Genome wide association (GWA) analysis of brain imaging phenotypes can advance our understanding of the genetic basis of normal and disorder-related variation in the brain. GWA approaches typically use linear mixed effect models to account for non-independence amongst subjects due to factors, such as family relatedness and population structure. The use of these models with high-dimensional imaging phenotypes presents enormous challenges in terms of computational intensity and the need to account multiple testing in both the imaging and genetic domain. Here we present a method that makes mixed models practical with high-dimensional traits by a combination of a transformation applied to the data and model, and the use of a non-iterative variance component estimator. With such speed enhancements permutation tests are feasible, which allows inference on powerful spatial tests like the cluster size statistic. Genome-wide association studies (GWAS) of neuroimaging data pose a significant computational burden because of the need to correct for multiple testing in both the genetic and the imaging data. Here, Ganjgahi et al. develop WLS-REML which significantly reduces computation running times in brain imaging GWAS. Quantitative brain phenotypes are based on structural images  or functional images (brain response to particular cognitive task or resting state). Genetic association at a hundred thousand locations in the human brain present immense statistical challenges including: low statistical power, need for multiple comparisons correction and like, other association studies, correction for population structure, a term that encompasses cryptic/family relatedness and population stratification.Genome-wide association studies (GWAS) of neuroimaging data can advance our understanding of human brain by discovering genetic variants associated with normal and disorder-related phenotypic variance in brain structure and function8 is generally thought to be a confounding factor that can lead to excessive false positives when ignored. This type of non-independence has been studied throughly in the recent GWA era13. While genomic data can be used to control for population stratification by including the top principal components as fixed effect covariates in a linear regression model14, usually individuals with close estimated relatedness from identity-by-state (IBS) matrix or different ethnicities are excluded from the study sample. This might not be a problem in genetic studies with six digit sample sizes, but may make substantial differences in GWA studies with neuroimaging phenotypes where sample size is much smaller. Also, even in a carefully designed GWA study, it is hard to avoid spurious associations because of population structure; in particular, it is likely that in studies with large sample sizes, such as the UK biobank possess some level of population structure. Although the emergence of large scale neuroimaging consortia like ENIGMA or CHARGE can help to conduct well-powered genetic association studies through meta analysis framework, still it is crucial to use a powerful statistical method at the site level. Hence, there is a compelling need for analytical techniques that addresses these challenges.In the GWA studies of unrelated individuals, non-independence due to latent population stratification or unknown (cryptic) relatedness26. It has been shown that the correction for the problem of latent population structure in GWA with an LMM is both effective and power preserving27.Linear mixed effect models (LMMs) using molecularly derived empirical relatedness measures have grown in use recently for both studies of related and unrelated individuals, since they do not require self-reported biological relatedness, providing a framework where such complexities are automatically accounted for. LMMs have been used as an alternative to ordinary least squares (OLS), providing a mechanism to model trait variance explained by a genetic relationship matrix (GRM); such variance captures the genome-wide similarity between “unrelated” individuals by modeling it as a random effectP-value leads to conservative statistical inference procedure as it ignores complex spatial dependence in the imaging phenotypes. Despite the many analytical techniques that have been developed to accelerate the GWA with LMM, these advances do not eliminate problems related to numerical optimization nor multiple testing problem. Furthermore, commonly used spatial inference tools, like cluster size28 or threshold-free cluster enhancement (TFCE) statistics29, depend on resampling-based inference methods to ensure valid control of false positives31. Familywise error rate (FWE) correction, controlling the chance of one or more false positives across the whole set (family) of tests32 requires the distribution the maximum statistic, can be computed for either voxels, ROIs, clusters or TFCE with a permutation test33, a standard tool to conduct inference in neuroimaging.These merits motivate the application of LMM for genetic association with high-dimensional imaging phenotypes. However, fitting LMM at each voxel in the brain is computationally intensive or even intractable at the voxel level since variance component estimation relies on likelihood function optimization using numerical methods. Moreover, search for genetic association across the genome at different locations with imaging phenotypes requires intense multiple testing corrections both for number of elements in an image and number of markers. Whether the association analysis is conducted for a few regions of interest (ROIs) or every voxel, naive application of Bonferroni correction for number of hypothesis testing in the image with usual GWA 34. Second, the complexity of association testing is dramatically decreased by projecting the model and phenotype to a lower dimension space, combined with use of a score statistic for association testing. This projection is based on the eigenvectors of the GRM adjusted for the fixed effect nuisance terms35. In this setting, the projected phenotype likelihood function is equivalent to that used with restricted maximum likelihood (REML) of the LMM (Method), going forward we call this approach simplified REML35. While both models have the same statistical properties, our particular projection provides several computational benefits that dramatically reduces LMM complexity: (i) The diagonalized covariance allows a non-iterative one-step variance component estimator34, taking the form of a weighted regression of squared projected data on eigenvalues of the GRM adjusted for nuisance fixed effect terms, an approach that we call weighted least squares REML (WLS-REML); (ii) The regression form of our estimator is easily vectorized, meaning that many image elements and SNPs can be tested in a single and fast computational test in several high-level programming languages (Method); (iii) Finally, the simplicity and fast computation of the score test statistic makes permutation testing feasible, allowing exact, non-parametric control over the FWE, accounting for the number of tests conducted over all image elements and genetic markers; we define two permutation schemes, free and constrained, where in the latter case the permutation is confined to exchangeability blocks defined based on the eigenvalues distribution.This paper makes two major contributions to reduce the complexity of LMM for genetic association with imaging phenotypes. First, the computational cost of variance component estimation is reduced by using a non-iterative one-step random effect estimatorS markers and V imaging phenotype elements on N individuals, the variance component likelihood optimization complexity of FaST-LMM35 which, to the best of our knowledge, is the fastest implementation of LMM is O(N3 + INV), where I is the average number of iterations, while for WLS-REML the random effect estimator (see Methods) it is O(N3 + NV) (the common O(N3) term is the time complexity of the GRM eigendecomposition). More critically, the estimation and test statistic computation complexity of FaST-LMM is O(SPN2V), where P is the number of nuisance fixed effects, while for WLS-REML (Eq. (O(SNV), a substantial reduction for imaging phenotypes when number of image elements V is much bigger than the sample size N. Even for a single trait GWA (V = 1), our proposed projection reduces the association (Eq. (O(SN) which is significantly less than FaST-LMM for large sample GWA.The reduced computational complexity of our method represents a significant advance over existing methods. The complexity of LMM association has two components, one for the variance component estimation, the other is for fixed effect parameter estimation and test statistic computation. For a GWA over EML (Eq. ) this ision (Eq. ) complex34, we introduced the WLS-ML random effect estimator that exploits a one-step optimization approach combined with eigen-rotation of phenotype and model (see Method for more details). The non-iterative estimator has a simple form, with variance components and fixed parameters each estimated by weighted least-squares regressions. In this paper, we evaluate our non-iterative ML and REML estimators (WLS-ML and WLS-REML) with their fully converged counterparts (Full ML or Full REML), comparing score, likelihood ratio (LRT) and Wald tests on intensive simulation studies; the two permutation schemes are also compared. Direct comparisons are made between FaST-LMM and our score test with WLS-REML using simulation and real data.In our previous workIntensive simulation studies are conducted to evaluate the proposed methods for association estimation and testing. The aim of the first study is to compare fully converged and one-step random effect estimators based on the simplified ML and REML functions. In the second study, the performance of various test statistics for the association testing are compared using a fully converged or one-step random effect estimators for ML and REML functions (see Supplementary Note β1) estimation  between FaST-LMM and simplified REML  as a nuisance covariateWe performed GWA of whole brain FA data, using a whole brain parcellation of 42 ROIs, as well as a voxel-wise analysis for 53,458 voxels , comparing the WLS-REML score test with the fully converged random effect estimators with FaST-LMM. We also evaluate the use of OLS with MDS as nuisance fixed effects regressors for control of population structure in GWA with unrelated individuals.The random effect estimators, one-step and fully converged REML are compared directly in Fig. Even with the tendency for genetic variance to be underestimated with the non-iterative method, the association statistic show remarkable concordance, with both approaches having almost the same performance Fig. . FaST-LMFigure P-values for 42 ROIs and 1,376,877 SNPs to assess association significance. Among the 42 × 1,376, 877 ≈ 57 million statistics, eight passed the permutation based FWE threshold −8) yields to a more stringent threshold 38; this gave an effective test count of 18.30. Application of a Bonferroni correction for 18 independent tests to the usual GWA alpha level (5 × 10−8). This Bonferroni threshold with effective number of tests yields a slightly more stringent threshold A permutation test was used to find FWE-corrected P-value of 0.01 to create clusters, and 1000 permutations were used to compute the maximum distribution of cluster size over space and SNPs, offering FWE control over the entire search space; voxel-wise FWE thresholds were also computed. The level 5% FWE-corrected voxel-wise statistic threshold was 66.42, producing six significant association out of 84 billion tests. The 5% FWE corrected cluster size threshold is 7370 but no SNP’s statistic map had a cluster exceeding this value; the largest observed cluster size is 6648, which had a image-wide, genome-wide FWE-corrected cluster size P-value of 0.09. We note that the effective number of independent tests is not applicable to cluster-wise inference30 and does not scale to voxel-wise inference. Also, it depends on an arbitrary GWAS threshold that depends on the chip used.Finally we performed voxel-wise genome-wide association analysis of 53,458 voxels with 1,376,877 SNPs, using our proposed WLS-REML score test for association. Cluster-wise inference was performed on each spatial association map; we used a threshold corresponding to a We compared