Genomic information can be used to study the genetic architecture of some trait. Not only the size of the genetic effect captured by molecular markers and their position on the genome but also the mode of inheritance, which might be additive or dominant, and the presence of interactions are interesting parameters. When searching for interacting loci, estimating the effect size and determining the significant marker pairs increases the computational burden in terms of speed and memory allocation dramatically. This study revisits a rapid Bayesian approach (fastbayes). As a novel contribution, a measure of evidence is derived to select markers with effect significantly different from zero. It is based on the credibility of the highest posterior density interval next to zero in a marginalized manner. This methodology is applied to simulated data resembling a dairy cattle population in order to verify the sensitivity of testing for a given range of type‐I error levels. A real data application complements this study. Sensitivity and specificity of fastbayes were similar to a variational Bayesian method, and a further reduction of computing time could be achieved. More than 50% of the simulated causative variants were identified. The most complex model containing different kinds of genetic effects and their pairwise interactions yielded the best outcome over a range of type‐I error levels. The validation study showed that fastbayes is a dual‐purpose tool for genomic inferences – it is applicable to predict future outcome of not‐yet phenotyped individuals with high precision as well as to estimate and test single‐marker effects. Furthermore, it allows the estimation of billions of interaction effects. This leads to more precisely estimated breeding values of not‐yet phenotyped animals and, if selection of animals is based on genomic breeding values instead of traditionally estimated breeding values, breeding costs can be drastically reduced due to the shortened generation intervals  than observations ; this makes testing of SNP effects a challenge. SNPs with significant impact on a trait can be identified with genome‐wide association studies (GWAS) typically based on successive single‐SNP investigations – one SNP is tested at a time while “walking” along the genome. Those SNPs being in high linkage disequilibrium (LD) with a causative variant will likely have a tiny p‐value implying a strong association with the trait. The high LD among SNPs complicates the correct identification of a causative variant, and this kind of testing also suffers from multiplicity. Several specific methods exist for controlling the rate of false‐positive detection. Ideally, the number of independent tests accounts for the LD between SNPs as was proposed by Gao, Starmer, and Martin ′ being the vector of observable traits of n individuals centred by the population mean and g=′ the effect at p SNPs. The (n×p) design matrix X={Xi,j} contains the genotype codes at locus j∈{1,…,p} for individual i∈{1,…,n}, where 1 and −1 indicate homozygous genotypes AA and BB, respectively, and the heterozygote is coded as 0. Let A denote the minor allele with minor allele frequency (MAF) fj≤1/2. The MAF is assumed to be known or may be estimated from SNP genotypes using, for example, the method of moments as fj=12n∑i=1n. The residual errors in e=′ are assumed to be independent and normally distributed with zero mean and variance σe2.Beside different strategies for suitable Selection‐and‐shrinkage approaches allow the simultaneous selection of those predictors that sufficiently map the trait and the estimation of their effect sizes. They are often implemented in a Bayesian . In Section 22.1X contain the standardised genotype codes. They are centred and scaled such that Xi,j is 2(1−fj)/sj and −2fj/sj for homozygous AA and BB, respectively, and (1−2fj)/sj for heterozygous individuals with scaling term sj=2fj(1−fj).The following investigations are based on model x=Xj, the j‐th column of X, and g=gj at a single locus j∈{1,…,p}.The approximate Bayesian method “fastbayes” is now further considered to include a testing procedure. According to Meuwissen et al. , the idep(y|g) is specified as a normal distribution with mean xg and covariance matrix Iσe2. The prior distribution of genetic effects is assumed to be a mixture of a Laplace distribution and a point mass at zero (δ0) with P(g=0)=1−γ. The formal prior density isThe likelihood function g^=E(g|y), which is given in closed form −1σe2, Y=(x′x)−1x′y and Y±=Y±λσ2. The ΘU and ΘL are the expected value of an upper and lower truncated normal distribution N, respectively, with truncation point zero. The Φ denotes the normal distribution function evaluated at some point x, and ϕ is the normal density function.A point estimate of the genetic effect is determined as the posterior expectation p loci simultaneously, the model y is corrected for all SNP effects except the one under investigation,gj(0)=0∀j. In iteration k=1,2,…,j=1,…,p until relative changes are small,In order to analyze X consists of three groups of columns, one for each kind of effect, that is X= comprising the standardized genotype codes for additive, dominance and epistatic effects. For dominance effects, the columns in Xd are coded according to Falconer's model in a random mating population in Hardy–Weinberg equilibrium 2/sj2 is used for homozygous AA, −2fj2/sj2 for BB individuals and 2fj(1−fj)/sj2 for heterozygous individuals. Four different types of epistatic effects can be distinguished: additive× additive, additive× dominance, dominance× additive, and dominance× dominance, leading to 2p(1−p) additional effects. A column in Xe coding for an epistatic effect contains the product of codes for the corresponding main effects. For instance, an additive× dominance effect at locus pair i and j is coded as −2(1−fi)/si·2fj2/sj2 if an individual is homozygous AA at locus i and homozygous BB at locus j. Again the Gauss‐Seidel‐like algorithm y that is corrected for all other effects except the current one in order to estimate the different kinds of genetic effects.Model b=′ with (n×q) design matrix W,σe2 in iteration k of the Gauss‐Seidel‐like algorithm y is corrected for the current estimates of fixed effects.In a real data analysis, also nongenetic factors affecting the trait have to be considered. Thus, model n et al.  and Wittn et al. , a type 2.2H0: g=0. For this purpose, the credibility κ of the highest posterior density (HPD) interval that is right to zero if g^>0 or left to zero if g^<0 is determined, that isg^>0, the interval borders are t1=0 andg^<0, t2=0 andg is inferred if 1−κ≤α, with an appropriately chosen type‐I error α. Let 1 denote the indicator function. The posterior probability is analytically derived asp(g|y) is bimodal due to the spike at zero, the posterior distribution function has a jump discontinuity at zero with step height 1p(y)f2(0); the smaller Y=(x′x)−1x′y, the larger the step height. For larger values of Y the density is approximately unimodal and symmetric  and validation set . Then, p=5,227 SNPs (every 10th SNP including the causative variants) were used for the evaluation. SNPs with MAF ⩽0.05 were removed, and thus 793 SNPs were additionally excluded on average. Twenty‐three SNPs were randomly preselected to be the causative variants, and additive and dominance effect were simulated for each of them. For each of the four kinds of epistatic effects, six SNP pairs were randomly drawn out of the 23 causative variants to interact. Dominance and epistasis explained about 10% and 29%, respectively, of the total genetic variance. Two different traits were achieved by adding different residual error terms to the sum of genetic effects, such that total genetic variation contributed either 30% (i.e. broad‐sense heritability H2=0.3) or 50% (H2=0.5) to the variation of y. The simulation was repeated 100 times. The fastbayes algorithm was executed using γ=0.005, λ=2pγ for additive and dominance effects and γ=10−6, λ=p(p−1)γ for epistatic effects, as suggested by Wittenburg et al.  was calculated. These characteristics determine the ability of an approach to select the loci relevant to genetic variation in a training set. Moreover, the ability to predict genetic values of future or not‐yet phenotyped animals was verified. Accuracy of genetic value prediction was assessed as the correlation between estimated and simulated genetic values in a test set.The main criterion for evaluation was the number of truly detected SNPs with significant impact on a trait. This was measured in terms of sensitivity and specificity for each kind of effect separately as well as overall by considering the joint set of SNPs that were significant in any kind of effect. A true positive result was obtained when the significant SNP was in a window of 100 kbp around the simulated causative variant. For instance, one gene per 100 kbp is expected in the mouse genome  and phenotypes of n=1521 animals. Rarely missing genotypes for these SNPs were imputed via Beagle 3.2  were estimated in the test set based on the effect estimates from the training set using a model with additive and dominance effects. The correlation between EGV and y served as a measure of accuracy. The γ leading to the highest accuracy was chosen. Then, to specify the hyperparameter for epistatic effects, a range of γ∈{10−7,…,10−3} was evaluated similarly. For instance, 10−7 corresponds to an expectation of four interactions per kind of effect. Using a smaller γ‐value would reflect the assumption of less than one interaction effect that is not envisaged. The final parameter values were employed in the genomic evaluation of the complete dataset.To show the performance of fastbayes on real data, data of a heterogeneous stock of mice ; fastbayes is available online at https://github.com/wittenburg/fastbayes. The search for the HPD interval was implemented as a grid search over the interval  with mL=10min(g^) and mU=10max(g^); the step size was (mU−mL)/2000. The dummy variables in Xe were set up on the fly to reduce memory allocation. The fastbayes was compared to Logsdon's vbay method , the full model containing 