We introduce a natural Bayesian hierarchical model that treats the latent association status of molecular QTLs as SNP-level annotations for candidate SNPs of complex traits. We detail a computational procedure to seamlessly perform enrichment, fine-mapping and colocalization analyses, which is a distinct feature compared to the existing colocalization analysis procedures in the literature. The proposed approach is computationally efficient and requires only summary-level statistics. We evaluate and demonstrate the proposed computational approach through extensive simulation studies and analyses of blood lipid data and the whole blood eQTL data from the GTEx project. In addition, a useful utility from our proposed method enables the computation of expected colocalization signals using simple characteristics of the association data. Using this utility, we further illustrate the importance of enrichment analysis on the ability to discover colocalized signals and the potential limitations of currently available molecular QTL data. The software pipeline that implements the proposed computation procedures,  Genome-wide association studies (GWAS) have been tremendously successful in identifying genetic variants that impact complex diseases. However, the roles of such studies in disease etiology remain poorly understood, primarily because a large proportion of the GWAS findings are located in the non-coding region of the genome. Recent advancements in high-throughput sequencing technology enable the systematic investigation of molecular quantitative trait loci (QTLs), which are genetic variants that directly affect molecular phenotypes . Linking molecular QTLs to GWAS findings intuitively represents an important step for interpreting the biological and clinical relevance of the GWAS results. In this paper, we describe a rigorous and efficient computational approach that assesses the enrichment and overlap between the GWAS findings and molecular QTLs. Importantly, we illustrate that the accurate quantification of overlapping between molecular QTL and GWAS signals requires reliable enrichment estimation. Our proposed approach fully accounts for the intrinsic uncertainty embedded in the association analyses of GWAS and molecular QTL mapping, and it outperforms the existing state-of-the-art approaches. Applying the proposed approach to the GWAS data of blood lipid traits and the whole blood expression QTLs (eQTLs) yields some novel biological insights and also illustrates the potential limitations of the currently available molecular QTL data. Genome-wide association studies (GWAS) have successfully identified many genomic loci that impact complex diseases and complex traits. Nevertheless, the molecular pathways that connect genetic variants to complex traits are still poorly understood, primarily because a considerable proportion of trait-associated signals are located in the non-coding region of the genome. With recent advancements in high-throughput sequencing technology, systematic investigations of cellular phenotypes have revealed an abundance of non-coding molecular quantitative trait loci (QTLs) –4. Integet al . We further denote the latent binary association status of each SNP i by dichotomizing its genetic effect βi, i.e., γi = 1 indicates that SNP i is genuinely associated , and γi = 0 otherwise. It can be argued that the aim of the GWAS is to make inference of the binary vector γ ≔ . In addition, we assign the standard spike-and-slab prior for each regression coefficient βi and a flat gamma prior for the residual error variance parameter τ.Without loss of generality, we consider a GWAS of a quantitative trait and describe its associations with i, i.e.,d ≔ , and we refer to α ≔  as the enrichment parameter: for a binary annotation, a positive α1 value indicates that SNPs with the feature have increased odds of being associated with the trait of interest, i.e., the annotated feature is enriched in the trait-associated genetic variants.Suppose that a single quantitative annotation  is available for each candidate genetic variant. We integrate the SNP-level annotation into the association analysis by specifying a natural logistic prior for each candidate SNP Yqtl, Gqtl). Intuitively, the true association status of each SNP with the molecular phenotype can be naturally incorporated as annotations in d, is practically impossible to obtain. Consequently, there is considerable uncertainty in annotating any causal molecular QTN. To fully characterize the uncertainty of the molecular QTL annotation and carry it over into the proposed integrative analysis, we propose embedding a latent covariate model for d in the prior d to be an unobserved random vector whose realization is drawn from the following probability distribution:d ∣ Yqtl, Gqtl) from a Bayesian multi-SNP association analysis of molecular QTL data  ⊕ γ[2] ⊕ ⋯ ⊕ γK][, and further approximate i, Assuming that the annotation ous work  proposesribed in , i.e., γribed in , the adad. The first stage focuses on finding the MLE d. In the second stage, we approximate Pr by iγ = 1, id = 1 ∣ y, G, Yqtl, Gqtl) by γi and di depend only on one relevant molecular phenotype and its corresponding genotypes rather than the full collection of the molecular phenotypes. We keep the current notation for the consistency of the presentation.) The subsequent sections provide the statistical and computational details within each stage.With the added latent covariate enloc , which is freely available at https://github.com/xqwen/integrative. Note that the computational procedure requires only summary-level information from both the molecular QTL data and GWAS data.We implement the computational procedure outlined above in the software package α given the observed summary statistics from GWAS and the fuzzy annotation of molecular QTLs. Recall that if the binary molecular QTL annotation is indeed known, then the EM algorithm that we previously described [α. With incomplete information on annotation data, we adopt a principled statistical strategy in missing data inference known as multiple imputation [m complete data sets by filling in, i.e., imputing, the missing entries of the binary annotation data. The imputed data sets are then individually analyzed using the existing EM algorithm, and the distinct estimates of d ∣ Yqtl, Gqtl).The primary objective of the enrichment analysis is to estimate the hyper-parameter escribed , 16 can putation , 18. Sped is Pr, i.e., the imputation of d should also be conditioned on the observed GWAS data. The proposed imputation distribution represents a simplified approximation and essentially assumes the independence between d and GWAS data, which is because Pr = Pr if and only if α1 = 0. Consequently, imputing from this simplified distribution  leads to conservative point estimates that are shrunk toward 0. (This is because each imputed data set is generated as if α1 is set to 0 a priori.) In practice, the underestimation of the true α1 under the simplified imputation distribution can be noticeable if the true α1 is much larger than 0 (which is evident in some of our simulation scenarios). Despite this shortcoming, we choose to work with the simplified imputation distribution, Pr, mainly because of its attractive computational property. For example, it can be obtained by a single run of genetic association analysis based solely on the molecular QTL data and applied in the integrative analysis of any GWAS data. In comparison, Pr is specific to each GWAS-molecular QTL data set pair, and its computation is considerably more expensive if not practically impossible. Importantly, the empirical evidence from the simulation studies suggests that the bias of the enrichment estimate due to the use of the simplified imputation distribution has non-significant impacts on the results of downstream fine-mapping and colocalization analyses.According to the missing data theory, the ideal probability distribution to impute m) necessary for reliable estimation has been systematically studied in the missing data theory. The common consensus in the statistical literature is that m should be determined by the percentage of missingness, and various theoretical and empirical studies [d is completely unobserved in our context, we are certain that di = 0 for the vast majority of the candidate SNPs based on inspection of the posterior distribution Pr. In fact, by examining the analysis results of cis-eQTLs from the GTEx whole blood data, we find that there are only ∼ 1.5% cis candidate SNPs with a posterior inclusion probability ≥ 0.01. Guided by this empirical evidence, we choose to impute m = 25 QTL data sets for each analysis. The number of imputed data sets  prior to α1. In practice, we select λ in a data-driven manner by assessing the degree of imbalance of the unobserved contingency table  are both relatively sparse in practice, which can lead to large variances for the estimated enrichment parameter γ, for all SNPs in GWAS. Specifically, we compute γ ∣ y, G, Yqtl, Gqtl) [K non-overlapping LD blocks [Given the point estimate of the enrichment parameter, we adopt an empirical Bayes procedure to infer the true association status, l, Gqtl) . In addil, Gqtl)  by decomD blocks  and perfiδ ≔ Pr denotes the PIP of SNP i being a causal molecular QTN.To account for the uncertainty of the association status of molecular eQTLs, we construct a two-component mixture prior for each SNP, i.e.,Because the vast majority of the LD blocks harbor no noteworthy association signals for any given complex trait, we follow the common practice in the GWAS analysis and adopt a pre-screening procedure to identify LD regions that are potentially interesting for fine-mapping analysis. Specifically, we use a rigorous Bayesian false discovery rate (FDR) control procedure  to screeWe find that the DAP-1 algorithm is practically adequate for fine-mapping most LD blocks in GWAS data, as we observe that the vast majority of the selected LD blocks harbor no more than a single association signal. Even if multiple GWAS signals co-exist in a single LD block, the DAP-1 algorithm can still be applied when aided by the conditional analysis approach proposed by . Alternai can be obtained asGiven the PIP from the fine-mapping analysis, the SNP-level colocalization probability (SCP) for SNP et al [regional colocalization probability, or RCP, by summing up the SNP-level colocalization probabilities (SCPs) of correlated SNPs within an LD block that harbors a single GWAS association signal. RCP is naturally interpreted as the probability of a genomic region harboring a colocalized signal. We recommend reporting both RCPs and SCPs in colocalization analysis. In practice, we only compute RCPs for the same LD blocks that are identified by the pre-screening step in the fine-mapping analysis. The rationale is simple: we do not expect an LD block to harbor a colocalized signal if it is unlikely to harbor a GWAS signal.Based on the discussion in the previous sections and following Gaun