There are many research studies have estimated the heritability of phenotypic traits, but few have considered longitudinal changes in several phenotypic traits together.To evaluate the progressive effect of single nucleotide polymorphisms (SNPs) on prominent health-related phenotypic traits by determining SNP-based heritability  was performed for significant SNPs.P = 1.22 × 10−8 for rs2272402 and P = 3.36 × 10−7 for rs7209788). De novo variants including rs4922117  of log-transformed high-density lipoprotein (HDL) ratios and rs2335418  of low-density lipoprotein were detected on GWAS.Each SNP heritability for the phenotypic mean of all sixteen traits through 6 periods (baseline and five follow-ups) were significant. Gradually, the forced vital capacity in one second (FEV1) reflected the only significant SNP heritability among longitudinal changes at a false discovery rate (FDR)-adjusted 0.05 significance level  contains supplementary material, which is available to authorized users. Single nucleotide polymorphism (SNP)-based heritability  were obtained for each individual. For each subject, both the average phenotypic traits and their longitudinal changes were estimated via subject-specific regression analysis, using intercepts and coefficients of ages, respectively. Each The respective Institutional Review Board (IRB) of Seoul National University reviewed and approved the informed consent, the study protocols and other documents (Permit No. E1605/002-003). All methods were performed in accordance with the relevant guidelines and regulations.Korea Associated Resource (KARE) data are based on a community-based epidemiological study and comprises subjects residing in Ansan (urban area) and Ansung  in the Gyeonggi Province of South Korea  analysis < 10−5, minor allele frequencies (MAFs) < 0.05, and genotype call rates < 95% were excluded. Furthermore, subjects with missing genotype call rates > 5% or sex-based inconsistencies were excluded. The missing genotypes for typed SNPs were imputed on the basis of the 1000-genome sequence reference data. After QC analysis, 305,158 SNPs were analyzed for SNP heritability and GWAS  at the period j, the following linear regression model was adjusted with repeated measures for each subject i as follows:i indicates the ith subject, and jth period observed value of subject i for trait k, i for trait k when he or she is k. The estimated values of The phenotypic averages and longitudinal changes for each subject were determined and used to estimate SNP heritability and for the GWAS. Significant differences in phenotypic variances were observed for each period, and such heteroscedasticity was considered for phenotypic averages and longitudinal changes for each subject as follows. First, the linear regression model for subjects of the same period was adjusted for traits. The effect of sex, age, and top 10 principal component (PC) scores estimated from the genetic relationship matrix were adjusted as covariates. Considering A schematic representation of the heritability analysis and genome-wide association study is shown in Fig. For those 6843 subjects, a multidimensional scaling (MDS) plot was generated Fig. . As showP = 1.665 −16, FDR = 2.664 −15). The subsequent three highest heritability traits were total cholesterol (TCHL), log(HDL), and low-density lipoprotein (LDL), with values of 0.265 , 0.241 , and 0.222 , respectively. These three traits are cholesterol-related. The heritability of waist was 0.218  and that of weight was 0.196 . The heritability was 0.195 for Hb  and 0.192 for log(TG) . The heritability of the other traits with an FDR larger than 1 −6 were less than 0.19.We calculated the descriptive statistics for mentclass2pt{minimP value was 0.0189. The heritability estimates of other traits were less than 0.1. The second highest heritability was 0.0941 for FVC, and its FDR-adjusted P value was 0.166. The heritability of waist was also relatively higher than that of other traits. Waist heritability and the FDR-adjusted P values were 0.0082 and 0.0657, respectively. The higher heritability estimates for Figure r = 0.58, P = 0.0045) in FEV1 . Table P values for log(TG) and log(HDL) than any other trait. The most significant variant for log(TG) was rs6589566 in ZPR1 with a P-value of 7.9 −38, the lowest P value among all 16 traits. Furthermore, ZPR1 is associated with TG  of log(TG) was proximal to BUD13, which is associated with TG  is proximal to LPL, which was strongly associated with HDL  of log(HDL) and rs2335418 (P = 3.2 −9) of LDL, which were previously unknown; however, both their proximal genes LPL and HMGCR are significantly associated with each trait  was the most significant variant both in FEV1 (P = 1.22 −8) and FVC (P = 1.40 −9) , and the SLC6A1 enhancer was associated with lung function. Other variants including rs7209788  for FEV1 and rs2668162  for FVC had P-values less than the 1 −6 threshold (S2 Table). From the regional plot , we found that rs4789777 is highly correlated with rs7209788 of FEV1. The Manhattan Plot and QQ plot for the model with Table In this study, SNP-based heritability estimates of 16 phenotypic traits were estimated longitudinal data from a 10-year follow-up of the KARE cohort. The GCTA tool was used with a two-stage approach to determine the heritability estimate of phenotypic mean and longitudinal changes in each trait. Moreover, chromosomal heritability estimates were determined and GWAS analyses were performed using the same approach. Overall, heritability estimates within the population-based cohort including KARE are potentially lower than those of pedigree or twin studies for all 16 traits, regardless of whether the response is Based on the present P = 2.13 −15) of log (HDL) and rs2335418 (P = 3.2 −9) of LDL were both unreported; however, their proximal genes LPL and HMGCR, respectively, were significantly associated with each trait  was significant in both FEV1 and FVC lung function. The SLC6A1 enhancer is associated with pulmonary function. Therefore, the present results are concurrent with previous findings regarding genes associated with each phenotype.On GWAS, the two-stage model elucidated significant variants associated with the traits and their changes in the longitudinal data. We confirmed several proven variants and identified some other significant unreported variants. In the case of the Among the 16 phenotypic traits in this study, only FEV1 displayed longitudinally significant heritability herein Fig. , thus reThis study has several limitations. First, the analysis of new variants in the present GWAS was not replicated for other cohorts. Second, the two-stage approach is statistically inefficient even though it is computationally fast. However, the sample size was very large, which hopefully minimized this problem. Furthermore, we considered subjects with at least three or more measurements, which potentially minimize statistical power loss. Third, gene-environment interactions were not analyzed, although the estimation of random effects in the mixed model was elusive. Fourth, GCTA itself has limitations for reasons such as data overfitting and skewed singular values Below is the link to the electronic supplementary material.


Genome-wide association studies (GWAS) have identified thousands of genomic regions affecting complex diseases. The next challenge is to elucidate the causal genes and mechanisms involved. One approach is to use statistical colocalization to assess shared genetic aetiology across multiple related traits  to identify causal pathways, prioritize causal variants and evaluate pleiotropy. We propose HyPrColoc , an efficient deterministic Bayesian algorithm using GWAS summary statistics that can detect colocalization across vast numbers of traits simultaneously . We perform a genome-wide multi-trait colocalization analysis of coronary heart disease (CHD) and fourteen related traits, identifying 43 regions in which CHD colocalized with ≥1 trait, including 5 previously unknown CHD loci. Across the 43 loci, we further integrate gene and protein expression quantitative trait loci to identify candidate causal genes. Statistical colocalisation is a method to identify causal genes and shared genetic aetiology across traits. Here, the authors describe HyPrColoc, an efficient Bayesian divisive clustering algorithm which integrates summary statistics from genome-wide association studies to detect clusters of colocalised traits from large numbers of traits. However, identification of the causal mechanisms underlying these associations and subsequent biological insights have not been as forthcoming, due to issues such as linkage disequilibrium (LD) and incomplete genomic coverage. One approach to aid biological insight following GWAS is to make use of functional data. For example, candidate causal genes can be proposed when the overlap in association signals between a complex trait and functional data (e.g. gene expression) is a consequence of both traits sharing a causal variant, i.e. the association signals for both traits colocalize. The abundance of significant associations identified by GWAS means that chance overlap between association signals for different traits is likely1. Consequently, overlap does not by itself allow us to identify causal variants2. Statistical colocalization methodologies seek to resolve this. By constructing a formal statistical model, colocalization approaches have been successful in identifying whether a molecular trait (e.g. gene expression) and a disease trait share a causal variant in a genomic region7, and potentially prioritise a candidate causal gene. Recently it has been proposed that colocalization methodologies can be further enhanced by integrating additional information from multiple intermediate traits linked to disease, e.g. protein expression, metabolite levels8. The underlying hypothesis of multi-trait colocalization is that if a variant is associated with multiple related traits then this provides stronger evidence that the variant may be causal8. Thus, multi-trait colocalization aims to increase power to identify causal variants. We show that by using multi-level functional datasets in this way can reveal candidate causal genes and pathways underpinning complex disease.Genome-wide association studies (GWAS) have identified thousands of genomic loci associated with complex traits and diseases , to identify colocalized association signals using summary statistics on large numbers of traits. The approach extends the underlying methodology of COLOC and MOLOC. Our major result is that the posterior probability of colocalization at a single causal variant can be accurately approximated by enumerating only a small number of putative causal configurations. Moreover, HyPrColoc identifies subsets (which we refer to as clusters) of traits which colocalize at distinct causal variants in the genomic locus by employing a novel branch and bound divisive clustering algorithm. We show that the multi-trait clustering method of HyPrColoc has several performance advantages over alternative colocalization approaches and apply HyPrColoc genome-wide to coronary heart disease (CHD) and many related traitsm traits share a causal variant ; and (ii) partitioning of traits into clusters, such that each cluster comprises traits sharing a causal variant. HyPrColoc only requires regression coefficients and their corresponding standard errors from summary GWAS . The approach makes three key assumptions: (i) for non-independent studies, that the GWAS results are from the same underlying population, i.e. that the LD pattern is the same across studies, (ii) that there is at most one causal variant in the genomic region for each trait , and (iii) that these causal variants are either directly typed or well