Identification of gene-by-environment interactions (GxE) is crucial to understand the interplay of environmental effects on complex traits. However, current methods evaluating GxE on biobank-scale datasets have limitations. We introduce MonsterLM, a multiple linear regression method that does not rely on model specification and provides unbiased estimates of variance explained by GxE. We demonstrate robustness of MonsterLM through comprehensive genome-wide simulations using real genetic data from 325,989 individuals. We estimate GxE using waist-to-hip-ratio, smoking, and exercise as the environmental variables on 13 outcomes  in the UK Biobank. GxE variance is significant for 8 environment-outcome pairs, ranging from 0.009 – 0.071. The majority of GxE variance involves SNPs without strong marginal or interaction associations. We observe modest improvements in polygenic score prediction when incorporating GxE. Our results imply a significant contribution of GxE to complex trait variance and we show MonsterLM to be well-purposed to handle this with biobank-scale data. Identification of gene-by-environment interactions is crucial to understand the interplay of environmental effects on complex traits. Here, the authors present MonsterLM, a method for estimating the proportion of trait variance explained by gene-by-environment interactions in a fast, unbiased manner on biobank-scale datasets. Many previous analyses have focused on identifying interactions with variants marginally associated with a phenotype of interest6. Hitherto, methods developed to estimate the overall effect of these interactions rely on variance component methods, due to the predictor (m) > observation (n) problem, where SNPs (m) vastly outnumber the participants (n)8. These methods are advantageous for smaller datasets; however, they can be limiting when applied to larger datasets due to computational burden7. Furthermore, variance component methods depend on strong assumptions about the underlying genetic model and often require a priori specification of parameters and/or hyper-parameters, such as polygenicity, minor allele frequency (MAF), and linkage disequilibrium (LD) dependence13. While never formally tested in the context of GxE, it has previously been shown that these assumptions can lead to important biases in heritability estimates16. Novel methods are thus needed to enable fast and unbiased calculations of the variance explained (R2) by GxE in large samples, on multiple traits and without the need for genetic model assumptions.Identifying gene-by-environment interactions (GxE) is difficult because individual interaction effects are expected to be small17, building on the observation that the multiple regression coefficient of determination can be used to accurately estimate heritability17. Extending this observation to include an environmental exposure variable and computing the interactions between genotypes and the environmental exposure allows us to examine the variance explained by genetic interactions with an environmental exposure. However, the large number of single nucleotide polymorphisms (SNPs) (m) compared to participants (n) presents a challenge for genome-wide analysis18. By partitioning the genome into non-overlapping regions, it becomes possible to estimate genome-wide interactions with environmental exposures by reducing m within each region to a size where m < n. Some challenges remain: First, LD spillage at the junction of blocks can theoretically inflate heritability estimates if many such junctions exist9. Second, any residual population stratification effects would be amplified if heritability at each region is overestimated and this effect is expected to be proportional to the number of blocks19. Third, computing prediction R2 on large blocks with high dimensionality can be slow. By using the conjugate gradient method20 with graphics processing unit (GPU) acceleration21, it is possible to perform multiple linear regression modelling efficiently on large  blocks. Thus, the potential for residual population stratification effects and LD spills are minimized since only 60 blocks or less are needed for genome-wide analyses and the variants included are LD-pruned. Furthermore, a block size of no more than 25,000 SNPs also ensures that n > 10 m for accurate estimations.Our proposed method is similar to the generalized random effects (GRE) modelN > 300,000). We hypothesize that GxE interactions contribute significantly to complex trait variance. Our objective is to quantify and characterize these contributions for 13 complex traits using four environmental exposures . We illustrate an overview of our computational analyses in Fig. In this work we propose MonsterLM, a method to estimate the proportion of variance explained by GxE, in a fast, accurate, efficient, and unbiased manner on biobank-scale datasets (p > 0.05) in all ten simulations. Furthermore, observed precision estimates (i.e. variance of estimates across the 12 simulations) did not significantly differ from the precision estimates predicted from Eqs.   and ten cardiometabolic blood biomarkers , two cardiometabolic diseases (Coronary Artery Disease [CAD] and Type 2 Diabetes [T2D]), and height. Of the 13 outcomes, we observed significant GxE with WHR for 8 outcomes  the analysis was repeated without adjustment, with consistent results  with the remaining 20% of participants  comprising the validation set. Using the eight outcomes with significant GxE interaction variance , we conducted univariate linear regression on the discovery set using each outcome and a single SNP as the predictor variable, repeating this process for all SNPs  used in the study and calculating −5 in the discovery set. When extending to more weakly associated SNPs (−1), we observed that between 72–89% of −5 and −1, respectively) was consistently lower as compared to their respective We observed that between 42–67% of the original lds Fig. .−5). Conversely, 3–28% of the original −5). When extending to more weakly associated SNPs, between 15–84% of −1); and between 30–84% of −1).We then similarly estimated the proportion of interaction variance  by incorporation of interaction effects for the outcome with the highest interaction variance, CRP 27.In benchmarking analyses, MonsterLM heritability estimates were consistent with alternative state-of-the-art methods Table . When co36. Several key advantages compared to other methods include: (i) computational efficiency (with two options in CPULS and GPULS) with biobank-scale individual-level data, (ii) no model specification beyond using additive genetic coding, (iii) extensibility to dichotomous exposures and outcomes, and (iv) and demonstrated genome-wide robustness. In many settings, inference methods for genome-wide SNP-heritability and GxE make assumptions about genetic architecture. These assumptions are parametrized by polygenicity (the number of variants with effects) and MAF/LD-dependence . Since the true genetic architecture of any given trait is unknown, existing heritability methods may yield vastly different estimates even when applied to the same data12. This is also the case for the estimation of genome-wide environment interactions, where different assumptions about the structure of interactions result in a variety of different estimates33. Although multi-component methods that stratify SNPs by LD/MAF can address these robustness issues, fitting multiple variance components to biobank-scale data is highly resource intensive37, and this problem is compounded when considering interactions where the number of variables analyzed increases two-fold. Alternate methods that explicitly model these dependencies are also sensitive to model misspecification13. Conversely, MonsterLM assumes an additive genetic model and does not apply further parametrization for underlying assumptions.When extending the comparison to the state-of-the-art, MonsterLM provides distinct advantages over current methods for GxE analysis Table 28–36. Se38. Our results suggest that genetic determinants of low-grade inflammation are dependent on adiposity distribution (WHR) and further research will be needed to understand the implications for CVD risk.Significant GxE with WHR was observed for 8 of the 13 outcomes studied. Interaction effects with WHR ranged from 0.009 to 0.071, and in all cases were of smaller magnitude than their heritability counterparts. These results have important implications for future research. First, our observations suggest that GxE can contribute significantly to complex trait variance. Second, genetic associations are likely to be heterogenous when comparing populations with dramatically different obesogenic environmental exposures. The observation that a majority of GxE effects do not come from SNPs with strong marginal effects suggests this may not impact top GWAS hits excessively. We also observed the presence of significant directionality effects for marginal effect SNPs and their associated interaction effects, which suggest an overall greater impact of genetic variation under certain environmental conditions. There are also potential clinical implications for these observations. For instance, CRP reflects low-grade inflammation and is strongly associated with risk of CVDOur results also provide some further insights into why identification of GxE has been challenging. Many prior studies have reasonably focused the search for GxE on variants with genome-wide significant marginal effects. Our results show that a majority of GxE effects are due to variants with unremarkable marginal effects , although variants with strong marginal effects remain preferred candidates for GxE interactions. We also show in a proof-of-concept analysis that incorporation of GxE can improve PS prediction, albeit very modestly.39. Second, in the event of collider effects with a covariate that is heritable through additive and heterogenous elements there could be some inflation of heritability estimates . Fourth, MonsterLM is susceptible to overestimating GxE variance when participant phenotypic and exposure missingness co-occurs in the same individuals. Fifth, the liability scale transformation for dichotomous outcomes could bias GxE estimates under specific conditions such as violation of the normality assumption needed for the Robertson transformation , if substantial non-additive effects exists34, or biases towards the null due to information loss in the transformation.Some limitations are worth mentioning. First, we quantile normalize all traits before analysis, and while this protects against potential scaling effects and is robust to