and Stephens  and Wen et al , we propδ1 = δ2 = 0.5 and α1 values in To demonstrate, we apply eCAVIAR and coloc. In particular, we argue that both of those approaches bypass enrichment estimation by making explicit assumptions on the enrichment parameters.In this section, we show that a priori, i.e., α1 is restricted to 0, then the prior for each SNP in GWAS becomes irrelevant to the molecular QTL data, and eCAVIAR.If the molecular QTNs and causal GWAS hits are assumed to be independent coloc model as a special approximation from our generalized modeling framework given the additional simplifying assumptions. Noticeably, coloc assumes that at most a single GWAS hit and/or a single QTN are located in the LD regions of interest. More importantly, it requires the user to specify the priors for p1 ≔ Pr, p2 ≔ Pr and p12 ≔ Pr. We show that these quantities can be equivalently parametrized within our modeling framework. For example,coloc also implicitly induces the marginal frequencies of causal GWAS hits ) and eQTNs ). Many have reported the sensitivity of the analysis results with respect to the subjective prior specification. We examine the performance of coloc when the priors are misspecified using our simulated data  can be intuitively estimated byM| denotes the number of rejected hypotheses [α, the Bayesian FDR control procedure simply ranks all candidate loci according to increasing values of (1 − RCPi) and rejects the null hypotheses for the largest set M, whereGiven a set of rejected hypotheses potheses , 25, 26.This study uses third party datasets and no additional ethics approval was needed.First, we perform simulation studies to benchmark the performances of the proposed enrichment and colocalization analysis approaches.z-statistics that are similar to the observed GWAS results. Specifically, we select real genotypes of 2.7 million overlapping SNPs used by both Wood et al [cis-eQTLs the GTEx. This particular posterior distribution is obtained by performing multi-SNP fine-mapping of the GTEx whole blood data via the adaptive DAP algorithm [i (γi) by drawing from a Bernoulli distribution whose success rate is determined by the logistic α0 and α1 values. Subsequently, a quantitative trait is simulated using a standard multiple linear regression model for which the residual error variance is set to 1, and the effect size of each causal SNP is drawn from a N distribution. Finally, we compute the single SNP association z-statistic for each SNP as the input for both the enrichment and the colocalization analyses. Although the sample size in the 1000 Genomes Project European panel is limited, we are able to adjust the values of α0  and ϕ  to roughly match the z-value distributions from the available large-scale GWAS meta-analysis. In particular, we estimate α0 and ϕ by analyzing the height data reported in Wood et al [α0 = −8.4 and ϕ = 0.4. Consequently, the distributions of the simulated z-statistics closely resemble the actual observed GWAS height data  as an observed continuous annotation. The second strategy, known as “best SNP imputation”, annotates the best associated cis candidate SNP of each eGene  as the causal eQTN.We also include two additional α1 value, which helps virtually dissect the relative variance and the bias of the point estimates from each estimation method. The results from various approaches are summarized in We compute the root-mean-square error (RMSE) for all methods to evaluate the overall accuracy of the corresponding point estimates, which is most relevant for the downstream analysis. In addition, we plot the averaged point estimates and corresponding standard errors from each simulated α1 is difficult even in the best case scenario: the point estimates show large variance even when the true values of γi and di are known. In comparison, we observe that the estimates obtained using the proposed approach are significantly stabilized by applying the proposed adaptive shrinkage. As α1 increases to relatively large values (> 3.0), the effects of shrinkage gradually diminish for all approaches: in the case that the true QTL annotation is known, the estimates become practically unbiased, although for the multiple imputation procedure, the resulting estimates are still notably biased toward 0, largely due to the simplified imputation distribution. Nonetheless, we note that the degree of bias has minimal impact on the subsequent colocalization analysis. The results clearly indicate that the multiple imputation procedure outperforms the two alternative ad hoc imputation approaches. The difference in performance between the proposed approach and the best SNP imputation is generally expected because the latter ignores the uncertainty due to LD and the potential multiple independent eQTLs within a gene. We observe that the mean imputation approach consistently  overestimates α1 for large α1 values, which becomes a serious concern for the downstream colocalization analysis.  for α1 = 3 and little power for smaller α1 values. Furthermore, despite the point estimates being downward biased, we observe that the proposed multiple imputation procedure provides excellent 95% interval estimates in the range of the α1 values examined experimentally: the coverage probability reaches 94.8%.Furthermore, we examine the statistical performance of the proposed approach for testing the null hypothesisFinally, the benchmarked computational time indicates that the proposed multiple imputation approach is highly efficient. We take advantage of the fact that the multiple imputation scheme is parallelizable and analyze each simulated data set on 8 simultaneous threads. Consequently, each enrichment analysis only takes approximately 4 to 5 minutes of real computing time.α1 = 4, which is close to our enrichment estimate of blood eQTLs in HDL GWAS hits from the real data. For each simulated data set, we perform the proposed colocalization analysis using two different fine-mapping strategies. The first strategy utilizes the individual-level genotype data from GWAS and obtains the GWAS PIPs by multi-SNP fine-mapping using the adaptive DAP algorithm. The second strategy assumes at most one causal GWAS hit within each LD block and computes the PIPs using the DAP-1 algorithm based only on the single-SNP association z-statistics. To evaluate the impact of the (imperfect) enrichment parameter estimate, we separately use the true and estimated  values (by multiple imputations) to construct the SNP-level prior α1 = 0 in prior eCAVIAR. In all cases, we compute the RCPs for all the pre-defined LD blocks in each simulated dataset. Additionally, we run the software package coloc on the simulated data. Because its setup is very different from the aforementioned approaches, particularly in its use of eQTL data, without diluting our main messages on the importance of enrichment estimation, we summarize its performance in section S.4 of To evaluate the performance of the colocalization analysis, we focus on the simulation setting of at any given FPR threshold; and iii) neglecting the enrichment analysis only yields slightly worse colocalization results.First, we construct receiver operating characteristic (ROC) curves to simultaneously evaluate the sensitivity and specificity of various colocalization analysis approaches. Specifically, we classify an LD block as harboring a colocalized signal if the corresponding RCP is greater than a pre-defined threshold. We vary the threshold from 1 to 0 to construct the ROC curve for each analysis scheme. The results are presented in α1 = 0 is extremely conservative, where the realized FDRs are nearly 0 and the power is significantly lower than all the other competing schemes. We therefore conclude that the accurate enrichment estimation has a critical impact on the quantification of the colocalized signals. In general, we find that the power to detect colocalized association signals is low across different schemes, i.e., < 40% at the 20% FDR level  of the GTEx project. The selection of the whole blood is informed by the consensus of multiple independent enrichment analysis approaches  to determine the relevant tissues for the blood lipid traits. In addition to biological relevance, we suspect that one of the driving factors is that the whole blood is one of the GTEx tissues with the largest sample size (338) in the current release of the data; it therefore has better power to detect cis-eQTLs with small to modest effects. The SNPs that are not directly genotyped are also imputed according to the same 1000 Genomes panel by the GTEx consortium. We perform the Bayesian multi-SNP fine-mapping analysis for the GTEx whole blood data using the adaptive DAP algorithm and generate the joint posterior distribution Pr while controlling for the SNP distance to the transcription start site (TSS) of the corresponding target gene. As shown in our previous results [To demonstrate the proposed computational approach in a practical setting, we perform an integrative analysis of the eQTL data from the GTEx project  and the et al . The bloPickrell , where a results , 22, thicis-eQTLs using the approach described in the Method section. This calculation only requires an approximate estimate of the genome-wide prevalence of causal eQTLs. Here, we show two different approaches for obtaining this estimate.Before conducting the proposed integrative analysis, we first compute the expected fraction of the GWAS hits of blood lipid traits that overlap blood cis-eQTLs and calculates the expected fraction of eQTNs from the posterior distribution bypd ≈ 1.47 × 10−3.The first approach utilizes the pre-computed posterior distribution of ad hoc approach to estimate pd without a Bayesian analysis of the cis-eQTLs. In particular, we note that the GTEx portal reports 6,784 eGenes  discovered in the whole blood samples at the 5% FDR level. Assuming that each eGene contains exactly one causal variant, we then estimate pd ≈ 6,784/6.1 × 106 = 1.11 × 10−3. Compared to the previous approach, which is more statistically rigorous, this estimate ignores potential multiple independent eQTNs within an eGene and the uncertainty embedded in the process of eGene discovery . Nevertheless, the two estimates have the same order of magnitude: we observe a causal cis-eQTL in approximately 1 out of 1,000 SNPs.Alternatively, we use a conservative α1 using the pd. The result (shown in pd), we should not expect a large fraction of the GWAS hits to overlap with the annotated cis-eQTLs unless the enrichment level is reasonably high. For example, even at α1 ∼ 5, which corresponds to a fold-change at ∼150, the expected fraction of colocalized GWAS signals is still less than 20%—in the case of the genetic variants associated with HDL, the expected number of colocalized signals is ∼10.We then calculate the expected fraction of GWAS hits overlapping causal eQTLs as a function of enrichment parameter shown in  indicatecis-eQTLs in the GWAS hits of the four lipid traits. As in the analysis of the simulated data sets, we