Scalable Exact AlGorithm for Large-scale set-based G×E tests, to permit G×E VC tests for biobank-scale data. SEAGLE employs modern matrix computations to calculate the test statistic and p-value of the GxE VC test in a computationally efficient fashion, without imposing additional assumptions or relying on approximations. SEAGLE can easily accommodate sample sizes in the order of 105, is implementable on standard laptops, and does not require specialized computing equipment. We demonstrate the performance of SEAGLE using extensive simulations. We illustrate its utility by conducting genome-wide gene-based G×E analysis on the Taiwan Biobank data to explore the interaction of gene and physical activity status on body mass index.The explosion of biobank data offers unprecedented opportunities for gene-environment interaction (GxE) studies of complex diseases because of the large sample sizes and the rich collection in genetic and non-genetic information. However, the extremely large sample size also introduces new computational challenges in G×E assessment, especially for set-based G×E variance component (VC) tests, which are a widely used strategy to boost overall G×E signals and to evaluate the joint G×E effect of multiple variants from a biologically meaningful unit . In this work, we focus on continuous traits and present SEAGLE, a  Human complex diseases such as neurodegenerative diseases, psychiatric disorders, metabolic syndromes, and cancers are complex traits for which disease susceptibility, disease development, and treatment response are mediated by intricate genetic and environmental factors. Understanding the genetic etiology of these complex diseases requires collective consideration of potential genetic and environmental contributors. Studies of gene-environment interactions (G×E) enable understanding of the differences that environmental exposures may have on health outcomes in people with varying genotypes . ExampleWhen assessing G×E effects, set-based tests are popular approaches to detecting interactions between an environmental factor and a set of single nucleotide polymorphism (SNPs) in a gene, sliding window, or functional region . Comparen × n (with n as the sample size) and may involve estimating nuisance variance components. When n is large, as in the case of biobank data, matrix computations whose operation counts scale with n3 are prohibitive in terms of computation time and storage.Large-scale biobanks collect genetic and health information on hundreds of thousands of individuals. Their large sample sizes and rich data on non-genetic factors offer unprecedented opportunities for in-depth studies on G×E effects. While the explosion of biobank data collections provides great hopes for novel G×E discoveries, it also introduces computational challenges. In particular, many set-based G×E tests can be cast as variance component (VC) tests under a random effects modeling framework , includin × n kernel matrices, thus lacking practical scalability. In the latter case, approximating the test statistics requires assumptions that may or may not be valid and are difficult to validate in practice. Our numerical studies in A number of methods attempt to ease this computational burden by bypassing the estimation of nuisance variance components, either through approximation of the variance or kernel matrices  or throun individuals in the order of 105, often at the same speed as state-of-the-art approximate methods  for performing G×E VC tests on biobank data. Here “exact” refers to the fact that SEAGLE computes the original VC test statistic without any approximations, rather than the null distribution of the test statistic being asymptotic or exact. Exactness and scalability are achieved through the judicious use of modern matrix computations, allowing us to dispense with approximations and assumptions. Our numerical experiments illustrate that SEAGLE produces Type 1 error rates and power identical to those of the original GxE VC methods , but at  methods . Compare methods , SEAGLE The rest of the paper proceeds as follows. We describe the standard mixed effects model for G×E effects and testing procedures , the comp-value. Let n individual responses for a continuous trait; p covariates whose leading column is the all ones vector for the intercept; L SNPs where L < n. Define the design matrix for the G×E terms as E on the diagonal.We present the standard mixed effects model for studying G×E effects, the score-like test statistic, and its Consider the linear mixed effects model ,y=XβX+Eb ∼N and c ∼N; ε ∼N; and k.Here, L SNPs as random effects rather than fixed effects. This choice avoids power loss for non-small L and numerical difficulties from correlated SNPs that can occur in a fixed effects model. To assess the presence of G×E effects with H0 : c = 0 in Model (1), one can apply a score-like test to the corresponding variance component with H0 : ν = 0.The SNP-set analysis models the G and G×E effects of the P = p + 1. The resulting null model becomes V = τGGT + σIn. Following  an eigenvalue decomposition of C to compute the λℓ’s in the weighted 3. Computing the p-values requires two eigenvalue decompositions: 1) an eigenvalue decomposition of We identify three computational bottlenecks.V−1 without explicit formation of the inverse  to demonstrate SEAGLE’s effectiveness on biobank-scale data. In the second, we simulate data from a fixed effects genetic model with larger n = 20,000 and n = 100,000 observations. This enables us to evaluate the testing performance when the data do not follow our modeling assumptions.We evaluate the performance of our proposed method SEAGLE using simulation studies from two settings. In the first, we simulate data from a random effects genetic model according to Model (1). This enables us to evaluate SEAGLE’s estimation and testing performance. We include experiments with a smaller https://www4.stat.ncsu.edu/˜jytzeng/software_simreg.php); ii) FastKM  the original G×E VC test (referred to as OVC) , as impl) FastKM , as impl) FastKM , as implL loci (L = 100 or 400) with minor allele frequency (MAF) less than 1% by randomly selecting L SNPs without replacement. Finally, in each replicate, we generate the genotypes of n individuals by randomly selecting two haploytpes with replacement. We also consider a confounding factor X and E, we then form the covariate design matrix X, and E together.In all simulations, we obtain the genotype design matrix software  to simuln × L genotype design matrix G  and the n × P covariate design matrix P = 3), we simulate the outcome data y according to the random effects model: β is set as the all ones vector of length P; b is generated from N; e is generated from N; and σ and τ are set to be 1. We set ν = 0 for Type I error analysis and ν > 0 for power analysis, where the actual value of ν is set so that the empirical power of various methods can be within 0.2 ∼0.9 when possible  and would depend on sample size . With ν = 0, we simulate N = 1,000 replicates and evaluate the results at the nominal level α = 0.05, except when assessing SEAGLE’s Type I error rates at α = 5 × 10−2, 5 × 10−3, 5 × 10−4, 5 × 10−5, and 2.5 × 10−6, where we consider N = 20,000,000 replicates. With ν > 0, we simulate N = 200 replicates to assess power.Given the N = 20,000,000 replicates. α-levels with p-values from H0: ν = 0 and τ = σ = 1 with N = 1,000 replicates, we compare the testing results of SEAGLE with OVC. τ and σ obtained from the SEAGLE and OVC REML EM algorithms. Both algorithms produce very small bias and MSE for τ and σ. The left and right panels in p-values, respectively, produced by SEAGLE and OVC. The panels show that SEAGLE and OVC produce identical test statistics and p-values, hence the “exactness” of the SEAGLE algorithm.We begin by examining the Type 1 error rate for SEAGLE with H0: ν = 0, we can compute the “true” score-like test statistic T by evaluating τ and σ values, and obtaining the corresponding p-value. We refer to this as the “Truth” and include it as a baseline approach. p-values from different methods, each over N = 1,000 replicates. We use the Kolmogorov-Smirnov (KS) test to examine whether or not these observed p-values follow the expected null distribution, i.e., to test for H0: the observed p-values follows Uniform . With τ = σ = 1, all methods exhibit similar p-value behavior and follow Uniform  except MAGEE   . The p-vp-values obtained from SEAGLE, OVC, FastKM, and MAGEE, compared to the Truth p-values at τ = σ = 1. We observe that MAGEE produces p-values with larger MSE than the other methods. p-values for each method, computed by first taking the absolute difference between a method’s p-value and the Truth p-value, then dividing it by the Truth p-value. The boxplots suggest that MAGEE exhibits higher bias and greater variance than SEAGLE, OVC and FastKM at τ = σ = 1.In p-value for each of the methods over N = 1,000 replicates with τ = σ = 1 and ν = 0. The right panel shows the same boxplots for just SEAGLE and MAGEE. Results show that at n = 5,000 observations and L = 100 loci, SEAGLE is faster than MAGEE on average. All replicates were computed on a 2013 Intel Core i5 laptop with a 2.70 GHz CPU and 16 GB RAM.Regarding the computational cost, the left panel in H0: ν = 0. SEAGLE performs identically to OVC with respect to Type 1 error rate at α = 0.05 while requiring only a fraction of the computation time, as demonstrated in n = 5,000 and L = 100 but produces much more conservative p-values at τ = σ = 1.ν > 0. SEAGLE again performs identically to OVC while requiring a fraction of the computation time. By contrast, MAGEE is nearly as fast as SEAGLE for n = 5,000 and L = 100 but has lower power when τ = σ = 1 and ν = 0.04.n simulations  with L = 100 and L = 400 loci and by setting τ = σ = 1. H0 : ν = 0. SEAGLE performs almost identically to Truth and OVC, and provides adequate coverage at the α = 0.05 level. Meanwhile, MAGEE produces conservative p-values. p-value for SEAGLE and MAGEE under H0 : ν = 0. SEAGLE is faster than MAGEE at both n = 20,000 and n = 100,000 when L = 100 and requires comparable computation time to MAGEE when L = 400. These timing results were obtained on a single core of an Intel Xeon Gold 6226 R (2.90 GHz) machine with 8 GB of RAM. HA: ν > 0 . SEAGLE exhibits greater power than MAGEE in all four scenarios considered.G:P = 3, e ∼N with σ = 1. The entries of γG and γGE pertaining to causal loci are set to be γG and γGE, respectively. The remaining entries of γG and γGE pertaining to non-causal loci are 0. We consider n = 20,000 or 100,000 observations with L = 100 or 400, and compare SEAGLE with MAGEE only since OVC and fastKM are unable to work on the sample sizes considered here. We select the first ℓ loci to be causal . We vary γG over 0.5, 1, and 1.5 for the ℓ loci to study the impact of the G main effect sizes. For each scenario, we report the signal-to-noise ratio (SNR), obtained by the ratio of the effect-term variance γGGE) to the error-term variance  in G, we report the median variance ratio as SNR.To study the performance of our proposed method when the data may not adhere to our model assumptions, we follow previous work  and simuN = 1,000 replicates with L = 100 for both n = 20,000 and 100,000, and setting γGE = 0 for all loci while letting the first ℓ = 40 loci to have non-zero γG. For both sample sizes, the SNR based on   Var(γGG)/Var(e) of γG = 0.5, γG = 1 and γG = 1.5, respectively. α = 0.05 over varying values for γG. While the Type 1 error rate for SEAGLE remains relatively unaffected by different γG values, MAGEE produces more conservative p-values as γG increases. This is consistent with the MAGEE assumption requiring a small G main effect γGGE)/Var(e) of γGE = 0.1 and 0.15, respectively. When L = 400, the SNR for the GxE effect is 0.0014 and 0.0024 for γGE = 0.075 and 0.1, respectively. The values of γG for the ℓ causal loci are set to be 0.5, 1.0, and 1.5 as before. For L = 100, the SNR for the G main effect is 0.015, 0.061 and 0.138 for γG = 0.5, γG = 1 and γG = 1.5, respectively. For L = 400, the SNR for the G main effect is 0.050, 0.201 and 0.453 for γG = 0.5, γG = 1 and γG = 1.5, respectively.For power evaluation, we simulate L = 100 