nonnormal-distribution types, it could also bias results towards the nullIn this report, we have developed a robust and well-controlled method for genome-wide GxE estimation. We established the presence of GxE in cardiometabolic traits. We observed that SNPs with weak marginal and interaction effects contribute to the majority of GxE variance. MonsterLM makes minimal assumptions about genetic architecture and is well-powered for both continuous and dichotomous outcomes. It is computationally efficient, robust, and versatile and can be used as the basis for future analyses of genome-wide environment interactions.42 (https://www.ukbiobank.ac.uk/). Men and women aged 40–69 years were recruited between 2006 and 2010, and extensive phenotypic and genotypic data were collected. Quality control of genotype data was applied for individual and SNP inclusion using PLINK version 1.9 (https://www.cog-genomics.org/plink2/). We selected 325,989 unrelated British individuals  from the UK Biobank with both genotype and trait data for inclusion in the analysis. An unrelated set of individuals were chosen to reduce genomic prediction inaccuracies43. Individual exclusion criteria included: (1) non-white British ancestry, (2) high ancestry-specific heterozygosity, (3) high genotype missingness (>0.05), (3) mismatching genetic ancestry, (4) sex chromosome aneuploidy, (5) mismatching gender sex and genetic sex, and (6) consent withdrawal at the time of analysis. Variants from the release version 3 of the UK Biobank data were used, which included those present in the Haplotype Reference Consortium and 1000 Genomes panels with imputation quality > 0.7 and had no deviation from Hardy-Weinberg equilibrium (P > 1 × 10−10)42. Our study focussed only on common variants; thus, genotypes were filtered by removing highly correlated SNPs with an LD r2 > 0.9 and removing SNPs with a MAF < 0.05. SNP exclusion criteria included: (1) SNPs with low imputation quality (INFO score ≤0.30), (2) call rate <0.95, and (3) ambiguous or duplicated SNPs. After all quality control (QC) filters, 1,030,579 SNPs and 325,989 individuals remained. Genetic variants were partitioned to minimize the number of blocks on each chromosome, with each block having a maximum SNP count of 25,000. Genotypes were standardized to have a mean of zero and standard deviation of one. We examined eleven continuous traits and two (dichotomous) cardiometabolic outcomes including: Apolipoprotein A, Apolipoprotein B, Total Cholesterol, C-reactive protein (CRP), Glucose, HbA1c, HDL-Cholesterol, LDL-Cholesterol, Triglycerides, Total Bilirubin, height, coronary artery disease (CAD) and Type 2 Diabetes (T2D). WHR, an exercise parameter, smoking status, and a randomly generated exposure were used as environmental exposures (E) to quantify GxE interactions.The UK Biobank is a large population-based study which includes over 500,000 participants living in the United Kingdom44, we randomly partitioned the UK Biobank participants into two sets: a discovery set containing 80% of the participants used for model building and a validation set containing the remaining 20% of the participants.For follow-up analyses, and to avoid the potential for overfitting from sample overlapR2); and step three calculates the estimated G and GxE with confidence intervals.MonsterLM estimates heritability (G) and GxE effects in three steps outlined in Fig. Y and E. Both Y and E are first quantile normalized, then regressed for age, sex, and population stratification , and quantile normalized once more. Two more transformations are applied to Y: (i) regression of the processed E then quantile normalization; (ii) and a heteroscedasticity adjustment for continuous outcomes. The aforementioned processing assumes continuous Y and E variables.The standard linear model for an outcome, n×m, where n is number of participants and m is number of SNPs:We denote the matrix of Y, we can leave As the environmental exposure is residualized from The standard linear model becomes:Given Y denoted as After computing n. This limitation is circumvented using the conjugate gradient method and GPU acceleration . If users are constrained by GPU hardware but have adequate RAM allocation (>200 GB RAM) then a CPU-least squares method (henceforth referred as CPULS) can be used to compute traditional least squares in parallel to estimate block-wise m) to minimize LD spillage between blocks and to optimize speed of the matrix calculation.MonsterLM enables multiple linear regression on biobank-scale datasets by parallelizing the calculation of least squares regression. The calculation is done such that the only practical limitation is the speed of the inversion of the }R2 Fig. ; Step 2.i using either j is the number of blocks used per analysis  and Y is residualized for E. Y and E.Once G or GE, with n the sample size and m the number of predictors. The 95% confidence (CI) of 45 available as “Variance.R2” in the MBESS46 R package where:45. The 95% CI for a single block, i = 1, can then be derived using the Wald estimate:G or GxE estimate, j blocks:i variance estimate from Eq. (To estimate the 95% CI for our genome-wide from Eq. . For theE), (ii) the continuous outcome is quantile normalized in each dichotomous group separately (referred to as “E stratified QN Y”) in Step 1, and (iii) standardizing (GxE) terms (Step 1).Applying MonsterLM with dichotomous exposures and continuous outcomes uses the same algorithm as with continuous variables Fig.  with a fY stratified QN E”); (ii) standardizing (Y), and (iii) and applying a liability scale transformation47 on the total estimates (Step 3)  Fig. .Ysim  were used and outcomes and exposures were simulated. Unless otherwise stated, outcomes and exposures were simulated assuming true (unobserved) effects (E was not dependent on G (i.e. E is not heritable) and the genetic and interaction effects for all SNPs were randomly generated from a standard normal distribution. Secondly, we considered models including a collider bias. A collider bias can occur when two conditions are met: a controlled-for environmental exposure is both heritable and influenced through an unobserved confounder; and that same unobserved confounder influences the outcome , explained 20% of the genetic variance of Y), and Y). In base model simulations, observed correlations between E and Y are due to the true set value . In collider simulations, there is no causal effect of E on Y or Y on E such that any observed correlation is entirely due to the collider bias.We tested 12 scenario conditions through simulations  non-null GxE effect where all For each simulated scenario, ten simulations were performed Fig. ; legend.MonsterLM robustness was further investigated by testing the impact of mean imputation for both the Y), and Y) to assess for type I error.MonsterLM performance was also validated with dichotomous outcomes in scenario 2 conditions. Genome-wide simulated variances were set at 50. M10 was selected due to its relevance as an obesogenic risk factor but minimal to negligible estimated additive genetic variance and correlation with outcomes . MonsterLM was applied as outlined in Fig. 2 < 0.1) and computed the direction of effect concordance for this subset. We then plotted the sign concordance twice: first as a function of univariate p-values p-values Z-tests were used to compare the proportion of directionally concordant marginal and interaction effects for each outcome in each threshold compared to a null proportion of 0.50.After computing SNPs were stratified by MAF and LDscore into a total of twenty bins: five MAF bins  and four LDscore quantiles . MAF and LDscore were calculated using a subset of 5000 participants from the UK Biobank. We then computed the variance explained . We then combined the selected SNPs into a single block from the discovery set and applied MonsterLM regression to obtain the multiple linear regression coefficients (G). Using these coefficients, we calculated the PSG in the validation set as:i, j is the SNP number and O represents the total number of SNPs included in this analysis. We then evaluated the predictiveness of each −2, 10−3, 10−4, 10−5) for each outcome.We calculated polygenic scores (PS) without interactions p-value from regressing each GxE interaction with outcome concentration in the discovery set. These interactions are selected from the subset of SNPs included in polygenic scores without interactions. The interactions passing the univariate −2, 10−3, 10−4, 10−5) were then included with the SNPs to create a single block. We applied MonsterLM regression to obtain the multiple linear regression coefficients  and, if included, its associated interaction (k). O represents the SNPs included in the P represents the interactions included, a subset of O. As with the We define 53  and GRE17 (https://github.com/bogdanlab/h2-GRE). MonsterLM heritability and GxE estimates were compared with mtg2 IGE28 (https://bio.tools/mtg2) and LDSC37 (https://github.com/bulik/ldsc).We compared MonsterLM estimates to alternative methods. For heritability, MonsterLM estimates were compared to BOLT2 ranged from 0.05 to 0.5. Sample size ranged from N = 50,000 to 400,000 individuals by increments of 10,000. For each condition, power was defined as the proportion of observed p-values less than 0.05 out of the 10,000 simulations.Statistical power was estimated using sets of 10,000 simulations. Non-central F-distributions were used to simulate the observed genetic and interaction effects at each genotype block, and genome-wide heritability and GxE estimates derived as previously described. True set adjusted RMonsterLM software (Supplementary Software Further information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Software 1Reporting SummarySource Data


