Understanding how natural selection has shaped genetic architecture of complex traits is of importance in medical and evolutionary genetics. Bayesian methods have been developed using individual-level GWAS data to estimate multiple genetic architecture parameters including selection signature. Here, we present a method (SBayesS) that only requires GWAS summary statistics. We analyse data for 155 complex traits (n = 27k–547k) and project the estimates onto those obtained from evolutionary simulations. We estimate that, on average across traits, about 1% of human genome sequence are mutational targets with a mean selection coefficient of ~0.001. Common diseases, on average, show a smaller number of mutational targets and have been under stronger selection, compared to other traits. SBayesS analyses incorporating functional annotations reveal that selection signatures vary across genomic regions, among which coding regions have the strongest selection signature and are enriched for both the number of associated variants and the magnitude of effect sizes. Methods to study how natural selection shapes genetic architecture of complex traits rely on individual level genome-wide association study (GWAS) data. Here, the authors present a Bayesian method using GWAS summary statistics to study genetic architecture and apply this to 155 complex traits. A negative relationship between effect size and MAF is a signature of negative (or purifying) selection3, which prevents mutations with large deleterious effects becoming frequent in the population. Understanding how natural selection has shaped genetic variation helps researchers to improve experimental designs of genetic association studies4 and the estimation of SNP-based heritability (the proportion of phenotypic variance explained by the SNPs)9. Inference on natural selection is also a critical step towards the understanding of the genetic architecture of complex traits. For instance, the theory of negative selection10 explains why the effects of common variants identified by genome-wide association studies (GWAS) are unlikely to be large12.The joint distribution of SNP effect size and minor allele frequency (MAF) is an essential component of the genetic architecture of human complex traits and is influenced by natural selectionS) in the model13. We detected negative 15. The BayesS model also allows us to estimate the SNP-based heritability and polygenicity (the proportion of SNPs with nonzero effects) to better describe the genetic architecture for a trait. The application of BayesS has been restricted to GWAS samples with individual-level genotypes but for most common complex diseases, only summary-level data are publicly available. Moreover, despite the implementation of a parallel computing strategy13, it remains computationally challenging to run BayesS for biobank-scale data, as the computing resource required increases linearly with the number of individuals or SNPs.We have recently developed a Bayesian method (BayesS) to estimate the effect size–MAF relationship, which was considered as a free parameter (16 (UKB) data and other published studies25, followed by time-forward simulations26 for evolutionary inference and SBayesS analyses that incorporated functional genomic annotation data. We detect widespread signatures of negative selection in the genetic architecture across 155 complex traits with a predicted mean selection coefficient of ~0.001 and a predicted mean proportion of human genome sequence being mutational targets of ~1%, among which common diseases show a relatively higher mean selection coefficient and a relatively smaller number of mutational targets. Meta-analysis across traits reveals differential signatures of negative selection across functional genomic regions, among which coding regions have the strongest selection signature and are enriched for both trait-associated variants and those with large effect sizes.In this study, we enhance the BayesS model such that the analysis only requires GWAS summary statistics and a sparse linkage disequilibrium (LD) correlation matrix from a reference sample. This method (referred to as Summary-data-based BayesS or SBayesS) opens an opportunity to disentangle the genetic architecture of complex traits (including diseases) using publicly available data sets of the largest sample sizes to date, with merely a small fraction of the computational resource required for BayesS. We perform extensive analyses to benchmark between SBayesS and BayesS, and apply the SBayesS methods to GWAS summary statistics from the full release of the UK Biobank13, namely SNP-based heritability (π) and the relationship between MAF and effect size (S), all of which are defined with respect to a certain set of SNPs (see the definition of 5). BayesS requires individual-level data. SBayesS is an extension of BayesS, but only requires GWAS summary statistics of the SNPs and LD information from a reference sample . Convergence is only concluded if all the three key parameters converge, which may not occur if the LD matrix from a reference sample is too divergent from that of the GWAS sample, or if the summary statistics are generated from a GWAS with low power or contain uncorrected population stratification, poor imputation or other errors such as misreported per-SNP sample size and allele frequency.BayesS is a method that can estimate three key parameters to describe the genetic architecture of complex traits by a Bayesian mixed linear model28, which point out a possible lack of fit of a point–normal mixture model to some traits, we further extended SBayesS to a multi-component mixture model (referred to as SBayesRS), following the framework of SBayesR29. In SBayesRS, each SNP effect is assumed to have a mixture of a point mass at zero and three normal distributions with mean zero and variances that differ by a factor of 10 (see the “Methods” section). This flexible prior accounts for a more complex genetic architecture with a spectrum of very small to very large effect sizes. The S parameter and overall polygenicity are estimated based on the SNPs across all nonnull mixture components.In light of recent studiesTo better understand the variability of regional genetic architecture in different parts of the genome, we incorporate functional genomic annotations into SBayesS to allow the three key parameters to vary in different annotation categories, e.g., coding, regulatory and repressed regions. We performed the functional partitioning SBayesS analysis (denoted SBayesS-strat) based on a two-component model that fitted SNPs in one annotation as the first component and the rest of the SNPs as the second component (see the “Methods” section). During MCMC sampling, the enrichment of a parameter in an annotation category is computed as the ratio of the sampled value of the parameter in the category to that for the whole genome (see the “Methods” section).n > 100k) as analysed in Zeng et al. 13. We used the HapMap3 SNPs as they were optimised to tag common genetic variants30 and are widely used in the literature which improves the comparability of our results with those generated using published GWAS summary statistics. Hence, the reported parameters are specific to this SNP set. For ease of computation, we used unrelated individuals of European ancestry from the interim release of the UKB data for the BayesS analysis (maximum n = 120k across traits) and the same data to generate GWAS summary statistics for the SBayesS analysis. We show in Fig. r = 0.998 for π and 0.965 for S).We ran both SBayesS and BayesS with ~1.1 million HapMap3 SNPs with MAF ≥ 0.01 for 18 quantitative traits  decreased from 50k to 20k but notable inflation in nref further decreased to 4k , we ran GWAS with sample sizes ngwas = 120k and 350k and found highly consistent parameter estimates between SBayesS and BayesS regardless of ngwas . Furthermore, with both nref = 50k and ngwas = 300k held constant, we benchmarked BayesS and SBayesS in a few different scenarios where the LD reference was a subset of the GWAS sample, an independent sample from the same or slightly different population, or a sample of different ancestry. The performance of SBayesS was almost independent of the overlap between the GWAS and LD reference samples as long as they are from the same population but started to deteriorate when the genetic discrepancy between GWAS and reference samples increased  region although the SBayesS results with and without the MHC region were very similar  had about 5%  SNPs with nonzero effects. The least polygenic traits were prostate cancer, age at menopause and male pattern baldness, which were affected by about 0.1–0.3% (1000–3000) common SNPs. The estimate of S was significantly negative (P < 0.001) in all the traits analysed (median On average across the 44 complex traits (including diseases), 1.8% of the 1.1 million common HapMap3 SNPs explained 18% of the phenotypic variance Fig. . The estmentclasspt{minima28. The absolute median value of We used the UKB classification code to classify the 44 traits into four categories related to disease, reproduction, physical measures, and cognition  for 274 UKB traits, among which 130 passed the convergence test and 110 of these were not included in the analyses above  and mutational heritability  to generate causal effects of the mutations on the focal trait (see the “Methods” section). Based on the LD correlation matrix computed from the unrelated individuals in the final generation of the simulated data, we directly simulated GWAS summary statistics with an equal sample size as in the UKB data analysis38 (see the “Methods” section). The genetic architecture parameters π and S were estimated by SBayesS and SBayesRS using 36k SNPs randomly sampled from the common sequence variants, a comparable SNP density to that of the 1.1 million HapMap3 common SNPs used in the real trait analysis .Although a negative estimate of πm and πm and S and used it as a proxy of the true value (see the “Methods” section). Regarding to the different distributions of selection coefficients, the true values of S were not highly correlated , suggesting the distribution of selection coefficient plays a role in determining S. Compared to the true value of S, the SBayesS estimate based on the causal variant genotypes tended to be more negative when selection strength was weak and selection coefficients followed a mixture distribution  Fig. –17. In aion Fig. . This ision Fig. . Compareπm and −4 and 10−3 with a mean of 0.0007 across traits . Compared to physical measures (mean πm = 0.011), the mean πm was significantly lower for disease  and was significantly higher for cognitive traits .While the predicted ies Fig. . Common 15. We excluded continuous annotations and annotations with flanking windows, resulting in 21 annotation categories such as the coding, regulatory, repressed and conserved regions  is the number of SNPs with nonzero effects in category c). While the fold enrichment of The functional annotation categories used in our analysis were from the LDSC baseline modelons Fig. , suggestons Fig. . The medTSS Fig. . The neg41 for most annotation categories  to the τ parameter in Eyre-Walker’s model3 and further drew inference on the average genome-wide selection coefficient. However, our forward simulations have shown that inference regarding the strength of selection cannot be made based solely on S but should take into account other genetic architecture parameters as well as the distribution of effect sizes. Despite the narrowly distributed 43. Our results suggest a relatively small mutational target size but relatively strong selection on variants for common diseases and relatively large mutational target size for cognitive traits, in line with the previous finding that brain-related traits are highly polygenic and the associated genetic variants are likely under strong selection11.Most traits had ude Fig. . By extrπ represents the proportion of SNPs with nonzero effects; this definition has also been used previously47. Our forward simulations showed that π is driven by both the mutational target size and selection strength, with increased average selection coefficient resulting in decreased 11 proposed an alternative definition of polygenicity, the effective number of independently associated variants or Me, which accounts for the distribution of per-SNP heritability across the genome. Despite the difference in definition, both π and Me estimates varied with the number of causal variants under different scenarios  with a regression slope of Me estimates = 3.4. This is highly