The popularization of biobanks provides an unprecedented amount of genetic and phenotypic information that can be used to research the relationship between genetics and human health. Despite the opportunities these datasets provide, they also pose many problems associated with computational time and costs, data size and transfer, and privacy and security. The publishing of summary statistics from these biobanks, and the use of them in a variety of downstream statistical analyses, alleviates many of these logistical problems. However, major questions remain about how to use summary statistics in all but the simplest downstream applications. Here, we present a novel approach to utilize basic summary statistics (estimates from single marker regressions on single phenotypes) to evaluate more complex phenotypes using multivariate methods. In particular, we present a covariate-adjusted method for conducting principal component analysis (PCA) utilizing only biobank summary statistics. We validate exact formulas for this method, as well as provide a framework of estimation when specific summary statistics are not available, through simulation. We apply our method to a real data set of fatty acid and genomic data. The confidential nature of genetic and phenotypic data also raises concerns regarding data privacy and security while transporting and using the data.3The availability of large amounts of disease, environmental, and genomic data provide researchers with unprecedented opportunities to explore the effect of genetic variants on phenotypes related to human health and, consequently, change the way we think about and treat diseases. Of specific interest are complex diseases with widespread impacts on societal wellbeing and that have largely unique etiology for each individual . The wealth of individual level data in biobanks presents the potential opportunity to characterize the genetic architecture of complex diseases that could, in turn, allow for the personalization of treatments. While this expanse of health and genetic information provides exciting possibilities, there are still many concerns associated with using this large amount of data.5 The use of these summary statistics alleviates many of the issues associated with privacy and security, as there is no individually identifiable information being shared. In addition, the use of summary statistics greatly diminishes the size of the analysis dataset, making the transport of data simpler and more efficient. Finally, the fact that the biobank runs these simple, but computationally intensive, analyses diminishes the computational cost and time of analyses for individual research groups.Currently, various organizations (such as GeneAtlas with the UK Biobank) publish summary statistics, such as results from simple linear regressions , between all combinations of phenotypes and genotypes in biobank data on hundreds of thousands of individuals.6 The flexibility to explore complex phenotypes is especially important in a meta-analysis, as the statistical power of the analysis of simple phenotypes might prompt unanticipated research questions. To continue to circumvent the computational and privacy problems in biobanks and meta-analyses and answer biologically relevant research questions, we need a way to explore complex traits (phenotypes) through these simple summary statistics.While the use of summary statistics in downstream analyses alleviate many of the problems associated with the use of large datasets, they limit researchers in the complexity of the analysis they can run. Biobanks often provide summary statistics that describe the relationship between genotypes and a single, simple phenotype, but many researchers are interested in complex combinations of phenotypes that more accurately describe clinically or biologically relevant traits. These same issues arise in the performance of meta-analysis, since meta-analysis can only investigate phenotypes as complex as the summary statistics that each individual cohort provides. However, more complex phenotypes are important to explore in genome wide association studies (GWAS), as analyzing combinations of phenotypes can help explore various genetic mechanisms behind specific traits of interest, such as pleiotropy between correlated phenotypes.y = f if we know the relationships between the genotypes with the individual phenotypes y1, y2,…, ym. Recently Gasdaska et al. (2019) provided a method to summarize a regression of a linear combination of known phenotypes against genotypes, and other studies have provided new multivariate methods for exploring multiple phenotype associations with GWAS summary statistics.11 Others have explored how to investigate these multiple phenotype associations within the context of a meta-analysis through summary statistics.14 Furthermore, simple methods such as covariate adjustment and traditional multivariate methods can be used to explore multiple phenotype associations.15 Multivariate methods such as principal component analysis (PCA) have also been used in GWAS and meta-analysis to increase the power of the analysis, which allows for the exploration of rarer genetic variants.17There is limited knowledge of how we can use published summary statistics for these more complex analyses. Ultimately, we wish to know whether we can make inferences about the relationship between genotypes and the combined phenotype While these individual methods are mathematically intuitive or have the ability to explore correlated phenotypes, we have not found a method that focuses on doing both. Previous studies have provided various complicated, yet effective techniques, but these techniques cannot be intuitively applied to a wide variety of GWAS situations. Therefore, we bridge the gap between existing methods by providing a simple, mathematically intuitive method which allows the exploration of multiple phenotype associations than can be used in the context of both a single GWAS or a meta-analysis. We present a method that provides formulas for the slopes, intercept, and standard error for a PCA of phenotypes of interest, while allowing for a user-specified set of covariates utilizing only widely available biobank summary statistics. We will first demonstrate our method of covariate adjustment for any number of covariates and phenotypes, and then demonstrate a method for performing PCA with summary statistics. We will validate these methods through simulation as well as a real data application of our methods to fatty acid and genotype data from the Framingham Heart Study.2.2.1.Y to denote an n × m matrix of observations of m phenotypes across n subjects. The column vector yh represents n observations on the hth phenotype where h ∈ {1, 2, …, m}. That is, yh = [yh1 · · ·yhn]′. Similarly, we will use the matrix X to denote an n × (p + 1) design matrix of n observations on p covariates, for p > 1. We will use the matrix Xk to reference a n × 2 design matrix with only 1 covariate, xk, for any k ∈ {1, 2, …, p}. For each simple linear regression model fit for yh ~ xk, we use the notation yh = Xkβhk, where βhk is a 2 × 1 vector of model coefficients. We will use bhk to reference the “slope” coefficient, or the second element of the vector βhk. For each multiple linear regression model fit for yh ~ X we use the notation yh = Xβh, where βh is a (p + 1) × 1 vector of model coefficients.Throughout this paper, we use the matrix y where y = Xβ + ε:We will frequently use the following formulas in the paper. For any response vector 2.2.7 and similar to those proposed in Zhu et al. (2015)14 and Kim et al. (2015).18 For h, j ∈ {1, 2, …, m},bh and bj are vectors of slope coefficients from simple linear regressions of yh against every genotype, and yj against every genotype, respectively.We assume we have the following summary statistics: slope and intercept estimates for simple linear regressions of each phenotype as a function of the genotype, minor allele frequency and variance of the genotypes , and covariance matrix of the phenotypes. While having a known covariance matrix of the phenotypes makes the following methods exact calculations, we will also demonstrate the accuracy of our methods using the following estimation used in Gasdaska et al. (2019)2.3.2.3.1.yh ~ x1, yh ~ x2, …, yh ~ xp and wish to describe the linear model yh ~ X, or yh = Xβ + ε.Suppose that we have fit models for β, we turn to k, l ∈ {1, 2, …, p}. For a single phenotype multiplied by a constant ch, chyh,β we solve for these matrices and apply them to To solve for jth diagonal entry of var We can manipulate 2.3.2.Y while adjusting for covariates.Suppose we want to analyze a linear combination of all phenotypes in the matrix β. To do so, we can still calculate X′X through X′y for a linear combination of phenotypes Xy calculated from β calculated from h, j ∈ {1,2, …, m}.We still will use 2.4.Y is centered. That is, that h ∈ {1, 2, …, m}. Then, if λj is the jth highest eigen-value of cov(Y), with associated eigen-vector jth principal component score of Y. So, the previously discussed methods can be applied to calculate the coefficients and standard errors of the modelAssume that 2.4.1.Y, we can post-hoc transform the summary statistics to center Y . If yh has mean μh, standard deviation σh, and yh = Xβh+εh, then regression coefficients describing a centered yh with the same covariates can be found by subtracting μh from the intercept and leaving all other coefficients unchanged. Standard errors remain unchanged with centering. Further, if we wish to standardize yh, regression coefficients can be found by subtracting μh from the intercept, and then diving all coefficients by σ. Standard errors for the standardized response’s coefficients are equivalent to their unstandardized standard errors divided by If the summary statistics do not center 2.5.y1, y2, and y3. Subjects’ ages and sexes were generated from Poisson and Bernoulli distributions, respectively. We generated our primary response phenotypes  to be associated with the first 10 SNPs, age, and sex. As a result of this specification, we saw average correlations of 0.30 between y1 and y2, −0.08 between y1 and y3, and 0.07 between y2 and y3 across all simulations.We simulated genomes across 2,000 subjects 1,000 times. Each genome consisted of 100,000 SNPs with minor allele frequencies generated from a beta distribution. Each subject had 5 phenotypes: age, sex, 2.5.1.y1 ~ SNP + age + sex and compared them to these values calculated using our methods with simple linear regression summary statistics. We calculated these values both using the true covariance matrix of our phenotypes, and using To address our post-hoc covariate adjustment, we first calculated slope coefficients and standard errors for the regression 2.5.2.y1, y2, and y3 and calculated slope coefficients and standard errors for the regression of the first principal component against SNP, age, and sex. We compared these values to those calculated using our methods with known summary statistics of yh ~ SNP + age + sex for h ∈ {1, 2, 3}. We calculated these values both using the true covariance matrix of our phenotypes, and using To address our PCA method, we calculated the principal component weights on 2.6.21 We applied our method to unrelated individuals in the Generation 3 and Offspring cohorts with a sample size of 1,454 with data on 408,595 SNPs after quality control. We investigated the Omega-3 and Omega-6 fatty acids. The production of Omega-3s and Omega-6s are highly related and therefore it is useful to determine how genotypes are associated with each of these groups, rather than each fatty acid individually. We did this by performing regressions on the principal components of the 4 Omega-3 and the 3 Omega-6 fatty acids. We performed both our posthoc covariate adjustment and PCA methods on the summary statistics of single marker tests for each fatty acid and covariate, and compared the results to models run in the traditional framework. We ran the models with two different sets of covariates: one set included the covariates age, sex, and cohort, while the other also included the other fatty acid group as covariates. Look to cited studies for more information regarding the results of past fatty acid GWAS and the Framingham cohort.21Previous genome wide association studies explored associations between SNPs and red blood cell fatty acid (RBC FA) levels indicative of various health measures such as cardiovascular health and inflammation using data from The Framingham Heart Study.3.3.1.3.1.1.