 0.3 on the underlying scale. Predictions on the observed scale were obtained for a given combination of levels of fixed effects. For ewes in a flock with an average effect, rearing a single lamb, and having suckled two lambs at the previous lambing, the difference between genotypes was 11% points on the observed scale: 62% for ++ ewes and 73% for L + ewes.FecL genotype were taken into account, lambs of ++ dams were about 300 g heavier at 30 days of age (P < 0.001) than lambs of L + dams. This difference accounted for about 3% of the lamb’s weight at this age.Genotype of the dam, flock, month of lambing, physiological status and birth type of the dam, and sex, birth and rearing type of the lamb had significant effects on 30dLW (P < 0.001). Male lambs were heavier than female lambs and the weight decreased when the birth type or the rearing type increased. When all possible sources of variation linked to dam prolificacy but independent of the Flock (P < 0.0001), month of lambing (P = 0.04), rearing type of the dam (P = 0.05), and lambing rank (P < 0.0001) had significant effects on the risk of mortality. The effect of genotype of the dam was not significant (P = 0.13) but the interaction between birth type of the lamb and dam genotype was significant (P < 0.0001). However, the difference between genotypes was significant only for twin litters (P < 0.001). In order to better characterize this effect, the model was run again for twin lambs only. The probability of death was higher for twin lambs of L + dams than for those of ++ dams and the estimated difference between the genotypes was 0.19 on the underlying scale. For a particular combination of fixed effects , these estimates converted to probabilities of 0.155 and 0.114, for L + and ++ dams respectively.FecL) of ++ and L + ewes (Table FecL (σ = 0.192). Ignoring the genotype effect led to a very small underestimation of additive polygenic values for ++ ewes and a large overestimation for L + ewes of about 1 standard deviation unit of the EBV|FecL  while the overestimation observed for the L + genotype increased slightly when the additive polygenic value increased .When the genotype effect was included in the model, there was no significant difference between estimated additive polygenic breeding values . Two reasons could explain these differences. First, the study performed in 2006 was based on a small number of genotyped animals. Moreover, before consistently genotyping replacement ewes, the cooperative excluded animals that were genetically estimated as very prolific. Males with an EBV for prolificacy greater than 1.5 standard deviation units above the mean, and ewes with an EBV greater than 3 standard deviation units above the mean were automatically discarded from the breeding program. This strategy, which was used from 1996 to 2010 to avoid animals that were too prolific, probably reduced the proportion of L + animals.The high stability of genotype frequencies observed since 2011 is not really surprising, despite the cooperative’s aim to achieve 50% of L + ewes. A substantial number of genotyped ewes ready for insemination were available only in 2012 and a too sudden change in genotype frequencies would not be suitable for the breeders.The considerable variation in genotype frequencies observed between flocks was somewhat surprising since by obligation, all replacement ewes in the nucleus originated from collective AI sires. This rule was set up at the beginning of the selection scheme in 1975 and is still compulsory. Therefore, these differences in genotype frequencies could result from the different strategies implemented by individual breeders to select their replacement ewes. Some breeders may select ewe lambs born as triplets, and most probably born from carrier dams, whereas others may avoid keeping these smaller ewe lambs. These counter-selection procedures, together with the higher mortality of progeny born from prolific carrier ewes, also explain the deviation from Hardy-Weinberg equilibrium observed for females. In contrast, the male selection strategy is imposed by the cooperative as a group strategy. It slightly favours the carriers, counterbalancing their higher mortality, which brings the male genotype frequencies back to Hardy-Weinberg equilibrium.FecL mutation on prolificacy found in the present study agrees with the first observations previously reported [FecL on prolificacy is also similar to the lowest effect of the Booroola gene stated in the extensive review performed by Fogarty [BMP15 gene that contains either the Hanna [BMP15 gene [GDF9 gene in Belclare [FecL mutation. As for most mutations that do not induce sterility at the homozygous level, the prolificacy of homozygous LL ewes is too high and not useful for breeders.The effect of the reported . As for reported ,6,17-20.reported . The est Fogarty . It is ahe Hanna  or Inverhe Hanna  mutationhe Hanna , or the Belclare , Thoka [Belclare , Santa IBelclare  also indThe significant interaction between the set of thresholds and genotype can be interpreted as a double effect of the genotype, impacting the mean of LS and also its variability in addition to the systematic increase induced by the mean change. If the difference between prolificacy of ++ and L + ewes had resulted only in a simple shift in the mean of the underlying variable, as was observed between breeds by Bodin and Elsen , it woulFecL mutation