imputed in all of the GWAS datasets8.HyPrColoc is a Bayesian method for identifying shared genetic associations between complex traits in a particular gene region using summary GWAS results. HyPrColoc provides two principal novelties: (i) Efficient computation of the posterior probability that all S to be a binary m × Q matrix, where m is the number of traits and Q is the number of variants. To increase the probability of identifying any underlying causal variant(s) in the region, the number of SNPs Q included in analyses should be maximised, i.e. the region should be well imputed. Sij is 1 if the jth variant is causal for the ith trait and 0 otherwise (H0) of no causal variant for any trait, hypotheses such as Hm: all m traits share a causal variant correspond to multiple configuration matrices, S . If the summary data between traits are correlated because a subset of the participant data was used in at least two of the GWAS analyses, then an extension to Wakefield’s approximate Bayes factors, which jointly models the trait associations, can be employed (‘Methods’). For a given hypothesis H and set of corresponding configurations S, p(S), can either be equal for all 2 and MOLOC8 to a framework that is suitable for the analysis of large numbers of traits. We adopt an approach which requires the specification of a partition of the traits into clusters, together with two interpretable parameters: p, the probability that a variant is causal for one trait; and pc, the conditional probability that a variant is causal for a second trait given it is causal for one trait (‘Methods’). As it will be helpful later, we refer to pc as the conditional colocalization prior. COLOC2 requires specification of three prior parameters {p1, p2, p12} and, while the scope of the configuration priors in HyPrColoc is different for more than a pair of traits, it is instructive to note that p ≡ pi, for m = 2. To help users of the COLOC2 software, our software allows users to specify the parameter p and one of either (i) pc; or (ii) p12, from which pc is computed. For simplicity and as a conservative measure, we assume a priori that the genetic association probability p and the conditional colocalization probability pc are equal for all traits. This approach allows sensitivity analyses assessing robustness of posterior inference to be routinely performed. However, it implicitly assumes traits are a priori exchangeable, e.g. assumes p1 = p2; this is supported across a range of designs (case/control or quantitative trait) but may lead to poorer performance in specific datasets14.where Q variants, the aim is to evaluate the PPFC, P(Hm|D), that all m traits share a causal variant within that region, given the summarized data D. According to Bayes’ rule, this is given by:For a pre-specified genomic region comprising p(D), requires the exhaustive enumeration of (Q + 1)m causal configurations, which is computationally prohibitive for m > 4, e.g. MOLOC8. HyPrColoc overcomes this challenge by approximating p(D) in a way that is both computationally efficient, i.e. has fast computational time, and tightly bounds the approximation error.Brute-force computation of the denominator, As we show in the ‘Methods’, the PPFC can be approximated asPR, PA > 0 are rapidly computable values that quantify the probability that two criteria necessary for colocalization are satisfied  or (ii) alignment (PA) selection . For each simulation scenario, 1000 replicates were performed.We created simulated datasets by resampling phased haplotypes from the European samples in 1000 Genomesm traits and in a region of Q variants, can be accurately approximated by computing m ≤ 4, traits the median absolute relative difference between the HyPrColoc and MOLOC8 posterior probabilities was found to be ⪅ 0.5%  in scenario (i) and  in scenario (ii). There is a considerable difference between the results from each scenario, but the PPFC is below the threshold for declaring colocalization in both situations.When at least one trait did not have a causal variant in the region the false detection rate was negligible. For example, we generated 100 quantitative traits, each from a study with sample size 10,000, in which 99 traits share a causal variant and the remaining trait had either: (i) a distinct causal variant or (ii) no causal variant in the region. In each scenario a causal variant explained 1% of trait variation. The 1st, 5th (median) and 9th deciles of the PPFC were (4 × 10r2 ≥ 0.99) with the true causal variant and for large numbers of traits, i.e. m ≥ 20, with sample size 20,000, the two variants were in perfect LD, i.e. r2 = 1  and false positive rate (FPR), see Methods for more details. We simulated 10 traits from non-overlapping datasets under three scenarios: (i) a single cluster of 10 colocalized traits; (ii) 2 clusters of 3 colocalized traits, the remaining 4 traits do not have a causal variant  and (iii) 4 clusters of colocalized traits, comprising 2 clusters of 3 traits and 2 clusters of 2 traits. Scenarios (ii) and (iii) are designed to simultaneously investigate potential false and true positive findings. Each cluster of colocalized traits share a single causal variant and causal variants between clusters are distinct, but can be in perfect LD, i.e. r2 = 1, with one another—we assess results when the single causal variant assumption is violated later. To mirror real scenarios in which data are taken from studies with different sample sizes, we take the number of individuals in each study (Ni) as a random draw from the set Ni ∈ {1k, 5k, 10k, 15k, 20k}. For comparison, we additionally present results when all studies have a large sample size by also performing an analysis in which Ni = 15k for all traits. In all scenarios, the causal variant for each trait explained 1% of trait variance and the probability parameters were set to 14, we assess sensitivity to the choice of colocalization prior pc, i.e. (1 − γ). Across a wide range of simulated data, Wallace14 demonstrated that setting p12 = 5 × 10−6 in COLOC (approximately pc = 0.05 in HyPrColoc) was generally a robust choice. Starting from this value, we evaluated results with more conservative choices of pc by performing three separate analyses for each dataset using pc ∈ {0.05, 0.02, 0.01}, equivalent to p12 ≈ {5 × 10−6, 2 × 10−6, 1 × 10−6} with p = 10−4 fixed14, in order to identify a robust choice of pc. These values can result in substantial differences in the prior probability of colocalization as the number of traits in a cluster increases (‘Methods’). For comparison, we compare HyPrColoc against the alternative of performing pairwise colocalization analyses using COLOC2, which restricts clusters’ sizes to two traits only. Results are presented in Figs. Here we assess the performance of the branch and bound (BB) divisive clustering algorithm to identify clusters of colocalized traits over a range of scenarios, several specifications of the conditional colocalization prior pc, improving to around 1 when the sample size of each study is large , relative to scenarios (ii) and (iii) where we observed little sensitivity to pc  up to 0.16, 0.1 and 0.08 when pc was 0.05, 0.02 and 0.01, respectively  when pc = 0.01, the 1st, median and 9th deciles of the FPR were all zero. The FPR reduced for the pairwise approach after thresholding, but the TPR reduced as well. In pairwise approaches, a cluster of 3 or more colocalized traits is identified if and only if all pairs of traits colocalize , the TPR of the pairwise method reduced after thresholding as only some of the pairs of traits passed the posterior threshold which increased the false negative rate. This is a drawback of methods which do not perform multi-trait colocalization. We repeated this simulation procedure for 20 traits and the results were similar  while maintaining a low FPR throughout. The HyPrColoc default pc = 0.02 is equivalent to setting p12 ≈ 2 × 10−6 which, for a pair of traits, is slightly more conservative than the recommended value of p12 = 5 × 10−6 by Wallace14. For more than a pair of traits, however, it can be much more conservative, e.g. setting pc = 0.05 (i.e. p12 ≈ 5 × 10−6) returns a prior probability of colocalization across 10 traits that is around 2000 times larger than when setting pc = 0.02 (i.e. p12 ≈ 2 × 10−6).We observed that both HyPrColoc and pairwise COLOC perform reasonably well across all three scenarios. The median accuracy and TPR is generally ≥0.75, for all three choices of 0.7 Fig. . This prpc and the threshold parameters In scenarios (i), (ii) and (iii), HyPrColoc identified the clusters of colocalized traits on average 50, 30 and 25 times faster than the pairwise COLOC approach, indicating some sensitivity in computational performance to the type of colocalization structure present in the data. These figures improved to 200, 100 and 75 times faster when analysing 20 traits. The computational gains of HyPrColoc make it practical to perform multiple rounds of colocalization analyses, each with different values of the prior https://github.com/cnfoley/hyprcoloc), offering further guidance on the choice of prior configuration probabilities and assessing any sensitivity of the clusters of colocalized traits identified to the choice of prior parameters.We further tested the algorithm using a variety of thresholds ≈0.75%) or the same amount of trait variance as the shared variant (≈1%).We assessed the performance of HyPrColoc when two or more traits have more than a single causal variant in the region. We simulated data for 10 traits and allowed up to 5 traits to have additional distinct causal variants in the region, so that the sample contains a mixture of traits which either satisfy or violate the single causal variant assumption. The data are generated under three scenarios, as previously, but now each cluster of colocalized traits share a single causal variant and half of the traits in a cluster have secondary distinct causal variants (‘Methods’). In terms of marginal genetic associations, the additional variants were randomly selected to explain either slightly less trait variance than the shared causal variant  HyPrColoc regularly identified 8 of 10 traits as jointly colocalized; in scenario (ii) 5 out of 6 traits and; in scenario (iii) both clusters of colocalized traits, comprising 5 and 3 traits respectively  where computationally practical, running pairwise analyses using a multi causal variant method, e.g. eCAVIAR5 or ENLOC6, on the traits or clusters of traits which are reported in (a) but are not identified as colocalizing with PRPA > 0.7 using the more stringent prior pc = 0.01 - this may help clarify if traits are being removed from clusters owing to the presence of additional non-shared causal variants, e.g. scenario (iii)  - and had greater variation between the 1st and 9th deciles when the single causal variant assumption was violated  Fig. , and shoii) Fig. .5 , another software package for colocalization which allows each trait to have multiple causal variants but is limited to the analysis of pair of traits only. We note that the SNP level CLPP measure of eCAVIAR is computed in the presence of multiple causal variants and is distinct from the SNP level probabilities, computed under a single causal variant assumption, which comprise the posterior probability measure returned by HyPrColoc and COLOC -  making comparisons between the methods challenging. We compare the methods as they are used in practice, summarizing HyPrColoc and COLOC using the posterior probability of the hypothesis that a cluster or a pair of traits colocalize14 and summarizing eCAVIAR using the SNP-level CLPP. Our choice of CLPP cut-off of 1% was shown to have a low FPR across a range of scenarios previously5. In our analyses we found that pairwise eCAVIAR