running time of our WLS-REML score test to that of FaST-LMM, which to our knowledge is the fastest implementation of LMM. The comparison was done using simulated and read data with a Intel(R) core(TM) 3.4 GHz i7-2600 CPU and 16 GB RAM. Parametric association testing of 5000 phenotypes with 6000 simulated markers using a sample of 300 individuals took 1 h with FaST-LMM, however, our implementation of the score test (Eq. (14-15)) only took 3 s. On real data, parametric whole genome association on 42 ROIs, required 756 min using FaST-LMM while our approach took only 2 min.Neuroimaging genetics has moved from establishing a heritable phenotypes to finding genetic markers that are associated with imaging phenotypes. Despite emerging world-wide consortia to boost GWA studies power using the largest possible sample sizes, there is a compelling need for powerful and computationally efficient analytic techniques that control for population structure at the site level. Moreover, GWA studies with neuroimaging phenotypes require fitting a model at each point (voxel/element) in the brain, and the large number of measurements presents a challenge both in terms of computational intensity and the need to account for elevated false positive risk because of the multiple testing problems both in terms of number of elements in image and number of markers being tested.43. The LMM has gained popularity as an alternate method for GWA of unrelated individuals to correct for population structure26. However, due to the required inversion of potentially large matrices, the general LMM is computationally intensive where the complexity includes the deriving of the GRM, variance component parameter estimation, fixed effect estimation, and the calculation of the required association statistic for each marker grows with sample size and number of candidate markers for association testing.There has been rapid advances in quantitative genetic statistical methods account for population structure in GWA studies of unrelated individuals. Linear mixed models allowing for the rigorous testing of genetic associations  have long been employed in human genetics as the standard to correct for the non-independence among subjects due to known familial relatedness in pedigree-based studiesO(SNV). Further improvements in speed can be achieved by using the WLS-REML random effect estimator with O(NV) that we found to be more accurate than the WLS-ML estimator.To tackle these problems, we used an orthogonal transformation that substantially reduced LMM complexity for GWA. The equivalence between projected model and REML function helped us to reduce complexity of association testing. Specifically, the projection reduces the information matrix to a scalar that enables efficient vectorized implementation of score test with time complexity We conducted intensive simulation studies, evaluating a broad set of test statistics for association testing using the simplified ML and REML functions accompanied by one-step and fully converged random effect estimators. The one-step random effect estimator using simplified REML function provides more accurate approximation of the fully converged one in comparison to the WLS-ML variance component estimator. The simulation and real data analysis shows that only minor differences in marker effect estimation and association test statistics between one-step and fully converged random effect estimator. However, the former requires less computational resources. Also, we could not observe any appreciable differences in performances in terms of the error rate and power using the GRM from unrelated individuals or kinship matrix from a family study.The WLS-REML random effect estimator is fast enough to be used to estimate voxel-wise heritability. Although the proposed one-step random effect estimator is not as accurate as fully converged one, it can be used for filtering a small number of elements for further investigation with more computational intense tools. Furthermore, when restricted to individuals with European ancestry we found LMM had genomic controls values closer to 1 than OLS values, indicating the success of the LMM in dealing with population structure.P-values was nearly as accurate as for the fully converged REML score test, meaning that permutation is not required for element-wise inference.We selected the score test based on the simplified REML function for further investigations because it only requires a single variance component estimate, common to all markers under the null hypothesis. Furthermore, efficient vectorized implementation of score test for images accelerates association testing. The null distribution of WLS-REML score test P-values between our proposed method and existing methods, current LMM approaches depend on numerical optimization and are not feasible for GWA of over 1000’s imaging phenotypes, such as found in the UKBiobank44 or Human connectome project which has related individuals. Moreover, a search for genetic association across the genome with imaging phenotypes requires intense multiple testing corrections both for number of elements in an image and number of markers. The reduced complexity of our proposed method due to a non-iterative random effect estimator and vectorized implementation of score statistic computation makes permutation-based FWE-corrected inferences feasible. Our permutation approach is more computationally efficient than others proposed in the genetics literature45, avoiding inversion of the phenotypic covariance on each permutation. Permutation provides flexible FWE inference for ROIs or the whole brain, voxel-wise or cluster-wise. Though methods based on effective number of independent tests are computationally efficient, they depend on an (1) arbitrary GWAS threshold that depends on the chip used, (2) these approaches are not applicable to cluster-wise inference and (3) do not scale to voxel-wise inference which are the standard spatial statistics in imaging. While our vectorized implementation of score statistics demands complete data, there are various imputation methods can be used prior to association analysis to address missingness.Genome wide association analysis of high dimensional imaging phenotype requires a computationally efficient LMM that can accommodate large sample sizes, provide multiple testing correction and complex spatial dependence among image elements. Although we have not observed significant differences of parametric O(N3 + INV) to O(N3 + NV). Further improvement in speed is also obtained by using the vectorized implementation of the score test based on simplified REML function. Our proposed method allows efficient implementation that reduces running time complexity to O(SNV). In addition, the efficient score test computation is fast enough to allow the permutation test to control family-wise error rate for number of elements in image and number of markers, and allow the use of spatial statistics like cluster size or TFCE.Whether using the linear mixed model for controlling population structure or kinship, high dimensional imaging phenotypes presents challenges in terms of computational intensity and elevated false positive risk; growing sample sizes and whole genome sequence data add to the computational burden. Our contribution in the acceleration of the exact LMM can be seen at two steps. First, covariance matrix estimation using WLS-REML random effect estimator reduces time complexity from 46, estimate a residual variance component conditional on each marker’s effect. In studies of “unrelated” subjects, this residual variance component often involves re-estimation of the GRM which is constructed excluding the candidate marker and surrounding markers in linkage disequilibrium.Several approximate or exact methods have been proposed to speed up LMM-based testing. Approximate methods assume the total polygenic random effect is same for all markers under the null hypothesis of no marker effect, hence the relevant residual genetic variance component is estimated only once using all markers. In contrast, exact methods, which is the recommended LMM practiceTo the best of our knowledge, the fastest implementation of exact LMM is Fast-LMM, which transforms the phenotype and LMM model with the genetic similarity matrix (GRM) eigenvectors and uses a profile likelihood approach to simplify variance component estimation. The eigenvector matrix diagonalisation along with the profile likelihood with only one variance parameter reduces optimization time substantially. In Fast-LMM the covariance matrix is estimated only under the null hypothesis of no marker effect, and then a generalized least squares (GLS) is applied to estimate the marker effect and the LRT is used for hypothesis testing. Note that small sample size behavior of this approach has not been validated; for example, using it for association analysis of imaging phenotypes with only 300 subjects might not be valid. In addition to concerns about the finite sample validity, Fast-LMM requires numerical optimization for each element (voxel/ROI) of image that makes it computationally intensive or essentially impractical for large-scale imaging phenotypes.N individuals can be written as:Y is the N-vector of the measured phenotype; X1 is a N-vector of a given marker’s minor allele count, implementing an additive genetic model; X2 is the N × (P − 1) matrix containing an intercept and fixed effect nuisance variables like age and sex; β1 is the scalar genetic effect; β2 is the (P − 1)-vector of nuisance regression coefficients and g is the N-vector of latent (unobserved) additive genetic effects; and ε is the N-vector of residual errors. The trait covariance, var(Y) = var(g + ε) = Σ can be writtenI is the identity matrix; and 2Φ is the GRM matrix where element  is calculated as:xik is the minor allele count of the ith subject’s kth marker, coded as coded as 0, 1 or 2; pk is frequency of the kth marker; and M is the total number of markers.At each voxel/element, a LMM for the genetic association for P = Σ−1(I − X(X′Σ−1X)−1X′Σ−1), the projection matrix. The fixed effect parameters are estimated using GLSUnder the assumption that the the data follows a multivariate normal distribution, the model specified by Eqs.  and 2)  2) have 46. Here we consider standard additive model covariance matrix parametrisation  as we c21. For completeness, we review shortly the simplified ML function, to be next followed by development of the simplified REML function. The simplified ML function is obtained by transforming the data and model with an orthogonal transformation S, the matrix of eigenvectors of 2Φ that crucially coincide with the eigenvectors of Σ:Dg = diag{λig} is a diagonal matrix of the eigenvalues of 2Φ.The simplified ML function for LMM is discussed in refs. β and ith element of ith row of The log likelihood takes on the exact same form as Eq.  for \docP = Σ−1(I − X(X′Σ−1X)−1X′Σ−1)35). Also, an alternate simplified form of the REML function can be obtained as follows:The REML function (Eq. ) is simpM = I − X(X′X)−1X′ be the residual forming matrix based on the fixed effects regressors. Since M is idempotent, it can be decomposed asA is the N × (N − P) matrix of the eigenvectors of M corresponding to the non-zero eigenvalues. Crucially, A also residualises the data, because it is orthogonal to the design matrix X:Let A′Y ~ N and the log likelihood of the transformed data isHence Now we show that this (Eq. ) is equiA(A′ΣA)−1A = P , we have that Eqs.  × (N − P) diagonal matrix of non-zero eigenvalues; and Sr is the N × (N − P) matrix of eigenvectors that corresponds to non-zero eigenvalues. Firstly, Sr is a valid A, because its columns are orthogonal 16. Thus we define the projected polygenic model by pre-multiplying N − P projected phenotype, genetic and residual vectors, respectively. In this fashion, the projected phenotype covariance matrix becomes diagonal:ith element of βs) and leads to a computationally efficient estimator and test statistic, described below.As mentclass2pt{minim the Eq. ). BesideU =  and N × 2 and (N − P) × 2 matrices; and λg is the vector of eigenvalues of (2Φ); M(2Φ)M; 1 and 1r are N and (N − P)-vectors of one, respectively; β and θ are updated based on WLS regression of U, respectively, as follows:θ is updated based on WLS regression of Ur as follows:j indexes iteration; θjML, and θjREML,, respectively; θ must be positive, hence the maximum operator. As usual, these updates are iterated until convergence criteria holds.We choose Fisher’s scoring method to optimize the simplified ML and REML functions because it leads to computationally efficient variance component estimators. The score and the expected Fisher information matrices for the simplified models can be expressed as:48. Such initial value for U, respectively:It has been shown that when the initial value is a consistent estimator, the estimator based on the first iteration is asymptotically normal and consistentUr:For REML, initial values for Hence our one-step, non-iterative estimators are:The score, LRT and the Wald tests can be used for the genetic association testing using either ML or REML functions of the model in Eq. .49 that requires the value of score and information matrices under the the null hypothesis constraint (H0:β1 = 0) for the simplified ML model -vectors of the projected phenotype and allele frequency count, respectively; and the projection matrix S2r is comprised of the eigenvectors of M2(2Φ)M2 with non-zero eigenvalues, The score statisticodel Eq.  can be wdel (Eq. ) can be 50 statistic is twice the difference of the optimized log-likelihoods, unrestricted minus H0-restricted. For ML this requires optimizing the likelihood function twice, once under the null H0:β1 = 0, once under the alternative. We denote the test statistic for this test TL,ML. A well-known aspect of REML is that it cannot be used to tests of fixed effects, since the null hypothesis would represent a change of the projection that defines the REML model. However, we can consistently use the same projection Sr2, under the unrestricted and restricted models, to diagonalise our covariance and carry out such a hypothesis test. To be precise, the unrestricted model isS2r, and the restricted model isThe LRTTL,REML.Following the same procedure as ML, the test statistic is denoted by 49 is the parameter estimate divided by the standard deviation of the estimate under an unrestricted model. For an vector parameter β and contrast C, it takes the formFor a scalar parameter, the Wald test33. It only requires an assumption of exchangeability, that the joint distribution of the error is invariant to permutation, and provides exact inference in the absences of nuisance variables, or approximately exact inference with nuisance variables51. Control of the FWE of a voxel-wise or cluster-wise statistic is obtained from a maximum distribution of the corresponding statistic. However naive use of permutation test for genetic association testing, ignoring dependence structure between individuals, leads to invalid inferences52. To the best of our knowledge, the only work that uses a permutation test for association analysis in the context of LMM uses the estimated covariance matrix under the null hypothesis to whiten the phenotype vector, yielding exchangeable data45. This approach requires estimating the covariance matrix for each phenotype for each permutation, a significant computational burden with high dimensional imaging data. Here we propose two permutation schemes that account for dependence explained by our model, one free and one constrained permutation approach.In neuroimaging the permutation test is a standard tool to conduct inference while controlling the family wise error rate (FWE)51. However, little work has been done for fixed effect inference using a permutation test in linear mixed models where the error term is correlated45.The genetic association testing in the context of LMM using a permutation test requires proper handling of fixed effect and random effect nuisance variables in order to respect the exchangeablity assumption. While there are a variety of methods for testing for a fixed effect when the errors are independent0:β1 = 0 null model residuals to create surrogate null data,Free permutation for the simplified ML model: For the simplified model (Eq. ) we creaged (Eq. ) methodsed model  with theWith this approach we obtain samples from the empirical null distribution of the maximum score, LRT and the Wald tests , where the maximum is taken over all voxels and SNPs to control FWE.0.Free permutation for simplified REML model: While the previous approach creates null hypothesis realizations by permuting the null-model residuals and adding back on estimated nuisance, here we will permute data after reduced-model eigen-transformation. We do this because projection removes the nuisance fixed effect covariates. In both cases, though, we must account for the dependence existing under HM2 be the residual forming based on X2 alone and define S2r as the transformation based on the non-trivial eigenvectors of M2(2Φ)M2, creating a model with dimension N − (P + 1):An alternate permutation scheme could be built based on projecting the LMM model (Eq. ) to the Constrained permutation for exchangeability blocks: In the free permutation approaches we permute despite the lack of exchangeability, but then permute the covariance structure to account for this. An alternate approach is to define exchangeability blocks where observations within each block can be regarded as exchangeable. Precisely, with exchangeability blocks, the assumption is that permutations altering the order of observations only within each block preserve the null hypothesis distribution of the full data.While not feasible for the original correlated model , in the Dg or We propose to define exchangeability blocks such that the range of 53 for multi-trait GWA. However, our proposed method is computationally more efficient due to NINGA.To fully exploit the computational advantage of our non-iterative, reduced-dimension projected model estimation method we require a vectorized algorithm. That is, even without iteration, the method will be relatively slow if the evaluation of the estimates is so complex that each phenotype must be looped over one-by-one. For fast evaluation with a high-level language like Matlab, the estimation process for a set of phenotypes must be cast as a series of matrix algebra manipulations. To exploit the computational advantage of this approach, the phenotype should be observed for all individuals. However, soft imputation methods can be used in case of missing phenotypes. An alternate approach has been proposed19 and efficient implementation of LMM, we follow leave one chromosome out approach where all markers on a chromosome being tested are excluded from the GRM27.In this section, we develop the vectorized algorithm for association one chromosome’s worth of SNPs and all image voxels/elements (subject to memory constraints). To avoid proximal contaminationYr and Xr be a (N − P) × V and (N − P) × G matrices of projected traits and allele frequencies, respectively, where V and G are number of elements in image and number of SNPs the tested chromosome, respectively. The score test requires parameter estimation under the null hypothesis constraints, and since X2 is the same for all SNPs, the estimated covariance matrix will be the same all markers the chromosome. Thus the covariance matrix only need to be estimated once as follows:F and Yr are Yr is F is the element-wise squaring of Yr; θ is the 2 × V matrix of OLS solutions which is matrix counterpart of 0 is the 2 × V matrix of zeros; and here V matrix; W and 1NV are the (N−P) × V matrices, where each column of W is 1NV is a matrix of ones. With the following notation,1V is the length-V column vector of ones, we can compute the variance components of the vectorized image asV column vectors of genetic and environmental variance components, respectively; and S is a (N − P) × V matrix which here each column of S is the element-wise reciprocal of the diagonal of the variance matrix of the corresponding image element’s data Yr for each element of image. In this fashion, the score statistic matrix for all markers being tested and the vectorized image can be expressed as:TS,R is a G × V matrix of score statistics for all SNPs and traits.Let Yr* (Eq. ) for one54.To validate our proposed methods for association estimation and inference for imaging data, we applied them on a dataset from healthy and schizophrenic individuals to perform ROI and voxel-wise genome wide association analysis using cluster wise inference. The sample was 54% healthy individual (175 control/155 schizophrenic) and had a mean age of 39.12 (SD = 14.9) where 50% of the sample is maleb = 0 and 1000 s/mm2), the entire protocol repeated three times.Imaging data was collected using a Siemens 3T Allegra MRI  using a spin-echo, EPI sequence with a spatial resolution of 1.7 × 1.7 × 4.0 mm. The sequence parameters were: TE/TR = 87/5000 ms, FOV = 200 mm, axial slice orientation with 35 slices and no gaps, 12 isotropically distributed diffusion weighted directions, two diffusion weighting values . The data were then processed using FSL’s tract-based spatial statistics  analytic method56 modified to project individual FA values on the hand-segmented ENIGMA-DTI skeleton mask. The protocol, target brain, ENIGMA–DTI skeleton mask, source code and executables, are all publicly available (http://enigma.ini.usc.edu/ongoing/dti-working-group/). The FA values are normalized across individuals by inverse Gaussian transform58 to ensure normality assumption. Finally, we analyzed the voxel and cluster-wise FA values with applying along the ENIGMA skeleton mask.ENIGMA-DTI protocols for extraction of tract-wise average FA values were used. These protocols are detailed elsewhereP < 10−6 and minor allele frequency 0.1 was used to ensure that sufficient numbers of subjects would be found in our sample in each genotypic group  using an additive genetic model. After all quality control steps, 962,885 out of 1,406,990 SNPs remain for genome-wide association analysis.In this study only genotyped single nucleotide polymorphisms (SNPs) from genome-wide information were included in the analysis. Visual inspection of multi-dimensional scaling analysis was used to extract individuals with European ancestry. SNPs from individuals with European ancestry that do not meet any of the following quality criteria were excluded: genotype call rate 95%, significant deviation from Hardy–Weinberg equilibrium The data that support the findings of this study are available from Dr. Peter Kochunov upon reasonable request.http://nisox.org/software/ninga/.Software implementation of this method, Nonparametric Inference for Genetics Analysis (NINGA), is available at Supplementary InformationPeer Review File


Uncovering the genetic architecture of these traits is necessary for improving wheat quality by marker-assisted selection (MAS). In the present study, a genome-wide association study (GWAS) was performed on a collection of 166 bread wheat cultivars to better understand the genetic architecture of flour color-related traits using the wheat 90 and 660 K SNP arrays, and 10 allele-specific markers for known genes influencing these traits. Fifteen, 28, 25, and 32 marker–trait associations (MTAs) for L*, a*, b*, and YPC, respectively, were detected, explaining 6.5–20.9% phenotypic variation. Seventy-eight loci were consistent across all four environments. Compared with previous studies, Psy-A1, Psy-B1, Pinb-D1, and the 1B•1R translocation controlling flour color-related traits were confirmed, and four loci were novel. Two and 11 loci explained much more phenotypic variation of a* and YPC than phytoene synthase 1 gene (Psy1), respectively. Sixteen candidate genes were predicted based on biochemical information and bioinformatics analyses, mainly related to carotenoid biosynthesis and degradation, terpenoid backbone biosynthesis and glycolysis/gluconeogenesis. The results largely enrich our knowledge of the genetic basis of flour color-related traits in bread wheat and provide valuable markers for wheat quality improvement. The study also indicated that GWAS was a powerful strategy for dissecting flour color-related traits and identifying candidate genes based on diverse genotypes and high-throughput SNP arrays.Flour color-related traits, including brightness (L Triticum aestivum L.) is among the most important food crops and is one of the most traded commodities in world markets . L* is a measure of flour brightness, ranging from 0 (black) to 100 (white); a* measures redness when positive or greenness when negative; and b* describes the yellow-blue color value, and is positive for yellowness and negative for blueness  is