2p(p−1) pairwise interactions could not be analyzed. To obtain a tendency whether vbay is able to reveal epistatic effects, the model dimension was further decreased. Again, every 10th out of the 5,227 SNPs was selected but without paying attention to keeping the causative variants among the selected SNPs. Considering MAF >0.05, 444 SNPs were retained on average. Additive and additive× additive interaction effects were analyzed, denoted as model M3* in Table Computing time was clearly in favor of fastbayes; it generally needed the least time, see Table ning 2pp− pairwiseThe difference in time increased in the real data analysis Table . AdditivBecause a multiuser computing system was employed, the memory allocation could only be approximated roughly for simulated data. Peaks in memory allocation have been observed when epistatic effects were estimated using fastbayes (⩽4 GB on average) and when main genetic effects were computed using vbay (⩽1 GB on average).66.1H2=0.5, see Table α=0.01, sensitivity for additive effects increased slightly by about 6% when the genome‐wide regression model was extended to include dominance effects but these were rarely identified; the sensitivity for dominance effects was 7%. The best outcome was observed if pairwise epistatic effects were also included in the model. Then, considering the joint set of significant SNPs over all kinds of effects, 50% of the causative variants were identified correctly. The higher the type‐I error was, the higher the sensitivity turned out; the maximum was observed if α=0.20. The specificity, however, remained very high (≥99.76%) in general. Larger α‐values led to a further but very small increase of sensitivity (results not shown), and specificity was still very high (e.g. ≥99.74% if α=0.50). This can be explained by the clear differentiation of zero and nonzero effects by the measure of evidence, see Additional File 1: effects close to zero coincidentally have a measure close to one. The genetic variance that could be explained by the significant effects was 89% at most. The accuracy of genetic value prediction achieved its maximum over all models at 82%.Considering the measure of evidence, the fastbayes approach identified about one‐third of the causative variants with additive contribution to the total genetic variation if 7−12% when the Bayes factor instead of the measure of evidence (α=0.20) was used for identifying the relevant SNPs. Both measures found the same significant effects but few additional effects, which were most often nonadditive, could be identified with the Bayes factor. The best result was achieved with the genome‐wide regression model including all kinds of genetic effects. Then, 42% of the causative variants with additive effects were detected on average. The sensitivity for dominance effects increased to 15% but sensitivity for epistatic effects remained rather constant at 27%; 56% of the causative variants were found overall, see Table The overall sensitivity of fastbayes further improved by about H2=0.3, the performance of fastbayes was worse than with H2=0.5, see Table 24−25% using the Bayes factor. The genetic variance explained by the significant SNPs decreased by 4%. The complex model including all kinds of genetic effects yielded again the best outcome regarding the ability to detect the relevant loci that capture most of the genetic variation but the accuracy of genetic value prediction was slightly reduced by 2% compared to a model containing additive and dominance effects; the correlation between simulated and estimated breeding values was 72%.With α=0.05. Using the Bayes factor, the overall sensitivity was increased but it was at most 0.87% in the model considering all kinds of effects and specificity was ≥99.42%. The correlation between simulated and estimated breeding values was 0.13%.Furthermore, the data that were generated without any impact of the causative variants were analyzed. It turned out that sensitivity was 0.17% at most and specificity was ≥99.88% over all kinds of effects and all models using the measure of evidence and, for instance, α=0.05) and vbay based on the model with additive and dominance effects, see Tables The ability to select the relevant loci and to predict the genetic values was similar using fastbayes . Though results obtained by fastbayes (α=0.05) and vbay have been rather similar based on simulated data, the real data analysis revealed differences regarding the dominance effects, see Figure Sle1c and Prdt1, respectively). The significance measures of both methods clearly differentiate between significant and nonsignificant effects  with known association to traits of the immune system =(a+1)(1−γ)a with some prior information a. The posterior expectation has been worked out in Additional File 3 and has been incorporated in the fastbayes algorithm. As the distribution of γ varies only little, the estimates of genetic effects and their measure of significance were not altered seriously in case of simulated data. As an example for H2=0.5 and based on the complex model including all kinds of genetic effects, on average one to two loci were additionally detected but the number of truly detected loci was almost unchanged. The sensitivity over all kinds of effects was 52 %. The significant loci explained about 90 % of the total genetic variance. The accuracy of genetic value prediction was 80 %.The specification of hyperparameters may have a great impact on the outcome of Bayesian approaches  for each locus or kind of effect j=1,2,…, where zero means exclusion and one the neutral weight. Similar to a weighted regression analysis, a vector of covariates x=Xjwj is considered in the one‐locus model As discussed in Van Steen , prior k8The extension of the approximate Bayesian approach “fastbayes” to include a marginal measure of significance allows now a quick scan of the genome to identify the SNPs that are relevant to genetic variation. The clear benefit of fastbayes is its dual‐purpose use: it estimates the effect sizes for all kinds of genetic effects (additive and nonadditive) and determines the significant SNPs or SNP pairs. It requires much less computing time in higher, realistic dimensions than other approaches for whole‐genome regression analyses. Due to its speed, it will also be valuable for the analysis of whole‐genome sequence data.Supplementary MaterialClick here for additional data file.Supplementary MaterialClick here for additional data file.Supplementary MaterialClick here for additional data file.Supplementary MaterialClick here for additional data file.


We propose FunSPU, a versatile and adaptive test that incorporates multiple biological annotations and is adaptive at both the annotation and variant levels and thus maintains high power even in the presence of noninformative annotations. In addition to extensive simulations, we illustrate our proposed test using the TWINSUK cohort  of UK10K WGS data based on six functional annotations: CADD, RegulomeDB, FunSeq, Funseq2, GERP++, and GenoSkyline. We identified genome-wide significant genetic loci on chromosome 19 near gene TOMM40 and APOC4-APOC2 associated with low-density lipoprotein (LDL), which are replicated in the UK10K ALSPAC cohort . These replicated LDL-associated loci were missed by existing rare variant association tests that either ignore external biological information or rely on a single source of biological knowledge. We have implemented the proposed test in an R package “FunSPU”.Despite ongoing large-scale population-based whole-genome sequencing (WGS) projects such as the NIH NHLBI TOPMed program and the NHGRI Genome Sequencing Program, WGS-based association analysis of complex traits remains a tremendous challenge due to the large number of rare variants, many of which are non-trait-associated neutral variants. External biological knowledge, such as functional annotations based on the ENCODE, Epigenomics Roadmap and GTEx projects, may be helpful in distinguishing causal rare variants from neutral ones; however, each functional annotation can only provide certain aspects of the biological functions. Our knowledge for selecting informative annotations  In recent years, large-scale whole-genome sequencing (WGS) data have been generated, such as those in the UK10K project and the ongoing NIH Trans-Omics for Precision Medicine (TOPMed) WGS program, providing unprecedented opportunities to investigate low-frequency variants and rare variants in association with complex diseases and traits. However, WGS-based association analysis of complex traits remains a tremendous challenge due to the large number of rare variants, many of which are non-trait-associated neutral variants. External biological knowledge, such as functional annotations based on the ENCODE, Epigenomics Roadmap and GTEx projects, can be helpful in distinguishing causal rare variants from neutral ones; however, each functional annotation can only provide certain aspects of the biological functions. To this end, we have proposed a versatile and adaptive association test, FunSPU, to exploit multiple sources of biological knowledge in the analysis of WGS data. We illustrate our proposed test using the TWINSUK cohort of UK10K WGS data based on six functional annotations. We identified genome-wide significant genetic loci associated with low-density lipoprotein, which are replicated in the UK10K ALSPAC cohort. These replicated loci were missed by existing rare variant association tests that either ignore external biological information or rely on a single source of biological knowledge. Moreover, to further increase the statistical power, we propose to incorporate a trait-specific global weight for each annotation based on partitioning the heritability.To address this analytical challenge, we propose a family of versatile and powerful tests called “FunSPU” that allow for incorporating multiple ramework . The funTOMM40 and APOC4-APOC2 that are associated with LDL, which are replicated in the UK10K ALSPAC WGS cohort . These replicated LDL-associated loci were missed by existing RV association tests that either ignore external biological information or rely on a single