had increased accuracy relative to HyPrColoc and pairwise COLOC, e.g. in scenario (i) median accuracy improved by as much as 0.15 (when sample sizes varied) and 0.2 (when sample sizes were large)  and protein expression28 quantitative trait loci (pQTL) information into our analyses to prioritise candidate causal genes (‘Methods’).We used HyPrColoc to investigate genetic associations shared across CHD29. Other traits colocalizing with CHD across multiple genomic regions were cholesterol measures (16 regions); adiposity measures (9 regions); type 2 diabetes  and; rheumatoid arthritis (2 regions). Moreover, by colocalizing CHD and related traits, our analyses suggest these traits share some biological pathways.Our genome-wide analysis identified 43 regions in which CHD colocalized with one or more related traits Fig. –3. Twent35. Importantly, 20 of these were reported after the CARDIoGRAMplusC4D study17. For example, FGF5 was sub-genome-wide significant (P > 5 × 10−8) with CHD in the 2015 data, but through colocalization with blood pressure, we highlight it as a CHD locus and it is genome-wide significant in the most recent CHD GWAS26. The remaining 18 regions were reported previously, but one, APOA1-C3-A4-A5, was sub-genome-wide significant in the CARDIoGRAMplusC4D study17 despite having been reported previously35. However, we used HyPrColoc to show that the association of major lipids colocalize with a CHD signal, highlighting this as a CHD locus in these data . Our results also illustrate that multi-trait colocalization analyses can provide further insights into well-known risk-loci of complex disease. For example, at the well-studied SH2B3-ATXN2 region35, HyPrColoc detected two cholesterol measures , two blood pressure measures  and rheumatoid arthritis (RA) colocalizing with CHD at the previously reported CHD-associated SNP26 rs7137828  and HyPrColoc identified a single variant that explained over 75% of the posterior probability of colocalization, supporting this SNP as a candidate shared CHD/TG variant.In thirty-eight of the 43 88%) colocalized regions, the candidate causal SNP proposed by HyPrColoc and/or its nearest gene, have been previously identifiedta Table . The loc8% coloca27 and protein28 expression into the colocalization analyses. We tested cis eQTL for 1828 genes and cis pQTL from the 854 published proteins across the 43 loci for colocalization with CHD and the related traits. Of the 43 listed variants (Tables P < 5 × 10−8) and a total of 125 such genes were identified. HyPrColoc refined this, identifying six regions colocalizing with eQTL for one expressed gene and one region, the FHL3 locus, colocalizing with expression of three genes  , with the G allele increasing DBP and risk of CHD. We furthermore show that the association colocalizes with expression of GUCY1A1 in whole blood, with the G allele reducing GUCY1A1 expression  and that BCAR1 expression colocalized with the CHD association (PPFC = 0.86). Other studies have implicated the locus in CHD34 and suggested BCAR1 as the causal gene in carotid intimal thickening42. We note that two CHD loci also colocalize with circulating plasma proteins, APOA1-C3-A4-A5, with apolipoprotein A-V and the APOE locus with apolipoprotein E 15 at seven loci . Despite the possible presence of multiple causal associations at other loci, HyPrColoc was still able to pick out single shared associations across traits: a result supported by our simulation study when additional distinct causal variants explain less or similar trait variation than that explained by a shared causal variant between colocalized traits .Of the 38 known CHD loci that colocalized with a related trait, 8 are reported to have a single causal variantd traits . In our 2, but enables colocalization analyses to be performed across massive numbers of traits, owing to the insight that the posterior probability of colocalization at a single causal variant can be accurately approximated by enumerating only a small number of putative causal configurations. HyPrColoc avoids repeated rounds of pairwise colocalization analyses which can inflate the false negative rate and have reduced performance in identifying a shared causal variant. The HyPrColoc algorithm was validated using simulations and used to assess genetic risk shared across CHD and related traits. Using CHD data from 201517, in which 46 regions were genome-wide significant (P < 5 × 10−8), our multi-trait colocalization analysis identified 43 regions in which CHD colocalized with ≥1 related trait. With this approach, we were able to identify CHD loci that were not known at the time of the data release (2015), demonstrating the benefit of synthesising data on related traits to uncover potential new disease-associated loci36. A further five regions, we postulate, may be identified as CHD loci in the future. Others have considered pleiotropic effects of CHD loci previously43, but our formal colocalization analyses are more robust, e.g. in the ABO region we show colocalization of T2D and DBP in addition to the previously reported pleiotropic effect with LDL. We integrated eQTL and pQTL data to prioritise candidate genes at some loci, e.g. GUCY1A1, BCAR1 and APOE.We have developed and applied a deterministic Bayesian colocalization algorithm, HyPrColoc, for multi-trait statistical colocalization analyses. HyPrColoc is based on the same underlying statistical model as COLOC44.The HyPrColoc algorithm identifies regions of the genome where there is evidence of a shared causal variant (by dissecting the genome into distinct regions) and also allows for a targeted analysis of a specific genomic locus of primary interest, e.g. when aiming to identify the perturbation of a biological pathway through the influence of a particular gene. Moreover, these region-specific analyses can highlight candidate causal genes, which will help improve biological understanding and may indicate potential drug targets to inform medicines developmentSH2B3, where multiple causal variants for the expression of this gene masks colocalization with the CHD signal, we discuss an approach to building colocalization analyses which might help support the single causal variant assumption . The computational advantages of HyPrColoc make it practical to assess sensitivity of results to the specification of prior and threshold parameters as part of regular use. The HyPrColoc software includes a tool to do this, visualizing any changes in the clusters of colocalized traits identified as parameters are varied. Nevertheless, other priors may be more appropriate for particular applications.We have described HyPrColoc under the assumption of at most one causal variant per trait. Future work is required to extend this methodology and algorithm to multiple-causal variants. We note that the reliability of results under the single causal variant assumption only break down when secondary causal variants explain as much trait variation as the shared variant . An examsumption . We noteIn summary, we have developed a computationally efficient method that can perform multi-trait colocalization on a large scale. As the size and scale of available data on genetic associations with traits increase, computationally scalable methods such as HyPrColoc will be increasingly valuable in prioritizing causal genes and revealing causal pathways.Yi denote one of i = 1,2,…,m, traits assessed in a maximum of m studies, i.e. two or more traits can be measured in the same study, and Gij denote the genotype of the jth genetic variant. It is assumed that the outcome model for Yi is given byLet αij is the intercept term and hi is a function linking the ith outcome to the genotype Gij, for all j = 1,2,…,Q genetic variants in the genomic region. The function hi is typically taken as the identity function for continuous traits and the logit function for binary traits. The aim of colocalization analyses is to identify genomic loci where there exists an Gij that is causally associated with at least two of the m traits. For each of the m traits and Q genetic variants, we assume that GWAS summary statistics where S) that can be grouped into sets (H). We use the notation set of hypotheses in which a collection of i traits share a causal variant, a separate collection of j traits share a distinct causal variant, and so on . The posterior probability of hypothesis H, given the combined data D from all m studies, can therefore be computed using /p(S0) is the prior-odds of configuration S0, i.e. no genetic association with any trait. See ref. 2 for a derivation with m = 2 traits. BF(S) is a Bayes factor which is the likelihood of the data being generated under S0.where 8. We note, however, that each causal configuration is equivalent to a model which, for each trait, details the location of the causal variant in the region. Hence, the problem of identifying a hypothesis and causal configuration with the greatest support given the data D, is equivalent to identifying the joint trait-variant model with greatest support13.We describe the space of multi-trait colocalization models using a set of mutually exclusive hypotheses and causal configurations as this approach extends the methodology and language used previously13 (ABF) for each trait i and genetic variant j, i.e.If the trait associations are calculated using independent studies (i.e. no overlapping samples in the GWAS datasets), the Bayes factors can be computed using Wakefield’s Approximate Bayes Factorszij, vij and wij are the Z-statistic, standard error and the prior standard deviation for 2, for continuous variables wij is set to 0.15 while for binary traits it is set to 0.2. As an example, the ABF for the hypothesis that all m traits colocalize at genetic variant j (where ABF (JABF)  . The JABm traits, m × m variance-covariance matrix of the regression coefficients . The correlation matrix th is also colocalized, conditional on the other k traits, increases as the number of colocalized traits k grows. The marginal prior probability of k traits colocalizing is always very small, however, which controls the false positive rate  while maintaining a low FPR throughout. Using the same posterior threshold of 0.7 and setting pc = 0.05 returned reasonable results. However, we do not recommend users set pc = 0.05 due to the slight increase in the 9th decile of the FPR in scenario (iii)  Fig. . If two ii) Fig. .47. This strategy benefits from: (i) not setting variant-level information and (ii) implicitly accounting for large differences in the causal configuration space between hypotheses, which limits the loss in power of the PPFC for very large m. These priors take the form,An alternative prior strategy is to assume uniform priors for each configuration within a hypothesiswhere Through simulations, we identified the conditionally uniform prior as less conservative than variant-level priors, having an increased false detection rate of colocalization. , 11. ThiP(Hm|D), Pscv, Pm−1,1) the posterior probability of full colocalization; (ii) the sum of the posterior probabilities in which no traits have a causal variant, a subset of m − 1 traits share a causal variant  and all m traits colocalize (Pscv); (iii) the sum of posterior probabilities in which a subset of m  − 1 traits share a causal variant and the remaining trait has a distinct causal variant  and; (iv) the sum of all posterior probabilities of at most one causal variant per trait . That is,To compute the posterior probability of full colocalization across a large number of traits we propose the HyPrColoc posterior approximation. Let PR, defined as:The HyPrColoc posterior is computed in two steps. Step 1 computes the regional association probability PA, defined as:Step 2 computes the alignment probability PR is computed using (m + 1)Q causal