−18 with mean intra-genomic variance 3.78 × 10−33 (max intra-genomic variance 1.52 × 10−32). Our standard error estimate had mean error 1.67 × 10−20 with mean intra-genomic variance 9.01 × 10−33 (max intra-genomic variance 5.62 × 10−32).Our method to describe covariate adjusted models proved to be exact to rounding errors when we assumed the true phenotype covariance matrix. We had mean slope error −1.68 × 10−9 with mean intra-genomic variance 2.99 × 10−9 (max intra-genomic variance 4.12 × 10−8). The standard error estimate had mean error 5.25 × 10−8 and mean intra-genomic variance 7.77 × 10−13 (max intra-genomic variance 1.96 × 10−11).When estimating the phenotype covariance matrix, our approximation still performed well. Our estimate of the slope had mean error 1.87 × 103.1.2.−19 with mean intra-genomic variance 2.64×10−33 (max intra-genomic variance 3.25 × 10−32). Our slope standard error estimate had mean error −3.30 × 10−19 with mean intra-genomic variance 5.66 × 10−35 (max intra-genomic variance (2.84 × 10−34).Our method to describe models that incorporated principal components proved to be exact to rounding errors when we assumed the true phenotype covariance matrix. Our slope estimate had mean error −2.48×101, y2, and y3, our estimate still performed well. Across all 1,000 genotypes, our slope estimate had a mean error of 2.00 × 10−7 with mean intra-genomic variance 5.11 × 10−7 (max intra-genomic variance 1.75 × 10−5). Our standard error estimate had a mean error of 8.85 × 10−7 with mean intra-genomic variance 2.70 × 10−10 (max intra-genomic variance 7.91 × 10−9). When approximating the covariance of y3.2.3.2.1.−7, our method reached the same conclusions as models fit on the raw data for every SNP. We display the accuracy of our model for the first principal component of Omega-3 fatty acids, adjusting for age, sex, and cohort in Our method approximated the results of models fit on raw subject-level data with high accuracy and low variance. 3.2.2.21 Using principal components and covariate adjustment we found a novel gene that has not yet been found associated with fatty acids before: PTPRM, and another (AGPAT4) that was only identified with a fatty acid ratio before on this sample.19The post-hoc covariate adjustment on both individual fatty acids and PCA for the Omega-3 and Omega-6 fatty acids hit genes that have been found in previous GWAS on fatty acids such as FADS1, ELOVL2, and LPCAT3.4.We have developed exact methods for describing the relationship between phenotypes and genotypes for covariate adjusted linear combinations of any number of phenotypes (including post-hoc covariate adjustment) as well as for PCA using summary statistics. We have supplied the mathematical frameworks for these methods and validated them through a simulation and a real data example of both post-hoc covariate analysis and PCA, as well as the combination of the two.17 Our real data application also demonstrates that covariate adjustment and PCA can and do affect the SNPs found in GWAS results and thus might lead to the exploration of new gene associations, and identified a novel gene.We have provided a simple, efficient method for utilizing covariates and PCA in GWAS and GWAS meta-analyses using only summary statistics. In a GWAS, these methods save in computation time, and cost, as well as the time and size of data transfers. The post-hoc covariate adjustment also allows researchers to explore multiple phenotype associations through adding phenotypes correlated with the response phenotype as covariates in a computationally and time efficient way. The use of our covariate and PCA method becomes even more time-saving in a meta-analysis, as individual cohorts do not need to rerun and resend more complex analyses for the meta-analysis in order to explore more complex phenotypes or covariate adjustments. The PCA method can also be applied to a principal component meta-analysis by using methods from Ried et al. (2016) to compute universal weights that are applied to individual cohort summary statistics.y1 and y2” = y1·y2 and “y1 or y2” = y1+y2−y1·y2. These logical statements help describe how many diseases are clinically diagnosed, and thus would aid in explaining the relationship between genetics and these diseases. Future work can also explore how to expand these methods into linear mixed-effects models in order to incorporate kinship matrices and account for relatedness in these models. We are also currently working on an R package that will perform the calculations for these methods to help their implementation.Even though our method is a useful tool to flexibly explore biologically meaningful phenotypes, we suggest that future work continue to explore leveraging summary statistics to explain other complex phenotypes. For example, multiplied phenotypes can explain both logical and and or statements as: “We also must acknowledgement some limitations of our method. Throughout our mathematical framework we assume that the genotypes follow HWE. Assuming HWE means that knowing the minor allele frequency of a genotype gives exact calculations for values such as the mean and variance of the genotype. In practice, not all genotypes included in a GWAS analysis exactly follow HWE, and thus future work should explore the robustness of this in assumption in practice, though we anticipate minimal impact in downstream analysis. Our real data analysis shows a representative application of the method; however, future work should continue to explore practical issues involved in the implementation of the method on real data. Detailed results not shown demonstrate that this method is minimally impacted by non-differential genotype errors in biobanks.Use of summary statistics to share both biobank data and individual cohort analyses within a meta-analysis alleviate many issues with privacy, data size and transfer, as well as computational cost and time, while the data itself presents an unprecedented opportunity to explore human health and genetically complex phenotypes. Our method provides exact formulas along with estimation techniques for using these summary statistics for covariate-adjusted linear models and multivariate methods, that in turn can help explain the biological mechanisms between phenotypes of interest. We have continued the work of previous methodological advances by leveraging these summary statistics to investigate the relationship between genetics and diseases. Future work will explore additional methods of combining phenotypes.1


Arabidopsis thaliana accessions in root system architecture (RSA) after root tip excision. Wound-induced changes in RSA were associated with 19 genomic loci using genome-wide association mapping. Three candidate loci associated with wound-induced LR formation were investigated. Sequence variation in the hypothetical protein encoded by the At4g01090 gene affected wound-induced LR development and its loss-of-function mutants displayed a reduced number of LRs after root tip excision. Changes in a histidine phosphotransfer protein putatively involved in cytokinin signaling were significantly associated with LR number variation after root tip excision. Our results provide a better understanding of some of the genetic components involved in LR capacity variation among accessions.Root systems can display variable architectures that contribute to nutrient foraging or to increase the tolerance of abiotic stress conditions. Root tip excision promotes the developmental progression of previously specified lateral root (LR) founder cells, which allows to easily measuring the branching capacity of a given root as regards its genotype and/or growth conditions. Here, we describe the natural variation among 120  Arabidopsis thaliana (Strong modulation of root system architecture (RSA) by environmental cues, such as nutrient and water availability has been a well-documented process in thaliana . In primthaliana . A subsethaliana  to initithaliana . Howeverthaliana . In addithaliana . The spathaliana . These rthaliana .+ TRANSPORTER1HIGH-AFFINITY K (HKT1), previously identified for its role in salinity tolerance by modulating sodium/potassium homeostasis  studies have contributed to the identification of natural variation in key genes controlling PR growth under control and abiotic stress conditions . Naturaleostasis . The tareostasis . RecentlTo explore the natural variation of LR branching capacity in Arabidopsis , we perfA. thaliana (L.) Heyhn. selected from the 1001 Genomes Project (ahp1 ahp2 ahp3 (1). Seeds were stored at 4°C for several weeks (>12) to break dormancy.Our population for GWA mapping consisted of 174 natural inbred lines  of  Project  based on Project . The lab Project . The ahphp2 ahp3  mutants −2⋅s−1). For each accession, 12 seeds were sown per petri dish in triplicate (36 samples/line). Sixteen consecutive sowings including 11 accessions each were established. Additionally, Col-0 was also included in all the sowings to be used as the growth reference accession and for normalization purposes (Seeds were surface-sterilized in 2% (w/v) NaClO and rinsed with sterile water before being transferred to 120 mm × 120 mm × 10 mm Petri dishes containing 75 mL of one-half-Murashige & Skoog (MS) medium with 2% sucrose, 8 g/L plant agar  and 1× Gamborg B5 vitamin mixture (Duchefa Biochemie). After 4 days of stratification at 4°C in darkness, plates were wrapped in aluminum foil and were transferred (0 days after sowing) to an MLR-352-PE growth chamber  at 22 ± 1°C during 3 days in a nearly vertical position. Plates were unwrapped (3 days after sowing) and grew during another 3 days with continuous light , at a resolution of 600 dpi, and saved as RGB color images in JPEG file format. Scanned images were processed using EZ-Rhizo  with avawn roots . LR numbwn roots .P-value < 0.05) unless otherwise indicated.Statistical analyses of the data was performed by using StatGraphics Centurion XV  and SPSS 21.0.0  software packages. Data outliers were identified based on aberrant standard deviation values and were excluded for posterior analyses as described elsewhere . One-sam2H) for the studied dataset was calculated as 2H = σG2/(σG2 + σGE2/e +σ2e2/re), in which σG2, σGE2, σe2, r, and e represent the estimated variances for the genetic effects, genotype-environment interactions, random errors, number of replications (12) and number of environments (three), respectively. The estimated variances for σG2, σGE2, and σe2 were obtained by ANOVA using normalized data values as regards to the Col-0 reference accession from 106 of the studied lines.The broad-sense heritability  we applied the ΔK method, as described elsewhere  > 6.5 were considered significantly associated to the studied trait ] with the studied trait, were downloaded from the GWAPP