induces shorter delays of pre-ovulatory luteinizing hormone (LH) and follicle-stimulating hormone (FSH) surges after sponge withdrawal [This effect on the mean and the variability is perhaps not common to all major genes that affect LS in sheep and could result from specific physiological mechanisms that are regulated by the Lacaune gene. It is known that, in contrast to other mutations, the thdrawal  and thatthdrawal . TherefoBMP15 C53Y mutation, which was still segregating in 2001 [FecL gene accounts for a very large part (42%) of the total additive genetic variance and this could explain the rapid increase in genetic progress for LS observed in this population.The estimates of the genetic parameters for prolificacy were in agreement with estimates reported in the literature from threshold models ,28 or fr in 2001 . FinallyThe rate of AI success was very high in this data and higher than the value reported in dairy Lacaune sheep , althougBMP15 and GDF9 mutations in the homozygous state [BMPR1B, BMP15, GDF9) [To our knowledge, this is first time that a major gene controlling prolificacy is reported to have an effect on fertility, except for some us state ,17-20,255, GDF9) . Indeed,5, GDF9) . Althoug5, GDF9) .FecL genotype of the dams on the weight of their lambs at 30 days was quite surprising and no similar effects have ever been described for other major prolificacy genes. The data available did not enable us to determine whether the difference between lambs was due to weight at birth, growth between 0 and 30 days, or both. A difference in weight at birth could be due to a higher rate of embryonic losses in the carrier ewes. It has been observed that, in the event of embryonic losses, the remaining foetuses weigh less at birth than foetuses from litters of similar size but without embryonic losses [FecL gene. In the breeding program used in this study, animals were selected on a genetic index, combining EBV for prolificacy and maternal ability. Thus, animals with very good prolificacy EBV were selected even if their dairy EBV was moderate, and conversely animals with a very high maternal ability value were selected even if their prolificacy value was slightly lower than average. Because the average prolificacy EBV of L + animals was higher than that of ++ ewes, it is possible that these L + ewes were selected despite their low maternal ability.The effect of the c losses . TherefoFecL gene most probably results from the higher ovulation rate and pregnancy wastage of L + ewes, as is the case for F + Booroola ewes [The likelihood of death was higher for twin lambs born from L + dams than from ++ dams. This result was surprising. Indeed, the effect of birth type on lamb mortality is well documented ,34, and ola ewes . HoweverFecL, was very large and can contribute to biased selection for polygenic values. Furthermore, the increase of bias when the additive polygenic value of L + ewes increased, might express an interaction of the FecL mutation with the rest of the genome or more simply with another gene. Although carrier sires of the BMP15 mutation are systematically discarded from breeding, this mutation is still present in the female population and might contribute to this interaction. The bias observed for ++ ewes was much lower, perhaps due to the high percentage of this genotype in the sample. For several reasons , the global genetic values should not be used for selection and the gene effect should be separated from the polygenic effects in the genetic evaluation. Before changing the entire evaluation system, a first improvement would be to estimate a pseudo polygenic EBV for animals with a known genotype. This pseudo polygenic EBV would be assessed by removing or adding the value of the genotype from the current individual EBV. However, in the future, the evaluation model will take the genotype effect into account, which will be estimated as in the present study. Individuals without known genotypes would be assigned a unique common genotype or individual probabilities of each genotype. Genotype probabilities can be calculated exactly using iterative peeling [When the evaluation model included the effect of genotype, the EBV accounted only for the polygenic effects and, as expected, there was no difference between the ++ and the L + animals. In contrast, when the genotype was not included in the model, its effect was not dissociated from the polygenic effects and was included in the EBV, which led to much higher EBV for L + than for ++ ewes. For L + ewes, this bias in the estimates of the additive polygenic values, assessed by the difference between EBV and EBV| peeling  when the peeling .FecL in the Lacaune sheep of the Ovi-Test population since 2011 has enabled us to better estimate genotype frequencies and the effect of this gene on prolificacy and fertility , as well as other important traits for breeders. The negative effects of the maternal genotype on growth and mortality of lambs are nevertheless relatively low in comparison to the effects on litter size and fertility after AI. The increase in variability of litter size due to the FecL mutation is not a negative outcome, to the extent that triplets are accepted by breeders. However, since some breeders wish to limit the number of triplets and to avoid litter sizes greater than 3 at all cost, management of the FecL gene should be associated with a reduction of litter size