configurations and PA is computed using an additional mQ(Q − 1) causal configurations. Hence, computation of PR and PA has Note that δR = 1−PR, δA = 1−PA andwhere PR and PA can be defined for various collections of hypotheses that partition Pall. However, the major insight is that the hypotheses contained in PR and PA are computed with minimal computation burden, i.e. computed using ≤mQ2 causal configurations, amongst all alternatives, making the HyPrColoc approximation tractable for very large numbers of traits m.. By defiPR, e.g. we can computeOur software allows for the assessment of the HyPrColoc approximation by increasing the number of hypotheses used to approximate PR and PR  the minimum probability required to accept evidence that all m traits are regionally associated m traits aligns at a single variant m traits sharing a single causal variant if PPFC and stops. If either m − 1 traits sharing a causal variant. At this point the traits are partitioned into two clusters: one containing m − 1 traits deemed most likely to share a causal variant and a second cluster containing the remaining trait. We repeat this process of branch selection and partitioning on the cluster of m − 1 traits until we identify either: (A) a cluster of traits of size k ≥ 2 whose regional and alignment statistics satisfy k traits colocalize is presented and the remaining m–k traits are assessed for evidence of colocalization using the branch selection and partitioning scheme. In scenario B, the trait is deemed not colocalize with any other trait in the sample and the BB selection algorithm is repeated using m − 1 traits. The entire process is repeated until all clusters of colocalized traits, whereby each cluster of traits colocalize at a distinct causal variant, have been identified, all other traits are deemed not to share a causal variant with any other trait.To identify complex patterns of colocalization amongst all traits, we propose a branch and bound (BB) divisive clustering algorithm that utilizes the HyPrColoc approximation to identify a cluster of traits with the greatest evidence of colocalization at each iteration  was randomly chosen from the set Ni ∈ {1,000, 5,000, 10,000, 15,000, 20,000}. Variant-level priors were chosen for the simulation study: we set p = 10−4 as in refs. 14 and, to assess sensitivity of results to the choice of conditional colocalization prior pc, we ran each simulation three times for each of pc ∈ {0.05, 0.02, 0.01}. Note that pc = 1 − γ, so this is equivalent to γ ∈ {0.95, 0.98, 0.99}. For a pair of traits, colocalization between the traits is 5 times more likely a-priori when setting pc = 0.05 relative to pc = 0.01. In the analysis of ten traits, however, colocalization between all ten traits is around 1 million times more likely a-priori when setting pc = 0.05 relative to pc = 0.01. The prior probability of colocalization is still very small ~10−11 when setting pc = 0.05, however. Hence, the different values of pc we have chosen can result in substantial differences in the prior probability of colocalization.To create genomic loci with realistic patterns of LD, for each simulation scenario we simulated 1000 datasets and for each dataset we resampled phased haplotypes from the European samples in 1000 GenomesThese data were generated under three scenarios: (i) a single cluster of 10 colocalized traits, each trait shares a single causal variant and 5 traits have secondary distinct causal variants; (ii) a single cluster of 6 colocalized traits, each of the 6 traits share a single causal variant and 3 traits have secondary distinct causal variants, the remaining 4 traits do not have causal variants and; (iii) 2 clusters of colocalized traits, cluster 1 comprises 6 traits sharing a single causal variant with 3 of 6 traits having secondary distinct causal variants, cluster 2 comprises 4 traits sharing a single causal variant with 2 of 4 traits having secondary distinct causal variants. To maximize the number of traits with additional causal variants in a cluster (up to the maximum of 5), in scenarios (ii) and (iii) the total number of clusters of colocalized traits were reduced relative to the single causal variant assessment.Measuring the accuracy, true positive and false positive rates of HyPrColocwhere TP and TN denote the true positive count and true negative count, and FP and FN denote the false positive count and false negative count. Hence, accuracy is the proportion of traits that are correctly identified as colocalizing or not colocalizing. To compare HyPrColoc with pairwise methods, we compute the TP, FP, TN and FN rates by aggregating information across all pairs of traits in the sample. A TP is measured when a pair of observations are correctly deemed to colocalize, a FP is measured when a pair of traits are incorrectly identified as colocalizing, a FN is recorded when a pair of traits are wrongly deemed not to colocalize and a TN is recorded when a pair of traits are correctly identified as not colocalizing.PAPR > 0.7. In the simulation study which allowed each trait a maximum of one causal variant in the region and with respect to scenarios (i), (ii) and (iii), when setting pc = 0.05 HyPrColoc identified clusters of colocalized traits with PRPA > 0.7 in approximately 70%, 93% and 99% of simulated datasets, when pc = 0.02 in approximately 65%, 91% and 98% datasets, reducing to around 60%, 86% and 97% of datasets when pc = 0.01. Pairwise COLOC identified pairs of colocalized traits with PRPA > 0.7 in over 96% of simulated datasets, across all three scenarios and specifications of pc. In the simulation study which allowed a maximum of two causal variants per trait, these figures reduced: when setting pc = 0.05 HyPrColoc identified clusters of colocalized traits with PRPA > 0.7 in approximately 65%, 80% and 93% of simulated datasets, when pc = 0.02 in ~60%, 72% and 92% datasets, reducing to around 55%, 65% and 85% of datasets when pc = 0.01. Pairwise COLOC identified pairs of colocalized traits with PRPA > 0.7 in over 94% of simulated datasets, across all three scenarios and specifications of pcWhen thresholding the posterior probability of colocalization, the TP, FP, TN and FN rates are computed after excluding traits which do not to colocalize with any other trait such that17, blood pressure , adiposity measures , glycaemic traits18, renal function19, type II diabetes20, lipid measurements21, smoking22, rheumatoid arthritis23 and educational attainment24 . We performed colocalization analyses in two steps. In step one, we assessed colocalization of CHD with the 14 risk-factors in pre-specified LD blocks from across the genome25. We used a conservative variant-level prior structure with p = 1 × 10−4 and γ = 0.98, i.e. 1 in 500,000 variants are expected to be causal for two traits, and set strong bounds for the regional and alignment probabilities, i.e. PRPA > 0.64. The full results from this analysis are available at https://jrs95.shinyapps.io/hyprcoloc_chd.The GWAS results used in the assessment of colocalization of CHD with related traits were taken from large-scale analyses of CHD24 Table . All datcis eQTL27  and cis pQTL28 (3301 samples) data in addition to the primary traits in a second step, using the same LD blocks as before. A colocalization analysis was performed for every transcript with data within each region. cis eQTL were defined 1MB upstream and downstream of the centre of the gene probe . cis pQTL were defined 5MB upstream and downstream of the transcript start site . We integrated gene expression information taken from whole blood tissue as: (i) the eQTLGen dataset27 has a large sample size relative to other publicly available gene expression data resources and; (ii) the pQTL data were also measured in whole blood tissues, so there was consistency in the tissue analysed.To prioritise candidate causal genes in regions where CHD and at least one related trait colocalized, we re-ran the colocalization analysis and included whole blood Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


The high cyanogenic glucoside content in some cassava varieties prevents herbivory but can be toxic for human consumption. The identification of an intracellular transporter gene and its allelic variation allow us to identify cultivars with up to 30% reduced cyanogenic glucoside content in cassava root. Manihot esculenta (cassava) is a root crop originating from South America that is a major staple in the tropics, including in marginal environments. This study focused on South American and African germplasm and investigated the genetic architecture of hydrogen cyanide (HCN), a major component of root quality. HCN, representing total cyanogenic glucosides, is a plant defense component against herbivory but is also toxic for human consumption. We genotyped 3354 landraces and modern breeding lines originating from 26 Brazilian states and 1389 individuals were phenotypically characterized across multi‐year trials for HCN. All plant material was subjected to high‐density genotyping using genotyping by sequencing. We performed genome‐wide association mapping to characterize the genetic architecture and gene mapping of HCN. Field experiments revealed strong broad‐ and narrow‐sense trait heritability . Two major loci were identified, encoding for an ATPase and a MATE protein, and contributing up to 7 and 30% of the HCN concentration in roots, respectively. We developed diagnostic markers for breeding applications, validated trait architecture consistency in African germplasm and investigated further evidence for the domestication of sweet and bitter cassava. Fine genomic characterization revealed: (i) the major role played by vacuolar transporters in regulating HCN content; (ii) the co‐domestication of sweet and bitter cassava major alleles are dependent upon geographical zone; and (iii) the major loci allele for high HCN in M. esculenta Crantz seems to originate from its ancestor, M. esculenta subsp. flabellifolia. Taken together, these findings expand our insights into cyanogenic glucosides in cassava roots and its glycosylated derivatives in plants. Manihot esculenta Crantz (cassava) is a starchy root crop that is widely grown throughout the tropics  for human and livestock consumption, and as feedstock for biofuels and other bio‐based materials   are called ‘sweet cassava’, whereas cultivars with 100–500 mg kg−1 FW are called ‘bitter cassava’  is more important; whereas in regions where the bitter cassava type dominates, it is the main carbohydrate source, generally complemented by a protein, such as a fish  are assayed as the HCN trait, a proxy representing total CGs  in cassava are synthesized in the leaves and then transported to the roots via the phloem  comprehensively understand the genetic architecture of the HCN trait  in cassava root; (ii) map the gene(s) associated with CG variation; (iii) develop a fast and cost‐effective molecular diagnostic toolkit for breeding purposes to increase selection efficiency; and (iv) investigate the role of HCN in domestication.et al., et al., H2) was calculated as 0.82 for HCN content, similar to previous observations reported on several species  that was higher than genotype‐by‐year variance (Vg × y), with the Vg × y/Vg ratio showing a year interaction value of 0.29. HCN‐deregressed best linear unbiased prediction (BLUP) shows a very high correlation with non‐deregressed BLUP, with a Pearson’s correlation coefficient of 0.99, indicating a balanced replication of individuals among the population studied   accounted for over 15.3% of the genetic variation  calling in n Figure .gcta  threshold of 5.733117, two significant peaks were identified on chromosomes 14 and 16, with 45 and 12 significant associated markers, respectively  in which six genes are annotated  is