The Bayes C analysis was performed with the JWAS package and 1-Mb genomic windows containing SNPs that explained > 0.37% of the genetic variance were considered as putative QTL. Candidate genes within 100 kb from the identified SNPs in single-locus GWAS or the 1-Mb windows were identified using gene ontology, as implemented in the Ensembl Genome Browser. The genes detected in association with FP  and CPP  were identified as candidates. Gene ontology revealed six novel candidate genes  significantly associated with MU whose functions were in protein catabolism, urea cycle, ion transportation and N excretion. One novel candidate gene was identified in association with ECPU (MAP3K1) that is involved in post-transcriptional modification of proteins. The findings should be validated using a larger population of New Zealand grazing dairy cows.The objective of this study was to identify genomic regions associated with milk fat percentage (FP), crude protein percentage (CPP), urea concentration (MU) and efficiency of crude protein utilization (ECPU: ratio between crude protein yield in milk and dietary crude protein intake) using grazing, mixed-breed, dairy cows in New Zealand. Phenotypes from 634 Holstein Friesian, Jersey or crossbred cows were obtained from two herds at Massey University. A subset of 490 of these cows was genotyped using Bovine Illumina 50K SNP-chips. Two genome-wise association approaches were used, a single-locus model fitted to data from 490 cows and a single-step Bayes C model fitted to data from all 634 cows. The single-locus analysis was performed with the Efficient Mixed-Model Association eXpedited model as implemented in the SVS package. Single nucleotide polymorphisms (SNPs) with genome-wide association  Milk fat and protein play a vital role in New Zealand’s milk payment scheme , howeverThe heritabilities in New Zealand dairy cows for percentage of milk fat (from 0.62 to 0.66) and milk crude protein 0.67) [ [7] are Genome-wide association studies (GWAS) scan the entire genome of an organism to discover associations between genetic markers and phenotypes. This is a crucial step in understanding the genes associated with the phenotype of interest. There are two major methods of GWAS depending on how the association between the marker and the trait is being tested. Single-locus GWAS is the simplest form of association testing and involves markers being fitted one at a time as fixed effects in a statistical model used to estimate the additive effect of the marker allele on the trait. The method relies on linkage disequilibrium (LD) between the markers being fitted and the causal mutation to find any evidence of association, unless the marker panel includes all sequence variants and other genomic features that represent the causal mutation. Testing the association of the phenotype with multiple markers fitted simultaneously as random effects is the other approach to GWAS. That approach takes advantage of the fact that linear functions of the multiple-markers being tested are in greater LD with the QTL in comparison to the single-locus GWAS approach and consequently, this increases the power of the experiment. Bayesian regression is one method of testing associations of multiple markers simultaneously with the phenotype.Many studies have reported candidate genes associated with FP ,11,12 anThe objective of this study was to identify genes and QTLs associated with FP, CPP, MU or ECPU, using either a single-locus approach or a multi-locus single-step Bayes C approach.Two herds comprising a total of 634 cows, from Massey University Dairy 1 and Dairy 4 farms, Palmerston North, New Zealand were used for this study. Test-day records from 467 cows milked in 2016–2017 and an overlapping group of 451 cows milked in the 2017–2018 production seasons were collected. These cows had a minimum of three herd-test records from lactations of not less than 150 days. Both herds comprised of mixed-breed Holstein Friesian (F) and Jersey (J) and F × J crossbred cows .Cows at Dairy 1 are managed in a once-a-day milking system with low levels of supplementary feeding and a low stocking rate (2.1 cows/ha). In contrast, cows in Dairy 4 are milked twice a day, with high levels of supplementary feeding and a higher stocking rate (2.8 cows/ha).Herd-test records on FP and CPP for each cow were collected on a monthly basis. Daily crude protein yield (CPY) was estimated at each month as the product of daily CPP and corresponding daily milk yield. The MU concentration for each cow was predicted by mid-infrared spectral data from additional milk samples collected only for three of the herd-tests per season, representing early (September), mid (December) and late (March) lactation. A daily composite sample of morning and afternoon milking followed by weighting according to morning and afternoon milk yields were used for estimating daily MU when twice-a-day milking was practiced, whereas the single sample was used when once-a-day milking was practiced on the sampling days. Milk samples were measured for MU at MilkTestNZ  using the CombiFossTM 7 instrument .Dietary metabolizable energy (DME) and dietary crude protein percentage (DCPP) were estimated by analyzing pasture, crop and supplementary feed offered to the cows using near-infrared spectroscopy. The total metabolizable energy (ME) requirements of each cow on each day of lactation was calculated as the sum of the estimated ME requirements for maintenance, pregnancy, lactation and live weight change, as described by Correa-Luna et al. . ApparenPhenotypes were collected from a total of 634 cows but only a subset of 490 cows were genotyped because sample collection for genotyping was done after the 2017–2018 production season and 114 of the cows milking in 2016–2017 had already been culled. DNA was extracted from the ear punch tissue samples which were then genotyped using Bovine Illumina 50K SNP-chips. SNP & Variation Suite  and ECPU were performed for 634 cows using the MEANS procedure of SAS package 9.4 .2a), within lactation permanent environment variance (σ2pw), across lactation permanent environment variance (σ2pa) and residual effects variance (σ2e) were estimated by fitting the following repeatability animal model as implemented in the JWAS package 0.7.3 [y is the vector of test-day phenotypes, X is the design matrix of fixed effects, b is the vector of fixed effects which included contemporary group defined by herd-test-date (HTD), parity, days in milk nested within each HTD, regression on proportion of F, and regression on F × J heterosis, Z is the design matrix of random animal additive genetic effects (u), W is the design matrix of within lactation permanent environment effects (p), K is the design matrix of across lactation permanent environment (c) effects and e is the vector of random residual errors. It was assumed that the animal additive genetic effects were distributed as u~N where A is the numerator relationship matrix, p~N where I1 is an identity matrix of order equals to the number of interactions between cows and production seasons; c~N where I2 is an identity matrix of order equals to the number of cows with records, and e~N where I3 is an identity matrix of order equal to the total number of test-day records.All the 634 cows with phenotypes were used for estimating variance components. Variance components for animal additive genetic variance (σge 0.7.3 :y = Xb +2) and repeatabilities (t) were calculated using the estimated variance components. The heritability for a trait was calculated as the proportion between the genetic variance and the phenotypic variance. The phenotypic variance was calculated as the sum of σ2a, σ2pw, σ2pa and σ2e. The repeatability of the trait was calculated as the proportion of permanent variance  and the phenotypic variance.The trait heritabilities , and s is a vector of marker effects. It was assumed that the animal additive genetic effects are distributed as u~N where A is the numerator relationship matrix for polygenic effects and σ2g is the additive genetic variance not explained by markers, representing some fraction (1–d) of σ2a from the pedigree-based best linear unbiased prediction model. The priors for marker effects have identical and independent mixture distributions, where each has a point mass at zero with probability π (marker effect is null), or a univariate-normal distribution with a null mean and variance σ2s, with probability 1 − π such that the scalar variance of the vector of genomic breeding values, i.e., var(Ms) reflects the additive-genetic variance explained by markers . The mixed model equations for the non-genotyped individuals was similar to model (2), except, M contains the imputed genotypes of non-genotyped individuals in this analysis instead of actual genotypes for genotyped individuals. Since this model deals with imputed genotypes, the model equation includes another matrix, H and vector m, where H is the incidence matrix corresponding to the imputation residuals and m is a vector of imputation residual effects.A single-step Bayes C linear mixed model (genomic data), as implemented in the JWAS package 0.7.3, was used to account for variance explained by SNP markers. The model used for estimating individual SNP effects was the same as model (1), other than the inclusion of random SNP effects that were fitted simultaneously using Bayes C priors (model 2). There is a model equation corresponding to genotyped animals and another one for non-genotyped animals. The following model equation was fitted for genotyped animals and included marker effects:2a, σ2pw, σ2pa and σ2e were those obtained fitting the repeatability model of Equation (1) and were considered as prior variances in estimating marker effects. The SNPs with non-zero effects in Bayes C have a common variance [2s whose prior was estimated as described by Fernando and Garrick [Pre-estimated values for σvariance  denoted  Garrick  (model 3The assumed proportion of SNPs with zero effect (π) was 0.997 for all the traits , correspM by the corresponding sample of marker effects s for that MCMC iteration. The posterior mean of variances (σ2m) of the sampled genomic breeding value for each iteration across all cows was used to estimate the genomic heritability (s2) which is the proportion of phenotypic variance explained by the additive effects of the SNPs . After including SNP effects in the model, heritabilities and repeatabilities of the traits were