loci. At n = 20,000, SEAGLE exhibits better power than MAGEE at all combinations of γG and γGE. Moreover, the difference in power increases for larger values of γG since MAGEE relies on the assumption that the G main effect size is small. At n = 100,000 and the same values of γGE, we report the power at α = 0.001 instead of 0.05 because the power at α = 0.05 is near 1 for both methods. We see that both methods produce similar results although SEAGLE still outperforms MAGEE at slightly smaller values of γGE. L = 400 loci. Similar patterns of relative power performance are observed as in the case of L = 100, except that the power difference between SEAGLE and MAGEE is more pronounced in L = 400.p-value < 10−6), there are 589,867 SNPs remaining, which are mapped to genes according to the gene range list “glist-hg19” from the PLINK Resources page at https://www.cog-genomics.org/plink/1.9/resources. There are a total of 13,260 genes containing > 1 SNPs for G×PA interaction analysis.To illustrate the scalability of the G×E VC test using SEAGLE, we apply SEAGLE and MAGEE to the Taiwan Biobank (TWB) data. TWB is a nationwide biobank project initiated in 2012 and has recruited more than 15,995 individuals. Peripheral blood specimens were extracted and genotyped using the Affymetrix Genomewide Axiom TWB array, which was designed specifically for a Taiwanese population. We conduct the gene-based G×E analysis and evaluate the interaction between gene and physical activity (PA) status on body mass index (BMI), adjusting for age, sex and the top 10 principal components for population substructure. The PA status is a binary indicator for with/without regular physical activity. Our G×E analyses focuses on a subset of 11,664 unrelated individuals who have non-missing phenotype and covariate information. After PLINK quality control  . For the 3 genes identified by SEAGLE only, i.e., ALOX5AP, BCLAF1 and PCDH17, their relevance scores are 6.16, 0.26 and 1.54, respectively. The expression of ALOX5AP has also been found associated with obesity and insulin resistance (TBPL1 (identified by MAGEE only) is not in the GeneCards relevance list with BMI or PA.The median run time of SEAGLE and MAGEE is 2.4 and 1.3 s, respectively, Both SEAGLE and MAGEE do not find any significant G×PA interactions at the genome-wide Bonferroni threshold 0.05/13,260 = 3.77 × 10rds.org)  to explords.org) . Two of sistance  as well sistance . On the We introduced SEAGLE, a scalable exact algorithm for performing set-based G×E VC tests on large-scale biobank data. We achieve scalability and accuracy by applying modern numerical analysis techniques, which include avoiding the explicit formation of products and inverses of large matrices. Our numerical experiments illustrate that SEAGLE produces Type 1 error rates and power that are identical to those of the original VC test , while rState-of-the-art computational approaches such as MAGEE bypass the traditional time-consuming REML EM algorithm, and instead compute an approximation to the score-like test statistic by assuming that the G main effect size is small. In practice, however, the G main effect size is often unknown. Our numerical experiments illustrate that SEAGLE generally achieves better Type 1 error and power with comparable computation time.τ and the noise effect parameter σ. The EM algorithm requires more time to converge when τ is small, particularly when τ is very close to zero. Furthermore, the EM algorithm also requires more computational time for data with larger dimensions, particularly as L grows larger. Despite these differences, the computational time for SEAGLE is at least comparable to that of MAGEE in all the many scenarios considered in this manuscript.In general, computational time differences between SEAGLE and MAGEE depend primarily on the effect size of the genetic main effect (G effect) and the size of the data, particularly the number of loci L. This is due to the fact that SEAGLE computes the score-like test statistic exactly and therefore requires an EM algorithm to estimate the main effect parameter n = 20,000 and n = 100,000 observations on ordinary laptops, without any need for high performance computational platforms. This makes SEAGLE broadly accessible to all researchers. Software for SEAGLE is publicly available as the SEAGLE package on GitHub (https://github.com/jocelynchi/SEAGLE), and is also available on the Comprehensive R Archive Network.We highlight the fact that most of our timing experiments were performed on a 2013 Intel Core i5 laptop with a 2.70 GHz CPU and 16 GB RAM. Therefore, SEAGLE performs efficient and exact set-based G×E tests on biobank-scale data with L × 1 annotation weight vector wj based on annotation class j, j = 1, …, J with J the total number of annotation classes, such as the scores derived based on tissue-specific regulatory annotations in G by diag(wj)G in SEAGLE and obtain the association p-value of the target variant set for annotation class j (denoted by pj), j = 1, …, J. Then we combine these pj’s across annotation classes using the Cauchy Combination Test  isSecond is the extension from a single environmental factor to a set of factors represented by ΣE = EET, ΣG = GGT and ΣGE is the element-wise product of ΣG and ΣE. Adaptation of SEAGLE’s scalable REML EM algorithm to the EM algorithm in Here Third is the extension from unrelated samples to family samples. With family samples, Model (1) will include an additional nuisance VC associated with kinship matrix to account for the within-family correlation. Similar scalable algorithms as for the multi-E analysis would also be useful for analyzing family samples.The last is the extension to other types of kernels  of the c


ABCG5/8 and ABO and demonstrate an extended locus heterogeneity at ABCG5/8 with different functional mechanisms. New loci comprise HMGCR, NPC1L1, PNLIPRP2, SCARB1 and APOE. Based on these results, we perform Mendelian Randomization analyses (MR) revealing a risk-increasing causal relationship of sitosterol serum concentrations and CAD, which is partly mediated by cholesterol. Here we report that phytosterols are polygenic traits. MR add evidence of both, direct and indirect causal effects of sitosterol on CAD.Phytosterol serum concentrations are under tight genetic control. The relationship between phytosterols and coronary artery disease (CAD) is controversially discussed. We perform a genome-wide meta-analysis of 32 phytosterol traits reflecting resorption, cholesterol synthesis and esterification in six studies with up to 9758 subjects and detect ten independent genome-wide significant SNPs at seven genomic loci. We confirm previously established associations at  Physterols are cholesterol homologs derived from plants, which are found in humans through consumption of plant products. Here the authors have performed a genome-wide meta-analysis of 32 serum phytosterol traits, with evidence suggesting causality between sitosterol and coronary artery disease. Normal diet contains approximately equal molar amounts of cholesterol and phytosterols, but, serum levels of phytosterols are kept ~200-fold lower compared to cholesterol5. A heterodimeric ATP-dependent transmembrane complex consisting of ABCG5 and ABCG8 hemi-transporters, expressed in intestine and liver, plays a key role in the excretion of sterols, keeping serum phytosterol concentrations low6.Phytosterols are cholesterol homologues synthesized by plants only. Therefore, phytosterol concentrations in mammals can be completely attributed to nutrition, where it can mainly be found in plant oils, nuts and seeds7. Pathologically increased serum concentrations of phytosterols resulting from loss of function mutations of ABCG5/G8 are described resulting in the severe condition of phytosterolemia, most prominently, sitosterolemia8. In a previous work, we identified genetic factors responsible for regulating serum phytosterol levels at physiological levels in the general population9. In this genome-wide association study (GWAS), we identified three independent common SNPs associated with phytosterols, two in ACBG8 and one in ABO. This study was performed with a limited sample size of 1495 subjects and replication in 2917 subjects. Still, until now, this has been the only GWAS of this phenotype.Phytosterol concentrations are known to be under tight genetic control11, see ref. 3 for a recent summary). A consumption of 1–2 g/day was shown to lower low-dense lipoprotein-cholesterol (LDL-C) plasma concentration by about 5–16%12. Several physiological explanations of this phenomenon were proposed, comprising competitive incorporation of cholesterol and phytosterols into micelles13 and a multitude of molecular regulatory processes of phytosterols on genes involved in cholesterol homeostasis14.Importantly, a certain level of phytosterols is discussed to be beneficial, as the cholesterol-lowering effect of phytosterol supplementation is well established . In line with these observations, in our former study, we found that all three variants associated with higher phytosterol levels were also associated with increased CAD risk9. On the other hand, a meta-analysis could not find any direct associations of phytosterols with CAD risk23 and the authors attributed cholestanol-to-cholesterol ratio as the causal factor driving the association seen in our former study24. A recent review25 disputes this interpretation by pointing out that the genetic effect size of the ABCG5/8 locus on cholesterol traits is much smaller than on phytosterols and that there is no evidence of a beneficial effect of phytosterol supplementation regarding CAD risk despite of a clear improvement of cholesterol parameters. A stringent Mendelian randomization analysis of that issue was not performed so far.Despite its cholesterol-lowering effect, the relationship between serum phytosterol concentrations and coronary artery disease (CAD) risk is conversely debated. Experimental studies of phytosterol-enriched diet in mice showed that phytosterols are atherogenic2, tissue and phytosterol species-specific effects26 and the close and complex interactions of phytosterols and cholesterol on several molecular levels14 making it difficult to separate the effects of phytosterols and cholesterol. Moreover, studies considering phytosterols as serum biomarkers often found a positive correlation with CAD endpoints22 while phytosterol supplementation as nutrition intervention more often find negative correlations28.These contradicting findings could be attributed to the small sample size of human studiesWe here presented the results of a meta-GWAS in a significantly larger sample of up to 9758 individuals from six studies to gain a deeper insight into the genetics of phytosterol metabolism by identifying additional genetic factors responsible for regulating serum phytosterol concentrations. We also analysed genetics of free and esterified phytosterol species as well as ratios of free to esterified phytosterols and of phytosterols to cholesterol or lanosterol. Based on our findings, we aimed at unravelling the causal relationships of phytosterols, cholesterol and CAD by performing a stringent multi-instrument Mendelian randomization analysis.Applying hierarchical clustering of the phytosterol traits revealed that absolute phytosterol serum concentrations are closely correlated. Ratios to lanosterol and free to esterified ratios are clearly separated. Clustering and correlation heatmap are presented in Supplementary Fig. Meta-GWAS results of 32 phytosterol traits and ratios showed no signs of genomic inflation in fixed effect modelling  are considered novel.The seven genome-wide significant loci comprise the two associations already discovered by our previous single study GWASWe first characterize additional results of the known loci.r2 = 0.97, p = 1.5 × 10−151 in unconditional analysis of the top-associated trait total sitosterol, p = 9.5 × 10−74 in conditional analysis). The conditional 99% credible set contains three SNPs in high LD with the lead variant (r2 > 0.96) including rs4245791. The conditional statistics of the new lead SNP rs4299376 colocalizes with an eQTL of ABCG8 in colon tissue29 (PP4 = 99.7%) and also with CAD (PP4 = 