The reaction norm analysis of stability can be enhanced by partitioning the contribution of different types of G × E to the variation in slope.Hordeum vulgare), with the adjusted mean yield from each environment used as the environmental covariable. Stability estimated from factor-analytic models, which can disentangle the two types of G × E and estimate stability based on rank-type G × E, was used for comparison. Adjusting the reaction norm slope to account for scale-type G × E using a genetic regression more than tripled the correlation with factor-analytic estimates of stability (0.24–0.26 to 0.80–0.85), indicating that it removed variation in the reaction norm slope that originated from scale-type G × E. A standardisation procedure had a more modest increase (055–0.59) but could be useful when curvilinear reaction norms are required. Analyses which use reaction norms to explore the stability of genotypes could gain additional insight into the mechanisms of stability by applying the methods outlined in this study.The slope of regression in a reaction norm model, where the performance of a genotype is regressed over an environmental covariable, is often used as a measure of stability of genotype performance. This method could be developed further by partitioning variation in the slope of regression into the two sources of genotype-by-environment interaction (G × E) which cause it: scale-type G × E (heterogeneity of variance) and rank-type G × E (heterogeneity of correlation). Because the two types of G × E have very different properties, separating their effect would enable a clearer understanding of stability. The aim of this paper was to demonstrate two methods which seek to achieve this in reaction norm models. Reaction norm models were fit to yield data from a multi-environment trial in Barley (The online version contains supplementary material available at 10.1007/s00122-023-04319-9. Genotype-by-environment interactions (G × E) occur when the performance of a genotype is dependent on the environment it exists in. The performance of some genotypes can be more sensitive to environmental factors, whilst others show greater stability across a range of environments. Genotypes that combine high overall performance with stability are appealing for their greater marketing potential and utility in mitigating the effects of climate change on crop production  models have been a popular choice for modelling G × E and the stability of genotypes across environments  represents the proportion of variance in the slope that is due to scale-type G × E. As such, the proportion of variance in slope due to rank-type G × E can be estimated as (1–r2). A genetic regression can also be used to derive breeding values for the reaction norm slope that is independent of the intercept variance , as recently applied in the reaction norm analysis of body weight in sheep  models can also separate scale-type and rank-type G × E when analysing the stability of genotypes across environments  and consisted of plot yields from 52 partially replicated trials distributed across 15 locations throughout Western Australia, New South Wales, Victoria, and South Australia. The trials took place in 2019  and 2020 .The data were provided by InterGrain Pty Ltd  data. The remaining 726 genotypes were almost fully replicated across the 15 environments and had SNP data.The SNP data were collected using the Illumina Infinium Wheat Barley 40 K SNP array Version 1.0 and was imputed to a set of 410 499 SNPs, as described in Keeble-Gagnère et al. . After iBecause there was a large number of genotypes without replication across environments, a two-stage analysis was used  of yield for each genotype, along with the corresponding weights. For each trial, the initial model consisted of an independent random genotype effect and a first-order separable autoregressive term for the error variance structure using the row and column dimensions of the trial. Based on this model, plots with mean yields deviating more than four standard deviations from their expectation were removed. Additional random ‘row’ and ‘column’ terms were fitted based on a log-likelihood ratio test with a threshold of  et al., .In the second stage, the performance of genotypes across the environments was analysed with RN and FA models utilising the BLUEs of yield and corresponding weights obtained in the first-stage analysis. Only the 726 genotypes with replication across environments and SNP data were considered in this stage. Of the 726 genotypes, 74 were removed from the analysis, as they were heterozygous for more than 12.5% of their SNPs. This left 652 genotypes, of which 606 were replicated across all 15 environments, with an additional 45 genotypes replicated in 14 environments. The remaining genotype was replicated in only six environments but was included in the analysis since it would contribute information through its genomic relationship to the population.The RN models require an environmental covariable (EC) that captures the environmental quality. Whilst it is increasingly common for ECs to consist of real environmental covariables, this was not available in our dataset. Instead, a joint-regression analysis was used (Eberhart and Russell The first RN model was a standard linear reaction norm (RN-L), which modelled the genetic effect of each genotype as a linear function of the EC. The second RN model used cubic polynomials (i.e. a nonlinear function) to model the genetic effect across the EC and was denoted RN-NL.The linear RN-L in simple matrix form was:The environment was fitted as the only fixed effect to account for differences in the mean yield between environments, and residual variance was estimated independently for each environment. The genetic variance of G was a relationship matrix based on SNP data, constructed using the first van Raden method variance matrix  used two common factors to model genetic effects that were common across the environments, along with specific genetic and residual variances for each of the 15 environments. FA-2 was described in matrix notation as follows:n × n diagonal matrix with elements The variance of the common factors and specific effects was modelled according to:b environments, was calculated following:The matrix The second FA model (RR-2) was a reduced-rank implementation of FA-2. RR-2 was identical to FA-2, except that the specific genetic variances for each of the 15 environments  and slope . Similarly, the first common factor in a FA model usually represents the overall breeding value (comparable to the intercept), with the second common factor capturing stability (comparable to the slope). Going beyond two common factors would make it difficult to compare stability between FA and RN models and was not required to achieve the objective of the study, which was to test how well the RN model scale corrections accounted for scale-type G × E. For reference, the two common factors accounted for on average 72.8% of the additive genetic variance (see results section), whilst fitting a third common factor explained an additional 9.14% (results not shown).Breeding values for overall performance and stability for each genotype were derived from FA-2 and RR-2 based on the methods outlined in Smith and Cullis . This inThe sign of the loadings represents contrasts between the environments  and re-ranking occurs. The degree to which the regression coefficients represent rank-type G × E can be assessed by comparing the absolute mean of the positive and negative loadings (or average contrasts), respectively, for the common factor. When the average contrasts are very different Fig. a, most oj, and i on the first common factor.According to Smith and Cullis , the loaBecause the second common factors in FA-2 and RR-2 contained a mix of positive and negative loadings that were similar in magnitude, they captured variation in stability due to rank-type G × E. Therefore, the responsiveness of genotypes to the second common factor (d (either 1 or 2) in environment j in was calculated using:d in environment j, and j. The average value of j environments was used to calculate the mean genetic variance explained by the common factors.The percentage of genetic variance in FA-2 that was explained by common factor The FA models provided a better fit to the data than the RN models based on the Akaike information criterion (AIC), Bayesian information criterion (BIC) and log likelihood Table . The linr) in RN-L was high (0.76), indicating that genotypes with larger intercepts also tended to have larger slopes. Based on the r2, this also implied that 57.8% of the variation in slope was due to scale-type G × E, whilst 42.2% was due to rank-type G × E.Overall, the first and second common factors in FA-2 explained 50.6 and 22.4% of the genetic variance across the environments, respectively . The percent of genetic variance explained by each common factor within the environments is also reported in Table S1. The genetic (co)variance of the random regression coefficients for RN-L and RN-NL are given in Table S2, along with correlations. The genetic correlation between the intercept and slope (R2) was also very high (0.96).Despite the differences in model fit, the correlations between GEBVs for overall performance in the RN models  Fig. a and b. FA-2 −0.2 and RR-2R-2 Fig. c and d. a1∗ Fig. e and f. N-L Fig. g and h. N-L Fig. . They wiIn RN-L, the genetic correlation between the intercept and slope  and the correlation between GEBVs for the intercept (08) Fig. b. This w08) Fig. c and d. The correlation between To explore reaction norm scale-corrections methods in more detail, the reaction norms for RN-L and RN-NL were plotted before and after applying the two correction methods Fig. . The twonts Fig. b. This wWhen the GEBVs were standardised by the genetic variance, the reaction norms for RN-L were no longer linear, whilst the variation of GEBVs was also constant across the EC in both models Fig. d and g. N-L Fig. e but to N-L Fig. h. The inThe MET dataset contained large differences in the genetic variance  and low genetic correlations (rank-type G × E) between environments across the EC, which is expected in populations where G × E is significant. This level and type of G × E is typical of METs collected in Australian plant breeding programs  Fig. . This islated 0.2 to 0.26 The GEBVs estimated using the standardisation method  which underly it. Stability estimated from factor-analytic models, which explicitly disentangle rank-type and scale-type G × E, was used for comparison. The two methods substantially increased the correlation with stability estimated from the factor-analytic models, indicating that they removed variation in the reaction norm slope that originated from scale-type G × E. The genetic regression method appeared to be the most effective, yielding estimates of stability that were highly correlated (0.80—0.85) to those estimated from the factor-analytic models. Although the standardisation method had a more modest increase, it could still be useful in situations where curvilinear RN models are required. Analyses which use reaction norms should consider implementing the scale corrections outlined in this study to gain additional understanding of the nature of G × E and stability in their population.Supplementary file1 (PNG 134 kb)Supplementary file2 (PNG 351 kb)Supplementary file3 (DOCX 15 kb)Supplementary file4 (DOCX 14 kb)Supplementary file5 (DOCX 14 kb)Below is the link to the electronic supplementary material.