re-estimated by replacing σ2a in the numerator and the denominator of the ratio with σ2g + σ2m.Markov chain Monte Carlo (MCMC) comprised 50,000 iterations and marker effects from each 50th iteration were used to estimate the genomic merit of all animals. The samples for genomic merit were obtained in each MCMC iteration by multiplying the matrix b, p and c estimated in model (1), respectively, in ASReml package 4.1 [e*) with the SNP genotypes was calculated in the SVS software (8.8), using the following additive, single-locus, mixed-model called Efficient Mixed-Model Association eXpedited (EMMAX) (with the variable definitions as in model 2):Cows (n = 490) with both phenotypes and genotypes were used for single-locus genome-wide association studies and the analyses were performed in two steps. In step 1 each test-day record for each trait was adjusted for non-genetic fixed effects, within and across lactation permanent environment of the cow to account for repeated measures on the same animal using the regression coefficients of kage 4.1 . The pheG) was computed in the form of identity-by-state using the same genotypes analyzed which was scaled using Gower’s centering approach as described by Kang et al. [G to obtain scaled G (Gs) as Gs = WG, where n is the number of cows, C = I − 11′/n and 1 is a length n vector of ones, and I is the identity matrix related to the number of cows.In this model, the association was tested for each SNP fitted separately as a fixed effect. A genomic relationship matrix  were plotted against the genomic locations of the markers using the annotation for bovine assembly UMD3.1 in SVS (8.8) software. The estimated marker associations were corrected for multiple testing using Bonferroni corrections [p-value of 0.05 (0.05/number of SNPs), and the suggestive threshold was estimated using a nominal p-value of one (1/number of SNPs). The Bonferroni corrected p-value threshold for genome-wide significant level was 1.11 × 10−6  which corresponded to 5.95 on a −log10 scale. The p-value threshold for suggestive associations was 2.22 × 10−5  which corresponded to a −log10 of 4.65. The SNPs that surpass the Bonferroni adjusted genome-wide p-value were described and their genomic position, allele substitution effect and closest gene were reported.The estimated associations were presented as Manhattan plots in which −logrections . The gen2a, σ2pw, σ2pa, σ2e and σ2m) obtained from the model Equation (1) were taken to be the prior variances in this analysis. The probability that SNPs would have zero effect on the trait was chosen to be 99.7% (π = 0.997). The SNP genotypes with non-zero effects in any particular iteration were simultaneously fitted in the model in that iteration along with phenotypes and pedigree in a single step.Genome-wide association analyses were performed separately for each milk composition trait and each of ECPU trait using a Bayes C linear mixed model as implemented in the JWAS package 0.7.3  includin−2% (1/2676 SNPs) and window explained at least 0.19% of genetic variance, which corresponds to 5 times the expected proportion of variance (3.74 × 10−2% × 5 = 0.19%), was considered as a suggestive significance level [−2% × 10 = 0.37%), were considered to reach genome-wide significance level. The SNP windows that surpass the genome-wide significance level were considered as putative QTL  and their genomic position, number of SNPs in each window, PVE (the genetic variance explained by each window divided by the genetic variance explained by the whole genome), window posterior probability of association  and associated genes were reported. The estimated proportion of genetic variance explained by each 1 Mb window was plotted against genomic locations of the markers using the qqman package in R software 3.6.2 [Marker effects were collectively used to predict the genomic merit of cows in chromosomal regions that include non-overlapping 1 Mb windows based on the physical map order ,29. Gibbce level  while thre 3.6.2 .Bos taurus reference genome in Ensembl (Ensembl release 94), using the UMD 3.1 assembly . The biological functions of significant genes were identified using the gene ontology  as implDescriptive statistics for the test-day milk composition and ECPU are presented in Estimates of variance components, heritabilities and repeatabilities of milk percentage traits, milk urea and efficiency of crude protein utilization using a univariate repeatability animal model are presented in The estimated variance components, heritabilities and repeatabilities of the traits applying the univariate single-step Bayesian  linear mixed model are presented in 2 of traits varied from zero to moderately high; s2 of ECPU was near zero, s2 of MU was low and s2 of milk percentage traits were moderate.The sp-value for FP are presented in p < 1 × 10−6) with FP at genome-wide significant threshold  and solute carrier family 52 member 2 (SLC52A2) (MROH1), and cleavage and polyadenylation specific factor 1 (CPSF1)  . Two sug (CPSF1) .The Manhattan plots based on a single-step Bayesian method are presented in Eight 1 Mb SNP windows from chromosomes 5, 6, 14, 15, 20 and 27 were significantly (PVE ≥ 0.37%) associated with FP a. The prTwenty 1 Mb SNP windows from 14 different chromosomes, including 3, 4, 5, 6, 8, 9, 13, 14, 17, 19, 21, 23, 24 and 26, were significantly (PVE ≥ 0.37%) associated with CPP b. The prEighteen 1 Mb SNP windows from 14 different chromosomes, including 3, 5, 6, 11, 12, 16, 17, 21, 22, 23, 25, 27 and 29, were significantly (PVE ≥ 0.37%) associated with MU c. The toOnly one 1 Mb SNP window from chromosome 20 was significantly (PVE ≥ 0.37%) associated with ECPU d. The PVDGAT1, glycerol-3-phosphate acyltransferase 4 (GPAT4), microsomal glutathione S-transferase 1 (MGST1), acyl-CoA oxidase 3, pristanoyl (ACOX3), and CCAAT enhancer binding protein delta (CEBPD). These genes were located at chromosome 6, 14 and 27 (GPT2)  .DGAT1, α-S1-casein (CSN1S1), β-casein (CSN2), α-S2-casein (CSN1S2), kappa-casein (CSN3), Bos taurus ribosomal protein S12 (RPS12), glutamate ionotropic receptor NMDA type subunit 2C (GRIN2C), eukaryotic translation initiation factor 3 subunit D (EIF3D), ADAM metallopeptidase domain 11 (ADAM11), the golgi SNAP receptor complex member 2 (GOSR2), HECT and RLD domain containing E3 ubiquitin protein ligase family member 6 (HERC6), and insulin-like growth factor 1 receptor (IGF1R). These genes were located on chromosomes 5, 6, 9, 14, 19 and 21 (TRIM45) and ubiquitin protein ligase E3 component n-recognin 5 (UBR5)  .GMDS), E2F transcription factor 7 (E2F7), solute carrier family 52 member 2 (SIAH3), solute carrier family 24 member 4 (SLC24A4), legumain (LGMN) and argininosuccinate synthase 1 (ASS1). Twenty genes were identified to be associated with MU at suggestive significant level  (MAP4K4), golgi-associated, γ adaptin ear containing, ARF binding protein 3 (GGA3), tripartite motif containing 63 (TRIM63) and CDP diacylglycerol synthase 1 (CDS1).The 1-Mb genomic window that was significantly associated with ECPU harbored one good candidate gene on chromosome 20, Mitogen-activated protein kinase 1 (MAP3K1) . SixteenMAP3K1) . These gThe ranges of FP (from 1.77 to 9.77%) and CPP (from 2.72 to 7.66%) found in the current study were within the ranges (1.84 to 11.32% and 2.76 to 6.77%) previously reported by Sneddon et al. . The hig2 and t were consistent with the literature for FP and CPP [2 for milk percentage traits was moderate, indicating good marker predictions for FP and CPP traits; s2 for MU was low, indicating comparatively low marker prediction for MU; and s2 of ECPU was zero, indicating poor marker prediction for ECPU. The s2 reported for FP (0.31) in this study is comparable with the estimate (0.35) found in another New Zealand study using a much larger dataset comprising mixed-breed cows [2 range reported for CPP (from 0.59 to 0.62) in Kemper et al. [2 in this study (0.38), could be a benefit of using high-density arrays (777K SNPs) for genotyping of their cows. The estimated s2 in the current study for MU (0.13) is comparable to estimated s2 (0.14) by Bouwman et al. [2 for all traits indicated that the markers explained considerable proportions of phenotypic variance of the traits, except for ECPU. The current study used 45K SNPs and therefore, the number of SNPs within causative gene is probably limited. However, the higher proportion of genetic variance explained by markers for milk constituents in the current study despite the small sample size, suggests there is considerable linkage disequilibrium among SNPs and causative genes.The estimates of h and CPP  for MU [ and CPP ,38 and f and CPP . The s2 eed cows . The grer et al.  in multited s2 0. by BouwmTwo SNPs in chromosome 14 were significantly associated with the FP at the genome-wide significant threshold, suggesting that these two SNPs might be in linkage disequilibrium with the QTL for FP. None of the SNPs for CPP, MU, and ECPU reached significance at the genome-wide threshold. This observation suggests that these traits are under the control of many genes, each with small effects which could not be detected with either the single-locus method or with the small number of animals available in this study.DGAT1 and SLC52A2) associated with FP. The association of DGAT1 with FP is widely reported [DGAT1 gene is also associated with very-low-density lipoprotein particle assembly in the liver (GO:0034379). The aggregation of lipoprotein in the liver subsequently causes fatty liver in lactating dairy cows [SLC52A2 has an assigned function of transportation of riboflavin (GO:0032218). Riboflavin is involved in the cellular metabolism of fats and proteins; therefore, the activity of this gene may affect the utilization of feed fats and proteins and ultimately this balances the proportion of feed constituents that converted into milk constituents. The relationships of SLC52A2 gene with FP of Chinese Holstein cows were reported recently by Wang et al. [The single-locus method (EMMAX) identified two candidate genes  and its association with milk production in Canadian Holstein Friesians was reported in a study by Nayeri et al. [MROH1 gene has no known biological function but their relationships with FP was reported [Two suggestive genes associated with FP were reported. The gene i et al. . The MROreported .2 (0.36) and was under control of a larger number of SNPs than found here. Therefore, it is not surprising the