consistent with the result reported in O’Connor et al. that their Me estimates were highly correlated with the estimates from our previous study13 for a number of traits (r = 0.9) but 4× smaller .Our polygenicity parameter πm and Since we only detected signatures of negative selection in real traits, our evolutionary simulations focused on the models of negative selection. To investigate the impact of both negative and positive selections, we extended our simulation scenarios by considering two additional positive selection-related parameters: average positive selection coefficient and proportion of beneficial mutational targets (see the “Methods” section). When considering both negative and positive selections in the simulations, we observed more complicated relationships between the genetic architecture and evolutionary parameters  with significant enrichment of per-NZE heritability, likely because of the coding mutations by nature having larger effect sizes and/or a mixture of negative selection on coding mutations with detrimental effects and positive selection on those with favourable effects. It is surprising to observe a relatively large S was closer to zero in the simulations considering both positive and negative selections than in the simulations only considering negative selection , which may not be an unbiased estimator of the number of causal variants (mC) especially when the causal variants are not observed. For example, mNZ will tend to be smaller than mC if some causal variants are not well tagged by any SNP markers but tend to be larger than mC if they are in high multi-locus LD with a number of SNPs. Thus, our polygenicity estimate should be best used to compare traits using the same set of SNPs, rather than an unbiased estimate of the number of causal variants. Fourth, we did not attempt to predict the evolutionary parameters for functional genomic categories because it would require simulating a genome with functional partitioning. Despite these limitations, our study highlights the impact of negative selection on the genetic architecture across complex traits and in different functional genomic regions. In addition to a better understanding of the genetic architecture, our methods can also be applied to genetic mapping and polygenic risk prediction through the use of the joint SNP effect estimates or the characterised underlying distributions of effect sizes as prior knowledge for other methods49.There are several limitations in this study. First, our inference on negative selection is based on HapMap3 common SNPs and therefore may not hold for the unobserved rare variants. In fact, we found by forward simulations a weaker magnitude of y is the vector of phenotypes adjusted for all fixed effects, X is the column-centred genotype matrix, β is the vector of SNP effects, and e is the vector of residuals with j is hj = 2pjqj, where pj is MAF and qj = 1 − pj. Let D be a diagonal matrix with nj is per-SNP sample size. Multiplying both sides of the equation by D−1X′ givesD−1X′ y = b, the vector of least-squares estimates of SNP marginal effects from GWAS, and 50. Let ε = D−1X′e. Then, the above equation can be written as35. As in BayesS, we assume the effect size is related to MAF through a parameter S:ϕ is a point mass at zero, and S (the relationship between MAF and effect size), π  are considered as unknown, with prior distributions of a standard normal, a scaled inverse chi-squared distribution (Supplementary Note), and a uniform distribution between zero and one, respectively. Specifying a different prior distribution to βj gives a form of other summary-data-based Bayesian alphabet models29.Let us consider an individual-level data-based multiple regression model for a GWAS cohort:entclass1pt{minimab) and LD correlation matrix (B) are sufficient statistics for the joint posterior distribution of β (Supplementary Note). Compared to model  and 2) are equivalent in terms of posterior inference because the GWAS estimates of SNP effects ( and (2)  are equi27, we estimated the posterior variance byT is the chain length, W is the within-chain variance, and B is the between-chain variance.We used MCMC algorithm to generate 50,000 posterior samples  from the joint posterior distribution of model parameters, based on which statistical inference was made. Details of the MCMC sampling scheme are shown in the Supplementary Note. The posterior mean was used as the point estimator, with the statistical uncertainty quantified by the posterior variance or its square root (posterior standard error), as shown below. We ran four parallel chains with different starting values of the parameters randomly sampled from their prior distributions. Following the method proposed by Gelman and RubinTo assess convergence in MCMC, we computed the potential scale reduction statistic51P < 0.0016). This is equivalent to a r2 threshold of 2 × 10−4 given a sample size of 50,000, resulting in each SNP, on average, being in LD with ~1000 SNPs on the same chromosome. We set ρjk = 0 but njk. This would inflate the residual variance and therefore deflate the heritability estimate. If a type II error occurs, i.e., ρjk ≠ 0 but For computational efficiency, we used a sparse LD matrix in the analysis where LD due to sampling variation were set to be zero. To this end, we tested whether LD between each pair of SNPs on the same chromosome is zero in the population when computing the LD correlation matrix using a reference sample. Under the null hypothesis that the true LD in the population is zero, we assume13, we computed the genetic variance β in each MCMC iteration. As described in Zhu and Stephens35, this is equivalent to the following quadratic term of β given the LD correlation matrix:r = Db and radj is the adjusted r for β. The residual variance  is that it allows the estimation of S in a specific functional annotation category. Compared to a recently published method, BLD-LDAK-Alpha9, that estimates the S parameter (denoted by α in their model) based on an infinitesimal model, our method accounts for a sparse genetic architecture. In addition to the estimation of per-SNP heritability, polygenicity and S for each category, we also defined per-nonzero-effect (per-NZE) heritability  by performing an eigen decomposition on the phenotypic correlation matrix55:λi is the ith eigenvalue of the phenotypic correlation matrix. Then, the posterior standard error of the mean was computed asWe combined the SBayesS-strat estimates across traits by calculating the median fold enrichment for each functional category. We reported the median instead of the mean in order to minimise the impact of outliers, especially for the per-NZE heritability estimate for which the denominator  is often estimated with large sampling variance. To account for the phenotypic correlation among the traits, we estimated the effective number of traits 57 and the imputed data provided by the UKB team16. We filtered HapMap3 SNPs30 with MAF < 0.01, HWE test P value < 1 × 10−6, missing genotype rate > 0.05, or imputation info score < 0.3. We further excluded SNPs in the Human Major Histocompatibility Complex (MHC) region, resulting in a total of 1,124,198 common SNPs for the analysis. The LD correlations in the reference samples were computed based on the effect alleles in the GWAS summary data. For quantitative traits, we standardised phenotypes to mean zero and variance one after removing the outliers (phenotype > 7 SD) and performed rank-based inverse normal transformation (RINT) within each sex group. Prior to GWAS, we pre-adjusted phenotypes by age, sex and first 10 principal components (PCs) provided by the UKB team after RINT if applied. For the publicly available summary statistics, we downloaded the data and matched the SNPs with those in the UKB data after excluding the strand ambiguous SNPs  in addition to the QC procedures above. For the GWAS summary data from the Neale Lab, we extracted 274 quantitative traits for which the GWAS was performed based on RINT phenotypes in their analysis pipeline.We performed GWAS analyses for 26 quantitative traits and 9 common diseases in the full release of the UKB data using PLINK 1.90 beta26 to run evolutionary forward simulations. A large sequence of 100 Mb was simulated, where a proportion of new mutations (πm) that had pleiotropic effects on fitness and trait emerged at random with an average selection coefficient of 10(s) ~ U, log10(πm) ~ U and μm) was set to 1.65 × 10−8 per base pair per individual per generation58, and the recombination rate was set to 1 × 10−8. We assumed a model of negative selection (see below for a scenario with positive selection), where all trait variants were deleterious to fitness and the other mutations were neutral. The causal effects were assumed to have a mixture of three normal distributions with small, medium and large variances: πm, the mixture distribution parameter 10, L being the genome length (100 Mb). For each trait mutation, the selection coefficient was modelled by βj followed a mixture distribution, sj also followed a mixture distribution with small and large selection coefficients. To break up the perfect proportionality between selection coefficients and squared effect sizes, two pleiotropic effect models were used to remodel the trait effect of causal variant conditional on its selection coefficient toward the end of the selection process. The first model is the Simons et al.12 model which assumes the causal effect on the focal trait (denoted as 1) following the distribution βj1 ~ N with nt being the number of traits on which the variant has an effect. The second model is the Eyre-Walker’s model3: δj = 1 or −1 determined at random, Sj = 4Nesj, Ne = 10,000 being the effective population size and εj ~ N. In the Eyre-Walker’s model, τ is the key parameter and σ2 is a nuisance parameter. For each set of causal variants, we simulated causal effects based on either the Simons et al. model with nt = 1, 2, 4 or 10 or the Eyre-Walker model with τ = 0.2, 0.5, 0.8, 1.0 and σ2 = 0.1.We used SLiM337 with population bottleneck and expansion was used to simulate a population that had undergone selection for 58,000 generations. The simulation started with an ancestral base population of Ne = 7310, which was expanded to 14,474 after 52,080 generations, a long period of neutral burn-in to allow the population reach mutation-drift equilibrium (~1.3 million years assuming 25 years per generation). In generation 55,960, 1861 individuals were split from the base population into a descendant population to mimic the out-of-African dispersal. In generation 57,080, the population size was further reduced to 1032 and then increased with an exponential rate of 0.0038 until generation 58,000, reaching to a final population size of 34,039. In the last generation of selection, we obtained the genotypes of ~2000 unrelated individuals (genomic relationship < 0.05) and computed the LD correlation matrix for all common causal variants and a random sample of 36k common SNPs, a comparable density as the SNPs used in the real trait analysis . Given the LD matrix and causal effects, we directly simulated the GWAS summary statistics for all variants38: β is the simulated causal effects based on different evolutionary models , and N = 350k is the sample size in the UKB dataset (see the Supplementary Note for more details). Using this approach, we were able to simulate a GWAS data set with comparable statistical power as in the real data analysis. We then used the same methods as those used in real trait analysis  to estimate the SNP-based heritability, polygenicity and S at either common causal variants or the random set of 36,000 common SNPs . The true value of SNP-based heritability was computed as S parameter was estimated using a linear regressionα1 is an OLS estimate of S according to the BayesS model, and the residuals ϵ are independent. When the distribution of causal effects is a mixture of multiple normal distributions, fitting a single intercept or multiple intercepts with respect to the mixture components has negligible impact on the OLS estimate of S  and average selection coefficient for the beneficial alleles  ~ U. In this scenario, a new mutation can either be beneficial or deleterious with a selection coefficient as modelled above given the average positive or negative selection coefficient. Note that only the Simons et al. model was used to simulate GWAS data in this scenario as the Eyre-Walker model only fits in the context of negative selection.To incorporate positive selection, we specified two more input parameters, i.e., proportion of trait mutations being beneficial . We then applied these polynomial equations to predict the evolutionary parameters in real data for 44 complex traits.We used a polynomial regression model to predict an evolutionary parameter from the estimates of the genetic architecture parameters for complex traits. The forward simulation data under either the Simons et al.Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