source of biological knowledge. We have implemented the proposed test in an R package “FunSPU”.Using extensive simulations and application to the UK10K WGS data , we compi = 1, …, n, Y =  is the vector of a trait, and Xi = ’ is the vector of the genotype scores of k RVs, for example, from a gene or some genomic region. Here, we use additive coding for each RV; that is, Xij is the count of the minor allele at RV j for subject i. For simplicity, we ignore other covariates in our model. We consider a generalized linear model (GLM):Yi, g is the identity link g(μ) = μ and the GLM is reduced to a linear model, whereas g is the logit link Yi. For the purpose of exposition, we introduce our proposed tests in the linear model framework with a quantitative trait and no covariates, though the methods can be similarly extended to binary traits, and adjusted for covariates in the GLM and score function framework [Suppose that for subject ramework , 22, 23.H0: β = ’ = 0, that is, there is no association between any of the RVs and the trait under H0. Our proposed tests are based on the score vector U = ’ for β and its covariance matrix V,Yi’s and Xi’s, respectively.We test the null hypothesis SPU(γ) test puts more weights on the larger component of U while gradually ignoring the remaining component. In particular, we have γ→∞. The SPU(∞) is closely related to the minP test (but ignores possibly varying variances of Uj’s); the two tests often perform similarly [SPU(γ) test depends on the choice of γ while the optimal choice of γ depends on the unknown true association pattern of the RVs to be tested, it would be desirable to data-adaptively choose the value of γ. To this end, the aSPU test takes the minimum p-value of the SPU(γ) tests as its test statistic: TaSPU = minγ∈ΓpSPU’ for k RVs from a gene region or sliding window based on a linear regression model. Let 0≤wlj≤1 denote the functional score from the lth of m properly scaled annotations for the jth of k RVs. The proposed functional annotation-based SPU test isa≥1 respectively control the individual variants’ and annotations’ relative contributions to the overall test statistic; e.g., γa = 1 treats all annotations equally, while γa = ∞ only considers the most significant annotation. The inner sum of weighted Uj with power γ is the weighted SPU, and they are normalized to the power of 1/γ before being subjected to the outer sum with power γa. Since the number of the RVs in this test statistic is identical across all m annotations, it is not necessary to further normalize the weighted SPU test by the number of RVs.Our proposed test is in the data-adaptive aSPU test framework. Importantly, the proposed test is adaptive at both the annotation and SNV levels. Suppose that we have the score vector a as the powers of the weighted SPU is similar to that for γ. In general, a smaller γa, e.g., γa = 1, is more effective when there are more informative annotations, each of which is roughly equally discriminative regarding the deleteriousness of the RVs for the trait of interest. In contrast, a larger γa is preferred if there is only one or fewer informative annotations that can well distinguish causal variants from neutral ones for the trait. As γa→∞, only the most significant weighted SPU is considered.The intuition to use γa priori knowledge about choosing γ and γa, we need to conduct a grid search over a set of possible values of both γ and γa. However, searching too many values will introduce extra variability and lead to reduced power. This effect was later confirmed when we used γa∈{1,2,3,…,8,∞} and γ∈{1,2,3,…,8,∞} in some preliminary simulations. Based on the results of aSPU tests [a∈Γa = {1,2,4,8,∞} and γ∈Γ = {1,2,3,…,6} for the rest of the study. We retained γa = ∞ as an approximation to the minP test and ignored some higher values of γ since the results tend to be similar to γ = 6.We aim to perform powerful tests when there are unknown association patterns of RVs and unknown informativeness of functional annotations. In practice, since we have no PU tests  and the a, e.g., γ∈Γ = {1,2,3,…,6} and γa∈Γa = {1,2,4,8,∞}, the proposed data-adaptive FunSPU test statistic is defined asTFunSPU. Therefore, we propose using a single layer of permutations (without covariates) or residual permutations (with covariates) to obtain p-values as done in aSPU [Y to obtain a new set of Y(b) for b = 1, …, B. Then, we calculate the null score vector U(b) and the corresponding test statistic p-values p-value of the FunSPU test Given a set of γ and γ in aSPU , 22. SpeUj, for example, due to varying MAF of the RVs. On the other hand, previous research has shown that it may be beneficial to account for the heterogeneity of variances in the SPU framework [Vjj is the jth diagonal element of V = Cov(U|H0) as given before.In the FunSPU test above, we ignored the possibly different variances of the score function component ramework . TherefoU weighted by each functional annotation, i.e., l = 1, …, m. We can obtain the genuine p-value p-values, m modified aSPU tests. This aSPU_minP test is similar, but not exactly equivalent to the case of FunSPU with γa = ∞: the latter chooses the maximum p-value directly, while the aSPU_minP test calculates the empirical p-value p-value TaSPU_minP as the new test statistic and resampling to calculate the final p-value.We considered alternative approaches to incorporate multiple functional annotations into the aSPU test. In contrast to the two-level FunSPU approach, we can obtain modified aSPU tests via the score vector p-values is Fisher’s meta-analysis approach, i.e., m p-values were independent, TaSPU_Fisher would follow a chi-squared distribution with 2m degrees of freedom. However, our U. Hence, we also use resampling approaches to calculate the final p-value. We can similarly apply the inverse-variance weighted method to aSPU_minP and aSPU_Fisher tests, respectively denoted as aSPUw_minP and aSPUw_Fisher.Another common method for combining Of note, aSPU_minP is closely related to the FST test . Specifim functional annotations equally a priori and completely relied on the data to adaptively combine multiple annotations in each test unit, for example, a sliding window. This may be less efficient in the presence of overall inferior or superior annotations for a trait of interest, in which case it would be desirable to globally down-weight inferior annotations (and up-weight superior annotations). To this end, we propose to modify the FunSPU test by introducing an annotation-level weight ρ = ′ and denote the modified test as wtFunSPU:In our proposed FunSPU test, we treated all a priori knowledge regarding the informativeness of a functional annotation for a given trait, we propose to estimate ρl based on some global correlation measure between the annotation weights, genotypes and phenotype. A promising approach is based on partitioning the heritability h2 by functional annotations [q = 1,…, Q, using the GCTA tool [q and regress β is used as the global weight ρ for the corresponding functional annotation in the wtFunSPU test. Prior to this calculation, we transform the functional annotation to positive integers q = 1,…, Q such that larger q corresponds to a more likely functional category. If a functional category has a very small number of SNVs or Since we assume no otations : a functCTA tool . We nextWe conducted extensive simulations to evaluate and compare the performance of our proposed functional annotation-based tests with existing association tests for RVs. To make the simulation study representative of real RV data, we randomly selected 200 RVs from chr16:56.8M~57.1M of the UK10K TWINSUK genotype data of 1,718 unrelated individuals. MAFs of the selected RVs were no larger than 1%.wj1,wj2,wj3) and 3 sets of random annotations  independently . We designated the first 100 RVs as causal variants  and the remaining 100 RVs as neutral variants . The informative annotations were generated from a uniform distribution U corresponding to causal variants and from U corresponding to neutral variants. All of the random annotations were generated from U. Second, we randomly selected k = k1+ k2 RVs: k1 causal RVs from j = 1, 2, …, 100 and k2 neutral RVs from j = 101, 102, …, 200. Third, we used only informative annotations to calculate the effect size βj = cβ for each causal RV. Fourth, the simulated phenotype was obtained from εi followed N and i = 1,2,…,1718. Furthermore, to evaluate the globally weighted wtFunSPU test, we calculated the correlations between the sum of the genotypes weighted by each annotation and simulated phenotypes for each of the 1,000 simulation replications, and used the mean of the 1,000 correlations as the global weight of each annotation, i.e., l = 1, 2, …,6), where Yi and Xij in each replication correspondingly.To evaluate power, we generated the simulated phenotypes as follows. First, we simulated 3 sets of informative annotations  in functional annotation-based tests . To test the effect of more “noisy” annotations, we implemented scenario B, which used only one informative annotation, all three random annotations and one dummy annotation in the tests. In both scenarios A and B, we used identical procedure as above to generate simulated phenotypes Yi~N , independent of k neutral RVs and 6 random annotations all from U in each replication. We set increasing numbers of neutral RVs with k = {8, 16, 32, 64, 128}.To evaluate the type I error rate, we simulated The empirical type I error rate was calculated based on 50,000 replications with the significance level α = 0.005, while the empirical power was calculated based on 1,000 replications for each scenario with α = 0.05. For permutation-based tests, 10,000 and 1,000 resamplings were conducted for each replication to evaluate type I error and power, respectively.As shown in U and U, respectively, the tests incorporating functional annotations, such as FunSPU, wtFunSPU, aSPU_minP and FST, always had higher power than tests that ignored functional annotations, such as aSPU, SKAT and T1. The FunSPU test appeared to be less powerful than aSPU_minP, suggesting a lack of efficiency in the former’s complete