variability, perhaps by canalyzing selection [The large amount of genotyping data accumulated for election . This paj ordered categories. However, any threshold model with two thresholds Y ~ N ; {τ1 , τ2} can be re-parameterized by a homothetic transformation that scales and shifts the set of thresholds to the values of a reference model and changes accordingly the parameters of the underlying variable.A threshold model of categorical traits supposes an underlying variable with a standard normal distribution and a set of thresholds which transforms this continuous variable into a multinomial variable with Ya ~ NYb ~ NYa ~ NYb* ~ N Thus, two models:η and a scaling effect σ of the underlying variable of the model for Yb*.It is then possible to interpret the differences of these models having the same set of thresholds, by a shift This homothetic transformation can be also used for re-parameterization of models with three thresholds ifIn other cases, an approximate re-parameterization can be done ifIn this case, the values of the two first thresholds of the common new set can be those of the reference threshold set In our particular case, if one argues that the third threshold for the ++ genotype (corresponding to litters of more than three lambs) was poorly estimated , it was possible to change the parameters by an approximate re-parameterization . This table shows the estimated thresholds and the mean and variance of the underlying variable obtained with the threshold model and the resulting mean and variance of the litter size. It also shows the common set of transformed thresholds with the mean and the variance of the underlying variable, which results in the same distribution for litter size on the observable scale than the estimated thresholds.Click here for filec} of thresholds. The figure represents the common set of transformed thresholds and the underlying variables y++ ~ N and yL+ ~ NL+* ~ N, with the same mean as for L + ewes and the same standardized residual variance as for ++ ewes and the resulting theoretical proportions of LS.Distribution of underlying normal variables and the transformed common set {τClick here for file


False positives in a Genome-Wide Association Study (GWAS) can be effectively controlled by a fixed effect and random effect Mixed Linear Model (MLM) that incorporates population structure and kinship among individuals to adjust association tests on markers; however, the adjustment also compromises true positives. The modified MLM method, Multiple Loci Linear Mixed Model (MLMM), incorporates multiple markers simultaneously as covariates in a stepwise MLM to partially remove the confounding between testing markers and kinship. To completely eliminate the confounding, we divided MLMM into two parts: Fixed Effect Model (FEM) and a Random Effect Model (REM) and use them iteratively. FEM contains testing markers, one at a time, and multiple associated markers as covariates to control false positives. To avoid model over-fitting problem in FEM, the associated markers are estimated in REM by using them to define kinship. The P values of testing markers and the associated markers are unified at each iteration. We named the new method as Fixed and random model Circulating Probability Unification (FarmCPU). Both real and simulated data analyses demonstrated that FarmCPU improves statistical power compared to current methods. Additional benefits include an efficient computing time that is linear to both number of individuals and number of markers. Now, a dataset with half million individuals and half million markers can be analyzed within three days. Genome-Wide Association Studies (GWAS) can reveal genetic-phenotypic relationships, but have limitations. To control false positives, population structure and kinship are incorporated in a fixed and random effect Mixed Linear Model (MLM). However, because of the confounding between population structure, kinship, and quantitative trait nucleotides (QTNs), MLM leads to false negatives, missing some potentially important discoveries. Here, we present a new method, Fixed and random model Circulating Probability Unification (FarmCPU). FarmCPU performs marker tests with associated markers as covariates in a fixed effect model and optimization on the associated covariate markers in a random effect model separately. This process enables efficient computation, removes the confounding, prevents model over-fitting, and controls false positives simultaneously. FarmCPU controls false positives as well as MLM with reductions in both false negatives and computing times. Researchers will not only be able to analyze big data, but will also have greater success with fewer mistakes when mapping genes of interest. Genome-Wide Association Studies (GWAS) use direct statistical tests as opposed to direct genetic inferences carried out in linkage analyses. Associations between a genetic marker and a phenotype happen for many reasons in addition to the genetic linkage between the tested genetic markers and functional causal polymorphisms–4. PopulQ matrix[Q matrix are fitted as fixed effects, the statistical tests on genetic markers (S) can be performed with GLM, one marker at a time. The model can be conceptually presented as y = Q+S+e, where y and e are phenotype and residuals, respectively. This model is also known as the Q model.Population structure is normally represented by proportions