observed very low genetic variance from the significant window for ECPU in the current study.Collectively, the relatively modest number of windows significantly associated with FP at the genome-wide threshold explain about 43% of the total genetic variance, this confirms the initial idea that a small number of genes have important roles in regulating FP. The top-most windows in this method and the top-most significant SNP in single-locus method were located within the DGAT1 gene. This indicates that both methods perform well when the effect of the gene is large. However, more genomic regions were identified by the single-step Bayesian method for FP than by the single-locus method. No SNPs reached the level of significance for CPP, MU and ECPU traits when the associations were tested using the single-locus method. However, some genomic windows for CPP, and MU, and one genomic window for ECPU, which harbored good candidate genes, became significant at the genome-wide level when the associations were tested using the Bayesian method. This was likely due to the greater power of detection of associations when the markers were fitted simultaneously as random effects in the model and therefore, more genetic variation was captured by the markers in comparison to single-locus methods . The PVEDGAT1, MGST1, GPAT4, ACOX3 and CEBPD genes were identified as being important for FP. The functions of DGAT1 were described earlier. Another important gene associated with FP is MGST1, which is related to cellular response to lipid hydroperoxide (GO:0071449). This gene was identified as a causative gene for FP in New Zealand mixed-breed dairy cows, although the functional relationship of the gene with FP has not yet been revealed [GPAT4 is involved in the fatty acid metabolic process (GO:0006631) and mammary gland development (GO:0030879). Genome-wide association studies have shown that this gene is highly polymorphic and highly significantly associated with FP in German Holstein Friesians [ACOX3 gene is also involved with the fatty acid metabolic process (GO:0006631) and GWAS has shown its relationship with fatty acids synthesis in Canadian Holstein cows [CEBPD is related with fat cell differentiation (GO:0045444), this process enhances synthesis and storage of fat. The suggestive gene GPT2 has a biological function related to regulation of biosynthesis (GO:0009058), therefore, the gene might be important in milk and milk component production. However, its association with FP in dairy cows has not yet been revealed through GWAS. Most of the genes associated with FP in the current study have previously been reported as candidate genes for FP, this gives confidence that the current findings could be applied in the selection of genetically superior New Zealand dairy cows.Under the assumptions applied for the single-step Bayes C method in the current study, five, twelve, six and one gene associated with FP, CPP, MU and ECPU were identified, respectively. The revealed . The genriesians ,48. The  GO:00714. This geDGAT1, CSN1S1, CSN1S1, CSN1S2, CSN3, RPS12, GRIN2C, EIF3D, ADAM11, GOSR2, HERC6 and IGFR1 were identified as candidate genes for CPP. The casein cluster genes CSN1S1-CSN2-CSN1S2-CSN3 encode αs1, β, αs2 and κ caseins, respectively. Casein is the most common type of protein in bovine milk and these genes are known to significantly affect the physical, chemical and the nutritional quality of milk [CSN1S1 (GO:0050821) and CSN3 (GO:0050821) genes are involved in the stabilization of encoded proteins by preventing their degradation. The association of these genes with milk protein composition has been reported in lactating dairy cows in many studies including Zhou et al. [RPS12 gene encodes the ribosomal protein (GO:0006412), which is a component of the 40S subunit of the ribosome (GO:0022627). Ribosomes are organelles that synthesize protein within the cell. This gene plays a vital role by coding for a structural constituent of the ribosome, which makes it highly likely to be an important candidate gene for milk protein synthesis. Gene GRIN2C has a known biological function of negative regulation of protein catabolic process (GO:0042177). The gene EIF3D codes for 3 Subunit D, which initiates the protein translation through mTOR signaling pathway [ADAM11 gene is related to proteolysis (GO:0006508), the hydrolysis of proteins into smaller polypeptides and/or amino acids by cleavage of their peptide bonds. The GOSR2 gene has a biological function related to protein transport (GO:0015031). This gene has been identified as a candidate gene for milk protein percentage in a meta-analysis in lactating cows [HERC6 is a gene related to protein ubiquitination (GO:0016567). This gene has been suggested as candidate gene for protein yield [IGF1R is involved with protein phosphorylation (GO:0016310). This gene is associated with milk protein yield in four dairy breeds [TRIM45 and UBR5 have biological function related to protein ubiquitination (GO:0016567). Some of the genes identified in association with CPP in this study were previously reported as good candidate genes using GWAS. This study identified additional genes associated with CPP in New Zealand dairy cows which can be potential candidate genes for the trait.Twelve candidate genes;  of milk . The gen of milk . Additiou et al.  and Sancu et al. . The RPS pathway . This pa pathway . The ADAing cows . The HERin yield  and lactin yield . The geny breeds , Simmenty breeds . Both suGMDS, E2F7, SIAH1, SLC24A4, LGMN, and ASS1, are closely related with protein metabolism and many steps in the urea cycle and excretion, including: protein catabolism, converting ammonia (NH3) to urea, transportation of ammonia through the blood stream and disposal of NH3. The SIAH1 gene is related to ubiquitin-dependent protein catabolic process (GO:0006511). These pathways result in the breakdown of unusable cellular proteins into amino acids and NH3, allowing cells to utilize the amino acids to generate vital proteins or energy [SLC24A4 has an assigned function in ion transport (GO:0006811) which involves movement of charged molecules into and out of the cell. Ammonia exists as ammonium ions (NH4+) at the physiological pH. The regulation of this gene is vital for efficient removal of NH4+ formed inside cells as a result of protein digestion. This process facilitates efficient transportation of NH4+ molecules into the liver where they can be converted to urea which is otherwise toxic. The E2F7 gene has a function related to hepatocyte differentiation (GO:0070365). Hepatocytes are the functional units of the liver and this gene regulates the generation of specialized hepatocytes from unspecialized cells. The process of hepatocyte differentiation is vital for efficient conversion of NH3 to urea in the liver. ASS1 is known to regulate the urea cycle of animals (GO:0000050). The overall reaction involves conversion of NH3 into urea and the urea cycle primarily takes place in the liver. A mutation in the ASS1 gene is associated with citrullinemia, which is an autosomal recessive urea cycle disorder that causes ammonia to accumulate in the blood causing lethal reaction in newly-born Holstein Friesian calves [GMDS gene is involved with the GDP-mannose metabolic process (GO:0019673). One of the key purposes of the cellular metabolism is to eliminate nitrogenous waste from the body. Variations in this gene are associated with milk fatty acid traits in Canadian Holstein dairy cows [The genes found to be in association with MU, r energy . The genn calves . The GMDiry cows , howeveriry cows  reported GO:00065. These piry cows  showed tMAP3K1, which was identified as a candidate gene associated with ECPU, is involved with protein phosphorylation (GO:0006468). Phosphorylation is a post-translational modification that proteins undergo, is responsible for their stability and is a process that can alter the mechanical properties of milk [MAP3K1 as a promising candidate gene affecting yields of milk, fat, protein, and percentages of fat and protein in Chinese Holstein cows. Genome-wide association studies also found that the MAP3K1 gene is associated with human breast cancer [MAP4K4 gene has been reported to be associated with milk yield, protein percentage, and mastitis susceptibility in Chinese Holstein cattle [GGA3 gene with feed use efficiency in dairy cows has not been previously reported, its association with average daily gain and average daily feed intake has been reported in chickens [CDS1 gene is known to affect the yields of milk and fat and percentage of protein in Italian sheep [The gene  of milk . Using Gon GO:00068. Phospt cancer . Therefoon GO:00068. Phospn cattle . Althougchickens . The TRIchickens  while thMilk urea is a by-product of protein metabolism and is an indication of inefficient protein use. In the current study it was demonstrated that genes related to protein metabolism were associated with MU and that genes related to milk protein production were associated with ECPU. Efficiency of crude protein utilization is related to protein intake and to milk protein yield. The observations made in this study provide evidence that the known phenotypic relationships between MU, ECPU and CPP traits are likely to be at least partially driven by genetic differences between cows.In our previous study using the same cows , highly The present study performed GWAS using 50K SNP-chips and reported some QTLs and genes for FP, CPP, MU and ECPU. These traits showed moderate to very low trait heritabilities using either single-locus or single-step Bayesian methods. The identification of the associations of traits in the current study with the single-locus analysis was likely limited by the small sample size. However, the Bayesian method was more sensitive and effective in detecting small associations. The study reported novel QTLs and genes affecting MU and ECPU and confirmed the previously reported candidate genes and QTLs for FP and CPP. The novel candidate genes found in this study could be potentially important as commercial molecular markers for marker-assisted selection. Selection for ECPU could have a substantial impact on the economy and cow wellbeing, while selection for reduced MU might ensure environmental sustainability. Validation of the results of this study using a larger dataset containing New Zealand dairy cows is essential in order to confirm the findings before implementing them into industry breeding programs.