web interface. We analyzed the sampling bias on GWAS by systematically removing one or several geographically isolated accessions and found that it did not make any difference to the detected SNP associations  > 6.5  for further studies.Genome-wide association mapping was performed using the GWAPP web interface markers . GWAS waed trait . Manhattciations . We seleSeedlings with T-DNA homozygous insertions in the annotated genes were identified by PCR verification with T-DNA specific primers and a pair of gene-specific primers . GenomicPrimers amplified 81–178 bp of the cDNA sequences . To avoiRNA extraction and cDNA synthesis were performed as described elsewhere . For reaRGS1-HXK1 INTERACTING PROTEIN 1, RHIP1) .Primer validation and gene expression analyses were performed by the absolute quantification method  by using, RHIP1)  was chosn = 467) LRs at 4 dae  was calculated for each of the studied traits . Heritability estimates ranged between 0.90 (LR emergence onset and LR density) and 0.95 (LR number). Broad-sense heritability for PR length was 0.93. Interestingly, we found a positive and significant correlation between LR number and PR length at 4 dae  and 9.42 ± 4.84 in Kidr-1 . Hence, reduced LR number in Ru3.1-31 compared to Kidr-1 was likely caused by its reduced PR length. Some accessions, such as Leo-1 and Voeran-1 displayed contrasting phenotypes as regards their LR number  although they displayed similar PR lengths , respectively.We studied wound-induced LR formation in a collection of 173 additional accessions selected from the 1001 Genomes Project . In 34 o lengths . On the  n = 29; . Ped-0 d n = 29; . As regan = 120 accessions) was polymorphic for those causal alleles. We determined the genetic relationship among the studied accessions using a Structure analysis with 319 genome-wide randomly selected and synonymous  SNP markers already available . Structure analysis of these accessions identified two distinct genetic groups  suggested that these traits were controlled by multiple genes, that some of the causal alleles are pleiotropic , and that the studied population . The significance of association was first evaluated with three different statistical models  > 6.5 and minor allele frequency (MAF) > 12% to select the SNPs being associated with a given trait. A total of 162 SNP associations were found with the LM method for the studied parameters  and only one SNP was found associated with LR density. The larger number of significantly associated SNPs was found for LR number (n = 114), with P-values ranging from 8.27 × 10−11 to 3.15 × 10−7. Consistently with our previous observation that PR length and LR number are significantly correlated, 11 SNPs were significantly associated with both traits; similarly, six significantly associated SNPs were shared between LR emergence onset and LR number , (2) presence of multiple significantly associated SNPs within an average of 10 Kpb genomic window, and (3) presence of, at least, one non-synonymous SNP within the selected region. We found five genomic regions putatively contributing to PR length variation in the studied population  and Star-8  in comparison to their wild-type siblings  uptake transporter which is highly expressed in root hairs  and carried alternative alleles of the Chr4:16128906 marker (At4g33530  encodes ot hairs . We founot hairs . The acc6 marker . We iden6 marker . None of6 marker .n = 32) and Pra-6  in LR numbers (n = 36) and Vie-0   that contributed to the observed variation in wound-induced LR formation in the studied population. Accessions sharing the CCG haplotype for these three markers displayed the smallest number of wound-induced LRs , while o numbers . The ind numbers . Similar n = 33) . HoweverA. thaliana PRs might use a specific pathway to activate LR formation when the PR is damaged (WUSCHEL-related homeobox11 (WOX11), which is involved in de novo regeneration of adventitious roots from leaf explants  with PR length at the excision day and with the time of LR emergence after excision. Some accessions, such as Leo-1 and Voeran-1, significantly differed in their LR number because of an earlier initiation of wound-induced LRs in Leo-1, which were also longer. Hence, Leo-1 contained alleles for higher LR branching capacity that positively contributed to an enhanced root system, which might allow survival in harsh environments. It will be interesting to evaluate whether differences in A. thaliana native distribution and the proposed postglacial colonization routes in this species . In all these cases, the causal polymorphism(s) might affect genes with pleiotropic effects on RSA. GWA mapping has facilitated the identification of the molecular variants underlying complex traits in crops, such as heterosis , grain senhanced disease resistance 4 (EDR4), which modulates plant immunity by regulating clathrin heavy chain 2 (CHC2)-mediated vesicle trafficking  of unknown function, which is expressed at higher levels in the endodermis of the elongation zone of the root and the mature xylem . Other officking . The profficking . One intfficking , which cfficking . AdditioAt5g19710 encodes a histidine phosphotransfer protein belonging to the AHP bridge components of the His-Asp phosphorelay transduction pathway of CK signaling . Five AH+ UPTAKE TRANSPORTER5 (KUP5)K that changes a Gln to His residue in a conserved transmembrane domain of the protein. Potassium is an essential element in plant growth as it affects osmotic regulation and cell water potential (We found a statistically significant association between a non-synonymous SNP in the coding region of otential . The Araotential , which motential . As propotential . We founotential , but theotential .Through GWA mapping we have identified a number of significant non-synonymous polymorphisms that accounted for some of the variation found in wound-induced RSA. Our results highlighted new regulators of LR formation in Arabidopsis and the further dissection of the developmental mechanisms involved might help to understand the genetic basis of the natural variation of root plasticity.JP-P was responsible for conceptualization and supervision and provided the funding acquisition. MJ and JP-P were responsible for methodology and performed the formal analysis. MJ, SI, and JP-P were involved in the investigation, writing of the original draft, and review and editing of the manuscript. AP was responsible for software development.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.


Background: The study of networks of affective mental states that play a role in psychopathology may help model the influence of genetic and environmental risks. The aim of the present paper was to examine networks of affective mental states  over time, stratified by genetic liability for psychopathology and exposure to environmental risk, using momentary assessment technology.Methods: Momentary AMS, collected using the experience sampling method (ESM) as well as childhood trauma and genetic liability (based on the level of shared genes and psychopathology in the co-twin) were collected in a population-based sample of female-female twin pairs and sisters . Networks were generated using multilevel time-lagged regression analysis, and regression coefficients were compared across three strata of childhood trauma severity and three strata of genetic liability using permutation testing. Regression coefficients were presented as network connections.Results: Visual inspection of network graphs revealed some suggestive changes in the networks with more exposure to either childhood trauma or genetic liability . Yet, statistical evaluation of differences across exposure strata was inconclusive.Conclusions: Although suggestive of a difference in the emotional dynamic, there was no conclusive evidence that genetic and environmental factors may impact ESM network models of individual AMS. Traditionally, mental disorders are conceived as categories based on statistical differentiation between symptoms that cluster together, ignoring the underlying causes. Vinogradov and colleagues  proposedThe network theory of mental disorders has gained traction as a novel conceptualization of psychopathology, where symptoms—not latent classes underlying symptoms—are studied as active elements interacting with each other in a symptom network. As an example, in a clinically relevant hypothetical scenario, if an individual suffers from sleep loss, this will lead to fatigue, which in turn may give rise to anxiety that may ultimately produce a feedback loop between anxiety and sleep loss, constantly activating all these symptom nodes in the network to develop into a mental-ill state, such as anxiety disorder –6. The nIn addition, networks can also be generated using AMS in healthy subjects rather than symptoms of a mental illness. In the network research, these momentary assessed AMS were also called emotions interchangeably. For example, the AMS down is part of the same continuum as the symptom depressed, but severity is far less. Therefore, besides symptom networks, AMS networks are of interest to get insight in the interplay between emotions over time . More imThe experience sampling method (ESM) prompts individuals to record their AMS , anomalous experiences , and context  after prompts  occurring at unpredictable moments throughout the day . Particit-1 (time lag) and an AMS at the current time point t, are represented by a directed arrow. The arrow or edge is also weighted, with the B coefficient expressing the effect size of the predictive associations. For example, an arrow from “relaxed” to “cheerful” weighted at 0.08 would mean that “relaxed” at t−1 predicts “cheerful” at t with a B coefficient of 0.08  according to a factor analysis of all AMS performed previously, taking into account the multilevel nature of the current sample . AccordiSecond, since in general population studies, many negative affect items have floor effects, so that the normality assumption is violated in analyses, to keep models analysable and interpretable, items with strongest floor effects were avoided. Variability was checked, for each of the AMS items described above, by including the current and lagged AMS in an autoregressive model. Subsequently, the proportion of participants with horizontal slopes was calculated per AMS item. A horizontal slope points to floor effects, demonstrating a restriction of range, which can result in a type II error .Finally, we selected AMS with a maximum within-person time-lagged variability, and that represent each quadrant of the four affective domains defined by valence  and arousal . This chChildhood trauma was assessed using the Childhood Trauma Questionnaire short form (CTQ-SF), which is a 25 item version of the Childhood Trauma Questionnaire including items on physical, sexual, and emotional abuse, and physical and emotional neglect, scored on a 5- Likert scale  , 32. TheThe Symptom Checklist-90-R (SCL-90-R), a reliable and valid self-report instrument for screening a range of symptoms occurring in the past week, was used to index the overall severity of psychopathology . The SCLGenetic liability to psychopathology was determined based on the SCL-90, value  in the co-twin and zygosity status, consistent with previous work , 34, 35.All analyses were performed using Stata version 13.0 . To takeTime-lagged variables were used as predictors in the multilevel models . Cheerfui stands for the assessment level, j for individuals, k for twin pairs and u7ijk for the random slope of time (see below).Where time is the beep number over days (1–50), the subscript As seen above, the B coefficients (B2–B6) are obtained using