Genetic improvement of grain quality is more challenging in hybrid rice than in inbred rice due to additional nonadditive effects such as dominance. Here, we describe a pipeline developed for joint analysis of phenotypes, effects, and generations (JPEG). As a demonstration, we analyze 12 grain quality traits of 113 inbred lines , five tester lines , and 565 (113×5) of their hybrids. We sequence the parents for single nucleotide polymorphisms calling and infer the genotypes of the hybrids. Genome-wide association studies with JPEG identify 128 loci associated with at least one of the 12 traits, including 44, 97, and 13 loci with additive effects, dominant effects, and both additive and dominant effects, respectively. These loci together explain more than 30% of the genetic variation in hybrid performance for each of the traits. The JEPG statistical pipeline can help to identify superior crosses for breeding rice hybrids with improved grain quality. Genetic dissection of hybrids is more difficult than inbreds as nonadditive effects are involved. Here, the authors report a pipeline for joint analysis of phenotypes, effects, and generations and demonstrate its usefulness in identification of loci associated with quality traits and improving predict accuracy in genomic selection of hybrid rice. Oryza sativa L.) as their staple food. With the improvements in living standards, consumers are paying more attention to rice end-use cooking quality1. Many rice quality traits, including protein content and chalkiness degree, are correlated with yield1. The yields of many rice hybrids are higher than those of conventional inbred varieties, but the grain quality of hybrids often needs improvement. To obtain both high-quality and high-yield rice hybrids, the quality traits of hybrids need to be thoroughly genetically dissected in order to identify superior crosses3.More than half of the world’s population consumes rice . A large HRR is one of the most important criteria for measuring milled rice quality. Appearance quality refers to how rice appears after milling and is associated with grain length (GL), grain width (GW), the grain length–width ratio (GLWR), and translucency/chalkiness of the endosperm. Most consumers prefer translucent rice as opposed to chalky rice. Cooking and eating quality include the easiness of cooking as well as the texture, springiness, stickiness, and chewiness of cooked rice, factors that are controlled by starch’s physical and chemical properties and involve amylose content and alkali spreading value. The amylose content (AC) of rice is known to play a crucial role in determining its cooked texture. The alkali spreading value (ASV) is a standard assay used to classify processing and cooking quality; it provides a simple means of classifying rice into high, intermediate, and low gelatinization temperature types. Protein content (PC) is a major index of rice grain nutritional quality. Since storage protein affects rice texture and processing quality, an intermediate PC is generally preferred4.Rice grain quality has been classified into milling, appearance, cooking and eating, and nutritional categories5. At present, dozens of grain size-related genes have been isolated from multiple rice germplasm resources, including the genes GS3, GL3.1, and GW7/GL7 that control grain length8, the genes GW2, GW5/qSW5, and GS5 that control grain width11, and the genes GS6, GS9, TGW6, and GW8/SPL16 that control grain size14. Chalky grains are considered low quality because of their poor appearance and undesirable cooking and milling qualities15. The rice gene OsRab5a regulates endomembrane organization and storage protein trafficking in rice endosperm cells, factors that affect the formation of amyloplasts16. Chalk5 encodes a vacuolar H + -translocating pyrophosphatase that influences grain chalkiness in rice17.Many rice grain quality traits in inbred varieties have been well studied. Multiple genes have been cloned and localized, and their mechanisms and functions have been investigated. Grain size is closely related to yieldWaxy and Wx18. There are several alleles of the Wx gene, including Wxa, Wxb, wx, Wxmp, Wxop, Wxin, and Wxmq. Zhou et al.19 cloned a defective soluble starch synthase gene (SSIIIa) responsible for resistant starch production and further showed that production depends on high expression of the Wxa allele. Rice varieties with an intermediate gel temperature, which is predominantly determined by the amylopectin structure, are generally preferred by consumers. The gene (chr06:6748398_6753302 (+ strand)), starch synthase II (OsSSIIa), is the major determinant of gel temperature4.The amylose content (AC) has the greatest influence on the cooking and consumption qualities. The synthesis of rice amylose is catalysed by a granule-bound starch synthase protein encoded by the genes 20. Genetic dissection of hybrids is more difficult than for inbred lines, as nonadditive genetic effects such as dominance are involved in addition to additive genetic effects. Furthermore, the joint analysis of these genetic effects requires the integration of both inbred and hybrid populations. In many analyses, heterosis is estimated as the difference between the hybrid and mid-parent values from parent–child trios to map loci associated with dominant effects. The dominant effects should be treated in both directions according to the reference allele. For example, heterozygous genotypes are coded to be homozygous genotypes of the reference allele in the dominant model and homozygous genotypes of the alternative allele in the recessive model21.In breeding programs, the selection of parental inbred lines for the development of superior hybrids is challenging22. When both hybrid and inbred parent populations are available, the differences and similarities among parental inbred phenotypes, hybrid phenotypes, general combining ability, and hybrid heterosis can be used to infer genetic effects. In maize, 1428 maternal inbred varieties were crossed with 30 paternal inbred varieties to generate 42,840 (1428 × 30) hybrids. There were 166 quantitative trait loci (QTLs) identified for three agronomic traits: days to tasselling, plant height, and ear weight. These QTLs were categorized into three classes 23 using comparisons to models with a single effect in a single population. Ideally, both additive and dominant genetic effects should be analysed simultaneously with both parental inbred and hybrid populations to maximize statistical power.Joint additive and dominant effect models have demonstrated superiority over models with separate effects. A genome-wide association study (GWAS) of 130,725 cattle using a joint additive and nonadditive model identified six dominant loci with impacts exceeding the largest effect variant identified by the corresponding additive effect modelV) and hybrid test crosses (T) were scored for phenotype for 12 quality traits. The parental inbred varieties are genotyped using whole-genome sequencing. The genotypes of hybrids are inferred from the genotypes of their parents. General combining ability (G) and heterosis (H) are derived for maternal inbred progeny and hybrids, respectively. We develop a statistical model and a computing pipeline to simultaneously analyse additive and dominant genetic effects using both original phenotypes (V and T) and derived phenotypes (G and H) from parental inbreds and hybrids, and identify 128 genetic loci associated with additive and/or dominant genetic effects on the 12 grain quality traits. These loci together explain more than 30% of the genetic variation in hybrid performance for each of the traits.In this study, we cross 113 male inbred varieties with five female inbred parents and generated 565 (113×5) hybrid test crosses. Both parental inbred varieties . The three peaks were more pronounced in test crosses than the peaks in inbred lines. High TD is preferred by customers; unfortunately, the five female parent inbred varieties were below average compared to the male parent inbred varieties. Consequently, hybrids had undesirable TD values compared to their male parent inbred varieties.Most of the 12 rice quality traits had normal distributions in inbred varieties, including PC, GW, MRR, and BRR , T (0.92), G (0.93), and H (0.84) , T (−0.5), G (−0.57), and H (−0.42). GL had moderate negative correlations with CD and PGWC, while GW had moderate positive correlations with CD and PGWC. As a function of GL and GW, their ratio GLWR (GL/GW) had a strong positive correlation with GL and a strong negative correlation with GW. GL, GW, and GLWR had very weak correlations with the remaining traits, especially AC, ASV, BRR, HRR, and MRR. These relationships should be considered during rice breeding for high yield and grain quality.Similar to studies reported in the literaturer2 value of 0.3 on average within ~200 kb in the parent inbred varieties  > 5%. Marker distributions were displayed as a heatmap for 12 chromosomes based on MAF  based on the 1,619,588 filtered SNPs. The first three principal components (PCs) explained 43.4% of the total variation in hybrid test crosses, compared to 27.6% in inbred varieties  were located at one end of the phylogenetic tree developed from the 1,619,588 filtered SNPs  Fig. . The pipV, T, G, and H) yielded higher power than analyses based on inbred varieties (V and G) or hybrid testcrosses (T and H). In total, 192 SNPs were identified as being associated with at least one of the 12 traits . Its genotypes had distinct phenotypic distributions in both inbred varieties and test crosses  are responsible for the AC. Among the 128 associated loci, 42 loci were located in or near (<200 kb) 17 known genes , GS3 (for GL and GLWR), and GW5 (for GW and GLWR). Additionally, BG1 (for GW and GL) was found in the hybrid and combination datasets24. OsGRF8 was found in the hybrids for GLWR and in the combined dataset for AC. This gene is a growth-regulating factor that affects grain length, grain width, and grain starch granule size25. For the milling quality traits , one significant locus was detected in the inbred dataset, compared with 19 in the hybrid dataset and 24 in the combined dataset. There were 17, 20, and 18 loci identified for GL, GW, and GLWR, respectively. Among the 18 loci identified for GLWR, a trait derived26 from GL and GW, three were shared with GL, and six were shared with GW. The three loci that were shared by GL and GLWR were also shared with GW.Many known genes were located within 200 kb of the identified loci. Three major genes of quality traits were identified: With the associated loci identified by GWAS, an immediate practical question was how to identify the new superior test crosses from the existing phenotypes and genotypes of inbred varieties and inferred genotypes of the hybrid test crosses. To answer this question, we first estimated the heritability of each trait to set a target for predictability. Heritabilities were estimated in inbred varieties for additive genetic effects only and in hybrid test crosses for additive, dominant, and total (additive + dominant) genetic effects Fig. . The totAs the 192 associated SNPs were identified by using the observations of the hybrids, the predictions made with these SNPs could not be used to assess applicability for future selection of superior testcrosses due to the overfitting problem. Therefore, we divided the entire population into training and testing populations and conducted GWAS on the training population only. The training population contained all of the inbred varieties. The hybrids were randomly divided into two groups. One group was taken as the testing population, and the other group was combined with inbred varieties as the training population. The newly detected SNPs were used to predict the phenotypes of the testing population. The observed phenotypes of the testing population were not used to determine the associated SNPs but instead were used