98.8%) but interestingly, not with cholesterol . The 99% credible set contains seven variants in high LD with the lead variant (r2 > 0.93) including rs41360247. Rs11887534 displays a strong deleteriousness score (CADD = 22.7). The minor allele represents a well-known non-synonymous coding mutation of ABCG8 (D19H), which results in lower phytosterol levels due to a gain of function mutation30. Colocalizations of this locus were observed with cholesterol (PP4 = 94.7%) and CAD (PP4 = 97.2%) but no eQTLs. Though, the signal for cholesterol is clearly weaker than for total sitosterol in terms of explained variance .Conditional analysis revealed four independent associations for that locus see Fig. . The sec−10 in conditional analysis). This variant lies in a common haploblock with the two strongest associations . The 99% credible set contains 16 variants. Among those, rs4148217 showed the highest CADD score of 14.8, since this variant is again a non-synonymous coding mutation of ABCG8 (T400K), which however, is considered benign. Thus, it is not clear whether this association is driven by gene regulation or protein function or both.A third independent association was observed for rs7598542 (5.1 × 10ABCG5 (1.1 × 10−14). The 99% credible set contains 12 variants, all in high LD (r2 > 0.89) with the lead variant. The strongest CADD score of 13.0 corresponds to rs8302 which is an intron variant of ABCG5 and in the 3’UTR of DYNC2LI1. But, no colocalizations of our phytosterol associations were observed with respective eQTLs.A fourth independent association was found for rs78451356 outside of the haploblock of the three variants above and in close proximity to In total, the four independent SNPs of this locus explain 6% of total sitosterol variance.ABO). Total campesterol is the best associated trait here. The top-associated variant is rs2519093 (p = 1.6 × 10−12) which is in perfect LD in terms of Lewontin’s D′31 with our formerly described variant rs657152 . In our former work, rs657152 showed strong LD with rs8176719 coding for the blood group O. Accordingly, a recessive model for rs657152 could be assumed. Analysing the haplotype frequencies of the T/C alleles at rs2519093 and the C/− alleles of rs8176719, it revealed that the T allele of rs2519093 associated with higher campesterol implies the C allele of rs8176719 corresponding to non-O blood groups . Accordingly, the recessive model of both SNPs showed stronger effect sizes and significances compared to the additive model . Total phytosterols alone are not associated. The locus is a known cholesterol locus with HMGCR as the causal gene. We, therefore, consider this association driven by zoosterols rather than phytosterol. Accordingly, the locus is colocalized with cholesterol (PP4 = 97.9%), and weakly, with CAD (PP4 = 56%).At 5q13.3, the top hit rs12916 is associated with quotients of phytosterols and free lanosterol . The ratio of campesterol and cholesterol is also significantly associated as well as other campesterol traits and total sitosterol. Other variants of the locus are in LD with SNPs associated with cholesterol32. The locus colocalizes with cholesterol (PP4 = 95.9%) but this signal is clearly weaker explaining much lesser variance than for total campesterol . The 99% credible set contains 24 variants. The most plausible candidate is NPC1L1 which transports several sterols from intestine to enterocytes33. In line with this, pharmaceutical inactivation of NPC1L1 by ezetimibe is an established treatment against sitosterolemia34.Strongest association at this locus was observed for rs217385 with total campesterol (p = 1.9 × 10−15). Other sitosterol traits including normalized total sitosterol as well as total stigmasterol are also associated with genome-wide significance. The top-variant is in some LD with variants reported to be associated with phospholipids . No colocalizations with cholesterol or CAD were observed. The 99% credible set contains four variants, all with similar posterior probability due to perfect LD. Among them, rs4751995 showed the highest CADD score of 10.4. This SNP is a variant of PNLIPRP2 appearing as both, an intron and an exon variant depending on splicing according to HG38 Genome built. The SNP is also a strong cis-eQTL of this gene in several tissues including colon, pancreas, stomach and small intestine. Accordingly, eQTL colocalizations in these tissues were observed. The gene is also biologically plausible because PNLIPRP2 shows high hydrolytic activity on phospholipid bile salt micelles36. Bile salt micelles influence phytosterol levels due to different affinities to zoo- and phytosterols37.This locus is driven by a total sitosterol association  with rs838880 reported in Teslovich et al.38. Accordingly, the SNP explains considerably more variance of sitosterol as compared to total cholesterol or LDL-C (0.5% vs. 0.013% respectively 0.02%). Regarding eQTLs the locus (weakly) colocalizes with an eQTL of SCARB1 in small intestine and colon tissue40 . According to the GWAS catalogue, the locus is also associated with PLA2 activity and mass. The 99% credible set comprises five variants, all in LD with the top-variant. These SNPs are intronic variants of SCARB1 with no relevant deleteriousness prediction (maximum CADD score 6.0). The scavenger receptor class B type I (SCARB1 or SR-BI) is a receptor of HDL and facilitates cholesterol delivery to steroidogenic tissues and cholesterol excretion in the liver42. As a possible mechanistic explanation of our results, we suppose that increased expression of SCARB1 improves uptake of cholesterol from micelles by enterocytes. In response, an increased phytosterol uptake by micelles is conceivable. This is in line with the SNP’s unidirectional effects on sitosterol and SCARB1 gene-expression.The strongest association at this locus was observed for rs10846744 with total sitosterol. Other associated traits comprise esterified sitosterol and the ratios free sitosterol to free cholesterol and total sitosterol to lanosterol. A week evidence for colocalization with CAD (PP4 = 70%) was found, but interestingly, not with total cholesterol (PP3 = 94%) or HDL-C (PP3 = 100%) despite of the fact that the locus was described for associations with different lipid traitsAPOE (R176C), representing the APOE-E2 allele. The locus colocalizes with cholesterol (PP4 = 100%) and CAD (PP4 = 99.7%) but no eQTLs. The cholesterol effect of this locus is larger than that of stigmasterol . Therefore, we consider this locus as driven by zoosterol rather than phytosterol associations. The effect directions of the variant on cholesterol and stigmasterol are identical at this locus. This is in agreement with the observation that phytosterols are accumulated in APOE knock-out mice but not in LDLR knock-out mice43, which was explained by increased blockage of sterol excretion rather than by absorption, which would expected to be lower in case of increased cholesterol synthesis44.Finally, we detected a genome-wide significant association with esterified and total stigmasterol at 19q13.32. The lead-SNP was rs7412 and the 99% credible set contains only this SNP. The SNP is a known miss-sense mutation of h2 = 72%, p < 1.3 × 10−5). The heritability estimate of total sitosterol showing strongest associations in our study was 63%. Since the seven independent variants found for this trait explain 7.4% of the variance, further variants for this trait are likely to exist.To assess the potential for future genome-wide association studies of phytosterol traits, we estimated their chip-heritability. Estimates were significant throughout and effect sizes are moderate to large. The largest heritability was estimated for total campesterol to cholesterol ratio and esterified campesterol . This constitutes a strong enrichment of OR = 2.65 (p = 7.8 × 10−41). Five loci where detected with suggestive significance (p < 1.0 × 10−6), namely 11q23.3 , 20q13.12 , 2p24.1 , 5q13.3 , 9p22.3 . These loci could be considered further candidates requiring replication. Full look-up results can be found in Supplementary Data We performed a look-up of 1,600 independent lipid loci reported in literature. Among those, 220 showed nominal significance with at least one of our phytosterol traits . We systematically compared genetic effects on absolute phytosterols, phytosterol to zoosterol ratios and esterification representing different facets of phytosterol metabolism including markers of resorption and synthesis of cholesterol. We identified ten independent genome-wide significant associations at seven loci, comprising five new loci robustly associated with multiple traits and related to functionally plausible genes. Since our associations provide strong genetic instruments, we performed a comprehensive Mendelian randomization analysis of the causal relationships of sitosterol, total cholesterol and CAD. It revealed a causal effect of higher plasma sitosterol levels on increased CAD risk that is only partly mediated by the increase of total cholesterol levels, thus supporting an atherogenic effect of phytosterols.9, we detected three independent variants of phytosterol traits. Two of them were located at 2p21 (ABCG5/8), while another one was located at 9q34.2 (ABO). We could confirm these findings in our present meta-analysis comprising a considerably larger sample size. We could also confirm that the genetic model at 9q34.2 could be assumed to be recessive, i.e. carriers of non-O blood groups show higher phytosterol levels, which is consistent with higher cholesterol levels45 and higher CAD risk46 of non-O carriers. The ABO locus is notorious for its pleiotropic effects on other traits including E-Selectin and other lipid species48.In our previous single study meta-analysisABCG8 in colon tissue, rs11887534 acts via a non-synonymous coding mutation. The situation for the third SNP, rs7598542, is less clear because on one hand it colocalizes weakly with an eQTL of ABCG8 in colon tissue, but on the other hand, the credible set also contains non-synonymous coding mutations. The fourth variant rs78451356 is outside of the haplo-block of the three other variants and the respective credible set contains functional intron variants of ABCG5. Of note, the independent variants at this locus do not show any colocalization signals with total cholesterol except for rs11887534 for which, however, the explained variance of sitosterol was much higher than that for total cholesterol. Thus, we conclude that this is a primary phytosterol locus and that observed associations with cholesterol are secondary to that.However, with respect to the 2p21 locus, our fine-mapping analysis with increased sample size revealed four rather than the previously reported two independent associations with putatively different functional mechanisms. While rs4299376 is a strong eQTL of HMGCR) locus associated with total brassicasterol to lanosterol was likely driven by lanosterol association. Likewise, the 19q13.32 (APOE) associated with esterified stigmasterol might also be driven by associations with other lipid species because the locus colocalizes with a total cholesterol association explaining a larger amount of total variance. It is worthwhile to mention that normalization to cholesterol or lanosterol, respectively, can induce genetic associations driven by these traits. Therefore, we recommend considering both, raw and normalized traits.Among the five new loci, the 5q13.3  effects of NPC1L1 variants on phytosterols in children49. PNLIPRP2 and SCARB1 both interact with micelles, which in turn express competitive zoo- and phytosterol uptake. There is experimental evidence regarding involvement of SCARB1 in sterol uptake shown by cell-culture experiments51 and over-expression in mice53. In contrast, such an effect could not be observed in SCARB1 knock-out mice54. Of note, 10q25.3 showed no colocalization with total cholesterol and 7p13 and 12q24.31 showed colocalization explaining much less total variance of cholesterol compared to the associated phytosterol traits. Thus, we again conclude that these loci are primary phytosterol loci and that cholesterol associations are down-stream effects.For the other three loci comprising 7p13, 10q25.3, 12q24.31 functionally