of individuals belonging to subpopulations, commonly known as the Q matrix,11, or bQ matrix,12,13 deK) matrix to define the relationship among individuals. Total genetic effects of individuals are fitted as random effects with variance and covariance structure defined by K. Conceptually, MLM with both Q and K can be written as y = Q+K+S+e and is also known as the Q+K model [Q and Q+K models control false positives better than naïve models such as the t-test, which only fits the testing markers[Q+K model performs better than the Q model or the K model alone when they can not be inclusively represented each other[Similarly, the entire set of genetic markers can be used to derive a kinship [Q and K in a MLM controls P-value inflation well, but also weakens the real associations.Another problem with MLM is that its advantage disappears for complex traits when they are associated with population structure. The MLM method was compared with a naïve test (without control over population structure and kinship) in an association study on 107 traits from 199 ms (SNPs). Both thTwo strategies have been developed to solve the confounding problem and improve statistical power for MLM methods. The first strategy, the Compressed MLM (CMLM), clusters individuals into groups and fits genetic values of groups—rather than genetic effects of individuals—as random effects. The CMLM method improves statistical power compared to regular MLM methods. FurtherThe second strategy changes the definition of kinship among individuals. Only the associated genetic markers are used as pseudo Quantitative Trait Nucleotides (QTNs) to derive kinship instead of all, or a random sample of genetic markers. Pseudo QTNs are expected to closely track some of the causative QTNs, and are selectively used to derive kinship for a specific testing marker. Whenever a pseudo QTN is correlated with the testing marker, it is excluded from those used to derive kinship. In the FaST-LMM-Select method, a pseudo QTN is considered correlated if it is within a 2Mb interval on either side of the testing marker. InsteadBoth above strategies conduct genetic marker tests one at a time. However, testing multiple markers simultaneously is more advantageous, and can be done by fitting pseudo QTNs in addition to the testing markers in a stepwise MLM, named Multi-Locus Mixed-Model (MLMM). The oveOur objective was to develop an improved statistical method that completely eliminates the confounding, and simultaneously improves statistical power and reduces computing time.Q, K, and pseudo QTNs. The second type of adjustment reduces confounding issues by either refining how K is derived from all the markers, or selectively including or excluding pseudo QTNs based on their relationship with the testing markers  to GLM, from ML markers .With the only exception on the naïve method, all the above methods incorporate the first type of adjustment. However, only a few methods incorporate the second type of adjustment. For example, CMLM replaces individuals’ genetic effects with groups’ genetic effects. MLMM adds pseudo QTNs as covariates, which are adjusted by using a step-wise regression procedure. The FaST-LMM-Select and SUPER methods selectively include pseudo QTNs to derive kinship for a specific testing marker. However, the confounding between testing markers and covariates still remains a problem. For example, MLMM retains the kinship un-adjusted. FaST-LMM-Select removes markers in kinship that are adjacent (within 2Mb) to testing markers. Yet, a To address the residual confounding problem, our idea was to divided MLMM into two parts: Fixed Effect Model (FEM) and a Random Effect Model (REM), and use them iteratively. FEM contains testing markers, one at a time, and multiple associated markers as covariates to control false positives. For the convenience of illustration, the associated markers were named as pseudo Quantitative Trait Nucleotides (QTNs). To avoid model over-fitting problem in FEM, pseudo QTNs were estimated by REM, where the pseudo QTNs are used to define kinship. FEM and REM are used iteratively until no change on pseudo QTNs. The P values of testing markers and pseudo QTNs are unified at each iteration. Simultaneously, our method completely controls false positives, eliminates confounding, and improves computational efficiency through the following four strategies:Use a single marker test with a FEM to retain efficient computation and to completely remove the confounding between kinship and the testing marker.Include pseudo QTNs as covariates in the FEM to control false positives.Estimate pseudo QTNs by using a maximum likelihood method in a REM to incorporate a map of markers and avoid model over-fitting.Unification of P values of pseudo QTNs in conjunction with tests on the other markers.The first strategy gives the benefits of efficient computation and the elimination of confounding between kinship and testing markers. The second strategy applies the first type adjustment on the testing markers. The third strategy incorporates a marker map into the estimation of pseudo QTNs by using the SUPER method. The pseudo QTNs are derived through a maximum likelihood method in REM and then used to derive kinship among individuals. Regardless of the number of pseudo QTNs, genetic variance and residual variance are the only unknown parameters. The limited number of parameters avoids the problem of model