to calculate the correlation coefficient with the predicted phenotypes. Cross validations were iterated until both groups were used as the testing population. This process was repeated 100 times. The mean of the squared correlation coefficients (R2_CV) for all iterations and replicates was used as the final assessment. The ratio of R2_CV to total heritability was used as the proportion of genetic variance explained by the detected SNPs.Pyramiding the genetic loci for the 12 traits with additive and/or dominant effects in GS improved the accuracy of hybrid performance prediction, especially compared with the commonly used method, i.e., genomic best linear unbiased prediction (gBLUP). More than 45% of the total genetic variation was explained by the identified markers for all traits except one (HRR) with 30% of the variation explained. These results demonstrated that pyramiding genetically identified additive and dominant loci can provide substantial power to predict hybrid performance, presenting opportunities to identify superior crosses from existing phenotypes and genotypes of inbred varieties and hybrids , the Fixed And Random Model Circulating Probability Unification (FarmCPU), and BLINK have advantages over single-locus models in both reducing false positives and increasing statistical power29. In multiple loci models, markers are iteratively incorporated as covariates if they are determined to be associated with the trait during testing markers one at a time. This makes it feasible for multiple loci models to incorporate additive and dominant effects simultaneously by having both additive and dominant marker genotypes. Additive and dominant genetic effects can be realized by concatenating the additive genotypes and dominant genotypes side by side into one genotype matrix for testing. We chose BLINK over FarmCPU and MLMM because both FarmCPU and MLMM involve kinship relations derived from selected markers or all markers31. When additive and dominant marker genotypes are merged, the derived kinship loses its original property of being either additive or dominant kinship.Reducing false positives and increasing statistical power are both critical factors in GWASWx18, GW532, GS333, and BG134 were in or near the cloned quality genes.In this study, the GWAS with BLINK was used to analyse the genetic bases of 12 rice grain quality traits in 113 parental varieties and their 565 hybrid test crosses. A total of 192 significant SNPs clustered into 128 significant loci were associated with at least one of the 12 traits. Among these loci, 42 were located in or near (<200 kb) 17 known genes  of identified loci were known genes related to rice quality, this study was unable to provide insight into the relationship between additive and dominant loci, especially the occurrence of overdominant loci. Among the 128 identified loci, there were only 13 loci with both additive and dominant effects on one of the seven traits , dominant by dominant interaction (DD), and additive by dominant interaction (AD and DA) models. For example, in the DD model only an individual that is heterozygous for both loci is coded as 1, and the rest are coded as 0. In the AA model, an individual homozygous for the alternative alleles at both loci is coded as 4. An individual homozygous for the alternative alleles at one locus and heterozygous at the other locus is coded as 2. An individual heterozygous for both loci is coded as 1, and the rest are coded as 0. Even with the reduced models, the computation increases dramatically for the epistatic terms37. Restriction to loci with additive or dominant effects can make computation feasible at the cost of missing loci with epistatic effects.In the current study, we limited our analyses to additive and dominant effects. JPEG can be extended to incorporate epistatic effects. For the additive genetic effects, genotypes are coded as 0 and 2 for the two homozygotes and 1 for the heterozygotes to form additive genotypes (A). For the dominant effects, genotypes are coded as 0 for homozygous and 1 for heterozygous to form dominant genotypes (D). A typical full model codes the haplotypes as dummy variables to represent the interaction between two lociDominant genetic effects contribute to many complex human diseases and to phenotypic variation among animals and plants. Additive-nonadditive joint analysis is more powerful than additive effect analysis. When both parent inbred varieties and hybrid test crosses are available, general combined ability and heterosis can be derived to further assist in dissecting additive and dominant genetic effects. However, both methods and computing tools are lacking for the joint analysis of phenotypes, effects, and generations (JPEG). To overcome this problem, we developed a JPEG pipeline using BLINK software and analysed 113 male inbred varieties, five female inbred varieties, and their 565 (113×5) hybrid test crosses for 12 rice quality traits and 1,619,588 SNPs. Multiple loci were identified that not only included many known cloned genes but also demonstrated the feasibility of identifying superior crosses from parent inbred varieties and their partial hybrid test crosses.https://www.cgris.net/cgris_english.html). The seeds included restorer varieties of 29 three-line wild-deficient hybrid rice and 86 accessions of microcore germplasm. In 2013, male parental varieties and hybrid test crosses were planted in Wuhan, China. The field trials were designed as randomized blocks and replicated twice, with 20 plants per field planted at a density of 5 × 8 inches. Field management, including irrigation, fertilizer application, and pest control, followed normal agricultural practices. The grains were harvested when fully ripe. In total, phenotypes of 12 rice quality traits were obtained from 113 parental varieties and 565 (113 × 5) hybrid test crosses. Two samples (Dongqiubo and Guangqiuai) with missing phenotypes were excluded from the analyses involving phenotypes.Following the diallel mating design, 115 indica rice accessions ; grain width ; GL/GW ratio (GLWR); chalkiness degree ; percentage of grains with chalkiness ; transparent degree (TD); amylose content (AC %), alkali spreading value (ASV); PC ; brown rice ratio ; milled rice ratio  and whole milled rice rate .After the materials had matured, three plants with uniform growth were selected from the middle eight plants, dried, and stored at room temperature for three months. The plants were then sent to the Agricultural College of Hunan Agricultural University for rice grain quality evaluation. A total of 12 rice quality traits of male parental varieties and hybrid test crosses were determined (Supplementary Data http://rapdb.dna.affrc.go.jp), and BWA software39 was used for all paired-end read mapping using default parameters. PCR duplicates were removed by “rmdup” in SAMtools version 1.12. SNP calling was performed using the GATK UnifiedGenotyper set for diploids using default filtering settings. SNP quality control was conducted by deleting SNPs with a missing rate >20% and minor allele frequency <5%. In total, 1,619,588 SNPs were obtained (Supplementary Data 40 (version 4.0). Hybrid test cross genotypes were inferred using parental SNP genotypic information. The genotypes were coded for both additive and dominant genotypes. The additive genotypes were coded as 0 and 2 for the two homozygotes and 1 for the heterozygotes. The homozygote with a nucleotide in lower alphabetical order was assigned the numeric value of 0, and the other homozygote with a nucleotide in higher alphabetical order was assigned the numerical value of 2. The dominant genotypes were coded as 0 for the two homozygotes and 1 for the heterozygotes.For each parental variety, genomic DNA was prepared from a single plant for sequencing. A sequencing library was established following the Illumina protocol. The genomes of 118 parental varieties were sequenced on an Illumina HiSeq2500 platform with an 11× sequencing depth on average. Raw reads with an N ratio > 10%, those with more than 50% of the Q value (<5) ratio, and with average values < 15 were removed from the raw reads. Nipponbare was used as the reference genome , and phylogenetic trees were drawn by iTOL online (http://itol.embl.de/). The program Admixture (version 1.3) was used to perform optimization of the number of subpopulations (K) in the range 2 to 1042. PCA was conducted using GAPIT43 (version 3.0) and was performed separately for parental varieties and hybrid test crosses. Genome-wide linkage disequilibrium (LD) was estimated by PLINK44 (version 1.9) as pairwise r2 values among SNPs within a window containing no more than 99999 SNPs. The parameters for the commands were “--r2 --ld-window 99999 --ld-window-r2 0”. The first “r2” specifies LD as r2. The second “r2” followed by “0” specifies the output for r2 values of 0 or above, which is everything. The parameter of “99999” specifies the windows size defined as the number of SNPs.Neighbour-joining (NJ) trees and principal component analysis (PCA) plots were used to infer the structures of the 118 rice parental varieties and 565 hybrid test crosses. A pairwise distance matrix derived from the simple matching distance for all the SNP sites was calculated to construct unweighted NJ trees using the software SNPhyloV for the inbred varieties and T for the test cross. Two additional types of observations were derived from V and T, i.e., general combining ability (G) (Supplementary Data H)  were normalized within each type to eliminate the differences between scales and averages. Observations were vertically concatenated as a single phenotype vector (Y) in the combined analysis, and the corresponding genotype matrix was generated. V and G shared the same genotype matrix, while T and H shared the same genotype matrix . We named this pipeline the joint analysis of phenotypes, effects, and generations (JPEG). This JPEG pipeline contains extraction and a combination of phenotypes, GWAS, and Genomic Prediction. The source code is available at GitHub (https://github.com/jiabowang/JPEG).The four types of observations . Similarly, both homozygous genotypes are coded as 0, while the heterozygous genotype is coded as 1 in the dominant genotype matrix (D). The dominant genotypes are all 0 s for V and G. An association test is based on whether an SNP has a non-zero additive effect or a non-zero dominant effect. An SNP with a non-zero additive effect only is defined as an additive locus. An SNP with a non-zero dominant effect only is defined as a dominant locus. An SNP with both a non-zero additive effect and a non-zero dominant effect is defined as an additive and dominant locus.Homozygous genotypes are coded as 0 and 2, while heterozygous genotypes are coded as 1 in the additive genotype matrix  algorithm to estimate the additive genetic variance, dominance genetic variance, and residual variance. The proportions of the additive genetic variance, dominance genetic variance, and total genetic variance (additive + dominant) over the total variance  were calculated as the corresponding additive heritability, dominant heritability, and total heritability, respectively.Additive genotype matrices were used to derive the additive genetic kinship matrices among inbred varieties and hybrid test crosses. Similarly, a dominant genetic marker matrix was used to derive dominant kinship relations among hybrid test crosses. Additive kinship and dominant kinship matrices define the covariance structure of the additive genetic effect and the dominant genetic effect. The kinship matrices were calculated with the VanRaden algorithmV and G belonged to the training group, while half of T and H belonged to the training group and the other half belonged to the testing group. Additive kinship was calculated from the additive genotypes corresponding to V, T, G, and H using the VanRaden algorithm45 implemented in GAPIT43. The observations corresponding to testing