linear regression analysis. Because the data includes multiple assessments per person and includes twins, we used a regression analysis that can give valid results despite the multilevel structure. The obtained regression coefficients can be interpreted the same way as in regular linear regression analysis. In terms of network analysis, those B coefficients are then used as weights for the time lagged associations between an AMS at a current time point and the AMS at the next time point. The higher the value of the regression coefficient or weights (in term of network language) the higher the chance the two AMS are associated over time and the value of it gives the quantification of the association.t-1 AMS variables excluded the last beep moment of a day as a lag of the first beep moment the next day. Analyses were performed across 3 strata of childhood trauma as well as across 3 strata of genetic vulnerability.As the time between lagged and current moment has to be contiguous, and all beep moments were in the waking period of the day, time was added to the models at the individual level, representing the standard procedure for analysis in network research  was included in all regression models since a lagged coefficient can be interpreted as an autocorrelation coefficient only if, conditional on all other fixed effects in the model, no systematic trend is present in the data. Because any trend that may be present could differ across participants, a random slope for research .p-values to be correctly estimated. However, this approach is not feasible in the present context, due to the large number of predictor variables and hence the large number of parameters that would need to be estimated (attempts to fit such models result in convergence problems). Therefore, a single random slope for time was included in the model (see above), and to obtain valid p-values, permutation tests examined the statistical significance of observed B coefficients.Mixed-effects models should ideally include random slopes for all time-varying predictor variables (and use fully unstructured covariance matrices for the random effects) . This prp-value. For this, data in which there is no association (the null hypothesis assumption) were analyzed. For example, for the first set of permutations, whose aim is to test the significance of each association between two AMS, i.e., each observable regression coefficient (see below), the dependent variable was removed from the data and shuffled in a random order and merged to the original data, while keeping the multilevel structure. The regression coefficients are calculated repeatedly for 1,000 times using that data to draw a normal, under the null hypothesis, distribution. The percentage of permuted regression coefficients that is to the more extreme end of this distribution than the observed regression coefficient gives the p-value (2-sided). The p-value is considered significant at the threshold of 0.0162 after Simes correction (0.0002 for between-groups comparison) (see below).Permutation testing is developed to obtain the distribution of regression coefficients under the null hypothesis. Subsequently, the observed regression coefficient obtained from the real analysis is placed on this normal distribution, to obtain a valid p-values for each regression coefficient (edge weight). The second type was performed to compare regression coefficients across different strata of genetic vulnerability and childhood trauma.Two different types of permutation tests were performed. The first type was used to obtain valid t) was removed from each record of the original data file and reassigned to the same participant in random order in a copy of the original data set. Because assessments were shuffled within participants, the level of clustering within the data described above was unchanged. Refitting the model based on the permuted data then provides estimates of the model coefficients under the null hypothesis of no association. By repeating this process, a 1,000 time, a distribution of the regression coefficients under the null hypothesis was generated. Then, the observed coefficients were compared with the respective regression coefficient under the null hypothesis distribution to obtain p-values . Given 2 × 3 × 6 × 6 tests for statistical significance, Simes correction for multiple testing was applied  in the network were tested for differences between the childhood trauma strata, regardless of the level of significance obtained with the first type of permutation testing. This same procedure was repeated for the different strata of genetic liability. Again, Simes correction for multiple testing was applied.The regression coefficients (B1–B6) obtained from the equation in section Associations Between t-1 AMS and Current AMS were represented in a graph to express the bidirectional time lagged associations between each set of two AMS.A complete set of analyses in one stratum yielded 36 unstandardized regression coefficients (B). These coefficients were represented in a graph using the following procedure:→Bcheerful−relaxed) at time point t, while controlling for all other variables. The elements on the diagonal are the autoregressive effects . This procedure was applied in the 3 strata of childhood trauma and the 3 strata of genetic liability, separately . Visualization of networks was obtained using R (qgraph package) (A 6-by-6 matrix with the regression coefficients (B) was constructed. The connection thus denotes the extent to which the AMS variable  at time point t-1 predicts another AMS variable  .node strength or strength is the sum of the absolute value of the weighted connections (both inward and outward) of a specific AMS, thus indexing the extent to which this AMS is connected in the network. Self-loops  are counted twice as to fulfill the definition of the Strength taking into account the fact that self-loops are good indicators of emotions inertia, previously described as an indicator of increased vulnerability and decreased psychological flexibility   . Betweenlsewhere , 41. Alllsewhere , 44. Nodn = 540). Participants were aged between 18 and 61 years . The larger part of the sample (63.5%) had a college or university degree, 35% had completed secondary education, and 2% had completed primary education only. The majority was in a relationship (75%), and most of the participants were employed (95%).Of the initial study population of 621 individuals, 610 completed the ESM procedure and returned the questionnaires. Twenty-five participants were excluded because of too few valid assessments, leaving a sample of 585 individuals ; the 45 sisters were excluded from the genetic liability analysis (The average childhood trauma score was 1.66 (SD 0.58), and the average SCL-90-R score was 1.37 (SD 0.33). Mean levels of AMS were as follows: Cheerful 4.63 (1.40); insecure 1.41 (SD 1.02); relaxed 4.77 (SD 1.44); anxious 1.23 (SD 0.76); irritated 1.58 (SD 1.28); down 1.36 (SD 0.96). Table p-values between groups was 0.0002  and the network in the other two genetic strata seemed larger . In addition, the small number of subjects in some of the genetic liability strata may have contributed to the observation that some findings did not survive Simes correction. For a more global overview of complete networks we refer to Supplementary Figures Network representations of momentary psychopathology in the ESM paradigm statistically may have low sensitivity in identifying and quantifying effects of childhood trauma or genetics, especially since many previous studies demonstrated specific molecular genetic significant associations with emotion dynamic parameters. Among them was the recent positive finding suggesting the link of the serotonin transporter gene polymorphism (5-HTTLPR) to emotional inertia of negative emotions applying the ESM methodology in collecting data . Yet, thAn important strength of the current study is that it used a large number of observations due to the nature of ESM methodology. This allowed us to compare three groups across both environmental and genetic exposures. Cross-sectional network analysis can be seen as an improved factor analysis or principal component analysis, visualizing connections between mental states assessed once over periods of weeks or months, with standard instruments . The preIt could be argued that childhood trauma can be a consequence of genetic liability because it can be a result of parents with more psychopathology having more problems with child upbringing (gene-environment correlation) . Howeverp-values. However, we have shown that by applying advanced statistical techniques, permutation tests, valid and interpretable results can be obtained. Such an approach may prove useful for other computational network problems; even though statistical power may be negatively affected. Third, considering that our participants were female with a high mean educational level, the results of this study may not be representative for men and those with lower educational level.This is the first study using the network methodology in answering an etiological research question involving genetic liability and early environment. As data were initially collected in the general population, some limitations are inherent. While the advantage of a representative sample is that it best captures the natural spectrum of psychopathology, a limitation is that negative affect items were rare and, therefore, not normally distributed. However, because items with high levels of variation were selected to avoid floor effects and because permutation tests  were performed, it did not lead to invalid methods of analysis. A second limitation was the impossibility to include random effects for the slope of all predictor variables in the model. Therefore, standard methods for testing the model coefficients would have led to invalid The present analyses sought to provide a micro-level perspective to what could be the phenotypic translation of the genetic and environmental liability to psychopathology. Although suggestive, this first study of differences between genetic liability and environmental strata did not show any evidence to support the hypothesis that genes and early adversity have an impact on emotional dynamics in daily life as measured by the current network methodology. In future work, the present exploration of the effect of genes and environment on the affective regulation network should be replicated using the sum scores positive and negative affect before expanding it to molecular genetic measures of risk such as polygenic risk scores or to the interaction between childhood trauma and genetic liability. For this, both general population studies as well as case-control studies should be designed to complete our understanding of the mechanisms underpinning mental disorders.Furthermore, further testing of the basic network of AMS as an intermediate phenotype may also be of value as networks can be seen as ecologically valid phenotypes, complementary to categorical diagnostic phenotypes in genetic studies.LH contributed to the conception of the work, the analysis, interpretation of data for the work, and to drafting it. MD contributed to the conception of the work, the analysis, interpretation of data for the work and to drafting and revising it. SG and WV contributed to the interpretation of data for the work, drafting and revising it. MD, CD, and ET contributed to the acquisition of data for the work, and to revising it. JvO contributed to the conception of the work, the interpretation of data for the work, and to revising it.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.


