Genetic risk prediction is an important goal in human genetics research and precision medicine. Accurate prediction models will have great impacts on both disease prevention and early treatment strategies. Despite the identification of thousands of disease-associated genetic variants through genome wide association studies (GWAS), genetic risk prediction accuracy remains moderate for most diseases, which is largely due to the challenges in both identifying all the functionally relevant variants and accurately estimating their effect sizes in the presence of linkage disequilibrium. In this paper, we introduce AnnoPred, a principled framework that leverages diverse types of genomic and epigenomic functional annotations in genetic risk prediction for complex diseases. AnnoPred is trained using GWAS summary statistics in a Bayesian framework in which we explicitly model various functional annotations and allow for linkage disequilibrium estimated from reference genotype data. Compared with state-of-the-art risk prediction methods, AnnoPred achieves consistently improved prediction accuracy in both extensive simulations and real data. BRCA1 and BRCA2 have been used to evaluate women’s breast cancer risk and as a guideline for early screening. However, genetic risk prediction models also present important challenges, including extreme high-dimensionality, limited access to and efficient computational methods for individual-level genotype data. To make use of rich GWAS summary statistics, we propose a novel method to address these challenges by integrating genomic functional annotations, which have been successfully applied in GWAS to generate biological insights. We demonstrate the improvement in accuracy in both extensive simulation studies and real data analysis of breast cancer, Crohn’s disease, celiac disease, rheumatoid arthritis and type-II diabetes.Genetic risk prediction plays a significant role in precision medicine. Accurate prediction models could have great impact on disease prevention and early treatment strategies. For example, mutations in  PLOS Computational Biology Methods paper.This is a Achieving accurate disease risk prediction using genetic information is a major goal in human genetics research and precision medicine. Accurate prediction models will have great impacts on disease prevention and early treatment strategies . Advancehttps://github.com/yiminghu/AnnoPred), a principled framework that integrates GWAS summary statistics with various types of annotation data to improve risk prediction accuracy. We compare AnnoPred with state-of-the-art PRS-based approaches and demonstrate its consistent improvement in risk prediction performance using both simulations and real data of multiple complex diseases.Explicit modeling and incorporation of external information, e.g. pleiotropy , 8 and LMethods). First, we estimate GWAS signal enrichment in 61 different annotation categories, including functional genome predicted by GenoCanyon scores [Xj and βj are the standardized genotype and effect size of the jth SNP, respectively, β, Methods).AnnoPred risk prediction framework has three main stages , including PRS based on genome-wide significant SNPs (PRSsig), PRS based on all SNPs in the dataset , PRS based on tuned cutoffs for p-values and LD pruning (PRSP+T), and recently proposed LDpred [Methods). AnnoPred showed the best prediction performance in all settings when the causal SNPs are highly enriched in annotated regions . In general, performance of PRSsig, PRSP+T, LDpred, and AnnoPred all improved under a sparser genetic model and higher trait heritability. PRSall showed comparable performance between sparse and polygenic models but its prediction accuracy was consistently worse than other methods. Sample size in the training set was also crucial for risk prediction accuracy. Increasing sample size could lead to continuous improvement in prediction accuracy under different settings .We first performed simulations to demonstrate AnnoPred’s ability to improve risk prediction accuracy. We compared AnnoPred with four popular PRS approaches (d LDpred . Mean coMethods). Enrichment pattern varies greatly across diseases , reflecting the genetic basis of these complex phenotypes. Functional genome predicted by GenoCanyon was consistently and significantly enriched for all five diseases. Blood was strongly enriched for three immune diseases, namely CD (P = 8.9×10−12), CEL (P = 7.0×10−15), and RA (P = 9.9×10−6), while gastrointestinal (GI) tract was enriched in CD (P = 2.6×10−5) and CEL (P = 1.4×10−4), both of which have a known GI component. For BC, epithelium (P = 7.4×10−4), GI (P = 5.9×10−3), and muscle (P = 6.1×10−3) were significantly enriched. A few studies have shown that breast cancer could arise from epithelial cells [Fig 2B and 2C).To illustrate the improved risk prediction performance in real data, we applied AnnoPred to five human complex diseases—Crohn’s disease (CD), breast cancer (BC), rheumatoid arthritis (RA), type-II diabetes (T2D), and celiac disease (CEL). We first estimated GWAS signal enrichment in different annotation categories . From the test, AnnoPred with 61 annotations performed significantly better than LDpred . Reversing the order of test  results in non-significant p-values for most tests (S11 Table), which further demonstrates that PRS incorporating functional annotations mostly encompasses the information of PRS without annotations. To test different methods’ ability to stratify individuals with high risk, we compared the proportion of cases among testing samples with high PRS. AnnoPred outperformed all other methods in CD, CEL, RA, and T2D . Next, we tested AnnoPred’s performance using only the 53 baseline annotations and observed a substantial drop in prediction accuracy for all diseases (S3 Table). AnnoPred with GenoCanyon and GenoSkyline annotations only  yields better performance than the 53 baseline annotations (S10 Table). For CD and T2D, by using these 9 categories AnnoPred even achieved higher accuracy than the model with all 61 annotation tracks added. These results highlight the importance of annotation quality in genetic risk prediction, and also demonstrate GenoCanyon and GenoSkyline’s ability to accurately identify functionality in the human genome. Since different diseases have various enrichment patterns, we also run AnnoPred with significantly enriched annotations  for each disease (S10 Table). In general, using only the significantly enriched annotations indeed improved the performance in most diseases.Correlations between the calculated PRS and disease status (COR) for different approaches are summarized in Tissue specificity plays an important role in genetic risk prediction. Integrating more functional annotations with higher tissue and cell type specificity may further increase risk prediction accuracy, especially when the tissue type that is biologically relevant to the disease is not well characterized by the seven available tissue tracks in our current analyses. To explore how these factors will affect the AnnoPred model, we performed a few follow-up analyses. We have recently expanded our GenoSkyline annotations to more than 100 tissue and cell types from the Roadmap Epigenomics Project . We inveS9 Table). For the rest diseases, results varied little from the original analysis. Besides COR, we also included AUCs for all the analysis performed (S9 and ), all of which showed consistent patterns.In order to study the effect of highly associated SNPs (e.g. SNPs in MHC regions for immune traits), we repeated the analysis on CD, RA, BC and T2D after removing the SNPs in MHC region . Re-analysis of CEL was unnecessary since the training summary statistics of CEL does not contain any SNP in the MHC region. After removing SNPs in MHC regions, the prediction accuracies for RA drops dramatically for all methods and AnnoPred remained to be the method with the best performance . We smoothed GenoCanyon scores by a 10Kb window, a strategy previously shown to improve robustness of functionality prediction [GenoCanyon is a statistical framework to predict functional regions in the human genome through integrative analysis of ENCODE epigenomic data and multiple conservation metrics . Later wediction . The smoediction . NotablyYN×1 and the genotypes XN×M are standardized with mean zero and variance one. We assume a linear modelX, β and ε are mutually independent. We also assume that β is a random effect and effects of different SNPs are independent. A key idea in the AnnoPred framework is to utilize functional annotation information to accurately estimate SNPs’ effect sizes. In order to achieve that, we first partition trait heritability by annotations using LD score regression [βi for the ith SNP, and is used to quantify SNP effect sizes. More specifically, assume there are K + 1 pre-defined annotation categories, denoted as S0, S1, …, SK with S0 representing the entire genome. Under an additive assumption for heritability in overlapped annotations, we have τ0, τ1, …, τK, quantify the contribution to per-SNP heritability from each annotation category. Denote the estimated marginal effect size of the ith SNP as l is the annotation-stratified LD score and N denotes the total sample size. Regression coefficients τk are estimated through weighted least squares. The estimated heritability of the ith SNP is then We assume throughout the paper that both the phenotype gression . Since gp0 is the proportion of causal SNPs in the dataset, and δ0 is a Dirac function representing a point mass at zero. The empirical variance of each SNP, i.e. c