UK Biobank is a major prospective epidemiological study, including multimodal brain imaging, genetics and ongoing health outcomes. Previously, we published genome-wide associations of 3,144 brain imaging-derived phenotypes, with a discovery sample of 8,428 subjects. Here we present a new open resource of GWAS summary statistics, using the 2020 data release, almost tripling the discovery sample size. We now include the X chromosome, and new classes of image derived phenotypes . Previously we had found 148 replicated clusters of associations between genetic variants and imaging phenotypes; here we find 692, including 12 on the X chromosome. We describe some of the newly found associations, focussing on the X chromosome and autosomal associations involving the new classes of imaging-derived phenotypes. Our novel associations implicate e.g. pathways involved in the rare X-linked syndrome STAR , Alzheimer’s disease and mitochondrial disorders. UK Biobank (UKB) is now approximately halfway through imaging 100,000 volunteers; the early-2020 release of brain imaging data contained data from almost 40,000 participants. This spans 6 brain MRI (magnetic resonance imaging) modalities, allowing the study of many different aspects of brain structure, function and connectivity. In conjunction with other data being recorded by UKB, which includes health outcomes, lifestyle, biophysical measures and genetics, UKB is a major resource for understanding the brain in human health and disease.1. At that point we identified 148 replicated clusters of associations between genetic variants and the phenotypes. We found links between IDPs and genes involved in: iron transport and storage, extracellular matrix and epidermal growth factor, development, pathway signalling and plasticity.Previously, we presented genome-wide association studies (GWAS) of 3,144 brain imaging phenotypes, with a discovery sample of 8,428 subjects2, reducing the likelihood of finding artefactual associations. GWAS summary statistics and Manhattan plots for all 3,935 phenotypes are freely available for download from the Oxford Brain Imaging Genetics (BIG40) web server (available at https://open.win.ox.ac.uk/ukbiobank/big40/), which also includes detailed tables of all IDPs, all SNPs (single nucleotide polymorphisms) tested, all association clusters, and an interactive viewer allowing for detailed interrogation of IDP associations with SNPs and nearby genes. We also provide a list of causal genetic variants for our top X chromosome clusters using a statistical fine-mapping approach3.We have now expanded and enhanced this work, with an almost threefold increase in sample size, an increase in the number of IDPs to almost 4,000, and with a focus on X chromosome associations carried out for the first time . The new classes of IDPs, computed on behalf of UKB and released for general access, are: subnuclei volumes in amygdala, brainstem, hippocampus and thalamus, Brodmann area FreeSurfer metrics and FreeSurfer-derived white-grey intensity contrasts. We have also greatly expanded our set of imaging confound variables4. While genetic females inherit two copies of the X chromosome, genetic males inherit only a single copy from the maternal line . The short pseudoautosomal regions (PAR) on the ends of chromosome X are homologous with parts of chromosome Y and can be analysed in the same way as autosomal chromosomes. For the non-pseudoautosomal region, a mechanism has evolved to balance allele dosage differences between the genetic sexes ; during female development, one copy is randomly inactivated in each cell. This means that maternally and paternally inherited alleles would be expected to be expressed in different cell populations within the body approximately 50% of the time. However, this dosage compensation mechanism (DC) is imperfect; it is currently thought that only 60-75% of X-linked genes have one copy completely silenced in this way5.We conducted sex-specific GWAS on autosomes (chromosomes 1-22) and the X chromosome, followed by a meta-analyses combining these, using Fisher’s method. The X chromosome accounts for about 5% of the human genome and incorporates over 1200 genes, including many which play a role in human cognition and development. However, testing for association with genetic variants on chromosome X requires special consideration4: males are treated as homozygous females with genotypes coded  according to whether they have 0 or 1 copy of the alternative allele. Joint analysis of genetic females and males with simulation studies6 suggest that type-I error control under this approach is reasonably robust to deviations from other assumptions , provided genetic sex is included as a covariate.To account for this in GWAS, it is common to assume full dosage compensation5. These studies suggest that only a small proportion of genes escape XCI, although the appropriate amount of DC shows considerable variation amongst traits. For educational attainment, Lee et al. 5 estimated a DC factor of 1.45, but concluded that little power was lost in their joint analysis irrespective of the assumed model.Recent studies have used the large sample sizes afforded by UKB to perform stratified analyses to estimate the degree of dosage compensation as a parameter across a broad variety of traits5. Nevertheless, results will be biased if the assumed DC model differs from the truth. An unweighted meta-analysis based on p-values using Fisher’s method (explored in our research), though potentially less powerful, should avoid this possible bias , and still have value in confirming signals from a joint analysis.While a joint analysis under a full DC model is a reasonable default, the power afforded by biobank-scale datasets also permits examination of possible sex-specific effects via stratified analyses. These stratified analyses can subsequently be meta-analysed; if the meta-analysis is based on estimated effects , appropriately chosen weights can give results almost the same as those from a joint genetic male/female analysis corresponding to any assumed DC modelBIG40) web server includes a summary statistics resource including results for our discovery cohort, and a full GWAS on all samples passing QC (with discovery and replication cohorts combined). A browsable interface is also provided for both of these subsets. In addition, the results of the sex-separated GWAS on chromosome X and autosomes are provided. We have also provided the summary statistics to the European Bioinformatics Institute (EBI) GWAS repository. More details about our resource are provided in Online Methods.The Oxford Brain Imaging Genetics (P) value for association that exceeds a 7.5 genome-wide significance threshold, and such that all of the pairs have variants that are close with respect to genetic distance. We assigned each of the phenotype/variant pairs to one and only one cluster. We defined a cluster as replicating if at least one of the phenotype/variant pairs had nominal significance in our replication cohort .We conducted a genome-wide association study using the 39,691 brain imaged samples in UK Biobank. We divided these samples into a discovery  and a replication  cohort. The details for the imaging and genetics processing and the cohorts are given in Online Methods. We applied automated methods for identifying local peak associations for each phenotype, and also for aggregating peaks across phenotypes into clusters of association. A cluster is a set of phenotype/variant pairs such that all of the phenotype/variant pairs have a –Log10(1 was 148). The 692 replicating clusters are distributed across all chromosomes, with between 8 and 60 clusters per chromosome. We grouped the IDPs into 17 categories (task fMRI activation category is the only category without at least one association). The number of associations per category ranges between 12 for the category volume of white matter hyperintensities (lesions) which consists of just one IDP, and 1,954 for the regional and tissue volume category. All of these associations are listed in BIG40 open web server.With these methods, we found 10,889 peak associations among all phenotypes and chromosomes , and found 1,282 clusters (692 replicating) after clustering the peak associations according to our automated methods (the number of replicating clusters reported in previous worktegories . Of the P) ≥ 11.1. (In this work we adjust for computing multiple GWAS by applying the Bonferroni correction on top of the standard GWAS threshold of –Log10(P) ≥ 7.5, resulting in a ‘Bonferroni’ threshold of 11.1.) These four clusters are investigated below, and Manhattan plots for the IDPs most associated with these clusters are displayed in Of all of our clusters of associations, 38 are on the X chromosome (12 replicating), and 4 of the X chromosome clusters have a phenotype/variant pair with association significance exceeding the more stringent Bonferroni corrected level of –Log10 as the causal genetic variant for 81/97 of the phenotype associations. The situation was similar for the other three clusters; in each case, the lead genetic variant found by our aggregation method was among the genetic variants found to be causal by CAVIAR.  The CAVIAR results are detailed in We provide a fine-mapping of the four X chromosome clusters using the CAVIAR softwarefull-scan). We also examined the heritability of each phenotype using linkage score regression7. The heritability for each of the phenotype categories is summarized in h2 value was more than one standard error greater than 0, the estimated value of h2 ranged from 0.01 to 0.41. The highest estimated heritability was found in phenotypes involved in regional and tissue volumes (as in previous work1), cortical grey-white contrast, and the intra-cellular volume fraction (ICVF) diffusion tensor imaging measure.BIG40 also provides summary statistics for a GWAS with the discovery and replication cohorts combined (a P) value of the lead association (in descending order). A summary of all replicating X chromosome clusters is provided in Full details for the lead associations for the X chromosome clusters (including clusters that do not replicate) are provided in 8. Our main GWAS analyses include sex as one of the confound variables . To assess the quality of this deconfounding, and to explore associations on the X chromosome that are driven by genetic sex, we conducted two additional GWAS in which we restricted our discovery cohort to just genetic females and (separately) just genetic males. We then combined these two additional GWAS in a meta-analysis using Fisher’s method. Clusters in our main analysis that are significant in the meta-analysis but not significant in one of the sex-specific scans may indicate sex-driven associations. Of the 12 replicating X chromosome clusters in the main analysis , one cluster (Cluster 2) is significant at the 11.1 level for one genetic sex, but not significant for the other genetic sex; Cluster 2 may therefore be driven by genetic males. To provide more direct evidence for this, we performed two-tailed z-tests to determine if the beta coefficients differ significantly between the genetic sexes. For Clusters 1 and 2, we found that the beta coefficients are nominally different . The differences between the sex-specific beta coefficients for the lead associations of Clusters 3 and 4 were not significant. Among all of our associations  with at least one of the sex-specific scans significant at the –Log10(P) ≥ 11.1 level, the signs of the effect sizes for genetic females and genetic males always matched. For significance at –Log10(P) ≥ 7.5, the signs matched 99.42% of the time . The clustering of the meta-analysis X chromosome scan produced 23 clusters. Twenty of these had lead associations within 0.25cM of one of the discovery cohort clusters derived from the original GWAS which pooled all subjects of both genetic sexes . Each of the four discovery cohort X chromosome clusters with lead association at the Bonferroni level , based on the P) values. For the sex-specific comparisons, there are SNP/phenotype pairs having reduced sensitivity compared with the original all-subjects GWAS , and other pairs with increased