P < 0.05, when we would expect 21 to replicate by chance. Notable significant, interpretable associations include: iron transport and storage genes, related to magnetic susceptibility of subcortical brain tissue; extracellular matrix and epidermal growth factor genes, associated with white matter micro-structure and lesions; genes that regulate mid-line axon development, associated with organization of the pontine crossing tract; and overall 17 genes involved in development, pathway signalling and plasticity. Our results provide insights into the genetic architecture of the brain that are relevant to neurological and psychiatric disorders, brain development and ageing.The genetic architecture of brain structure and function is largely unknown. To investigate this, we carried out genome-wide association studies of 3,144 functional and structural brain imaging phenotypes from UK Biobank . Here we show that many of these phenotypes are heritable. We identify 148 clusters of associations between single nucleotide polymorphisms and imaging phenotypes that replicate at  Genome-wide association studies of brain imaging data from 8,428 individuals in UK Biobank show that many of the 3,144 traits studied are heritable, and genes associated with individual phenotypes are identified. MRI can therefore provide intermediate endophenotypes that can be used to assess the genetic architecture of such disorders.Brain structure and function vary between individuals and can be measured non-invasively using magnetic resonance imaging (MRI). The effects of neurological and psychiatric disorders such as Alzheimer’s disease, Parkinson’s disease, schizophrenia, bipolar disorder and autism can be seen in MRI dataStructural MRI measures of brain anatomy include tissue and structure volumes, such as total grey matter volume and hippocampal volume, while other MRI modalities allow the mapping of different biological markers such as venous vasculature, microbleeds and aspects of white matter microstructure. Brain function is typically measured using task-based functional MRI (fMRI), in which subjects perform tasks or experience sensory stimuli; task-based fMRI uses imaging sensitive to local changes in blood oxygenation and flow caused by brain activity in grey matter. Brain connectivity can be divided into functional connectivity, where spontaneous temporal synchronizations between brain regions are measured using fMRI with subjects scanned at rest, and structural connectivity, measured using diffusion MRI (dMRI), which images the physical connections between brain regions based on how water molecules diffuse within white matter tracts. For those not familiar with the neuroimaging field, we have provided a glossary in Supplementary Note 1.2. Participants were 40–69 years old at recruitment, with one aim being to acquire as rich data as possible before disease onset. Identification of disease risk factors and early markers will increase over time with emerging clinical outcomes3. A brain and body imaging extension will scan 100,000 participants by 2020, with brain imaging including three structural modalities, resting and task-based fMRI, and diffusion MRI4  for 3,144 IDPs, covering the entire brain and including ‘multimodal’ information on grey matter volume, area and thickness, white matter connections and functional connectivity, at 11,734,353 single-nucleotide polymorphisms (SNPs) in up to 8,428 individuals with both genetic and brain imaging data. We used two separate sets of data from UK Biobank to evaluate replication of significant genetic associations from the discovery phase. We also carried out multi-trait GWAS, SNP heritability analysis, genetic correlation analysis of IDPs with brain-related traits and an analysis of enrichment of genomic regions with different functions. Previous large-scale GWAS imaging studies have focused on narrower ranges of phenotypes including studies of: grey matter volume in seven subcortical regions by combining data across more than fifty studieshttp://www.ukbiobank.ac.uk/ethics/), and these ethical regulations cover the work in this study. Written informed consent was obtained from all participants.The UK Biobank has approval from the North West Multi-centre Research Ethics Committee (MREC) to obtain and disseminate data and samples from the participants (http://big.stats.ox.ac.uk/), which allows users to browse associations by SNP, gene or phenotype. This was built from the PheWeb code base (https://github.com/statgen/pheweb/) and extended to allow easier searching of phenotypes. In addition to the brain IDP GWAS results, the browser also includes GWAS results from more than 2,500 other traits and diseases.All results are available on the Oxford Brain Imaging Genetics (BIG) web browser (h2) of all IDPs and whether h2 is significantly different from 0 at the nominal 5% significance level  are much more highly heritable. By contrast, most of the resting-state node amplitude IDPs show significant evidence of SNP heritability; the task-related fMRI IDPs do not.Figure 14 , via a genetic correlation analysis  threshold of 7.5, we found 1,262 significant associations between SNPs and the 3,144 IDPs. These associations spanned all classes of IDPs, except task-related fMRI  threshold of 7.5 controls for the number of tests carried out across SNPs and accounts for the correlation structure between genetic variants. Of these 1,262 associations, 844 and 455 replicated at the 5% significance level using our two smaller replication datasets  > 11, which additionally corrects for all 3,144 GWAS carried out  > 11. The Oxford Brain Imaging Genetics (BIG) web browser (http://big.stats.ox.ac.uk/) allows researchers to view the PheWAS for any SNP of interest. We found that 4 of the 78 SNPs were associated  > 4.79) with all 3 classes of structural, dMRI and functional measures, and these were all SNPs in cluster 31 of Extended Data Table Supplementary Figs. 7, and of hippocampal volume in 33,536 subjects 18.Overall, our results clearly replicate the majority of the loci identified by the ENIGMA consortium in two separate GWASs of seven brain subcortical volume IDPs in up to 13,171 subjects19. In total, we found 17 genetic loci that can be linked to genes that broadly contribute to brain development, patterning and plasticity  or near genes  that are known to affect iron transport and storage, or neurodegeneration with brain iron accumulation (NBIA)21 . In addition, we identified four SNPs that either encode or are eQTLs of genes involved in transport of nutrients and minerals: SLC44A5 , SLC39A8 , SLC20A2  and SLC39A12 . For more details, see Supplementary Note 3.A major source of cross-subject differences seen in T2* data are microscopic variations in magnetic field, often associated with iron deposition in ageing and pathology22). For instance, by looking at the difference between the average T2* image from subjects with no copies versus one copy of the rs4428180 (TF) non-reference allele, we found effects of this SNP not just in the putamen and pallidum, but also in additional, smaller regions of subcortical structures not included as IDPs , an eQTL of BCAN, is associated with one dMRI microstructural measure in the genu of the corpus callosum; rs3762515 (P = 4.27 × 10−13), in the 5′ UTR of EFEMP1, with the volume of white matter lesions; and rs67827860 . Overall, the vast majority of forebrain white matter-related dMRI IDPs were associated with SNPs related to genes that encode proteins involved in the extracellular matrix and epidermal growth factor signalling. These proteins have key roles in synaptic plasticity and myelin repair, and are associated with multiple sclerosis, stroke, amyotrophic lateral sclerosis and major depressive disorder (Supplementary Note 3).Notably, three SNPs related to our white matter IDPs were in genes or eQTLs of genes encoding three proteins of the extracellular matrix (ECM): rs2365715 . This gene encodes an enzyme that facilitates posterior organ development and prevents human neural tube defects, including spina bifida30. Second, we found two SNPs associated with dMRI IDPs of the crossing pontine tract  in genes that regulate axon guidance and fasciculation during development , P = 1.76 × 10−19; Fig. ROBO3, which is specifically required for axons to cross the midline in the hindbrain ; mutations in ROBO3 result in horizontal gaze palsy, a disorder in which the corticospinal and somatosensory axons fail to cross the midline in the medulla31. Notably, all three significant associations with the IDP of the crossing pontine tract were found using the tensor mode of anisotropy (MO), a measure that is particularly useful in regions of crossing fibres32.Two additional examples further illustrate meaningful correspondences between the locations of our brain IDPs and significantly associated genes. First, the volume of the fourth ventricle, which develops from the central cavity of the neural tube, was found to be significantly associated with a SNP in, and eQTL of, P traits in one GWAS, these tests can avoid the need to correct for multiple genome-wide scans. We used a multi-trait test (see 10(P) > 7.5 (Supplementary Table 10(P) > 8.86 and 138 of these 170 SNPs had a P value < 0.05 in the larger replication set of 3,456 samples. There can be large differences in P values between the multi-trait tests and the individual IDP tests  and all were eQTLs of microtubule-related genes . The extended MAPT region has been repeatedly associated with Alzheimer’s and Parkinson’s diseases, frontotemporal dementia, and progressive supranuclear palsy (Supplementary Note 3).Three of these loci showed associations with the dMRI tensor mode of anisotropy measures . This locus is also part of a multimodal cluster from our single-trait GWAS that includes subcortical and cerebellar grey matter volumes, pallidum T2* and dMRI in midbrain white matter tracts  > 7.5) and at a more stringent threshold (−log10(P) > 11) designed to (probably over-conservatively) control for the number of IDPs tested. Our use of multi-trait tests uncovered further novel loci. We find associations with all the main IDP groups except the task fMRI measures .Bringing together researchers with backgrounds in brain imaging and genetic association was key to this work. We have uncovered a large number of associations at the nominal level of GWAS significance . The genes linked to brain development and plasticity tended to be related to mental health disorders, including major depression disorder and schizophrenia, whereas those that encoded iron-related proteins tended to be related to neurodegenerative disorders, such as amyotrophic lateral sclerosis, Parkinson’s disease and Alzheimer’s disease. We also uncovered enrichments of functional annotations for many of the structural and diffusion IDPs.A valuable aspect of this work has been to link the associated SNPs back to spatial properties of the voxel-level brain imaging data. For example, we have linked SNPs associated with IDPs to both highly spatially localized and widely spatially distributed effects, restricting these voxelwise analyses to the same imaging modality from which the original phenotypic association was found . In addition, looking at PheWAS plots has been useful when working with so many phenotypes. It has allowed us to investigate the overall patterns of association and has led to the identification of SNP associations that span multiple modalities.We used two additional sets of 930 and 3,456 samples to replicate a large number of the associations uncovered at the discovery phase. Over coming years, the number of UK Biobank participants for whom imaging data are available will increase to 100,000, allowing more complete discovery of the genetic basis of human brain structure, function and connectivity. Combining the discovery and replication samples is also likely to lead to novel associations, as will the use of methods that can analyse the huge IDP × SNP matrix of summary statistics of association. A potential avenue of research will involve attempts to uncover causal pathways that link genetic variants to IDPs and then to a range of neurological, psychiatric and developmental disorders.The UK Biobank brain imaging protocol consists of six distinct modalities covering structural, diffusion and functional imaging, summarized in Supplementary Table 5. These are available from UK Biobank, and it is these IDPs from the 2017–2018 data releases that we used in this study.The raw data from these six modalities have been processed for UK Biobank to create a set of IDPs38 (https://surfer.nmr.mgh.harvard.edu) to model the cortical surface , as well as modelling several subcortical structures. We used both the T1 and T2 FLAIR images as inputs to the FreeSurfer modelling (or just the T1 when the T2 was not available). FreeSurfer estimates a large number of structural phenotypes, including volumes of subcortical structures, surface area of parcels identified on the cortical surface, and grey matter cortical thickness within these areas. The areas are defined by mapping an atlas containing a canonical cortical parcellation onto an individual subject’s cortical surface model, thus achieving a parcellation of that surface. Here we used two atlases in common use with FreeSurfer: the Desikan-Killiany–Tourville atlas (denoted DKT39) and the Destrieux atlas (denoted a2009s40). The DKT parcellation is gyrus-based, whereas Destrieux aims to model both gyri and sulci based on the curvature of the surface. Cortical thickness is averaged across each parcel from each atlas, and the cortical area of each parcel is estimated, to create two IDPs for each parcel. Finally, subcortical volumes are estimated, to create a set of volumetric IDPs.In addition to the IDPs directly available from UK Biobank, we created two extra sets of IDPs. First, we used FreeSurfer v6.0.0http://www.fmrib.ox.ac.uk/ukbiobank/). In addition to this being a very large number of IDPs from which to interpret association results, these individual IDPs tend to be substantially noisier than most of the other, more structural, IDPs. Hence, while we did carry out GWAS for each of these 1,695 connectivity IDPs, we also reduced the full set of connectivity IDPs into just six new summary IDPs using data-driven feature identification. We performed this dimensionality reduction by applying ICA41, applied to all functional connectivity IDPs from all subjects, to find linear combinations of IDPs that are independent between the different features (ICA components) identified42. We carried out the ICA feature estimation without any use of the genetic data, and we maximized independence between component IDP weights (as opposed to subject weights). We used split-half reproducibility (across subjects) to optimize both the initial dimensionality reduction  and also the final number of ICA components . The resulting six ICA features were then treated as new IDPs, representing six independent sets  of the original functional connectivity IDPs. These six new IDPs were added into the GWAS analyses. The six ICA features explain 4.9% of the total variance in the full set of network connection features, and are visualized in Supplementary Fig. http://www.fmrib.ox.ac.uk/ukbiobank/).Second, we applied a dimension reduction approach to the large number of functional connectivity IDPs. Functional connectivity IDPs represent the network edges between many distinct pairs of brain regions, comprising in total 1,695 distinct region-pair brain connections (4). For the GWAS in this study we did not try to impute missing IDPs owing to the low levels of correlation observed across groups.We organized all 3,144 IDPs into 9 groups  reference panel43 and a merged UK10K + 1000 Genomes reference panel. We first identified a set of 12,623 participants who had also been imaged by UK Biobank. We then applied filters to remove variants with minor allele frequency (MAF) below 0.1% and with an imputation information score below 0.3, which reduced the number of SNPs to 18,174,817. We then kept only those samples (subjects) estimated to have recent British ancestry using the sample quality control information provided centrally by UK Biobank6 (using the variable in.white.British.ancestry.subset in the file ukb_sqc_v2.txt); population structure can be a serious confound to genetic association studies44, and this type of sample filtering is standard. This reduced the number of samples to 8,522. The UK Biobank dataset contains a number of close relatives (third cousins or closer). We therefore created a subset of 8,428 nominally unrelated subjects following procedures similar to those described previously6. After running GWAS on all the (SNP) variants in the 8,428 samples we applied three further variant filters to remove variants with a Hardy–Weinberg equilibrium P value <10−7, remove variants with MAF <0.1% and keep only those variants in the HRC reference panel. This resulted in a dataset with 11,734,353 SNPs.We used the imputed genetic dataset made available by UK Biobank in its July 2017 releaseWe used two separate datasets to replicate the associated variants found in this study. The first set of 930 subjects was a subset of the 1,279 subjects with imaging data that we did not use for the main GWAS, who had primarily been excluded because they were not in the recent British ancestry subset. An examination of these samples according the genetic principal components (PCs) revealed that many of those samples are mostly of European ancestry  imaging confounds (b) measures of genetic ancestry, and (c) non-brain imaging body measures.45.We identified a set of variables that were likely to represent imaging confounds, for example those associated with biases in noise or signal level, corruption of data by head motion or overall head size changes. For many of these we generated various versions . This was done in order to generate a rich set of covariates and hence reduce as much as possible potential confounding effects on analyses such as the GWAS, which are particularly of concern when the subject numbers are so highr = 0.52) and so it is worth using fMRI-derived head motion estimates as confound regressors for all modalities.Age and sex are can be variables of biological interest, but can also be sources of imaging confounds, and here were included in the confound regressors. Head motion is summarized from resting and task-based fMRI as the mean displacement (in mm) between one time point and the next, averaged over all time points and across the brain. Head motion can be a confounding factor for all modalities and not just those comprising timeseries of volumes, but is readily estimable only from the timeseries modalities. Nevertheless, the amount of head motion is expected to be reasonably similar across all modalities . The intention is that these can be useful as ‘confound variables’; for example, these might be regressed out of brain IDPs before carrying out correlations between IDPs and non-imaging variables. TablePosition is the Z-position of the coil (and the scanner table on which the coil sits) within the scanner (the Z axis points down the centre of the magnet). BrainCoGZ is somewhat similar, being the Z-position of the centre of the brain within the scanner . BrainCoGX is the X-position (left–right) of the centre of the brain mask within the scanner. BrainBackY is the Y-position (front–back relative to the head) of the back of brain mask within the scanner.The exact location of the head and the radio-frequency receiver coil in the scanner can affect data quality and IDPs. To help to account for variations in position in different scanned participants, several variables have been generated that describe aspects of the positioning  with spline-based smoothing. We then applied PCA and kept the top 10 components, to generate a basis set that reflects the primary modes of slowly changing drifts in the data.UK Biobank brain imaging aims to maintain as fixed an acquisition protocol as possible during the 5–6 years that the scanning of 100,000 participants will take. There have been a number of minor software upgrades (the imaging study seeks to minimize any major hardware or software changes). Detailed descriptions of every protocol change, along with thorough investigations of the effects of these on the resulting data, will be the subject of a future paper. Here, we attempted to model any long-term (over scan date) changes or drifts in the imaging protocol or software or hardware performance, by generating a number of data-driven confounds. The first step was to form a temporary working version of the full subjects × IDPs matrix with outliers limited (see below) and no missing data, using a variant of low-rank matrix imputation with soft thresholding on the eigenvaluesi indicates quantile normalization of variables, and m indicates median-based outlier removal . If no subscript is included, no normalization or outlier removal was carried out. Certain combinations of normalization and powers were not included, either because of very high redundancy with existing combinations, or because a particular combination was not well-behaved. The full set of variables used to create the confounds matrix are: a, age at time of scanning, demeaned (cross-subject mean subtracted); s, sex, demeaned; q, four confounds relating to the position of the radio-frequency coil and the head in the scanner (see above), all demeaned; d, ten drift confounds (see above); m, two measures of head motion ; and h, volumetric scaling factor needed to normalize for head size47.To describe the full set of imaging confounds we use a notation where subscript The full matrix of imaging confounds is then:45.Any missing values in this matrix are set to zero after all columns have had their mean subtracted. This results in a full-rank matrix of 53 columns . Additional discussion on the dangers and interpretation of imaging confounds in big imaging data studies, particularly in the context of disease studies, has been published6, and we used these PCs as covariates in all of our analyses. The matrix of imaging confounds, together with a matrix of 40 genetic principal components, was regressed out of each IDP before the analyses reported here.Genetic ancestry is a well-known potential confound in GWAS. We ameliorated this by filtering out samples that were not of recent British ancestry. However, a set of 40 genetic principal components (PCs) has been provided by UK Biobank4. We therefore also carried out some analyses involving variables relating to blood pressure (diastolic and systolic), height, weight, head bone mineral density, head bone mineral content and two principal components from the broader set of bone mineral variables available . Supplementary Fig. There exist a number of substantial correlations between IDPs and non-genetic variables collected on the UK Biobank subjectshttps://jmarchini.org/sbat/) to calculate additive genetic heritabilities for the P = 3,144 traits. To estimate genetic correlations we used a multi-trait mixed model. If Y is an N × P matrix of P phenotypes (columns) measured on N individuals (rows) then we use the model:U is an N × P matrix of random effects and ε is an N × P matrix of residuals, and these are modelled using Matrix normal distributions as follows:K is the N × N kinship matrix between individuals, B is the P × P matrix of genetic covariances between phenotypes and E is the P × P matrix of residual covariances between phenotypes. We estimate the covariance matrices B and E using a new C++ implementation of an EM algorithm48 included in the SBAT software (https://jmarchini.org/sbat/).We used a linear mixed model implemented in the SBAT (sparse Bayesian association test) software (K). This RRM was calculated from the 8,428 nominally unrelated individuals using fastLMM (https://github.com/MicrosoftGenomics/FaST-LMM). We used the subset of imputed SNPs that were both assayed by the genotyping chips and included in the HRC reference panel, and so will essentially be hard-called genotypes. In addition, all SNPs with duplicate rsids (reference SNP cluster IDs) were removed. PLINK (http://www.cog-genomics.org/plink/2.0/) was used for file conversion before input into fastLMM.For the marginal heritabilities and genetic correlation analysis we used a realized relationship matrix (RRM) for the kinship matrix  approach for RRM calculation. We ran this test on the main set of 8,428 samples and on the replication samples. For the replication analysis we used the estimates of B and E from the main set of 8,428 samples. This test was implemented in SBAT software.We used a multi-trait mixed model to test each SNP for association with different groupings of traits (Supplementary Table https://jmarchini.org/bgenie/) to carry out GWASs of imputed variants against each of the processed IDPs. This program was designed to carry out the large number of IDP GWAS required in this analysis. It avoids repeated reading of the genetic data file for each IDP and uses efficient linear algebra libraries and threading to achieve good performance. The program has already been used by several studies