plausible genes could be assigned, namely A limitation of our association analyses is that we adjusted for the binary variable “lipid lowering medication” as determined by ATC category “C10”. This does not consider dosing schemes, which are scarcely available in population-based studies. Moreover, we did not distinguish between sub-categories of ATC C10. In the majority of cases, statins were prescribed . All other categories were much less prescribed (6% respectively 5%). Ezetimibe was rarely prescribed (<2% of cases).7. It needs to be pointed out that our estimates refer to the so-called “chip heritability”, i.e. variants which are covered by the chosen genotyping platform including well-imputable variants. Thus, these estimates are a lower bound of the total heritability. In our study, we estimated for example a heritability of 63% for sitosterol. On the other hand, discovered variants only explained 7.4% of variance. This suggests that phytosterols are complex traits and that there are more variants to be discovered in future meta-GWAS efforts. Accordingly, our look-up of loci associated with other lipid traits  revealed several additional associations with nominal or suggestive significance. Larger sample sizes are required to validate these associations and to find low frequency variants. Moreover, studies in other than European ancestries are required to reveal any ethnicity-specific variants or effects.In our analysis, phytosterols showed a moderate to high heritability and our estimates are in the same order of magnitude as those of twin studies55 excluding all cytobands with phytosterol associations. In sensitivity analyses, we also restricted instruments of sitosterol to the independent variants of the 2p21 locus for which a clear functional role in phytosterol excretion is established. Instruments of total cholesterol were also restricted to the 14 strongest associations. We further considered methods for MR, which are more robust regarding type I pleiotropies. Similar results were observed throughout suggesting that our MR analysis is not biased by type I pleiotropies. Interestingly, we could show both, a significant direct effect of increased total sitosterol on elevated CAD risk and a significant indirect effect mediated by total cholesterol. Effects were in roughly the same order of magnitude. This observation was confirmed by considering normalized sitosterol, again showing a positive causal effect on CAD risk. Considering CAD summary statistics from Japanese samples yielded roughly the same results. It needs to be pointed out, however, that this type of Mendelian randomization analysis is performed under the assumption of comparable instrumental variable effects on sterols between Europeans and Japanese. Comparing allelic frequencies of instrumental variants between these ethnicities revealed larger differences. Thus, further investigations are required to validate our causal estimates for non-European ethnicities. As another limitation, by Mendelian randomization one estimates the effect of a small live-long increase of total serum sitosterol on total cholesterol or CAD risk. The effects of short-term dietary or pharmaceutical interventions cannot be estimated by this method.The close inter-relationship of phyto- and zoosterols raises questions regarding causes and consequences of observed genetic associations and with respect to the conversely discussed relationship of phytosterols and CAD. For a formal analysis of the causal inter-relationships between total sitosterol, total cholesterol and CAD, we applied Mendelian randomization. We aimed to distinguish between a direct causal effects of total sitosterol on CAD and an indirect effect mediated by total cholesterol. This is not trivial because it requires independent genetic instruments for total sitosterol and total cholesterol while genetic associations are often observed for both traits in parallel. We therefore selected genetic instruments for which type I pleitropy can be excluded as far as possible, either based on the functional role of the candidate gene or by sole or particularly strong genetic associations for one of the traits only. For sitosterol instruments, we considered six independent genome-wide significant variants discovered in the present study. All showed clearly stronger effect sizes with sitosterol than with total cholesterol. For total cholesterol, we considered 36 variantsIn summary, our study extends the number of variants and loci associated with serum phytosterol traits. It also provides further candidate genes to be confirmed in future studies. Contributing to the ongoing discussion of a potential role of phytosterols on the risk of CAD, our Mendelian randomization analyses provided evidence for both, a direct and a cholesterol-mediated detrimental effect of sitosterol on CAD risk.The overall analysis workflow and study design is depicted in Supplementary Fig. 57, LIFE-Adult58, LIFE-Heart59, LURIC60, the Sorbs62 and the Young Finns study63 (YFS). All study participants were of European ancestry. Brief study descriptions are provided in Supplementary Data Six studies contributed to the present analysis: KORA64. We performed adjustment of measured quantities regarding batch-effects by treating time of measurement as batch parameter. Function ComBat of the R-package “sva” was applied for that purpose65 . See Supplementary Data The following parameters were measured in some or all of the contributing studies: serum concentrations of free and esterified brassicasterol, campesterol, sitosterol, stigmasterol, cholesterol and free lanosterol. In KORA, LIFE-Adult, LIFE-Heart and Sorbs sterol measurements were performed centrally at the Institute of Laboratory Medicine, University of Leipzig using liquid chromatography tandem mass spectrometry following the same analytical protocol for all studies. The measurement technique is explained in detail inIn LURIC, serum levels of total brassicasterol, campesterol, lanosterol, sitosterol, stigmasterol as well as free and total cholesterol were measured with gas-chromatography mass-spectrometry. In YFS, serum levels of total campesterol, cholesterol and sitosterol were also determined using gas-chromatography mass spectrometry.Descriptive statistics of available traits per study can be found at Supplementary Data Genome-wide association analyses were performed for the following traits if available: Total, free and esterified phytosterols (12 traits at maximum). Moreover, we considered a number of physiologically relevant ratios, namely those of free to esterified phytosterols (4 traits), free and total phytosterols to lanosterol (8 traits), and to total cholesterol (8 traits), respectively. Ratios represent reaction equilibria of phytosterol esterification and phytosterols normalized to lanosterol or to cholesterol as measures of endogenous cholesterol synthesis, respectively cholesterol absorption. Thus, at maximum, 32 traits were analysed.To visualize correlation structure between our traits, we performed hierarchical clustering. This analysis is based on the phytosterol data of the studies KORA, LIFE-Adult, LIFE-Heart and Sorbs measured by the same method. For the clustering, we consider partial correlation coefficients as measures of similarity of traits controlling for the covariates age, sex, log(BMI), diabetes status, lipid lowering medication and study. Traits were log-transformed prior to analysis. Clustering was performed using the “hclust” package of the software R.Genotypes were measured by using SNP micro-arrays: Affymetrix Gene Chip Human Mapping 500 K Array Set (Sorbs), Affymetrix Axiom CEU1 , Affymetrix custom array (LIFE-Heart), Affymetrix Genome-Wide Human SNP Array 6.0 , Illumina 200k MetaboChip (LURIC), Illumina Omni 2.5/Illumina Omni Express (KORA) and Illumina Human 670k BeadChip (YFS). Sample and SNP quality control was performed according to study specific criteria, see Supplementary Data 66 based on 1000 Genomes Phase 1 reference panel  or 1000 Genomes Phase 3 reference panel (KORA). Genotype data was translated to forward strand annotation using NCBI b37 (hg19) coordinates.Genotypes were imputed using IMPUTE2A standardized analysis plan was developed to harmonize genome-wide association analyses of single studies. Analyses were performed centrally for the cohorts KORA, LIFE-Adult, LIFE-Heart and Sorbs. Analysts of the two external cohorts, LURIC and YFS, were asked to follow the same analysis plan.67, respective traits were also adjusted for the relatedness structure applying mixed model analysis as represented in the “polygenic” function of the “GenABEL” package of R.Traits were log-transformed to approximate Gaussian distributions. To minimise confounding, traits were adjusted for age, sex, log(BMI), diabetes status and lipid lowering medication  code “C10”). Regression analyses were also adjusted for genetic principal components when indicated. Due to excess relatedness in the Sorbs study68 , PLINK 2.0  or SNPTEST 2.569 (YFS) assuming an additive gene-dose model. X-chromosomal markers were analysed assuming total X-inactivation, i.e. male genotypes were coded as A = 0 and B = 2 and female genotypes are coded as AA = 0, AB = 1 and BB = 2. As effect estimates, slopes of the gene-dose in linear regression analysis and respective standard errors are reported. P-values correspond to two-sided testing.Association analyses were performed using PLINK 1.9Sample sizes and SNP numbers available per study and trait are provided in S3.70. SNPs not in the reference panel , with missing values in alleles  or statistics , mismatching alleles or mismatching chromosomal position with respect to the reference were discarded. SNPs were filtered for weighted minor allele frequency (MAF) > 2% which corresponds to minor allele count >17 as calculated for the smallest study . Genotyped SNPs were filtered for call rate >95% and p(HWE) > 10−6. Imputed SNPs were filtered for imputation quality score >0.5 and for deviation from reference allele frequency <20%. Finally, the alleles were harmonized so that the same effect allele was used in all studies. Number of quality controlled SNPs per study is presented in Supplementary Data Summary statistics of all studies were checked and harmonized using EasyQC71 if λ > 1.Variance inflation factor λ was calculated for single study GWAS. Test statistics were corrected by genomic controlI2 < 0.7.Altogether 32 traits and up to 9758 samples per trait were meta-analysed. Fixed effects inverse variance meta-analysis of single study gene-dose effects was performed as primary statistics. Random effects meta-analysis results were also reported. Meta-analysis results were filtered for number of contributing studies >2 and heterogeneity The number of resulting SNPs ranged from 7,827,943 to 8,212,880 in dependence on the trait analysed . We also visually inspected the regional association plots of genome-wide significant loci and removed those with lack of support, i.e. no other variant with at least suggestive significance (p < 10−6).A ABO) a recessive mode of inheritance can be assumed, we analysed possible deviations from the standard additive model in cohorts for which we had access to the raw genotype data  using the “DOMDEV” option of Plink. The null-hypothesis of this test is that heterozygote effects are zero under an additive model.Since for one of the loci (72 for details). In brief, linkage disequilibrium (LD) between markers was calculated based on genetic data from 1000 Genomes Phase 1, version 3 reference panel for European samples. Priority pruning of the top-list was performed by assuming a variant as tagged when the variant is in LD (r² ≥ 0.5) with a tag-SNP of stronger association with any trait. Loci are defined by cytobands.Annotation of Meta-analysis results was done by an in-house workflow (see ref. 73 are reported as candidate genes due to proximity. SNPs were annotated by further resources comprising known trait associations via LD-based lookup (r2 ≥ 0.3) of the most recent GWAS Catalog74, expression quantitative trait loci (eQTLs) by LD-based lookup (r2 ≥ 0.3) based on Genotype-Tissue Expression (GTEx v7)75 and (updated) own data76 and by various deleteriousness scores