sensitivity (likely because a given association is stronger for the sex in question than for the other sex). The meta-analysis paired-difference distribution demonstrates that sex-separated GWAS followed by meta-analysis gives increased sensitivity to finding genetic associations in the X chromosome.The differences in sensitivity between the main GWAS , the sex-specific GWAS and the Fisher meta-analysis are visualised concisely in We now examine the four main X chromosome clusters in greater detail. The details for these additional investigations are summarized in 3.5 × 10–21) is located about 10 kb away from, and is an eQTL of FAM58A (or CCNQ). The eQTLs reported throughout this work were assessed as significant according to the Genotype-Tissue Expression (GTEx) project. Mutations in this gene lead to STAR , a rare X-linked developmental disorder recently identified9, for which notable brain variations have been observed such as incomplete hippocampal inversion, thin corpus callosum, ventriculomegaly and cerebellar hypoplasia10. In addition, while FAM58A codes for an orphan cyclin with undescribed function, it has been shown recently to interact with CDK1011. Of particular relevance considering the many white matter IDPs associated with Cluster 1, mutation of the gene CDK10 has been observed in a case study to lead to a rudimentary corpus callosum and paucity of white matter surrounding the lateral ventricles11.Cluster 1 comprises 5 SNPs, associated in total with 96 IDPs, all capturing differences in the properties of white matter tracts distributed throughout the cerebrum. This is described more in 12. This SNP is located in an intron of DUSP9 (MKP4), a gene that codes for a phosphatase whose overexpression specifically protects against stress-induced insulin resistance. This may be related to another consistent aspect of these nIDP associations with Cluster 1: the diet of UK Biobank participants with intake of sweet food and drinks .The SNPs of Cluster 1 are further associated with an array of non-imaging-derived phenotypes (nIDPs—phenotypes not derived from MRI) largely related to health (including diagnosed diseases and operative procedures), as well as some variables not necessarily health-related . Interesvs white matter intensity contrast, in limbic and temporal regions, and brain areas making up the default-mode network13. The top SNP  is located in a pseudoautosomal region of chromosome X, i.e., a genetic region homologous between chromosomes X and Y — in an intron of DHRSX, and is an eQTL of the same gene. The genetic association with the grey-white intensity contrast IDP for this SNP was mainly driven by the male UK participants (as described above). The male-dominated aspect of the association between DHRSX and the brain has also been observed in a study showing that four PAR genes, including DHRSX , are up-regulated in the blood of genetic male patients with ischemic stroke14.Cluster 2 comprises 9 SNPs associated altogether with 17 IDPs, all of which are grey matter 15.While the majority of the nIDPs associations with the SNPs of Cluster 2 were related to diagnoses and operative procedures, half of these pointed at thyroid-related issues, in addition to the nIDP of workplace temperature, which may be related to thyroid function . Remarka–15) is located in a PAR in an intron of SPRY3. This genetic variant is also an eQTL in many brain regions of a variety of genes whose mutations are involved in developmental and neurodevelopmental disorders: RAB39B, which plays a role in normal neuronal development and dendritic process, is associated with cognitive impairment16, X-linked intellectual disability17 and Waisman syndrome in particular, an X-linked neurologic disorder characterised by delayed psychomotor development, impaired intellectual development, and early-onset Parkinson’s disease18; TMLHE is associated with X-linked autism19; CLIC2, with X-linked intellectual disability20; and BRCC3, with an X-linked recessive syndromic form of moyamoya disease21. It is also an eQTL of F8, and F8A1 (DXS522E/HAP40), a likely candidate for the aberrant nuclear localisation of mutant huntingtin in Huntington’s disease. Considering the distribution of the brain IDPs in the occipital lobe, it perhaps lends additional credence to the consistent, but yet not understood, observation of volumetric and sulcal differences in these visual grey matter regions in Huntington’s disease gene carriers22.Cluster 3 includes 9 genetic variants associated with 28 IDPs of local brain volume. All 28 IDPs are located in the occipital lobe except for the volume of the brainstem and fourth ventricle. The top genetic variant  is located just <150 basepairs from ZIC3, which plays a key role in body pattern formation and left-right asymmetry. Mutations in this gene are thought to be involved in 1% of heterotaxy (situs ambiguous and inversus) in humans23. This may explain why the distribution of the higher-order grey matter regions associated with Cluster 4 follows the pattern of the fronto-parietal networks, which are notoriously left-vs-right segregated24. In particular, the supramarginal gyrus is known to show the strongest asymmetries from an early developmental stage25, and to be connected by white matter tracts that share a genetic influence with human handedness26. ZIC3 is also involved in neural tube development and closure, and mutations in this gene cause, in addition to neural tube defects and cerebellum hypoplasia, consistent histological brain alterations with abnormal laterality and axial patterning, including a disorganised cerebral cortex27.Finally, Cluster 4 comprised 8 genetic variants associated with volume of grey matter regions in the dorsolateral prefrontal cortex and the lateral parietal cortex . The top genetic variant in this cluster  ≥ 11.1, replication , and which were distinct from the loci reported in previous work34 . Of these 48 clusters, 7 involved associations with phenotypes from among the 3 new classes of UKB brain imaging phenotypes analyzed here. Of these 7 clusters, 2 (Cluster 271 with lead variant rs1368575 and Cluster 1070 with lead association rs3814883) were not related to previous brain imaging literature, and were not intergenic and were without eQTLs. The remaining 5 clusters  is in an exon and an eQTL of MARS2, a mitochondrial methionyl-tRNA synthetase, and is associated in particular with parietal TC . Mutations of MARS2 have been linked to spastic ataxia, as well as neurodevelopmental delay, and white matter abnormalities , cortical and cerebellar atrophy, as well as corpus callosum thinning36. This variant is further associated primarily with many nIDPs related to mass and body fat, as well as nIDPs involving allergy, sleep and red blood cell count and shape (according to the Open Targets Genetics platform).The first of these most novel clusters related to previous brain imaging work (Cluster 163) included 12 distinct replicated variants associated with 31 IDPs, all but two related to the contrast between the intensity of the white matter and grey matter (tissue contrast: TC) generated by FreeSurfer, widespread across multiple cortical ROIs2.4 × 10–17), associated mainly with temporal, parietal and prefrontal TC, is in an intron and eQTL of the gene PLD1. This gene codes for a phospholipid enzyme that has been shown to regulate the trafficking of the protein βAPP37, the precursor of the amyloid beta whose plaques are a critical factor in the pathogenesis of Alzheimer’s disease. Increased expression of PLD1 has been noted in the brains of Alzheimer’s disease patients both in the hippocampus and temporal lobe38, and PLD1 is upregulated in the mitochondrial membrane from brains of patients with Alzheimer’s39. The top genetic variant of this cluster is in addition related to nIDPs of red blood cell count and shape (Open Targets Genetics).The second cluster (Cluster 270) encompassed 13 replicated variants which were predominantly associated with the TC of 48 different cortical regions across the whole cerebrum. Its top variant , is associated with TC in the superior temporal cortex, and is located in an intron of HMBS, and is an eQTL of both HMBS and VPS11 in many brain tissues . The gene HMBS codes for an enzyme of the biosynthetic pathway of haem production. As such, mutations in HMBS are known to be related to acute intermittent porphyria, an autosomal dominant defect in the biosynthesis of haem. Acute intermittent porphyria manifests itself mainly as a neurological disorder, involving the autonomous, central and peripheral nervous systems, with acute life-threatening neurologic attacks. Deep cerebral white matter myelination abnormalities40, and axonal neuropathy41, have been observed in patients and animal models, as well as deficiencies in mitochondrial complexes in Hmbs mutant brain, suggesting that mitochondrial energetic failure also plays an important role in the expression of the disease42. In addition, mutations in VPS11 in 5 patients have been suggested as leading to infantile onset leukoencephalopathy with brain white matter abnormalities, severe motor impairment, cortical blindness, intellectual disability, and seizures, as well as in a significant reduction in myelination following extensive neuronal death in the hindbrain and midbrain in an animal model43. The variant rs549893 is associated with nIDPs of body mass index, body fat mass and body fat percentage (Open Targets Genetics).The third cluster (Cluster 841) consisted of 8 replicated loci all associated solely with measures of TC in 15 mainly higher-order cortical areas. We find that the lead variant in this cluster  is associated with TC measures in the supramarginal, inferior and superior parietal cortex, and it is intergenic, and is an eQTL in cortical and subcortical tissues of RMDN3/FAM82A2, coding for a regulator of microtubule dynamics. This tether protein is involved in facilitating the lipid transfer by increasing the contact sites between the endoplasmic reticulum and mitochondria, particularly in the brain44. The protein FAM82A2 was found down-regulated in the frontal and parietal lobes in patients with Parkinson’s disease with dementia, with a dramatic reduction in the activity of the mitochondrial complexes45. Recently, reduced levels of the RMDN3 protein  have also been found in the temporal cortex of the brains of Alzheimer’s disease patients, suggesting that a disruption of endoplasmic reticulum-mitochondria interactions mediated by RMDN3 might be part of the neuropathological process in Alzheimer’s 46. A proxy genetic variant for the top variant of this fifth cluster  is further associated with nIDPs of blood count and hypertension (Open Targets Genetics).The fourth genetic cluster (Cluster 1029) comprised 17 replicated loci related again predominantly to TC in 45 widespread cortical areas. The lead variant for this cluster  is associated with TC in an array for temporal, parietal and prefrontal cortical areas. This locus is in an exon of the gene CLEC18A, which codes for a C-type lectin that has only been recently characterized, and shown to be expressed in the brain, in microglia47. This locus is also part of a 40-panel of genes that make it possible to distinguish cardioembolic from large-vessel ischemic stroke with high accuracy48. A proxy locus for the top genetic variant  is further associated with measures of body mass and percentage, as well as blood count and alcohol intake frequency (Open Targets Genetics).The final interpretable cluster (Cluster 1067) comprised 31 replicated loci associated with a total of 51 IDPs of TC spread across higher-order cortical regions, as well as 19 other IDPs of cortical thickness , regional volumes  and white matter diffusion. This cluster’s most significant variant  has increased by 30%, now reaching 10 million. It is now therefore a good time to update our large-scale GWAS, now with almost 4,000 imaging-derived phenotypes - thousands of distinct measures of brain structure, function, connectivity and microstructure. The number of replicated clusters of imaging-genetic associations identified has more than quadupled since our previous work. We have made all of the GWAS summary statistics openly available via the new FAM58A (CCNQ), DHRSX, SPRY3, F8A1, F8, BRCC3, TMLHE, RAB39B, CLIC2 and ZIC3 are involved in the associations we report.We also studied brain imaging associations in the X chromosome, and autosomal associations with novel phenotypes. We identified 4 X chromosome clusters that replicate at the GWAS+Bonferroni level (increasing the standard 7.5 level according to Bonferroni correction