necessary for improving wheat quality by marker-assisted selection (MAS).Bread wheat (r = 0.8)  for flour color-related traits have been identified using bi-parental populations , based on linkage disequilibrium (LD), is an effective complementary strategy to QTL mapping in dissecting associations between genotype and phenotype in germplasm collections  identify the genetic basis underlying flour color-related traits in a collection of 166 bread wheat accessions using the wheat 90 and 660 K SNP arrays, and 10 allele-specific markers for known relevant genes; and (2) propose candidate genes affecting flour color-related traits based on biochemical information and bioinformatics analyses, with the ultimate aim of facilitating molecular breeding. Finally, the genetic determinants of flour color-related traits could be identified more accurately by GWAS using diverse genotypes and high-throughput SNP arrays.The association panel used in this study was a genetically diverse collection, comprising 166 elite bread wheat cultivars mainly from Yellow and Huai Valley of China, but also Italy, Argentina, Japan, Australia, and Turkey. Information about the accessions, including cultivar names, origins and subpopulation identity, was described in Table Briefly, the materials were grown in the 2012–2013 and 2013–2014 in randomized complete blocks with three replications at Anyang  and Suixi , providing data for four environments. Each plot comprised three 2 m rows in 2012–2013 and four rows in 2013–2014, with 20 cm between rows. Agronomic management was performed according to local practices.http://www.cwbrabender.com) with a 0.15 mm sieve. Kernel hardness was determined with a Single Kernel Characterization System . Moisture and protein contents were measured using a Near Infrared Transmittance . The data of kernel hardness, moisture and protein content were only used to calculate how much water is required to tempering, so we did not describe these in this manuscript. Before milling, samples were conditioned to 14, 15, and 16% moisture overnight for soft , medium , and hard (HI > 60) types, respectively, as mentioned by Jin et al. , redness (a*) and yellowness (b*)] were measured with a Minolta colorimeter  using the Commission Internationale de l'Éclairage (CIE) L* a* b* color system, respectively . Briefly, basic statistics such as means, standard deviation, and minimum and maximum values were calculated with the UNIVARIATE procedure. Analysis of variance was performed using the PROC MIXED procedure, where environments were treated as fixed effects, and genotypes, genotype × environment interaction and replicates nested in environments as random effects. Broad-sense heritability (h2) was calculated following Zhai et al. (r) among the flour color-related traits was calculated using the PROC CORR procedure based on BLUP values.Statistical analysis was carried out using SAS 9.2 software . SNP allele clustering and genotype calling were performed using the polyploid version of GenomeStudio software . The default clustering algorithm was initially used to classify each SNP call into three allele clusters. Manual curation was then performed for more accurate genotyping. Markers with a minor allele frequency (MAF) < 5%, and more than 20% missing data were removed from the data matrix. After stringent filtration 259,922 SNP markers from the wheat 90 and 660 K SNP arrays were integrated into a common physical map for GWAS. The physical positions of SNP markers were obtained from the International Wheat Genome Sequencing Consortium  and used in association analysis.Genomic DNA was extracted from seedling leaves using the CTAB (cetyltrimethylammonium bromide) method  replicates. For each K, five independent runs were carried out. According to Evanno et al.  among alleles, and significance was computed by 1,000 permutations using TASSEL  curve was fitted using XLSTAT . The critical r2-values beyond which LD is due to true physical linkage was calculated by taking the 95th percentile of the square root transformed r2-values of unlinked markers  vs. expected –log10  under the null hypothesis that there was no association between marker and phenotype. A false discovery rate (FDR) of 0.05 was used as a threshold for significant association .Marker-trait association analysis was performed separately for each environment and BLUP values across four environments using the MLM in TASSEL. Association mapping model evaluations were based on visual observations of the quantile-quantile (Q-Q) plots, which are the plots of observed –logTo assess the pyramiding effect of favorable alleles of MTAs for flour color-related traits identified in this study, the BLUP value for each trait in each accession was regressed against the number of favorable alleles using the line chart function in Microsoft Excel 2016.http://www.ncbi.nlm.nih.gov/), European Molecular Biology Laboratory (http://www.ebi.ac.uk/) and European Nucleotide Archive (http://www.ebi.ac.uk/ena) public databases following Zhai et al. .In addition, chromosomal locations and physical distances of 40 known genes influencing flour color-related traits, mainly involved in terpenoid backbone biosynthesis and carotenoid biosynthesis and degradation, were evaluated using IWGSC RefSeq v1.0. If the physical distances between MTAs identified in this study and known genes were less than LD decay, the MTAs were considered to be co-located with these known genes. Following Colasuonno et al. , these 4*, b* and YPC where nearly 3 to 16-fold differences were observed  were observed for these traits, indicating that genetic effects played a determinant role for each trait (Table P < 0.001), except for L* × a* (Table * was negatively correlated with L* (r = −0.71) and a* (r = −0.68). YPC was negatively correlated with L* (r = −0.28) and a* (r = −0.89), and positively correlated with b* (r = 0.83).High broad-sense heritabilities . In general, subgroup 1 comprised 62 cultivars primarily derived from Shandong province and abroad; subgroup 2 consisted of 54 varieties predominantly from Henan, Shaanxi and Anhui provinces; and subgroup 3 included 50 cultivars mainly from Henan and Hebei provinces.According to Evanno et al. , ΔK was r2, calculated as the 95th percentile of the distribution of r2 of unlinked markers, was 0.082, and thus all values of r2 > 0.082 were probably due to physical linkage. The intersection between the threshold r2 and the LOESS curve was at 8 Mb, which was considered as the LD decay rate of the population. Similarly, the LD decay was 6, 4 and 11 Mb for A, B and D sub-genomes, respectively.For the whole genome the threshold 10 (P)-values were closed to the expected distribution, suggesting that the MLM model (Q + K) was appropriate for association analysis of flour color-related traits in this study. One hundred MTAs for flour color-related traits were detected, and 78 were identified in all four environments (Table * (28), b* (25) and L* (15). The associations between markers and flour color-related traits are shown by Manhattan plots in Figure As shown in the Q-Q plots Figure , the obsts Table . The higAX_108930866) were identified in three environments, and the remaining MTAs were detected in all four environments. The two most significant markers were AX_111612184 on chromosome 2B and Pinb-D1 on chromosome 5D, explaining 11.0–16.4% and 12.7–17.5% of phenotypic variation, respectively.MTAs of brightness were detected on chromosomes 1A, 1B, 1D, 2A, 2B, 3A, 4A (2), 4B, 5A, 5B, 5D (2), and 7A (2), each explaining 7.1–17.5% of the phenotypic variation across environments (Table AX_111611571), 4A (AX_109058420) and 4B were identified in three environments, and the other 25 MTAs were significantly associated with a* across all four environments. The MTA on chromosome 1A (AX_108727598) showed the strongest association with a*, explaining phenotypic variation ranging from 14.6 to 20.0%.For redness, the MTAs were distributed on chromosomes 1A 2), 1B (2), 1D, 2A (2), 2B (2), 2D, 3D, 4A (2), 4B, 4D, 5A, 5B (2), 5D, 6A (2), 6B (2), 6D, 7A, 7B (2) and 7D, individually explaining 6.5–20.0% of the phenotypic variation ,AX_109848219), 2B (2), 3A, 3B, 5B (AX_94508455), 5D (AX_108930866), 6B (2) and 7A (AX_111616453) were detected in three environments, whereas the others were significant for b* in all four environments. The MTAs on chromosomes 2A (2), 2D and 7D, and Pinb-D1, Psy-A1 and Psy-B1 showed stronger association with b*, explaining more than 15% phenotypic variation in some environments.Yellowness MTAs, located on chromosomes 1A 2), 1B (2), 1D, 2A (2), 2B (2), 2D, 3A, 3B, 4A, 5B (2), 5D (2), 6A, 6B (2), 7A (2), 7B (2) and 7D, explained phenotypic variation ranging from 6.6 to 20.7% ,AX_111611571) and 3B (AX_108968661) were identified in three environments, while the remaining were observed in all four environments. The MTAs on chromosomes 1A (AX_108727598), 1D, 2B (AX_89310598), 5B (AX_110577474) and 1B•1R translocation showed stronger association with YPC than other MTAs.For yellow pigment content, we detected MTAs on all chromosomes, explaining 6.9–20.9% of the total variation  gene involved in sesquiterpenoid and triterpenoid biosynthesis  encoding the dihydrolipoyl dehydrogenase (DLD) enzyme, and the other (IWB31766) corresponds to leghemoglobin reductase (LBR), both involved in glycolysis/gluconeogenesis. Either one or even both genes are potential candidates for the observed MTA in this genomic region. AX_111471334, corresponding to phosphomannomutase (PMM) gene, is a potential candidate gene for the MTA on chromosome 3B  for YPC. IWB36240, significant for a* and YPC, corresponds to 4-hydroxy-3-methylbut-2-en-1-yl diphosphate synthase (MDPS) gene involved in terpenoid backbone biosynthesis.The putative biological functions of 1,543 significant SNP markers associated with flour color-related traits identified in the present study were assigned (data not shown). Briefly, FPPS2) was located about 4.19 Mb from AX_111611571 significant for L*, a*, b* and YPC (Table AX_94596570 (2D), AX_109058420 (4A) and AX_95195654 (7D) associated with a*, b* and YPC was located about 8.65, 1.31 and 1.13 Mb from isopentenyl pyrophosphate isomerase (IPPS), 1-deoxy-D-xylulose 5-phosphate reductoisomerase (DXR) and PSY1 genes, respectively. The mevalonate kinase (MK) gene on chromosome 2A was located in close physical proximity with AX_110044577 (0.82 Mb) associate with both L* and YPC. AX_108749277 (4B) and AX_108940832 (6D) significant for a* and YPC was located 1.72 and 1.69 Mb from carotenoid β-ring hydroxylase 2 (BCH2) and 9-cis-epoxycarotenoid dioxygenase 4 (NCED4) genes, respectively. The lipoxygenase 2 gene (LOX2) on chromosome 5A was 5.12 Mb from AX_111736921 controlling L*. AX_111736921 significant for L* on chromosome 7A was close to peroxidase gene (POD) (1.85 Mb). The cis-zeta-carotene isomerase gene (ZISO) on chromosome 5B was detected at a distance of 1.44 Mb from AX_110952518 associated with b*. AX_109996966 significant for b* was located about 1.07 Mb proximal to the lycopene β-cyclase gene (LYCB). Notably, most of candidate genes, except for LOX2, POD, ZISO, LCYB and PMM, controlled more than one flour color-related traits.Based on the reference wheat genome sequences from the IWGSC RefSeq v1.0, the 40 known genes influencing flour color-related traits were mapped on the physical map Table . BrieflyGWAS has become an efficient tool for genetic dissection of complex traits. Among the diverse accessions analyzed in this study, substantial phenotypic variation in flour color-related traits indicated a wide range of genetic diversity Table . Based oSpurious associations are often the result of structured relationships within the population and may be reduced by taking population structure into account  and redness (r = −0.68) and yellow pigment content was negatively correlated with redness (r = −0.89) and positively correlated with yellowness (r = 0.83). As expected the strong phenotypic correlations among flour color-related traits were generally based on a large number of shared MTAs  with lower b* and YPC. In this situation, these multi-trait regions could be important targets to reduce b* and YPC and increase L* simultaneously.To improve flour color-related traits, using multi-trait markers in MAS may increase QTL pyramiding efficiency. Most Chinese foods, such as steamed buns and noodles, typically require a white or creamy flour type  and