including CADD77 and RegulomeDB78. All resources were downloaded at July 1st, 2020.Lead SNPs of loci are defined as the tag SNPs showing the strongest association with any trait. All genes within 50 kilobases (kb) distance and up to four genes within a 250 kb distance to a SNP according to Ensembl79, and reactome .We also annotated the nearby genes and eQTL genes per locus by assigning respective pathways retrieved from KEGG, GO, DOSE80. First, we performed stepwise model selection (cojo-slct) to identify independent variants per locus. If more than one such signal was observed, we calculated conditional statistics (cojo-cond)81 for every independent variant by controlling for the other independent variants, respectively. As LD reference panel we used the combination of available genotypes of LIFE-Adult and LIFE-Heart .To identify secondary hits per locus, we considered the best-associated trait and applied the tool GCTA (version 1.92.0beta3)r2 = β2/(β2 + N*se(β)2)82, where β is the fixed meta-effect of Beta estimates of the single study linear regression analyses, se(β) its standard error and N the total sample size. For the 2p21 locus, the conditional statistics were used. Total explained variance is calculated by summing up the explained variances of single independent SNPs contributing to the respective trait.After determining independent SNPs via Cojo analysis, we calculated their respective explained variance using the formula 84. In case of more than one independent variant per locus, conditional statistics were used per independent variant. We then calculated respective Approximate Bayes Factors (ABF) by applying the R-package “gtx”. The required prior distribution of the standard deviation was constructed empirically by the difference of the 97.5th and the 2.5th percentile of SNP effects of the respective locus divided by (2*1.96). In our data, this quantity ranged in between 0.014 (locus 9q34.2) and 0.051 (2p21).After determination of independent signals, we aimed at identifying the respective set of SNPs containing the causal variant with high certainty. For this purpose, we considered the set of SNPs within ±500 kb of the independent lead SNP and their respective effect estimates and standard errorsDerived ABFs were used to calculate the posterior probability of a variant being causal for the observed association. We ordered variants in descending order of their posterior probability and determined the respective cumulative probability. Applying a cut-off of 99% cumulative probability yielded the 99% credible set of SNPs for the respective variant. We also considered the relaxed cut-off of 95%. Variants of the credible sets were annotated as described above. The CADD score was considered as primary criterion to identify functionally relevant variants within the credible sets.85.We estimated the heritability of all considered GWAS traits using the raw genotype data of LIFE-Adult and LIFE-Heart and applying GCTA. This approach results in the so called “chip-heritability”86 by searching for total cholesterol , low density lipoprotein-cholesterol , high density lipoprotein-cholesterol  and triglycerides . Download was performed at 20th August 2020. We only considered variants for which genome-wide significance was reported (3770 unique SNPs). Of those, 3067 were available in our data and high quality association results were available for 3003 of them. After pruning, 1600 independent variants were obtained.We also systematically searched for co-associations of our traits with reported lipid loci to detect possible associations, which did not achieve genome-wide significance in our study. Lipid loci were retrieved from the GWAS Catalogp-value <3.48 × 10−3 across all analysed traits. This corresponds to a 5% significance threshold accounting for multiple trait testing and was obtained on the basis of the empirical p-value distribution of our 8,299,000 SNPs with association results. We tested for an enrichment of co-associated phytosterol traits using a one-sided exact binomial test.Phytosterol traits are considered co-associated if achieving a minimum LCAT, ACAT, SOAT1 and SOAT2 by considering all SNPs within a 500 kb range around these genes.Finally, we searched for candidate genes of phytosterol esterification, namely 87. Cis-eQTLs were retrieved from GTEx v7 29. Coincidence of signals was tested by pairwise colocalization analyses of loci88. This method evaluates the posterior probability of five hypotheses . Posterior probabilities of these five hypotheses are defined as positive and sum up to 100%. We consider a posterior probability of ≥75% as sufficient to support one of the hypotheses. Loci were again defined by a ± 500 kb window around the respective lead SNPs.We tested whether the independent loci coincide with loci of other lipid traits, coronary artery disease (CAD) or cis-eQTLs of candidate genes in different tissues. The latter could provide a potential functional explanation of the considered variant e.g. for those for which no causal non-synonymous coding mutation could be detected in the respective credible set. For 2p21, conditional statistics were used for that purpose. Publicly available summary statistics of the considered traits are available from recent GWASThe role of phytosterols in the development of coronary artery disease is controversially discussed. Therefore, we exploited the results of our genome-wide association analysis to perform Mendelian randomization analyses. We aimed at answering the question whether there is a causal relationship of phytosterols on CAD and to what extend this effect is mediated by cholesterol.89), we also performed a sensitivity analysis restricting to the independent SNPs of the 2p21 locus only, since this locus is functionally well established for its role in phytosterol excretion.Since the strongest instrumental variables were obtained for total sitosterol, we focused on this trait throughout. Six independent genome-wide associations identified in our meta-GWAS were considered as instruments, namely three independent variants from the 2p21 locus and the three genome-wide significant hits at 7p13, 10q25.3 and 12q24.31, respectively. The fourth independent variant from 2p21 could not be used due to missing CAD summary statistics. To avoid any biases due to possible type I pleiotropies . This was achieved by removing cytobands with phytosterol associations. Again, to avoid type I pleiotropy, we also performed these analyses restricting to strong instruments, i.e. variants with p < 10−20. Summary statistics for CAD were retrieved from van der Harst et al.90.For total cholesterol, we used 36 SNPs as instrumental variables not associated with phytosterol levels  are available.Finally, to analyse possible translations to other ethnicities, we performed Mendelian randomization analyses using CAD summary statistics from Japanese subjects92, i.e. by the following three steps Estimate the causal effect of total sitosterol on total cholesterol (α)Estimate the causal effect of total cholesterol on CAD (β)The direct and indirect causal effect of total sitosterol is estimated as recommended by Burgess et al.Then, the indirect effect constitutes on the product of α and β, while the direct effect can be estimated by γ minus the indirect effect. For causal effect estimation, we used the inverse-variance weighting method as implemented in the R package “MendelianRandomization”. Other methods  were also considered for sensitivity analysis.Further information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1-19Reporting Summary


Genome-wide association study (GWAS) has become the main approach for detecting functional genes that affects complex traits. For growth traits, the conventional GWAS method can only deal with the single-record traits observed at specific time points, rather than the longitudinal traits measured at multiple time points. Previous studies have reported the random regression model (RRM) for longitudinal data could overcome the limitation of the traditional GWAS model. Here, we present an association analysis based on RRM (GWAS-RRM) for 808 Chinese Simmental beef cattle at four stages of age. Ultimately, 37 significant single-nucleotide polymorphisms (SNPs) and several important candidate genes were screened to be associated with the body weight. Enrichment analysis showed these genes were significantly enriched in the signaling transduction pathway and lipid metabolism. This study not only offers a further understanding of the genetic basis for growth traits in beef cattle, but also provides a robust analytics tool for longitudinal traits in various species.FGF4, ANGPT4, PLA2G4A, and ITGA5 were promising candidate genes for BW. Moreover, these genes were significantly enriched in the signaling transduction pathway and lipid metabolism. These findings will provide prior molecular information for bovine gene-based selection, as well as facilitate the extensive application of GWAS-RRM in domestic animals.Body weight (BW) is an important longitudinal trait that directly described the growth gain of bovine in production. However, previous genome-wide association study (GWAS) mainly focused on the single-record traits, with less attention paid to longitudinal traits. Compared with traditional GWAS models, the association studies based on the random regression model (GWAS-RRM) have better performance in the control of the false positive rate through considering time-stage effects. In this study, the BW trait data were collected from 808 Chinese Simmental beef cattle aged 0, 6, 12, and 18 months, then we performed a GWAS-RRM to fit the time-varied SNP effect. The results showed a total of 37 significant SNPs were associated with BW. Gene functional annotation and enrichment analysis indicated  With the development of the high-throughput chip technologies and the completion of whole-genome sequencing of swine , cattle Numerous GWAS have been widely performed on single-record traits of beef cattle, such as birth weight, weaning weight, and yearling weight (YW) ,9, and sBody weight (BW) is an economically important longitudinal trait in beef cattle that greatly influences growth performance . Until nAll animals and protocols in the study were approved by the ethics committee of the Institute of Animal Sciences, Chinese Academy of Agricultural Sciences (CAAS), Beijing, China . A total of 808 male individuals in this study were derived from the Chinese Simmental beef cattle resource population established in Ulgai, Xilingol League, Inner Mongolia of China from 2008 to 2014. After weaning, the cattle were moved to the Beijing Jinweifuren fattening farm for fattening in the same feeding strategies and management conditions. Body weight was measured for each individual at 0, 6, 12, and 18 months after birth, respectively. Here, the body weight data were consistent with the data in the study by Duan et al. .http://zzz.bwh.harvard.edu/plink/, accessed on 1 July 2021) was used for quality control of SNPs according to the following empirical excluded criteria: (1) minor allele frequency (MAF) < 0.01; (2) SNP call rate (CR) < 95%; (3) Hardy–Weinberg equilibrium value p < 1 × 10−6; (4) Mendelian error of SNP genotype above 2%; (5) Individuals with more than 10% SNPs deletion; (6) SNP marker sites with missing chromosomal location information. All the misplaced and duplicated SNPs were also excluded from the analysis. Ultimately, 671,192 SNPs with an average marker interval of 3 kb on 29 autosomal chromosomes remained for subsequent analysis.Blood samples for the experimental population were collected along with the periodic quarantine inspection of the farm. Genomic DNA was isolated from blood samples using the TIANamp Blood DNA Kit , and the high-quality DNAs with the A260/280 ratio ranging 1.8–2.0 were considered for further analysis. In this study, the Illumina BovineHD Beadchip with 774,660 SNPs  was used for qualified DNAs genotyping and Illumina’s Infinium II Assay was selected as the genotyping platform. The SNPs were uniformly distributed on the whole bovine genome with a mean inter-marker space of 3.43 kb. SNP chips were scanned and analyzed using the Infinium GenomeStudio software . PLINK v1.9  by PLINK v1.9 . Our prek at time t; j with time t; k, respectively; k at time t. Here, lth fixed regression coefficient; lth random regression coefficients for additive genetic effect and permanent environmental effect of the kth individual, respectively; lth basis function at time t, i.e., the value of the Legendre polynomial (covariable).The general expression of the random regression model is as follows:s et al. . For insThe Equation (1) can be denoted as:m out of n individuals for which phenotypic values are measured; km represents the phenotypic record for individual k and the total number of records for all individuals is m × 1) of phenotypic values of all individuals. The parameters in the equation are defined as follows: Parameter f is a vector of fixed environmental effect and parameter fm + 1) of fixed regression coefficients; Parameter We assume that there are For matrix form (3), we have the (co) variance matrices of all random effects:t. The function expression of lth fixed regression coefficient of SNP additive effect; lth basis function at time t.Based on the general random regression model, the functional GWAS model (fGWAS-C) for the association analysis of longitudinal traits has been proposed by Ning, C. , which ap-value for GWAS analysis was calculated as follows:p < 0.05; m is the total number of SNPs after quality control [The threshold  control .p-value and then the Ensembl–BioMart was used to match these SNPs with the bovine reference genome UMD 3.1 . Candidate genes in the target region were screened through the National Center for Biotechnology Information (NCBI) database , cattle QTLdb [p-value adjusted using the Benjamini–Hochberg approach  was considered to be the threshold value for significantly enriched GO terms and pathways. Using ToppCluster and Cytoscape v3.8.0 to plot the network diagram between candidate genes and their belonged GO terms/pathways. The STRING  was used to perform PPI network analysis.The significant SNPs associated with BW were screened according to the threshold le QTLdb , and prele QTLdb . The p-vUsing SPSS v20.0 to calculate the measurement values of body weight at four growth stages. All data were expressed as means ± standard deviation (M ± SD). Microsoft Excel 2010 software was used to check up the data with normality test.The BW values of Chinese Simmental beef cattle at 0, 6, 12, and 18 months of age were tested for normality. As shown in 10(p) versus expected −log10(p) in the Q–Q plot represented most points revolving around the 45° line, indicating there was no inflation or systematic bias in this study, as well as population stratification was well controlled. The Manhattan plots showed that a total of 37 significant SNPs associated with BW trait were identified, most of which were located on Bos taurus autosome (BAT) 1 (five SNPs), BAT 2 (three SNPs), BAT 11 (four SNPs), and BAT 12 (three SNPs). Two SNPs were found on each of the seven chromosomes , and only one SNP was distributed on each of the eight chromosomes . The SNP with the smallest p-value (p = 7.55 × 10−8) was located on BAT 10: 101,577,026 bp (BovineHD1000029459). However, some SNPs had the lowest significance levels, i.e., the p-value of BovineHD1100004962 and BovineHD1100011885 located on BAT 11 was 2.54 × 10−6 and 3.42 × 10−6, respectively. The detailed information of all significant SNPs was displayed in The quantile-quantile (Q–Q) and Manhattan plots of GWAS-RRM analysis are shown in ITGA5, ANGPTL4, and FGF4, respectively. Three significant SNPs were identified at the region of 26.11-33.58 Mb on BAT12, of which BvineHD1200027798 and BovineHD1200026844 were close to genes SHISA2 and CHMP3, respectively. No candidate genes were detected in four significant SNPs including BovineHD0200018897, BovineHD0700012290, BovineHD1100030552, and BovineHD2900008350, located on BAT2, BAT7, BAT11, BAT12, and BAT29, respectively. The detailed information on these genes was listed in In this study, 37 significant SNPs were identified for BW trait, of which 33 were located within or near candidate genes through searching Ensembl, NCBI, and QTL databases. As shown in FGF4, ANGPT4, ITGA5, and PLA2G4A involved in no less than two KEGG pathways deserved further attention and discussion. Additionally, based on animal QTLdb, the previous reports and gene function analysis, several candidate genes including TBC1D5, SHISA2, PDE1C, and COCX6 were also identified to affect the BW trait. The information of these candidate genes was listed in To further understand the function of candidate genes, GO and KEGG enrichment was performed using the R package “clusterProfiler” . As showFGF4, ANGPTL4, PLA2G4A, and ITGA5) were significantly enriched in the above pathways, which implied these genes might play special roles in regulating the BW trait.Longitudinal traits can better reflect the growth and development patterns of livestock and poultry. Therefore, mapping and analyzing the significant SNPs and functional genes affecting longitudinal traits have important economic value for beef cattle breeding. It is worth noting that GWAS-RRM is the main approach to analysis longitudinal traits, which could better control FPR and improve the accuracy of estimated breeding values (EBVs) ,18, thusFibroblast growth factors (FGFs) are important growth factors that participate in many developmental and physiological processes [FGFs, thus causing developmental disorders, i.e., skeletal diseases, infertility, and cancer [FGF family, FGF4, and FGF14, regulate fibroblasts formation and the development of growth traits such as BW trait [FGF4 was identified in three cattle breeds  [FGF4 was related to the regulation of bovine embryo development [FGF4 was associated with trophoblast proliferation in mice, and FGF4 null mice showed a peri-implantation lethal phenotype [FGF4 was an important indicator in the growth and development of animals.rocesses . FGF sigd cancer . RelevanBW trait ,37. The  cattle) , and its cattle) . Sato etelopment . Consisthenotype . This evAngiopoietin-like 4 (ANGPTL4), known as a novel peroxisome proliferator-activated receptor target gene, is a key regulator of triglyceride, non-esterified fatty acid (NEFA) concentrations, and plasma cholesterol [ANGPTL4 is also widely expressed in many bovine tissues, such as liver, subcutaneous adipose tissue, rumen, omasum, abomasum, etc., among which the first two are important tissues for ANGPTL4 synthesis [ANGPTL4 has been recognized as an adipokine in bovine adipose tissue and its expression could affect bovine body fat [ANGPTL4 might regulate BW trait by influencing the formation of adipose tissue. Additionally, previous studies have reported ANGPTL2, a homologous family gene of ANGPTL4, influences the development of the bovine BW trait [ANGPTL4 could be recognized as the candidate gene regulating the BW trait for further research.lesterol . Just asynthesis . Under fynthesis , which pynthesis . ANGPTL4body fat . Notablybody fat , thus itBW trait . Taken tPhospholipase A2 (PLA2) is classified into three groups according to their chemical properties and molecular structure, namely cytosolic (cPLA2), secretory (sPLA2), and Ca2+-independent PLA2s [cPLA2 could stimulate the release of arachidonic acid [cPLA2 induced by Temozolomide could also cause the suppression of cell growth [cPLA2 is an important regulator in various muscle development. Gluck et al. proposed cPLA2 activation was essential for the proliferation of bovine aortic smooth muscle cells [cPLA2 alpha was identified to be responsible for striated muscle growth and fertility in mice [cPLA2, known as PLA2G4A, was significantly enriched in two signal transduction pathways, including the MAPK signaling pathway (bta04010) and Ras signaling pathway (bta04014). As mentioned above, the MAPK signaling pathway could stimulate the growth of skeletal muscle [cPLA2 was forecasted to be the promising gene affecting the bovine BW trait via the involvement in muscle development.nt PLA2s . Previounic acid , which dnic acid . Phosphol growth . More imle cells . In the  in mice . In the l muscle . Hence, integrin alpha-2 (ITGA2) and integrin alpha-11 (ITGA11), have been proven to regulate the BW trait of swine and sheep, respectively [integrin alpha-5 (ITGA5) was speculated to be associated with bovine BW trait. ITGA5 participated in various cellular processes, such as cell adhesion, survival, proliferation, differentiation, and migration of myoblasts [ITGA5 was recognized as a potential biomarker for cancer treatment. Previous studies have shown ITGA5 could promote the proliferation, migration, and invasion of oral squamous cell carcinoma through activating the PI3K/AKT signaling pathway [ITGA5 was a mediator for the proliferation and migration of retinal pigment epithelial cells [ITGA5 knockdown or overexpression could inhibit or accelerate cell growth, respectively. Fang et al. reported ITGA5 participated in integrin β1 overexpression, which caused growth arrest of breast cancer cell [ITGA5 could reduce adherence capacity to fibronectin and inhibit tumor growth in lung cancer cells [ITGA5 has been proposed to regulate porcine drip loss by mediating cell adhesion and extracellular matrix [ITGA5 on the weight of beef cattle, thus ITGA5 as a molecular marker for bovine growth traits needs further investigation.Integrins are a family of heterodimeric cell-surface adhesion receptors that affect cell-matrix interaction. Some integrins encoding genes, including ectively ,52. In tyoblasts , adipocyyoblasts , and caryoblasts . Its difyoblasts , thus IT pathway . Chen etal cells . ITGA5 kcer cell . Larzabaer cells . In addir matrix . HoweverTBC1 domain family member 5 (TBC1D5), encoding GTPase-activating protein (GAP) for Rab7, is a high-affinity ligand of the retromer cargo selective complex VPS26/VPS29/VPS35. Previous studies showed TBC1D5 was an important novel regulator that rerouted ATG9-containing vesicular carriers toward sites of autophagosome formation [TBC1D5 could promote the intracellular growth of L. pneumophila [TBC1D5 might play a special role in BW at 18 months of age in Chinese Simmental beef cattle [TBC1D5 was also identified as the functional gene for the bovine BW trait in the present study. However, the molecular mechanism by which TBC1D5 influences bovine BW remains to be elucidated.Combined with previous studies and gene function analysis, except for candidate genes listed above, several known or potential candidate genes were also identified to affect bovine BW trait in this study. ormation . Bärlochumophila . Notablyf cattle . ConsistSHISA9 affected the growth and development traits such as pre-weaning gain in sheep and BW in beef cattle [Protein shisa-2 homolog 2 (SHISA2) identified in this study belongs to the same family as SHISA9, which encodes an endoplasmic reticulum protein against both Wnt and FGF signaling to affect the development of Chicken and Xenopus embryos [SHISA2 not only regulated F-actin distribution but also directly mediated the maturation of membrane protein for myoblast fusion. Its overexpression could inhibit myoblasts’ proliferation but promote premature fusion [SHISA2 overexpression led to increased cell growth and invasion [SHISA2 was identified to be involved in growth and development in duck skeletal muscle [SHISA2 might regulate BW trait via affecting the development of bovine skeletal muscle.Previous studies have demonstrated that f cattle ,64. Prot embryos ,66. Liu e fusion . Human Sinvasion . In the l muscle . As mentl muscle , thus imPhosphodiesterase (PDE1C) regulates the stability of growth factor receptors such as PDGFRβ [PDE1C positively regulated smooth muscle cells (SMCs) growth, proliferation, migration, and neointimal hyperplasia [PDE1C was screened in proliferating human arterial SMCs in primary culture, but not in the quiescent SMCs [PDE1C might be the candidate gene affecting bovine BW trait through signal-trait GWAS [PDE1C mainly rely on human and mouse SMCs, with less research on beef cattle, thus the functions of PDE1C in beef cattle should be further investigated.s PDGFRβ . which is PDGFRβ ,72. Cai erplasia . In agreent SMCs , which iait GWAS . HoweverCytochrome c oxidase subunit 6C (COX6C) is eventually transported to mitochondria to form the cytochromec oxidase (COX) complex [COX6C overexpression could induce cell growth retardation [COX6C might be a valuable gene for bovine growth and development. complex . Duggan  complex . The exp complex . COX6C oardation . TherefoFGF4, ANGPTL4, PLA2G4A, and ITGA5) and two significantly enriched pathways regulated bovine BW trait by affecting the growth and development of skeletal muscle and adipose tissue. The function of these candidate genes and pathways have been analyzed and discussed in detail. Moreover, further studies will be necessary to clarify their molecular mechanisms and physiological implications in regulating BW trait. This study not only offers molecular information for genomic selection of bovine growth and development traits but also provides the reference for the large-scale application of GWAS-RRM analysis of longitudinal traits in other livestock and poultry.In conclusion, GWAS-RRM has been recognized as the main analysis model for longitudinal traits as it could decrease FPR and increase statistical powers. Based on this method, the present study mainly revealed four most promising candidate genes (