is a constant calculated from the following equation Based on per-SNP heritability estimates, we propose two different priors for SNP effect sizes to add flexibility against different genetic architecture. For the first prior, we assume that SNP effect size follows a spike-and-slab distributionWe do not directly use he model . Such pehe model . Therefohe model , we use Var = V, the total number of SNPs to be M0, and the overall proportion of causal SNPs to be p0. The total heritability th SNP, use th SNP, and let Ti is Ti. Following these notations, we haveIn the first prior, we assumed the same proportion of causal SNPs but different effect sizes across annotation categories. We now describe the second prior that assumes different proportions of causal SNPs but the same effect size across annotation categories. To be specific, we assume the causal effect size to be p0 is treated as a tuning parameter for both prior functions in our analysis.Finally, β is:β and By Bayes’ rule, the posterior distribution of b (e.g. a LD block) and the corresponding genotype matrix is Xb and sample correlation matrix is b, and Xb− and βb− denote the genotype matrix and effect sizes of SNPs not in region b. The conditional distribution of βb is:However, βb, each element of βb follows a mixed normal distribution conditioning on βb. Therefore, we apply a Gibbs sampler to draw samples from b . Specifically, we ran AnnoPred on the data of Crohn’s disease with different sizes of block and found that the results were robust to the sizes. In practice, the size of block b is specified by the total number of variants divided by 3,000.Although it is difficult to derive EA denotes the posterior expectation as described above. In practice, the individual-level genotype matrix is not available and we use the LD matrix estimated from a reference panel or the validation samples to substitute b as described in [p0 can be tuned in an independent cohort. For the data analysis described in this work, we adopted a cross-validation scheme to select tuning parameter due to the challenge in finding multiple independent cohorts without overlapping with the training GWAS summary statistics. The training datasets in our real data analyses and simulations are always fixed, i.e. GWAS summary statistics. We did not perform a classical cross-validation by using different subsets of the complete data to train and test our prediction model. The purpose of cross-validation in our study is purely parameter tuning. To select a suitable tuning parameter, we divide the independent testing dataset  into two equal parts (A and B), and select the tuning parameters by optimizing prediction accuracy on dataset A. We then evaluate prediction accuracy using the remaining half of testing data, i.e. dataset B. Finally, we repeat the analysis one more time by choosing the tuning parameter on dataset B while evaluating the prediction accuracy on dataset A. Results from these two separate analyses are averaged to quantify model performance. For T2D where multiple independent cohorts are available (phs000237 and phs000388), we used an independent cohort for parameter tuning and the other for evaluating performance (S12 Table). The results are consistent with the cross-validation.PRS is calculated using the following formularibed in . Choicessig and PRSall were both calculated as the inner product of marginal effect size estimates and the corresponding genotypes. PRSall used all the SNPs that are shared between training and testing datasets while PRSsig only used SNPs with p-values below 5 × 10−8 in the training set. PRSP+T used SNPs passing both LD pruning and p-value thresholding. The thresholds are tuned in an independent dataset over a grid . LDpred can be viewed as a special case of AnnoPred, assuming the whole genome as the only functional annotation. This is because when enrichment is constant , per-SNP heritability estimates would be nearly constant and therefore results in similar performance to LDpred. We have performed an additional simulation to demonstrate this using WTCCC genotype data with ~15K individuals and ~330K variants. We randomly divided the genome into two parts (two annotations) and uniformly selected causal SNPs. Then the traits were simulated in a similar way as other simulations in this paper. We estimated per-SNP heritability using LDSC in the two annotation categories, respectively. We ran the procedure for 100 times and the distributions of estimated per-SNP heritability in both regions are summarized in the figure below . All the tuning parameters were tuned through cross-validation as we did for AnnoPred. Besides all these PRSs, we also compared AnnoPred with a evaluating method used in [).We compared AnnoPred with several commonly used risk prediction methods based on summary data of association studies. PRSGiven that many large-scale GWAS summary statistics have included almost all available cohorts for a disease of interest, it is challenging to find independent datasets with individual-level genotype and phenotype information and sufficient sample sizes. We were able to identify ideal validation datasets for the five diseases we analyzed in this paper. The performance of different methods on more traits shall be evaluated when we get access to more data in the future.A1 and A2, which we assume are known when applying AnnoPred. Denote the heritability of the trait as m . Causal variants were generated as follows: A1, A2 and the rest from (A1UA2)C corresponding to a high enrichment of signals in A1 and A2. Effect sizes of causal variants were sampled from We simulated traits from WTCCC genotype data, which contain 15,918 individuals genotyped for 393,273 SNPs after filtering variants with missing rate above 1% and individuals with genetic relatedness above 0.05. We first generated two annotations and each annotation was simulated by randomly selecting 10% of the genome, denoted as x1, x2, …, xn and y1, y2, …, yn, respectively. And the hypothesis we want to test isμx and μy represent the population mean of accuracies of LDpred and AnnoPred. We used H0 is true. Specifically, we first pooled xi′s and yi′s together. Then N = 106 times and we calculated H0. And the p value could be approximated by In order to evaluate the improvement in accuracy, we performed a permutation test to compare the CORs of AnnoPred and LDpred. Suppose the CORs of LDpred and AnnoPred in simulations are N is the number of individuals, M is the total number of variants and Ms is the number of variants used in simulation) for the four scenarios are ~135K, ~67K, 37K and ~11K. For each effective sample size, we simulated traits under four settings: h2 = 0.25, p = 0.001; h2 = 0.25, p = 0.01; h2 = 0.5, p = 0.001; h2 = 0.5, p = 0.01, where p represents the proportion of causal variants .To further study the effect of sample size on prediction performance, we simulated traits using SNPs of chromosome 1, chromosomes 1 and 2, chromosomes 1 to 4 and the whole genome while keeping the same proportion of causal variants and heritability to mimic the situation of increasing sample size. The corresponding relative sample sizes  [case = 1,689 and Ncontrol = 2,891) [case = 16,003 and Ncontrol = 41,335) [case = 966 and Ncontrol = 70) [case = 1,666 and Ncontrol = 2,038) [case = 1,829 and Ncontrol = 2,892) [case = 662 and Ncontrol = 517) [case = 517 and Ncontrol = 213; Hispanic: Ncase = 477 and Ncontrol = 102) [case = 1,716 and Ncontrol = 530) [For Crohn’s disease, we trained the model using summary statistics from International Inflammatory Bowel Disease Genetics Consortium  . Samples= 2,891) . For bre 41,335) , and tesol = 70) . Shared = 2,038) . For rhe= 2,038) . WTCCC s= 2,892) . For typ= 2,892) . We usedl = 517) . Samplesl = 102) . Sampleshttps://github.com/yiminghu/AnnoPred.AnnoPred software and source code are freely available online at S1 Fig(TIFF)Click here for additional data file.S2 Fig(TIFF)Click here for additional data file.S3 FigThe horizontal line marks no enrichment.(TIFF)Click here for additional data file.S4 FigDashed line marks the true per-SNP heritability.(TIFF)Click here for additional data file.S5 Fig(TIFF)Click here for additional data file.S6 Fig(TIFF)Click here for additional data file.S7 Fig(A) Breast cancer (B) Type-II diabetes (C) Comparing consistency of SNPs’ effect direction between training and testing datasets. Each bar quantifies the proportion of SNPs with consistent effect directions. The association tests and effect size estimation on the testing data are underpowered due to the limited sample size.(TIFF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 TableThe highest AUCs are highlighted in boldface.(XLSX)Click here for additional data file.S3 TableThe highest AUCs are highlighted in boldface.(XLSX)Click here for additional data file.S4 TableThe highest AUCs are highlighted in boldface.(XLSX)Click here for additional data file.S5 TableThe highest correlations are highlighted in boldface.(XLSX)Click here for additional data file.S6 TableThe highest AUCs are highlighted in boldface.(XLSX)Click here for additional data file.S7 TableThe highest CORs are highlighted in boldface.(XLSX)Click here for additional data file.S8 Table(XLSX)Click here for additional data file.S9 TableThe highest CORs/AUCs are highlighted in boldface.(XLSX)Click here for additional data file.S10 TableThe highest CORs/AUCs are highlighted in boldface.(XLSX)Click here for additional data file.S11 Table(XLSX)Click here for additional data file.S12 Table(XLSX)Click here for additional data file.S1 Text(DOCX)Click here for additional data file.