YPC (0.87 ± 0.30 μg.g−1) than lines carrying the Psy-A1a allele (9.56 ± 1.84 and 1.34 ± 0.39 μg.g−1), while higher a* was associated with the Psy-A1b allele (−0.66 ± 0.28 vs. −0.97 ± 0.32). b* (11.52 ± 1.55) and YPC (1.77 ± 0.34 μg.g−1) values for 19 cultivars with the Psy-B1a allele were significantly higher than those of 146 lines with Psy-B1b (8.46 ± 1.75 and 1.09 ± 0.36 μg.g−1), whereas lines carrying the Psy-B1b allele generated higher a* (−0.80 ± 0.30 vs. −1.32 ± 0.27). For Pinb-D1, lines with the Pinb-D1b allele produced significantly lower L* (89.95 ± 0.56) and higher b* (9.64 ± 1.76) than those with Pinb-D1a (90.75 ± 1.12 and 7.67 ± 1.70). Cultivars with the 1B•1R translocation had significantly higher b* (9.65 ± 1.03) and YPC (1.39 ± 0.44 μg.g−1) than those without (8.05 ± 0.91) and (0.97 ± 0.29 μg.g−1), while non-1B•1R translocation genotypes were associated with higher a* (−1.02 ± 0.34 vs. −0.72 ± 0.28) (data not shown). These results confirmed that Psy-A1, Psy-B1, Pinb-D1 and the 1B•1R translocation were major-effect loci for flour color-related traits, and can be considered as stable and useful for MAS in breeding programs. However, e-Lcy3A, Talcye-B1, TaPds-B1 and Lox-B1 were not significantly associated with flour color-related traits as they have been reported previously , the two MTAs in this work may be new loci associated with this trait. Similarly, MTA for a* located on chromosome 2A  and MTA for YPC on chromosome 7D  were not matched to any previously identified QTL. Hence these loci are likely to be new and should be attractive candidate regions on which to focus further in dissecting the genetic architecture of flour color-related traits in wheat. Notably, MTAs on chromosomes 1A  and 2B  showed stronger association with a* than Psy-A1 and Psy-B1 in at least three environments (data not shown). Similarly, 11 MTAs on chromosomes 1A , 1D, 2B , 4D, 5B (379722302–379722372 Mb), 5D, 6A , 6B (2), 6D, and 7B  explained much more phenotypic variation of YPC than Psy-A1 and Psy-B1 in at least three environments (data not shown). These demonstrated that GWAS is a powerful mapping approach for identifying genomic regions underlying variation in flour color based on diverse genotypes and high-throughput SNP arrays; they also confirmed previously detected QTL and revealed novel QTL that were not found in bi-parental populations previously.Because no QTL for LAX_109030196) participated in sesquiterpenoid and triterpenoid biosynthesis; DLD (IWB35120), LBR (IWB31766) and PMM (AX_111471334) were involved in glycolysis/gluconeogenesis; and MDPS (IWB36240) played a role in terpenoid backbone biosynthesis. These genes can be considered potential candidate genes for flour color-related traits.Knowledge of the functions of significant SNP markers provides a very useful tool for identification of candidate genes for traits under investigation. Based on a comparative genomics approach, annotations of flanking sequences of significant SNP markers predicted that some genomic regions encode proteins that are important components of pathways linked to carotenoid biosynthesis and degradation Table . For exaFPPS2, IPPS, DXR and MK), five genes involved in carotenoid biosynthesis , and two related to carotenoid degradation (LOX2 and POD). Therefore, the co-linearity of 11 known genes and 23 MTAs suggested that these might be candidate genes for flour color-related traits. In fact, all these candidate genes should be confirmed in bi-parental population mapping or by reverse genetic approaches.Over the past decades, the gene discovery in bread wheat has been largely limited due to the absence of reference genome sequences. However, recent advances in high-throughput genotyping platforms and publicly available wheat genome sequences offer researchers new opportunities to achieve their goals. Based on the reference wheat genome sequences from the IWGSC RefSeq v1.0, 40 known genes influencing flour color-related traits were assigned to chromosome locations Table . Eleven FPPS1, POD, FPPS2, MK, aldehyde oxidase 3, carotenoid β-ring hydroxylase, geranylgeranyl transferase I β-subunit, geranylgeranyl transferase I α-subunit and catalase 3 , a* (−0.91 ± 0.34) and higher b* (9.17 ± 1.95) and YPC (1.25 ± 0.42) than those with the “G” . Seventy-four cultivars with the “A” SNP in POD showed significantly lower L* (90.05 ± 0.90) than those with “G” (90.48 ± 0.88). For MK, lines with the “C” SNP had significantly higher L* (90.75 ± 1.02) and lower YPC (1.09 ± 0.26) than those with the “G” (90.25 ± 0.90 and 1.18 ± 0.43).Out of 40 known genes blasted against the available dataset of SNP marker sequences  between numbers of favorable alleles and phenotype were 0.94, 0.72, 0.91 and 0.87, respectively. Higher b* and YPC are desirable for yellow alkaline noodles and human health, while most Chinese foods typically require a white or creamy flour type with lower b* and YPC. In this situation, cultivars with minimum  or maximum  numbers of favorable alleles for b* and YPC can be used as breeding parents to achieve defined color and nutritional properties of end-use products.To assess the pyramiding effect of favorable alleles of MTAs for flour color-related traits, we examined the number of favorable alleles in each accession, and the BLUP value for each trait was regressed against the number of favorable alleles. The favorable alleles of significantly associated SNPs showed additive effects on brightness, redness, yellowness and yellow pigment content Figure . As the *, chromosome 2A  for a* and chromosome 7D  for YPC. Two and 11 loci explained much more phenotypic variation of a* and YPC than phytoene synthase 1 gene (Psy1), respectively. Based on biochemical information and bioinformatics analyses 16 predicted candidate genes were related to carotenoid biosynthesis and degradation, terpenoid backbone biosynthesis and glycolysis/gluconeogenesis. We will confirm these candidate genes in bi-parental populations and do some gene function analysis in the future.We performed a genome-wide association analysis on 166 bread wheat cultivars using the wheat 90 and 660 K SNP arrays and 10 allele-specific markers, and identified 100 MTAs for flour color-related traits. Broad comparison of MTAs identified in this study with QTL in previous reports indicated many common loci conditioning flour color-related traits, and four MTAs detected were new, including MTAs on chromosome 7A (2) for LThe genomic regions associated with flour color-related traits identified in this study bring new insights to understanding the genetic basis of these traits, and new markers are useful for wheat quality improvement by MAS. Moreover, the candidate genes may serve as promising targets for study of the molecular mechanisms underlying flour color-related traits in wheat. This study also confirmed that GWAS is a powerful approach to validate known genes for complex traits and identify novel loci.SZ performed the experiment and wrote the paper. SZ, JL, and DX analyzed data. WW, JY, PZ, and YW participated in the field trials. YH, WM, and SC assisted in writing the paper. ZH and XX designed the experiment and wrote the paper. All authors 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.


Capsicum is one of the major vegetable crops grown worldwide. Current subdivision in clades and species is based on morphological traits and coarse sets of genetic markers. Broad variability of fruits has been driven by breeding programs and has been mainly studied by linkage analysis. We discovered 746k variable sites by sequencing 1.8% of the genome in a collection of 373 accessions belonging to 11 Capsicum species from 51 countries. We describe genomic variation at population-level, confirm major subdivision in clades and species, and show that the known major subdivision of C. annuum separates large and bulky fruits from small ones. In C. annuum, we identify four novel loci associated with phenotypes determining the fruit shape, including a non-synonymous mutation in the gene Longifolia 1-like (CA03g16080). Our collection covers all the economically important species of Capsicum widely used in breeding programs and represent the widest and largest study so far in terms of the number of species and number of genetic variants analyzed. We identified a large set of markers that can be used for population genetic studies and genetic association analyses. Our results provide a comprehensive and precise perspective on genomic variability in Capsicum at population-level and suggest that future fine genetic association studies will yield useful results for breeding. Capsicum spp.) is one of the major vegetable crops grown worldwide, largely appreciated for its economic importance and nutritional value. Pepper originated in Western North America and South America and then expanded and diversified in the other Southern and Central American regions. The taxonomic arrangement of the genus has been recently revised establishing the existence of 35 species distributed in 11 clades1, the most important of which are Annuum  Baccatum  and Pubescens (C. pubescens). The population structure of Capsicum spp. inferred from genetic markers mostly reflects the known taxonomic grouping, however it highlights sub-groups within C. annuum and admixture between C. chinense and C. frutescens3. Although these studies were carried out on a large number of accessions, both are based on small number of markers , therefore the population structure of the different Capsicum species has never been investigated deeply. Pepper presents a wide diversity in fruit size and shape achieved after a successful selection process. The early steps of domestication involved key traits such as non-deciduous fruits and the orientation of fruit tip from erect to pendant. Further steps of selection resulted in wide variability of fruit shape and size comparable to other Solanaceae4. Nevertheless, unlike other cultivated Solanaceae, such as tomato8, the genetics underlying fruit shape in pepper is limited to findings from quantitative trait loci (QTL) analysis in a few biparental mapping populations , as carried out for capsacinoid content24 and peduncle length25, but never performed for fruit morphology attributes in Capsicum.Technical advances in high-throughput phenotyping allow us to precisely measure and describe the determinants of fruit shape and size using standard ontologiesCapsicum and measured thirty-eight fruit shape and size attributes in 220 C. annuum accessions. We used these data to (i) uncover genomic properties of the pepper genome, (ii) describe population structure within the Capsicum genus at a resolution never achieved before, (iii) study natural selection, and (iv) discover significant associations between genetic markers and traits related to pepper fruit shape and size in C. annuum. Finally, we discovered a non-synonymous change in the sequence of Longifolia 1-like gene associated with variance in C. annuum fruit shape.In this study we discovered 746k high-quality polymorphic sites from analyzing sequence data of 373 pepper accessions from eleven species of Capsicum widely used in breeding programs. It includes 373 accessions belonging to eleven Capsicum species, of which five are wild , and the range of distance between two consecutive fragments varies from 3 to 278,100 bp . The majority of the fragments (85.9%) are intergenic.Genomic DNA extracted from accessions was digested with the restriction enzyme 22, we identified 1,382,545 polymorphic sites, of which 746,450 have Phred-scaled quality scores (QUAL) > 10 and were considered for all downstream analyses  or multi-nuclotide polymorphisms . Insertions and deletions (InDels) represent 1.9% of all variants and their size ranges from deletions of 30 nucleotides to insertions of 20 nucleotides. InDels of three or multiples of three nucleotides are more frequent in genic region compared to intergenic ones, suggesting a preference for InDels that add or remove triplets over those causing frame-shifts mutations  fall within exons.By aligning sequence reads along the reference genomeses Fig. . These fely Fig.  and thisCapsicum species with >10 accessions, we further investigated genomic diversity. The average number of segregating sites per species is 440,600 and it is roughly proportional to sample size. C. annuum is an exception to this trend, and contains less variation than expected given the number of haploid