data-adaptive strategy to combine multiple annotations. On the other hand, wtFunSPU and wtFunSPUw outperformed aSPU_minP and FST, supporting the effectiveness of the global weighting scheme. Between the latter two, aSPU_minP had an increasing edge over FST in the presence of larger number of neural variants, due to its going beyond burden (SPU(γ = 1)) and variance-component (SPU(γ = 2)) tests with additional γ parameters. We also observed that the inverse-variance weighted tests always outperformed the original tests, e.g., wtFunSPUw versus wtFunSPU, and this advantage became more obvious with a higher proportion of neutral RVs. Lastly, the power of the aSPU_Fisher test was similar to that of the aSPU_minP test until the number of neural variants increased to 64 and 128, when the former became less powerful than the latter.Regarding power, we first considered scenario A , which wNext, we considered a weaker scenario for our proposed tests. In scenario B , we usedWe also compared the computational time needed for different methods. As shown in −6, and sample-level QC to exclude samples in poor concordance with their corresponding GWAS data[To further evaluate the performance of our proposed tests on real data, we applied FunSPU and other state-of-the-art tests, including SKAT, T5 burden test and FST (combined test), to assoGWAS data. Since ts =  were transformed into  by f(s) = (7-s)/6, whereas the Funseq categories s =  were transformed by f(s) = (1+s)/7. We substituted the missing values or zero values with 0.01  or 0.0001 (GERP++). There was no missing value in CADD and GenoSkyline for the RVs considered here. We considered six types of functional annotations for RVs. CADD, FunSeq, FunSeq210 scale. To achieve this genome-wide significance level, we used a step-up permutation strategy [B = 10,000 permutations for all sliding windows and gradually increased B; if those sliding windows with estimated p-values <10/B, we increased B to 10 times the current value and re-estimated the p-values for these sliding windows. The number of permutations in the final stage was B = 108. Of note, the variant-specific score functions in aSPU, aSPU_minP, FunSPU and wtFunSPU were not weighted by MAF, while those in aSPUw, aSPUw_minP, FunSPUw, and wtFunSPUw were inverse-variance weighted, where variants with lower MAF were up-weighted. By default, SKAT and FST used Beta weights to up-weight variants with lower MAF [We employed a sliding window approach to group RVs with a window length of 10k base pairs (bp) and a step size of 8.75k bp, resulting in 319,306 windows in total. Using the conservative Bonferroni procedure, we set the family-wise error rate at 0.05 with a significance level = 0.05/319306 = 1.56e-07, which equals 6.81 on the -logstrategy , 28. We ower MAF , 17.p-value inflation, suggesting that the FunSPU tests could control the type I error rate well in genome-wide scans. p-value in the TWINSUK discovery cohort by any of the association tests under consideration. To confirm our findings in the TWINSUK cohort, we performed replication analysis of the genome-wide significant sliding windows in the ALSPAC cohort. As shown in p-value < 0.05/24 = 2.1e-3 based on the Bonferroni correction for 24 sliding windows: 3 by at least one of the functional annotation-based tests  and one by the aSPU test. In contrast, none of the 6 sliding windows identified by the FST test in the discovery cohort was replicated; neither did SKAT nor T5 replicate any sliding window.As shown in TOMM40, APOE and APOC4-APOC2 genes. These loci have been previously identified and replicated to be associated with LDL by large-scale meta-analysis of GWAS common variants [APOE plays a central role in lipoprotein metabolism and neurodegeneration [APOE has three isoforms, 2, 3, and 4: APOE2 is associated with elevated plasma LDL level and increased cardiovascular disease risk, whereas APOE4 is associated with increased risk of Alzheimer’s disease[APOE[TOMM40/APOE locus and additionally APOC4-APOC2 locus that harbor LDL-associated RVs with fewer than a couple of thousand samples, suggesting that the power of the FunSPU test was boosted by incorporating external biological knowledge.Three of the four replicated sliding windows were close to each other on chromosome 19 around variants –31. Numeneration –34. Specs disease, 36, a rease[APOE. Here weTOMM40 and APOC4-APOC2 gene regions for Funseq2, Funseq, RegulomeDB and GenoSkyline  and applied the aSPU test to each sliding window which had at least two RVs. For a sliding window with a single RV, we merged it with its neighboring sliding window. As shown in To further investigate whether the We have proposed a versatile and adaptive association test, FunSPU, to exploit multiple sources of biological knowledge in the analysis of WGS data. It is adaptive at both the annotation and variant levels, and thus maintains high statistical power, even in the presence of noninformative annotations and a larger number of neutral variants. We have further proposed a globally weighted wtFunSPU test to more effectively down-weight less informative functional annotations in a trait-specific manner. Using the UK10K WGS data, we demonstrated that our proposed FunSPU test and its extensions, including the wtFunSPU and aSPU_minP tests, are more powerful tools to identify genome-wide significant loci than existing RV association tests that either ignore external biological information or rely on a single source of biological knowledge. The FunSPU family of tests would thus serve as a powerful and complementary tool for ongoing and future large-scale WGS studies, such as the NHLBI TOPMed project  of over The six functional annotations we considered here are diverse in terms of resources and features. For example, GERP++ is a seq2, based on which we derived a single global weight. This is in line with the “sieve principle”, which justifies using aggregated data to estimate a much smaller number of weights and then using them in subsequent hypothesis testing of small units of data  with controlled family-wise error rate [To further de-noise noninformative annotations, we proposed a novel trait-specific measure based on partitioning the heritability and used it as a global weight for each annotation in the wtFunSPU test. Interestingly, our proposal is along the line of estimating group-specific weights in the context of weighted hypothesis testing , 42, thoror rate . Our proror rate  to calcu8 residual permutations for the top sliding windows to reach the genome-wide significance threshold. We expect that further implementation of the core functions in the C language should reduce the computational burden to a more affordable level. In addition, it would be desirable to develop some asymptotic theory and test to save the computational time. Of note, some asymptotic theory has been developed for the aSPU test in the context of testing two high-dimensional means for common variants [We have some practical considerations for our proposed tests. First, some functional annotations are not well-defined across the whole genome, resulting in relatively high missing data rates, for example, 68% for Funseq; the missing scores may reduce the reliability of annotation-based association tests. On the other hand, considering multiple complementary functional annotations simultaneously may at least partially remedy the problem of missing information. Second, by employing parallel computing and a step-up residual permutation strategy for the FunSPU family of tests, we are able to perform computationally feasible genome-wide scans for WGS data. For example, in the UK10K TWINSUK WGS data application, it took 24 hours for 500 computing cores to complete the sliding window-based FunSPU scan in R, including 10variants ; howeverhttps://github.com/sputnik1985/FunSPU, and to be posted to R/CRAN.We have implemented the proposed FunSPU test and its extensions in an R package “FunSPU”, available at S1 Fig(PDF)Click here for additional data file.S2 Fig(PDF)Click here for additional data file.S3 Fig(PDF)Click here for additional data file.S4 Fig(PDF)Click here for additional data file.S5 Fig(PDF)Click here for additional data file.S6 Fig(PDF)Click here for additional data file.S7 FigGlobal quantile-quantile (QQ) plots for association analysis of rare variants with HDL in the UK10K TWINSUK cohort: (A) FunSPU (genomic control λ = 1.004), (B) FunSPUw (λ = 1.076), (C) wtFunSPU with global weights (λ = 1.004), and (D) wtFunSPUw with global weights (λ = 1.047).(PDF)Click here for additional data file.S8 FigGlobal QQ plots for association analysis of rare variants with LDL in the UK10K TWINSUK cohort: (A) FunSPU (genomic control λ = 0.611), (B) FunSPUw (λ = 0.805), (C) wtFunSPU with global weights (λ = 0.642), and (D) wtFunSPUw with global weights (λ = 0.789).(PDF)Click here for additional data file.S9 FigGlobal QQ plots for association analysis of rare variants with BMI in the UK10K TWINSUK cohort: (A) FunSPU (genomic control λ = 0.604), (B) FunSPUw (λ = 0.825), (C) wtFunSPU with global weights (λ = 0.635), and (D) wtFunSPUw with global weights (λ = 0.825).(PDF)Click here for additional data file.S10 FigGlobal QQ plots for association analysis of rare variants with SBP in the UK10K TWINSUK cohort: (A) FunSPU (genomic control λ = 0.601), (B) FunSPUw (λ = 0.821), (C) wtFunSPU with global weights (λ = 0.631), and (D) wt-FunSPUw with global weights (λ = 0.793).(PDF)Click here for additional data file.S11 FigLocusZoom plots of association test results for LDL at the locus around TOMM40 and APOC4-APOC2 in the UK10K TWINSUK cohort: (A) FunSPU, (B) wtFunSPU incorporating global weights, (C) aSPU, and (D)-(I) aSPU incorporating a single functional annotation: (D) GERP++, (E) Funseq2, (F) CADD, (G) Funseq, (H) RegulomeDB, and (I) GenoSkyline (blood).(PDF)Click here for additional data file.S12 Fig(PDF)Click here for additional data file.S1 Table(PDF)Click here for additional data file.S2 TableThe corresponding phenotypes: (A) HDL, (B) LDL, (C) BMI, and (D) SBP.(PDF)Click here for additional data file.S3 Table(PDF)Click here for additional data file.S4 Table(PDF)Click here for additional data file.