over-fitting. The fourth strategy enhances the MLMM's algorithm for calculating the P values of pseudo QTNs. Because all pseudo QTNs are examined for each genetic marker tested, we identify and use only the most significant P value among all tests for each pseudo QTN.i is the observation of the ith individual; Mi1, Mi2,…, Mit are the genotypes of t pseudo QTNs, initiated as an empty set; b1, b2, …, bj are the corresponding effects of the pseudo QTNs; Sij is the genotype of the ith individual and jth genetic marker; dj is the corresponding effect of the jth genetic marker; and ei is the residuals having a distribution with zero mean and variance of Our proposed method requires that the FEM and REM proceed in an iterative fashion. The FEM tests markers, one at a time, and uses a set of pseudo QTNs as covariates. The model can be written as:Each of the testing markers receives a P value except those designated as pseudo QTNs and used as covariates. Initially, these pseudo QTN markers are assigned “NA" (Not Available) for their P value. As each pseudo QTN is examined for each testing marker, the NA is replaced with the most significant P value for that pseudo QTN, which becomes the P value of its corresponding marker. We call this process substitution .i and ei stay the same as in Eq . Simulated data were also used to examine FarmCPU's computational efficiency in response to variations in number of markers and sample size.Arabidopsis thaliana samples genotyped at 250,000 SNPs[We reanalyzed a published dataset and performed enrichment study on candidate genes to validate the associated loci. When we reanalyzed the 107 traits of 199 ,000 SNPs with FarTo validate the associated loci on flowering time, we extracted the known candidate genes and conducted an enrichment study. We divided the whole genome into small regions  and categorized each region into either a gene region containing at least one candidate gene or a non-gene region containing no candidate genes. We calculated an enrichment coefficient as the ratio between the numbers of gene regions versus non-gene regions. An enrichment coefficient of 1 is expected for a random association. For the top association, the enrichment coefficient equaled 2.4 for the naïve and GLM methods, 3.8 for the MLM method, and 8.9 for the FarmCPU method . For theArabidopsis thaliana[We compared FarmCPU with other six methods selected from different categories. These methods are: (1) naïve method (t-test); (2) GLM; (3) MLM thaliana, human[2 thaliana,28, maiz thaliana, mouse[3 thaliana, and pig thaliana. The resArabidopsis thaliana as example, the P values were overwhelmingly inflated under the naïve method (FLOWERING LOCUS C (FLC)[Arabidopsis thaliana  that conthaliana .Arabidopsis thaliana with connected subpopulations. The second is the East Asian lung cancer dataset with mild-isolated subpopulations. The third is the WTCCC1 controls dataset with distinct-isolated subpopulations. The plots of the first three PCs are displayed in We examined null distribution of FarmCPU compared with two other extreme methods. One is the naïve method, t-test, which is expected to exhibit inflation of P values. The other is the MLM method, which controls inflation well. Three datasets with different level of population stratification were used to examine null distribution. The first is We randomly shuffled simulated phenotypes to completely break the association between phenotypes and genotypes. There is no QTN controlling the shuffled phenotypes. No inflation of P values was expected, even with the naïve t-test . As expeArabidopsis thaliana data, we put all QTNs on chromosomes 1–3. There were no QTNs on chromosome 4 and 5. The P values of markers on chromosomes 4 and 5 were expected to have uniform distribution. As expected, we observed the P values by using t-test were inflated. The inflation was due to the LD across chromosomes. The t-test was not able to correct the inflation. In contrast, MLM fall into the range of uniform distribution . Then, we classified SNPs into QTN areas and non-QTN areas. A QTN area included a QTN and nearby SNPs within 100,000 base pairs on each side. All other SNPs were classified into non-QTN areas. We used SNPs located in non-QTN areas to derive the null distribution. Again, the t-test method exhibited the inflation problem. The MLM showed minor “inflation”, which was possibly due to linkage to the nearby real QTNs. FarmCPU had a lesser inflation than MLM with respect to being closer to the null distribution ). Numbers of false positives of FarmCPU and t-test under different P-value thresholds were recorded. The numbers of false positives of FarmCPU were lower in order of magnitude than the ones by using t-test for all combinations between resolutions and levels of P-value thresholds .As the third setting mixed QTN-areas and non-QTN-areas, the real association signals were also mixed into the null distribution. False positives should be investigated in conjunction of statistical power under same FDR and Type I error. These are summarized in the following section.Genetic markers were classified into the ones on QTN-area and non-QTN area to evaluate statistical power under different levels of FDR and Type I error. The markers on non-QTN areas were used to derive null distribution. For a specific level of Type I error, power was defined as the proportion of QTNs detected. For each level of