population were set to “NA” to run gBLUP in GAPIT for prediction. The correlations between observed and predicted observations were calculated for the hybrids in the testing population. The testing of hybrids was iterated until both groups were tested. All processes were repeated 100 times. The mean squared correlation coefficient across all groups and replicates was used to assess the accuracy of the gBLUP.We conducted cross-validations using the classical genomic Best Unbiased Linear Prediction (gBLUP) as the reference to evaluate the capability to select superior test crosses. All the parent inbred varieties were used as a training population. The hybrids were randomly divided into two equal groups. One group was selected as a testing population, and the other group was joined with the parent inbred varieties as the training population. In other words, all The most critical goal in hybrid breeding is to identify new superior crosses with existing genotypes of inbred varieties and phenotypes of inbred varieties and their hybrids. The predictions for hybrids using the associated additive and dominant loci identified previously in the GWAS could not be used to evaluate their predictability due to potential model overfitting because these loci were derived from the hybrids. To assess the capability, we repeated the GWAS on the training population only during the cross-validation analyses. Similar to the cross-validation for the gBLUP, we randomly divided the hybrids into two equal groups. One group of hybrids was selected as a testing population. The remaining hybrid group and the parent inbred varieties were used as the training population. The GWAS model with both additive and dominant genetic effects was implemented using BLINK on the training population only. The newly-detected SNPs with additive effects and SNPs with dominant effects in the final iteration of BLINK were used as explanatory variables in GAPIT to predict the phenotypes of the hybrids in the testing population using the gBLUP model. The kinship was derived from both additive and dominant genotypes. The correlation coefficients between observed and predicted observations were calculated for the hybrids in the testing population. The testing population was iterated until both groups were tested. All processes were repeated 100 times. The mean squared correlation coefficient across all groups and replicates was used to assess the capability to identify new superior crosses.Further information on research design is available in the Supplementary informationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Reporting Summary


There is currently little evidence that the genetic basis of human phenotype varies significantly across the lifespan. However, time-to-event phenotypes are understudied and can be thought of as reflecting an underlying hazard, which is unlikely to be constant through life when values take a broad range. Here, we find that 74% of 245 genome-wide significant genetic associations with age at natural menopause (ANM) in the UK Biobank show a form of age-specific effect. Nineteen of these replicated discoveries are identified only by our modeling framework, which determines the time dependency of DNA-variant age-at-onset associations without a significant multiple-testing burden. Across the range of early to late menopause, we find evidence for significantly different underlying biological pathways, changes in the signs of genetic correlations of ANM to health indicators and outcomes, and differences in inferred causal relationships. We find that DNA damage response processes only act to shape ovarian reserve and depletion for women of early ANM. Genetically mediated delays in ANM were associated with increased relative risk of breast cancer and leiomyoma at all ages and with high cholesterol and heart failure for late-ANM women. These findings suggest that a better understanding of the age dependency of genetic risk factor relationships among health indicators and outcomes is achievable through appropriate statistical modeling of large-scale biobank data. Many phenotypic characteristics and the risk of common complex disease change across life, reflecting a range of different age-specific biological processes. Here, we show that 74% of 245 genome-wide significant genetic associations with age at natural menopause show a form of age-specific effect. Menopause is the permanent cessation of the menstrual cycle in women following the loss of ovarian function and occurs at an average age of 51 years, with 4% of the female population experiencing early menopause prior to age 45. Current evidence suggests that early menopause is associated with a risk for cardiovascular diseasei and SNP j) μ is the intercept, j in chromosome k, the general form for CAMP model for each SNP i denotes the ith individual, jth marker value, j is located at, j, j. j and we define it in two ways. The effect-size function t asWe present a marginal Cox age-specific mixed proportional hazards (CAMP) model paired with a unique significance-testing framework. Following the success of many genome-wide association studies (GWASs), more attention has been attributed to better characterizing SNP effects under different environmental conditions, leading to genotype-covariate analyses.yi=μ+xijβon in ageβj(t)=βj0t, we can define the test statistic function j as the square of the ratio of effect size and the standard error of the effect sizeAt each time point j. To do this, we use a BayesW model,i, the age at onset of a disease φ, μ is an intercept, φ, α is the Weibull shape parameter. For each group, we assume that L is the number of mixture components. We estimated the hyperparameters such as genetic variance and prior inclusion probability by grouping markers into “MAF-LD” bins, as recent theory suggests this yields improved estimation.j. This gives a two-step leave-one-chromosome-out (LOCO) approach, where first a BayesW model is used to estimate the genetic predictor and then a marginal age-specific CAMP model is used for the second step. Next, we discuss how we can conduct significance testing in the second step in an efficient manner while ensuring that the type I error is bounded below the fixed threshold α even with a more complex model.All that remains is to estimate α and given the null hypothesis of no effect at SNP j  at which the variable has an effect on the phenotype.This naturally gives us a rule for hypothesis testing at time Furthermore, we can show that the quantiles of α) is bounded when using the Suppose that we have estimated effect sizes t under the null hypothesis To prove the lemma, we need to demonstrate that We suppose, in contradiction, that under the null hypothesis, there exists some time point Given this, we can write the following inequalities,α as given the effect and variance estimates.An important corollary of this result is that we can use http://www.ukbiobank.ac.uk. The UK Biobank has ethics approval from the North West Multi-centre Research Ethics Committee (MREC). We first restricted our analysis to a sample of European-ancestry UK Biobank (UKB) individuals. To infer ancestry, we used both self-reported ethnic background (UKB field 21000-0) and genetic ethnicity (UKB field 22006-0) and selected coding 1 in both cases. We projected the 488,377 genotyped participants onto the first two genotypic PCs calculated from 2,504 individuals of the 1,000 Genomes project. Using the obtained PC loadings, we then assigned each participant to the closest 1,000 Genomes project population, selecting individuals with PC1 projection < absolute value 4 and PC2 projection < absolute value 3. Samples were also excluded based on UKB quality control procedures with individuals removed of (1) extreme heterozygosity and missing genotype outliers; (2) a genetically inferred gender that did not match the self-reported gender; (3) putative sex chromosome aneuploidy; (4) exclusion from kinship inference; and (5) withdrawn consent. We used genotype probabilities from version 3 of the imputed autosomal genotype data provided by the UKB to hard call the genotypes for variants with an imputation quality score above 0.3. The hard-call threshold was 0.1, setting the genotypes with probability This project uses UK Biobank data under project 35520. UK Biobank genotypic and phenotypic data are available through a formal request at We created the phenotypic data of ANM similarly to Ojavee et al.https://genomics.ut.ee/en/content/estonian-biobank). Similar to the UKB data, we used the age range of 33–65 and thus excluded women with age of menopause outside this interval. In the total Estonian Biobank data, there were 195,432 individuals genotyped on the Illumina Global Screening Array (GSA), which were imputed to an Estonian reference created from the whole-genome sequence data of 2,244 participants.To replicate the findings, we used the Estonian Biobank with 70,082 women . For access to be granted to the Estonian Biobank genotypic and corresponding phenotypic data, a preliminary application must be presented to the oversight committee, who must first approve the project. Ethics permission must then be obtained from the Estonian Committee on Bioethics and Human Research, and finally a full project must be submitted and approved by the Estonian Biobank. This project was granted ethics approval by the Estonian Committee on Bioethics and Human Research  regression model is used, which requires a gene-gene correlation matrix. This correlation matrix is calculated by first simulating 10,000 random phenotypes by drawing phenotypes from a normal distribution and then associating them to the genotypes of the 1000 Genomes phase 3 non-Finnish European samples. The GWAS gene Z scores for each of the 10,000 simulated GWAS signals alongside the Pearson correlations between the GWAS gene Z scores are then calculated. Correlations between simulated GWAS gene Z scores reflect the underlying LD patterns and chromosomal organization of genes. An additional 10,000 GWASs were simulated to empirically determine enrichment p values, and, finally, an additional 100 simulations were used to estimate the false discovery rate (FDR).Downstreamer implements a strategy that accounts for LD structure and chromosomal organization, operating in two steps. In the first step, gene-level prioritization scores were calculated for each age group’s summary statistics and a null distribution. This aggregates p values per variant into a p value per gene while accounting for local LD structure. GWAS gene p values were calculated for all 20,327 protein-coding genes (Ensembl release version 75). The gene p values were then converted to gene https://www.ebi.ac.uk/ena) containing 56,435 genes and 31,499 samples covering a wide range of human cell types and tissues. 