apply the multiple imputation approach for each lipid trait by imputing 25 independent binary eQTL annotations from the joint posterior distribution of the blood cis-eQTL data.Next, we apply the proposed multiple imputation procedure to estimate the enrichment level of whole blood cis-eQTLs in lipid traits and their corresponding 95% confidence intervals in We show the enrichment estimates of blood ch trait . We findcis-eQTLs in whole blood. Although the true fractions of overlaps may have large variations due to the uncertainty embedded in the enrichment estimates (as indicated by their large CIs), these estimated expected fractions should reflect the relative difficulty in finding colocalized signals in each lipid trait.We then plug in the enrichment estimates and calculate the expected fraction of colocalized GWAS hits for each trait from the previously constructed power curves. In summary, we expect that 18%, 3%, 6% and 0.2% of GWAS hits in HDL, LDL, TC and TG overlap with causal et al [−8), their reported loci consist of a subset of ours. We further conduct the multi-SNP fine-mapping analysis on each identified GWAS locus, but we find no strong evidence that any of the loci harbors more than one association signal.Given the enrichment estimates, we proceed to perform the colocalization analysis. Specifically, we apply the Bayesian FDR control procedure  implemenet al  controllcis regions of multiple genes. Our solution to this problem is to compute an RCP for each LD block with respect to each gene that has at least one cis candidate SNP residing in the block. In particular, we construct the SNP prior Another practical issue arising in the eQTL analysis is that a single SNP can locate in the eCAVIAR and coloc, and we show the comparisons of the RCPs computed using the different approaches in eCAVIAR yields a highly concordant ranking of potential colocalized signals with enloc. However, the numerical values of the RCPs from eCAVIAR are generally smaller because of its assumption α1 = 0. The exception is in the case of TG, where the estimated coloc analysis is conducted using its default subjective priors for all 4 lipid traits, i.e., p1 = 10−4, p2 = 10−4 and p12 = 10−6. Overall, there is a larger degree of discrepancy in ranking colocalized signals compared to eCAVIAR and enloc. One of the reasons is that the default priors imply α1 = 4.6 for all 4 traits, which appear to be inappropriate for LDL, TC and TG. In addition, these priors also indicate a much higher marginal frequency of causal GWAS hits and a much lower marginal frequency of eQTNs compared to our estimations from the data. Although there is generally good concordance of probability quantification for very strong colocalization signals, we find that the severely misspecified priors make the colocalization analysis results less reliable.For comparison, we also perform the colocalization analysis using the existing approaches In summary, our analysis identifies 21 unique genomic region-gene pairs with an RCP ≥ 0.50. We summarize the results in cis-eQTL for gene LILRA3, has an SCP value of 0.979, showing a strong SNP-level colocalization signal with the GWAS hit of HDL.  However, the majority of the loci still carry many candidate SNPs due to common LD patterns present in the genetic data of both complex traits and molecular phenotypes. UBASH3B in a 52 kb genomic region on chromosome 11. Our analysis identifies 54 SNPs with a joint RCP = 0.645; however, the strongest individual SCP is merely 0.036. Additionally, the SNP-level PIPs for GWAS and cis-eQTL associations also exhibit a similar pattern: although there is not a single SNP taking high PIP values, the cumulative PIPs of the region are close to 1 for both GWAS and cis-eQTLs. We further compute the pair-wise LD of the 54 member SNPs based on the genotype data from the GTEx samples and confirm that all SNPs are indeed highly correlated.For a small proportion of the identified loci, we find that the colocalized signals can be effectively narrowed down to only a few SNPs. For example, SNP rs103294, a et al [⋆ in † in PSRC1 and Teslovich et al [SORT1 by the more comprehensive molecular evidence presented in Musunuru et al [SORT1 but very strong evidence of association with PSRC1 in whole blood; however, in liver, rs629301 shows strong associations with both genes with evidence for SORT1 being stronger . In addition, the same SNP also shows a strong association with CELSR2 in liver. We repeat the colocalization analysis using the GTEx liver eQTL data. Not surprisingly, we find that the same genomic region presents the strongest colocalization signals with all 3 genes among all liver-expressed genes, with RCPs = 0.691, 0.684 and 0.675 for SORT1, PSRC1 and CELSR2, respectively. The decrease of the RCP values is attributed to the lower eQTL enrichment estimate in liver . The case of SNP rs629301 in liver discussed previously is also an example of this type. Although this phenomenon is relatively well known in studies of molecular phenotypes, it certainly makes elucidating the molecular mechanism of causal GWAS variants more challenging.Finally, we note that a single GWAS association can be colocalized to eQTL signals of multiple genes. For example, our analysis indicates that the likely causal HDL variant in the genomic region chr2:85537312-85555478 is possibly associated with the expression levels of 3 different genes , it seemingly assumes that the enrichment level is very high , which is a strong assumption. In summary, we have demonstrated that the enrichment parameter plays a critical role in the colocalization analysis, and we believe that the best strategy to deal with this parameter is to learn it from the observed data, as we have demonstrated throughout.Compared to the existing methods for colocalization analysis, the most important distinction of our proposed approach is the natural integration of the enrichment estimation. Throughout the paper, we have illustrated the importance of obtaining accurate enrichment estimates on the downstream quantitative evaluations of colocalization. Our main conclusion is that the accurate enrichment estimates based on currently available data may not have an overall large effect on altering the ranking of potential colocalization signals; however, it is critically important for the calibration of the corresponding colocalization probabilities and has a profound impact on the outcome of formal statistical testing procedures. Existing probabilistic model-based approaches typically make explicit assumptions on the enrichment levels of molecular QTLs in the causal GWAS hits , as we have shown for the cases of pd in the near future. Accordingly, based on Importantly, our simulation and real data analyses apparently illustrate the limitations of currently available association data: we have shown that the confidence intervals of enrichment estimates are typically large and the expected fractions of colocalized GWAS signals are only modest, which are consistent with our observations from practice in the field. In particular, we note that most current molecular QTL  studies are conducted with only modest sample sizes due to cost considerations. Although many of these studies successfully identified an abundance of trait-associated genomic loci with large effects, the power required to uncover molecular QTLs with small to modest effects is lacking. Many molecular QTL studies have started scaling up their sample sizes, and novel analytic approaches, e.g., joint eQTL and allelic-specific expression (ASE) analysis , have shet al [Our proposed statistical model and inference procedure are completely general for analyzing two sources of genetic association data. Note that it is statistically equivalent to treating GWAS data as annotations for eQTL mapping. Our choice of presenting eQTL as an annotation is simply motivated by better biological interpretation of the model and our enrichment analysis. It can be shown that when individual-level data are available for both eQTL mapping and GWAS analysis, the choice of annotation should not alter the inference results under the proposed model. More generally, the proposed statistical framework is applicable for analyzing any pair of phenotypes to colocalize the association signals, as in applications demonstrated by Pickrell et al .Note that caution should be exercised when attempting to interpret the biological relevance of the identified colocalization signals. In colocalizing an eQTL and a GWAS hit, a seemingly obvious implication is the relevance of the target gene of the eQTL in the disease process. However, as we demonstrated in the analysis of the blood lipid data, there are cases in which other important biological factors should be considered: for example, the relevance of the tissue where the eQTLs are derived from. Although it is generally possible to statistically evaluate the biological relevance of eQTLs from different tissues for a specific complex trait through enrichment analysis, the currently available GTEx data are not satisfactory for this purpose because of the significant variations in sample size across tissues.  A more elegant solution is to utilize eQTL annotations generated from joint multi-tissue eQTL mapping approaches , 33, whiet al [In Testlovich et al , the autS1 Text(PDF)Click here for additional data file.S1 Figz-statistics are quite similar. The boxplot indicates that the extreme values from the two distributions are very much comparable; the density plot suggests that the simulated z-statistics are more concentrated around 0 and are hence slightly conservative.The overall distributional patterns of (EPS)Click here for additional data file.S2 Figad hoc imputation methods. The “best case” uses the true association status for both complex traits and molecular QTLs, whereas the “true annotation” utilizes the true association status from molecular QTLs only. The “best snp imputation” annotates the SNP showing the strongest association evidence in an eGene as its sole eQTN. The “mean imputation” annotates each SNP by its PIP. This figure highlights the difficulty in estimating ad hoc imputation alternatives.The proposed multiple imputation approach is compared to three methods utilizing added information that is unattainable in practice and two (EPS)Click here for additional data file.S3 Fig(EPS)Click here for additional data file.S4 FigeCAVIAR and enloc. The comparison indicates that the two approaches rank candidate loci with high concordance. However, the RCPs computed by eCAVIAR are much more conservative because of the assumption α1 = 0.For each trait, we compute the RCPs for each identified locus-gene pair using (EPS)Click here for additional data file.S5 Figcoloc and enloc. Although the two approaches generally agree on the very strong signals, there is considerable discrepancy in both ranking and quantification of the signals.For each trait, we compute the RCPs for each identified locus-gene pair using (EPS)Click here for additional data file.