Glycine max (L.) Merr.] production around the world. Soybean plants can ameliorate this stress with improved water-saving, sustained N2 fixation during water deficits, and/or limited leaf hydraulic conductance. In this study, carbon isotope composition (δ13C), which can relate to variation in water-saving capability, was measured. Additionally, nitrogen isotope composition (δ15N) and nitrogen concentration that relate to nitrogen fixation were evaluated. Decrease in transpiration rate (DTR) of de-rooted soybean shoots in a silver nitrate (AgNO3) solution compared to deionized water under high vapor pressure deficit (VPD) conditions was used as a surrogate measurement for limited leaf hydraulic conductance. A panel of over 200 genetically diverse soybean accessions genotyped with the SoySNP50K iSelect BeadChips was evaluated for the carbon and nitrogen related traits in two field environments  and for transpiration response to AgNO3 in a growth chamber. A multiple loci linear mixed model was implemented in FarmCPU to perform genome-wide association analyses for these traits.Drought stress is a major limiting factor of soybean [13C, δ15N, nitrogen concentration, and transpiration response to AgNO3, respectively, were significantly associated with these traits. Candidate genes that relate to drought stress tolerance enhancement or response were identified near certain loci that could be targets for improving and understanding these traits. Soybean accessions with favorable breeding values were also identified. Low correlations were observed between many of the traits and the genetic loci associated with each trait were largely unique, indicating that these drought tolerance related traits are governed by different genetic loci.Thirty two, 23, 26, and nine loci for δThe genomic regions and germplasm identified in this study can be used by breeders to understand the genetic architecture for these traits and to improve soybean drought tolerance. Phenotyping resources needed, trait heritability, and relationship to the target environment should be considered before deciding which of these traits to ultimately employ in a specific breeding program. Potential marker-assisted selection efforts could focus on loci which explain the greatest amount of phenotypic variation for each trait, but may be challenging due to the quantitative nature of these traits. Glycine max (L.) Merr.] seeds are an important source of protein and oil for a range of applications. Drought stress is the most important abiotic factor affecting soybean production, and can cause large decreases in yield [Soybean [in yield . Use of in yield . Therefo12C isotope of carbon in photosynthesis, and therefore discriminate against the heavier 13C isotope, which constitutes only around 1% of the atmosphere [13C, CID) or carbon isotope ratio (δ13C). Carbon isotope composition has been used as an indirect method for selection of genotypes with improved productivity in drought-stressed environments. However, it should be noted that in some cases CID has not been a good indicator for drought tolerance or did not produce consistent genotypic rankings across environments [Certain morphological and physiological traits could reflect the ability of soybean plants to better tolerate drought stress. Carbon isotope composition has been previously identified as a useful screening method to understand photosynthetic tradeoffs and water-saving capabilities of C3 plant species in certain environments . C3 planmosphere . Carbon ronments –10.13C in at least two environments [13C [Additionally, previous genome-wide association studies (GWAS) and quantitative trait locus (QTL) mapping studies have identified genomic regions controlling carbon isotope composition in soybean. In one of these studies, 373 diverse maturity group (MG) IV soybean genotypes were grown in four environments and 39 single nucleotide polymorphisms (SNPs) were identified with GWAS that had significant association with δronments . Anothernts [13C . Previou2 from the atmosphere. This nitrogen fixation provides a supply of nitrogen (N) to the plant that is used for growth and development, as well as providing nitrogen in the crop residue for subsequent crops when soybean is used in a crop rotation. However, symbiotic N2 fixation can be affected by limited water availability, and certain soybean genotypes are more sensitive than others in regards to N2 fixation during drought stress [2 fixation during water deficits had the most consistent and greatest yield advantage compared to four other traits using 50 years of weather data across U.S. soybean growing regions [Soybean is a legume which uses a symbiotic association with bradyrhizobia to fix Nt stress –18. A pr regions .2 fixation during water deficits. In addition, PI 471938 has been reported to have tolerant N2 fixation as soil dries [2 fixation during drought conditions, with lower foliar N concentrations having superior fixation during water deficits [2 fixation rate. In contrast, genotypes with lower plant N concentrations may continue to fix nitrogen during water deficits due to a lack of this feedback. Four QTLs for foliar N concentration were previously identified on Chr 13, 16, and 17 using a ‘KS4895’ × ‘Jackson’ RIL population [Using a three-stage screening process,  identifiil dries . Differedeficits , 17, 18.pulation .15N) could be a useful evaluation tool given that 15N is present at much greater levels in soil compared to the atmosphere [15N found in a soybean plant would be decreased if it is actively fixing N2 from the atmosphere, and could be an indicator of how much nitrogen fixation is affected by drought stress [Nitrogen isotope composition (δmosphere –25. The t stress . A previt stress .3) solution under high vapor pressure deficit (VPD) conditions resulted in some genotypes expressing a decreased transpiration rate, and it was hypothesized that this decrease in transpiration was a result of silver ions blocking silver-sensitive aquaporins. PI 416937, a slow-wilting genotype with low hydraulic conductance, exhibited an insensitivity to silver nitrate by not decreasing its transpiration rate when subjected to the inhibitor solution [Leaf hydraulic conductance is defined as the water flux through the leaf per unit water potential driving force, and is a measure of how readily water flows through the leaf . Limitedsolution . Given tsolution .13C, δ15N, and foliar nitrogen concentration from leaf samples collected in two field environments. Additionally, this panel was evaluated for transpiration response to silver nitrate under high VPD conditions in a growth chamber. The objectives of this study were to identify genomic regions controlling these traits using genome-wide association analyses, validate genomic loci for these traits across environments or studies, and identify genotypes in the panel which have favorable breeding values for these traits.In this study, a genetically diverse panel of over 200 soybean genotypes was evaluated for δ13C), nitrogen isotope composition (δ15N), and foliar nitrogen (N) concentration were evaluated in two field environments (GA-15 and GA-16). Based on the analyses of variance (ANOVA), genotypes, environments, and their interaction were statistically significant (p < 0.05) for all carbon and nitrogen related traits , 72% (GA-16), and 62% across both environments , 40% (GA-16), and 17% across both environments (Both)  was observed between δ13C and N concentration  values calculated from across both environments, correlations between the carbon and nitrogen related traits were from r = − 0.52 to 0.71 Table . The mos13C using the sum across the two individual environments  breeding value for N concentration using the sum across both individual environments   values ranged from − 2.33 to 1.00 within individual replications  on Chr 4 were in the same genomic region, and were found in GA-15 and across both environments, respectively  > 4) SNPs ranged from − 0.19 to 0.13  > 4) SNPs. The allelic effects ranged from − 0.14 to 0.11 for the SNPs significantly associated with δ15N (Table 15N both in GA-16 and using the across both environments BLUPs (Table For δ2) across all significant SNPs for N concentration was 50, 35, and 21% for GA-15, GA-16, and across both environments (Both), respectively.Twenty seven SNPs tagging 26 loci were identified in the GWAS for nitrogen concentration  > 4) associated with NDTR following silver nitrate treatment ) in each environment and using across environments data. Eight, six, and seven candidate genes were identified for δ13C, δ15N, and N concentration, respectively, near these most significant SNPs  of the SNPs with the lowest 13C, δ15N, and nitrogen concentration from leaf samples collected in two different field environments. In addition, this panel was also evaluated for transpiration response to silver nitrate under high vapor pressure deficit conditions in a growth chamber. Using genome-wide association mapping, genomic regions were identified controlling each of these different drought tolerance related traits and the results were compared to previous mapping studies for these traits. In addition, genotypes in the panel were identified which possessed favorable breeding values for these drought tolerance related traits.In this study, a genetically diverse panel of over 200 soybean genotypes was evaluated for δ15N found in a soybean plant would be decreased if it is actively fixing N2 from the atmosphere, and lower N concentrations have been shown to correlate with superior fixation during water deficits. However, given the high protein content of soybean, and the amount of nitrogen required to produce protein in seed, lower N concentrations could well be a poor trait for a soybean genotype to possess. Water-transporting proteins called aquaporins are involved in water movement through cell membranes [Carbon isotope composition can relate to photosynthetic tradeoffs that result from variation in water-saving capabilities. Nitrogen fixation can be highly sensitive to drought stress –16, and embranes , and popembranes , 31, 35.embranes , 29. All13C were in a similar range to those observed in two previous carbon isotope association mapping studies [15N due to differences in the units used for these measurements. Analyses of variance (ANOVA) showed that genotype, environment, and their interaction were statistically significant (p < 0.05) for all carbon and nitrogen related traits evaluated with the association panel (Table p < 0.05), correlations were generally high between the two environments. Correlations for δ13C and nitrogen concentration were all above r = 0.70 between the two environments tested, indicating the genotypes performed similarly across environments. The lowest correlation was for δ15N at r = 0.28, which suggests this trait could be subject to environmental influence, such as nitrogen levels in the soil.Values for δ studies , 12  have been previously correlated with limited leaf hydraulic conductance, which is a beneficial trait in certain drought stress environments [Low or negative DTR to silver nitrate values (transpiration less affected by AgNOronments . Given tp < 0.05)  Table , and her5) Table . This lo5) Table . Given tp < 0.0001; −log10(P) > 4) SNPs for carbon and nitrogen related traits were found on all 20 soybean chromosomes . Locus 32 identified with GWAS for δ13C in the current study is found within the CID 1–5 QTL on Chr 19 identified in [13C from two previous association mapping studies [13C in [Previously identified QTLs for CID are numbered with their approximate physical