One of the largest sources of emission in the ruminant sector is methane (CH4), accounting for approximately 40% of the sectors total emissions. With climate change being a growing concern, emphasis is being put on reducing greenhouse gas emissions, including those from ruminant production. Various genetic and environmental factors influence cattle CH4 production, such as breed, genetic makeup, diet, management practices, and physiological status of the host. The influence of genetic variability on CH4 yield in ruminants indicates that genomic selection for reduced CH4 emissions is possible. Although the microbiology of CH4 production has been studied, further research is needed to identify key differences in the host and microbiome genomes and how they interact with one another. The advancement of “-omics” technologies, such as metabolomics and metagenomics, may provide valuable information in this regard. Improved understanding of genetic mechanisms associated with CH4 production and the interaction between the microbiome profile and host genetics will increase the rate of genetic progress for reduced CH4 emissions. Through a systems biology approach, various “-omics” technologies can be combined to unravel genomic regions and genetic markers associated with CH4 production, which can then be used in selective breeding programs. This comprehensive review discusses current challenges in applying genomic selection for reduced CH4 emissions, and the potential for “-omics” technologies, especially metabolomics and metagenomics, to minimize such challenges. The integration and evaluation of different levels of biological information using a systems biology approach is also discussed, which can assist in understanding the underlying genetic mechanisms and biology of CH4 production traits in ruminants and aid in reducing agriculture’s overall environmental footprint.Ruminant supply chains contribute 5.7 gigatons of CO Global as (GHG) , Ontarioas (GHG)  which ha to 2 °C . Of the  factors . Approxioduction . Variousulations  and chemulations . Despiteerations . Breedinin sheep  Low CH4 H4 sheep .FE) and its association with CH4 in ruminant species , statistical analysis, and biological interpretation (OTU) profiles  which is nontoxic, physiologically inert, and stable  and inversion-dispersion methods which allow animals to be measured in their natural environment . One reported issue with this method is the need to know the location of the emission source(s), i.e., the animal, however this issue has been limited by narrowing the paddock. Using a narrow paddock also increases the range of useable wind directions, thus increasing the likelihood of a measurable concentration downwind of the paddock . Another method to determine CH4 is through proxies, such as feed intake, milk production and composition, and feces. A review by 4, therefore, this section provides a general overview on major techniques used for CH4 prediction. There is increased interest in using proxies as indicators of CH4, including measures of milk fatty acids, milk mid-infrared (MIR) spectroscopy, and rumen metabolites . Methane production in ruminants is heritable with estimates ranging from 0.12 to 0.52  to be successfully implemented. Additionally, limitations should be considered, such as training populations for specific livestock that commonly have crossbred or mixed populations , which may result in less accurate and more biased genomic predictions unless larger and well-structures training populations are designed, and breed composition is accounted for. Another factor to consider is antagonistic effects between CH4 emissions and desirable production traits, which should be considered when selecting for CH4 reduction  and predicted CH4 emissions (PME) has been reported , the Efficient Dairy Genome Project , and the Resilient Dairy Genome Project (http://www.resilientdairy.ca).The relatively small number of CHhenotype . Further factors , and be reported , suggest 0.62; 4 . The use 0.62; 4  and for  0.62; 4  and 0.35 0.62; 4 , may be 62; 4  which has been significantly associated with inflammatory bowel disease in human  and Peroxisomal Biogenesis Factor 2 (PEX2) which is hypothesized to be important to lipid metabolism and fatty acid oxidation in cattle , Chytridiomycota , and Fibrobacteres (Fibrobacter sp.) phyla. Presently, metagenomic sequencing of host microbiomes and microbial genomic sequencing of various sample types, including the rumen microbiome, is expanding (www.rmgnetwork.org/), and the development of the reference microbial genome catalog is expanding  and archaea  dominated in nearly all samples. Thus, making it possible to mitigate CH4 emissions by developing strategies to target the few dominant methanogens including vaccines or small-molecule inhibitors  and ages. Additionally, the relationship between the rumen microbiome and the host phenotype have been better understood by characterizing the metabolomic profiling from divergent groups relating to disease (P = 0.059) in rumen fluid compared to high-RFI steers. Thus, indicating more active microbial fermentation and relatively higher CH4 production in low-RFI steers. Due to the differences observed between groups, rumen fluid serves as a valuable method to collect information on metabolites and their association with CH4 production .Metabolomic analysis in dairy cattle has largely focused on identifying milk metabolites , which coduction . van Gasl status . In relamissions . Wang et disease , FE  technology, has enabled the study of culture independent and complex microbial communities  present in the rumen and their activity . In addition, modeling of kinetics and dynamics of the rumen microbiome should also be explored to understand and appropriately assess the function of the rumen microbiome and its association with other -omics levels. More recently, the Illumina MiSeq system  has been used for metaxonomic sequencing of small genomes such as bacteria, while reducing error rates by up to two magnitudes . ApplicaPCR) and RNA/DNA amplicon-based sequencing (amplicon-seq) metagenomics, by providing more efficiency and throughput. Traditional quantitative polymerase chain reaction (qPCR) is known to be efficient, inexpensive, and specific, for target analysis, but has low-throughput capability and is therefore not as beneficial for metagenomic analysis. Comparably, RNA/DNA amplicon-seq, which is now considered a metataxonomic analysis, of phylogenetic marker genes has been used for profiling microbial communities using 16S rRNA/rDNA gene amplicon data for prokaryotic organisms  or 18S rRNA/rDNA gene amplicon data and Internal Transcribed Spacer (ITS) region amplicon for eukaryotic organisms or rumen fungi  can also be used to assess trait associations with compositional and functional potential of the rumen microbiome. Archaeal genomes of the ruminant rumen microbiome exist, with methanogenic archaeon classified. However, more research is needed to better understand the relationship between methanogens and CH4 emissions, as proportional differences in methanogenic archaeon’s does not directly associate with CH4 production (Metagenomic-assembled genomes (oduction .RNA-Seq) has recently been used for profiling of RNA molecules isolated from microbiome  due to its high reliability  is another technique used in metabolomic studies, and unlike NMR, it can detect metabolites at nanomolar to picomolar concentrations (LC-MS) and gas chromatography-MS (GC-MS) have been combined with MS. Gas chromatography-MS is less sensitive than LC-MS, but it is generally more robust and reproducible  and six nonvolatile metabolites  positively related with CH4 intensity, whereas, uridine diphosphate-hexose B, and citrate were negatively related with CH4 intensity  and CH4 in dairy cows. They found that the use of different methods for MFA collection and analysis between studies results in difficulty to identify a clear pattern on the association between MFA and CH4 , insertions and deletions, and the identification of differentially expressed splice variants in the entire transcriptome  which is most commonly performed on tissue RNA-Seq and provides information on networks and clusters of highly correlated genes to be linked to cattle FE , which uses GWAS to identify QTLs and significant SNPs associated with a metabolite. This allows identification of SNP-Metabolite trait associations or mQTL (PLS) to determine correlations between milk traits and metabolite profiles. To further integrate this approach with other -omics information, genetic correlations of metabolite profiles with traits such as CH4 emissions can be done.Integrative approaches are currently being applied to uncover information associating different levels of omics, and further investigation of multi-level analysis is needed, such as integrating the genome, transcriptome, and metabolome. As the genome and transcriptome directly affect metabolite levels which result in changes to metabolite profiles; this highlights the importance of evaluating these levels as a system since specific metabolites are greatly affected by specific genetic features, and approaches are emerging to connect genomics with metabolomics. Integrative analyses include metabolite genome-wide association study ( or mQTL . In addi4 emissions at a system level.To integrate rumen microbiome features, other machine learning approaches have been used in studies aiming to identify relationships between the microbiome and host phenotypes, including penalized regression, support vector machine, Random Forest, and artificial neural networks . Althoug4 in ruminants is increasing. The development of cost-effective ways to mitigate CH4 has become a key priority worldwide, and this may be achieved by improving breeding strategies for more economically and environmentally efficient animals. Using previously collected data and existing resources in combination with high-throughput “-omics” technologies will advance our knowledge of the functional understanding of the metabolome and metagenome of ruminants. Increased integration of metabolomics and metagenomic information with other high-throughput “-omics” technologies and systems biology analyses are needed to provide a deeper understanding of the genes and metabolic pathways that influence the regulation and variation of CH4 production in ruminant animals.Due to the negative environmental impact of global warming, the demand to mitigate CH