Here we introduce Scoary, an ultra-fast, easy-to-use, and widely applicable software tool that scores the components of the pan-genome for associations to observed phenotypic traits while accounting for population stratification, with minimal assumptions about evolutionary processes. We call our approach pan-GWAS to distinguish it from traditional, single nucleotide polymorphism (SNP)-based GWAS. Scoary is implemented in Python and is available under an open source GPLv3 license at The online version of this article (doi:10.1186/s13059-016-1108-8) contains supplementary material, which is available to authorized users. Whole-genome sequencing (WGS) of bacteria is routinely performed in many laboratories all over the world, producing enormous amounts of accurate genome data, the majority of which is poorly understood. Genome-wide association studies (GWAS) have in human medicine and genomics become a workhorse for linking genetic variants in a population with observed phenotypes, but bacterial GWAS have only very recently started to emerge –9. TheseBacterial GWAS cannot directly adopt eukaryotic methods due to a number of important idiosyncrasies of bacterial evolution and the bacterial genome. Notably, the entire bacterial genome is considered to be in linkage disequilibrium, chromosomes and plasmids recombine internally and across phyla, and population samples are often stratified into multiple clusters of clonally related isolates. However, one advantage is that some mutations, at least clinically relevant ones, have high penetrance and are subject to high selective pressure. This makes causal links easier to establish, i.e. smaller sample sizes can result in statistically significant associations.Many bacterial phenotypes can be linked to the presence or absence of particular genes that are inherited through descent or acquired through lateral gene transfer. The full complement of all genes among a set of genomes is referred to as the pan-genome , 12. TheStaphylococcus epidermidis. We further report the power of our software over a range of sample sizes by subsampling of a large Streptococcus pneumoniae dataset, demonstrating high power in sample sizes larger than 100. Finally, we investigate how gene penetrance and sample size affect the power to detect causal genes using simulated data and benchmark our program against the program PLINK [Here we present and benchmark Scoary, an easy-to-use, ultra-fast tool for studying the association between pan-genome genes presence or absence and observed phenotypes. We term the method “pan-GWAS” to distinguish it from traditional SNP-based GWAS. Each candidate gene in the accessory genome is sequentially scored according to its apparent correlation to predefined traits. Genes that pass the initial screening are re-analyzed while incorporating information on the phylogenetic structure of the sample. This correction step makes minimal assumptions about evolutionary processes and directly infers population structure from the input data. This ensures reproducibility as well as accessibility for users with limited bioinformatics and population genetics skills, as they need not experiment with ill-informed mutation rate parameters or even inform the program about population structure at all. In order to ensure the validity of results, Scoary implements a post-hoc label-switching permutation test. As few as 20 samples can in some cases be enough to implicate a causal gene, which we demonstrate by applying our method to study linezolid resistance in am PLINK , which ham PLINK .Scoary is implemented as a standalone python script with SciPy  as it isTo enable the efficient execution of these computationally demanding tasks, they are performed by Scoary in a multiprocessing environment. Using 50 samples with a total of 23,133 gene families, we fully analyzed every gene for associations to three different traits in 7 s when tested on a standard desktop computer with 4 CPU cores and 8 GB RAM. The internal algorithm makes very few assumptions and, as such, does not require extensive parameter estimation. Two files are needed as input: a genotype  matrix and a trait file. The former is created by Roary and can be fed directly to Scoary. The latter has to be created by the user and is a simple matrix  describing the phenotype status for each strain. Traits must be binary, but more complex data  can also be used by breaking observations into dummy categories.An overview of the Scoary workflow can be seen in Fig. For each phenotype supplied via columns in the traits file, Scoary does the following: first, correlated genotype variants are collapsed. Plasmid genes, for example, are typically inherited together rather than as individual units and Scoary will collapse these genes into a single unit. Each candidate variant then receives its own null hypothesis of no association to the trait. As a first and optional filtration step, a Fisher’s exact test is performed on each variant in a population-agnostic manner. This happens as follows: A 2 × 2 table is created, the levels being positive or negative for the trait and gene, respectively, and the number of isolates in each cell is then counted. Variants that are present in every input isolate are excluded since they provide no information as to which variants are responsible for a trait that is differentially distributed in the sample. Similarly, variants that are not present in any input isolates are excluded .Since the program investigates a potentially huge number of null hypotheses, additional filtration can be specified using the Bonferroni and Benjamini–Hochberg adjustments , 17 to cp values (2.8E-6) for both matrices. In Fig. An assumption in Fisher’s test is that all isolates have a random and independently distributed probability for exhibiting each state Fig. . As suchp = 0.5 for each possible outcome irrespective of the genotype. Pairs that contrast in one variable but not the other (e.g. 1–0|0–0) are not considered informative [If the null hypothesis is true, there should be approximately equally as many 1–1|0–0 pairs as 1–0|0–1 pairs  , 22. Henormative .P values corresponding to the best and worst scenarios are calculated with binomial tests and both values are reported. Using our example above, the best pairing (7/7 1–1|0–0 pairs) would correspond to a p value of 0.015 and the worst pairing (6/7 1–1|0–0 pairs and 1/7 1–0|0–1) would correspond to a p value of 0.125. Note that it is not quite clear how to interpret such a p value range as some possible pairings might be better than others  and the number of possible pairings associated with one scenario could be much higher than the number of possible pairings associated with the other [p values are less than the predetermined alpha in order to score the association as significant.This method allows probabilities of evolutionary change to vary throughout the tree, but does not actually require that these probabilities or an explicit evolutionary model be specified. There are usually many possible maximal pairings and among these some might provide more support for a significant association than others. Given a maximal number of pairs that contrast in both the gene and the trait states, Scoary calculates the maximum and minimum number of pairs that support an association. In the following, we will assign the terms “best” and “worst” pairings for these respective scenarios. Figure he other . A consep value is returned as (r + 1)/(N + 1) [An additional test implemented by Scoary is that of label-switching permutations. This is achieved by making random permutations of the phenotype data and calculating the associated test statistic (maximum number of 1–1|0–0 pairs divided by maximum number of pairs) for each permutation. The permutation statistics are sampled under a situation where the null hypothesis is true, since any association between the genotype and phenotype is broken by the random sampling. If N is the number of permutations and r is the number of test statistics observed to be higher or equal to the unpermuted statistic, the empirical /(N + 1) . Dependip values. The output can be controlled by a number of optional parameters, such as max number of hits and p value cutoff.The output of Scoary is a single list of significant genes per trait. Each trait results file reports the highest scoring genes, i.e. those genes that were most associated (either positively or negatively) with the trait, sorted by Staphylococcus aureus (MRSA) and methicillin-resistant coagulase-negative staphylococci (CoNS) [Linezolid (LZD) is an oxazolidinone-type antibiotic used to combat Gram-positive bacteria such as methicillin-resistant i (CoNS) . LZD-resi (CoNS) .Staphylococcus epidermidis by applying the algorithm to a set of 21 isolates for which public WGS data and LZD minimum inhibitory concentration (MIC) values had been published [We applied Scoary to identify genes associated with high-level resistance to LZD in ublished . MIC valcfr, as significantly associated with high-level resistance to linezolid, although the high end of the pairwise comparison p value range exceeded 0.05  that were associated with the trait, which were significant (p < = 0.05) after pairwise comparisons. Fisher’s test additionally identified several other genes as significant prior to population-aware analysis, but upon inspection of the population distribution these were found to be lineage-specific effects and were concordantly not reported as significant by the pairwise comparisons test.Scoary correctly predicted the well-known LZD resistance gene 05 Table . AdditioStreptococcus pneumoniae, erythromycin resistance is bestowed by the presence of the erm gene [S. pneumoniae sampled from a refugee camp in Thailand [erm gene was significantly associated with resistance.Erythromycin is a macrolide-type antibiotic compound used against a wide range of bacterial infections. In erm gene . To estiThailand  with eryerm gene was relatively rare in the sample  and the subsets were randomly selected without regard for genotype or phenotype status. As a general rule, equal proportions of each genotype/phenotype variant would be associated with higher power, while lower power than that demonstrated here would be attained in a sample dominated by one genotype/phenotype status   in the range of 20–200 and for each sample size N we sampled ten random subsets of N isolates. On each of these datasets, we ran Scoary with three different filtration cutoffs: (1) population-naïve Fisher’s exact test p value < 0.05; (2) same as (1), but with the additional requirement that the entire range of pairwise comparisons p values were < 0.05; (3) same as (2), but with the additional requirement that the empirical p values of the variant after 1000 permutations were ≤ 0.05. Table In order to understand how Scoary is affected by the phenotypic penetrance of causal genes under various sample sizes, we additionally tested the power of Scoary on simulated data. The simulated genomes were created with a custom script see “”. BrieflOur results demonstrate that Scoary performs remarkably very well at small sample sizes. At 90% phenotypic penetrance, the mean F1 score  see “Me” is abovAlthough originally designed for human GWAS, a few microbial association studies , 29 haveWe have developed a method to score the components of a pan-genome for associations to traits. Our method is implemented in an open-source tool named Scoary and can be run on all modern computers with python and SciPy installed.Staphylococcus genus database. The pan-genome was constructed using Roary 3.4.2 [Sequence data (accession number SRP039360) was downloaded from NCBI Sequence Read Archive (SRA), subsampled to coverage 50 with khmer 2.0 , and assry 3.4.2 . Scoary ftp://ftp.sanger.ac.uk/pub/pathogens/Streptococcus/pneumoniae/. These were annotated with PROKKA 1.11. The pan-genome was constructed using Roary 3.4.2. We created a custom script that randomly sampled a predetermined number of isolates  from the full set of 3085 and ran Scoary 1.6.3 with the --restrict_to parameter. This was done ten times for each sample size and replicated for each filtration scenario 1, 2, and 3, as described in the Sequences that were previously assembled by Chewapreecha et al.  as well https://github.com/AdmiralenOla/Simulate_pan_genome) that worked as follows. Evolution starts with a single root genome with 3000 genes and an additional set of 6000 genes that could possibly be acquired (representing the entire pan-genome). At the onset of evolution, each genome in the collection independently acquires and loses genes at gene-specific rates sampled from a uniform distribution (0.0–0.01 per time). At each mutation event, each genome also has a chance to duplicate itself (representing a branching event), after which the duplicate is added to the collection. When the total number of genomes in the collection reaches a predetermined desired sample size, evolution stops and the pan-genome is returned in a file similar to Roary’s gene presence/absence file. Two parameters can be specified by the user: (1) the desired number of samples; and (2) the causal gene penetrance, defined here as the probability of also acquiring/losing the studied phenotype simultaneously to an acquisition/loss of causal gene event. We ran this script ten times for each possible combination of the following parameters: sample size: 25, 50, 75, 100, 150, 200; penetrance: 90, 75. The p value cutoff was set based on initial simulation rounds. The F1 score was calculated as the harmonic mean of the precision and recall rate, here defined as follows: Precision = Number of true positives divided by the number of positives returned. Recall (sensitivity) = Fraction of true positives that are actually identified as positives. The mean F1 score is reported for each parameter combination.We created a custom script , requiring at least five isolates in each group and a pairwise population concordance (ppc) significance of less than 0.05 for grouping. Association analysis was carried out with the Cochran-Mantel-Haenszel association statistic (−−mh flag) to condition on the clusters. We used the Benjamini-Yekutieli adjusted https://github.com/AdmiralenOla/Scoary. Its only non-standard dependency is SciPy [Scoary is implemented in Python (2.7+ and 3.x) and is available under an open source GPLv3 license at is SciPy  version