located within the Manes.16G007900 gene. Manes.16G007900 is annotated as a multidrug and toxic compound extrusion or multi‐antimicrobial extrusion (MATE) protein. MATE transporters are a universal gene family of membrane effluxers present in all kingdoms of life. MATE transporters have been implicated directly or indirectly in the mechanisms of detoxification of noxious compounds and are able to transport CGs  located 22 Kb from the candidate MATE gene  is located in Manes.14G074300, a gene coding for an integral membrane HPP family protein involved in nitrite transport activity  is located in Manes.14G073900.1, coding for a plasma membrane H+‐ATPase. H+‐ATPase mediates the influx of H+ associated with aluminimum (Al)‐induced citrate efflux coupled with a MATE co‐transport system . A multi‐kernel mixed model with the top significant SNPs in chromosomes 16 and 14 (S16_773999 and S14_5775892) as the first and second kernels, with the rest of the genome as the third kernel, explained 30, 7 and 63% of the marker‐based variance, respectively. A three‐kernel mixed model to determine the variance explained by chromosomes 14, 16 and the rest of the genome showed that the proportion of variance explained by the three kernels are 16, 50 and 34%, respectively. Chromosomes 14 and 16 tagging SNPs for the candidate SNPs explains 8 and 36% proportions of variance, respectively, whereas the rest of the genome explains 56% of the variance. We found evidence for local interactions within chromosome 16, most likely as a result of high LD around the region /2) = 1.6024, with three interactions clearly separated by 1 Mb between each pair of SNPs     and the other wild accessions of Manihot glaziovii and Manihot pruinosa (homozygote A:A) were clustered in distinct clades  was higher than genotype‐by‐environment variance (Gg × e), with the ratio (Vg × e/Vg) showing a high interaction of 0.86. The estimated deregressed BLUPs ranged from 0.0009 to 2.5638, with an average of 0.5242 (Table 10(0.05/53547) threshold of 6.029765, two significant peaks were identified on chromosomes 14 and 16, respectively  was higher than genotype‐by‐environment variance (Gg × e), with the Vg × e/Vg ratio showing a lower interaction of 0.42, compared with that of the African population alone   values of 13.9219 and 89.5362, respectively, whereas Manes.16G008000 is not and shows low expression levels  cassava variety to evaluate gene expression , germplasm from African counterparts showed much less genetic variance and heritability . Latin America/Brazil is the primary center of domestication, from where cassava was only introduced to Africa in the 16th century, which could explain the probable genetic bottleneck and the observed difference between the two populations , which was congruent with the region found on chromosome 14 associated with HCN variation in our current data sets. Whankaew et al. . The validation of the genetic architecture of HCN in an African population, the joint GWAS analysis between Africa and Latin America (Brazil), and the whole‐genome imputation of the African–Brazilian data set using HapMap as a reference for chromosome 16 confirms these results and shows that the genetic architecture of HCN is conserved, based on our data sets. Homozygous reference alleles at the loci identified showing lower HCN content are in agreement with the finding that acyanogenic plants are homozygous recessive at one of the loci  and another region in chromosome 14  gradients  and a plasma membrane H+‐ATPase‐coupled transporter on chromosome 14, as involved in HCN content regulation. In cassava genome version 6.1, the HCN biosynthesis gene cluster is located on chromosome 12 within a 75‐kb interval, including a couple of changes in orientation and gene arrangement  showed local epistasis interaction with a 1.36‐Mb region located 772 055–775 833 bp downstream. Epistatic effects that arise from alleles in gametic disequilibrium between closely located loci can contribute to long‐term responses, as recombination disrupts allelic combinations that have specific epistatic effects and the detection of epistasis is a key factor for explaining the missing heritability  . We also observed that the closest homology observed for MATEs in cassava is in line with the results of the MATE protein alignment, which displays the highest homology between MATE genes on chromosome 16 and chromosome 17  with Manes.17G038400, indicating that our candidate had undergone double‐duplication events. This finding would need further investigation to clarify the potential fate of the observed tandem duplication . MATE candidate gene topology prediction suggests that our candidate MATE protein shares a similar topology in the membrane as those observed in the MATE protein family, and functions as an efflux carrier that mediates the extrusion of toxic substances  for candidate SNP S16_773999, which is in line with its phenotypic characterization for HCN content by Perrut‐Lima et al.  and cluster separately from M. esculenta subsp. flabellifolia  regulation in cassava root and the identification of closely linked SNP markers to enhance efficiency and cost‐effectiveness through marker‐assisted selection. Further steps can include: (i) the deployment of diagnostic markers for breeding applications; (ii) the development of co‐expression studies to further assess the source–sink relationship of HCN metabolism in multi‐environmental conditions and the impact of low HCN levels on pest and disease control in cassava; (iii) the breeding and introduction of low‐HCN cassava varieties that are high yielding and disease resistant to regions often affected by agricultural and health‐related crises, such as konzo, especially in sub‐Saharan Africa. Altogether, the present study consolidates our understanding of the genetic control of CG variation in cassava root and provides further insights into using genomics of diverse genetic background populations.https://www.embrapa.br), located in Cruz das Almas, Bahia, Brazil, were used for this study  of Brazilian Agricultural Research Corporation . This data set comprises plant material from the International Institute of Tropical Agriculture .A second data set including 1363 African accessions was obtained from the open‐source cassava breeding database  to a final concentration of 60 ng μl−1, and the quality was checked by the digestion of 250 ng of genomic DNA from 10 random samples with the restriction enzyme EcoRI .DNA extraction was performed following the protocol described by de Albuquerque et al.  and Ogbo . After filtering  and imputation (AR2 > 0.8)  is taken at mid‐root for each root, between the peel and the center of the parenchyma. The cut root cube and five drops of toluene (methylbenzene or phenyl methane) are added to a glass test tube and the tube is tightly sealed with a stopper. To determine the qualitative score of HCN potential on a color scale of 1–9, a strip of Whatman filter paper is dipped into a freshly prepared alkaline picrate mixture until saturation. The saturated filter paper is then placed above the cut root cube in the glass tube and tightly sealed for 10–12 h before recording the color intensity , and included 18 locations, 23 years and 393 trials, for a total of 8244 accessions and a total of 33 523 observations from IITA . The phenotyping protocol was performed using the same protocol as for the Brazilian data set. A total of 636 unique accessions with phenotypic and genotypic information from 228 trials were retained for further analysis for the African data set.African phenotypic data were collected from the breeding database Cassavabase  is the residual variance and is assumed to be randomly distributed, Yijkl represents the phenotypic observations, µ is the grand mean, ci is the random effects for clone with ci∼N, βj is a random effect for clone nested in combination of year, kr is a random effect for combination of year and rep, assumed to be normally distributed with , and ld is a fixed effect for years. Variance components from our mixed model were used to compute the broad‐sense heritability according to the method described by Holland et al. , the bias induced by pre‐correction and induced heterogeneous residual variance  of the candidate SNP to be tested for an association, x is the SNP genotype indicator variable, g‐ is the accumulated effect of all SNPs except those on the chromosome where the candidate SNP is located and e is the residual. We used a Manhattan plot with Bonferroni threshold as a test of significant SNP associations, and compared the observed −log10(P) values against the expected values using the quantile–quantile plot. Local LD analysis was performed on significant regions in GWAS based on an r2 threshold of >0.8 to identify candidate genes. GWAS was also performed on a unique set of 1536 individuals (GU panel) from , M. esculenta (v.6.1) and S. bicolor (v3.11) genomes from Phytozome . The sequences were submitted to the TransportTP prediction server (http://bioinfo3.noble.org/transporter/) for membrane domain identification and gene curation, according to the Transporter Classification Database (TCDB) guidelines  were used to generate coding sequences (CDSs) and translated protein sequences for 241 accessions in a fasta format. Subsequent alignment and maximum‐likelihood phylogenetic trees were generated using mafft   vs. Physical (bp) positions.Click here for additional data file.Table S1. Raw HCN data set from Latin America .Table S2. Summary statistics, variance components and broad‐sense heritability for HCN.Table S3. All 1389 BLUPs for the Latin American  data set and the list of 1246 BLUPs with genotype information used for GWAS.Table S4. Significant SNPs from Latin American data set .Table S5. Significant SNPs from GWAS on 523 unique individuals.Table S6. Cultivated and cassava progenitor differentiating loci comparison: Manihotesculenta versus Manihotesculenta subsp. flabellifolia.Table S7. Designed KASP marker sequences.Table S8. HCN KASP segregation results.Table S9. All 242 significant epistasis interaction pairs of SNPs higher than Bonferroni correction threshold (two‐way test result).Table S10. Single point mutation prediction for Manes.16G007900 and Manes.16G008000.Table S11. List of countries and regions in sub‐Saharan Africa with their average BLUP values.Table S12. Raw African data set phenotypes.Table S13. African BLUPs used for GWAS analysis.Table S14. Significant SNPs from African germplasm GWAS analysis.Table S15. Raw African (IITA) and Latin American (Embrapa) phenotypes.Table S16. All 1882 combined BLUPs for Africa (IITA) and Latin America (Embrapa) GWAS.Table S17. Significant SNPs from African and Brazil germplasm.Table S18. Significant SNPs from whole‐genome imputation of chromosome 16 GWAS using HapMap II and raw GBS data set; 5000 SNP windows were used.Click here for additional data file.Data S1. Whole‐genome sequence data set for all MATE genes in cassava, Arabidopsis and sorghum.Data S2. Multiple sequence alignment for all MATE genes in cassava, Arabidopsis and sorghum.Click here for additional data file.Methods S1. Proportion of variance explained by markers.Methods S2. Genome‐wide epistasis interactions.Methods S3. Cultivated and cassava progenitor differentiating loci analysis.Methods S4. KASPAR marker design and assessment.Methods S5. Candidate gene protein topology and structure prediction.Methods S6. Single point mutation prediction.Methods S7. Geographical distribution of HCN.Methods S8. GWAS in African population and joint African and Latin American analysis.Click here for additional data file.Appendix S1. Population structure analysis.Appendix S2. Phylogenetic tree.Appendix S3. Geographical distribution of sweet and bitter cassava.Click here for additional data file.