The present study was conducted to estimate the (co)variancecomponents for birth and weaning weight (BW and WW) in 8142 Awassi sheepbetween 2015 and 2017. Estimates were calculated with single-traitanalysis by the average information restricted maximum likelihood (AI-REML)method, using a derivative-free algorithm by fitting six differentunivariate animal models. The negative of the log-likelihood function(LogL), Akaike information criterion (AIC), and Bayesian informationcriterion (BIC) tests were used for selecting the best fitted model. Inaddition, the goodness of fit between the two models was compared with thelikelihood ratio test (LRT). Depending on the models,  Awassi sheep is one of the mostcommon breeds grown in Turkey . In addition, it is recognized asan important genetic resource for the sheep industry in more than 30countries in the Middle East and all over the world .Consumers in the Middle East prefer Awassi mutton due to its taste. Falconerand Mackay (1996) have reported that many nongenetic factors play animportant role in different quantitative characteristics. Birth weight (BW)and weaning weight (WW), which are quantitative characters, are importantselection criteria for prenatal and postnatal growth performance inlivestock breeding. In sheep breeding, the first 3-month weights duringweaning of sheep are important production characteristics . Many researchers reported significant effects oflambing year, sex, and maternal age on BW and WW .The yields to be improved by selection are affected by the geneticperformance of the individual and environmental factors. In addition toreducing the effects of environmental factors to increase the degree ofaccuracy in selection, accurate estimation of the components that make upthe genetic structure is required. In farm animals with long maternallifespans, such as sheep, the phenotype of the offspring is determined notonly by their genetic potential and environment, but also by the environmentprovided by their dams. The maternal effect on the offspring has been knownsince the beginning of animal breeding, and therefore it has been studiedincreasingly with developed software programs in recent years.Direct additive, maternal additive, and maternal permanent environmentalvariances are considered important factors that determine the lamb's geneticgain and therefore performance . Inthis connection, several studies have been done on heritability estimates and itsconstituent elements .The aims of this study were to estimate the variance and covariancecomponents, to compare different models for the BW–WW measurements of theAwassi lambs, and to reveal the importance of including maternal effects todesign true breeding programs for genotypic selection of Awassi lambs. Forthis purpose, direct additive, maternal genetic and the maternal permanentenvironmental effects were calculated by applying six animal models.22.1The study was carried out in Osmaniye province, districts, and villagesbetween Awassi is warm and very well adopted to arid conditions; it is one ofTurkey's indigenous breeds with a high ability to adapt to differentenvironments. Awassi sheep are raised in southeastern Anatolia, and the highmilk production is one of the remarkable traits of the breed. Newborn lambswere kept together with their dams for three months (90 d) until weaningage. The birth weight (BW) and weaning weight (WW) at 3 months of agewere recorded as growth traits. BW was taken within 24 h of the birth of lamb,and WW was taken on 3-month weights with digital hand weighing scales(up to 10 g sensitivity). The regional breeders kept their lambs insimilar feeding and management conditions. Except for the winter period,they apply a feeding with a nomadic system based on the pasture and stubblegrazing. They feed their animals mainly with hay and a small amount of grainin winter.The material of this study was obtained from the Awassi Sub-Project in whichelite herds were created in Osmaniye province within the scope of the nationalcommunity-based animal improvement project. The records collected from 249rams, 2416 sheep, and 8142 lambs between 2015–2017 years were used.2.2A preliminary least-squares analysis of variance was performed with a generallinear model (GLM) with SPSS software  to determine the maineffects that will take place in the individual animal model. The least-squares analysis showed that the effects of sex of lambs ,type of birth , year of birth , and age ofdam  were found to be statistically significant  method, using a derivative-freealgorithm by WOMBAT software . The matrix representation of sixsingle-trait animal models that used for genetic analysis were given asfollows:The total heritability . The most appropriate model forconvergence of REML solutions was assumed when the average difference inlikelihood functions in successive iterations was less than The log-likelihood (LogL) test, Akaike information criterion (AIC), andBayesian information criterion (BIC) were performed to determine the best model.These likelihood-based tests are 3The structure of the data set used in this study is presented in Table 1.According to descriptive statistics the coefficient of variation for WW ismuch lower than BW (Table 1).Least-squares means for fixed effects and standard errors for BW and WW areshown in Table 2, and they were estimated for BW and WW as Estimates of (co)variance components and genetic parameters for BWs ofAwassi lambs obtained with different models are presented in Table 3. Thedirect additive genetic variance was found to be lower in Models 2, 3, 4, 5,and 6 when compared with Model 1. Similar results have been reported forvarious goat and sheep breeds . Estimates of maternal permanent environmentalvariances in Models 4, 5, and 6 for BW were as 0.0145, 0.0073, and 0.001,respectively. The estimates of Correlations between direct additive genetic and maternal genetic effectswere calculated as In addition, the most suitable model was selected initalics as the best modelaccording to LogL, AIC, and BIC criteria for the estimation of geneticparameters for the BW and WW of Awassi lambs (Tables 3 and 4). Models 1,2, and 3 were mentioned as the best model according to BIC, AIC, and LogLcriteria, respectively. Also, Models 2, 3, and 4 were found to bemore statistically significant than Model 1 according to LRT (In Table 4 the results showed that Model 2 was selected as the bestmodel with respect to all criteria. Also, Models 2, 3, 4, 5, and 6 were found tobe significant compared to Model 1 according to LRT (In Model 4, 5, and 6 the The In present study, Tables 3 and 4 show that the estimates of maternal genetic and maternalpermanent environmental effects for WW were increased when compared with theestimates for BW. Also, Tables 3 and 4 show that the 4This research was conducted to compare different models based on predictionsof genetic parameters and to show whether maternal effects could betterexplain the genetic effects on BW and WW traits. Overestimation ofphenotypic variation, in other words, low total heritability, may be due tothe low litter sizes, inconsistency in records, and poor maintenance,feeding, and herd management in the farms. It is thought that by improvingthese factors, the reliability in estimations would be increased.Consequently, the maternal effect should be taken into consideration for thepurpose of improving accuracy in parameter estimations and thereforeincreasing the success of breeding programs.10.5194/aab-65-121-2022-supplementThe supplement related to this article is available online at: https://doi.org/10.5194/aab-65-121-2022-supplement.


Improving the overall production of rice with high quality is a major target of breeders. Mining potential yield-related loci have been geared towards developing efficient rice breeding strategies. In this study, one single-locus genome-wide association studies (SL-GWAS) method (MLM) in conjunction with five multi-locus genome-wide association studies (ML-GWAS) approaches  were conducted in a panel consisting of 529 rice core varieties with 607,201 SNPs.LOC_Os09g02830 and LOC_Os07g31450) were characterized to affect GW and TGW, separately.A total of 152, 106, 12, 111, and 64 SNPs were detected by the MLM model associated with the five yield-related traits, namely grain length (GL), grain width (GW), grain thickness (GT), thousand-grain weight (TGW), and yield per plant (YPP), respectively. Furthermore, 74 significant quantitative trait nucleotides (QTNs) were presented across at least two ML-GWAS methods to be associated with the above five traits successively. Finally, 20 common QTNs were simultaneously discovered by both SL-GWAS and ML-GWAS methods. Based on genome annotation, gene expression analysis, and previous studies, two candidate key genes (These outcomes will provide an indication for breeding high-yielding rice varieties in the immediate future.The online version contains supplementary material available at 10.1186/s12870-021-03146-8. Oryza sativa L.) is one of the three major food crops supporting more than 50% of the whole population worldwide [http://www.stats.gov.cn/). While in the world, the average production of rice from 1994 to 2019 is 654.78 million tonnes per year, accounting for 27.28% of total cereals output . The growing global population and the deteriorating environment issue new challenges to the breeding of high-yielding crops [GS3 [GW5 [gw5 showed wider grain compared to the wild type. The WTG1/ OsOTUB1 [WTG1 showed narrow, thin, and long rice grains as a result of slim cells. The OsSPL13 is a SQUAMOSA promoter-binding-like protein [Rice  has become a powerful tool for mining QTL associated with complex traits , 12. Sinetc. In such QTL, it mostly contained numerous associated SNPs (Single nucleotide polymorphisms). While in multi-locus GWAS methods, when all the potentially associated markers were identified in the first step. These markers were submitted into a model in further analysis and true QTNs (Quantitative Trait Nucleotides) were further confirmed by the likelihood ratio test [To address the shortcomings of SL-GWAS, multi-locus GWAS (ML-GWAS) has been developed as a multi-dimensional genome scan method in which the effects of all markers are estimated at the same time . In parttio test .In the current study, a large-scale natural population of 529 rice accessions with five yield-related traits and 607,201 SNPs was conducted by a hybrid method of one SL-GWAS (MLM) algorithm and five ML-GWAS  models. We aim to investigate common QTNs via multiple methodologies and then deduce potential candidate genes to accelerate molecular marker-assisted breeding and boost rice production.Five yield-related traits  were selected to examine whether significant phenotypic variances exist in the yield among the 529 rice varieties. The results manifested that the parameters were varied for accessions to their corresponding traits Table . For insp-value< 0.001 except the relationship between TGW and YPP . GL and GW had a negative relation with PPC = − 0.40, which was corresponding with a previous study [Furthermore, the