sequences, which likely reflects the recent loss of diversity due to intensive selective breeding  and reference-guided analysis, we were only able to discover InDels up to a few tens of bp. Among species, C. annuum is the least diverse while C. chacoense is the most variable, despite possible variant detection bias due to the fact that the reference sequence belongs to C. annuum.To summarize, we discover 746k variable sites by analyzing 605k fragments of average size 81 bp that cover 1.8% of the genome of Capsicum species with at least two accessions  to summarize the observed genetic variation among accessions and species. The first two components explain the 24% of the observed variation separating three main domesticated species: C. annuum, C. baccatum, and C. chinense. While describing almost one-fourth of the variance, clustering within the first two components is not complete, and a number of accessions are positioned in between clusters. The third and fourth components (5% of explained variance) separate C. pubescens and C. chacoense between them and from the cluster of domesticated species  is 61% (median CV = 45%) and the largest CV is >300%, suggesting that in many cases the standard deviation exceeds the mean value of the trait Fig. . The leaC. annuum accessions into two clusters  as fixed effects. SNPs were filtered for missingness (<5%), minor allele frequency (>1%), and Hardy-Weinberg equilibrium , leaving 559,684 SNPs for the association analyses.Having observed concordance between genetic and phenotypic clustering in Association tests identified eight variants on three chromosomes, significantly associated  with seven traits Table . All theβ = −0.15 aA/aB, P = 5.43E-09) and for ProximalFruitBlockiness .On chromosome 10 we observe two clusters of variants separated by 4.7 Mbp associated with traits determining whether a fruit is squared or pointed through evaluation of asymmetry, blockiness and the shape of the distal end of the fruit Fig. . The firβ = 18.47°, SE = 2.96, P = 4.97E-09).The second cluster on chromosome 10 includes two intergenic variants 10 bp apart and in full linkage, associated with the trait DistalAngleMacro that reflects how much a pepper is pointed and measures the angle between best-fit lines drawn through the fruit perimeter on either side of the distal end point: the smaller the angle the more pointed the pepper. Each minor allele for variants 10:28759675 and 10:28759675 increases is estimate to increase the angle by 18° , contributing to produce pointed fruit.On chromosome 11 we detect a significant association between one intergenic SNP and the Ellipsoid trait. The Ellipsoid index fits precision of the actual shape of the fruit to an ellipse: smaller values indicate ellipsoidal fruits and measures the fraction of area left out of a fitted ellipse (a.o.e.). The range of Ellipsoid in our data vary from 0.002 a.o.e. to 0.21 a.o.e., and the effect of each minor allele increases of the a.o.e. , as well as the a.o.e.  contributing therefore to make the fruit elongated. Consistently, the minor allele increases the LobednessDegree, i.e. the dispersion of several distances from the center of weight to the perimeter, up to 16.97 mm . Finally, the FruitShapeIndexExternalI, i.e. the ratio of the maximum height to the maximum width (mA/mB), is increased by the minor allele . Overall, the alleles of the SNP 3:183386147 specify whether a fruit is circular or elongated as measured by effect size on four phenotypes. The signal at the SNP 3:18338614 is the only one significant in region (±2 Mb) containing 26 genes  in C. chinense and C. frutescens, while its frequency in C annuum is 0.76, suggesting that T could be the ancestral state (Table Oryza sativa (rice) SLG7. Both LONGIFOLIA and SLG7 activate longitudinal organ expansion35.The SNP 3:183386147 has two alleles, T and C. In our collection, the T allele is fixed in te Table . CA03g16Longifolia 1-like is expressed in the leaves and in the immature stages of the pepper fruits  and confirmed in several studies  is located 100 Mb downstream the cluster of variants on chromosome 10. While it is encouraging to imagine an overlap between previously identified QTL and the current analysis, it is important to keep in mind that the underlying methods and power of resolution are different and that the fruit shape is a complex, polygenic trait.Both genomic regions overlap with QTLs linked to fruit shape and elongation previously identified in pepper7. One of these, the Ovate-like gene, has been reported in pepper to be involved in fruit elongation38. Beyond this, no other single genes information is reported, therefore, the genetic loci underlying fruit shape are not yet comprehensively explored. Despite the appropriateness of the promising association found in Longifolia 1-like, further work will be necessary to fine map the signals that we found and fully understand the genetic asset behind pepper fruit shape and size.Among Solanaceae, the genetic basis of fruit shape have been extensively studied in tomato, leading to the identification of major QTLs and genesCapsicum genome that are informative on overall genomic variability, population structure and genetic association that demonstrate the potential of making discoveries from population studies in this species. We can therefore predict that future studies based on more extensive sequencing and that can exploit haplotype-based information will allow both a better understanding of the evolutionary history of pepper , and discoveries that can guide the breeding process and inform genomic selection. As an example, a more in depth study of the properties of the non-synonymous change in Longifolia 1-like can guide applications in breeding that aim to modify pepper fruit appearance.We present results form analyzing a small fraction of the et al.26. Reads were mapped to the reference genome22 using BWA MEM39. Variant calling was done using Freebayes v1.2.040 with standard parameters. Missing genotypes were imputed and the imputed genotypes were phased using Beagle v4.142.Genotype by sequencing was carried out as described in Taranto 43 with K ranging from 1 to 10. One thousand bootstrap replicates were run to estimate parameter standard errors. Ten-fold cross-validation (CV) procedure was performed and CV scores were used to determine the best K value.Model-based ancestry estimation was obtained using the ADMIXTURE softwareCapsicum includes both domesticated (landraces) and wild varieties  was estimated as a ratio of the variance of the trait explained by genotypic component and the total phenotypic variance (h2 = VG/VP) according to the formula described here45.Our world-wide collection of seeds from 373 accessions belonging to the genus es Table . Informa46, controlling for admixture and relatedness between individuals as random effects using a genetic similarity matrix estimated from the data with the same software. Bonferroni-corrected genome-wide threshold for p-value is 1.786723e-08 and was calculated taking as reference a p-value of 0.01 and considering 559,684 markers.Genome-wide association analysis was performed using a linear mixed model implemented in GEMMA47 to display the chromosomal location along the pepper genome of the genome-wide signicantly associated SNPs.We used PhenoGram48 as it is able to model the statistical uncertainty of genotypes and missing data and it has an implementation of the PC-based selection statistic of Galinsky et al.32 working on genotype likelihoods. The filtering of variants was performed in ANGSD based on genotype likelihoods, and admixture analyses were performed in PCAngsd to filter out C. annuum samples which had an admixture proportion <90% for the C. annuum cluster.PC-based selection scan was based on PC estimated using PCAngsd2 (0.99) in the standard curve. The amplicons were obtained through the combination of the primers LG1-F (GAAAACCAAACGAGAAGTCCG), LG2-F (AAAGACGAGCAGTTGGAAGAG) and LG1-R (GGGCTCCAAGAATCTAAACCTAG). The actin gene (GenBank accession number GQ339766) was used as reference . Primer pairs were designed by using the online tool available at https://eu.idtdna.com/scitools/Applications/RealTimePCR. Oligo specificity was checked by using the tool “in silico PCR” (https://solgenomics.net/tools/in_silico_pcr) coupled with the database Capsicum annuum cv 334 Genome CDS (release 1.55). This tool confirmed the specificity of the primers. Prior to the gene expression analysis, the standard curve for the three amplicons was established using four fold cDNA dilution series and three replicate  and 264 bp (LG2) of the region of the CA03g16080 target gene that includes the T/C mutation. LG1 and LG2 were tested for their efficiency , Elephant Ear (TT), Miniconico (CC), and Masquerade (CC) , 6.25 ng cDNA and 300 nM of each primer , nuclease free water to final volume. qRT-PCRwas carried out on a CFX96 TouchTM Real-Time PCR Detection System . Thermocycling conditions were as follows: 95 °C for 2 min, 40 cycles of 95 °C for 10 sec and 60 °C for 30 sec. A final ramping stage 65–95 °C, +0.5 °C each 5 sec was performed to confirm the absence of dimers and multiple products. Relative expression values were determined using the 2ΔΔCt method implemented in the Gene Expression Module of the CFX Manager Software (Biorad).Four accessions among those sequenced for this study, thus with known genotype at the at position 183386147 on chromosome 3, were chosen to assess gene expression if CC) Fig. . Samples49.The exon-intron structure of the CA03g16080 gene was drawn using the Gene Structure Display Server 2.050 I-Tasser (Iterative Threading ASSEmbly Refinement)51 for structure predictions and protein modelling. I-Tasser returned five best models and we selected three out of them, having the higher C-scores (from −1.55 to −1.85) and excluded the remaining two models, due to their lower C-scores . The best models obtained have been used for evaluating structural properties by visual inspection with molecular viewers, and we integrated a complete evaluation with the results of other prediction tools, as and MAESTRO (Multi AgEnt STability pRedictiOn tool)52, a tool for evaluating the possible effect of amino acid substitution on protein stability.The amino acidic sequence of the gene CA03g16080 was used to generate a 3D model of the protein and to evaluate structural properties. In the absence of templates suitable for applying the homology modelling approach, we used a strategy based on the integration of predictions by means of different tools. We used PredictProteinSupplementary figuresDataset 1