Genome-wide association studies performed on triglycerides (TGs) have not accounted for epigenetic mechanisms that may partially explain trait heritability.P ≤ 10− 5). We evaluated the association of these 22 significant genetic variants showing POO effects with close DNA methylation probes associated with TGs. A total of 18 DNA methylation probes located in the vicinity of the 22 SNPs were associated with at least 1 phenotype and 6 SNP-probe pairs were associated with DNA methylation probes at the nominal level of P < 0.05, among which 1 pair presented evidence of POO effect. Our analyses identified a paternal effect of SNP rs301621 on the difference between pre- and posttreatment TG levels (P = 1.2 × 10− 5). This same SNP showed evidence for a maternal effect on methylation levels of a nearby probe . Using a causal inference test we established that the observed POO effect of rs301621 was not mediated by DNA methylation at cg10206250.Parent-of-origin (POO) effect association analyses using an agnostic approach or a candidate approach were performed for pretreatment TG levels, posttreatment TG levels, and pre- and posttreatment TG-level differences in the real GAW20 family data set. We detected 22 genetic variants with suggestive POO effects with at least 1 phenotype (We performed POO effect association analyses of SNPs with TGs, as well as association analyses of SNPs with DNA methylation probes. These analyses, which were followed by a causal inference test, established that the paternal effect at the SNP rs301621 is induced by treatment and is not mediated by methylation level at cg10206250. Despite the success of genome-wide association studies (GWAS) conducted for lipid levels, particularly triglyceride (TG) levels, to discover common risk alleles, the genetic factors identified to date only account for a small part of the genetic variance of this trait. Genetic studies have largely focused on DNA sequence variations. Sources of this unexplained heritability might include epigenetic mechanisms such as DNA methylation. Epigenetic modifications are heritable changes influencing gene expression without alterations of the underlying DNA sequence. Few epigenome-wide studies have been conducted for lipid levels, particularly TG levels –6. HowevOur approach consisted in combining POO effect associations with association of nearby DNA methylation probes with TGs followed by a causal inference test to assess whether methylation mediates the observed POO. This approach has been successful in identifying differentially methylated cytosine-phosphate-guanine (CpG) sites that mediate the association between a genetic variant and a phenotype under a POO effect .We performed POO effect association analyses of pretreatment TG levels, posttreatment TG levels, and pre- and posttreatment TG-level differences in the real GAW20 family data set, using a linear regression approach implemented in the quantitative transmission disequilibrium test (QTDT) software . We cond1–2), the average natural-log TG posttreatment (TG3–4), and the natural-log TG difference between pre- and posttreatment (∆TG1–4) using a linear mixed-effect model to account for familial correlations and adjusted for age, sex, center , and smoking .The real data example for GAW20 is from the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) study data set . This st-at option to perform a total association analysis [j in family i is modeled as: Yij = α + βGGij + eij where βG is the genetic effect of the minor allele (a) of the SNP and Gij is the number of minor alleles carried by child j in family i.GWAS genotyping was performed on DNA extracted from blood drawn at baseline, using the Affymetrix Genome-wide Human SNP Array 6.0. Association analyses were conducted using the QTDT software with and without accounting for POO effects. From the real data, we analyzed 823 genotyped individuals from 173 families . We evaluated the association of principal components calculated in the GAW20 data set with the traits evaluated in this study. As population stratification was not expected to be a major concern, we used the QTDT analysis . This mo−of, −ot, −om, and −op) to get estimates of parental origin of the alleles [j in family i is: Yij = α + βmatG1ij + βpatG2ij + eij where βmat is the genetic effect of a maternally inherited minor allele, βpat is the genetic effect of a paternally minor allele, G1ij is the estimated number of minor allele inherited from the mother, and G2ij is the estimated number of minor alleles inherited from the father. The -at -ot tests for difference between paternal and maternal transmissions (βpat = βmat), the -at -of uses a saturated model where maternal and paternal inherited alleles are modeled separately (βpat = βmat = 0), whereas the -at -om and -at -op tests for maternal effect (βmat = 0) or paternal effect (βpat = 0) only. We modified the QTDT to test 1 parental effect while adjusting for the other parent contribution (om_op and op_om models).Then, our association analyses focused on POO effects on TG in the offspring. This approach involves modeling the phenotype as a function of covariates and genotypes, taking parental original of each allele into consideration . We use  alleles . The modhttp://www.ebi.ac.uk/gwas/search?query=triglycerides). We selected 14 European-ancestry GWAS after excluding GWAS performed on specific phenotypes (responses to treatment) or related phenotypes . A total of 129 variants in 59 regions were reported associated with TG levels at P < 10− 5 . We used a ± 50-kb window around the reported SNPs to define candidate loci. We used an arbitrary threshold of 10− 5 to declare a SNP association suggestive under the POO effect model . We then used an agnostic approach over the full genome with the same arbitrary threshold of 10− 5 to declare a SNP association suggestive under the POO effect model .Selection of suggestive POO effects was performed using 2 different approaches. We first used a candidate approach in regions known to be associated with TG levels using the GWAS catalog (2), natural-log TG posttreatment (TG4), and natural-log pre- and posttreatment TG difference (∆TG2–4) using a linear mixed-effect model adjusted for age, sex, center, and smoking to account for familial correlations. From the real data, we analyzed 679 and 403 individuals from 163 and 136 families with genotypes and methylation available at exam 2 or 4, respectively. We selected all DNA methylation probes associated with at least 1 trait at the nominal level of P < 0.05.DNA was extracted from CD4+ T cells and the proportion of sample methylation at > 450,000 CpG sites was quantified by using the Illumina Infinium Human Methylation 450 K BeadChip from blood drawn in both visit 2 and visit 4 for each participant. We selected DNA methylation probes located within a ± 50-kb window around the suggestive SNPs under the POO effect model. We performed epigenetic association analyses of natural-log TG pretreatment , among which 6 were associated with TG1–2, 1 with TG3–4, and 12 with ∆TG1–4. Among the SNPs previously reported to be associated with TG level, only 8 were associated with the phenotypes (TG1–2) at P ≤ 10− 3 and no SNP showed strong POO effects (P > 10− 3). Using a candidate approach, we identified 2 SNPs with a suggestive POO effect (P < 10− 5), among which 2 were associated with TG1–2  and 1 was also associated with TG3–4 . We identified 18 DNA methylation probes located in the vicinity of these SNPs that were associated with the phenotypes at P < 0.05 . We detected 6 SNP-probe pairs with association (P < 0.05) in at least 1 model with QTDT (Table 1–4 (P op_om = 1.2 × 10− 5) and detected a maternal effect of the same SNP on methylation levels of a nearby probe . The observed paternal effect of rs301621 remains significant when adjusting for DNA methylation at cg10206250 (P op_om = 5.5 × 10− 5) and is also associated with posttreatment TG (P op_om = 0.001).Using an agnostic approach on the genome, we identified 19 SNPs with a suggestive POO effect (P ≤ 5 × 10− 8) or the candidate approach threshold (P ≤ 1.2 × 10− 5). The tested methylation probes were only associated with the tested phenotypes before multiple testing correction. This could be from a lack of power because of the small number of individuals analyzed. However, we detected 19 SNPs with suggestive POO effects (P < 10− 5) and this may reflect new mechanisms of action of these SNPs, particularly in previously reported loci such as SNP rs10417097 on chromosome 19 in the PBX4 gene [1–2 and TG3–4 (P ≤ 10− 5) and associated with methylation levels of cg10738025  and few of them were strongly associated with the phenotypes at P ≤ 10− 3. This could be from a lack of power because of the small number of individuals analyzed.We detected 3 SNPs with POO effect associations that reached the multiple-testing correcting threshold using the agnostic approach (BX4 gene , 13 withWe performed association analyses in the real GAW20 data set to identify POO effects on TG levels in offspring. These analyses were followed by association analyses of SNPs with DNA methylation probes adjusting for TG levels. Interestingly, the G allele of rs301621 was associated with pre- and posttreatment TG difference when transmitted by the father and with methylation levels of cg10206250 when transmitted by the mother. We showed that this paternal effect is induced by treatment. Using a causal inference test, we demonstrated that the observed POO effect of rs301621 on the difference between pre- and posttreatment TG level was not mediated by DNA methylation at cg10206250. Further investigation in a larger number of participants is needed to confirm the POO effects identified in this report.