Soybean is an important plant used for food, feed and many industrial purposes. Interest in soybean breeding is growing in Central Europe, including Poland. A very large number of soybean accessions are stored in gene banks, but less than 1% of them have been used for breeding. Here, we present genotypic data as well as phenotypic data on plant and seed performance, including seed chlorophyll fluorescence traits, and on yield components within a collection of soybean accessions that are conserved in the Polish Gene Bank at the Plant Breeding and Acclimatization Institute-National Research Institute.The materials used consisted of sub-collections: 79 Polish genotypes, including old traditional cultivars, 24 Canadian, 21 American, 21 Swedish and 31 from Central and Eastern European Countries, 9 from France and 6 from Japan. In total, 9602 high quality SNPs were derived from DArTseq, a method utilising GBS technology. GWAS, performed with the BLINK model, revealed that a total of 41 significant SNPs were mapped for days to flowering, flower colour, plant height, days to pod formation, 100 seed weight, pod colour, seeds and hilum colour and steady-state chlorophyll fluorescence under light (Ft_Lss). This is the first report about the diversity of traditional old Polish soybean cultivars.The online version contains supplementary material available at 10.1186/s13104-021-05750-1. Glycine max (L.) Merr.] is one of the oldest and most important oilseed and protein crops in plant production worldwide. Soybean diversity has been extensively described in many reports, and is relatively low [Soybean [vely low –7. For tGenetic resources stored in gene banks may be an important source of novel genetic variation which would be of interest to breeders if well documented and characterized with both genotyping data as well as phenotype data for traits of interest such as maturity, plant height, yield components, seed performance. To select a phenotyping method that is suitable for large-scale crop breeding research, it needs to be non-destructive and efficient; such as the steady-state chlorophyll fluorescence under light (Ft_Lss) .Most studies have been conducted on Asian and American collections –4 with rhttp://dane.agrobank.pcss.pl/jbrowse/), soybean and pea for more effective molecular breeding of new cultivars well adapted to changing climate conditions [The objective of our work was to develop and implement a national management system for crop plant genetic resources as part of the AGROBANK project  at the Pnditions , 11. ForA collection of 196 soybean accessions, including old, traditional cultivars, stored at the Polish Gene Bank (NCPGR) was evaluated using DArTseq: 80 Polish, 24 Canadian, 21 American, 21 Swedish, 31 from Central and Eastern European Countries, such as: Russia, Germany, Austria, Hungary, Ukraine and Lithuania, 9 from France, 6 from Japan, 1 from former Yugoslavia and 3 genotypes of unknown origin. The Polish accessions were selected to cover the diversity of Polish accessions held at the Gene Bank with priority given to those with key phenotypic traits in Polish breeding programs. This was then supplemented with non-Polish accessions from countries where a particular trait is most frequent. A set of 145 genotypes was preliminary evaluated under field conditions (based on the number of seeds available for each accession in the NCPGR). Passport data, listed in Additional file Field experiment was conducted in 2019 on the experimental field of Plant Breeding and Acclimatization Institute-National Research Institute (PBAI-NRI), Radzikow near Warsaw, Poland. No specific permissions were required. No endangered or protected species were involved.The experiment was conducted in a completely randomised design. Accessions were manually sown in 2 rows at 28 plants per row, row length of 2 m, plant spacing of 7 cm, and row spacing of 45 cm. Visual plant and seed traits were measured according to the ECPGR descriptors for soybean, with some modification , days to pod formation (DAY_POD_FORM), days to maturity (DTM), leaflet number (LF_NUM), leaf shape (LF_SHP), plant flower colour (FLW_CLR) and plant growth type (PL_GROW_TYPE). Days to flowering (DAY_FLW) is the number of days from planting to the day when 50% of the plants in a row have flowered, days to pod formation (DAY_POD_FORM) is the number of days from planting to the day when 50% of the plants start pod formation and days to maturity (DTM) is the number of days from planting to when 80% of pods have attained their final colour.Ft_Lss), one measurement was taken using a PlantScreen™ S.C. System (Photon System Instruments—PSI) for each of 10 subsamples which themselves contained 20 seeds each.Thirty plants (15 per replication) were used to measure plant height  after flowering time and yield components after harvesting: pods per plant (POD_PLT), seeds per pod (SED_POD), mature pod colour (POD_CLR). Hundred seed weight (g) (SED_WT) was determined in 3 replications. For visual determination of seed size and their performance, two sub-samples of 50 seeds each was used to assess seed coat colour (SED_CLR), hilum colour (HILM_CLR), seed coat surface lustro (SED_SURF_LUSTRO) and seed coat pattern (SED_PAT). To determine the steady-state fluorescence in light intensity /chloroform/isoamylalcohol method . DNA qua196 genotypes were genotyped by Diversity Arrays Technology (DArT) Pty Ltd, Australia, using DArTseq . SNP calDArT data was handled using the dartR v1.1.11 package  in the RUsing the 9602 SNPs and the 195 genotypes passing the data filtering process, we looked at the population diversity present within the genotypes. Principle coordinate analysis (PCoA) was undertaken, using dartR, and an unrooted phylogenetic tree was constructed. The R package, ape v5.3  was usedGWAS analysis was conducted using the GAPIT v2018.08.18 R package , 18 usinThis is the first report in which detailed phenotypic traits have been detailed in Polish soybean accessions, taking into account plant morphology, yield components and many seed performance traits. Commercially important appearance quality traits include mature pod colour, seed coat colour, hilum colour, seed coat surface, seed coat pattern and have been evaluated for all genotypes.Flowering time, time to pod formation and maturity are important for improving the adaptability and yield of seed crops in different environments. The variation difference for these traits were 7.53%, 8.54% and 7.11% respectively. A wide variation was detected for yield components: pods per plant (POD_PLT) with a coefficient of variation (CV) of 46.7% (range 16.0–91.7) and for 100-seed with CV 16.1% (range 3.2–29.0 g).Ft_Lss measurements by PlantScreen™ S.C. System was significantly correlated with visual assessments  but with more rapid and higher throughput of measurements. Suggesting it to be a fast and accurate method by which seed coat colour and uniformity can be characterised for many seeds samples stored at the Gene Bank. Ft_Lss is moderately positively correlated with 100-seed weight . This information can form the basis on which to drive genetic improvement in soybean.All seed performance traits showed remarkable variation: seed coat colour—66.24% (from black or brown to green or yellow), seed coat surface lustro—24.8% (from shiny to heavy bloom), seed coat pattern–212.4% (from light hilum to striped), hilum colour—49.3% (from and seed thickness—17.2%). The black seeds are uncommon and found in only a few genotypes originating from Poland and the USA. Raw phenotypic data and summary points of trait values are available in Additional files A total of 20,600 SNP markers across 196 genotypes were generated by DArTseq. Of these, 2613 (12.7%) markers had no missing data while 16,055 (77.9%) of markers had missing calls in less than 10 genotypes. One genotype was removed (199S) due to having more than 10% missing calls among the 16,055 markers. A further 3370 monomorphic markers were removed together with 2655 markers which were not 100% reproducible according to the DArT metric RepAvg. Where a DArTseq tag contained more than one SNP, one was selected at random. In total 9602 SNP markers and 195 genotypes were retained for further analysis.The PCoA Fig.  and NeigOf the 9602 SNPs, 6000 markers had complete data  and were evenly spread across the 20 chromosomes with between 220 (chr11) and 391 (chr8) markers per chromosome.Of the 24 phenotypes analysed, 9 were found to have at least 1 marker-trait associations with a total of 41 markers associated with those traits  data.Additional file 4. Phenotype summary plots for traits with marker-trait associations (MTAs).Additional file 5. Pearson correlation coefficients of phenotypic traits.Additional file 6. Unrooted NJ tree with 100 bootstrap replicates. Only bootstrap values ≥ 80% are shown.Additional file 7. Table of significant marker-trait associations (MTAs).