These findings support the notion that learned GFs not only are good predictors for traits but also have specific biological implications regarding regulation of gene expressions. To differentiate the new method from conventional GP models, we called MLLASSO a directed learning strategy supervised by intermediate omic data. This new prediction model appears to be more reliable and more robust than conventional GP models.Genomic prediction (GP) aims to construct a statistical model for predicting phenotypes using genome‐wide markers and is a promising strategy for accelerating molecular plant breeding. However, current progress of phenotype prediction using genomic data alone has reached a bottleneck, and previous studies on transcriptomic and metabolomic predictions ignored genomic information. Here, we designed a novel strategy of GP called multilayered least absolute shrinkage and selection operator (MLLASSO) by integrating multiple omic data into a single model that iteratively learns three layers of genetic features (GFs) supervised by observed transcriptome and metabolome. Significantly, MLLASSO learns higher order information of gene interactions, which enables us to achieve a significant improvement of predictability of yield in rice from 0.1588  to 0.2451 (MLLASSO). In the prediction of the first two layers, some genes were found to be genetically predictable genes (GPGs) as their expressions were accurately predicted with genetic markers. Interestingly, we made three dramatic discoveries for the GPGs: (i) GPGs are good predictors for highly complex traits like yield; (ii) GPGs are mostly eQTL genes ( Although genome‐wide association studies (GWAS) have successfully identified thousands of trait‐associated genetic loci for human diseases and plant agronomic traits in the past decade  aims to construct a statistical model for predicting phenotype using genome‐wide markers jointly  , for improving GP. The key idea of MLLASSO is to implement an innovative directed learning strategy that allows us to learn three layers of genetic features  supervised by transcriptomic and metabolomic data using genetic variants as instrumental variables (IV), which has been proven to be an efficient statistical technique to select and estimate optimal instruments (Lin A rice recombinant inbred line (RIL) population with previously reported data sets was used in this study, which contains 210 lines with 1619 bins (synthetic markers), 24 994 gene expressions (transcripts), 1000 metabolites and four agronomic traits including yield per plant, tiller number per plant, grain number per panicle and 1000 grain weight (KGW). A more complete description of the data is given in the Experimental procedures section.At first, we used the LASSO method to perform GP with all 1619 bins and found that the predictability of yield was 0.1588, which was evaluated by a 10‐fold cross‐validation (10‐fold CV) test  and PD > 1 (PD = the 90th percentile―the 10th percentile)’ to screen the whole transcriptome, leaving only 5467 genes passing the criterion and these genes were subject to further analysis Table . Subsequet al., h2) (see predictability = 1.574 (h2)2 − 0.608 (h2) + 0.078, with a goodness of fit of 0.9375  see  for the  see  foret al. (α = 0.55 (Table We then asked whether GFs.1L (integrating genomic and transcriptomic information) can improve predictability over GP using only genomic information. Unexpectedly, when we used the whole GFs.1L to predict yield with the LASSO method, the predictability was not improved but was slightly decreased from 0.1588 to 0.1189 via the 10‐fold CV test  than that (0.1588) of genomic markers, but the predicted transcriptome does not achieve expected predictability to our surprise. The rationale behind this might lie in the great noises of poorly predicted transcripts of PT.1L.GUGs, which harass the feature selection of the LASSO method. However, when the value of alpha is increasing, the corresponding predictability of yield shows a general uptrend and the maximal predictability is achieved as 5 Figure a. When t5 Figure  and not We now focus on PT.1L.GUGs that were not predictable with genetic variants in the first layer. In this case, we speculate that their expressions may be affected by other regulator genes (such as PT.1L.GPGs). To confirm our conjecture, we asked whether or not the predictabilities of PT.1L.GUGs can be improved by combining genomic markers and the predicted expressions of PT.1L.GPGs as a new input.Let us continue to take group 1 as an example, 3113 genes out of 3584 PT.1L.GUGs (3113/3584~86.86%) have increased their predictabilities and the average gain is 0.0764 Figure . As the β = 0.25 (Table α = 0.55) and PT.2L.GPGs (depending on beta) to build a second layer of genetic feature of PT.1L+2L.GPGs. When we used PT.1L+2L.GPGs to predict yield, the predictability showed a general uptrend as beta increasing from 0.0 to 0.70 and achieved the maximum of 0.2451 when β = 0.65  to predict yield and monitored the predictability while beta increases. As a result, the predictability achieved the maximum of 0.2207 when 25 Table b, where 65 Table c. This tHaving provided a variety of evidences to support the conclusion that multiple layers of learned genetic features can improve GP for yield, we now further examine whether or not the conclusion applies to other traits. We constructed the third layer of LASSO to learn the third layer of genetic features GFs.3L based on PT.1L+2L.GPGs  supervised by the observed metabolome  Table . At the α = 0.55 and β = 0.25 of the second layer to predict 1000 metabolites and then used their predicted values to predict yield trait, the predictability of yield (0.1898) was not significant improved compared with the predictability of the second layer. We noted that the values of α = 0.55 and β = 0.25 were optimal for accurate prediction of gene expressions and were not necessarily optimal for accurate prediction of metabolites. Meanwhile, we define genetically predictable metabolites of the third layer (PM.3L.GPMs) as those metabolites with the condition of their third‐layer predictabilities > gamma (gamma is a third tuning parameter between 0.0 and 0.90) and then we adopted the 10‐fold CV test to determine the optimal value of gamma. For this reason, we performed a grid search on the combination of alpha, beta and gamma to determine the optimal combination of alpha, beta and gamma for metabolite prediction  were more predictable than using genome alone  show that the differences are statistically significant  have been improved with PT.1L+2L.GPGs or PM.3L.GPMs over GP  are computed as the linear combination of PT.1L+2L.GPGs (predicted gene expression), which contains useful information of gene interactions, suggesting that MLLASSO has learned higher order information of gene interactions.et al., cis‐eQTLs (37.2%) and 8568 are trans‐eQTLs (62.8%). Taking group 1 as an example, a detailed analysis of PT.1L.GPGs showed that, out of 1883 PT.2L.GPGs, 1317 are cis‐eQTLs and 515 are trans‐eQTLs, that is more than seventy per cent (1317/(1317 + 515) ~ 71.89%) of PT.1L.GPGs are cis‐eQTLs  ~ 59.78%) of PT.2L.GPGs are trans‐eQTLs  give a rational explanation about why the expressions of PT.1L.GPGs are well predicted with genomic markers. In contrast, the variation of trans‐eQTL gene within the population is not only determined by the cis‐regulatory elements of itself but also affected by other genes, which explains why the expressions of PT.2L.GPGs are poorly predicted with genomic markers only.In summary, an eQTL analysis demonstrated that PT.1L.GPGs are mostly et al., To provide a biological interpretation, two well‐predicted gene sets, that is PT.1L.GPGs and PT.2L.GPGs Table , and a pet al., We next performed TF family enrichment analyses on three gene sets, that is PT.1L.GPGs, PT.2L.GPGs and PT.2L.GUGs by using a comprehensive resource of plant TF database ‘PlantTFDB 4.0’ . For example, a QTL named MLLASSO integrates multiple layers of omic data into a single model that enable us to learn three layers of intermediate variables or genetic features. In each layer, each genetic feature is learned under the supervision of one specific gene expression or metabolite. This gives the machine a specific direction to optimize linear combinations of genetic markers and then to form a module of biological network. When predicting a phenotype using these learned modules, recomposition between them might learn high order information of gene interactions. This is what we called a ‘directed learning’ strategy and it is the most significant contribution of the current study.Ghd7 gene was ranked the first with the greatest coefficient (1.2883) in the backtracking result. Notably, the second bin was Bin893 with a coefficient of 0.7162, which contains another reported gene hd1 controlling response to photoperiod , and sparse selection of significant variables and their biological interpretations. We believe that it will be of general interests to a broad field of integrative analysis studies. The current study contributes to the field of genomic selection with an innovative prediction framework of directed learning as well as several specific technologies including backtracking. We believe that application of the MLLASSO model to various species will accelerate mechanism discoveries of complex traits and molecular breeding of plants.indica rice varieties  is a numerically coded genotype for individual i at bin j.The data set consists of 210 RILs of rice that were derived from nine rounds of selfings from the cross between Zhenshan 97 and Minghui 63, two elite et al., et al., et al., Gene expressions of transcriptomic data were measured by extracting RNA collected from flag leaves in the microarray sequencing platform. A total of 24 994 genes were recorded from all the 210 RILs, forming a 210 × 24 994 feature matrix  . The predictability is defined as follows:SS=∑i=1n(yi−y¯)2 is the total sum of squares and PRESS=∑i=1n(yi−y^i)2 where y^i is the predicted trait value using training samples excluding the group containing yi.The tuning parameter et al., et al., The main idea of MLLASSO was inspired by the instrumental variable (IV) analysis from a published work  be a feature matrix of gene expressions and Zn × p =  be a feature matrix of genomic markers, where n is the sample size, p is the number of genes and q is the number of genomic markers. Using genotypes as instrumental variables, the linear model jointly fits the data  is described below,β0 and Γ0 are regression coefficients with dimensions p × 1 and q × p, respectively, η and E are random errors with dimensions n × 1 and n × p, respectively. Lin et al.  be the feature matrix of genome and Xn × q =  be the feature matrix of transcriptome. The first layer LASSO uses a regularization methodology with L1‐penalty to predict X based on Z. Let 0 < α<1 be a discrimination threshold, based on which we define X^GPG.1L= as a feature matrix of predicted expressions of GPG.1L with predictability > α in the first layer, where k is the number of GPG.1L. We then define Xn×mGUG.1L= as a feature matrix of observed expressions of GUG.1L with probability ≤ α in the first layer LASSO, where m is the number of GUG and k + m = p.The framework of our MLLASSO is similar to the 2SR method, but we created two layers of predicted transcriptome and one more layer of predicted metabolome whereas 2SR only has one layer. Let L1‐penalty to predict XGUG based on the combination of Z and X^GPG.1L. Let 0 < β<1 be another discrimination threshold, based on which we define X^GPG.2L= as a feature matrix of predicted expressions of GPG.2L with predictability > β in the second layer, where l is the number of GPG.2L.The second layer of LASSO uses a regularization methodology with Mn × t =  be the feature matrix of metabolome, where t is the number of metabolites. The third layer of LASSO uses a regularization methodology with L1‐penalty to predict M based on the combination of X^GPG.1L and X^GPG.2L. MLLASSO jointly models the data  usingYn × 1 is a vector of phenotypes, δ0, β0, Ψ0, Ω0, Φ0 and Γ0 are all regression coefficients with dimensions t × 1, k × t, l × t, k × m, q × m and q × p, respectively, and χ, η, ε and E are all random errors with dimensions n × 1, n × t, n × m and n × p, respectively. The regularization method with L1‐penalty applies to all three layers and each layer selects an optimal set of sparse representatives of the regression coefficients. In this particular study, n = 210, q = 1619, p = 5467, t = 1000. And when α = 0.55, β = 0.25, we have k = 1883, m = 3584 and l = 1767.Let et al., http://bioinfo.cau.edu.cn/agriGO/analysis.php) that was specifically designed for agricultural species. It currently supports 45 species including Arabidopsis thaliana, Oryza sativa and Zea mays, and their overall 292 data types. PlantTFDB 4.0 used gene annotation information from MSU(v7) database (Kawahara et al., http://planttfdb.cbi.pku.edu.cn/index.php?sp=Osj.We used two bioinformatics tools to perform gene ontology analysis and TF family enrichment analysis. AgriGO (Tian Y and genotype Z.From the four simultaneous Equations in The authors declare no conflict of interest.Table S1 Heritabilities and predictabilities of 5467 gene expressions in first layer.Table S2 Predictabilities of ten groups of 10‐fold‐cross‐validation.Table S3 Comparisons of predictabilities of 3584 PT.1L.GUG in the first layer and in the second layer.Table S4 Comparisons of predictabilities of 138 PT.2L.GPG in the first layer and in the second layer.Table S5 Comparisons of predictabilities of 1000 metabolites based on genome and PT.1L+2L.GPGs.Table S6 Gene IDs of PT.1L.GPGs. and PT.2L.GPGs.Table S7 Results of GO enrichment analyses of PT.1L.GPG, PT.2L.GPG and PT.2L.GUG.Table S8 TF family enrichment analyses of PT.1L.GPG, PT.2L.GPG and PT.2L.GUG. TF family names along with their pfam ID and enrichment results of P‐value and odd.ratio are shown.Table S9 The list of selected bins and their coefficients of backtracking of MLLASSO. The list of selected bins and their coefficients of single layer LASSO are also showed as a comparison.Click here for additional data file.Data set S1 Four agronomic traits of 210 RILs rice population.Click here for additional data file.