for the number of IDPs tested). Among these four top X chromosome clusters, we find associations involving diffusion measures distributed in white matter tracts and grey/white matter intensity contrasts. We also find associations involving occipital lobe grey matter, and fronto-parietal grey matter. These associations are relevant to a diverse set of variations in brain development and pathologies including the recently identified STAR condition , Waisman syndrome, early-onset Parkinson’s disease, X-linked autism, Alzheimer’s disease and Huntington’s disease. Cardiovascular conditions such as ischemic stroke, moyamoya syndrome and premature coronary heart disease are also implicated. The X chromosome genes The X chromosome is typically understudied in GWAS, and many of the X chromosome loci we identify are now implicated in genetic associations with brain imaging phenotypes for the first time. Ploidy, the Barr body and potential confounding with genetic sex complicates X chromosome analysis. To address this, we performed sex-specific GWAS, and a meta-analysis combining the sex-separated analyses. We showed significant overlap between the sex-separated meta-analysis and the main GWAS , providing evidence against confounding . This also allowed us to investigate if a given association was sex-driven . For example, we found evidence that Cluster 2 for our brain-gene associations is driven by associations in genetic males.49. While TC shows strong changes with ageing in prefrontal, lateral parietal, superior temporal and precuneus regions—those overall demonstrating the most significant associations with genetic variants—it is unclear what underlying tissue properties might be driving these effects in the MRI signal ratio35. Here TC, being almost entirely the only type of IDP showing significant genome-wide associations with our mitochondrial-related genetic clusters, appears to be specific and sensitive to mitochondrial function. These genetic-imaging findings are likely in line with the recent discovery that mitochondrial dysfunction, which emerges early during the ageing process, might prompt the catabolism of the myelin lipids of the white matter as an adaptive response to address brain fuel and energy demand50. This catabolic process perhaps explains the results previously observed with TC in ageing35.Four of the autosomal clusters of association with grey-white tissue contrast were related to mitochondrial proteins and function. In the brain, mitochondrial disorders manifest themselves primarily as demyelinated lesions in the white matter, or as stroke-like lesions in both grey and white matter. More rarely, they present with cortical and subcortical necrosisBIG40 resource , and with freely available summary statistics. We hope that this dissemination will be valuable for the next generation of neuroscience research.Enhancing our understanding of the mapping between genotype and phenotype may lead to advances in neuroscience and improvements in outcomes for brain pathologies. Deeply phenotyped resources such as UK Biobank provide an opportunity to update the known genotype/phenotype mappings for a wide spectrum of brain imaging phenotypes as more samples and more phenotypes are released. It is crucial that such updates are provided on open platforms, accelerating the potential impact of brain imaging genetics. We have done that here with the open We describe the image processing and genetic preprocessing and the association studies, including the procedures that are X chromosome specific, and the details of our sex-specific analyses. Specific details about our protocols are provided in the Life Sciences Reporting Summary.51. After removal of subjects as part of the genetic processing (see below), we used data from 33,224 subjects. These were then randomly split into a discovery sample of 22,138 subjects  and a replication sample of 11,086 subjects . The ages in the discovery sample were: Females: mean age = 63.6 ± 7.3 years, min = 45.1, max = 81.8. Males: mean = 65.0 ± 7.6, min = 46.1, max = 81.8. In the replication sample: Females: mean = 63.7 ± 7.4, min = 46.3, max = 81.6. Males mean = 65.0 ± 7.6, min = 46.1, max = 81.0. The exact numbers of subjects vary across IDPs, according to patterns of missing data, with the maximum numbers given above (for IDPs with no missing data), and the minimum numbers being just 16% lower. The BIG40 online table listing the IDPs includes the exact number of subjects  for each IDP. The details for these IDPs  are summarized in We used brain IDPs from the “40k”  UK Biobank data release in early 2020, as processed by WIN-FMRIB on behalf of UKB52, the UK Biobank data includes 6 MRI modalities: T1-weighted and T2-weighted-FLAIR (Fluid-Attenuated Inversion Recovery) structural images, susceptibility-weighted MRI (swMRI), diffusion MRI (dMRI), task functional MRI (tfMRI) and resting-state functional MRI (rfMRI). We (and colleagues)have developed and applied an automated image processing pipeline on behalf of UK Biobank51, https://www.fmrib.ox.ac.uk/ukbiobank/fbp. This removes artefacts and renders images comparable across modalities and participants; it also generates thousands of image-derived phenotypes (IDPs): distinct measures of brain structure and function.As described in detail inhttp://biobank.ctsu.ox.ac.uk/showcase/showcase/docs/brain_mri.pdf and listed in full on the BIG40 server https://open.win.ox.ac.uk/ukbiobank/big40/).In this work we used the 3,913 IDPs available from UK Biobank, spanninga range of structural, diffusion and fMRI summary measures . In this paper we refer to all of the above 3,935 measures together as “the IDPs.” Each IDP’s Nsubjects × 1 data vector had outliers removed . We discarded subjects where 50 or more IDPs were missing .We also used 16 QC measures available from UKB, as well as 6 compact summary functional connectivity features  confounds, we used the same set of thresholds for automatic selection of these higher-order confounds. Given the slightly different set of subjects used here  compared with those in2, this resulted in the 602 ‘maximal’ set of confounds (reported in2) being reduced here to 597 confounds.The data was then split into discovery and replication samples, and the remaining steps below applied to each sample separately. Each IDP’s data vector was quantile normalised1. Of the samples, 39,944 are included among the 41,016 samples in the UK Biobank for which IDPs are available, after the genotyping quality control procedures for sample removal specified in53. We removed samples without recent UK ancestry as determined by the in.white.British.ancestry.subset variable in the file ukb_sqc_v2.txt provided in the meta-data for UK Biobank. This variable selects samples based on self reported ancestry and genetic principal component thresholds. We also remove subjects based on relatedness, forming a maximal unrelated subset using the procedures recommended in53. This results in a maximally unrelated subset of 34,298 samples with recent UK ancestry and accepted genotyping and imaging quality control. We divided this set into a discovery and reproduction cohort according to a random 2/3 and 1/3 (respective) proportion, resulting in a discovery cohort of 22,865 samples and a reproduction cohort of 11,433 samples.We consider the 488,377 samples included in the Spring 2018 release of the UK Biobank, and proceed with a preprocessing and discovery/reproduction paradigm similar to that described in53. This resulted in discovery cohorts of 22,853  for the non-pseudoautosomal region and 22,844 for the pseudoautosomal regions, and replication cohorts of 11,430 for the non-pseudoautosomal region and 11,426 for the pseudoautosomal regions .For the X chromosome, fewer samples were available after exclusions due to variation in karyotype or additional aspects of genotype quality control described in 54) and Hardy-Weinberg equilibrium (HWE). We apply filters for MAF ≥ 0.001 and INFO ≥ 0.3 and HWE –Log10(P) ≤ 7. For the X chromosome, we apply these filters using the qctool software version 2.0.1 and the -infer-ploidy-from sex flag. This implies that genetic males contribute half as much as genetic females towards MAF and INFO for the non-pseudoautosomal region of the X chromosome. Further, as has been recommended 55, for the X chromosome the HWE filters are applied after computing for genetic females only. After these filters, of the 93,095,645 genetic variants included in UK Biobank in chromosomes 1:22, 16,445,196 remain. And of the 3,963,707 genetic variants in the X chromosome, 657,883 remain .Next, we consider quality control filters for the minor allele frequency (MAF), information score (INFO53. We used the bgenie software53 to conduct the GWAS and record the effect sizes (beta), standard errors and –Log10(P) values for the associations. The effect sizes were recorded in the direction of the alternate allele. The phenotypes were scaled to have unit variance after deconfounding. The variants on chromosomes 1:22 were not scaled. Therefore, an effect size of 1.0 indicates that each copy of the alternate allele generally confers an increase in the phenotype by one standard deviation. For the non-pseudoautosomal region of X, the dosages for genetic males were scaled by a factor of 2.0 so that they lie in the range , respecting the Barr body.We performed linear association tests on the samples in the discovery cohort. We performed these tests between each of the 17,103,079 genetic variants and each of the 3,935 IDPs described above . The genotypes were provided by UKB, and details for imputation (including X chromosome imputation) and genetic principal component construction are provided inP) value for each variant . For the Manhattan plots, we applied an additional filter of MAF ≥ 0.01 to all variants. A method for extracting hits (peak associations) from a genome-wide association study was developed in1. We applied that method to extract hits from the 3,935 scans with –Log10(P) values exceeding the GWAS threshold of 7.5 , and annotated the Manhattan plots with these hits . For each of the hits, we conducted a replication analysis by performing a linear association test on the samples in the replication cohort and record the effect sizes, standard errors and –Log10(P) values for the replication. We extended the method from1 in order to automatically generate clusters. A cluster is a set of phenotype/variant pairs such that each variant in the cluster is a peak association for its corresponding phenotype, and such that all variants are within a 0.25cM (centimorgans) distance of the phenotype/variant pair with highest –Log10(P) value in the cluster. Each phenotype/variant pair identified as a hit appears in one and only one cluster. The details of this clustering method are provided in Online Methods. We provide a software package called Peaks implementing these clustering methods, and have released it under the open source BSD 2-clause license.We produced Manhattan plots for each of the 3,935 IDPs, plotting the –Log10. Summary statistics for the associations of all genetic variants (with MAF ≥ 0.001) for the discovery cohort , are available for download on the BIG40 open web server.Other methods for extracting lead associations include Bayesian methods such as CAVIARall samples in the UKB 2020 release of approximately 40,000 brain imaged samples). The genetic variants considered in this scan are the same genetic variants passing our filters for the discovery cohort reported on in this paper (with MAF ≥ 0.001). The sample size of each association test (after considering missing phenotypes and X chromosome exclusions due to aneuploidy) are also provided .We also provide for download on the BIG40 open web server the summary statistics for a version of this genome-wide association study conducted on the union of the discovery and replication cohorts considered in this study  values. We then combined these two scans in a meta-analysis using Fisher’s method58, providing a –Log10(P) value which is more strongly controlled for sex-specific effects. The equation for the combined p-value under this meta-analysis method is as follows: We also considered a scan for association on genetic male samples only, and also a scan for association on genetic females only . For these scans, in the non-pseudoautosomal X chromosome region, 11,885 genetic female samples were used, and 10,968 genetic male samples were used. For the pseudoautosomal regions, 11,882 genetic female samples were used and 10,962 genetic male samples were used. As in the main analysis, the number of samples per phenotype varies due to