positions on the SoyBase website  in [p < 0.0001; −log10(P) > 4) SNPs within 1 Mb of each other on Chr 13 and 20 (Table No QTLs for δnt study . A compant study  and the Ndfa) in . No SNPsThis is the first report of association mapping for this trait to the authors’ knowledge in any crop species. A previous QTL mapping study for limited leaf-hydraulic-conductance identified QTLs on Chr 3, 5, 10, and 12 . The locArabidopsis thaliana showed that a member of the WD40 gene family functions in drought stress tolerance by modulating nitric oxide accumulation and stomatal closure [A total of 21 gene models were identified near the most significant SNP across each trait and environment tested. A gene model located at locus 11 for carbon isotope composition, Glyma.10 g047500, is a protein phosphatase 2C family protein  to target given the quantitative nature of the genetic architecture for many traits that could lead to soybean drought tolerance improvement, and some of these traits could be associated with poor agronomic performance.Many different genotypes were identified in the current study with favorable breeding values for drought tolerance related traits and could be utilized by breeders to improve soybean drought tolerance directly with forward breeding or be used as parents to create mapping populations to further understand the genetic architecture for these traits. Genotypes with positive breeding values for δIn addition, accessions in the current study often had favorable breeding values for certain traits, but then also had less favorable breeding values for other traits  at the time of sample collection. Five leaves were randomly selected from each of the two-row plots at the third trifoliolate leaf below the top of the plants. These leaves were placed in seed envelopes, and stored in a − 200 C freezer until they could be processed at a later date. For isotope analysis, 100–150 samples were processed at one time by transferring leaf samples to 50 ml Falcon tubes and placing them in a lyophilizer for two days to freeze dry. The samples were then ground to a fine powder by placing 4.5 mm zinc plated BBs in the tubes and grinding them using a Geno/Grinder . Immediately before using this ground leaf tissue for isotope analysis, the tubes were placed in a drying oven to ensure all residual moisture was removed. In an effort to further keep out moisture, the Falcon tube caps were wrapped with Parafilm immediately after this second drying step.Leaf samples were collected from field plots of the association panel grown in Athens, GA in 2015 (GA-15) and 2016 (GA-16) and used for stable isotope analysis. More information about sowing dates, row spacing, and management of these plots can be found in . Based ohttp://sisbl.uga.edu/ratio.html. The quantity of 13C in the leaf samples was compared to a reference standard Pee Dee Belemnite, and these δ13C values were used for further analyses. δ13C was expressed in units per mil (‰) using the following equations [Stable isotope analysis was then performed using a Carlo Erba NA1500 CHN combustion analyzer coupled to a Delta V isotope ratio mass spectrometer via the Conflo III open split interface. Three experimental replications of the dry leaf tissue of each genotype were analyzed at the Center for Applied Isotope Studies, University of Georgia, Athens, GA. A detailed protocol for the procedure can be found at quations :\docume15N in the leaf samples was compared to air and expressed in units per mil (‰) according to the following equations:The quantity of − 1.Nitrogen concentration was expressed as g kgSoybean plants for evaluation of transpiration response to silver nitrate were grown in a greenhouse at the University of Georgia in Athens, GA, USA under a 16 h day and eight hours night lighting regime. Three seeds of each genotype were sown in 32 oz. styrofoam cups using a Fafard 2B soil media . Approximately 1.5 weeks after seedling emergence, the plants were thinned to one plant per cup and maintained under well-watered conditions by watering each pot twice daily until the soil reached water holding capacity. Once the soybean plants reached the V3-V4 growth stage (approximately four weeks after sowing), the tests for response to the silver nitrate inhibitor began .0 C and 60% relative humidity (RH) overnight in dark conditions.The tests were conducted over two days. In the afternoon of the first day, the soybean plants were removed from their growing media in the greenhouse and de-rooted using clippers. A second cut on the stem was then made underwater adjacent (1–3 cm away) to the first cut using a razor blade. The remaining shoot was then placed in a 250 mL Erlenmeyer flask filled with deionized water and the mouth of the flask was sealed with Parafilm to avoid water evaporation. Plants in flasks were then placed in a walk-in Conviron growth chamber at approximately 200 C, and decrease RH to 30% to obtain a higher vapor pressure deficit (VPD) in the growth chamber. The observed VPD for the chamber was between 1.56–2.33 kPa across replications of the experiment (Table W). Each soybean shoot was then transferred to a 60 mL amber glass bottle containing a 200 μM solution of silver nitrate (AgNO3) under semi-dark conditions. This AgNO3 solution concentration was previously shown to best differentiate the transpiration response of drought tolerant versus susceptible soybean plants in [I). Differences in the amount of time that elapsed between weight measurements were accounted for in the TRW and TRI calculations by changing the denominator in increments of minutes. Decrease in transpiration rate  was then calculated as follows:In the morning of day 2, the growth chamber settings were adjusted to turn the lights on, raise temperature to 30lants in . ParafilDue to limitations in the size of the walk-in growth chamber and ability to weigh the flasks/bottles in an orderly and timely fashion, eight separate replications of this experiment were conducted Table . Each reThe association panel was genotyped with the SoySNP50K iSelect BeadChip . DNA extAnalyses of variance (ANOVA) was conducted using PROC GLM in SAS version 9.4 . For the response variables relating to carbon and nitrogen traits, genotype was treated as a fixed effect, and environment, genotype-by-environment interaction, and replication within environment were random effects. For transpiration response to silver nitrate, a model was created with genotype as a fixed effect and replication as a random effect, with NDTR as the response variable. Broad-sense heritability was calculated on an entry-mean basis according to  with theBest linear unbiased predictors (BLUPs) were calculated from both across and within environments and used as the phenotype values for subsequent GWAS analyses. The BLUP calculations for carbon and nitrogen related traits across both environments were performed using JMP Pro . The model was built by treating genotype, environment, genotype-by-environment, and replication within environment as random variables using the Standard Least Squares personality and REML method. For individual environments for carbon and nitrogen related traits and transpiration response to silver nitrate, genotype and replication were used as variables and treated as random to calculate BLUPs.Sclerotinia sclerotiorum [Fixed and random model Circulating Probability Unification (FarmCPU) was used to perform the genome-wide association analyses for all traits evaluated . FarmCPUrotiorum .p-values generated from the FarmCPU output. The significance threshold  > 4) was used to determine if SNPs were significantly associated with the traits of interest. This threshold is less stringent than a Bonferroni-corrected threshold, but is more stringent than many other soybean GWAS studies using 50 K SNP genotyping data [Manhattan plots were visualized with the ‘qqman’  and ‘CMping data , 49, 50.2 and estimate linkage disequilibrium (LD) blocks. Using D′ > 0.8 to extend the spine, LD blocks were identified by chromosome with the Solid Spine of LD option. These LD blocks were used to determine if significant  > 4) SNPs that are physically close (less than 1 Mb) were at the same locus (genomic region) controlling the trait of interest. Significant SNPs not part of the same LD block were deemed different loci controlling the trait. Allelic effects were calculated by taking the mean difference in phenotypic values for the trait between the two alleles at a particular SNP, and were provided as part of the FarmCPU output. A negative effect value indicates that an individual possessing the second nucleotide alphabetically for this SNP would have lower phenotypic values, whereas a positive effect value would have higher phenotypic values. The direction, negative or positive, of the effect is based on how the genotype data was converted from HapMap to numerical format using GAPIT [2) by significant  > 4) SNPs was calculated using a linear regression in R. The model lm(BLUP ~ SNP1 + SNP2 + …) was used to determine the total amount of phenotypic variation explained by all significant SNPs for a given trait in a particular environment.Haploview version 4.2 software  was usedng GAPIT  prior top < 0.0001; −log10(P) > 4) SNPs in each individual environment and with the across environments BLUPs. Breeding values across the individual environments were also summed and used for comparisons. Allelic effects for a given SNP were considered negative if the allele contributed to lower phenotypic values, and positive if it increased phenotypic values. Heterozygous and missing allele calls were not included in the breeding value calculation.Breeding values for the traits were calculated by summing the allelic effects for all significant  > 4) SNPs from GWAS in each environment and across environments for each of the carbon and nitrogen related traits. Glyma2.1 gene models within plus or minus 10 kb of the SNP physical position were recorded and further investigated. The median distance between SNP markers used in the GWAS was 9 kb, and the mean distance was 26 kb. Although identifying all gene models in LD with significant SNPs would be ideal, the efforts were focused on models in close proximity (within plus or minus 10 kb), which approximately spans this distance between markers.Using SoyBase , candidaGlycine max Wm82.a2.v1 version of the soybean genome. This identified 88 gene models which had “aquaporin” in their functional annotation. In comparison, 82 of these gene models were also found when searching for “aquaporin” on the SoyBase website (www.soybase.org). The physical locations of the full list of 88 gene models having an aquaporin annotation from Phytozome were used to make comparisons between the significant  > 4) SNPs identified for transpiration response to silver nitrate from the GWAS results to see if any aquaporin genes were in or near these regions.Given the hypothesized relationship between transpiration response to silver nitrate and sensitivity of aquaporin populations in soybean , 30, 53,Additional file 1. Breeding value ranks for accessions tested for canopy wilting, carbon isotope composition (δ13C), nitrogen concentration, nitrogen isotope composition (δ15N), and normalized decrease in transpiration rate (NDTR) in response to silver nitrate (AgNO3) treatment.Additional file 2. Genome-wide Manhattan plots for carbon and nitrogen related traits.Additional file 3. Candidate genes and their functional annotation identified using the Glyma2.1 gene models in SoyBase within plus or minus 10 kb of SNPs significantly associated with carbon and nitrogen related traits.