The locus hap_2B_9 explained 15.9 and 17.8% of the variation of protein content and protein loss, respectively. All these pleiotropic haplotype loci offer breeders the unique opportunity for further improving multiple traits, facilitating marker-assisted selection in durum wheat, and could help in identifying genes as functional annotations of the wheat genome become available.Durum wheat was introduced in the southern prairies of western Canada in the late nineteenth century. Breeding efforts have mainly focused on improving quality traits to meet the pasta industry demands. For this study, 192 durum wheat lines were genotyped using the Illumina 90K Infinium iSelect assay, and resulted in a total of 14,324 polymorphic SNPs. Genetic diversity changed over time, declining during the first 20 years of breeding in Canada, then increased in the late 1980s and early 1990s. We scanned the genome for signatures of selection, using the total variance Fst-based outlier detection method (Lositan), the hierarchical island model (Arlequin) and the Bayesian genome scan method (BayeScan). A total of 407 outliers were identified and clustered into 84 LD-based haplotype loci, spanning all 14 chromosomes of the durum wheat genome. The association analysis detected 54 haplotype loci, of which 39% contained markers with a complete reversal of allelic state. This tendency to fixation of favorable alleles corroborates the success of the Canadian durum wheat breeding programs over time. Twenty-one haplotype loci were associated with multiple traits. In particular,  Triticum turgidum L. ssp. durum Desf. Husn., 2n = 4x = 28; genome AABB) is an important crop in Canada, grown on an average of approximately 2 million hectares and comprising about 25% of total wheat area  wheat milling grades defined by the Canadian Grain Commission . Only vaWhen it is necessary to bring new diversity for particular traits into the breeding programs, it is imperative to return the elite materials to a new state of equilibrium as quickly as possible. Efficient means to identify both core essential adaptation and quality traits in addition to new traits being introgressed can facilitate this process. Starting in the late 1990s, molecular markers became an important tool for Canadian wheat breeding programs. However, the lack of tightly linked diagnostic markers, QTL × environmental interactions and prevalence of QTL background effects have limited the application of marker assisted breeding for some traits . AdvanceAssociation mapping (AM) is increasingly being adopted as a complementary method to bi-parental linkage mapping to identify genotype–phenotype associations. Several AM studies have been conducted to dissect the genetic basis of durum grain yield , grain aTherefore, the main objectives of this study were to scan the genome of elite Canadian durum wheat lines tested in the pre-registration trial for selection footprints and relate these genomic regions to phenotypes. The availability of such loci targeted by selection would be a valuable resource for developing markers and/or investigating gene candidates controlling the traits of interest we analyzed, in particular grain yield, protein loss and pasta quality traits.∗, pasta b∗ and pigment loss as previously described . For grain yield concentration which was measured on composites of locations within years (175 lines), year, location, replication, and genotype, and their interactions were considered random; for grain protein and yellow pigment concentrations (186 lines), years, locations, genotypes, and interactions were random; for gluten strength and color traits measured on yearly composites (170 lines), genotypes and years were random. The analyses included all genotypes tested (up to approximately 300 depending on trait) in the registration trials, not just those used in the present study, to provide a better estimate of random variances and covariances .DNA extraction and genotyping with the 90K iSelect assay chip were carried out as reported in our previous paper . A totalRht-B1b, an allele known to confer semi-dwarf growth habit in wheat  was performed between all 4B association signals and this gene using MIDAS software  as implemented in the Arlequin 3.5 software . SignifiThe subset of 4,235 highly polymorphic SNPs was used to scan the genome for signatures of selection, using three approaches: the total variance Fst-based outlier detection method implemented in Lositan , the hieq-values < 0.05). As a result, the Fst cut-off for declaring outliers was 0.20 for Arlequin and Lositan, and 0.15 for BayeScan  of 5% was applied and haplotype loci with P-value ≤ 0.05 were declared significant. The allelic effect of haplotypes was estimated as the difference between the mean value of the lines carrying these haplotypes and the mean value of the entire population for each trait, as previously described  to declare loci being under selection are shown on Supplementary Figure hap_5A_5) to 100% .The distribution pattern of markers under selection was different between chromosomes Figure , outlierP-value ≤ 0.05) different between sub-populations for all of the traits, except grain yield. Many traits were significantly  correlated to each other  positive correlation, r = 0.82.Wide phenotypic variation was observed among lines in the breeding panel for all of the traits Table . Sample hap_1B_2 on chromosome 2B was associated with dough extensibility, gluten index, dough tenacity and deformation energy while hap_4B_2 (chromosome 4B) was associated with pigment loss, pasta b∗, protein loss, semolina pigment and protein content. The phenotypic variations explained by the pleiotropic loci varied depending on the traits. For example, hap_4B_1 explained 20.6, 17.9, 16.6, and 12.1% of the phenotypic variance of pigment loss, pasta b∗, dough extensibility and gluten index, respectively, whereas hap_4B_2 explained 6.8%  to 16.8% (protein loss) of the phenotypic variation.The association analysis detected 54 haplotype loci, of which 39% (21/54) were associated with at least two traits. For quality traits (Table hap_7A_6) to 15.9% (hap_2B_9) of the phenotypic variation  and explained 3.5  and explained 12.1 % of gluten index variation.A total of five loci, P-value ≤ 0.05) associated with pasta b∗, explaining 5.4 (hap_6A_3) to 17.9% (hap_4B_1) of the phenotypic variation.Five loci, located on chromosomes 1A, 4B (2 loci), 6A, and 7B, were significantly  on grain yield, explained 43.9 and 38.5% of the phenotypic variation of plant height and grain yield, respectively. On the other hand, hap_4B_1 was strongly associated (r2 = 0.90) with the dwarfing gene Rht-B1b and explained 30.0% of the phenotypic variation of plant height.A total of 11 haplotype loci were associated with plant height and/or grain yield Table . These lhap_1B_5 and hap_2A_1 consisted of 100% (7/7) and 91% (10/11) markers with a complete reversal of allelic state, respectively. For each haplotype locus, the time at which the switch in allelic state occurred varied among SNPs, regardless of the number of traits the haplotype locus was associated with. For example, for hap_1B_5 associated with only semolina pigment, the switch in allelic state occurred in the early 1960s (Tdurum_contig85180_99), in the late 1980s (BobWhite_c17644_456) and in the 2000s (IACX6346) , in the 1985s , and in the 1990s (wsnp_Ex_rep_c66615_64916512)  percent of haplotype loci associated with the traits we investigated contained markers with a complete reversal of allelic state  percent of the haplotype loci under selection harbored markers with a complete reversal of allelic state. This tendency towards fixation of favorable alleles in our material corroborates the success of the Canadian durum wheat breeding programs over time.Previous studies showed that haplotype-based analysis increases the power of QTL detection  and explThirty-six (30/84) percent of the haplotype loci under selection failed to be associated with any of the traits that we investigated. Because these loci showed strong evidence of directional selection, the lack of an association signal could suggest that they might be controlling traits that we do not have data for, and we didn’t analyze here. Therefore, these loci could still be of interest for further investigations when more phenotypic data becomes available.hap_4B_1 located on chromosome 4B explained 20.6, 17.9, 16.6, and 12.1% of the phenotypic variance of pigment loss, pasta b∗, dough extensibility and gluten index, respectively. This result is congruent with many studies that reported major QTL for yellow pigment on chromosome 4B  to 17.8% (hap_2B_9) of the phenotypic variance. The haplotype locus hap_2B_9, explaining the highest proportion (17.8%) of protein loss variance, also explained 15.9% of the variation of protein content. This result is not surprising given the strong positive (r = 0.82) correlation between these two traits; the higher protein content the bigger the protein loss. Similarly, High semolina protein content determines end-use products quality such as texture, appearance and firmness. However, because of its negative correlation with grain yield , selectihap_4A_5 located on chromosome 4A, explained 38.5% of the phenotypic variance. Yield is the most important and genetically complex trait in wheat, being controlled by a large number of small effect QTL across all chromosomes  to high (43.9%) proportion of the phenotypic variance depending on the trait. For grain yield, of the six haplotype loci that were detected, omosomes . Many QTomosomes . The majomosomes . Nonetheomosomes . In contomosomes . A numbeomosomes . In partomosomes  and 3B  and hap_4B_1 (chromosome 4B) explained 43.9 and 30.0% of the variance, respectively. The Rht-B1b gene was mapped on chromosome 4B. These results are consistent with those of many studies that reported major QTL for plant height on chromosomes group 4 in both durum and hexaploid wheat , hap_4A_5  and hap_4B_1 , offers breeders the appealing opportunity for improving multiple traits. Indeed, pinpointing the genes controlling these traits and identifying causal mutations would be greatly resourceful to the wheat community. However, tracking down causative genes is not trivial and might take several years, especially when dealing with many complex traits. For sake of information, we retrieved the genes and their annotations  or were clustered at only few localized regions on the chromosome . The association analysis detected 54 haplotype loci, of which 39% contained markers with a complete reversal of allelic state. This tendency towards fixation of favorable alleles corroborates the success of the Canadian durum wheat breeding programs over time. All of the loci under selection uncovered by this study could be helpful in the identification of genes related to many traits of interest as functional annotations of the wheat genome become available, and to facilitate marker-assisted selection in durum wheat.AN designed the experiment, performed all analyses and wrote the manuscript. JKH contributed to the initial draft and edited the manuscript. KTN and SW edited the manuscript. AKS, FRC, JMC, and YR collected phenotypic data and edited the manuscript. CJP supervised the project, designed the experiment, collected phenotypic data and edited the 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.