Advancements in high-throughput technologies have made it feasible to study thousands of biological pathways simultaneously for a holistic assessment of health and disease risk via ‘omics platforms. A major challenge in ‘omics research revolves around the reproducibility of findings—a feat that hinges upon balancing false-positive associations with generalizability. Given the foundational role of reproducibility in scientific inference, replication and validation of ‘omics findings are cornerstones of this effort. In this narrative review, we define key terms relevant to replication and validation, present issues surrounding each concept with historical and contemporary examples from genomics (the most well-established and upstream ‘omics), discuss special issues and unique considerations for replication and validation in metabolomics (an emerging field and most downstream ‘omics for which best practices remain yet to be established), and make suggestions for future research leveraging multiple ‘omics datasets. But I do claim that the unique exceeds the treatment by scientific method.” Wolfgang PauliAdvances in high-throughput technologies have ushered in an era of “big data”, wherein researchers are no longer relegated to investigating single biological pathways. Rather, scientists grapple with a newfound ability to study thousands of pathways simultaneously for a more holistic understanding of (patho)physiology. The analysis and interpretation of large, high-dimensional biological data is spearheaded by the ‘omics fields comprising genomics, epigenomics, transcriptomics, proteomics, and metabolomics. The oldest and best known ‘omics is genomics, or the comprehensive study of DNA within an organism’s genome. Genomics is complemented by epigenomics, the study of the complete set of potentially reversible epigenetic modifications made to the DNA sequence. The next ‘omics layer is transcriptomics, the systematic study of RNA transcripts and gene expression. Following transcriptomics is proteomics, the study of proteins and their role in carrying out basic life processes. At the end of the ‘omics cascade is metabolomics, the study of low-molecular-weight compounds in biological tissues and fluids.While much of the data generated by the ‘omics fields in the last two decades have been qualitative or semi-quantitative in nature, rigorous quantitative analysis is key to formulating and testing novel hypotheses with the greatest potential to yield actionable next steps in the health sciences. Yet, a major challenge of quantitative ‘omics research revolves around the reproducibility of findings—a feat that lies in balancing false-positive findings  with generalizability  but also exhibits the most inter- and intra-individual variability, thereby making replication and validation more challenging. We begin by defining key terminology, followed by a presentation and discussion of commonly used approaches, summarize guidelines  for rigoWhile the practice of replication and validation is considered to be de rigueur in genetic epidemiology and genomics, there remains confusion regarding the two commonly used terms. Confirmation studies often seek to “replicate” or “validate” results without defining what this attempt comprises. As pointed out by Igl et al. , investiReplication is the more straightforward of the two types of confirmatory studies. When replication is the goal, the original and confirmatory study samples should be independent but similar  to reduce systematic differences, and the laboratory method used should be identical. Under these conditions, discrepancies in results are presumably due to random variation. Clarke et al.  describeReplication is particularly challenging for metabolomics, given that circulating metabolites are subject to metabolic flux , even in the absence of alterations to upstream ‘omics that influence metabolism. This phenomenon contributes not only to inter-individual variability , but also intra-individual variability in compounds due to factors for which researchers do not typically collect information, such as time of day of data collection , season The term “validation” is less straightforward, and refers to a few distinct concepts. The most established meaning of the term predates the era of ‘omics discovery, and refers to comparisons of specific laboratory techniques against a gold standard and is usually conducted on the same population. A hypothesis-free association study may yield several associations of interest (“hits”) in the discovery sample. The practice to date has been to validate such hits using the more expensive and time-consuming methods. In genomics, this approach has historically involved Sanger sequencing to confirm the nucleotide sequence. In metabolomics, this process involves implementation of targeted metabolomics assays to measure absolute concentrations of metabolites on a specific biochemical pathway following an initial associational discovery analysis of data generated on an untargeted metabolomics platform. In such a scenario, the discovery and validation samples are from the same population so that the only variation is introduced by the laboratory technique rather than systematic differences between populations. This form of validation is best suited for novel laboratory techniques or platforms and is less applicable to large-scale population-based studies.The second distinction is internal vs. external validation. Internal validation is used in the development of predictive models that seek to identify features most strongly associated with the disease or biological condition of interest. Building the predictive model requires a training dataset to identify a set or a group of features that account for maximal variability in the biological condition. After training, the model is tested on an independent dataset or multiple resampled datasets to assess model validity. Techniques like bootstrapping and cross-validation optimize the model and check for overfitting. Examples of such approaches include random forests ,19, a clp-values, given an allowable error rate. The FDR procedure has been successfully applied to datasets with a relatively large number of true positive associations, such as gene expression data. However, the use of FDR procedures for MWAS is compounded by the correlated nature of individual metabolic pathways , and lack of available annotations for much of the human metabolome. Thus, assignment of molecular formulas to spectral peaks during the data processing step of metabolomics pipelines does not yield comprehensive structural identifications that are critical to biological understanding [With the advent of genome-wide association studies (GWAS) and GWAS consortia like the U.K. Biobank  or indusstanding . SufficeAround the time when genetic consortia rose to prominence, it also became commonplace to reduce the dimensionality of big data by aggregating the molecular variables into pathways to first identify pathways of interest prior to assessment of individual features within the pathways. Dimension reduction is especially attractive and biologically intuitive for metabolomics analyses. Widely-used multivariate procedures include unsupervised principal components analysis ,13,26 anThe traditional approach to validating ‘omics findings begins with identifying a set of features that are associated with biological trait of interest at a predefined threshold of statistical significance, then further exploring the feature of interest in follow-up analyses. As discussed in the previous section, conservative corrections for multiple comparisons improve the reproducibility of ‘omics findings, but because metabolomics features are not independent, such correction is overly conservative. Moreover, corrections based on the number of aggregate pathways rather than single features have been shown to be insufficient , leavingp-values, leaving the analysis vulnerable to false-positive findings even after adjustment for multiple comparisons [p-value, but also the magnitude of association . This notion is fundamental to Sir Bradford Hill’s first guideline for evaluating causality: the strength of an association provides support for a causal effect of an exposure on disease risk [Of note, the most widely-used approach to selecting signals for further follow up  relies solely on parisons . One remase risk . This isase risk  for addiIn practice, there are a number of statistical techniques that focus on identifying a set of predictors from a high-dimensional dataset on the basis of magnitude of association, in addition to statistical significance. For example, the simulation extrapolation (SIMEX) algorithm has been successfully used for metabolomics data  estimatep-value information with functional annotation when selecting hits for validation may improve reproducibility. These characteristics, summarized by Gorlov et al. [Alternative strategies, such as Bayesian analyses providing a priori estimates that the association is falsely positive , are occv et al.  into a cv et al. , and is The increasing affordability of next-generation technologies has prompted re-evaluation of validation practices beyond single feature associations. That is to say, by prioritizing whole genes in genomics, differentially methylated regions of the genome in epigenomics, clusters of RNA transcripts in transcriptomics, groups of metabolites in metabolomics, and more recently, networks for multiple ‘omics variables. Validation of such integrative analyses requires internal cross-validation approaches to ensure stability and consistency in the ‘omics clusters. Many of these approaches follow those implemented in the field of genomics, but have been successfully applied to metabolomics or multiple-‘omics datasets. These include stability analyses to evaluate the optimal number of clusters , sample Once findings from the discovery stage have been prioritized for validation, considerations of the appropriate population for follow-up tests become paramount. The ideal choice of population lies between the Scylla of split-sample analysis  and the Charybdis of choosing a follow-up cohort that is so systematically different from the discovery one that any chances for successful validation are diminished.2 level [In the first scenario, dividing the original sample into two subsamples and requiring statistical significance at a given level α in each of the subsets yields lower statistical power than analyzing the entire dataset at the α2 level . This ap2 level ; or K-fo2 level  may be eIn the second scenario of selecting an independent validation population, all efforts must be undertaken to harmonize the phenotype definitions and other experimental conditions across the discovery and validation samples. To reduce systematic variation, statistical models used in the validation stage should also mirror those used in the discovery stage as closely as possible. Unaccounted sources of variation between samples, whether due to discrepant trait measurements, covariate adjustment, or population characteristics, can lead to falsely negative results in the validation stage. Differences between discovery and validation populations need to be documented and, if possible, accounted for statistically. Importantly, criteria for reconciling phenotypic definitions must be established prior to analysis to avoid cherry-picking only the definitions that yield statistical significance in the validation stage.Special caution has been applied to validation efforts across different ethnic groups. This is intuitive and imperative for genomics studies. For metabolomics, the importance of similarity of race/ethnic distributions in discovery and validation populations has been debated. On the one hand, differences in genetic architecture undoubtedly affect multiple aspects of physiology and disease etiology, and accounting for such differences will identify metabolomics profiles associated with a biological outcome that are independent of race/ethnicity. In this scenario, researchers may be interested in identifying a biomarker that performs well in a specific racial or ethnic group, such as the example of ethnicity-specific serum biomarkers of coronary artery disease , or the What constitutes a validated finding? As the data landscape expands and statistical methods evolve, this question is critical to the success of ‘omics science. Generally, a validated finding refers to an association between some feature and a phenotypic trait, where sufficient evidence exists to support a causal effect of the former on the latter. Sufficient causal evidence, in turn, most commonly refers to reproducibility as defined using established guidelines . We propIn addition to the biological plausibility and experimental evidence guidelines discussed above, several other Hill’s postulates can be used to contemplate the quality of causal evidence supporting a given association. Consistency is directly related to reproducibility: are the same findings repeatedly observed in different places, people, circumstances and times? Strength of the association refers to its magnitude, and distinguishes between mere statistical significance (easy to obtain given large enough sample sizes) and a meaningful effect, the latter of which will require longer-term follow-up studies in the field of metabolomics to understand how differences in a given metabolite concentration related to future health outcomes. Coherence situates the new finding within the existing body of evidence, and finally, considering the criterion of specificity can elucidate the etiologic architecture of a trait. While Hill himself warned against using his criteria as a checklist for causality, they nonetheless provide a useful framework for evaluating evidence generated by discovery and validation studies.2r, and others). Currently, the predictive power of ‘omics findings lags far behind reproducibility, likely due to insufficient sample sizes to detect all true effects as well as other relevant factors that explain trait variance . It is important to remember that successful validation – as defined by establishing reproducibility and, if possible, functional relevance – represents a necessary but not sufficient step towards using ‘omics findings to predict disease risk and, ultimately, serve as a way to identify viable avenues to improve health outcomes.With the growing relevance of direct-to-consumer profiling  in the wNature in 2016, 90% of scientists responded that there was either a “slight” or “significant” crisis of reproducibility in science [In a survey conducted by  science . This na science , emphasiIn 2007, the Metabolomics Standards Initiative (MSI) put forth a set of recommendations on minimal reporting standards for the laboratory chemical analysis, as well as data analysis . These sP-values to identify “hits” – namely, consideration of the magnitude of effects. Additionally, while not formally discussed herein, researchers should be aware of statistical phenomena that may impact the magnitude of effects detected in initial discovery studies , and employ a priori considerations of statistical power.For metabolomics specifically, replication and validation is critical and challenging given the higher degree of variability in metabolites, and the vulnerability of metabolite concentrations to lifestyle and environmental factors that are of markedly less concern in other ‘omics fields, notably genomics. Regardless, several topics discussed in this review are relevant to metabolomics analyses, including the need for confirmation via replication in independent study samples, the importance of internal and external validation (the latter of which requires selection of an appropriate study population to reduce systematic variability), selection of appropriate methods to correct for multiple comparisons, and use of criteria beyond The use of multiple ‘omics datasets is becoming increasingly popular in all facets of life science. In the biomedical sciences, genomics-metabolomics analyses using undirected network-based approaches have demonstrated capacity to recreate true biochemical pathways  and homeThe above concepts are the embodiment of innovative studies that capitalize on multiple ‘omics datasets to unveil findings with meaningful implications for actionable next steps. The rapid growth of ‘omics technologies and statistical packages to analyze such data necessitates the need to establish best practices for bioinformatics and analytical workflows within each individual ‘omics field, as well as for multiple ‘omics. Given that reproducible research is the foundation upon which scientific inference is made, statistical validation and replication serve as pillars that flank the journey from hypothesis testing to informing next steps for preventive or therapeutic action.