Inbreeding increases the risk of certain Mendelian disorders in humans but may also reduce fitness through its effects on complex traits and diseases. Such inbreeding depression is thought to occur due to increased homozygosity at causal variants that are recessive with respect to fitness. Until recently it has been difficult to amass large enough sample sizes to investigate the effects of inbreeding depression on complex traits using genome-wide single nucleotide polymorphism (SNP) data in population-based samples. Further, it is difficult to infer causation in analyses that relate degree of inbreeding to complex traits because confounding variables  may influence both the likelihood for parents to outbreed and offspring trait values. The present study used runs of homozygosity in genome-wide SNP data in up to 400,000 individuals in the UK Biobank to estimate the proportion of the autosome that exists in autozygous tracts—stretches of the genome which are identical due to a shared common ancestor. After multiple testing corrections and controlling for possible sociodemographic confounders, we found significant relationships in the predicted direction between estimated autozygosity and three of the 26 traits we investigated: age at first sexual intercourse, fluid intelligence, and forced expiratory volume in 1 second. Our findings corroborate those of several published studies. These results may imply that these traits have been associated with Darwinian fitness over evolutionary time. However, some of the autozygosity-trait relationships were attenuated after controlling for background sociodemographic characteristics, suggesting that alternative explanations for these associations have not been eliminated. Care needs to be taken in the design and interpretation of ROH studies in order to glean reliable information about the genetic architecture and evolutionary history of complex traits. Inbreeding is well known to increase the risk of rare, monogenic diseases, and there has been some evidence that it also affects complex traits, such as cognition and educational attainment. However, difficulties can arise when inferring causation in these types of analyses because of the potential for confounding variables  to bias the observed relationships between distant inbreeding and complex traits. In this investigation, we used single-nucleotide polymorphism data in a very large  sample of seemingly outbred individuals to quantify the degree to which distant inbreeding is associated with 26 complex traits. We found robust evidence that distant inbreeding is inversely associated with fluid intelligence and a measure of lung function, and is positively associated with age at first sex, while other trait associations with inbreeding were attenuated after controlling for background sociodemographic characteristics. Our findings are consistent with evolutionary predictions that fluid intelligence, lung function, and age at first sex have been under selection pressures over time; however, they also suggest that confounding variables must be accounted for in order to reliably interpret results from these types of analyses. Inbreeding occurs when genetic relatives have offspring, and is associated with increased risk of disorders and decreased health and viability in offspring –3. This FROH and has been shown to be the best genome-wide estimate of autozygosity [n > 10,000) are required to detect likely effects of FROH in outbred human populations because of the low variance in levels of genome-wide autozygosity in such populations. Previous studies of FROH in humans have found evidence consistent with inbreeding depression for several complex traits, including height, forced expiratory volume in one second (FEV1), educational attainment, and cognitive ability (g) [FROH may suggest that directional selection has acted on these traits ancestrally.Because all humans are related to one another, even if distantly, inbreeding is a matter of degree. In the last decade, the increasing availability of genome-wide single nucleotide polymorphism (SNP) data has allowed scientists to infer degree of distant inbreeding, or the proportion of the genome that is autozygous, using runs of homozygosity (ROHs)—long stretches of SNPs that are homozygous . The totzygosity ,6. Howevlity (g) –10, withlity (g) ,12 or rility (g) ,14. ThesFROH -trait relationships. It is likely that propensity to outbreed  is related to multiple sociodemographic variables in parents , and these parental trait values may influence offspring trait values, thereby inducing an FROH -trait relationship that has nothing to do with the genetic effects of inbreeding depression. In a recent study conducted in the Netherlands, a relatively small, densely populated country with a strong history of latitudinal religious assortment, Abdellaoui et al. [FROH (i.e. less inbred) and increased risk for major depressive disorder (MDD); this counter-intuitive association disappeared when the models accounted for religious assortment. This suggests that the original FROH−MDD association occurred for sociological rather than genetic reasons: religious individuals had higher average levels of autozygosity than non-religious individuals, probably due to denominational restrictions on mate choice that were only recently relaxed [FROH analysis to date, Joshi et al. (2016) found a significant relationship between FROH and four complex traits: height, FEV1, cognitive ability (g), and educational attainment [FROH and the complex traits is likely a due to a genetic mechanism, directional dominance, rather than to sociodemographic confounds. However, the FROH–trait effect sizes decreased by ~20–35% after controlling for SES; it is possible that inclusion of additional, or more relevant, sociodemographic covariates could have changed these conclusions.One challenge in autozygosity research in humans is in the causal interpretations of any observed i et al.  found a  relaxed , and rel relaxed . In anottainment . When edFROH and psychiatric disorders in ascertained samples [FROH results. Using the Psychiatric Genomics Consortium (PGC) MDD data from 9 samples, Power et al.[FROH and MDD in three German samples but, strangely, a significant negative relationship between FROH and MDD in six samples from non-German sites. Similarly, in 2012 we found a small but highly significant association between schizophrenia and FROH across 17 case-control datasets . We areFROH analyses. Using simulations, the authors show that FROH -based measures of inbreeding can overestimate the inbreeding effect size compared to SNP-based measures. The authors go on to show that a SNP-based measure of inbreeding calculated from the correlation between uniting gametes, FUNI, provides unbiased estimates of inbreeding effects when causal variants are well-tagged by measured SNPs. However, unlike FROH, which captures the effects of both common and rare recessive causal variants [FUNI underestimate the effects of  recessive causal variants that are poorly tagged by measured SNPs [FROH rather than SNP-based measures of inbreeding in the current study because we were interested in investigating the evidence for directional dominance on complex traits, which is theoretically manifested via a higher proportion of rare and recessive causal variants. We also chose to focus on FROH for comparability with previous findings, as FROH has been the standard metric in the field for assessing inbreeding depression to date.Finally, a recent study by Yengo et al.  quantifivariants , SNP-basred SNPs . We chosFROH with several complex traits. We used whole-genome SNP and phenotypic data from the UK Biobank  to address two principal questions: (1) is there evidence consistent with directional dominance on traits related to fitness and health, such that increased FROH is associated with lower trait values? and (2) do FROH-trait relationships persist after controlling for multiple background sociodemographic variables? This sample is population-based, reducing concerns about ascertainment-induced confounds, and includes information on multiple relevant sociodemographic control variables and traits previously associated with FROH .N varied by phenotype) with genotypes available.Our data came from the UK Biobank, a population-based sample from the United Kingdom. In total, 502,682 individuals were recruited from 2006–2010 from 22 centers across the UK. Participants were given a touchscreen interview that included questions about demographic characteristics, health history, and lifestyle information , and some anthropometric and physical measures were collected. DNA was extracted from whole blood and genotyped using either the Affymetrix UK Biobank Axiom array or the Affymetrix UK BiLEVE Axiom array. Detailed genotyping and sample QC procedures are described in Bycroft et al.  