power, the corresponding FDR was defined as the proportion of false positives , GLM and MLM. The comparisons were performed on simulated traits with heritability of 50% controlled by varied number of QTNs . FarmCPU was consistently superior to both GLM and MLM  Figs. AsWe simulated phenotypes controlled by 100 QTNs with varied levels of heritability, low (30%), moderate (50%), and high (70%). We found that FarmCPU was consistently superior to GLM and MLM. For example, for the trait with 50% heritability, we recorded the number of true and false positives among 100 replicates by using a threshold of 1% after Bonferroni multiple test correction. There were 639, 513, and 520 true QTNs that were detected by FarmCPU, MLM and GLM, respectively, at a cost of 32, 250, and 257 false positives .It is common that QTNs are not part of testing genetic markers unless the markers are dense enough. We performed tests with QTNs included, or excluded, from the genotypic data. The phenotypes were simulated with a heritability of 50% and controlled by 100 QTNs. A QTN was considered detected when a SNP fell into the preset resolution of 10,000, 50,000, or 100,000 base pairs on either side of the QTN. Results indicated that FarmCPU outperforms both GLM and MLM  in eitheFitting population structure, such as Q matrix or PCs, as covariates is an effective way to capture phenotypic variation due to non-genetic effects, however, the incorporation also causes confounding with causal genes. Therefore, there is side effect for such incorporation. We examined the tolerance of FarmCPU when fitting PCs as covariates in both cases, with and without non-genetic effects. We simulated non-genetic effects by adding and subtracting 50% of phenotypic standard deviation in two ethnic groups (Korean and Japanese) and leaving the other group (Chinese) unchanged. Non-genetic effects cause about 25% of phenotype variation. Even without incorporating PCs, FarmCPU outperformed FaST-LMM that incorporated PCs  Figs. AsIn situations without non-genetic effects, we also examined the effect of including PCs as covariates using a human population dataset. PCs wera. The effect of the ith QTN was ai. Two levels of a were tested, 0.9 and 0.95. In both cases, FarmCPU outperformed MLM  underlying a trait are known, each genetic marker can be tested by fitting only the true QTNs as covariates in GLM. When the proportion of known QTNs is reduced, the statistical power is reduced. Amazingly, FarmCPU, without any prior knowledge of true QTNs, has higher power than GLM that incorporated 50% known true QTNs as covariates .We expected that using prior knowledge in FarmCPU could further improve statistical power. To test this expectation, we examined simulated phenotypes by incorporating true QTNs. The results indicated that the statistical power of FarmCPU improved further with prior knowledge. Additionally, we found that the greater the proportion of true QTNs incorporated, the greater the improvement in statistical power .In addition to improved statistical power, FarmCPU is also computationally efficient. We theoretically analyzed the computing time complexity and measured the actual performance for datasets with specific number of markers and sample size. The factors impacting computing time were investigated to further improve computational efficiency.O(nm). For a complex trait, because bigger sample sizes will be able to identify more pseudo QTNs, the computational complexity is linear to m and superlinear to n. When sample size further increases, as the total number of genes is fixed for a trait, the computational complexity is linear to both m and n. The FaST-LMM algorithm is used in REM with a computing time linear to n. Therefor REM in FarmCPU has computational complexity of O(n). REM does not involve tests on genetic markers, therefore, takes only a small proportion of computing time—especially when m is relative large. Overall, the computational complexity of FarmCPU is O(nm).The computing time of the FEM in FarmCPU is linear to number of markers (m) and sample size (n). For a simple trait, because the number of iterations and the number of pseudo QTNs (t) underlying a trait are constant, the computational complexity of the fixed effect model is K, attaining optimization on variance components, and performing association tests. GRAMMAR-Gamma's (implemented in GenABEL) time for association tests is linear with n, but its times for building the K matrix and optimization on variance components are the square and the cube of n, respectively. Both FaST-LMM-Select and SUPER use an algorithm from FaST-LMM, which prevents formatting of the K matrix. Rather, optimization is directly performed from the singular value decomposition of the genetic markers used to define kinship among individuals. Because the number of such markers (M) is much less than the number individuals, these two models have a computing time complexity that is linear with n. For FarmCPU, times for both optimization on variance components and performing association tests are linear with n. Comparisons of FarmCPU and other common methods are summarized in We compared the theoretical computational efficiency of FarmCPU with the following common statistical models: GLM, MLM, GRAMMAR-Gamma, FaST-LMM, FaST-LMM-Select, SUPER, and MLMM. Similar to previous comparisons,18,20, wO(nt).The largest memory of the REM in FarmCPU is to store