to analyse genetic data from the UK Biobank50. We fit an additive model of association at each variant, using expected genotype count (dosage) from the imputed genetic data. We ran associated tests on the main set of 8,428 samples and the replication samples.We used BGENIE v1.2 (10(P) > 7.5. We applied an iterative process that starts by identifying the most strongly associated variant, storing it as a lead variant, and then removing it, and all variants within 0.25 cM from the list of variants . The process was then repeated until the list of variants was empty. We applied this process to each GWAS using two filters on MAF: (a) MAF > 0.1%, and (b) MAF > 1%. We grouped associated lead SNPs across phenotypes into clusters. This process first grouped SNPs within 0.25 cM of each other, and this mostly produced sensible clusters, but some hand curation was used to merge or split clusters based on visual inspection of cluster plots and levels of linkage disequilibrium between SNPs. For some clusters in Extended Data Table Most GWAS analyse only one or a few different phenotypes, and often uncover just a handful of associated genetic loci, which can be interrogated in detail. Owing to the large number of associations uncovered in this study, we developed an automated method to identify, distinguish and count individual associated loci from the 3,144 GWASs (one GWAS for each IDP). For each GWAS we first identified all variants with –log10(P) > 7.5) by a Bonferroni factor  = 3.5) that accounts for the number of IDPs tested, giving a threshold of –log10(P) > 11. This assumes (incorrectly) that the IDPs are independent and so is likely to be conservative, but we preferred to be cautious when analysing so many IDPs.We adjusted the genome-wide significance threshold , autism spectrum (https://www.med.unc.edu/pgc/) and sleep duration (http://www.t2diabetesgenes.org/data/) and also seven disease traits: attention deficit hyperactivity disorder, schizophrenia, major depressive disorder and bipolar disorder (https://www.med.unc.edu/pgc/), Alzheimer’s disease (http://web.pasteur-lille.fr/en/recherche/u744/igap/igap_download.php), stroke  and amyotrophic lateral sclerosis (http://databrowser.projectmine.com/). The number of samples in each of these studies and the DOIs for the corresponding studies are provided in Supplementary Table We used linkage disequilibrium score regressionhttps://github.com/bulik/ldsc) to compute the genetic correlation between the IDP and the trait, with linkage disequilibrium measurements taken from the 1000 Genomes Project (provided by the maintainers of the LDSCORE regression software). We filtered the SNPs to include only those with imputation INFO ≥ 0.9 and MAF ≥ 0.1%. Only INFO scores for major depressive disorder, schizophrenia and attention deficit hyperactivity disorder were provided by the source studies, and so for these three analyses we applied the INFO threshold to both the SNPs from our study and also the source study. For the remaining six studies, an INFO filter was applied to the SNPs from our own study. Owing to low levels of heritability of the functional edge IDPs, all of these were removed from this analysis. As calculation of genetic correlation between traits only really makes sense if both traits are themselves heritable, we only used those IDPs with z-scores for significantly non-zero heritability greater than 4. In total, we used 897 IDPs. To account for correlations between IDPs, we used the raw phenotype correlation matrix to simulate z-scores (and associated tail probabilities) using samples from a multivariate normal distribution with that same correlation matrix.For each IDP–trait pair, we used the LDSCORE regression software . We used 24 functional categories: coding, UTR, promoter, intron, histone marks H3K4me1, H3K4me3, H3K9ac5 and two versions of H3K27ac, open chromatin DNase I hypersensitivity site (DHS) regions, combined chromHMM/Segway predictions, regions conserved in mammals, super-enhancers and active enhancers from the FANTOM5 panel of samples. For each IDP, the enrichment of each functional category was summarized as the proportion of h2 explained by the category divided by the proportion of common variants in the category. For each IDP and each annotation we used the two-sided enrichment P value as reported by the LDSCORE regression software. We labelled those P values as enriched or depleted depending on whether the enrichment estimate was greater or less than 1. We stratified these P values accordingly into 23 groups of IDPs.We used the LDSCORE regression software to carry out the heritability enrichment partitioning analysis into different functional categories (http://www.fmrib.ox.ac.uk/ukbiobank/gwaspaper/). Pre-compiled binaries for the latest version of BGENIE and SBAT are available at https://jmarchini.org/software/. This software is currently licensed free for use by researchers at academic institutions. Commercial organizations wishing to use these packages must enquire about a licence from the University of Oxford. Brain image processing was largely carried out with FSL  and further Matlab-based preparation of IDPs and imaging confounds utilized code from FSLNets (https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FSLNets).Most of the software and code used in this study are publicly available, including custom Matlab scripts used to prepare IDPs for GWAS (Further information on research design is available in the Any methods, additional references, Nature Research reporting summaries, source data, statements of data availability and associated accession codes are available at 10.1038/s41586-018-0571-7.Supplementary InformationThis file contains Supplementary Notes. It includes a glossary of MRI terms, winner’s curse correction of post-hoc power analysis of replication studies, further detail for SNP associations with imaging phenotypes, and genetic correlation with neurodegenerative, psychiatric and personality traits.Reporting SummarySupplementary FiguresThis file contains Supplementary Figures S1-S22.Supplementary TablesThis file contains Supplementary Tables S1-S13.


Triticum durum Desf.), grown under rainfed conditions in different Mediterranean environments in Southern Spain . The findings show a total of 37 marker-trait associations (MTAs) which affect phenotype expression for three quality traits . MTAs could be mapped on the A and B durum wheat subgenomes  through the recently available bread wheat reference assembly (IWGSC RefSeqv1). Two of the MTAs found for quality traits (gluten index and SDS) corresponded to the known Glu-B1 and Glu-A1 loci, for which candidate genes corresponding to high molecular weight glutenin subunits could be located. The GS prediction ability values obtained from the breeding materials analyzed showed promising results for traits as grain protein content, sedimentation and gluten indexes, which can be used in plant breeding programs.Climatic conditions affect the growth, development and final crop production. As wheat is of paramount importance as a staple crop in the human diet, there is a growing need to study its abiotic stress adaptation through the performance of key breeding traits. New and complementary approaches, such as genome-wide association studies (GWAS) and genomic selection (GS), are used for the dissection of different agronomic traits. The present study focused on the dissection of agronomic and quality traits of interest  assessed in a panel of 179 durum wheat lines ( Triticum durum) is one of the most important crops in the Mediterranean diet. It is mainly grown in the Mediterranean basin  and oduction . Associaoduction  based onoduction . It has oduction , 8, qualoduction , 10, biooduction , 12 and oduction , 14.While MAS uses markers which are significantly linked to qualitative traits, and is integrated with traditional phenotypic selection and long selection cycles , genomicThe application of GS in plant breeding programmes is possible due to the availability of high-throughput molecular markers, which cover the entire genome and facilitate trait value prediction , 23, 24.Durum wheat is well-adapted to semi-arid and arid environments as the Mediterranean , despiteSeveral AM and GS analyses of yield and quality traits in durum wheat, were performed in limiting environments , 33–35. http://www.aetc.es/). This cropping area presents different macro-environments, which differ in temperature and quantity of precipitations. These unpredictable conditions result in important abiotic stresses, mainly drought and/or heat stresses, which strongly affect the final phenological stages, such as anthesis and grain filling [The present study was carried out in different areas in Southern Spain , which produces the 70% of the Spanish durum wheat production  due to the high clay soil content. Fields were managed following the standard agricultural practices in each location . The trials were planted in 7.2mlocation  and all 3, SDS), whole grain protein , yellow colour (YC) and grain yield . IAS was the only trait which was visually assessed at the field trials, and consists of evaluating the seedling vigour and amount of soil covered as a value, that for elite material falls within a typical 5–10 range . For quality assessment, SW and WGP were measured using Near-infrared spectroscopy (NIRs), following Williams and Norris [Seven agronomic traits were evaluated at different stages of development: initial agronomic score (IAS), specific weight , gluten index , sedimentation index ik was the genotype-by-location interaction effect of the ith genotype in the kth location, and εikn was the corresponding residual. Only μ and gi were treated as fixed effects.The adjusted entry means for each year for the association mapping study was estimated based on the following model:pij was the trait performance of the ith genotype in the jth year, μ was the intercept, gi was the genetic effect of the ith genotype, yj was the effect of the jth year, and εij was the corresponding residual. Only μ and gi were treated as fixed effects. The adjusted means over the years were used to calculate the phenotypic correlation (Pearson correlation coefficient) across the traits.The adjusted means of each genotype over the years was estimated with the following model:pimn was the trait performance of the ith genotype in the nth replication of mth environment (year-by-location combination), μ was the intercept, (gt)i was the genetic effect of the ith tester, (gc)i was the genetic effect of the ith candidate, em was the effect of the mth environment, and εimn was the corresponding residual. Only μ was treated as a fixed effect. The variance components for experimental lines and durum wheat varieties were extracted separately by using the ‘dummies’ package in R. The significance of variance component estimates was tested by model comparison with likelihood ratio tests where the halved P values were used as an approximation [Nr.Env and Nr.Rep represent the number of environments and number of replicates, respectively.To provide an overview of the different sources of the phenotypic variation for both experimental lines and released varieties and to estimate heritability, we fitted the following model:ximation . Broad-spimn was the trait performance of the ith genotype in the nth replication of mth environment (year-by-location combination), μ was the intercept, gi was the genetic effect of the ith genotype, em was the effect of the mth environment and εimn was the corresponding residual. Only μ was treated as a fixed effect. Broad-sense heritability was estimated for released varieties as To extract the overall variance components for the tester population, we fitted the following model:Tru1I) from ThermoFisher before the DartSeq analysis. The results were visualized by electrophoresis in a 0.8% agarose gel. DartSeqTM genotyping and mapping of the corresponding markers of the wheat genome sequence from the International Wheat Genome Sequencing Consortium (IWGSC) was performed at Diversity Arrays (diversityarrays.com), as described by Sukumaran et al. [Plant tissue samples were obtained at the 4-leaf stage and the tissue was immediately frozen using dry ice. The DNA was isolated using approximately 100mg of frozen leaf and the DNeasy Plant Mini Kit from Qiagen, following the manufacturer’s instructions. The concentration and quality of the DNA samples were assessed by electrophoresis in a 0.8% agarose gel using lambda DNA as the standard. The absence of nucleases in the DNA samples was checked by performing an incubation at 37°C