We analyFROH for ease of comparison with Joshi et al.’s and others’ results [We examined 26 traits related to health, fitness, or sociodemographic characteristics  missing call rate > 0.02, or c) had a minor allele frequency (MAF) < 0.05. We also excluded individuals with discordant self-reported gender and genetic sex, a missing genotype call rate > 0.02, and we removed the minimum number of individuals so that all remaining subjects were unrelated at Because the sample was predominately European ancestry, we restricted analyses to individuals of European ancestry  as identified by visual inspection of plots of genomic principal components. We followed sample and genotypic quality control that has become typical in ROH analyses. In particular, we excluded SNPs if they a) deviated from Hardy-Weinberg equilibrium at p<1×10f option ) (n = 312 of 0.90) between target SNPs and 50 surrounding SNPs (plink command:—indep 50 5 10). After these procedures, 263,609 SNPs and 404,524 individuals remained. For our main analysis, we called ROHs as being ≥65 homozygous SNPs in a row, set the minimum KB length very low , with no heterozygote calls and three missing variant calls allowed (5% of the SNP threshold), per recommendations from Howrigan et al. (2011) for genotype data of similar SNP density. We required ROHs to have a density greater than at least 1 SNP per 200 kb  and split an ROH into two if a gap >500 kb existed between consecutive homozygous SNPs. These analyses used the following commands in Plink 1.9 [9 bases) to calculate FROH, the proportion of the genome likely to be autozygous.After QC, we pruned out SNPs that were in strong linkage disequilibrium with other SNPs by removing those that had a variance inflation factor > 10  and comparing to the effect of FROH from shorter ROHs (a proxy for more distant inbreeding). We defined recent inbreeding as the proportion of the genome contained in autozygous regions longer than 8.5 Mb (FROH_long) and distant inbreeding as the proportion of the genome in autozygous regions shorter than 8.5 Mb (FROH_short), as FROH_long and FROH_short had approximately equal variances  in our sample. An autozygous segment spanning < 8.5 Mb should originate from a common ancestor at least 6 generations ago on average [We also tested the relative importance of recent vs. distant inbreeding by calculating  average .FSNP) for each individual, using the—het flag in Plink 1.9 [In addition to calling ROHs, we also calculated a measure of SNP-by-SNP homozygosity .Because it is calculated with genotyped SNPs, FROH was used as the primary predictor of the traits of interest in analyses described below. The distributions of ROH lengths and FROH are shown in FROH using the model in the equation below, where C is a matrix of covariates  and ε represents the residual error term.z-scores for ease of comparison with previous findings in the literature. In addition, for ease of interpretation, we reverse-coded some of the phenotypes such that lower values represented what we thought were likely to be lower fitness and/or less desirable outcomes . We were primarily interested in the estimate of FROH with the trait, controlling for covariates . For binary traits, we ran logistic regression models with the same covariates as in the linear regression models for quantitative traits.As noted above, all quantitative phenotypes were standardized to intra-sex FROH and the traits listed above. Because confounding factors such as population stratification, SNP missingness, call quality, and plate effects can influence FROH, we included the batch number, percentage of missing SNP calls per sample in the non-imputed genotype data, and the first 20 ancestry principal components , as well as age, age2, and sex, in all of the regression models unless explicitly stated.We ran a total of three sets of models for each trait. The first set of models was designed to test for a simple relationship between FROH-trait relationships. In addition to the above covariates, in these models we also included income, years of educational attainment, Townsend Deprivation Index , and whn region ), and soFROH-trait relationships were due to homozygosity at common versus rare alleles. To do this, we included FSNP as a covariate in addition to the covariates from the second set of models above. Because common SNPs can often predict (are in linkage disequilibrium with) other common SNPs but typically poorly predict rare SNPs, FSNP captures effects of homozygosity at common SNPs only whereas FROH captures the effects of homozygosity at both common and rare SNPs [FSNP and FROH as predictors simultaneously in the regression equation allows insight into the degree to which observed inbreeding effects are due to homozygosity at common versus rare alleles.In our third set of models, we tested the degree to which observed are SNPs . In the FROH, and FSNP are shown in FROH and income, grip strength, height, fluid intelligence score (FI), and forced expiratory volume in one second (FEV1), and observed significant positive associations between FROH and age at first sexual intercourse (AFS) and religious group participation  were significantly associated with FROH_short, while its associations with income, grip strength, and height were not significant  and increased for FEV1 (by 4.2%) , the betas associated with .2%) see . AFS, FI, and FI . FinallyFSNP) was included as an additional covariate, AFS and FI remained significantly associated with FROH after accounting for multiple testing and FEV1 was marginally significant , and found weak evidence that background sociodemographic characteristics may be partially mediating a few of the observed relationships between FROH and complex traits  was not significantly associated with FROH in any of our models, contrary to several previous reports [p = 2.18e-4) relationship between FROH and income (which itself was correlated with years of education at r = 0.37), but we found no evidence for an association between FROH and either years of education or the binary variable measuring whether or not an individual attended college. The reason for the discrepancy in findings for education is unlikely to be due to sampling variability because the two confidence intervals do not overlap  when we accounted for sociodemographic covariates, and was somewhat smaller than that found by previous studies even when we did not control for sociodemographic variables . Joshi et al. in particular analyzed a much more diverse overall sample than the present study, including multiple cohorts from European, African, and Asian populations. Another difference is in the measurement of intelligence across studies: our measurement for general cognitive ability was the unweighted sum of the number of 13 fluid intelligence questions answered correctly, given as part of the UK Biobank’s cognitive function assessment, while Howrigan et al. [g as their measure of general cognitive ability, “calculated as the first unrotated principal component of test scores across diverse domains of cognition”. Furthermore, our regression models controlled for the first 20 ancestry principal components, while Howrigan et al. controlled for the first 10 and Joshi et al. the first 3.In comparing results across recent publications and the current one, it is important to note the differences in populations, samples, and measurements across studies. Both Howrigan et al.  and Joshn et al.  converteFROH and AFS, FI, and FEV1, even after controlling for homozygosity at common variants with FSNP, suggest that the variants contributing to lower trait values are biased toward being rare and recessive, consistent with predictions from a partial dominance model of inbreeding depression [There are two major evolutionary theories for why inbreeding depression occurs : the ovepression  and conspression ,34. FEV1pression –38, traipression . Thus, oFROH is a novel finding, to the best of our knowledge, though associations between FROH and reproductive phenotypes have been observed previously, for different proxy measures . Our finding is consistent with a body of research suggesting that