MAP4 on chromosome 3. Our primary interest is to compare the performance of standard and sparse-data approaches for single-variant tests and variant-collapsing tests for sets of rare and low-frequency variants. We analyze both the real and the simulated phenotypes.Availability of genomic sequence data provides opportunities to study the role of low-frequency and rare variants in the etiology of complex disease. In this study, we conduct association analyses of hypertension status in the cohort of 1943 unrelated Mexican Americans provided by Genetic Analysis Workshop 19, focusing on exonic variants in  Despite the success of genome-wide association studies, much of the genetic contribution to complex diseases and traits remains unexplained. Therefore, an increasing number of studies have turned to low-frequency and rare variant association analysis for additional explanation of disease risk or trait variability. For binary phenotypes, single-variant analyses of low-frequency and rare variants are challenging because the conventional logistic regression approaches often violate the large-sample-size assumption for test statistics, resulting in poor type 1 error control or low statistical power . The staIn this report, we analyze the exome-sequence data and both the real and simulated phenotype data of the unrelated Mexican American sample to evaluate and compare the performance of single-variant and variant-collapsing methods for association analysis.i = 1, …, 1943 indexes the individuals, HTNi indicates hypertension status of the ith individual ; AGEi is the age at the time of examination, SEXi is the gender of the individual, and m variants , and To relate genotypes to hypertension, we consider the logistic regression modelm = 1, we apply 2 types of nonstandard approaches: Firth-type penalized logistic regression likelihood ratio (LR) tests [i(β) is the Fisher information matrix. This is a generalization of Haldane’s statistic for sparse 2 × 2 table analysis, where For a single-variant analysis with R) tests –8, and sR) tests , and comK subregions, then pool the variants within each subregion, and test K null hypotheses mk indicates the number of variants within the k-th subregion . For convenience, we determine the subregions on the basis of physical proximities among the variants.For variant-collapsing analysis, we consider a MAF-based weighted burden test , a nonbuMAP4 gene on chromosome 3 in the real and the simulated phenotype data sets. For the imputed variants, we analyzed the predicted dosages rather than their best-guess genotypes. In addition, we examined all polymorphic variants, including the singletons to assess the extremes at which the tests break down. For the standard and penalized logistic regression tests, we used the R glm function and pmlr  package [SKAT [K = 6 based on a visual inspection of the physical positions of the variants  greater than 140 mm Hg or a diastolic blood pressure (DBP) greater than 90 mm Hg. We also defined individuals on antihypertensive medication to be hypertensive regardless of their SBP and DBP levels.Q1 generated under no genetic effects. Because SIMQ1 did not have binary phenotypes, we dichotomized Q1 to create hypothetical disease status Q2, letting Q2 correlate with AGE and SEX through Q1. We let Q2 = 1 if Q1 was greater than 51.2 and 0 otherwise, such that the disease prevalence for Q2 was 17.8 %, the same as the prevalence of hypertension in SIMPHEN, which we used for evaluating power. The hypertension phenotype was derived from blood pressure phenotypes generated under a model with more than 1000 variants in more than 200 genes [For the simulated phenotypes, 2 data sets were available, “SIMQ1” and “SIMPHEN,” each with 200 replicates. SIMQ1, designed for evaluating type 1 error rates, contained normally distributed 00 genes .MAP4 variants, only 90 were polymorphic in the sample of 1943 unrelated individuals. These variants had MAFs ranging from 0.00027 to 0.34. As expected, rare variants (MAF <1 %) were most prevalent in the sample; except for 4 common variants, all variants had MAF less than 5 % . The burden, SKAT and SKAT-O  tests, each of which pooled all polymorphic variants within the K = 6 subregions defined in Table MAP4 gene to be significant either .We found that the standard score test rejects the null hypothesis far more often than the other single-variant tests (results not shown), suggesting that it may be anti-conservative. This agrees with published simulations under a case-control design  and is cG > 0 dosage, denoted by It has been demonstrated that for a genome-wide study with a large sample size, minor allele count (MAC) is the key parameter determining test calibration . Becausep values for rare variants revealed departures from the expected distribution under the null hypothesis of no genetic effects with some discrepancies among tests. For example, for var_3_47660325, with p value distributions were close to the expected, except in the upper tail where all tests seemed to be anticonservative  plots of the single-variant test ted Fig. . For loweg, Fig. . As expeeg, Fig. .Fig. 3Q-Examination of empirical type 1 error rates for the single-variant tests demonstrates that no method performed uniformly better than others for the rare variants with very low MACs Fig. . For exa.01 Fig. , but waseach of the rare variants, but had 100 % power for the low-frequency and the common variants at the significance levels of 0.01 and 0.05. For the low-frequency variants, tests had discrepant p values, and differential power at a stricter significance level. For example, in Fig. p values of less than 0.01; however, the 2 LR tests had consistently lower p values than the 3 score tests. At a significance level of 1e–06, the standard and penalized LR tests had 91 and 82 % power, respectively, whereas the standard, the small-sample-variance, and the small-sample-variance-kurtosis score tests had less than 10 % power.All the single-variant tests had power of less than 20 % to detect Among the 4 subregions with at least 1 functional variant, power was nonnegligible only in subregions 4 and 6 Table . Figure MAP4 gene on chromosome 3, using both the real and the simulated phenotypes in unrelated Mexican Americans.In this article, we evaluated standard and sparse-data methods for single-variant and variant-collapsing tests to examine the association between a hypertension phenotype and exonic variants in MAP4 variants significantly associated with hypertension. A limitation of our analysis is that we did not make any adjustment for ancestry admixture/population structure. In genetic association studies of admixed populations such as Mexican Americans, addressing differential ancestral backgrounds is important to avoid false positive or negative association signals [In the analysis of the real phenotype data, none of the single-variant and the variant-collapsing methods detected  signals , 15.p values as it suggests large-sample approximations for test statistics may be invalid.In our simulation investigation, we found that the sparse-data approaches improve type 1 error control, but their power remains low for detecting the rare variant effects. Because power of the association tests depends on both frequency and effect size of rare variants, even with large effects, the tests may detect rare variants only in studies with large samples. We may be more successful in identifying rare variants when we use joint or meta-analyses combining data or summary statistics from different studies . For thAlthough previous simulation studies have shown that collapsing tests can have greater power than single-variant tests , our in


A genome-wide analysis uncovered a total of 160 significant marker-trait associations (MTAs), of which 32 were LW-specific, 59 were PF-specific, and 69 were in common between the two water management systems. LW-specific associations were identified for several agronomic traits including days to maturation, days from flowering to maturation, leaf traits, plant height, panicle and seed traits, hundred grain weight, yield and tillering. Significant MTAs were detected across all the 12 rice chromosomes, while clusters of effects influencing different traits under LW or in both watering conditions were, respectively, observed on chromosomes 4, 8, and 12 and on chromosomes 1, 3, 4, 5, and 8. The analysis of genes annotated in the Nipponbare reference sequence and included in the regions associated to traits related to plant morphology, grain yield, and physiological parameters allowed the identification of genes that were demonstrated to affect the respective traits. Among these, three  and seven  candidate genes were, respectively, identified to co-localize with LW-specific associations and associations in common between the two water treatments. For several LW-specific MTAs, or in common among the two treatments, positional co-localizations with previously identified QTLs for rice adaptation to water shortages were observed, a result that further supports the role of the loci identified in this work in conferring adaptation to LW. The most robust associations identified here could represent suitable targets for genomic selection approaches to improve yield-related traits under LW.A rice GWAS panel of 281 accessions of  Rice is cultivated under both anaerobic  and aerobic (upland) conditions, with more than 75% of rice supply coming from 79 million ha of irrigated lowlands . IrrigatNevertheless, high-yielding rice varieties bred for lowland cultivation systems are generally subjected to yield loss in aerobic soils , so thatA rice ideotype adapted for the cultivation under aerobic conditions should possess a combination of morpho-physiological traits such as root distribution in the soil profile, nutrient uptake, and dynamics of tillering and grain filling , which aBesides linkage mapping, genome wide association studies (GWAS) represent an additional genetic tool for the identification of rice gene variants that underlie adaptation to aerobic conditions. The emergence of more cost-effective and high-throughput genotyping platforms have allowed the application of GWAS for QTL mapping in plants . Since Gjaponica rice accessions genotyped for over 200,000 SNPs . This panel is composed of 70 tropical and 211 temperate japonica accessions. Most of these accessions (147) were selected in Italy, 32 in United States, 25 in Portugal, 19 in Spain, 10 in Bulgaria, 10 in Argentina, 6 in France, and the remaining were developed elsewhere but considered well adapted to Italian agro-climatic conditions. Detailed information regarding the accessions is reported in Supplementary Table The accession panel used in this study includes 281 Field trials were set up at the Research Centre for Cereal and Industrial Crops in Vercelli . The soil in this area is a sandy-type  with pH = 6.36. The entire panel was tested using two different water management systems . A completely randomized design, with three replicates per watering condition was adopted. Each plot consisted of three 170 cm-long rows 10 cm spaced, each one containing about 60 plants (180 plants/plot). Evaluations were carried out during the 2012 and 2013 growing seasons, following standard agronomic practices for rice growth.In the PF trial sowing was performed in dry conditions; the field was flooded (10 cm water) when the majority of the cultivars reached the three-leaf stage  and kept in this condition throughout the whole growing season until 30 days before harvesting. In the LW trial, sowing was performed as above; six tensiometers  were evenly installed in the field and watering was applied when the average soil water potential reached values lower than -30 KPa at a depth of 20 cm.Table 1 and described below.The 281 rice accessions were phenotyped for the different trait categories listed in Days to flowering (DF) and days to maturity (DM) were counted starting from the sowing date. Plots were considered as flowered when at least 50% of the plants extruded 1/3 of the panicles, while the maturation date was assumed when at least 50% of panicles showed 2/3 of dried rachis. Days from flowering to maturity (DFM) were calculated as DM – DF.