Orofacial clefts are the most common malformations of the head and neck region. Genetic and environmental factors have been implicated in the etiology of these traits.MEGA) to identify common genetic variation associated with nonsyndromic orofacial clefts. The data cleaning of this dataset allowed for screening of annotated sex versus genetic sex, confirmation of identify by descent and identification of large chromosomal anomalies.We recently conducted genotyping of individuals from the African population using the multiethnic genotyping array (UPD) on chromosome 22. We also identified a de novo deletion on chromosome 18. In addition to chromosomal anomalies, we identified cases with molecular karyotypes suggesting Klinefelter syndrome, Turner syndrome and Triple X syndrome.We identified the first reported orofacial cleft case associated with paternal uniparental disomy (patObservations from our study support the need for genetic testing when clinically indicated in order to exclude chromosomal anomalies associated with clefting. The identification of these chromosomal anomalies and sex aneuploidies is important in genetic counseling for families that are at risk. Clinicians should share any identified genetic findings and place them in context for the families during routine clinical visits and evaluations. Syndromic clefts (SC) are clefts with other structural and cognitive phenotypes and they account for 30% of all clefts. There are over 500 Mendelian clefting syndromes currently indexed in OMIM (Nonsyndromic clefts (NSC) are the most common forms of clefts accounting for 70% of all clefts  is a situation whereby an individual has inherited a pair of homologous chromosomes from the father Engel, . patUPD Although paternal and maternal uniparental disomy (UPD) in orofacial clefts are very rare, they have been reported on chromosomes 6, 7,10, 12,15 16 and 21  process, we identified individuals with chromosomal anomalies on several chromosomes including uniparental disomy on chromosome 22, large chromosomal deletions and duplications.22.1Eligible subjects are individuals who have nonsyndromic OFC and were born to Ghanaian, Ethiopian, and Nigerian parents. The offspring of Caucasians and Asians were excluded. Eligible cases were identified following IRB approval through the free clefts surgical repair projects. Currently, the network for treatment of clefts in Africa is enhanced, due to the efforts of the Pan African Association for Cleft Lip and Palate (PAACLIP). This network is supported by cleft charities, and all members use a common, standardized protocol for phenotyping. In addition, the grant requires that surgeons at all centers perform standardized physical examinations and take clinical photographs, and that full descriptions of the cleft phenotypes and all other recognizable malformations are entered into a clinical database. Signed informed consent were obtained from all participating families, and every family recruited into the study was assigned a unique identifier number (UNID). Data from all recruited families were entered remotely at each center in Africa, into a secured REDcap database (REDCap) database . Each sample was quantified using Qubit (http://www.invitrogen.com/site/us/en/home/brands/Product-Brand/Qubit.html) and divided into a stock and several working aliquots. This set‐up allowed us to verify sample identity using the stock if mislabeling or cross‐contamination of the working aliquot was suspected during sample handling. As a preliminary quality check, gender reported in the Redcap database was confirmed using Taqman XY genotyping. A 25ul aliquot of consented samples with confirmed genetic sex and DNA concentration of ≥ 50ng/ul was sent for MEGA array genotyping at the Center for Inherited Disease Research (CIDR).Saliva samples were labeled at the Butali laboratory in Iowa and assigned a unique identification (UNID) number prior to DNA extraction. DNA extraction was done at the Butali lab using the Murray lab protocol (2.3The expanded Illumina Multi‐Ethnic Genotyping Array (MEGA) v2 15070954 A2 (genome build 37) that contains over 2 million Single Nucleotide Polymorphisms and over 60,000 rare variants selected from populations of African origin was used for genotyping. Genotyping was carried out on 3,347 samples which included 3,198 unique samples and 70 duplicates. HapMap controls (70 unique samples and 9 duplicates) were also genotyped as part of the quality control process.2.4The goal of the data cleaning process was to identify a high‐quality genotype dataset that can be used for detecting significant genotype associations with nonsyndromic clefts. This process included sex chromosome checks, a check for missing call rates, batch effects, identification of large chromosomal anomalies, confirmation of relatedness  and establishment of continental ancestry with respect to HapMap samples using methods described in Laurie et al.  and implTo identify aneuploid or mosaic samples systematically, we used the “Circular Binary Segmentation” (CBS)  on chromosome 22. The UPD is apparent from the nearly complete homozygosity on chromosome 22 Figure  for an ade novo 23MB deletion on Chromosome 18 was also identified. BAF and LRR plots of this individual and its parents are shown in Figure de novo. About 30 individuals with large autosomal deletions and duplications were identified (data not provided).Furthermore, an affected individual with a 4We conducted genotyping of individuals from the African population using the multiethnic genotyping array (MEGA) v2 15070954 A2 to identify genetic variation associated with presumed nonsyndromic clefts. The data cleaning of this dataset allowed us to check the annotated versus genetic sex, confirm identify by descent and identify large chromosomal anomalies. We identified an individual with UPD on chromosome 22 and the result of our analysis strongly indicates that the UPD observed is of paternal origin. Previous UPD associated with clefts has been reported in other chromosomes and are mainly due to maternal UPDs as a result of advanced maternal age during pregnancy leading to trisomy rescue and error ). The 23MB de novo deletion included the ZADH2 gene which has been reported in DECIPHER for most individuals with developmental disorders including clefts. Over 50% of individuals with large deletions including the child with a de novo deletion had CLP. Large deletions in individuals with CL/P have been previously reported (Maarse et al., The There are inconsistent reports of clefting in some individuals with sex aneuploidies (Perrotin et al., It is very important to carry out detailed clinical evaluation of children with apparent nonsyndromic clefts by individuals with the skill to investigate family history, environmental exposures and do a thorough clinical exam on child and parents. Genetic testing to exclude chromosomal anomalies may be indicated by the findings of these exams and also in cases of prenatal detection of clefting where phenotyping is more difficult. This study is limited by clinical examination information available at birth or within a few days after delivery. Therefore a detailed periodic exam is advised in order to identify associated anomalies that may become clinically obvious days after birth. This is because over 15% of clefts with associated anomalies are caused by chromosomal defects (Rasmussen et al., None to declare.