Pearson correlation coefficients (PCC) among the five traits were also estimated Fig. . All paius study . GL was To understand the population structure of the panel, PCA analysis was performed using 607,201 SNPs, which was mentioned in the Methods section. Five conceivable subpopulations were respectively distinguished via PC1, PC2, and PC3  as the distribution of these SNPs within the whole genome was summarized in Fig. The LD decay distance was further estimated using the identified SNPs. As delineated in Fig. p-value =1.65 × 10− 6, respectively  to identify QTL and five ML-GWAS  methods to identify QTNs Fig. . As for ly Table . As figuly Table f and 2i,qYPP-3-1, qYPP-4-2, qYPP-5-2, qYPP-7-2, qYPP-10-1, and qYPP-10-2). Notably, qYPP-7-2 was determined across all five ML-GWAS approaches, explaining the 0.28 ~ 1.79% of the phenotypic alteration. Five QTNs  were mapped by four or more ML-GWAS models.A total of 74 significant QTNs (LOD ≥ 3) were simultaneously defined to be associated with the above five objective traits by at least two ML-GWAS methods Table . Among tqGL-3-3, qGL-3-4, and qGL-3-5 overlapped with GS3 (Grain Size 3). Stunningly, three QTLs, qGL-5-1, qGW-5-1, and qGW-5-2, controlling multiple traits (GL and GW) simultaneously existed in the same region on chromosome 5, which were adjacent to GW5 (Grain Width 5). These regions are generally regarded as pleiotropic. Additionally, we found 51 novel QTLs such as qYPP-4-1, qGL-10-1, qTGW-11–2, and qTGW-12–1 without coinciding with or adjacent to the known genes.Moreover, we compared 161 published rice yield-related genes’ locations with 74 significant QTNs and their genomic ranges (300 kb up- and down-stream around the associated QTNs) Fig. . Nearly In addition, we compared the results of ML-GWAS and SL-GWAS and a total of 20 common QTNs were identified Table . Four, fqTGW-7-1, which was located at 18,639,992 bp on chromosome 7, was identified associated with TGW using both SL-GWAS and ML-GWAS methods. This QTN was detected tightly related to TGW with LARmEB, pKWmEB, and ISIS EM-BLASSO methods with the LOD ranged from 3.57 to 11.64  associated with TGW with an R2 of 7.79%  protein. Then, we defined four haplotypes of LOC_Os07g31450  based on the missense mutations in the gene. The accessions with the favorable HapD displayed significantly higher TGW than those with the HapA, HapB, and HapC types   was defined for this QTN. In this region, LOC_Os09g02830 is annotated as OsMADS78 which belongs to the MADS-box family. OSMADS78 has been confirmed to be an important regulator of early seed developmental transition and impacts both rice seed size and quality [OsMADS78 is far from being understood. Here, our study speculated that OsMADS78 might contribute to rice grain width regulation.The  quality . NeverthThe conventional single-locus methods like the general linear model (GLM) and MLM have been widely implemented to identify genetic variants in many cereals –32. HoweIn the present study, we adopted the MLM model and five ML-GWAS methods to analyse five yield-related traits of 529 rice core germplasms. Consequently, 152, 106, 12, 111, and 64 significant SNPs, while 3, 19, 8, 53, and 56 QTLs were detected by MLM underlying GL, GW, GT, TGW, and YPP, respectively Table .GS3 on chromosome 3. Whereas, many loci on other chromosomes failed to meet the threshold, indicating that it was difficult to find new loci from other chromosomes when applied traditional MLM. Afterward, a lot of significant QTNs presented across ML-GWAS models were not only situated on chromosome 3, but also widely distributed on other chromosomes, among which QTNs examined by at least three methods are worthy of further research. These data explicated that the ML-GWAS algorithms are considered more effective, powerful, and robust when applying to investigate the small-effect QTNs for yield-related traits.Likewise, 161, 136, 160, 189, and 171 significant QTNs were identified using ML-GWAS methods linked with the above five traits successively. We noted that the number of QTLs mapped by MLM was less than the QTNs identification of five ML-GWAS algorithms, especially of those about GT and YPP. The previous study observed similar findings in GWAS analysis of soybean seed size, suggesting that the recognition results of the five ML-GWAS methods outperformed those of the two SL-GWAS programs. In addition, the QTNs distribution detected by ML-GWAS approaches were more dispersed compared with MLM. For instance, as described in Fig. GS3, GW2, and GW5 have been identified and their functional roles were deeply elucidated [GS3, the first molecular characterized QTL for grain size, controls grain weight and length, with minor impacts on grain width and thickness [GW2 (Grain width 2), negatively regulates grain width [GW2 homologs in common wheat plays a critical role in the genetic control of grain weight and protein content traits [GW5 influences grain width and weight acting in the brassinosteroid pathway and overexpression of GSE5/GW5 resulted in narrow grains [Over the past decade, numerous rice yield-related genes such as ucidated , 40. Amohickness . GW2  was located near the region of GS3 for grain length. The QTN cluster on chromosome 5  was mapped nearby GW5. Moreover, there were 51 novel QTNs excluded in the genomic regions of the past reports. Therefore, these identified makers may be the potential QTNs controlling rice grain and productivity.In the current study, we characterized 74 QTNs for five yield-related traits that were simultaneously identified using two or more ML-GWAS methods. Compared with the mapped loci of the previous studies, 23 QTNs and its ±300 kb genomic ranges overlapped the known genes. On chromosome 3, the QTN hotspot (qTGW-7-1 and qGW-9-2) were validated with major effects associated with yield-related traits using both SL- and ML-GWAS approaches. In the candidate qTGW-7-1 related to grain weight, LOC_Os07g31450/CHR729 is a kind of CHD protein, which encoded protein contains 2259 amino acids, belonging to the CHD3 subfamily [CHR729 has been reported to play an essential role in multiple aspects of rice root and seed development. As an example, CHR729 can control seedling development through the gibberellin pathway [CHR729 might be related to grain weight, and transcriptional expression analysis reflected that CHR729 was highly expressed in young panicles. The role played by CHR729 in regulating rice grain and even productivity is worthwhile for further study and confirmation.Using the efficient mixed-model association, two robust QTLs  belongs to the MADS transcription factor family. MADS family is a large family with conserved MADS-box domains, whose members widely take part in the key regulatory pathways of plant growth and reproduction (including flower formation) [OsMADS16/SPW1, which is homologous to APETALA3 in Arabidopsis, belongs to the Class B in the ABC model of flower organ development, determining the properties of slates and stamens in rice flower organs [OsMADS13 controls ovule identity [OsMADS26 negatively regulates resistance to rice blast and drought tolerance [OsMADS23, OsMADS25, OsMADS27, OsMADS57, and OsMADS61 determine root development [OsMADS78 may be related to grain width in rice. Recently, Paul et al. reported that OSMADS78 modulates early seed developmental transition and impacts rice grain length, grain width, 1000 grain weight, and grain quality [In the candidate rmation) . The OsMrmation) , 49. Forr organs . Moreoveidentity . OsMADS2olerance . And OsMelopment . Althougelopment , nearly  quality . This co quality .qTGW-7-1 and qGW-9-2, closely associated with TGW and GW separately, were presented across both SL-GWAS and ML-GWAS analyses. Besides, two key annotated genes (LOC_Os07g31450 and LOC_Os09g02830) underlying the above two target genomic ranges were mined. In summary, many robust QTLs and two candidate genes were supposed to potentially modulate grain shape and productivity in rice. This research made a beneficial attempt by a combinatory approach of ML-GWAS methods and will facilitate the detection of yield-related QTNs.In this study, a total of 74 QTN hotspots were simultaneously detected for five yield-related traits by two or more ML-GWAS methods. Among them, The complete phenotypic records of 529 rice core accessions were downloaded from RiceVarMap v2.0 , an intehttp://ricevarmap.ncpgr.cn/phenos/). The detailed information, including experimental design, years, replicate, could be found in a study [http://www.sas.com/).The yield-related agronomic characters include grain length (GL), grain width (GW), grain thickness (GT), thousand-grain weight (TGW), and yield per plant (YPP) were downloaded from RiceVarMap2 website ( a study . Meanwhihttp://ricevarmap.ncpgr.cn/v1/) [High-quality re-sequencing raw data of 529 germplasms were derived from RiceVarMap (.cn/v1/) . The det.cn/v1/) .2) of alleles, meanwhile the whole population and sub-populations were implemented by software PopLDdecay [The matrix of pairwise genetic distance derived from 607,201 SNPs was implemented to construct phylogenetic trees by SNPhylo with the default parameter . PrincippLDdecay .p-value = 1.65 × 10− 6) was calculated by negative log.In our case, GWAS was performed in 529 rice varieties with 607,201 high-quality SNPs. A mixed linear model (MLM) was carried out for single-locus method to evaluate the trait-SNP association analysis for agriculture traits using the Tassel software. The first three principal components (PCs) and kinship matrix were used as covariates to correct population structure for decreasing false-positive rate in MLM. The genome-wide significance threshold (https://cran.r-project.org/web/packages/mrMLM/index.html) were used to map candidate QTNs, including mrMLM, FASTmrMLM, FASTmrEMMA, pLARmEB, and ISIS EM-BLASSO. All parameters were set at default values, and the critical LOD score was set to 3 for robust QTNs at the last stage. All these five methods used the PCA and kinship matrices in our study. The Manhattan and QQ plots for GWAS were displayed using the R package CMplot (https://github.com/YinLiLin/R-CMplot). QTNs were named as Q + the initial letter of traits name abbreviations + chromosome number + occurrence sequence [Five ML-GWAS methods within the mrMLM R package (sequence .http://rice.plantbiology.msu.edu/pub/data/Eukaryotic_Projects/o_sativa/annotation_dbs/pseudomolecules/version_6.1/), protein domain function in previous reports, and transcriptome information , the candidate genes for each trait were further mined.The QTNs identified by at least two different ML-GWAS methods were regarded as the putative candidate loci. Local LD blocks containing at least two SNPs were calculated with all imputed SNP using the PLINK 1.9 software . The locThe haplotypes of the candidate gene were determined based on the missense SNP, then the Wilcox-test was used to test the phenotypic difference among each haplotype. The characters of each trait were visualized with box plots using the R 3.6.1 language .Additional file 1: Figure S1. Distribution of SNP markers on Chromosomes. The x-axis represents the number of SNPs in the 1 Mb window, and the y-axis represents 12 chromosomes of rice. Different colors represent different numbers of SNPs.Additional file 2: Figure S2. Manhattan plots of the SL-GWAS and ML-GWAS for yield. (A-E) Manhattan maps representing five traits of GL, GW, GT, TGW, and YPP, respectively; The x-axis displays the chromosome label, and the y-axis displays -log10 . The dotted and solid gray lines show significant associations between SNPs and phenotype value with threshold levels of p-value < 1.65 × 10− 6 and p-value < 8.25 × 10− 8, separately. Red, green, blue, purple, yellow, and grey dots represent mrMLM, FASTmrEMMA, pLARmEB, pKWmEB, ISIS EM-BLASSO, and MLM models. (F-J) QQ plots represent MLM analysis of the above five traits.Additional file 3: Table S1. Statistical analysis of five rice yield-related traits.Additional file 4: Table S2. SNPs and QTLs mapping information in MLM analysis.Additional file 5: Table S3. The 161 published genes and their functional information of yield traits in rice.Additional file 6: Table S4. QTN simultaneously detected by both ML-GWAS and MLM methods.