Aegilops tauschii is the diploid progenitor of the D subgenome of hexaploid wheat (Triticum aestivum L.). Here, the phenotypic data of kernel length (KL), kernel width (KW), kernel volume (KV), kernel surface area (KSA), kernel width to length ratio (KWL), and hundred-kernel weight (HKW) for 223 A. tauschii accessions were gathered across three continuous years. Based on population structure analysis, 223 A. tauschii were divided into two subpopulations, namely T-group (mainly included A. tauschii ssp. tauschii accessions) and S-group (mainly included A. tauschii ssp. strangulata). Classifications based on cluster analysis were highly consistent with the population structure results. Meanwhile, the extent of linkage disequilibrium decay distance (r2 = 0.5) was about 110 kb and 290 kb for T-group and S-group, respectively. Furthermore, a genome-wide association analysis was performed on these kernel traits using 6,723 single nucleotide polymorphism (SNP) markers. Sixty-six significant markers, distributed on all seven chromosomes, were identified using a mixed linear model explaining 4.82–13.36% of the phenotypic variations. Among them, 15, 28, 22, 14, 21, and 13 SNPs were identified for KL, KW, KV, KSA, KWL, and HKW, respectively. Moreover, six candidate genes that may control kernel traits were identified . The transfer of beneficial genes from A. tauschii to wheat using marker-assisted selection will broaden the wheat D subgenome improve the efficiency of breeding. Aegilops tauschii  is the diploid progenitor of the D subgenome of hexaploid wheat  and a vital genetic resource for the improvement of wheat quality and yield  have synthesized hexaploid wheat lines by crossing elite tetraploid durum with A. tauschii  and tauschii . Howevertauschii . Thus, ttauschii . The A. anmai 42  and heavanmai 42 . With thA. tauschii  is a third-generation genetic marker technology. SNPs are abundant and have traits such as high frequency and good genetic stability. Currently, SNP genetic studies are widely used for kernel yield, disease resistance, and stress resistance. Genome-wide association study (GWAS) based on linkage disequilibrium (LD) has been widely adopted to identify loci significantly associated with important and complex morphological traits in several species, including tauschii ,b, rice tauschii , wheat , kernel width (KW), kernel width to length ratio (KWL), kernel surface area (KSA), and kernel volume (KV) were evaluated in all three environments, and hundred-kernel weight (HKW) was evaluated in 2018 and 2019. Kernel morphologic traits, including KL, KW, KWL, KSA, and KV, were scanned using an Epson XL scanner system   and analyzed using the Win-SEEDLE Pro 2012a image analysis system  software. Hundred-kernel weight was calculated as two times the weight of 50 kernels.All escribed . Spikes Analysis of variance (ANOVA) was conducted using the “car” package in the software R 3.5.1 H’) was calculated based on BLUP values for six kernel traits using the formula.The broad-sense heritability was calculated using the Pi is the number of materials in the i level of a specific trait in the total percentage of copies, and Ln is the natural logarithm  to obtain the physical location , which contains both mutational and recombination history, as evaluated for linked/syntenic loci (p < 0.001). The LD analyses was conducted separately for the T-group and S-group, respectively. The LD estimates between marker pairs were obtained using TASSEL 3.0, the mean r2 over different genetic distances was calculated for the T-group and S-group, respectively.Population structure was analyzed using the Bayesian inference program STRUCTURE 2.3.4 based on the linkage ancestry model . A total10(p) = 3.00 as previous studies  . The sig studies . Manhatt studies .Based on Aet v4.0, putative genes in 10 Kb upstream and downstream of the significant SNPs were selected and then annotated using KEGG Orthology Based Annotation System 3.0 (KOBAS 3.0) . ArabidoA. tauschii reference genome Aet v4.0 with MAF >5%, missing data <20%. The 6,723 SNPs were evenly distributed on seven chromosomes of A. tauschi  contained 139 A. tauschii, including 137 of A. tauschii ssp. tauschii and two A. tauschii ssp. strangulata. Meanwhile, the LD analyses were conducted separately for the T-group and S-group two lineages. The mean r2 values gradually decreased with increasing pairwise distance. The extent of LD decay distance (r2 = 0.5) was about 110 and 290 kb for T-group and S-group, respectively  differences among genotypes and environments, except for HKW. The coefficients of variation of the six kernel traits among three environments ranged from 8.49 to 48.99% (p < 0.01) higher than those in the T-group  to 0.98 (between KSA and KV) . All cor results . Meanwhiclusters . ResultsGWAS was performed on all six traits using 6,723 SNPs among three environments. A total of 141 significant SNPs were identified for six kernel traits with phenotypic variation explained (PVE) ranging from 4.82 to 17.14% . The higcontig17143_54, located on chromosome 5D at 538.15 Mb, was strongly associated with KV with 13.02% PVE  could affect embryo development, cause seed surface atrophy, increase the number of cells to increase organ size, or affect kernel size through ethylene response. Thus, the six A. tauschii genes maybe directly or indirectly regulate kernel growth or regulate kernel size.Based on Aet v4.0, putative genes in 10 Kb upstream and downstream of the significant SNPs were homologous comparison using KOBAS 3.0. A total of 38 predicted genes were selected. Thirty-six and 38 genes were homologous to arabidopsis and rice, respectively . Six pre to MST1 , MAC3B  differences were noted among genotypes and environments; A. tauschii showed high diversity, indicating high research and utilization value, and it could make a major contribution to broadening the genetic diversity of the wheat D subgenome. In the present study, heritabilities of kernel traits were medium to high. In previous studies, moderate or high heritabilities were also observed in A. tauschii  with the population structure results. Similar results have been reported in nd wheat . A previ results . This rebspecies . Indeed,bspecies . Thus, tp-value was 1.49 × 10–4 for the 6,723 SNPs, with a corresponding −log10p) = 3.00, 66 significant loci were identified for kernel traits using 6,723 SNPs markers by GWAS. To the best of our knowledge, to date, only two studies have reported QTL for kernel characteristic traits in A. tauschii based on GWAS . Of note, a mutation of STR1 alone resulted in a shrunken seed phenotype. The shrunken seed phenotype was associated with delayed/arrested embryo development  transgenic alleles increase hybrid maize yield, as ZAR1 increased plant and organ size primarily through increasing cell numbers , and correlation and linear regressions analyses showed that HKW increased with increasing KL, KW, and KV. Kernel size traits affected kernel weight and, subsequently, yield. Our research results revealed that there are favorable varieties with longer and wider kernels in both subspecies of A. tauschii. Based on BLUP values, a total of 66 significant SNPs was identified using GWAS, and six candidate genes were identified as potential genetic drivers of these yield-related traits. The identified SNPs/genes will speed up the wheat breeding by MAS and genome-editing technology. It is expected that the excellent target gene from the D subgenome can be successfully introduced into wheat, so as to increase the yield of wheat and broaden the genomic resources of wheat.This in-depth study of The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.QW and NY drafted and revised the manuscript and contributed to data analysis. HC, HH, YL, HS, KZ, XJ, and SY performed the phenotypic evaluation and helped with data analysis. SL helped to perform linkage disequilibrium analysis and revise the manuscript. CL, GC, and ZY helped to draft the manuscript. YL designed and coordinated the study and revised the manuscript. All authors have read and approved the final manuscript for publication.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Linear mixed models (LMMs) can be applied in the meta-analyses of responses from individuals across multiple contexts, increasing power to detect associations while accounting for confounding effects arising from within-individual variation. However, traditional approaches to fitting these models can be computationally intractable. Here, we describe an efficient and exact method for fitting a multiple-context linear mixed model. Whereas existing exact methods may be cubic in their time complexity with respect to the number of individuals, our approach for multiple-context LMMs (mcLMM) is linear. These improvements allow for large-scale analyses requiring computing time and memory magnitudes of order less than existing methods. As examples, we apply our approach to identify expression quantitative trait loci from large-scale gene expression data measured across multiple tissues as well as joint analyses of multiple phenotypes in genome-wide association studies at biobank scale. These datasets have grown to the size of hundreds of thousands of individuals  with milIdentifying these associations requires statistical models that can account for biases in study design that can negatively influence results through false positives or decreased power. Linear mixed models (LMMs) have been a popular choice for controlling these biases in genomic studies, utilizing variance components to account for issues such as population stratification . These mHowever, these approaches are computationally intensive. Existing approaches for fitting these models are cubic in time complexity with respect to the number of samples across all contexts , 26. Her22.1n individuals, t contexts, and c covariates, we fit the following linear mixed modelFor multiple-context experiments with i and sample j in Y come from the same individual, and X is structured such that both an intercept and the covariate effects are fit within each context. For sake of simplicity, dimensions of nt assume that there is no missing data; however, this is not a requirement for the model. We note that this definition of K models within-individual variability as a random-effect, while within-context or across-individual variability is not included.Where The full and restricted log-likelihood functions for this model areN is the total number of measurements made across the individuals and contexts where d H=K+δI . These l2.2δ by refactoring them in terms of constants calculated from eigendecompositions of H and SHS, where SHS eigendecomposition with a matrix-vector multiplication  is knownThe inverse of a block diagonal matrix can also be computed by inverting each block individually. Moreover, using the Sherman-Morrison formula , the invH−1, we can show algebraically thatGiven each entry of f (i) = i%t (modulo operator) provides the context of a given 0-indexed column of X, g(i) = i//t (integer division) provides the covariate of a given index. A group g defines the set of individuals that share the same number of measured contexts tg. The expression “ind tg measured contexts that include context i and j.where δ pre-computed, specifically the sum of covariate interactions within the sets of individuals indicated above, E is constant with respect to δ and each entry of the symmetric matrix D can be calculated in linear time with respect to the number of groups, which is less than or equal to the number of contexts t. For a given δ, we can compute XTH−1X in O(t(tc)2) time complexity. Both the restricted and full log-likelihoods require the calculation of (XTH−1X)−1. The restricted log-likelihood requires the additional calculation of Note that with all values independent of O((tc)3) time complexity.These operations can be done in P(X) denote a projection matrix and M(X) = (I — P(X)). Note that both P(X) and M (X) are idempotent. The term remaining term in the likelihood functions, R, can