We use this crop species to examine the genetic controls of high levels of sugar accumulation, identify genetic mechanisms for the accumulation of nonstructural sugars, and link carbon allocation with iron transport. We identify a species-specific tandem duplication event controlling sugar accumulation using genome-wide association analysis, characterize multiple allelic variants causing increased sugar content, and provide further evidence of a putative neofunctionalization event conferring adaptability in Sorghum bicolor. Comparative genomics indicate that this event is unique to sorghum which may further elucidate evolutionary mechanisms for adaptation and divergence within the Poaceae. Furthermore, the identification and characterization of this event was only possible with the continued advancement and improvement of the reference genome. The characterization of this region and the process in which it was discovered serve as a reminder that any reference genome is imperfect and is in need of continual improvement.Simple sugars are the essential foundation to plant life, and thus, their production, utilization, and storage are highly regulated processes with many complex genetic controls. Despite their importance, many of the genetic and biochemical mechanisms remain unknown or uncharacterized. Sorghum, a highly productive, diverse C The continued existence of biology on Earth is largely dependent on the creation of sugar generated through carbon fixation. As one of the most fundamental sources of energy for life, understanding the biological controls of the synthesis and regulation of sugar flux in plants is critical for the continued improvement of agricultural productivity regardless of system. Sugar is not only used as a source of energy for plant cells, but it is also used as a signaling molecule for key developmental and physiological changes spanning the life cycle of the plant. Sugar and its myriad biological regulators and sensors are linked to seed development and growth, hormone signaling, carbon metabolism, stress response and programmed cell-death initiation .Zea mays, Saccharum officinarum, Panicum virgatum and Sorghum bicolor, serves as an excellent and relevant system for understanding the genetic determinants of sugar accumulation. Not only are these plants critical in the food production system, but some  are also largely grown for their harvestable supply of nonstructural sugars. Sorghum, a C4 grass native to the Horn of Africa, is a diverse species  using a diversity panel that was specifically designed to dissect the genetic determinants of biomass constituents   on a Perten DA7250. Cellulose and hemicellulose were estimated based on acid detergent fiber (ADF) and neutral detergent fiber (NDF) (www.dairylandlabs.net) using a previously described protocol for water-soluble carbohydrates  decay in sorghum ranging from 15-20 kb (Phylogenetic comparisons consisted of the amino acid sequences from sorghum to the other putative vacuolar iron transporters (VITs) within the Poaceae. Phylip’s protein parsimony algorithm was used to find the best tree given the amino acid sequences from Phytozome. The tree was constructed using the Interactive Tree of Life software . CompariA total of 17 individuals were sequenced: 16 diverse accessions from the BAP and BTx623, the reference genome, as a control. The 16 individuals were selected based on the segregation of SNPs S4_64019119 and S4_64019913, historical importance in sweet sorghum breeding, variation in composition of nonstructural sugars, and a limited range in anthesis date to remove any confounding variables. The Cornell University Institute of Biotechnology’s Genomic Facility extracted the DNA, developed primers, and sequenced Sobic.004G301500. DNA was extracted directly from seed using the Qiagen Plant DNA extraction kit. Primers were developed using the reference sequence (BTx623) on Phytozome. Additional seed of BTx623 was sent as a control. Sanger sequencing was performed using the left and right primer sequences GGATTCATTCTAGGTATCGAACGAGC and GCCAATTGTGATCCATTTATTGCCAG, respectively. The final sequencing product included the entire coding region of the gene, the promoter region, and approximately 100bps upstream and downstream of the target gene. Gene sequences were aligned using Clustal W alignment  was creaccc1 knockout and the AtVIT1 construct were obtained from Professor Mary Lou Guerinot at Dartmouth College. The experiment was modeled after previously reported methods from her lab .The two sorghum alleles were synthesized and confirmed by Genscript based on the open reading frame sequences from Rio and BTx623. These alleles were PCR amplified using the same forward primer R/BF 5′ ATGCATGGTACCATGTTTTACGCCTTTGCTGATAAGC 3′ and separate reverse primers RioR 5′ ATGCATCTCGAGGATGCGGACGACAAGACATGC 3′ and BTx623R 5′ ATGCATCTCGAGGATGCGGACGCGACA TGCGTC 3′ and then cloned into gateway entry vector pENTR4, before being transferred to the Gateway yeast destination vector pAG426-GAL-EGFP. Saccharomyces cerevisiae strain DY150https://doi.org/10.25387/g3.11929392.All germplasm used in this study is publicly available through the USDA-ARS Germplasm Repository Information Network. Genomic data are available through PRJNA298892. File S1 explains development of NIR curves. File S2 provides the phenotypic data used in the analysis. File S3 provides the graphs of LD decay. File S4 is the alignment files for candidate genes. File S5 is a more thorough explanation of yeast complementation study. File S6 is the GWAS results and the full list of genes within LD. File S7 is the multiple sequence alignment file for the candidate genes. File S8 lists the phenotypic values and correlations used to make WSC were negatively correlated with cellulose, hemicellulose, and lignin as a percentage of dry matter . IndividInterestingly, WSC has the highest correlation with yield of any of the biomass components. It is known that lignin, a key structural component, is correlated with increased biomass (Using the compressed mixed linear model (CMLM) from GAPIT 2, the GWAS identified a total of five SNPs that passed the Bonferroni significance threshold . These fa priori candidates may not have yielded the results researchers intended, and that genome-wide analysis may provide more clarity on which genetic determinants increase sugar accumulation.Although numerous studies have attempted to explicate the genetic basis of increased nonstructural sugars in sorghum, causal genetic variants have yet to be identified. Many of these studies have looked at expression of known genes such as sugar transporters and invertase enzymes  and height. Independent GWAS results for both height and flowering time did not reveal any loci that co-localized among phenotypes. Although recent evidence has disproven the relationship of sugar content and height  allele in sorghum . This is surprising because individuals were not selected for additional sequencing based on yield. They were selected on their segregation of the associated alleles, the observed sugar content, and the historical value in both syrup and sugar breeding programs. This unexpected result lends credence to the claim that sugar may be a key phenotype in driving increased biomass yield, rather than just a tradeoff between structural and nonstructural compositional components.ccc1 . Loss of ccc1 causes an inability to store iron in the vacuole which leads to buildup of iron in the cytoplasm, and an iron hypersensitivity phenotype  with the underlying assumption that increasing available photosynthate translates to improved yield. This assumes that the limiting factor of plant growth is indeed photosynthetic efficiency and that both plant metabolic processes and carbon-sink relationships are fully optimized. The data presented here suggests that increasing available sugars actually increases overall plant yield and sink strength rather than the simple reallocation of carbon among various sinks; if the relationship between increased productivity and increased sugar content is true, it would indicate that the genetic determinants influencing carbon allocation are not optimized and that greater productivity gains could be achieved by focusing on improved sink strength.Cropping systems must become more productive in light of unpredictable climatic changes; in order to do so, the crops themselves must become more resilient in the face of these challenges. However, the genetic determinants of crop productivity remain poorly understood. In terms of source/sink dynamics, much emphasis is placed on improving source sequestration (GWAS remains an extremely powerful method for identifying genomic variants controlling phenotypic variation. The identification of SNPs that overlap with a novel duplication event unique to sorghum not only serves as an intriguing target for crop improvement, but also supports the hypothesis that duplication events are critical for adaptation and improved fitness by developing novel functionality and increasing phenotypic variation. Since duplicated genes can gain a new function or be relegated to oblivion over time through evolutionary redundancy, the retention of this duplication event in sorghum offers promise that this region may be of importance not only for the elucidating the evolution of sorghum, but also may be important for continuing crop improvement efforts. Despite strong evidence for a possible neofunctionlization event, molecular techniques, specifically transgenic methodologies, will need to be employed for definitive confirmation. To test this hypothesis, we recommend editing Sobic.004G301500 in RTx430 or BTx623 to the allele present in ’Rio’ or ’Wray’ genotypes to see if the edited alleles increase WSC.4 grasses, demonstrates that homologous comparisons may not be as valuable as perceived. Furthermore, the reliance of homology without genomic loci that have been experimentally implicated through association studies or linkage mapping may not fully capture the genetic determinants of complex genomic interactions unique to the species being studied. Further evaluation of grass genomes and genomics is imperative for the continued increase in their productivity to meet the demand for food, feed, fuel and fiber in the 21st century.Considering how few of the genes identified through GWAS have had any true functional annotation, it is critically important that the members of the Poaceae serve as priorities for further gene characterization and validation studies. The recent emergence of alternative pathways unique to certain clades, specifically the C