∗FLW∗0.75 while panicle length (PL) as difference between PH and PNH.Flag leaf length (FLL), flag leaf width (FLW), plant total height (PH), and panicular node height (PNH) were measured on five representative plants for each plot . Leaf area (LA) was calculated as FLLTable 1 were measured on hulled  and naked  seeds.One hundred seeds were randomly chosen from grains obtained from each plot and scanned images of these seeds were analyzed with the software WinSeedlePro V.2011. The morphology descriptors listed in The number of tillers per linear meter (TPM) and yield of 50 representative panicles (PW) were recorded for each plot. The HGW was obtained for each plot using hulled (HGW) and naked (NHGW) seeds.Nitrogen Balance Index (NBI), an indicator of the plant nitrogen status , was recFrequency distributions of phenotypic data were tested for normality using the Shapiro–Wilk function in R environment. Analysis of variance (ANOVA) was performed using the “aov” function in R environment to assess significance of genotypes (G), year (E), genotype × year interaction (G×E) and replicates within each environment (PF and LW). Components of phenotypic variances were estimated by fitting a mixed model by the Restricted Maximum Likelihood method, considering G, E and G×E as random factors. Broad sense heritability (H) was calculated according to 2G is the genetic variance, σ2GE is the genotype × environment interaction variance, σ2e is the residual variance, E is the number of environments, and r the number of replicates. Finally, to find out whether or not traits are correlated to each other, Pearson coefficients were calculated in R using the standard “cor.test” function and the significance of correlations was assessed with the t-test implemented in the “cor.test” function.where σThe accessions included in the rice panel were genotyped-by-sequencing (GBS) following a pipeline described by 1  the Evanno method of ΔK was used, implemented in the free software Structure Harvester . Accessions with a minimum membership  of 0.7 were assigned to a subpopulation, while the remaining were considered as admixed. The phylogenetic tree, represented with iTOL2 was implemented with the results of the Structure analysis, together with the information relative to the varieties of the panel.To investigate the genetic stratification of the rice panel, three different methodologies based on principal components (PCA), phylogenetic clustering and a Bayesian model-based analysis, were used on a subset of 9,996 random SNP markers (833 markers/chromosome). The PCA was performed using Tassel v5.2.0  based onarvester . Once der2) among 5,000 randomly selected markers was performed by the R package “LDcorSV v1.3.1”  was used for GWAS, with the kinship matrix (K) as a random effect to take into account the population stratification.For the genome-wide association analysis, the least-square means by year for the traits listed in p-value of the association to the phenotypic traits was calculated for each marker; the significance threshold to declare a marker as associated was set to 0.05 after correction for multiple testing using the false discovery rate (FDR) method according to 10 in the Manhattan plot (even below the FDR threshold). Clusters of SNPs in full LD showing the same p-value in association analysis were considered as a peak region.Two separate association analyses were performed for the two different watering treatments (PF and LW) with Tassel v5.2.0. The program was run with the following parameters: no compression, genetic and residual variance estimated for each marker (P3D OFF). A Oryza sativa reference sequence (Os-Nipponbare-Reference-IRGSP-1.03) and reported in Supplementary Table 4 . The frequency distributions of phenotypic classes indicate that these traits are quantitative and continuous, suggesting a complex genetic control . When trait values of rice accessions subjected to the two watering treatments were compared, higher mean values were observed in PF, while for DF, DM, FLW, and FLA no statistically different values were recorded between LW and PF (Table 2). However, for average values of DF, DM and DFM, LW resulted in moderately significant delayed flowering, maturation and grain filling period .In the present work, a total of 26 traits related to plant phenology, morphology, and physiology (pre-harvest traits) as well as seed morphology and yield (post-harvest traits) were measured on 281 Table 2).Differences between the minimum and maximum trait values in PF ranged from 1.3 (for FLA) to 4.9 (for LA) fold changes with the majority of the traits (15 out of 25) showing a fold change higher than 2; whereas for LW, the range of fold changes was from 1.3 (for FLA) to 10.5 (for PW) with 18 traits out of 26 showing a fold change higher than 2. The coefficients of variation (CVs) in LW varied from 8% for flavonoid content (FLA) to 36% for LA and TMP, while in PF CVs ranged between 7 and 34% for DM and LA, respectively . In general, the seed width/length ratio, defining the commercial class of each variety, was not influenced by LW. For traits related to plant morphology, 16, 3, and 8 varieties showed higher LA, total plant height (PH) and PL in LW, respectively. Finally, for physiology-related traits, 25 varieties evidenced higher chlorophyll (CHL) and NBI values in LW  for all traits and genotypes highlighted that accessions generally performed worst for yield-related traits in LW (Table 2). These values suggest that genetic factors greatly contribute to the variance of measured traits.The analysis of variance within each treatment indicates that, in most cases, the effect of the year was highly significant. The genotype effect was always highly significant for all traits in both water management systems .Pairwise Pearson’s coefficients of correlation among the traits were calculated for each water management system (r = 0.84) was observed; on the contrary, DF was negatively correlated with grain and panicle weight (r = -0.76 for HGW and r = -0.80 for PW). These correlations were not significant under PF conditions . A negative correlation (r = -0.8) was observed between TPM and HGW , most likely indicating that under LW, plants producing more tillers had grains of smaller size.Forty-four correlations specific for the LW condition were identified , and 35 varieties classified as admixed  indicates that the first (PC1) and the second (PC2) coordinates accounted together for 32% of the total variability . PC1 clearly separates the sub-populations defined by Structure and corresponding to the temperate and tropical japonica subgroups. The admixed accessions clustered in between, reflecting the contribution of both sub-populations in their pedigree. A neighbor-joining clustering of the whole panel, implemented with the classification of the accessions and the membership results from the STRUCTURE analysis, indicates that different clustering methods utilized to unveil the population stratification provided similar results, although a few exceptions were revealed . Indeed, 13 varieties classified as tropical japonica clustered in the group of temperate accessions and, 10 of them were classified as admixed in the STRUCTURE analysis. The unexpected classification and the admix status of these lines suggest that these rice varieties are the result of breeding programs which exploited accessions from these two rice groups. The position in the neighbor-joining tree of the rice accessions showing LW/PF values above the 95 percentile  for the PW and HGW traits did not highlight any obvious clustering, suggesting that alleles conferring adaptation to LW condition in this panel are generally contributed by unrelated accessions. However, considering the LW/PF value for the PW trait, four accessions included in the 95 percentile were clustered, suggesting a common origin of the adaptive alleles in these four accessions, a finding that is supported by the common country of origin  for three of them  as well as between the two groups (K1 and K2) identified by the STRUCTURE analysis (H = 0.29 in both) resulted in values only slightly smaller  was 911.7 kbp, ranging from 355 kbp for chromosome 11 to 1,295 kbp for chromosome 8  for these associations ranged between 3.40 and 14.95 . Moreover, in Supplementary Figure S4 the position on the Nipponbare reference sequence of the peak markers and associated regions of MTAs LW-specific and present in both conditions for which candidate genes were identified, is indicated with respect to the position on the Nipponbare reference sequence of candidate genes. The analysis allowed the identification of positional relationships of several MTAs with genes known to underlie the corresponding traits  ranging between 4.9 and 11.4%. A total of 13 associations were detected by more than 1 SNP and 3 of these  were identified by 11, 12 and 20 markers, respectively. Furthermore, the size of the associated regions ranged from 21,531 to 1,178,593 bp. Three markers were associated with multiple traits: SNP S10_15368426 was associated with DM (both watering treatments) and DFM (PF only), while S7_20912737 and S10_17323647 were associated with both DF and DM .The analysis yielded 22 significant associations , with a percentage of the variance explained  gene, which encodes a B-type response regulator promoting flowering by activating the florigen gene RICE FLOWERING LOCUS T 1  corresponds to the SUI1 (SHORTENED UPPERMOST INTERNODE 1), a gene coding for a putative phosphatidyl serine synthase and representing a negative regulator of the uppermost internode elongation in rice  that were demonstrated to be involved in plant morphology. Rice plants over-expressing OsOFP2 (Os01g0625900) exhibit dwarfism, as this gene modulates NOX and BELL transcription factors, which control vascular development, and showed a reduced expression of the GA biosynthetic enzyme GA 20-oxidase 7 and thus a lower GA content  and corresponding to the “green revolution gene” Sd1, whose mutations resulted in a reduced plant height in rice  locus was included in the sequence intervals detected by FLW-4-1 and LA-4-1 (both present in LW and PF). Rice mutants in the Nal1gene exhibited narrow leaves with a decreased number of longitudinal veins  increased yield in modern indica cultivars as its presence resulted in a higher number of spikelets , was identified. The gene encodes for an A20/AN1 zinc-finger which negatively regulates GA homeostasis and thus cell elongation in rice  with R2 ranging between 4.4 and 9.0%, were detected for yield-related traits. Eighteen of them were detected by more than one SNP, and the region varied between 8,562 and 1,588,290 bp  which are known to affect yield-related traits  co-localized with MTAs detected in both conditions and affecting grain weight (HGW and NHGW) and panicle weight (PW). Os05g0187500 encodes for the GW5 (GRAIN WIDTH5) protein and co-localized with HGW-5-1, NHGW-5-1 and other seed traits, present in both LW and PF conditions , already described above as associated to leaf-related traits (FLW and LA), is located in the regions associated to panicle  and grain  weight. Allelic variation at Nal1 was demonstrated to affect yield acting on the number of spikelets  encoding locus Os04g0663600 was observed . Allelic variations in WOX1 exhibit correlation with the expression levels of cytokinin regulators and the formation of axillary buds, which in turn deeply affect the tillering capacity  between 4.5 and 6.5% , a key enzyme of polypropanoids biosynthesis , showed co-localization with the PF-specific FLA-1-1. Shikimate kinase is a key enzyme of the shikimate pathway, which represents the biosynthetic route for the biosynthesis of aromatic amino acids , which building blocks for the production of chorismate and thus of flavonoids , with an explained variance , on chromosome 8 for TPM and NSW  and on chromosome 12 for HGW, CHL and NBI  and NHGW-10-1(LW-specific) and marker S7_23302632, that on chromosome 7 was associated with both SW-7-1 (present in LW and PF) and NHGW-7-1 (PF-specific).japonica rice, respectively. These discrepancies could be explained considering different factors such as SNP densities and/or kinship among accessions, as previously discussed  adapted to this water condition. Accumulation of these alleles conferring