165 leading PCs representing 50% of the variation were selected. For protein-coding genes, centered and scaled eigenvectors for these 165 components  were calculated. The co-regulation matrix is then defined as the Pearson correlation between the genes from the scaled eigenvector matrix, with diagonal zero and Pearson r values converted to Z scores. To identify pathway and disease enrichments, the Human Phenotype Ontology (HPO), KEGG, Reactome and Gene Ontology (GO) Biological Process, Cellular Component, and Molecular Function databases were used. A Z score per pathway or term per gene is calculated, giving how much each gene contributes to these gene sets. We collapsed correlated genes in parallel with the GWAS step to ensure compatibility with the GWAS gene Z score and scaled all pathway Z scores to zero mean and unit variance.In the second step, the gene-level prioritization scores were associated with the co-regulation matrix and pathway annotations. We used a previously generated co-regulation matrix that is based on a large multi-tissue gene network.Z scores were rank-based inverse-normal transformed. A linear model was used to correct for gene length, as longer genes will typically harbor more SNPs. Genes with a Pearson correlation Z scores to the pathway Z scores and co-regulation Z scores, with β is the estimated effect size of a pathway, term, or gene from the co-regulation matrix; ω is the gene-gene correlation matrix; X is the design matrix of real GWAS Z scores; and y is the vector of gene Z scores per pathway, term, or gene from the co-regulation matrix. β for the 10,000 random GWASs were estimated in the same way and used to estimate the empirical p value for β. These two analyses result in pathway enrichments and core gene prioritizations, respectively. The gene-gene correlation matrix derived from the 10,000 permutations is used as a measure of conditional covariance of the error term (ω) in the GLS to account for the relationships between genes due to LD and proximity. We present full results for each age in Real and simulated GWAS We used LD score regression to calculate genetic correlations among the test statistics generated using ,∗cases∗controls)/(cases+controls).We calculated the causal effect estimates that ANM at different ages has on various traits  using Me,,We show in the 45 to 52 . For sig45 to 52 . That is45 to 52 . In concFor quantifying the existence of age-specific effects, we first test the null hypothesis of whether the slope term UK women C. 37 of  the UKB  and S1,  the UKB , yieldin the UKB , making p=0.051, .Table 2RSecond, we observe that the number of regions affecting ANM changes considerably with the peak number of ANM-affecting regions observed at age 49 A. Moreov,In contrast with most associations discovered at age 49, the general trend across 245 significant SNPs is that the effect size estimates shrink toward zero B. That mOur analysis differs in one other key way from previous ANM genetic association studies. Here, we do not censor women who were placed on hormone replacement therapy (HRT). In survival models, declaring HRT individuals as censored makes the modeling assumption that age-at-HRT start and ANM are independent. They are clearly not, as for women on HRT there is a correlation between the age of HRT and ANM of 0.58 within the UKB. For women who were placed on HRT prior to the recorded date of ANM, this correlation is stronger at 0.69. A Cox Proportional Hazards model for ANM including a categorical covariate of whether a woman was given HRT prior to menopause  shows that censoring for HRT prior to ANM would significantly censor for earlier menopause , which is downstream of We conduct a number of follow-up analyses to support our age-specific association results. First, we test for significant enrichment of the summary statistics generated by our approach for each age group. For all categories showing significant enrichment after Bonferroni multiple testing correction, we find that their significance does not hold across all age groups .Figure 3Effect sizes for ANM between the ages of 41–49 were enriched in genes differentially expressed in the uterus, thyroid, prostate, ovary, fallopian tubes, and cervix within the Genotype-Tissue Expression (GTEx) consortium data . AdditioOur next follow-up analysis used LD score regression, where we find that genetic correlations across ages are significantly less than 1 A. GenetiBetween 41 and 49 years, we find a significant positive genetic correlation of observed ANM values with age at last birth and age at first birth B, implyiOf significant note, genetic propensity for breast cancer was significantly associated with a later ANM B before We also find significant genetic correlations implying that genetically mediated later ANM is correlated with a lower genetic predisposition to hypothyroidism, stroke, major depression, blood albumin levels, and obesity prior to age 51 B. For woWe find a significant positive genetic correlation of ANM values with both educational attainment and fluid intelligence between 41 and 49 years B, implyiIn a further follow-up analysis, we used MR, which utilizes the randomized inheritance of genetic variations in the population, to estimate the potential causal effect a modifiable risk factor or exposure has on a health-related outcome of interest. We used menopause at different ages as an exposure in five different MR methods  that must be repaired through the homologous recombination pathway, with oocytes that do not properly repair DSBs after this first phase of meiosis undergoing apoptosis. Here, early-ANM-associated common variants are enriched at loci, harboring genes involved in the DNA repair and replication checkpoint processes, such as RNA polymerase II, histone methyltransferase complex, and histone acetylation . One-carThere are several important caveats to our study. First, we have assumed that the effect size can only change linearly with age, whereas in reality, they could consist of more complicated patterns that could be captured with piece-wise exponential models. However, introducing many more parameters on a genome-wide scale would lead to a high multiple-testing burden, potentially hampering the capability to detect the actual signal. Furthermore, especially for traits with a moderate range of values (90% of the observed ANM happens between ages 45 to 55, Second, the current implementation of the model is not computationally efficient, and to handle the computational burden we have utilized the computational resources of two universities to produce these results. Our objective was simply to highlight the existence of changing genetic relationships between phenotypes and health outcomes across the lifespan. Although it is possible to make marginal analyses embarrassingly parallel, it is inherently time consuming to fit a CAMP model. Scaling the inference requires new research into novel algorithms for computationally heavy high-dimensional statistical problems of this kind.Finally, our study focused only on European ancestry individuals in the UK and Estonian Biobanks, and future analyses must take into account populations with more diverse ancestries to get a fuller picture of the genetic architecture of ANM across the globe. This requires research into statistical models that are capable of learning both shared and unique age-dependent effect sizes across populations, and it requires large-scale data to be collected from worldwide populations.In summary, we propose an analysis approach for GWASs of age-at-onset phenotypes using a two-stage mixed linear-association model, where marker effect sizes are estimated using a CAMP model. Our approach provides a better understanding of the genetic basis of ANM and applies to any form of time-to-event phenotype.


Triticum aestivum L.) is widely grown in sub-tropical and tropical areas and, as such, it is exposed to heatstress especially during the grain filling period (GFP). Global warming has further affected its production and productivity in these heat-stressed environments. We examined the effects of heatstress on 18 morpho-physiological and yield-related traits in 96 bread wheat accessions. Heat stress decreased crop growth and GFP, and consequently reduced morphological and yield-related traits in the delayed sown crop. A low heat susceptibility index and high yield stability were used for selecting tolerant accessions. Under heatstress, the days to 50% anthesis, flag-leaf area, chlorophyll content, normalized difference vegetation index (NDVI), thousand grain weight (TGW), harvest index and grain yield were significantly reduced both in tolerant and susceptible accessions. The reduction was severe in susceptible accessions (48.2% grain yield reduction in IC277741). The plant height, peduncle length and spike length showeda significant reduction in susceptible accessions, but a non-significant reduction in the tolerant accessions under the heatstress. The physiological traits like the canopy temperature depression (CTD), plant waxiness and leaf rolling were increased in tolerant accessions under heatstress. Scanning electron microscopy of matured wheat grains revealed ultrastructural changes in endosperm and aleurone cells due to heat stress. The reduction in size and density of large starch granules is the major cause of the yield and TGW decrease in the heat-stress-susceptible accessions. The most stable and high-yielding accessions, namely, IC566223, IC128454, IC335792, EC576707, IC535176, IC529207, IC446713 and IC416019 were identified as the climate-smart germplasm lines. We selected germplasm lines possessing desirable traits as potential parents for the development of bi-parent and multi-parent mapping populations.Bread wheat ( Triticum aestivum L., 2n = 6X = 42, BBAADD), an important cereal crop, is a staple food for 40% of the world’s population [Bread wheat (pulation . It provpulation . Wheat wpulation . Climatepulation . Therefopulation . With inpulation . Studiespulation .The narrow genetic base of elite cultivars necessitates the screening of germplasm conserved in genebanks to enhance resilience against stressors . The effThe Indo-Gangetic Plains (IGP) region of India contributes about 15% of global wheat production. However, about 51% of its area might be re-classified as a heat-stressed (HS) short-season production mega-environment by 2050 . GloballSeveral adaptive morpho-physiological traits like early ground cover, epicuticular wax, leaf rolling, stay-green, biomass and flag-leaf area contribute to heat-stress tolerance in wheat ,25. AdapGenotype–Environment (G × E) interactions are important factors in the expression of quantitative traits such as yield and its component traits. A stability analysis has been used to identify varieties with a superior performance and yield stability under different environments . GermplaPlant materials consisted of a subset of 96 bread wheat accessions (79 indigenous and 17 exotic collections), selected from a large genebank collection of wheat , which iRabi seasons of years 2018–2019 and 2019–2020. The farm area lies in the North–Western Plain Zone (NWPZ) of wheat production with a semi-arid and sub-tropical climate and sandy- loam alluvial soil, slightly alkaline in pH and low in organic matter content. In each crop season, two sowing dates were (i) normal  environment) and (ii) late-sown wheat . Thus, in late-sown wheat, accessions were exposed to heatstress during GFP. The combination of year and sowing dates made our field experiments have four environments, which included two NS and two HS environments for testing the stability of wheat germplasm under heatstress. The field trials were laid out in an Augmented Block Design (ABD) with fiveblocks, where four checks, namely, Raj3765, HD2932, WR544 and HD2967, were randomized and replicated in each block. Each experimental plot consisted of three rows of a 2.0 m length with 25 cm spacing between rows (1.5 m2 area). The standard crop management practices for irrigated ecology were followed for raising a healthy wheat crop. Weather parameters like the temperature and rainfall were recorded during the crop period of 2018–2019 and 2019–2020. Crop duration was expressed in standard meteorological weeks (SMW).Field experiments were conducted at Experimental Farm, ICAR-NBPGR, New Delhi, situated at 28.649° N latitude, 77.152° E longitude and 220 m altitude, during the The morpho-physiological and yield traits related to heat-stress tolerance were recorded as per the Manual on Physiological Breeding II: A field guide to wheat phenotyping . The traMature grains from heat-stress tolerant and susceptible accessions of bread wheat were transverse sectioned into three small pieces. The middle sections were mounted on an aluminum stub using double-side adhesive carbon tape. The specimens were uniformly coated with a thin layer of gold–palladium using an Emitech SC7620 sputter coater. Specimens were examined under a Scanning Electron Microscope  operated at 10.0 kV using a secondary electron detector. The aleurone