missingness  is the cumulative distribution function of a chi-squared random variable with v degrees of freedom, and fp and mp are the p-values of the genetic female and genetic male scans, respectively.Here Peaks which implements these methods. The Peaks software provide an implementation of the algorithm in1 (in the Identifying associated genetic loci subsection of the Methods section) for uncovering peak associations for each phenotype, and an extension to co-localization of hits across phenotypes.In genome-wide association studies with thousands of phenotypes, we must determine when two peak associations for two different phenotypes are related, in the sense that the peak variants are close together in genetic distance and/or linkage disequilibrium. For studies in which the number of phenotypes (or strength and complexity of genetic associations) amounts to only a few supra-threshold results, such matching can be done by hand by examining recombination maps and linkage-disequilibrium diagrams. Such by-hand work is not feasible for studies with thousands of phenotypes. In this work, we provide a new automated method to coregister peak associations across many phenotypes. We provide a software package P), and then assigning all lead associations for all phenotypes within 0.25cM of that genetic variant to the same cluster. The details are as follows: For each chromosome, convert the chromosome’s peak associations into an array.P) of each genotype/phenotype pair, using the O(n) running time heapify algorithm described in59.For each chromosome, convert the chromosome’s array into a binary max-heap keyed on the –Log10(O(Log(n)) time. This extracted pair is the lead association of the cluster. Then, the 0.25 cM-cover is removed from the chromosome’s heap, which is also an O(Log(n)) operation. The cluster is outputted (including the removed aspects).For each chromosome, while the chromosome’s heap is not empty, extract the maximum genetic variant/phenotype pair from the heap to create a new cluster. This can be done in n extractions and deletions the total running time is O(n Log(n)), which is optimal as it is tight to the sorting lower bound of O(n Log(n)), and since sorting is a relaxation of clustering and a lower bound of a relaxation has running time no worse than the original problem.Since there are at most To combine peak associations into clusters that span phenotypes, we use a ‘greedy’ algorithm which delivers an optimally efficient clustering of genetic variant/phenotype pairs. The algorithm works by first identifying the peak associations for each phenotype . Then, by iteratively extracting the genetic variant/phenotype pair with the top –Log10(Peaks software implementing these methods is available on github at https://github.com/wnfldchen/peaks.The open source Extended Data Figures 1 and 2Supplementary Tables 1-6


This article describes a new software (GIBBSTHUR) that provides Bayesian estimation of variance components and predictions of breeding values for ranking traits generated from equine competitions based on a Thurstonian approach. The GIBBSTHUR software was developed in FORTRAN 90 and can be executed in UNIX, OSX, or WINDOWS environments, and is freely available in a public repository (https://github.com/lvaronaunizar/Gibbsthur).(1) Background: Ranking traits are used commonly for breeding purposes in several equine populations; however, implementation is complex, because the position of a horse in a competition event is discontinuous and is influenced by the performance of its competitors. One approach to overcoming these limitations is to assume an underlying Gaussian liability that represents a horse’s performance and dictates the observed classification in a competition event. That approach can be implemented using Montecarlo Markov Chain (McMC) techniques with a procedure known as the Thurstonian model. (2) Methods: We have developed software (GIBBSTHUR) that analyses ranking traits along with other continuous or threshold traits. The software implements a Gibbs Sampler scheme with a data-augmentation step for the liability of the ranking traits and provides estimates of the variance and covariance components and predictions of the breeding values and the average performance of the competitors in competition events. (3) Results: The results of a simple example are presented, in which it is shown that the procedure can recover the simulated variance and covariance components. In addition, the correlation between the simulated and predicted breeding values and between the estimates of the event effects and the average additive genetic effect of the competitors demonstrates the ability of the software to produce useful predictions for breeding purposes. (4) Conclusions: the GIBBSTHUR software provides a useful tool for the breeding evaluation of ranking traits in horses and is freely available in a public repository (https://github.com/lvaronaunizar/Gibbsthur). Ranking traits are used frequently as selection criteria in competitive horse breeding programs ,2; howevAnother interesting approach is to assume an underlying Gaussian liability that represents the horse’s performance and dictates the observed classification in competition events ,7. The oThe objective of this note is to present a new free software (GIBBSTHUR) that implements the Bayesian estimation of variance components and the prediction of breeding values for ranking traits based on a Thurstonian Model. In addition, the software can analyze continuous and threshold traits jointly with the underlying liability of the ranking traits.l) that is transformed into ranking in competitions (t). The model for the underlying variable can include systematic, random environmental and additive genetics effects, and a residual effect whose variance has to be predefined. Systematic effects generally include, among others, sex, year, or type of competition, but for ranking traits, it is interesting to include an “event” effect in order to take into account the heterogeneity of the level of the competitors linked with the prestige of the competitive events. The liability can be modelled alone or in conjunction with other continuous or threshold traits through the additive genetic, random environmental, or residual covariances between them.The Thurstonian Model assumes an underlying variable or liability (l and a continuous Gaussian trait (y) which includes systematic and random additive genetic effects only. The probability distribution of l and y, given the remaining parameters in the model, is the following multivariate Gaussian distribution (MVN):lb and yb and la and ya are the systematic and additive genetic effects for the liability (l) and the continuous (y) traits, respectively. Furthermore, lX, yX, lZ, and yZ are the corresponding incidence matrices, and R is the residual covariance matrix. The prior distribution of the additive genetic effects is the following multivariate Gaussian distribution:A is the numerator relationship matrix and G is the additive genetic covariance matrix. In addition, the prior distributions of R and G are Inverted Wishart. The program uses a Gibbs Sampler approach [To illustrate the model, suppose a simple bivariate model composed of approach  to obtaiapproach .kjl is the liability of the jth individual at the kth completion event and ELSE denotes the liabilities at the same and other competition events and the systematic and additive genetic effects for the ranking trait and the correlated Gaussian trait. Further,i,j) element of jth data at the kth event with the vectors of systematic , which must include the names of the pedigree and data file; the number of additional traits and their nature ; the description of the model of analysis for all the traits ; and the hyperparameters of the Gibbs sampler implementation that comprise the total number of iterations, the number of burn-in iterations to discard, and the thin interval. The pedigree file must include a list of the individual, sire, and dam entries numbered from 1 to the number of individuals. The program allows the user to include genetic groups for unknown sires or dams. The data file must have an entry for each data, and should include the level for each systematic, random, and additive genetic effect, numbered from 1 to the maximum number of levels for each effect; and the performance for the continuous, threshold, and ranking traits. Missing data should be coded as 0. There is no limit to the number of competitors per competition. Empty positions are admitted in the results of competitions.The software (GIBBSTHUR) was developed in FORTRAN90 and is based on the TM software . It is ahttps://github.com/lvaronaunizar/Gibbsthur.The execution of the program generates the following files: “Results.txt”, “Breeding.txt”, “Solutions.txt”, and “Iterations.txt”. The file “Results.txt” includes a summary of the posterior mean and standard deviations for the variance and covariance components; the heritabilities; the ratios of variance; and the additive genetic, permanent environmental, and residual correlations. They are computed with the output of the Gibbs sampler iterations after the burn-in. The file “Breeding.txt” includes the posterior mean and standard deviations of the breeding values for the ranking traits and the additional traits, and they can be directly used for selection purposes. The file “Solutions.txt” includes the posterior mean and standard deviations of the systematic and random environmental effects for the ranking and the additional traits. The file “Iterations.txt” includes the samples of each iteration of the Gibbs sampler for the variance and covariance components, which can be used to analyze in detail the marginal posterior distributions. A more detailed description is available at A simple pedigree comprising 100 sires and 500 dams generates 2000 horses that compete randomly in 2000 events of 10 horses each. On average, each horse competes in 10 events. The liability was generated by a model that included a general mean, one additive genetic effect, and a residual. The additive genetic and residual variances were set to 0.25 and 1  at 95% of the posterior distributions, which confirmed that the software can retrieve the simulated parameters for continuous and ranking traits. Slight differences between the mode of the posterior distributions and the simulated values can be expected, given the small size of the dataset. The correlation between the predicted and the simulated breeding values was higher for the continuous (0.89) than it was for the liability of the ranking trait (0.83), although, in both cases, the correlation was very strong because the amount of information available for each horse was large .The ability to discriminate between the performances of the individuals in competition events is illustrated in One of the main limitations of using ranking traits for the breeding evaluation of competitive horses is that competition events often are structured into categories based on their prestige or monetary reward and, therefore, the participation of horses in those events is not random, because the most prestigious events attract the best horses and the worst horses tend to participate in other events, which have a lower average performance. Gianola and Simianer  proposedThe ability to capture the level of the competition events is illustrated by the results shown in As expected, there was a negative correlation (−0.55), which indicated that the most exigent events required a higher breeding value for the winner of the competition because the liability of the winner was set to zero. Therefore, competitions with the best horses (average genetic level) are associated with low “event” effects, while competitions of the worst horses have high “event” effects. In addition, In the event with the highest estimated effect, the predicted breeding values of 5 of 10 horses were ranked in the top 10%, and 8 out of 10 had a positive predicted breeding value. In contrast, in the event with the lowest estimated effect, all the horses had a negative predicted breeding value, and five had breeding values that were among the worst 10% of individuals. Nevertheless, the proposed approach might work well if the distribution of horses in events is random, as it was in the simulated example, or if the degree of structuring is small. In cases in which the structuring is high, Legarra and Ricard [The GIBBSTHUR software provides a useful tool for the breeding evaluation of ranking traits in horses. It can analyze ranking traits jointly with other categorical or continuous traits.