reproductive traits, like AFS, in non-human populations are under more intense selection pressures than non-fitness traits [FROH and AFS decreased by ~20% after accounting for sociodemographic variables. Furthermore, sociodemographic variables were not measured on parents , and the single dichotomous variable for religious group participation that we used as a proxy for religiosity is unlikely to capture the full confounding effects of religious observance on sexual behaviors. Thus, the association between inbreeding and age at first sexual intercourse that we observed in this study should be interpreted with caution.The positive relationship we observed between AFS and o et al. ). The FRs traits ,40. If as traits ,42. HoweFROH studies that we are aware of, is that ROH associations might be due to third-variable explanations. Unlike GWAS analyses, where parental or offspring sociodemographic traits are unlikely to be associated with allele frequencies and therefore are unlikely to bias GWAS results, it takes only a single generation of parental inbreeding to strongly influence FROH levels in offspring. For example, higher income might be associated with greater opportunities to meet mates of diverse origins and to higher outbreeding; offspring of higher income parents might thereby have not only lower levels of autozygosity, on average, but might also differ on any traits influenced genetically or environmentally by parental income. While sociodemographic confounding is particularly problematic in ascertained samples where cases and controls are drawn from different populations , the possibility of confounding cannot be eliminated, even in population-based samples, unless relevant sociodemographic variables among parents are measured and controlled for or other  designs are used. For example, in a study of approximately 2,000 individuals of Dutch ancestry, Abdellaoui et al. [FROH and the subjects’ own educational attainment (p = 0.045), but found highly significant negative associations between the subject’s FROH and their parents’ educational attainment . These relationships were entirely mediated by the geographic distance between parents’ birthplaces, such that parents with higher educational attainment tended to be more geographically mobile, increasing their chances of mating with someone genetically dissimilar from themselves and thus creating systematic differences in levels of inbreeding across levels of educational attainment in their offspring.There were three central limitations in the current study. The most important one, which applies equally to all other i et al.  found onr = 0.25–0.40; [FROH -trait relationships were likely to be underestimated in the present report, and thus causal interpretation of our results may not be warranted.Having information on parents’ birth location, education, income, mobility, level of religious involvement, and so forth is important in order to control for the possibility that these sociodemographic variables are associated with both higher levels of (distant) inbreeding and lower offspring trait values. Unfortunately, the UK Biobank has limited parental information other than indirect measures such as whether one was breastfed. In the current study, we used sociodemographic responses of the offspring as imperfect proxies for parental responses, which is effective only to the degree that offspring values on these sociodemographic variables are positively correlated with their parents’ values. For example, parental educational , inc25–0.40;  are impeFROH_short is an imperfect measure of truly distant inbreeding , it may be that FROH_short is less susceptible to confounding from recent assortative mating than FROH_long (a measure of more recent inbreeding). The three traits  that were significantly associated with FROH even after the inclusion of sociodemographic covariates were also significantly associated with FROH_short . When controlling for measures of background sociodemographic characteristics –which should at least partially reflect parental characteristics–we found that two (height and grip strength) of the five significant FROH and complex traits.Nevertheless, our results generally replicate previous findings in humans –9 and arS1 Text(DOCX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 TableFROH and FSNP, as well as age, age2, sex, batch number, sample missingness, and the first 20 principle components. We report the average Beta and p-value across the 100 simulations for each MAF class of causal variants (CVs).Linear regression models included both (DOCX)Click here for additional data file.S5 TableFAssociation of ROHwith 26 traits in smaller sample of individuals unrelated at pihat > 0.05, for two sets of models: 1) controlling for age, age2, sex, the first 20 principal components, sample missingness, and batch number as covariates, and 2) also controlling for sociodemographic variables. The quantitative traits  are listed first in the table, followed by diagnoses and binary traits . Phenotypes with a significant relationship with FROH (p < 0.002 after multiple testing correction) are bolded; those with an asterisk are also significantly associated with FROH after controlling for sociodemographic covariates . BP, blood pressure; FEV1, forced expiratory volume in 1 second; FVC, forced vital capacity; BPD, bipolar disorder; MDD, major depressive disorder; df, degrees of freedom; SE, standard error.(DOCX)Click here for additional data file.S6 Table2, sex, batch number, per-sample SNP missingness, and the first 20 principal components. Phenotypes with a significant relationship (p < 0.002 after multiple testing correction) with FROH from recent inbreeding are bolded, while those with a significant relationship with FROH from distant inbreeding are starred. The quantitative traits  are listed first in the table, followed by diagnoses and binary traits . BP, blood pressure; FEV1, forced expiratory volume in 1 second; FVC, forced vital capacity; BPD, bipolar disorder; MDD, major depressive disorder; df, degrees of freedom; SE, standard error.All models controlled for age, age(DOCX)Click here for additional data file.S7 TableAll models controlled for age, age2, sex, batch number, per-sample SNP missingness, and the first 20 principal components. Phenotypes with a significant association (p < 0.002 after multiple testing correction) with FROH_long are bolded, while those with a significant relationship with FROH_short are starred. The quantitative traits  are listed first in the table, followed by diagnoses and binary traits . BP, blood pressure; FEV1, forced expiratory volume in 1 second; FVC, forced vital capacity; BPD, bipolar disorder; MDD, major depressive disorder; df, degrees of freedom; SE, standard error.(DOCX)Click here for additional data file.S8 Table2, sex, batch number, per-sample SNP missingness, the first 20 principal components, and seven sociodemographic variables. Phenotypes with a significant relationship (p < 0.003 after multiple testing correction) with FROH from recent inbreeding are bolded, while those with a significant relationship with FROH from distant inbreeding are starred. The quantitative traits  are listed first in the table, followed by diagnoses and binary traits . BP, blood pressure; FEV1, forced expiratory volume in 1 second; FVC, forced vital capacity; BPD, bipolar disorder; MDD, major depressive disorder; df, degrees of freedom; SE, standard error.All models controlled for age, age(DOCX)Click here for additional data file.S9 TableFROH (p < 0.003 after multiple testing correction) are bolded, while those with a significant relationship with FSNP are italicized. The quantitative traits  are listed first in the table, followed by diagnoses and binary traits . BP, blood pressure; FEV1, forced expiratory volume in 1 second; FVC, forced vital capacity; BPD, bipolar disorder; MDD, major depressive disorder; df, degrees of freedom; SE, standard error.Phenotypes with a significant relationship with (DOCX)Click here for additional data file.S1 FigFROH is cut off at 0.05 for clarity. There were 583 individuals who had FROH > 0.05; these individuals were not excluded from analyses.The histogram of ROH lengths is cut off at 6500 Kb for clarity; similarly, the histogram of (DOCX)Click here for additional data file.S2 FigThe histogram of FSNP is cut off at |0.01| for clarity; 77 individuals had levels of SNP-by-SNP homozygosity greater than 0.1 or less than -0.1.(DOCX)Click here for additional data file.