layer, endosperm cells and starch granules were observed, and their images were captured.a/Xb)/(1 − Ya/Yb), where Xa and Xb are mean values of the GY of an individual accession under the HS and the NS environment, respectively; Ya and Yb are mean values of the GY of all accessions under the HS and the NS environment, respectively.Adjusted mean values were used for the statistical analyses of ABD trial data of 18 traits recorded under NS and HS environments over 2 years. An analysis of variance (ANOVA) was performed following a test of the homogeneity of variances and applying Aitkin’s transformation using SAS software version 9.4 . Pearson2ph), genotypic variance (σ2g), phenotypic coefficient of variation (PCV), genotypic coefficient of variation (GCV), broad sense heritability (H2) and genetic advance (GA) were calculated on mean data of four checks using SAS software.We used HSI values to categorize wheat accessions as highly tolerant (HSI < 0.50), tolerant (HSI = 0.51–1.0), susceptible (HSI = 1.0–1.50) and highly susceptible (HSI > 1.50). The phenotypic variance (σ2H) % = (σ2g/σ2ph) × 100 and genetic advance (GA) = H × k × σph, where σph is the phenotypic standard deviation and k is the constant 2.06 at 5% selection intensity, were computed. The diversity estimates were derived using the Shannon–Weiner index [i is the relative frequency in the ith class of the jth trait and ln is the natural logarithm of Pi. The extent of diversity was interpreted as H′ < 0.5: low, H′ = 0.5 to 1.0: high and H′ > 1.0: very high. The traits showing H′ > 1.5 revealed a great genetic diversity among the accessions.Heritability  and small S2di. These genotypes are well adapted to both the environments. The genotypes having a higher mean, βi > 1 and a small S2di are adapted to the favorable (NS) environment. The genotypes with a higher mean, βi < 1 and a small S2di are specially adapted to the unfavorable (HS) environment. Four categories of accessions were made, viz., highly tolerant, tolerant, susceptible and highly susceptible based on the mean, stability and HSI.We performed a stability analysis usingthe Eberhart and Russell (1966) model  with WinThe maximum and minimum temperatures and rainfall during the GFP of 2018–2019 and 2019–2020 crop growing seasons are presented in The differences in the climatic conditions in the environments were reflected by the variations observed for the phenological and agronomic traits, as presented in Accessions IC393878 and IC252725 showed the highest GFP of 39.5 and 32.0 days under NS and HS environments, respectively. Accession EC577013 had the tallest plants (150.9 cm) under NS, while accession EC576585 had the tallest plants (127.0 cm) under the HS environment. However, accession IC335792 produced the shortest plant (84.9 cm) under NS and accession IC443653 had the shortest plants (73.2 cm) under the HS environment. Accession IC277741 produced the highest grain yield (802.5 g) in the NS environment, while accession IC566223 produced the highest grain yield (598.1 g) under the HS environment. The lowest grain yield (300.1 g) was produced in accession IC542509 under NS, whereas accession IC539287 produced the lowest yield (176.7 g) under the HS environment. Accession IC573461 showed the highest TGW (52.2 g) under the NS environment, while accession IC539221 produced the highest TGW (46.6 g) under the HS environment. Accession IC443653 showed the highest harvest index (48.0%) under the HS environment.Bread wheat accessions exhibited a significant variation for most of the physiological traits. They showed a high variability in physiological traits such as plant waxiness and leaf rolling . AccessiH2 (>70%) were recorded for DA (84.9% under NS and 85.4% under HS) and GL (77.9% under NS and 89.3% under HS) in both environments; CC (75.9%) and PL (79.4%) in HS; and LR (71.4%) in the NS environment. A genetic advance was the highest for PW (33.2%) followed by LR (30.5%) under the NS environment.A wide range of genetic variability was recorded for most of the traits . PCV wasThe Shannon–Weiner diversity index (H′) revealed a high morpho-physiological diversity among studied bread wheat accessions considering all traits under NS (H′ = 1.56) and HS environments (H′ = 1.47). The most diverse traits were PW (H′ = 1.90), CTD (H′ = 1.88), NSS (H′ = 1.79) and NDVI (H′ = 1.78) under NS, while under the HS environment, NSS (H′ = 1.78), PW (H′ = 1.77), MSI (H′ = 1.70) and CTD (H′ = 1.69) displayed a high phenotypic diversity. The grain length showed the least variability under both NS (H′ = 1.19) and HS (H′ = 1.14) environments. The frequency distribution for 12 important phenological, physiological and yield-related traits, namely, DA, GFP, CC, CTD, NDVI, MSI, PW, LR, PH, PL, TGW and GY, also supported the existence of a widerange of genetic variability in the germplasm .A UPGMA dendrogram grouped all the 96 wheat accessions into six major clusters using data of 18 morpho-physiological traits recorded under the HS environment .viz., accession IC566223, IC529207, IC535176, EC534487, IC252348, IC401976, IC075240, IC539531 and EC574731, grouped in cluster III along with two national check varieties, HD2932 and HD2967. Accession IC542509 took the longest time to 50% anthesis (119 days in NS and 94 days in HS environment), produced the lowest yield in both the NS and HS environments and formed a solitary accession in cluster VI. Accessions EC576585, IC536162, IC252999, EC190899, IC252867, IC536050, IC416075, IC572925, IC443653 and WR544 flowered early (<69 days) in the HS environment and were grouped in cluster I.Most of the accessions were included in the first three clusters, and cluster I, II and III consisted of 21, 42 and 17 accessions, respectively. The remaining three clusters grouped 16 accessions with cluster IV, V and VI having 10, 5 and 1 accessions, respectively. Most of the accessions adapted to heatstress, Grain yield associated positively with GFP, PW, LR, SL, HI and GW under the HS environment a. HoweveTGW showed positive associations with GFP, HI, GL and GW under both NS and HS environments. However, under heatstress, TGW was associated positively with PH, PL and FLA, but negatively with MSI, LR and DA. Strong positive correlations were recorded between PH and PL, and SL and NSS, under both the environments. GFP associated positively with GW, TGW and HI, but negatively with DA under both the environments. Similarly, DA also associated negatively with HI, TGW and GW under both environments. Among the physiological traits, positive associations were observed between PW and LR under both the environments. NDVI associated positively with both CC and CTD under the HS environment. The cooler canopy (CTD) showed positive correlations with DA, PH, PL, FLA, SL and NSS under the HS environment. However, CTD associated positively with MSI under NS and negatively under the HS environment.2. The heatstress prevailed, at the onset of the reproductive phase and during the grain development stage, decreased SL, NSS, GL and GW. The heatstress during GFP had an adverse effect on grain yield and TGW, and reduced these traits by 138.6 g and 6.0 g, respectively. Among the physiological traits, CC, NDVI and MSI were reduced by 4.2, 0.14 and 7.2%, respectively, under heatstress. However, CTD increased from 6.2 to 6.9 °C under the HS environment to maintain an optimal sub-cellular temperature during GFP. PL and LR were also increased from 6.2 to 6.9 and 5.8 to 6.5, respectively, under the heatstress. A boxplot analysis clearly showed the differential effect of heatstress on morpho-physiological traits in tolerant and susceptible accessions  were observed in both the heat-stress-tolerant and -susceptible accessions under the NS environment, whereas unstructured, shriveled LG with a prominence of small starch granules (SG) were present in the wheat grains developed under the HS environment. The density of LG  was higher in both heat-stress-tolerant and -susceptible accessions in the NS environment, whereas, in the HS environment, the density of LG reduced slightly in tolerant accessions while it was considerably reduced in the susceptible accessions. The density of SG  was higher in both tolerant and susceptible accessions under the heatstress.p < 0.01) among accessions  and environments (E) for both the traits  < 1 and HSI < 0.5 and producing >500 g of grain yield were considered as highly tolerant genotypes  populations . AccessiThe production and productivity of bread wheat are adversely affected due to terminal-heat stress as a result of delayed sowing in many parts of India . We evalThe wheat accessions showed a varied response to heatstress and provided an ample scope for the selection of trait-specific accessions. We observed a high level of variability in the germplasm accessions. A non-significant genotype × year (G × Y) interaction for most of the traits reveals that accessions had similar expressions in both the years. The significant G × Y interactions for NDVI in both environments; TGW under NS; and PH, PL, SL and GL under the HS environment suggest that accessions performed differently over the years for these traits. Our results corroborate earlier studies ,55, whicThe response to heat stress involves physiological adaptations, required to protect vital cellular functions like photosynthesis and homeostasis of metabolites ,57. The Grain yield, a complex quantitative trait, is controlled by many interactions between morphological, physiological and related parameters. Under the HS environment, the yield showed positive correlations with GFP, HI, GW, PW and LR. The positive correlation of yield with GFP reveals that a longer grain development period is a vital factor for improving yield under heatstress. In a previous study , grain yIn our study, CC did not show an association with GY, but CTD revealed a significant association with GY only under the heatstress. Similarly, Elbasyoni  also obsHeat stress during GFP adversely affects the grain size in bread wheat. In our study, the effect of heatstress on GW was more severe as compared to GL, which resulted in shriveled grains in susceptible accessions. The development of shriveled grains in the susceptible accessions was due to changes in the ultrastructure of aleurone cells and starch granules in endosperm. Our findings on grain development under heatstress corroborate a recent study , whereinGrain development is influenced by various metabolic processes occurring in leaves, mainly the production and translocation of photoassimilates and importing of precursors for the biosynthesis of grain reserves, minerals and other functional constituents . Hence, Heat-stress adaptation is a complex phenomenon and is influenced by several factors such as the genotype and its interaction with the environment over a long period of time. A wheat plant achieves adaptation through variation in phenology and other related traits determining the plant architecture . Hence, Wheat genetic resources used in the present study represent a part of the reference set for heat-stress tolerance and hence exhibited a high extent of genetic variability for morpho-physiological and yield-related traits. The terminal-heatstress in the late-sown bread wheat crop negatively affected grain yield and its contributing traits. The higher temperature than the optimum temperature during GFP reduced the grain size, and eventually decreased TGW and grain yield under the HS environment. The ultrastructural analysis of matured grains showed that the decrease in size and density of large starch granules in endosperm is the main cause of the yield and TGW reduction in the heat- stress-susceptible accessions. The high yielding accessions possessing desirable morpho- physiological traits and adaptation to the HS environment were identified and selected, which could be utilized for the development of mapping populations and the genetic improvement of bread wheat for heat tolerance.