be reformulated as followsLet a and vector b are a function of δ and can be algebraically formulated asThe scalar δ pre-calculated, a and b can be calculated in linear time with respect to the number of groups.where δ since they are not required for finding its optimal value, indicated by the ≈ symbol. We can reformulate the entire likelihood functions as followsNote that O((tc)3 + n).These likelihoods are maximized for 2.3N = nt and all ti = t. Hence,When there is no missing data, the likelihood functions can be further simplified. Note that in this case, X, and K are permuted resulting in samples being sorted in order of context, and the covariates in X are sorted in order of context, we can decompose H and X intoIf the input terms y, where δ. Next, we show that δ.Note that the remaining determinant in R as follows.This form of The term δ.Now we can reformulate the log-likelihoods, omitting terms that do not depend on δ. Moreover, both derivatives have the same rootBoth functions are differentiable with respect to u and v can be calculated by performing a separate OLS regression for each context, which can be completed in O(t(nc2+ c3)) time for a naive OLS implementation. Compared to the methods described above, this approach requires no iterative optimization and the estimate is optimal. Our implementation has a time complexity of O(c3+ nc2+ tcn).The scalar values 2.4We installed EMMA v1.1.2 and manually built GEMMA from its GitHub source . We edited the source code of GEMMA to prevent the automatic addition of intercept term in the design matrix (commented out lines 1946 to 1954 of src/param.cpp).Data were simulated using the mcLMM package. Sample sizes of 100, 200, 300, 400, and 500 were simulated with 50 contexts. Context sizes of 4, 8, 16, 32, and 64 were simulated with 500 samples. Data were simulated with 2.5We simulated gene expression levels in multiple tissues for individuals where there were no eQTLs. In other words, gene expression levels were not affected by any SNPs. We considered 10,000 genes and 100 SNPs resulting in one million gene-SNP pairs. We simulated 1,000 individuals. We also examined false positive rates with 500 and 800 individuals. We generated 49 such datasets where the number of tissues varied from 2 to 50. To simulate the genotypes for each subject, we randomly generated two haplotypes (vectors consisting of 0 and 1) assuming a minor allele frequency (MAF) of 30%. To simulate gene expression levels from multiple tissues among the same individuals, we sampled gene expression from the following multivariate normal distribution:N × T vector representing the gene expression levels of N individuals in T tissues and K is an NT × NT matrix corresponding the correlation between the subjects across the tissues. Ki,j= 1 when i and j are from two tissues of the same individuals, Ki,j= 0 otherwise. Here, we let where y is an α = 0.05).After generating the simulation datasets, we first ran mcLMM to obtain the estimated effect sizes and their standard errors, as well as the correlation matrices. The results from mcLMM were used as the input of METASOFT for meta-analysis to evaluate the significance. False positive rate was calculated as the proportion of gene-SNP pairs with p-values smaller than the significance level  across all tissues, and this similarity would be stronger among some subsets of tissues. For 19,600 null effects, we set vided in .βj = 0. For 400 non-null effects, we sampled βj from a multivariate normal distribution with mean of 0 and variance of 0.01I, where I is a 44 × 44 identity matrix.▀ Shared, unstructured effects: non-null effects are shared in all tissues but the sharing is unstructured or independent across different tissues. For 19,600 null effects, we set mash) and the correct labels of null effects and non-null effects.After simulating the gene expression levels y, we first ran mcLMM on the simulated datasets to acquire the estimated effect sizes and their standard errors, as well as the correlation matrices. We then applied METASOFT for meta-analysis with mcLMM outputs to evaluate the significance. For mash, we first performed simple linear regression to get the estimates of the effects and their standard errors in each tissue separately. These estimates and standard errors were used as the inputs for mash, which returned the measure of significance for each effect, the local false sign rate (lfsr). Finally, we employed the “pROC” R package  to calcu2.7https://gtexportal.org/home/datasets). The subject-level genotypes were acquired from dbGaP accession number phs000424.v8.p2. The GTEx v8 dataset includes 49 tissues from 838 donors. We selected 15,627 genes that were expressed in all 49 tissues. We only included SNPs with minor allele frequency (MAF) greater than 1% and missing rate lower than 5%. We applied mash and mcLMM plus METASOFT to the GTEx v8 dataset in our analysis.The Genotype-Tissue Expression (GTEx) v8 dataset  was usedmash uses the estimated effect sizes and standard errors of these gene-SNP pairs to learn the correlation structure of different conditions/tissues. We used the top significant SNPs to set up the data-driven covariances. We then fit mash to the random set of gene-SNP pairs with the canonical and data-driven covariances. With the fitted mash model, we computed the posterior summaries including local false sign rate (lfsr) [Since mash requires observation of the correlation structure among non-significant tests and data-driven covariance matrices before fitting its model, we prepared its input by selecting the top SNP with the smallest p-value and 49 random SNPs  in every gene from the eQTL analysis in the GTEx v8 dataset. There were 560,475 gene-SNP pairs in total. e (lfsr)  for the We applied mcLMM to the same set of gene-SNP pairs. We regressed out unwanted confounding factors in gene expression levels for each tissue with a linear model using covariates provided by GTEx. Covariates of each sample included top 5 genotyping principal components, PEER factors  ). Hard imputed genotype data from the UK Biobank were LD pruned using a window size of 50, step size of 1, and correlation threshold of 0.2. SNPs were further filtered for minor allele frequency of at least 0.01 and a Hardy-Weinberg equilibrium p-value greater than 1e-7 using Plink 2 . SamplesThe following data fields were retrieved: age at recruitment (Data-Field 31), sex (Data-Field 21022), BMI (Data-Field 23104), body fat percentage (Data-Field 23099), 10 genetic principal components (Data-Field 22009), HDL Cholesterol (Data-Field 30760), LDL Direct (Data-Field 30780), Apolipoprotein A (Data-Field 30630), Apolipoprotein B (Data-Field 30640), and Triglycerides (Data-Field 30870). Continuous phenotypes were visually inspected and triglycerides were log-transformed due to skewness. Data were filtered for complete observations. All fields were scaled to unit variance and centered at 0.HDL cholesterol, LDL cholesterol, Apolipoprotein A, Apolipoprotein B, and triglycerides were combined as response variables in the LMM and age, sex, BMI, body fat percentage, and the top 10 genetic principal components were used as additional covariates in the model. Each SNP was marginally fit with mcLMM. The coefficients output by this model for each phenotype were meta-analyzed to calculate FE p-values using METASOFT as packaged with Meta-Tissue v 0.5. The top GWAS hits for five different chromosomes (one per chromosome) were validated using the NHGRI-EBI GWAS catalog  and comp33.1To demonstrate the efficiency of mcLMM compared to existing approaches, we applied our method to simulated data of varying sample sizes and number of contexts. For these simulations, we simulated a sampling rate of 0.5, which indicates that only half of all possible individual-context pairs of observations are expected to be sampled.We first applied our method to simulations with a fixed number of 50 contexts and varied the sample size from 100 to 500. From these experiments, we observed that mcLMM requires computational time orders of magnitude less than EMMA and GEMMA. Similarly, when we fixed the number of samples at 500 and varied the context sizes from 4 to 64, we observed dramatically reduced runtimes for mcLMM.nt by nt matrices. In these simulations, existing approaches quickly grow memory requirements, with usages that grow to dozens of gigabytes for modestly sized datasets in the thousands of samples. mcLMM allows large-scale studies to be performed on relatively little computational resources  and mcLMM with missing data (iterative model). We observed a dramatic speedup, with sample sizes of 500,000 individuals across 10 contexts completed in under 10 seconds for the optimal model compared to around 15 minutes for the iterative model.3.2We utilized mcLMM to reduce the computational resource requirements of the Meta-Tissue pipeline, which fits a multiple-context LMM and combines the resulting effect sizes using METASOFT . While pα = 0.05 for mcLMM coupled with METASOFT. In our simulation with true positives, we observed an increased area under the receiver operating characteristic (AUROC) for mcLMM coupled with the random effects (RE2) METASOFT model compared to mash (We compared our approach to a method known as mash . This ap to mash .mash (Next, we compared the number of significant associations identified in the GTEx dataset. The mash approach utilized gene-SNP effect sizes estimated by the GTEx consortium within each tissue independently. Concordant with our simulations, we observed that the Meta-Tissue approach, utilizing mcLMM for vast speedup, identified more significant eQTLs than mash . These a3.3As a practical application of the efficiency of mcLMM, we performed a multiple phenotype GWAS in the UK Biobank. A multiple phenotype GWAS associates SNPs with several related phenotypes in order to increase the effective sample size for greater power, under the assumption that the phenotypes are significantly correlated. For our analysis, we combined HDL and LDL cholesterol, Apolipoprotein A and B, and triglyceride levels across 323,266 unrelated caucasian individuals in the UK Biobank. In total, 1,616,330 observations of these related phenotypes were fit as responses in the LMM.The mcLMM approach completed this analysis over 211,642 SNPs with an additional 14 covariates, parallelized over each chromosome, within a day. Each chromosome was analyzed on a single core machine with 32 GB of memory, with each test taking around 2 seconds to complete. We identified several significant loci, a subset of which replicate previous findings for specific phenotypes included in the model, such as HDL cholesterol  Figure . Existin4We presented mcLMM, an efficient method for fitting LMMs used for multiple-context association studies. Our method provides exact results and scales linearly in time and memory with respect to sample size, while existing methods are cubic. This efficiency allows mcLMM to process hundreds of thousands of samples over several contexts within a day on minimal computational resources, as we showed in simulation and in the UK Biobank. The association parameters learned by mcLMM can further be utilized with the METASOFT framework to provide powerful meta-analysis of the associations, as we showed in the GTEx dataset.K is low rank, such as in the case when multiple samples are genetically identical or clustered in genome wide association studies as described in FaST-LMM [Previous approaches have derived related speedups for LMMs when the matrix FaST-LMM . In thisFaST-LMM , 13.Our approach builds upon these findings and we optimize the method specifically for the low rank matrix with known eigenvalues described in the model, thus avoiding any spectral or singular value decompositions. Furthermore, when there is no missing data, our method can compute the optimal model parameters with a closed form solution requiring no iterative optimization of likelihood functions. We also note that mcLMM models covariance across contexts within an individual while the FaST-LMM approach, described above, models covariance across individuals within each context. This specific model fit by mcLMM arises in multiple-context association studies, such as the approach employed by Meta Tissue  for iden