Chromosome doubling is an important step in the production of maize doubled haploid (DH) lines to induce fertility in the male and female reproductive organs of haploid plants. Chromosomal doubling is routinely accomplished by treating haploid seedlings with mitosis-inhibiting chemicals. However, chromosomal doubling involves several labor-intensive steps and toxic chemicals. Spontaneous chromosomal doubling without any chemical treatments occurs at high frequency in haploids from a few maize genotypes. This study focused on elucidating the genetic components of two traits important for using spontaneous doubling in maize-breeding programs, namely, haploid male fertility (HMF) and haploid fertility (HF). In two different sets of diallel crosses, haploids were derived and assessed for HMF and HF in two environments in replicated trials. The results revealed significant genotypic variations for both traits. The general combining ability (GCA) and specific combining (SCA) were significant for both traits. Significant and positive GCA effects of up to 14% and 9% were found for HMF and HF, respectively. No significant reciprocal effects and genotype-by-environment (G×E) interactions were found for HF in both experiments, but HMF showed significant effects for both in one of the experiments. The GCA effects were more important than the SCA effects for HMF and HF across environments, implying that selection could facilitate their improvement. The high correlations between F1-hybrid performance and mid-parent values, as well as that between F1-hybrid performance and GCA effects, also supports the assumption that these traits are controlled by a few genes. SCA effects also played a role, especially when lines with low spontaneous doubling were used as parents. Overall, spontaneous doubling can be introgressed and improved in elite germplasm with selection, and it has the potential to be employed in DH pipelines. The technology for generating plants with a gametic number of chromosomes and using them to produce completely homozygous inbred lines is generally referred to as doubled haploid (DH) technology. DH technology can fix gametes from segregating populations into homozygous inbred lines in a single generation, thereby dramatically accelerating the pace at which improved cultivars can be developed. DH technology is recognized as one of the important tools in maize breeding to accelerate genetic gains. The use of DH lines in maize breeding increases the genetic variance among the lines tested, phenotype-to-genotype correlation and selection accuracy ,2. Toget0 nursery) and self-pollinating fertile DH plants to produce seed for DH lines (D1 lines). The process of maize DH-line production is well documented in several publications [2O gas [DH technology in maize encompasses (1) the production of haploids by crossing the germplasm from which the DH lines are anticipated with pollen from maternal haploid inducers, 2) the identification of haploids from diploids at the seed or seedling stage using genetic markers or natural differences among haploids and diploids, 3) subjecting the haploid seedlings to chromosomal-doubling treatments using mitosis-inhibiting chemicals, and 4) caring for the treated haploid plants in the field  and specific combining ability (SCA), for use in genetic-diversity evaluation, parental selection and hybrid development ,21,22. CRogers’ genetic distance estimates based on 190,000 Genotyping by Sequencing (GBS) SNP marker data revealed a high variation in the relatedness among the parental lines. The genetic distances among the 13 parental lines used in both diallel experiments ranged from 0.35 to 0.44, with a mean of 0.42. In the 78 pairwise comparisons, only 11.5% had genetic distances <0.40. Most of the pairs of parents (87.5%) fell between 0.40 and 0.44 in distance. The principal component analyses (PCAs) showed clustering among the inbred lines . The firA significant variation for both HMF and HF was found among the parental lines used in both the diallel experiments . In the Among the hybrids, wide variations for both HMF and HF were noticed in both the diallel experiments . The meaAnalyses of variance (ANOVAs) for HMF and HF for both of the diallel experiments are shown in 2A) was higher than the dominance genetic variance (σ2D) in both the experiments for both HMF and HF. The Baker’s ratios for HMF and HF were 0.73 and 0.70 in the Diallel I experiment and 0.78 and 0.71 in the Diallel II experiment, respectively. A moderate magnitude of the narrow-sense heritability was observed compared to that of the broad-sense heritability.Estimates of the additive variance, dominance variance and heritability are presented in Estimations of GCA effects for HMF and HF for both diallel experiments are presented in In the second diallel experiment, CML364, with high spontaneous doubling, showed positive and significant GCA effects . The twoThe correlations between the mid-parent value and F1-hybrid performance were high for both HMF and HF . In the Estimates of the SCA effects for HMF and HF for the two diallel experiments are shown in Improving the chromosomal-doubling efficiency in maize haploids can unfold the full potential of DH technology, which could facilitate new selection approaches that are currently not feasible due to the lower efficiency of artificial chromosomal-doubling methods. High chromosomal-doubling efficiency can facilitate phenotypic or marker-assisted selection for simple traits and genomic selection for complex traits at the haploid stage . This coTwo traits associated with spontaneous chromosomal doubling, namely, HMF and HF, showed greater variation in the inbred lines used in this study, and the data agree with a previous report on these lines . The sig2A) compared to dominance variance (σ2D) in both the experiments and higher estimates for the narrow-sense heritability over those for the broad-sense heritability also indicate the predominance of the additive effects for both HMF and HF in tropical maize.The larger proportion of the mean squares of the GCA compared to SCA for HMF and HF suggests that the additive genetic effect was the main contributor to their inheritance in the F1 hybrids in the two evaluated environments. In a diallel experiment with a fixed-effects model, even though the estimates of additive and dominance variances are less important , the GCAAll the F1 hybrids  assessed in the two diallel experiments revealed a varied magnitude of SCA effects in different groups . In a grThe correlation between the mean parental values and F1-hybrid performance for HMF and HF in both the diallel experiments clearly indicates that merely knowing the per se performance is enough for predicting the performance of hybrids for HMF and HF with limited field experiments. Furthermore, by knowing the GCA effects of lines, the accuracy for finding the best possible combinations with high HMF and HF is also high . These hIn our previous study, 400 CIMMYT maize lines (CMLs) were characterized for their response to spontaneous chromosomal doubling, which indicated a wider variation for HMF and HF in tropical inbred lines . In thisR1-nj-marker expression [R1-nj-marker expression [R1-nj marker. Hence, haploids were identified based on their strikingly poor vigor, erect leaves and paleness of leaves, as described earlier [R1-nj-marker expression.The diallelic populations and parental inbred lines were grown in four rows and crossed to the tropical haploid-inducer hybrid of CIM2GTAIL1009 × CIM2GTAIL006  in the 2pression . In Dialpression . The hyb earlier . In the R1-nj-marker expression, haploids were identified in the lab based on the seedling traits and transplanted to the field. Any false positives observed were eliminated based on their superior plant vigor and broad and drooping leaves after 20–30 days of planting [For each diallelic cross and parental line, 100 putative haploid kernels were planted in Mexico, directly in the field in the summer season of 2019 at Metztitlan  and winter season of 2020 at Agua Fria using an alpha-lattice design with two replications. For the hybrids with complete inhibition of planting ,34. Haplplanting . The HMFhttp://www.R-project.org/).DNA from all 13 inbred lines was extracted from seedlings having 3–4 leaves and genotyped using a Genotyping by Sequencing (GBS) platform at the Institute for Genomic Diversity, Cornell University, Ithaca, USA, as per the procedure described in earlier studies ,35. The ijkmy represents the phenotypic performance of the ijth genotype  in the mth replication in the kth environment, µ is an intercept term, ijg is the genetic effect of the ijth genotype , kl is the effect of the kth environment, ijk(gl) is the interaction of the ijth genotype  with the kth environment, mkr is the effect of the mth replication in the kth environment, and ijkme is the residual error term.The statistical analysis was carried out using the AGD-R  Version 5.0 statistical software . AnalysiF tests. Estimates of the GCA and SCA effects were calculated, and their significance was determined by t tests. Further variance-components estimates were computed for GCA, SCA and reciprocal (REC). All the calculations were performed using the AGD-R software. Pairwise Pearson’s correlation coefficients (r) were calculated between the F1 hybrids (F1P) and mid-parent values (MPV), r(MPV: F1P). Furthermore, we also tested the Pearson’s correlation of F1P with the sum of the GCA effects of both the parents, r(GCA: F1P), for each diallel experiment.The diallel analysis was carried out by applying Griffing’s Model I (fixed model) Method 1  . The meaThe significant GCA effects compared to the SCA effects of spontaneous-doubling-associated traits, namely, HMF and HF, indicate that breeding programs can improve these traits based on additive genetic effects. It is possible to predict the hybrid performance for HMF and HF based on the per se performance of inbred lines. Information on the GCA effects of the parental lines could be used to improve the prediction and forecast the best possible hybrid combinations for both the traits. Three tropical inbred lines with high GCA effects for both the traits were identified, which can be used to transfer the high spontaneous-doubling response to elite tropical maize germplasm through either recurrent selection or marker-assisted selection. Breeding programs, especially with resource limitations, could greatly benefit from such improved germplasm, as the need for artificial chromosome doubling is eliminated, which needs laboratory and greenhouse facilities.