small fractions of improved phenotypic values for a given trait, as suggested by the estimated Figures 7 and Supplementary Figure S4) with the final aim of establishing multiple relationships for the MTAs identified and providing a list of robust MTAs for adaptation to LW conditions.Using grain yield under reproductive-stage drought as a selection criterion, a number of large-effect QTLs for grain yield under reproductive-stage drought for both upland and lowland conditions have been identified and recently reported . PositioAmong the LW-specific associations, PW-2-1 , NHGW-10-1  and HGW-12-1 , are present in both LW and PF conditions and could represent robust associations , further reinforcing this association. Similarly, DM-4-2  overlapped with a sequence interval on chromosome 4 delimited with markers C513 and RM349 , which controls drought avoidance.For this category of MTAs, it was observed that DFM-3-2  overlapped with sequence intervals related to drought avoidance on chromosome 3 , identifEhd1 gene, DF-2-2 , which lies in the region of the OsCOL4 gene, DFM-3-2  and DFM-10-3 (LW-specific), which is in the region of the OsMADS56 candidate.Additional robust loci include DM-10-3 (LW-specific) closely located to the Nal1 gene. Furthermore, the association FLL-1-2  was included in a LD block spanning the interval 28,186,751–29,184,329 bp, containing the S1_28597986 marker identified by Among the several associations detected for leaf morphology, FLW-4-1  overlapped with a 775.7 kb interval identified by D35 and HDA702 genes are localized. Allelic variation in the first one demonstrated to be implicated in the GA biosynthetic pathway, therefore influencing GA levels which in turn affects plant height  which included the marker S6_22330734 associated to the same trait by t height ; insteadf OsNAC6 . The assf OsNAC6 .SUI1 candidate gene, the genomic interval identified by PNH-1-2 (LW-specific) which co-localized with the OsOFP2 and Dlf1 genes, PH-1-2 and PNH-1-3 (present in both PF and LW) which includes the “green revolution gene” Sd1 and LA-4-1 (present in both LW and PF), which co-localizes with the Nal1 gene.Additional robust loci, are PL-1-1 (present in both LW and PF), which is located in proximity of the GW5. Furthermore, overlapping with drought avoidance-related regions  and genomic prediction of lines-progenies of bi-parental crosses involving accessions belonging to the reference population (across generations) for complex traits investigated also in the present work, namely flowering date, nitrogen balance index, and yield-related traits. In the Genomic Selection study, we observed that the use of phenotypic and genotypic data from the reference population to train the prediction model allowed the prediction of the performances, in both the approaches  with accuracies superior to 0.5, even for complex traits such as grain yield, when the parameters that affect the accuracy are optimized .japonica rice panel. The GWAS analysis provided a large number of significant associations, an expected result considering the high number of phenotypic traits investigated, and, among them, 32 were LW-specific, while 69 were in common between LW and PF. Genomic regions where clustering of multiple traits affecting performances under LW and both water management conditions were identified and could be hot-spots for adaptation to LW conditions. The robustness of several of these effects was assessed through the identification of genes whose allelic variation could affect the phenotypic response to LW and through verification of positional relationships with QTLs previously identified as involved in rice adaptation to drought stress or reduced water availability. Since the GWAS panel used in this study was successfully used in a recent Genomic Selection approach, involving both cross validation and genomic prediction across generations ; it is therefore expected that the accumulation of alleles here identified as conferring improved phenotypic values under LW or both cumulated (LW and PF) conditions through Genomic Selection should allow recovery of japonica rice lines with improved adaptation to LW conditions.Results obtained in the present work indicate that most of the 281 rice temperate and tropical accessions of our panel are penalized for several agronomically relevant traits when grown under LW. However, performances of several accessions in LW were similar to those obtained under PF, suggesting that genetic variability for adaptation to LW conditions is present in our AnV, FD, AT, and CB carried out the data analyses and wrote the manuscript. FD, CB, RP, GO, PR, DC, SU, and MBH participated in field and post-harvest evaluations of phenotypic traits. AnV, FD, AF, PC, and FB performed the data analysis and revised the paper. GS, PP, LC, and GV designed the study and revised the paper. All authors have read and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The genetic component of complex disease risk in humans remains largely unexplained. A corollary is that the allelic spectrum of genetic variants contributing to complex disease risk is unknown. Theoretical models that relate population genetic processes to the maintenance of genetic variation for quantitative traits may suggest profitable avenues for future experimental design. Here we use forward simulation to model a genomic region evolving under a balance between recurrent deleterious mutation and Gaussian stabilizing selection. We consider multiple genetic and demographic models, and several different methods for identifying genomic regions harboring variants associated with complex disease risk. We demonstrate that the model of gene action, relating genotype to phenotype, has a qualitative effect on several relevant aspects of the population genetic architecture of a complex trait. In particular, the genetic model impacts genetic variance component partitioning across the allele frequency spectrum and the power of statistical tests. Models with partial recessivity closely match the minor allele frequency distribution of significant hits from empirical genome-wide association studies without requiring homozygous effect sizes to be small. We highlight a particular gene-based model of incomplete recessivity that is appealing from first principles. Under that model, deleterious mutations in a genomic region partially fail to complement one another. This model of gene-based recessivity predicts the empirically observed inconsistency between twin and SNP based estimated of dominance heritability. Furthermore, this model predicts considerable levels of unexplained variance associated with intralocus epistasis. Our results suggest a need for improved statistical tools for region based genetic association and heritability estimation. Gene action determines how mutations affect phenotype. When placed in an evolutionary context, the details of the genotype-to-phenotype model can impact the maintenance of genetic variation for complex traits. Likewise, non-equilibrium demographic history may affect patterns of genetic variation. Here, we explore the impact of genetic model and population growth on distribution of genetic variance across the allele frequency spectrum underlying risk for a complex disease. Using forward-in-time population genetic simulations, we show that the genetic model has important impacts on the composition of variation for complex disease risk in a population. We explicitly simulate genome-wide association studies (GWAS) and perform heritability estimation on population samples. A particular model of gene-based partial recessivity, based on allelic non-complementation, aligns well with empirical results. This model is congruent with the dominance variance estimates from both SNPs and twins, and the minor allele frequency distribution of GWAS hits. Risk for complex diseases in humans, such as diabetes and hypertension, is highly heritable yet the causal DNA sequence variants responsible for that risk remain largely unknown. Genome-wide association studies (GWAS) have found many genetic markers associated with disease risk . HoweverThere are many hypotheses which attempt to explain the ‘missing heritability’ problem –5. GenetThe standard GWAS attempts to identify genetic polymorphisms that differ in frequency between cases and controls. A complementary approach is to estimate the heritability explained by genotyped (and imputed) markers (SNPs) under different population sampling schemes , 15. StrSNP-based heritability estimates have concluded that there is little missing heritability for height and BMI, and that the causal loci simply have effect sizes that are too small to reach genome-wide significance under current GWAS sample sizes , 16. FurThe design, analysis, and interpretation of GWAS are heavily influenced by the “standard model” of quantitative genetics . This moA weakness of the multiplicative epistasis model , 31 whenWe further explore the power of several association tests to detect a causal gene region under each genetic and demographic model. We find significant heterogeneity in the performance of burden tests , 38, 39 In total, our results show that modeling gene action is key to modeling GWAS, and thus plays an important role in both the design and interpretation of such studies. Further, the model of gene-based recessivity best explains the differences between estimates of additive and dominance variance components from SNP-based methods  and fromin silico, we need to impose a trait onto simulated individuals. In doing so, we introduce strong assumptions about the molecular underpinnings of a trait and its evolutionary context.As in ,we simulHow does the molecular genetic basis of a trait under natural selection influence population genetic signatures in the genome? This question is very broad, and therefore it was necessary to restrict ourselves to a small subset of molecular and evolutionary scenarios. We analyzed a set of approaches to modeling a single gene region experiencing recurrent unconditionally-deleterious mutation contributing to a quantitative trait subject to Gaussian stabilizing selection. The expected fitness effect of a mutation is always deleterious because trait effects are sampled from an exponential distribution. Therefore, we do not allow for compensatory mutations that may occur in more general models of stabilizing selection. Specifically, we studied three different genetic models and two different demographic models, holding the fitness model as a constant. Parameters are briefly described in P = G + E. G is the genetic component, and h, that controls the degree of recessivity; we call this model the complete MR (cMR) when h = 0 and the incomplete MR (iMR) when 0 ≤ h ≤ 1. Here, h = 1 corresponds to co-dominance, which is different from the typical formulation used when modeling the fitness effects of mutations directly. It is also important to note that here recessivity is being defined in terms of phenotypic effects; this may be unusual for those more accustomed to dealing directly with recessivity for fitness effects. An idealized relationship between dominance for fitness effects and trait effects of a mutation on an unaffected genetic background is shown in We implemented three disease-trait models of the phenotypic form The critical conceptual difference between recessive models is whether dominance is a property of a locus (nucleotide/SNP) in a gene or the gene overall. Mathematically, this amounts to whether one first determines diploid genotypes at sites  or calculates a score for each haplotype . For completely co-dominant models, this distinction is irrelevant, however for a model with arbitrary dominance one needs to be more specific. As an example, imagine a compound heterozygote for two biallelic loci, i.e. genotype Ab/aB. In the case of traditional multiplicative recessivity the compound heterozygote is wild type for both loci and therefore wild-type over all; this implies that these loci are in different genes  because the mutations are complementary. However, in the case of gene-based recessivity , neithermi causative mutations on the ith haplotype, we may define the additive model asci,j is the effect size of the jth mutation on the ith haplotype. Each ci,j is sampled from an exponential distribution with mean of λ, to reflect unconditionally deleterious mutation. In other words, when a new mutation arises its effect c is drawn from an exponential distribution, and remains constant throughout its entire sojourn in the population.For a diploid with The GBR model is the geometric mean of the sum of effect sizes on each haplotype . We sum mAa) or homozygous (maa) for causative mutations,Finally, the MR model depends on the number of positions for which a diploid is heterozygous (h = 0 is a model of multiplicative epistasis with complete recessivity (cMR), and h = 1 closely approximates the additive model when effect sizes are small.Thus, σs = 1 such that the fitness, w, of a diploid is proportional to a Gaussian function  ∼ 0.08, we set σe = 0.075 for the additive codominant model, σe = 0.053 for the gene based and complete multiplicative recessive models and σe = 0.068 for the incomplete mutliplicative recessive model (h = 0.25).Broad-sense heritability can be calculated directly from our simulated data as e models , 89. In Popt = 0. When determining fitness for the site based models, we subtract one from all phenotypes. This implies that Br) growth/Mean[H2]constant. This ratio is plotted as a function of the mean effect size of causative mutations (λ). For co-dominant models, H2 ∼ 8% and H2 ∼ 4% imply environmental standard deviations of σe = 0.075 and σe = 0.011 respectively. For recessive models, H2 ∼ 8% and H2 ∼ 4% imply environmental standard deviations of σe = 0.053 and σe = 0.075 respectively. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.The y-axis is the ratio of mean broad-sense heritability under recent rapid growth to mean broad sense heritability for a constant-sized population, (TIFF)Click here for additional data file.S3 Figλ: the mean effect size of a new deleterious mutation. Data are plotted as the mean across model replicates ± the standard error of the mean. Solid curves show values for constant sized population simulations and dashed curves show values for rapid population expansion simulations. The data is grouped by expected level of heritability and genetic model. For the additive model, H2 ∼ 8% and H2 ∼ 4% imply environmental standard deviations of σe = 0.075 and σe = 0.011 respectively. For recessive models, H2 ∼ 8% and H2 ∼ 4% imply environmental standard deviations of σe = 0.053 and σe = 0.075 respectively. Note the scales of y-axis for each plot. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.Genetic load(burden), (TIFF)Click here for additional data file.S4 Figλ. Shown here are the gene-based (GBR), additive co-dominant (AC), incomplete multiplicative recessive (Mult. recessive (h = 0.25); iMR) and complete multiplicative recessive (Mult. recessive (h = 0);cMR) models. Solid lines show the additive variance alone and dotted lines show the combined additive and dominance variance. All data shown are for models where H2 ∼ 0.08. These particular results are robust to changes H2 when VG is not changed, as is the case here. The additive and dominance genetic variance is estimated by the adjusted r2 of the regression of all markers (and their corresponding dominance encoding) with MAF ≤ x onto total genotypic value Click here for additional data file.S5 Figλ. Note they log10 y-axis scale in A. The mean effect size is the value pulled from the exponential distribution with mean λ, not the fitness effect or the quantitative genetic effect size. The data are calculated for all risk mutations segregating in the simulated populations. Data are plotted as the mean across model replicates. For visual clarity, standard errors are not shown. In panel A, the standard error bars overlap zero under rapid population growth. The data for mean frequency are grouped by demographic scenario; the left panel shows values for constant sized population, the right panel shows values for the rapidly expanded populations. For mean effect size plots the solid curves show the constant sized population data and the dashed curves show the data for the rapidly expanded populations. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.A) The mean frequency and B) mean effect size of a segregating risk variant over (TIFF)Click here for additional data file.S6 Figλ: the mean effect size of new causative mutation. The data plotted as mean over simulation replicates ±se. The data are calculated for the entire simulated population. B) The mean genetic value of a gamete, i.e. the average sum of mutational effect sizes on a gamete as a function of λ. Data are plotted as the mean across model replicates ± the standard error of the mean. In the case the gene-based recessive model, this value is also the expected value of the mean phenotype and is accurate within the sampling variance of the mean environmental variate and random pairing of gametes in diploid. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.A) The mean number of deleterious mutations per gamete in the population as a function of (TIFF)Click here for additional data file.S7 Fign = 100 individuals, the relative site frequency spectrum is calculated as the proportion (y-axis) of all polymorphic sites which belong to each frequency class (x-axis). Sites with frequency was above 18 were grouped, into one category to improve visualization. The data are grouped by λ, the mean effect size of a new risk mutation, and the demographic scenario. Data shown are for simulations in which the predicted broad sense heritability is H2 ∼ 8%. Plotted values are the mean proportion across simulation replicates. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.For a sample (TIFF)Click here for additional data file.S8 Fign = 100 individuals, the relative site frequency spectrum is calculated as the proportion (y-axis) of all polymorphic sites which belong to each frequency class (x-axis). Sites with frequency was above 18 were grouped into one category to improve visualization. The data are grouped by λ, the mean effect size of a new risk mutation, and the demographic scenario. Data shown are for simulations in which the predicted broad sense heritability is H2 ∼ 8%. Plotted values are the mean proportion across simulation replicates. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.For a sample (TIFF)Click here for additional data file.S9 Fign = 100 individuals, the relative site frequency spectrum is calculated as the proportion (y-axis) of all polymorphic sites which belong to each frequency class (x-axis). Neutral variants are in orange and risk variants are shown in green. Y-axis is on a square-root scale and X-axis is on a log10 scale to improve visualization. The data are grouped by λ, the mean effect size of a new risk mutation, the demographic scenario and genetic model. Data shown are for simulations in which the predicted broad sense heritability is H2 ∼ 8%. Plotted values are the mean proportion across simulation replicates. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.For a sample (TIFF)Click here for additional data file.S10 Figλ, with empirical data for comparison. The degree of dominance h was varied from 0.1 to 0.75; perfect co-dominance here is h = 1. Empirical data were downloaded from the NHGRI-EBI GWAS database (http://www.ebi.ac.uk/gwas/) on 02/03/2015, diseases and inclusion criteria are as in [Horizontal violin plots depict the distribution of minor allele frequencies (MAF) of the most strongly associated single marker in a GWAS. Individual hits are plotted as translucent points and jittered to provide a sense of the total number and density of hits. Each panel contains simulated data pooled across model replicates for each value of re as in . In case(TIFF)Click here for additional data file.S11 Figλ. The data are calculated for all risk mutations segregating in the simulated populations. Moments were calculated using the boost C++ statistical accumulators library. Data are plotted as the mean across model replicates ± the standard error of the mean. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.The skewness A) the number of mutations per gamete and B) the genetic value  of a gamete over (TIFF)Click here for additional data file.S12 Figλ. The data are calculated for all risk mutations segregating in the simulated populations. Moments were calculated using the boost C++ statistical accumulators library. Data are plotted as the mean across model replicates ± the standard error of the mean. Shown are the additive co-dominant (AC), gene-based (GBR) and complete multiplicative recessive (Mult. recessive (h = 0); cMR) models.The kurtosis A) the number of mutations per gamete and B) the genetic value  of a gamete over (TIFF)Click here for additional data file.S13 Figλ. The arbitrary dominance coefficient is parameterized such that h = 0 is complete recessivity, h = 1 would be exact co-dominance and h = 2 would be complete dominance. Multiplicative recessive (MR) models shown are only for h = 0.25.Broad-sense heritability in a population sample of 6000 as a proportion of population wide broad-sense heritability. Data are grouped by demographic scenario, model and (TIFF)Click here for additional data file.S14 Figpqα2. (B) Cumulative percent of variance explained across the risk allele frequency, based on regression estimates and classical formula. 1000 unlinked markers were simulated with effects drawn from an exponential distribution with mean 0.1 and population frequencies drawn from the neutral Wright-Fisher allele frequency distribution. Sample data for 5000 individuals were then generated by sampling genotypes at each marker based on its allele frequency. We plot the regression estimate of variance explained by each marker against Fisher’s classic result [VG = 2pqα2.(A) Regression estimates of variance explained by markers versus the classical formula 2c result : VG = 2p(TIFF)Click here for additional data file.S15 Figh. Values are based on idealized fitness effects of a mutation on a previously unaffected genetic background. The the relationship between fitness and trait dominance is influenced by the trait effect size. We varied trait effect sizes from 0.01 to 1, and values are colored based on the trait effect.The dominance of fitness effects, (TIFF)Click here for additional data file.S16 FigHistogram GWAS hits (n = 1208) obtained from the NHGRI-EBI GWAS database for disease discussed in . Data ar(TIFF)Click here for additional data file.S17 FigVA) as a function of allele frequency using regression . Solid lines are the standard additive model. Dashed lines are the GBR model of [VA explained by all mutations. This effect is, however, short lived, and disappears by the end of the epoch defined by N = 1,861. This result is consistent with transient increases in variation under recessive models reported by [(A) Population size change over time. Colored numbers represent population sizes at different times where we estimated the cumulative additive genetic variance Click here for additional data file.S18 FigVG changes over time under this model. The right column shows how the mean number of deleterious mutations per individual changes. The models shown are: a = additive, g = GBR, and m = multiplicative with varying degrees of dominance (h). The main difference is between additive models (a or m with h = 1.0) and recessive models . The former models are largely insensitive to changes in N, while the recessive models show transient increases in VG and “load” immediately following a bottleneck (consistent with [VG is ≈ 4μ for additive models and ≈ 2μ for recessive models [The left column of panels shows how ent with ). Howevee models , 89, ande models .(TIFF)Click here for additional data file.S19 Figh). For large effect size models, under which there are relatively more mutations that experience strong selection, we see the characteristic drop in the burden ratio following the bottleneck and rebound following re-expansion [The burden ratio  is calcuxpansion .(TIFF)Click here for additional data file.S20 Figh).The burden ratio  is calcu(TIFF)Click here for additional data file.S21 Fighttp://www.ebi.ac.uk/gwas/) on 02/03/2015, diseases and inclusion criteria are as in [A non-parametric comparison between distribution of allele frequencies between simulated and empirical GWAS hits. Shown are the -log10(p) values from the two-sample Kolmogorov-Smirnov test between the simulated and empirical allele frequencies. The lower and upper horizontal lines show where p = 0.05 and p = 0.001 respectively. Empirical data were downloaded from the NHGRI-EBI GWAS database (re as in . In case(TIFF)Click here for additional data file.S22 FigNs ≤ x on a log scale for various values of λ. The dashed lines show the analytical result and the solid curves are empirical cumulative distribution functions based on a sample of 500 mutation effects from an exponential distribution. The analytical result is an approximation obtained by assuming there is only a single deleterious mutation.The probability of a new mutation with 2(TIFF)Click here for additional data file.S23 Figs = x on a log scale for various values of λ. The analytical result is an approximation obtained by assuming there is only a single deleterious mutation. For λ of 0.25 and 0.5 there is a large mass of lethals near s = 1.The probability of a new mutation with (TIFF)Click here for additional data file.S1 TableThis table contains information specifying the empirical studies used in the manuscript. The data were obtained from the NHGRI-EBI catalog of published genome-wide association studies. All information fields contained in the download of the GWAS catalog are presented here.(XLSX)Click here for additional data file.