using a restriction enzyme  below 5% were filtered out and a missing ratio over 5%. After quality control, 16,383 DArT and 5,649 single-nucleotide polymorphism (SNP) markers remained. The remaining missing values were imputed following He et al. . The kinThe population structure was assessed applying principal coordinates analyses (PCoA) based on modified Rogers’ distances  using thY stands for the adjusted entry means of the genotypes per year, a is a vector of group effects, β is a vector of year effects, s is a vector of SNP effects, u is a vector of polygene background effects and e is a vector of residual effects. W, X, S, and Z are incidence matrices relating Y to a, β, s, and u, respectively. To check whether the population structure was adequately controlled by the model, a QQ-plot was drawn, based on the observed P-values and expected P-values of all markers. The significance of marker-trait associations was tested with the Wald F statistic. The false discovery rate (FDR) controlling procedure [2) was estimated using analysis of variance (ANOVA) with QTLs reordered according to the P-values, and the effects of detected QTLs were estimated using a standard multiple regression approach. The genome-wide associations study (GWAS) was performed using the software ASREML-R. Associated DartSeq and SNP markers were blasted against the wheat reference assembly RefSeqv1 (IWGSC 2018) with no indels or mismatches allowed, using an ad hoc Java program, to confirm their physical mapping location on the A or B genomes. For candidate gene identification, the results were filtered selecting those hits with best e-value for each marker and the candidate genes were manually selected based on gene annotations. Differential gene expression analyses were carried out using RefSeqv1 gene models and two R libraries .The following mixed linear model was used for association mapping:rocedure  was used2 was used. This value was estimated between any pair of markers within one chromosome. To determine the genome-wide linkage disequilibrium, mapped SNP markers were used in the panel of 179 wheat lines. The calculations were made using Python to establish the average LD decay.For linkage disequilibrium (LD), the algorithm RY is the adjusted entry means over the years, 1n is the vector of ones, n is the number of genotypes, a was the additive marker effect, Z is the design matrix for additive effects of the markers and ε is the residual.Based on the adjusted entry means over the years, a ridge regression best linear unbiased prediction (RR-BLUP) was applied. Details of the implementation of the models have been described earlier . BrieflyThe prediction ability, which was defined as the Pearson’s correlation coefficient between predicted values and adjusted entry means, was checked by five-fold cross-validation. 1000 cross-validation runs were performed and for each run, four fifths of the genotypes were randomly sampled as a training population to estimate marker effects, which were then used to predict the performance of the remaining genotypes. Genomic prediction was applied separately to SNP and DArT markers.To verify the appropriateness of the assessed breeding trial design  for the subsequent statistical analyses, yield correlations were analysed among the three replicates of the varieties at the two sites, and found mean estimates of 0.70 (ranging from 0.42 to 0.97).2) was specific weight (SW) with h2 = 0.71, followed by initial agronomic score (IAS) and whole grain protein (WGP) with h2 = 0.63 and h2 = 0.61, respectively. As expected, the h2 value for YIELD was low (h2 = 0.13). For released varieties, the traits with the highest heritability values were GI, IAS and SDS, with h2 = 0.88, 0.85 and 0.80, respectively. The heritability of WGP was also higher in the released varieties (h2 = 0.74) than in the experimental lines (h2 = 0.61). In contrast with the experimental lines, for released varieties the SW presented low heritability (h2 = 0.30), while the YIELD showed a high value (h2 = 0.85), probably as consequence of the reduced number of analysed varieties.Variance components of the total samples are shown in The phenotypic correlation values presented a wide range. The highest value observed was r = 0.53 between GI and SDS, followed by SDS—WGP (r = 0.37), SW—YC (r = 0.36) and SW–YIELD, and also WGP—YC (both r = 0.30). SDS and YIELD showed an intermediate value of r = 0.24. The lowest values were found for GI-IAS, GI-SW, IAS-SDS, GI-YC, WGP-YIELD, IAS-WGP and YC-YIELD (ranging from 0 to 0.07) .A total of 5,711 SNPs and 14,979 DArT markers were mapped across the two constitutive genomes of durum wheat. In the case of SNP markers, 44% of the markers were located on the A genome and 56% on the B genome. The highest marker density was found in chromosomes 1B, 2B, 5B and 7A with a total of 558, 550, 512 and 496 markers, respectively. Chromosomes 4B and 5A showed the lowest number of located loci . For DArT markers, 41% of the markers were placed on the A genome and 59% on the B genome. The highest marker density was found in chromosomes 3B, 1B, 2B and 6B with a total of 1,593, 1,439, 1,427 and 1,416 loci, respectively. Chromosomes 4B and 5A contained the lowest number of loci  .2 value between marker pairs fell below 0.2 at around 1 to 5cM , followed by DArT22904 and DArT26318, both unmapped, with effects of 11.52 and 10.50, respectively. We can also highlight marker effects for DArT1762 and DArT6596, placed on chromosomes 1B and 3A, with values of 9.85 and 9.52, respectively. Linked to SDS, the markers DArT26104 (unmapped) and DArT24559, placed on chromosome 1A, showed effects of 7.37 and 5.46, respectively. Finally, for SW, the marker effects had a narrower range from 0.1 (DArT2892) to 1.62 (SNP2318). Two major associations were detected, one for GI  and one for SDS , based on Flint-Garcia et al [2 detected in AM analysis.After analysis of the seven agronomic traits assessed, 37 MTAs were found for three quality traits  . Twenty https://plants.ensembl.org/Triticum_aestivum/Info/Index) showed that two DArT markers were related to some important proteins with nutrient’s reservoir activity (DArT1744 (located in chromosome 1BL) was associated with GI, and corresponds to the Glu-B1 locus [TraesCS1B01G570600LC.1 (3278kb from the marker) encoding a Glu1B y-type HWM glutenin subunit; and TraesCS1B01G330000.1 (8414kb), encoding a Globulin 1 protein. The marker DArT24559 (located in chromosome 1AL) was associated to SDS, and corresponds to the Glu-A1 locus. It is located closed to three HMW subunit genes: TraesCS1A01G317500.1 (-3016kb from the marker) encoding a Globulin 1 protein; TraesCS1A01G466400LC.1 (-17452kb) encoding a Glu1Ay; and TraesCS1A01G466500LC.1 (-7321kb) encoding a Glu1Ay protein. Differential expression analyses highlighted two of these high confidence genes, TraesCS1B01G330000.1 in chromosome 1BL, and TraesCS1A01G317500.1 in chromosome 1AL  over the different locations and years of assessment. This is in agreement with Gonzalez-Ribot et al. [2 = 0.24), in unrelated high-yield durum lines grown under water stress in Mediterranean environments.Yield is greatly influenced by both environmental conditions and genotype , 55, rest et al. , who obtAs previous studies highlighted –64, yiel2 = 0.62) in comparison with previous studies [Blanco et al.  emphasis studies , 72 repo2 = 0.88) and SDS (h2 = 0.80), and also a positive correlation between them (r = 0.53).Gluten strength (GStr) is a highly significant trait in durum wheat , in direThe genome-wide association analysis is becoming a popular approach to dissect the genetic base of complex traits in durum wheat. Previous AM and QTL mapping studies found QTLs involved in quality traits in most of chromosomes , 75–79. 2:7, F9 or double haploids, respectively). Bread wheat MTA studies also found major QTLs associated with SDS in this chromosome [Markers found in association with SDS were all located on chromosome 1B (0.06–16.14% of phenotypic variation), consistent with previous studies across environments and conditions, which used different marker types and populations , 79, 85 romosome , 86.Finally, novel MTAs for SW were found on chromosomes 1A, 2A and 3A (0.58 to 5.79% of phenotypic variation). Studies in durum and bread wheat, carried out in a wide range of environments and conditions, placed markers in association with this trait in several other chromosomes , 75, 84.Gli-B1 locus, consistent with the previous selection carried out for the favourable γ-gliadin 42 allele in this elite material, we could detect MTAs for the Glu-B1 [Glu-A1 [DArT1744 and DArT24559). By blasting both markers, we have precisely mapped the Glu-B1 and Glu-A1 loci on the wheat reference genome (IWGSC 2018) and proposed the corresponding candidate genes among the gene models annotated as HMW subunits (Glu-A1 locus [DArT1744 (chromosome 1BL) associated with GI, was found close to the gene models TraesCS1B01G570600LC.1 and TraesCS1B01G330000.1, encoding for HMW glutenin subunits (a Glu1B y-type and a Globulin 1 proteins respectively). The locus Glu-B1 was previously located within a meta-QTL (MQTL6) which contains several QTLs for yield components and gluten strength [DArT24559 (chromosome 1AL), in association with SDS, was located within MQTL6 [TraesCS1A01G466400LC.1, TraesCS1A01G466500LC.1 and TraesCS1A01G3175 00.1), also encoding HMW subunits (Glu1A y-type and a Globulin 1). These novel markers and candidate genes located on the RefSeqv1 wheat genome reference [Glu-B1 and Glu-A1 loci are new resources for durum wheat breeding and support the potential of the GWAs approach.The relationship between durum wheat gluten strength and HMW- glutenins is well known and controlled by major loci . While we Glu-B1 , 87, 88  [Glu-A1  loci ) and several conditions; or Bentley et al. [The use of models focused on genomic prediction in wheat breeding programs reduces the breeding cycle, giving an increase in genetic gains. Nevertheless, genomic prediction studies taking into account the genotype-by-environment (GxE) interactions are still reduced on durum wheat . In thisy et al.   are similar to those reported by Sukumaran et al.  , sedimentation index (SDS) and specific weight (SW)), which is of great importance for the final durum wheat product, and presented a wide range of effects in the phenotype expression. Most associated DartSeq and SNP markers were mapped to the A and B bread wheat sub-genomes using the available closely-related bread wheat reference IWGSC RefSeqv1. The application of GS was successful for most of the traits in the breeding materials analysed and showed promising results, especially for quality traits such as grain protein content or those in which MTAs were found . GS showed promising results which support its use in current plant breeding programmes. These results can be used in current plant breeding programmes for key quality traits in durum wheat under Mediterranean rainfed conditions with a limited water supply.S1 FigGlu-A1 and Glu-B1 loci in chromosomes 1A and 1B.Analysis of candidate genes found in  Differentially expression was indicated for each gene: SFS—severe stress field conditions; MFS—mild field stress conditions; P1h - osmotic stress as polyethylene glycol (PEG) 1hour; P6h - osmotic stress PEG 6hours.(TIFF)Click here for additional data file.S2 Figst April to 30th June. ; Tmax: maximum temperature (°C); GDD: Growing Degree Days, thermal sum using 4°C as base temperature).a) Relation between yield and maximum temperature mean (°C) by location and year for durum wheat varieties for final stages; b) Relation between yield and thermal sum from 1(TIFF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 TableMean, maximum and minimum values for temperature (maximum temperature (Tmax), average temperature (Tmed) and minimum temperature (Tmin)) (°C), rainfall (Pp) (mm) and evapotranspiration (Eto) (mm/day) for the five locations assessed. Daily values are also include in separated sheets for each location.(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S8 Table(XLSX)Click here for additional data file.S9 Table(XLSX)Click here for additional data file.S10 Table(XLSX)Click here for additional data file.S11 Table(XLSX)Click here for additional data file.S12 Table; SW, specific weight (g); YC, yellow colour; GI, gluten index (%); SDS, sedimentation index (cm3); and YIELD, yield (Kg/ha)). Means were calculated for three replications of the durum varieties at the five locations, and one plot per genotype for experimental lines at two sites.(XLSX)Click here for additional data file.