the genotype table with n individuals and t pseudo QTNs. The memory footprint is linear to n and t. FarmCPU's FEM uses only a small proportion of the memory footprint compared with the FarmCPU’s REM. Therefore, FarmCPU's memory complexity is FarmCPU R package was compared with several other packages for actual computing time and memory usage. The other packages were selected to represent different categories. GLM was represented by PLINK. MLMM waMost statistical methods were developed to solve big data with a focus on either marker size or sample size, but not on both simultaneously. For example, FaST-LMM and GeneABEL could be used for either larger samples, or more markers, but not for both. For a dataset with ten thousands individuals and one million markers, both FaST-LMM and GenABEL failed. FarmCPU completed the analysis on a laptop in less than four hours . In addiFalse positives can be reduced by fitting covariates to adjust the association tests on markers. The common covariates are population structure and kinship among individuals. However, the confounding between these covariates and testing markers also produce false negatives. The iterative usage of the fixed effect and random effect models in the FarmCPU method integrates both the markers and the covariates together by optimizing the covariates and using substitution. Testing markers in a fixed effect model makes FarmCPU computationally efficient. The optimization of pseudo QTNs in a random effect model involves only two parameters  in addition to the number and size of bins of the SUPER GWAS method. Therefore, the problem of model over-fitting is much less compared to including pseudo QTNs and testing markers in the same model. SUPER's bin method takes the map information into account, which effectively reduces redundancy among pseudo QTNs.The REM part of FarmCPU has converging problem for the optimization of genetic and residual variance components when one of the components is near zero. This issue is common for a trait with extremely low heritability or a permuted phenotype that has zero heritability. In this case, no pseudo QTNs are associated with the trait. Fortunately, this situation can be detected statistically under a threshold (e.g. 1%) after multiple test correction through the fourth step of the FarmCPU procedure (see online methods). The multiple test correction can be performed with Bonferroni method at lowest computing time. Permutation test costs more time with benefit of improved power  to contribute an additional 25% of the phenotype variance. These added levels of environmental effects meant that the non-genetic effect was about 170 times greater than the QTN effect. Even in this situation, FarmCPU without fitting PCs as covariates still outperformed MLM that incorporated PCs as covariates  Figs. FiCompared with MLMM, FarmCPU uses an improved version for calculating the P values of the pseudo QTNs. MLMM calculates P values using all pseudo QTNs as covariates in the model and excludes testing markers, an approach we named “onsite”. Instead, FarmCPU uses the most significant P value out of each pseudo QTN in conjunction with the tests on all markers. We named this process "substitution". As demonstrated, substitution dramatically improves statistical power .FarmCPU's improved statistical power and control on false positives generate a fresh look to the Manhattan and QQ (“Q” stands for Quantile) plots . The skyHigh marker densities and increased sample sizes, driven by the reduction of genotyping cost, are producing big datasets for analysis. Most sthttp://www.ZZLab.net/FarmCPU.URL: The FarmCPU software package  is available at m genetic markers, one at a time. Pseudo QTNs are included as covariates to control false positives. Specifically, the FEM can be written as follows:i is the observation on the ith individual; Mi1, Mi2,…, Mit are the genotypes of t pseudo QTNs, initiated as an empty set; b1, b2, …, bj are the corresponding effects of the pseudo QTNs; Sij is the genotype of the ith individual and jth genetic marker; dj is the corresponding effect of the jth genetic marker; ei is the residual having a distribution with zero mean and variance of Our proposed method uses the Fixed Effect Model (FEM) and the Random Effect Model (REM) iteratively. The FEM is employed to test i and ei stay the same as in Eq  and positions by using the SUPER algorithm. Mathemaas in Eq  and ui iThe iterative usage of the FEM (1) and the REM (2) is specifically described by the following steps:Step 1: Set known candidate QTNs as pseudo QTNs, otherwise leave pseudo QTN set empty.Step 2: Perform association tests by using the FEM with pseudo QTNs as covariates. Genetic markers are fitted as fixed effects, one at a time.Step 3: Substitution: When the testing marker is one of the pseudo QTNs, the testing marker is not solvable. As each pseudo QTN is examined for every marker, we use the most significant P value for the corresponding marker. We call this process substitution.Step 4: If no marker passes a threshold  after multiple test corrections, take the result from Step 3 as final; otherwise, go to Step 5.Step 5: Whole genome is divided into bins, and the SNP with the most significant P value in each bin represents the bin. Bin size  and number of bins (e.g. from 10 to 100 with step of 10) are optimized in the REM. The combination of size and number with the minimum REML value