Methods have been developed for Mendelian randomization that can obtain consistent causal estimates under weaker assumptions than the standard instrumental variable assumptions. The median-based estimator and MR-Egger are examples of such methods. However, these methods can be sensitive to genetic variants with heterogeneous causal estimates. Such heterogeneity may arise from over-dispersion in the causal estimates, or specific variants with outlying causal estimates. In this paper, we develop three extensions to robust methods for Mendelian randomization with summarized data: 1) robust regression (MM-estimation); 2) penalized weights; and 3) Lasso penalization. Methods using these approaches are considered in two applied examples: one where there is evidence of over-dispersion in the causal estimates , and the other containing outliers . Through an extensive simulation study, we demonstrate that robust regression applied to the inverse-variance weighted method with penalized weights is a worthwhile additional sensitivity analysis for Mendelian randomization to provide robustness to variants with outlying causal estimates. The results from the applied examples and simulation study highlight the importance of using methods that make different assumptions to assess the robustness of findings from Mendelian randomization investigations with multiple genetic variants. X,IV1: the variant is associated with the exposure U of the exposure-outcome association, andIV2: the variant is independent of all confounders Y conditional on the exposure X and confounders U  for invalid variants, with each αj having a 0.5 probability of being multiplied by -1. ϕj was set to zero for all j.Scenario 2—Balanced pleiotropy, InSIDE satisfied: αj ∼ U for invalid variants, and ϕj was set to zero for all j.Scenario 3—Directional pleiotropy, InSIDE satisfied: ϕj ∼ U for invalid variants, and αj was set to zero for all j.Scenario 4—Directional pleiotropy, InSIDE violated: If a genetic variant is associated with a confounder of the risk factor–outcome association, then this will affect the variant’s association with both the risk factor and the outcome, leading to the violation of the InSIDE assumption. Using this observation, data were simulated to consider the following four scenarios:Gj were coded to correspond to a single nucleotide polymorphism with minor allele frequency 0.3. If a genetic variant was a valid IV then αj and ϕj were set to zero in all four scenarios. In Scenarios 2 to 4, the number of invalid IVs was set to 1, 3 and 6. The causal effect of the risk factor on the outcome was either θ = 0  or θ = 0.3 . The effects of the genetic variants on the risk factor (The genetic variants 2 statistic), mean F statistic, and mean I2 statistic are contained in Table A in the 2 values were greater than 3% for all of the scenarios, and the minimum mean F-statistic was 20.8. The I2 statistic ranged from 39.1% to 80.9%. Since violations in the no measurement error (NOME) assumption of the genetic associations with the risk factor can lead to attenuation towards the null for the MR-Egger estimates, and this attenuation is approximately equal to the I2 statistic, we expected the MR-Egger estimates for the positive causal effect to be severely attenuated towards the null [The mean proportion of variance in the risk factor explained by the genetic variants  are given in Table B in the When all of the genetic variants were valid IVs , all of Although the mean estimates in Scenario 2 Tables  and 4 weIn Scenario 3 , the IVW method produced biased causal estimates with inflated Type I error rates, and the degree of bias increased with the number of invalid IVs. With one invalid instrument, estimates from the robust methods were only slightly biased and Type I error rates were fairly well controlled. As the number of instruments increased, bias in the estimates for the robust methods also increased, although the magnitude of bias was smaller than the IVW method, and Type I error inflation was less severe. Robust regression with penalized weights performed reasonably well when there was 1 or 3 invalid instruments. Although the median methods give unbiased estimates asymptotically , when pleiotropic effects are directional there is some bias with a finite sample.In Scenario 4 , all of the robust methods produced biased estimates. When there were only one invalid instrument, the magnitude of bias from the robust methods was less severe than the IVW method, and this was particularly true for robust regression with penalized weights. As the number of invalid IVs increased, the performance of the robust methods worsened, and there was little advantage in applying the robust methods compared to the median estimator in Scenario 4 when 6 of the 15 genetic variants were invalid IVs. In this scenario, bias is greater for the weighted median than for the simple median method as the invalid genetic variants are on average more strongly associated with the risk factor than the valid ones. This is because invalid variants are associated with the risk factor directly and via their effect on the confounder. In practical applications, invalid genetic variants will not necessarily be more strongly associated with the risk factor than valid ones, and so the simple median will not necessarily perform better than the weighted median method.While results were fairly similar for most of the methods, results from the MR-Egger method were often quite different. This is because the other methods are fairly similar in their assumptions  and their mode of operation . This highlights the importance in an applied analysis of performing a range of methods that make different assumptions, rather than multiple methods that make similar assumptions .Results from applying robust regression and penalized weights to the MR-Egger method are provided in Table D in the Finally, results from the one-sample setting are provided in Tables E and F in the 2 values were comparable with the original simulation study. The IVW model with: 1) the full set of genetic variants; 2) robust regression; 3) penalized weights; and 4) robust regression and penalized weights were all applied to the dataset. The Lasso penalization method with the heterogeneity stopping rule was also considered.Since many of the methods described in this paper are based on asymptotic theory, it was anticipated that there would be an improvement in the performance of the methods when the data were generated with a larger number of genetic variants. We therefore repeated the simulation study for Scenarios 2–4 for 1 000 simulated datasets with the number of genetic variants increased from 15 to 100, and the number of invalid IVs increased from 1, 3 and 6 to 5, 15 and 30. The bounds of the uniform distribution used to generate the genetic associations with the risk factor ; 2) robust regression; 3) penalized weights; and 4) robust regression and penalized weights, and the Lasso penalization method with the heterogeneity stopping rule are provided in Results from the simulation study for the IVW model with: 1) the The reduction in the strength of the IVs led to weak instrument bias, and there was severe attenuation towards the null for the positive causal effect . For theAPOE gene region, the proposed methods were able to give null estimates that were unaffected by these outlying variants.In this paper, we have introduced three robust approaches for Mendelian randomization with summary level data that downweight the influence of heterogeneous causal estimates. The applied examples considered in this paper illustrate the importance of using a variety of methods in a Mendelian randomization analysis. The results from the robust methods support a null causal effect of BMI on schizophrenia risk. While the IVW and MR-Egger methods produced positive estimates that were strongly influenced by pleiotropic variants in the We also performed a simulation study to compare the robust approaches to the IVW, simple median, weighted median, and MR-Egger methods. The simulation study highlighted the sensitivity of the IVW method to violations in the IV assumptions, and the requirement for robust methods to be considered in the sensitivity analysis of a Mendelian randomization study. The simulations also demonstrated the impact of violating the NOME assumption on the estimates from the MR-Egger methods. Since it was not feasible to adjust for the violation of the NOME assumption through the SIMEX method  in the sRobust regression with penalized weights consistently produced the least biased estimates in the simulation study. Although the power and bias of this approach was significantly better than the standard IVW method when the IV assumptions were violated, it suffered from poor coverage and increased Type I error rates, particularly when there was a high proportion of invalid instruments. When there was only one invalid instrument, robust regression with penalized weights produced more precise estimates than the median estimator. However, as the number of invalid instruments increased there was little advantage of using robust regression with penalized weights compared to the median estimator.Throughout this paper, we have assumed that heterogeneity of the causal ratio estimates is indicative of violations in the IV assumptions, particularly the presence of pleiotropic effects. However, heterogeneity among the causal ratio estimates may arise for a number of reasons . For exaThe simulation study has highlighted some of the disadvantages of excluding or downweighting genetic variants from Mendelian randomization analyses. Excluding genetic variants with heterogeneous causal estimates will generally reduce the standard error of the estimate. However, too much penalization can potentially result in artificial overconfidence in the precision of the causal estimate, leading to poor coverage of the true causal effect and increased Type I error rates, as seen for Lasso penalization. If the excluded genetic variants are truly invalid IVs then removing them from the analysis will reduce bias and improve the precision of the causal estimate. However, outlying or heterogeneous causal ratio estimates may be valid IVs, and so removing them from the analysis would be inappropriate. On balance, it may be more appropriate to consider approaches that reduce the contribution that heterogeneous ratio estimates have on the causal estimate, such as the median estimator or robust regression, rather than excluding them from the analysis. If a large number of variants are identified as outliers, then researchers should consider reporting that the Mendelian randomization analysis is inconclusive, rather than reporting a causal estimate.The purpose of this paper was not to promote one robust method for Mendelian randomization over another, but to emphasize the need for multiple sensitivity analyses that make different sets of assumptions. Although we acknowledge that none of the proposed methods performed significantly better than the median estimator, the extensions proposed in this paper should provide additional confidence in the findings from a conventional Mendelian randomization analysis, particularly when the causal estimates are consistent. Genetic variants that are downweighted or excluded from the analysis by the robust methods should be examined for pleiotropy to determine whether they should be removed from the dataset. The methods proposed here are likely to be useful for Mendelian randomization analyses performed for large numbers of risk factors in an automated manner, such as for -omics risk factors measured on a high-throughput platform. These methods can help a researcher rapidly triage whether a positive causal estimate from the standard IVW method is evidenced just by a small number of variants (as in the LDL-cholesterol and Alzheimer’s disease example), or by the majority of variants.The methods introduced in this paper, particularly robust regression with penalized weights, may be more suited to certain scenarios than the median estimator. In the applied example for LDL-C and AD risk, there were two variants that appeared to be clear outliers. The median estimator and robust regression with penalized weights both suggested that there was a null causal effect of LDL-C on AD risk, but the estimates from the median estimator were less precise. This observation of robust regression producing more precise estimates was also observed in the simulation study when there was one invalid IV. Robust regression with penalized weights may be a useful addition to sensitivity analyses in Mendelian randomization when there are a small proportion of variants with heterogeneous causal estimates.We found that the Lasso penalization method may be more appropriate in an applied setting, where the estimates can be reported over a range of values of the tuning parameter. The practicality of applying Lasso penalization to the simulation study was more restrictive, and required an automated approach to selecting the tuning parameter.Whilst we appreciate the limitation of only considering methods with uncorrelated genetic variants, we argue that robust methods should be used when the IV assumptions are in doubt, and therefore using one genetic variant from each gene region is a sensible  approach for robust methods in an applied Mendelian randomization analysis. This is because including multiple variants from a single region may mean that region receives a disproportionate weight in the analysis, and so the validity of the analysis would be overly dependent on the validity of these variants. This could be problematic as correlated variants are likely to all be valid or all be invalid, particularly if they are all in the same gene region. If an analyst does want to include correlated variants in an analysis, this can be done by first calculating the appropriate weighting matrix based on the inverse-variance weights and the correlations between variants, and multiplying the genetic associations by the Cholesky decomposition of this matrix, as described previously . SoftwarThe violation of the NOME assumption limited the utility of the simulation study as the estimates from MR-Egger could not be compared to the robust methods. Given that MR-Egger is frequently used as part of a sensitivity analysis in Mendelian randomization studies, this could be viewed as a weakness of the simulation study.R2 statistic similar) and found that there was significant attenuation towards the null due to weak instrument bias. We had thought that the performances of some of the robust methods would have improved by increasing the number of genetic variants as the methods are based on asymptotic theory. However, we did not find any significant improvements in the methods, and in some cases, the performance of the models worsened with the increased number of genetic variants.The main simulation study was also limited by the number of genetic variants considered in the data generating model. Since GWASs are now being performed on large study populations, and estimates of genetic associations are publicly available from large consortia, only considering 15 variants in the simulation study may have been conservative. We tried to rectify this limitation by re-performing the simulation study with 100 genetic variants Click here for additional data file.S2 AppendixAdditional results from the simulation study.(PDF)Click here for additional data file.