Zea mays L.), but the characterization of their genetic architectures remains challenging. Previous studies of hybrid maize have shown the contribution of within-locus complementation effects (dominance) and their differential importance across functional classes of loci. However, they have generally considered panels of limited genetic diversity, and have shown little benefit from genomic prediction based on dominance or functional enrichments. This study investigates the relevance of dominance and functional classes of variants in genomic models for agronomic traits in diverse populations of hybrid maize. We based our analyses on a diverse panel of inbred lines crossed with two testers representative of the major heterotic groups in the U.S. (1106 hybrids), as well as a collection of 24 biparental populations crossed with a single tester (1640 hybrids). We investigated three agronomic traits: days to silking (DTS), plant height (PH), and grain yield (GY). Our results point to the presence of dominance for all traits, but also among-locus complementation (epistasis) for DTS and genotype-by-environment interactions for GY. Consistently, dominance improved genomic prediction for PH only. In addition, we assessed enrichment of genetic effects in classes defined by genic regions (gene annotation), structural features (recombination rate and chromatin openness), and evolutionary features . We found support for enrichment in genic regions and subsequent improvement of genomic prediction for all traits. Our results suggest that dominance and gene annotations improve genomic prediction across diverse populations in hybrid maize.Single-cross hybrids have been critical to the improvement of maize ( Dominance has been proposed as a major driver of genomic complementation in maize hybrids , effects of significant quantitative trait loci (QTL), or genome-wide polygenic effects. Studies on testcrosses or diallel mating designs seem to support the presence of directional dominance, particularly for grain yield (GY) , PH, and GY—in panels representative of the diversity in North-American hybrid maize. We analyzed two hybrid panels. One was derived from crosses between a diverse sample of maize inbred lines and either of two testers, B47 and PHZ51, belonging respectively to the SS and NSS heterotic groups. The other was derived from crosses between the U.S. Nested Association Mapping panel and PHZ51. Our study investigated the determinants of genotypic variability in hybrid maize, based on gene action (additive and/or dominance effects) or functional enrichments  .In this study, two panels of maize lines were evaluated for hybrid performance: the North Central Regional Plant Introduction Station association panel  and the U.S. Nested Association Mapping panel . The Ames panel is a subset of temperate inbred lines from the diversity panel described by preprint). Briefly, a subset of up to 80 RILs from each of the NAM families was selected to reduce differences in flowering time across families: the later RILs from the earliest families and the earlier RILs from the latest families, for a total of 1799 RILs. All NAM RILs were crossed with the same tester, PHZ51.The hybrid Ames panel (Ames-H) was derived from a subset of 875 inbred lines, which were selected to reduce differences in flowering time while favoring genetic diversity based on pedigree. Two inbred lines were selected as testers: one NSS inbred (PHZ51) and one SS inbred . Inbreds were assigned to one or two testers based on known heterotic group: SS inbreds were crossed with PHZ51, while NSS inbreds were crossed with B47; inbreds with unknown heterotic group, as well as inbreds belonging to the Goodman association panel , West Lafayette (IN), Kingston (NC), Lincoln (NE), Aurora (NY), and Columbia (MO)—for a total of nine environments: 11IA, 11IN, 11NC, 11NE, 11NY, 11MO, 12NE, 12NC, and 12MO. In NAM-H, hybrids were evaluated at five locations—Ames (IA), West Lafayette (IN), Kingston (NC), Aurora (NY), and Columbia (MO)—during 2010 and 2011 for a total of eight environments: 10IA, 10IN, 10NC, 10MO, 11IA, 11IN, 11NC, and 11NY. The following traits were measured in each hybrid panel: DTS (number of days from planting until 50% of the plants had silks), PH (centimeters from soil to flag leaf), and GY (tons per hectare adjusted to 15.5% moisture). In 11NY, only PH and DTS were measured . Both Ampreprint).Phenotypic evaluations were conducted under augmented block designs, where blocking was used to reduce competition for light due to heterogeneous height and/or phenology (only checks were replicated within environments). In Ames-H, blocks were combinations of tester (PHZ51 or B47), maturity (early or late), and expected PH ; checks were B73 × PHZ51 (up to six replicates per block) as well as PHZ51 × B47, B47 × PHZ51, and a maturity commercial check (each replicated once per block). In NAM-H, blocks were NAM families; checks were B73 × PHZ51 (≤ 15 replicates per block) and the non-B73 parent crossed with PHZ51 (≤ 7 replicates per block) (i (fixed), j and year k , l within environment jk , ig’s) as fixed, models with genotype effects as random were also fitted to estimate genotypic variance n is the number of hybrids evaluated in either panel and i (For each combination of panel (Ames-H or NAM-H) and trait , genotype means of hybrids were estimated by the following linear mixed model, fitted by ASREML-R v3.0 (Whole-genome sequencing (WGS) SNPs were previously called in the Hapmap 3.2.1 reference panel , to avoid SNPs private to any of these sets. Marker scores at selected WGS SNPs were then inferred for each hybrid by CreateHybridGenotypesPlugin in TASSEL v5.0. The marker data at selected WGS SNPs in Ames-H (n = 1106) and NAM-H (n = 1640) consisted of the matrix X of minor allele counts, where minor alleles were defined by frequencies in the Hapmap 3.2.1 panel, and the matrix Z of heterozygosity, which coded homozygotes as 0 and heterozygotes as 1.After imputation, s ≥ 0.8;  and minoP of coordinates at the first three PCs in Ames-H and NAM-H was obtained by: (i) adjusting allele counts by their observed mean in the Goodman panel and (ii) mapping adjusted allele counts to PCs by SNP loadings, i.e., V is the Principal component (PC) analysis (PCA) was performed using the R package irlba v2.3.3  in the Gftp://ftp.ensemblgenomes.org/pub/plants/release-40/gff3/zea_mays/Zea_mays.AGPv4.40.gff3.gz). Gene proximity bins  indicated whether any given SNP was within 1 kb of an annotated gene (< 1 kb away from start or end positions).Gene positions were available from v4 gene annotations, release 40  in juvenile root and shoot tissues in B73  at SNPs was determined in the Hapmap 3.2.1 panel. Similarly to Evolutionary constraint at SNPs was quantified by genomic evolutionary rate profiling (GERP) scores  matrix of minor allele counts at Genome-wide additive effects were estimated under a genomic best linear unbiased prediction (GBLUP) model , as foll v1.3-15 .w consisted of polygenic dominance effects and Z was the (noncentered) matrix of heterozygosity at To account for dominance, the GBLUP model was extended to the dominance GBLUP (DGBLUP) model, as follows: v1.3-15 .i, the coefficient of genomic inbreeding was calculated as Under a model of directional dominance without linkage or epistasis, inbreeding depression is characterized by a linear negative relationship between the inbreeding coefficient and fitness . In the R consisted of genomic inbreeding values (linear and quadratic) and R. Significance of Directional effects of inbreeding were analyzed as fixed effects under an extension of the DGBLUP model (1). The following model was fitted: v1.3-15 .j), the following genome-wide association study (GWAS) model was fitted in Ames-H or NAM-H: P-values from Wald tests by the method of X by GEMMA v0.98.1, with 1,000,000 and 10,000,000 MCMC iterations for burn-in and sampling, respectively , GWAS models were extended in Ames-H to incorporate dominance for both fixed effects and random effects: To assess additive and dominance effects (GWAS models were fitted under the efficient mixed-model association expedited (EMMAX) approximation of km (lm) SNPs in bin k (l) and k (dominance effects in bin l). The significance of variance partitions was assessed by likelihood ratio tests, comparing the REML of the evaluated model to that of a baseline model. Model (3) was fitted by REML using the R package regress v1.3-15 (w), because of collinearity of additive and dominance effects in this panel (due to only one inbred tester in NAM-H). Two types of variance partition were analyzed: partition by one feature (baseline: DGBLUP in Ames-H and GBLUP in NAM-H), and partition by both gene proximity and another feature (baseline: partition by gene proximity only in DGBLUP or GBLUP).Effects of functional features on the amplitude of marker effects were captured by linear mixed models which partitioned the genomic variance by annotation bins. For each feature , the following functional enrichment model was fitted: v1.3-15  in Ames-ith diagonal element of matrix G adjusted for fixed effects, i.e., Q. The proportion of variance explained by additive marker effects in DGBLUP was estimated by k* was calculated by the ratio of i.e., the proportion of genomic variance explained by bin k*, over i.e., the proportion of SNP effects in bin k* (and similarly for dominance effects at bin l*) [model (3)].The proportion of variance explained by marker effects in GBLUP was estimated by t-test) and difference to another model .Prediction accuracy of genomic models  was characterized by the Pearson correlation between observed genotype means and their predicted values in validation sets. For models trained in Ames-H, a validation set was 1 of the 24 NAM-H populations. This validation scheme assessed prediction models for genomic selection in biparental breeding populations, and was compared to a “leave-one-population-out” cross-validation scheme where, for each validation set (population), models