will be used to select pseudo QTNs. In each iteration, the number of pseudo QTNs is bounded by a function of sample size , remove the less significant pseudo QTN.Step 7: If no new pseudo QTNs are added, or if the specified maximum number of iterations is reached, stop. Otherwise, go back to Step 2.Arabidopsis thaliana, human, maize, mouse, and pig.We used previously published datasets from multiple species that included Arabidopsis thaliana. The first dataset includes 199 samples, with 216,130 SNPs and 107 phenotypes[http://archive.gramene.org/db/diversity/diversity_view). The kinship matrix and principal components were calculated by GAPIT[We used two datasets of  by GAPIT using 10https://www.ebi.ac.uk/ega/datasets/EGAD00000000002). The kinship matrix and principal components were calculated by GAPIT using 10% of SNPs sampled randomly.One human dataset, “WTCCC1 controls dataset”, ID # EGAD00000000002, was obtained from EMBL-EBI (The European Molecular Biology Laboratory–The European Bioinformatics Institute). Respecthttp://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000716.v1.p1). The kinship matrix and principal components were calculated using 10% randomly sampled or total SNPs by GAPIT and PLINK, respectively.The other human dataset, “East Asian lung cancer dataset”, ID # phs000716.v1.p1, was obtained from dbGaP. Respecthttp://www.panzea.org/!#genotypes/cctl). The kinship matrix and principal components were calculated by GAPIT using 10% of SNPs sampled randomly.The maize genotype dataset includes 2,279 inbred lines, each with 681,258 SNPs. The phenotype is flowering time measured as days to silk  with 12,226 SNPs. The phenotype is weight growth intercept. The kinThe pig genotype dataset has 820 samples (412 Large White and 408 crosses from Large White and Landrace) with 64,212 SNPs. The phenotype is last rib back-fat thickness. All SNPArabidopsis thaliana to simulate genetic effects and generate phenotypes by adding residual effects. The QTNs underlying these phenotypes were randomly sampled from the real genotypes. The QTN effects followed a geometric distribution with an additive effect of parameter a. The effect of the ith QTN was ai. The parameter a was set to 0.9, 0.95, and 1 as described in previous studies[h2 is heritability. Simulations were performed using a variety of QTN numbers and heritability values, and with QTNs included and excluded from the genotypic data for association tests. For each combination of factors, simulations were repeated either 100 or 1,000 times, specified for each experiment.We used real genotype datasets from human and s studies. PhenotyStatistical power, Type I error, and FDR were examined simultaneously in association tests on simulated phenotypes with known QTNs, using the method described by Segura et.al and two Arabidopsis thaliana. The whole Arabidopsis thaliana genome was divided into gene regions and non-gene regions. The genes and their extensions, 10,000 base pairs on either side, were considered gene regions with a total length of 4,552,815 base pairs (3.9% of whole genome). The remaining areas were considered non-gene regions with total length of 114,616,742 base pairs (96.1% of whole genome). The average hit per base pair was defined by number of associated SNPs divided by total length. The ratio of average hit on gene regions to the average hit on non-gene regions was used as the enrichment coefficient. The random hits were expected to have an enrichment coefficient of 1.The flowering time candidate genes from the database reported by Atwell et. al,  were used to evaluate the associated SNPs on 23 flowering time traits in S1 Fig(DOCX)Click here for additional data file.S2 Fig(DOCX)Click here for additional data file.S3 Fig(DOCX)Click here for additional data file.S4 Fig(DOCX)Click here for additional data file.S5 Fig(DOCX)Click here for additional data file.S6 Fig(DOCX)Click here for additional data file.S7 Fig(DOCX)Click here for additional data file.S8 Fig(DOCX)Click here for additional data file.S9 Fig(DOCX)Click here for additional data file.S10 Fig(DOCX)Click here for additional data file.S11 Fig(DOCX)Click here for additional data file.S12 Fig(DOCX)Click here for additional data file.S13 Fig(DOCX)Click here for additional data file.S14 Fig(DOCX)Click here for additional data file.S15 Fig(DOCX)Click here for additional data file.S16 Fig(DOCX)Click here for additional data file.S17 Fig(DOCX)Click here for additional data file.S18 Fig(DOCX)Click here for additional data file.S19 Fig(DOCX)Click here for additional data file.S20 Fig(DOCX)Click here for additional data file.S21 Fig(DOCX)Click here for additional data file.S22 Fig(DOCX)Click here for additional data file.S23 Fig(DOCX)Click here for additional data file.S24 Fig(DOCX)Click here for additional data file.S25 Fig(DOCX)Click here for additional data file.S26 Fig(DOCX)Click here for additional data file.S27 Fig(DOCX)Click here for additional data file.S28 Fig(DOCX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.S5 Table(DOCX)Click here for additional data file.S6 Table(DOCX)Click here for additional data file.S7 Table(DOCX)Click here for additional data file.S8 Table(DOCX)Click here for additional data file.S9 Table(DOCX)Click here for additional data file.S10 Table(DOCX)Click here for additional data file.S11 Table(DOCX)Click here for additional data file.S1 File(DOCX)Click here for additional data file.