Setaria italica), the second largest cultivated millet crop after pearl millet, is utilized for food and forage globally. Further, it is also considered as a model crop for studying agronomic, nutritional and biofuel traits. In the present study, a genome-wide association study (GWAS) was performed for ten important agronomic traits in 142 foxtail millet core eco-geographically diverse genotypes using 10 K SNPs developed through GBS-ddRAD approach. Number of SNPs on individual chromosome ranged from 844 (chromosome 5) to 2153 (chromosome 8) with an average SNP frequency of 25.9 per Mb. The pairwise linkage disequilibrium (LD) estimated using the squared-allele frequency correlations was found to decay rapidly with the genetic distance of 177 Kb. However, for individual chromosome, LD decay distance ranged from 76 Kb (chromosome 6) to 357 Kb (chromosome 4). GWAS identified 81 MTAs (marker-trait associations) for ten traits across the genome. High confidence MTAs for three important agronomic traits including FLW (flag leaf width), GY (grain yield) and TGW (thousand-grain weight) were identified. Significant pyramiding effect of identified MTAs further supplemented its importance in breeding programs. Desirable alleles and superior genotypes identified in the present study may prove valuable for foxtail millet improvement through marker-assisted selection.Foxtail millet ( Setaria italica) is a C4 self-pollinated cereal crop known to be cultivated since 5000–6000 BC on the banks of Yellow River in China1. The crop has major agronomic advantages in terms of being relatively cheap to cultivate, tolerant to biotic and abiotic stresses4, efficient in water use5 and nutritionally rich7. It is a major crop in the arid and semi-arid regions of Asia, sub-Saharan Africa and China8 and has increasingly emerged as one of the promising climate-resilient crops in the present decade9. Moreover, foxtail millet has a relatively smaller diploid genome of 510 Mb11 and is considered as an ideal C4 model system for genetic studies involving C4 photosynthesis, agronomically important stress responses, bioenergy potential2 among many others. Despite possessing such attractive agronomic traits, endeavours to understand, dissect and utilize the genetic diversity and generate mapping resources of the crop has been limited14. Thus, a better understanding of the genetic basis influencing the variation in agronomic traits stands to significantly augment crop improvement strategies through conventional breeding or biotechnological approaches.Foxtail millet  based genome-wide association study (GWAS) has higher mapping resolution due to the utilization of historical recombination events available in a natural population18. GWAS has been widely conducted in each of the important crops and model plant systems  for several traits including agronomic, quality, disease resistance, etc.24. However, in foxtail millet, only a few studies are available on GWAS26.In foxtail millet, linkage-based QTL mapping has been conducted for several agronomic traits including yield, grain weight, flowering days, seed number, etc.27. Given this, high-quality SNPs distributed throughout the foxtail millet genome were mined using Double Digest Restriction Associated DNA (ddRAD) sequencing of 142genotypes. GWAS was performed for ten agronomic traits using 10367 SNPs through FarmCPU approach. Superior alleles and genotypes identified in the present study stand to significantly facilitate the improvement of foxtail millet as a viable and efficient climate resilient crop through marker-assisted selection and other useful crop improvement programmes in the future.Advancements in technologies like next-generation sequencing (NGS), genotyping-by-sequencing (GBS) and SNP chips further improve the utility of GWAS through the development of high-density genotyping data. Further, to deal with false positives due to population structure and multiple testing in GWAS, statistical tools are being continually developed2 = 0.47) was observed for FLL/FLW. However, TGW and GY were negatively correlated to the maximum extent (r2 = −0.716).Descriptive statistics including minimum, maximum, mean and standard deviation revealed a wide range of variability for each of the ten traits across 142 genotypes and summarized in Supplementary Table GBS enabled the identification of ~30,000 SNPs. After filtration , 12460 SNPs were selected for physical mapping on foxtail millet chromosomes. Out of 12460 SNPs, 10367 were mapped on nine major scaffolds of foxtail millet. These major scaffolds (1–9) were considered as nine chromosomes (1–9), respectively, hereafter. The mapped 10367 SNPs covered a total of 399.9 Mb of foxtail millet genome. Thus, the average SNP frequency in foxtail millet genome was observed as 25.9 SNPs/Mb. On individual chromosome, the number of SNPs ranged from 844 (chromosome 5) to 2153 (chromosome 8) (Table p < 0.05) LD; however, a minimum of 7461 SNP pairs crossed the significance level of LD on chromosome 6. The whole genome average maximum r2 value found as 0.46 which dropped to its half (0.23) as distance 177 Kb; thus, considered as whole genome LD decay distance and above which LD decayed  were associated with two traits (FLW/TN and GY/TN) each, respectively. Above mentioned 81 MTAs were present on all the nine chromosomes  were identified for ten traits using FarmCPU Table  with p-vviz., C9.37225457 , C9.37443288  and C9.38068016 . Two MTAs associated with GY were present on chromosome 3  and chromosome 7 . Similarly, two MTAs associated with TGW were found on chromosome 6  and chromosome 9 . The above mentioned seven high confidence MTAs were further subjected to downstream analysis including the estimation of allele effect, identification of desirable allele and pyramiding effect of desirable alleles.To eliminate the false positive due to multiple testing, the MTAs were filtered following Bonferroni correction. Out of 81 MTAs, only seven MTAs could fulfill Bonferroni criteria, thus considered as high confidence MTAs Table . These sThe allele effect was determined for each allele of SNPs involved in seven MTAs involving three traits that fulfilled the Bonferroni criteria Table . For allTotal 27 candidate genes were identified which were residing within 25 Kb regions (upstream and downstream) of seven high confidence MTAs for threes traits , see Table 2 = 0.40; p ≤ 0.000). A similar trend was observed for TGW. Mean TGW values of genotypes with two (3.1 g), one (2.4 g) and without any desirable alleles (1.5 g) showed significant difference among them . For FLW, genotypes with three desirable alleles had significantly wider flag leaf (2.4 cm) than genotypes with no desirable allele (1.7 cm) and one desirable allele (1.5 cm). However, no significant difference was observed for FLW in genotypes with two desirable alleles and three desirable alleles.The pyramiding effect of desirable alleles (including more than one SNP associated with the trait) was calculated for above mentioned three traits involving seven MTAs  were identified Table . For FLW32. However, in foxtail millet, only a couple of studies are available where GWAS was utilized to identify genomic regions controlling traits of interest26. Genetic diversity of panel is important prerequisites for GWAS and has been conducted in our earlier study26 which suggested that the panel is diverse. Out of 142, 89 genotypes were collected from different parts of India including Andhra Pradesh, Bihar, Tamilnadu, Jammu & Kashmir, Karnataka, Maharashtra, Madhya Pradesh, Rajasthan, Uttara Khand and West Bengal; remaining 53 genotypes were exotic and belonged to nine different countries . Further, population structure creates confounding in GWAS results. Thus it is important to conduct population structure analysis. Our earlier study26 suggested that there were five subpopulations in the panel.GWAS has always been a potential approach for genetic dissection of complex traits, and it has been successfully utilized in a number of crops including wheat, rice, pearl millet, maize and cotton33. In the present study, utilization of 142 genotypes which are sufficiently diverse suggested their suitability for GWAS. The size of the population used in the present study is slightly small but found to be comparable with GWAS conducted in other cereal crops including millets36. It has been suggested that small population size may be inefficient for the identification of significant associations with minor effect37. In the present study, we have identified significant MTAs even after implementing the most stringent Bonferroni correction. This suggested that the population size is good enough for GWAS; although, we agree that a larger population may lead to the identification of more MTAs. Descriptive statistics and frequency distribution ; genome-wide decay distance was found to be 177 Kb, which is well at par with the earlier study25. The rapid LD decay suggested that the population used in the present study is sufficiently diversified and suitable to conduct GWAS. Thus, the rapid LD decay and higher mapping resolution also made the study useful for cloning of QTLs.GWAS is based on LD which itself is affected by