were trained on the remaining 23 populations in NAM-H. For models trained in NAM-H, a validation set was 1 of 10 random subsets in Ames-H. These subsets were created by a random partition stratified by tester and population cluster , so that all validation sets equally represented variation over population clusters and testers. This validation scheme assessed prediction models for evaluation in diverse panels. The significance of prediction accuracy for any genomic model was tested for nonzero mean , imputed marker scores at WGS SNPs , raw phenotypic measurements (Ames-H and NAM-H), estimated genotype means (Ames-H and NAM-H), and functional annotations. Raw marker scores at WGS SNPs in Hapmap 3.2.1 are publicly available  for prediction in NAM-H. Table S5 describes the prediction accuracy in NAM-H by directional effects of inbreeding in Ames-H. Table S6 describes the prediction accuracy of GWAS models. Table S7 presents the significance of variance partition by panel and functional feature. Table S8 describes the genomic heritability captured by functional classes in functional enrichment models. Table S9 describes the genomic prediction accuracy of functional enrichment models. Figure S1 shows the population clusters in Ames-H, inferred by k-means clustering (k = 4). Figure S2 depicts linkage disequilibrium (LD) in Ames-H and NAM-H. Figure S3 shows allele frequencies among female parents in Ames-H and NAM-H. Figure S4 shows the significance of marginal additive effects in GWAS in Ames-H and NAM-H. Figure S5 shows the SNP enrichment by bin for structural and evolutionary features in Ames-H and NAM-H. Figure S6 shows the SNP enrichment by bin for structural and evolutionary features in Ames-H and NAM-H, while accounting for enrichment by gene proximity.Supporting data can be downloaded from While the Ames hybrid panel (Ames-H) has a few hybrids with an affinity to semitropical lines like CML 247, it is, for the most part, comprised of hybrids closely related to SS lines like B73 and NSS lines like Mo17 . Comparer = 0.77) . Average LD values along chromosomes decay at similar rates, reaching 0.1 at 160 kb in Ames-H and 151 kb in NAM-H. Allele frequencies among female parents are also concordant between Ames-H and NAM-H (r = 0.88), but there are SNPs at low frequency in NAM-H (< 0.5) that segregate at frequencies between 0 and 1 in Ames-H .LD patterns are quite similar in both hybrid panels. After adjustment for population structure and relatedness . In contrast, consistency in genetic effects is higher for PH  and DTS  (Table S1). Therefore, DTS, PH, and GY represent three distinct levels of sensitivity to genotype-by-environment interactions, being respectively weak, moderate, and strong.Three agronomic traits were analyzed in Ames-H and NAM-H: DTS, PH, and GY adjusted for differences in flowering time among hybrids. The relatively low accuracy of genotype means for GY ], fixed QTL effects from association mapping, and directional effects from analysis of genomic inbreeding [Materials and Methods: model (2)]. Furthermore, we expected gains in genomic prediction accuracy to be achieved by any type of dominance effects in an extraneous panel (NAM-H)  . DominanP-value ≤ 2.2 × 10−11), capturing 35, 23, and 41% of genomic variance for DTS, PH, and GY, respectively  for DTS in Ames-H and NAM-H, respectively . For PH and GY, no QTL effects are significant except for one QTL in NAM-H for GY (Table S2). GWAS signals for DTS show limited consistency between Ames-H and NAM-H, with no overlap of high-confidence QTL across panels .GWAS models reveal multiple significant QTL effects for DTS . There are five and seven high-confidence QTL  in chromosomes 3, 1, and 9 . But, doF) on agronomic traits. For PH and GY in Ames-H, only linear effects of genomic inbreeding are significant ; therefore, female parents in Ames × B47 may also contribute to better predictions for GY, especially in NAM-H populations of tropical origin.Prediction accuracy within NAM-H  is consistently higher than prediction accuracy from Ames-H to NAM-H, especially for GY . Indeed,P-value = 0.021), and no significant differences for DTS and GY .Incorporating dominance effects in GBLUP models results in significant gains in prediction accuracy for PH only ]. Moreover, we expected gains in prediction accuracy achieved by functional enrichment models across panels  were conducted in Ames-H and NAM-H. Under the hypothesis that there are differential effects across functional classes, we expected SNP enrichment (enrichment in genomic heritability by class of SNPs) in functional enrichment models   between Ames-H and NAM-H (r = 0.92), the higher significance of partitions in NAM-H could be due to a systematic increase in statistical power, due in part to the larger sample size in NAM-H (n = 1640 vs.n = 1106).Partition of genomic variance by proximity to annotated genes is significant for all traits in Ames-H and NAM-H, based on likelihood ratio tests combined by Fisher’s method . Because evolutionary constraint and chromatin openness are positively associated with gene density, enrichment at these features may be due to functional enrichment by gene proximity . One notable exception is MAF for GY , which indicates some promise for SNP enrichment by MAF classes. However, enrichments by MAF classes are inconsistent across panels, with rare SNPs (MAF ≤ 0.01) being functionally enriched only in NAM-H, for example .Partition of genomic variance explained by recombination rate, chromatin openness, MAF, and GERP scores is significant, for DTS in NAM-H only, for PH in both panels (except MAF), and for GY in NAM-H only (except MAF) , PH , and GY , compared to a DGBLUP model , compared to a GBLUP model  and GY  , partition of genomic variance by gene proximity increases prediction accuracy for DTS  or a GBLUP model (from NAM-H to Ames-H) does not improve prediction accuracy, regardless of traits or validation schemes . Moreover, epistatic effects in linear mixed models vary depending on how marker variables are centered, in a way that can be arbitrary  significant variance partition by dominance effects  and (ii)No QTL effects were detected in Ames-H for PH or GY, whereas previously published analyses have reported significant additive and dominance QTL effects for these traits . In conte.g., e.g., hyperbolic functions), so that additive genetic effects on gene expression may translate into nonadditive effects on agronomic traits. Importantly, benefits and costs of gene expression are affected by intragenic interactions . The relevance of genic regions for capturing genotypic variability in hybrid maize is consistent with hypotheses about biological causes of heterosis (hybrid vigor) related to gene expression, namely, (i) nonadditive inheritance of gene expression and (ii) nonlinear effects of gene expression on agronomic traits . Proposeacross panels. Therefore, prediction models were assessed for their ability to sustain accuracy across distinct population backgrounds. Genomic prediction accuracy was estimated in NAM-H to reflect genomic selection applications in biparental breeding populations crossed to a single tester. These populations serve as useful validation sets because they exemplify interheterotic populations, as crosses between PHZ51 (an NSS line) and NAM inbred lines (related to the SS pool by ≥ 50% through the common B73 parent). Therefore, these populations are good examples of breeding populations crossed to a relevant tester. In contrast, genomic prediction accuracy was estimated in Ames-H to reflect a different situation where diverse panels are evaluated for hybrid performance, in genomic prospection  lose their potential. This caveat is exemplified by differences in QTL effects for DTS between Ames-H and NAM-H, and the consequent lack of gain in accuracy by prediction models based on QTL effects  should result in gains of prediction accuracy that are robust to differences in population backgrounds, as is observed here . Therefore, gains in prediction accuracy by gene proximity should be expected in a broad range of population and species contexts.Enrichment of SNP effects emphasizes causal loci; therefore, enrichment procedures such as QTL detection or variance partition can improve the accuracy of genomic prediction models. However, as genetic effects vary between populations, enrichments about small functional classes (statistically significant improvements in fit, but a genetic model accounting for epistatic interactions appears more plausible according to analyses of QTL and genomic inbreeding. Thus, the choice of prediction procedure should probably come from multiple pieces of evidence in favor of a given genetic model, rather than a single statistical test about the genomic prediction model. In the case of GY, prediction accuracy across panels is probably hindered by genotype-by-environment interactions, which could be accommodated by models incorporating environmental covariates (e.g., While functional enrichments by gene proximity appeared beneficial for all traits, incorporating polygenic dominance effects resulted in gains in prediction accuracy for PH only . The lacOur analyses point to genetic models in hybrid maize that involve interactive effects and emphasize genic regions. While dominance may be relevant to all three traits, other nonlinear effects seemed important for DTS and interactions with environments appeared critical for GY. Consistently, genomic prediction models were improved by dominance effects for PH only. In contrast, genomic prediction models benefited from functional enrichment in genic regions for all traits. Although gene proximity appeared most useful and meaningful in our study, the value of structural and evolutionary features for genomic prediction deserves more attention. Our results call for further investigation about the biological basis of genetic complementation and the underlying interactive effects that could enable more robust prediction of genotypic variability in hybrid maize.