several factors including physical linkage, recombination, selection, genetic drift, etc.47. Although correction for population structure plays a vital role in reducing false positives, overcorrection may lead to false negative results22. Therefore, we initially tested the model fitting for population structure correction. Q-Q plots of all the ten traits showed the proper distribution of observed p-values over expected, which suggested that the association model used in this study is the best fit and maximized the confidence of GWAS results. Further, false positives may also arise due to multiple testing, because in each test using single SNP there is at least 5% error and with an increase in the number of SNPs  overall experimental error increases. Several statistical tools are available for multiple testing correction27. In the present study, we also applied corrections for multiple testing  during GWAS. Here, we observed that out of 81 MTAs (associated with ten traits) only seven MTAs (associated with three traits) qualified Bonferroni correction. Although multiple testing corrections are important to reduce false positive, it becomes highly stringent due to the use of thousands of makers; and may lead to false negatives. Thus, FDR is also considered as a tradeoff and escaped detection of genuine MTAs in earlier studies49. In our study, we also observed that even MTAs with a very significant p-value (10−5) could not qualify multiple testing correction criteria. Thus, all the 81 MTAs may not be false, and thus, need further validation; however, seven MTAs those fulfilled the multiple testing correction criteria had more confidence.A major limitation of GWAS is false positives that arise due to population structure. However, false positives may be reduced with the use of statistical models51. In foxtail millet, linkage-based QTL mapping has been conducted for a number of agronomic traits such as days to heading, peduncle length, grain weight biomass, spikelet, yield, etc.52 using biparental mapping population. The identification of 81 MTAs in the present study adds to the existing knowledge of the genetic architecture of traits considered. Further, single locus analysis furnishes biased results since the background is not considered in this approach. Given this, we have conducted multi-locus analysis by considering the background genome as cofactor using recently developed FarmCPU approach53. Interestingly, out of 81 MTAs, 60 were present on the same chromosome where QTL/s for the same traits were reported in earlier studies42 . The above mentioned seven high confidence SNPs also found crucial in identifying important candidate genes underlying these traits. Candidate genes present close vicinity of associated SNPs identified in the present study may be validated in the future so that can be deployed in breeding. For validation, one can use candidate gene-based association mapping using large population, or functional characterization through RNAi, VIGS, etc. Identification of desirable alleles of these MTAs will enable their efficient utilization in crop improvement programs. Interestingly, the significant pyramiding effect of multiple MTAs for the single trait in our study suggested that the associated SNPs may combine to improve the trait substantially. For three traits , three desirable genotypes were identified with a maximum number of desirable alleles. These genotypes may be used as a donor in foxtail millet breeding program. Intercrossing of these genotypes may combine desirable traits to develop improved high yielding foxtail genotype.26 and million SNPs25. The present study provides better resolution of trait mapping using 10 K SNPs as compared to an earlier study26. Jia et al.25 conducted GWAS for 47 agronomic traits using 916 accessions and 0.8 million SNPs developed through whole-genome sequencing. The present study, where GWAS was conducted for ten agronomic traits  with lesser SNPs and accessions, may be questioned for its novelty. There are two parameters which made present study novel- (i) utilization of different accessions with different genetic background and (ii) phenotyping in different environments. These two parameters enabled us to identify some novel genomic regions associated with agronomic traits  at the research fields of National Institute of Plant Genome Research (NIPGR), New Delhi, India, in a randomized complete block design with three replications. Mean data over the years of each of the 10 traits were utilized during the present study. The traits included days to flowering (DOF), plant height (PH), tiller number (TN), flag leaf length (FLL), flag leaf width (FLW), peduncle length (PedL), panicle length (PanL), tiller maturity (TM), grain yield (GY), and 1000 grain weight (TGW). Descriptive statistics, frequency distribution and Pearson’s correlation coefficient between all possible trait-pairs were analyzed using SPSS v17.0 software.The phenotypic data of 142 foxtail millet genotypes previously reported by Gupta 54. The DNA samples were RNase treated to remove RNA contamination, and the quality and quantity were checked on 1% agarose gel and NanoDrop 1000 (Thermo Scientific). For genotyping, Double Digest Restriction Associated DNA (ddRAD) sequencing approach was used55, and sequencing was done using Illumina Hiseq4000 . Raw Fastq reads were demultiplexed allowing one mismatch to obtain reads for each sample. Data were filtered on the basis of RAD TAGs. Filtered reads were then subjected to 5′ and 3′ base trimming. Illumina 5′ and 3′ adapter sequences were also removed. Paired-end alignment was performed using Bowtie2 (version 2-2.2.9) program with default parameters to the reference genome (http://genome.jgi.doe.gov). The aligned samples and the reference genome sequence are used for variant calling using default settings of SAMtools version 0.1.18.DNA was extracted from one-month-old leaf samples of 142 genotypes using the CTAB method2) analysis was performed for the whole genome as well as individually for each of the nine chromosomes using window size 50 with the help of software TASSEL v5.0. To estimate LD decay, non-linear regression curve was utilized56, and LD decay distance was estimated as the physical distance between SNPs where average r2 reduced to half of the maximum LD value.LD (in terms of r53) was used. This method is highly efficient and also eliminates confounding issues arising due to population structure, kinship, multiple testing correction, etc. This method utilizes both Fixed Effect Model (FEM) and a Random Effect Model (REM), iteratively. REM estimated pseudo-quantitative trait nucleotides (QTNs) and FEM tested marker using pseudo QTNs as covariates. First, three components identified through principal component analysis (PCA) using TASSEL v5.0 were included as a covariate in the association test model. SNP with p-value < 0.001 declared as significant MTAs. Bonferroni-corrected p-value threshold was set as 0.01. To show the model fitting (accounting for population structure), quantile-quantile (Q-Q) plots were also analyzed. The Q-Q plot showed the distribution of observed and expected p-values (association test statistics). Desirably in case of appropriate model fitting, Q-Q plots should show a solid line  represented no biasness; and sharp curves at the end which represented a small number of true associations among thousands of unassociated SNPs. The extent of deviation of curve end from the diagonal is the measure of the power of test statistics.SNPs with <30% missing data and >5% minor allele frequency were utilized for GWAS. All the 142 genotypes used for GWAS were having <30% missing genotypic data. For the association test, a recently developed method called Fixed and random model Circulating Probability Unification (FarmCPUi) of each allele of SNPs (significantly associated with trait following Bonferroni correction) was estimated following Zhang et al.57. Kruskal–Wallis test was performed to identify whether the alleles differ considerably for the associated traits. Subsequently, favourable alleles were identified for each of the trait considered according to the breeding objective. For traits with negative selection, ai < 0 was considered as desirable allele; while, for a trait with positive selection, ai > 0 was considered as a desirable allele.Phenotypic effect (aThe pyramiding effect was estimated in the case where more than two SNPs were found to be associated with the same trait (after Bonferroni correction). To determine the pyramiding effect, linear regression was performed using the number of desirable SNP alleles for traits (independent variable) and corresponding trait values of the genotypes that contained different numbers of desirable SNP alleles (dependent variable). Genotypes with a maximum number of desirable alleles and desirable phenotype were considered as a desirable genotype.Setaria italica v2.2 . Transcripts present within 25 Kb regions from both sides of associated SNPs were fetched along with their description.To identify putative candidate genes residing at the close vicinity of high confidence SNPs, the associated SNPs were mapped to the reference genome Supplementary information