Scientific Reports 10.1038/s41598-021-90774-7, published online 22 June 2021Correction to: The original version of this Article contained typographical errors in the Equations.In Table 1, fourth column, the Equation “Polygenic effect variation” was incorrect:now reads:In the Materials and methods section, under the subheading “Robustification of LMM based GWAS by using the outlier modification rule (proposed)”,b is the vector of random polygenic effects which follows N, where σg2 is the polygenic variance component, and K = (kijt) is the m × m genomic relationship matrix.”“now reads:b is the vector of random polygenic effects which follows N, where σg2 is the polygenic variance component, and K = (kjt) is the m × m genomic relationship matrix.”“And,F-statistic for testing the null hypothesis Ma = 0 for an arbitrary full-rank p × q matrix M13,60.”“When the maximum likelihood (ML) or restricted maximum likelihood (REML) variance component now reads:F-statistic for testing the null hypothesis Ma = 0 for an arbitrary full-rank p × q matrix M13,60.”“When the maximum likelihood (ML) or restricted maximum likelihood (REML) variance compontent And,m groups corresponding to the m genotypic labels of the selected most significant SNP. For example, let“(ii) Divide the phenotypic data into n = n1 + n2 + ……..+ nk.be the partition of phenotypic observations corresponding to the selected SNP, where, lth  group using the β-weight function defined by(iii) Detect the outlying observations from the i =  1, 2, …, n”where now reads:m groups corresponding to the m genotypic labels of the selected most significant SNP. For example, let“(ii) Divide the phenotypic data into n = n1 + n2 + …….. + nm.be the partition of phenotypic observations corresponding to the selected SNP, where, lth  group using the β-weight function defined by(iii) Detect the outlying observations from the i = 1, 2,  …, nl”where Additionally, Equation 7 was incorrect:ylk in the lth group is defined based on the β-weight function mentioned below:“An outlying phenotypic observation τl is the pth quantile value of the empirical distribution of where the threshold value now reads:yli in the lth group is defined based on the β-weight function mentioned below:“An outlying phenotypic observation τl is the pth quantile value of the empirical distribution of where the threshold value In Table 3, fourth column, the Equation “Polygenic effect variation” was incorrect:now reads:Under the subheading “Genotype simulation”,m = 2000 SNPs were generated for n = 1000 individuals, and these individuals were taken from k = 3 distinct population by considering different minor allele frequencies (MAFs). To do this, first, a set of mlatent vectors {v1, v2, …..vm} was generated from a multivariate normal distribution with mean zero and variance–covariance matrix Cov = ρ|j-k|64,65. In our simulation, we considered ρ = 0.5 to avoid the linkage disequilibrium (LD) between the SNPs. Finally, two cutoff values s1 and s2 were used to convert the design matrix V =  = [vij] of latent vectors to the genotypic score matrix “For this purpose, s1 and s2 determine the minor allele frequency.”where now reads:m* = 2000 SNPs were generated for n = 1000 individuals, and these individuals were taken from k = 3 distinct population by considering different minor allele frequencies (MAFs). To do this, first, a set of latent vectors {v1, v2, …..vm*} was generated from a multivariate normal distribution with mean zero and variance–covariance matrix Cov = ρ|j-k|64,65. In our simulation, we considered ρ = 0.5 to avoid the linkage disequilibrium (LD) between the SNPs. Finally, two cutoff values s1 and s2 were used to convert the design matrix V =  = [vij] of latent vectors to the genotypic score matrix “For this purpose, s1 and s2 determine the minor allele frequency.”where Furthermore, in the section “Phenotype simulation,”m1 = 4 SNPs were considered as causal variants and the remaining m2 = m-m1 = 1996 SNPs were allocated as polygenic variants (effects).”“In every situation, now reads:m1 = 4 SNPs were considered as causal variants and the remaining m2 = m* - m1 = 1996 SNPs were allocated as polygenic variants (effects).”“In every situation, Lastly, in the section “Consequence of phenotypic outliers on the partition of total variations”,now reads:The original Article has been corrected.


Understanding the genetic basis of performance stability is essential to maintain productivity, especially under severe conditions. In the present study, 268 Iranian bread wheat landraces and cultivars were evaluated in four well-watered and two rain-fed conditions for different traits. According to breeding programs, cultivars were in a group with a high mean and stability in terms of GY, GN, and SW traits, while in terms of PH, they had a low mean and high stability. The stability of cultivars and landraces was related to dynamic and static stability, respectively. The highest number of marker pairs and lowest LD decay distance in both cultivars and landraces was observed on the B genome. Population structure differentiated indigenous cultivars and landraces, and the GWAS results for each were almost different despite the commonalities. Chromosomes 1B, 3B, 7B, 2A, and 4A had markers with pleiotropic effects on the stability of different traits. Due to two rain-fed environments, the Gene Ontology (GO) confirmed the accuracy of the results. The identified markers in this study can be helpful in breeding high-performance and stable genotypes and future breeding programs such as fine mapping and cloning. Triticum aestivum L.) is the most important cereal for humans and has an undeniable role in food security. Therefore, increasing grain yield and yield stability have been prioritized by breeding programs to maintain wheat productivity. However, such a goal is challenged by the genotype-by-environment interaction (GEI) because a polygenic attribute like grain yield is controlled by numerous major and minor effect genes that interact with each other and the environment2. Thus, genotypes usually show a wide range of reactions before being introduced in a multi-environment trail (MET), leading to changes in their performance rankings and thus more confusion for breeders.Bread wheat  and additive main effects and multiplicative interaction (AMMI) statistics, namely AMMI stability value (ASV)17 and Modified AMMI stability index (MASI)18, emphasize stability, while Finlay and Wilkinson19 regression coefficient (bi) measures adaptability. In other words, Wi measures dynamic stability20, while low values of bi are estimates of static stability8. The method of harmonic mean of the relative performance of the genetic values (HMRPGV) provides estimates of adaptability and genotypic stability based on mixed models21. Several statistics have simultaneously examined performance and stability, including the yield stability index (YSI)22 and weighted average of absolute scores from the singular value decomposition of the matrix of BLUP for the GEI effects generated by an LMM and response variable (WAASBY) index23. In one of the latest statistics, while emphasizing different traits in MET analysis, the multi-trait stability index was introduced24.Stability statistics with almost simple calculation operations have long been the most important methods for assessing the stability of genotypes. Such statistics usually have a clear interpretation and can cover various aspects of stability, including static and dynamic types. Stability in the static concept refers to the constant performance of the genotype in different environments. In contrast, stability in the dynamic concept is the performance of the genotype that is constant according to the estimated or predicted level of the environments. These concepts are equivalent to biological and agronomic stability, respectively25. Determining molecular markers associated with quantitative traits and indices of trait stability and adaptability can help identify regions of the genome that control GEI26. Furthermore, identifying genomic regions that affect stability can facilitate the selection process27. In addition, understanding the interaction of QTL-by-environment is also important because most related QTLs are not stable across environments, and the repeatability of marker-trait associations (MTA) is widely disturbed by the GEI28. MTAs have been identified for the stability index on chromosomes 4B and 7B29. In a genetic architecture study, the grain yield stability of wheat and other traits using the GWAS approach identified several SNPs on different chromosomes that affected their mean traits and stability9. In addition, the role of functional markers, including photoperiod genes, in performance stability has been revealed14. The combination of GWAS and genomic prediction suggested that dissecting the genetic basis of yield stability would be more complex than the one in grain yield29. Other similar studies identified stability-related QTLs in the barley30, soybean27, and rice31. However, there are a few studies on the dissection of GEI using genome-wide association studies in wheat. The present study investigated the stability of Iranian bread wheat in terms of different traits and diversity indices of SNP markers. Then, to understand the genetic basis of GEI, we used association analysis for stability indices and examined the ontology of the identified genes.Different chromosomal regions are involved in wheat adaptationThe effects of genotype, environment, and GEI were significant at different probability levels for the four traits in the total population and subpopulations Table . Due to 2 values of cultivars were higher than landraces, especially in B and D genomes. Such a difference in distance (cM) can also be seen in the D genome  and the B genome, most markers in landraces were identified on the B and A genomes. There were 22 and 14 significant associations for HMRPGV in cultivars and landraces, respectively. Chromosomes 4A and 2A for cultivars and 3D for landraces were important. WAASBY was significantly associated with 24 and 21 SNPs in cultivars and landraces. These markers were mainly distributed on chromosomes 6B, 2B, and 2D. Although bi for cultivars and landraces had the lowest MTAs in the D genome, this genome  contained the highest MTAs considering the total genotypes. Finally, among all the indices, YSI in the cultivars was associated with the highest number of SNPs in the B genome . Except for PH, some of the identified MTAs were involved in important biological and molecular processes for all traits. These genes were distributed on different chromosomes, including 1A, 1B, 1D, 2D, 3A, 4A, 4B, 6A, 6B, and 7A, with chromosome 4B, 1B, and 7A having the highest number  can lead to increased stability and yield in wheat50. Therefore, it is possible to say that yield stability is controlled by genes with pleiotropic effects. However, as the experiment was performed in the same place and under different conditions, the correlation between grain yield in different environments may be a reason to observe common SNPs. In this regard, the lack of correlation between the environments resulted in no common SNP for the GWAS performed in 9 environments33. Although several common MTAs were identified in for GY, GN, SW, and PH traits and different stability indices, these traits are not exclusive and independent. Thus, it is possible to select both traits and stability indices in Iranian wheat cultivars and landraces since most significant MTAs  were not common among the trait values and stability indices. Lozada and Carter9 identified 12 SNP loci linked to both trait value and stability parameters in Pacific Northwest winter wheat. Two major effect SNP markers of Tdurum_contig61410_542 (1B) and BS00022542_51 (7B), were associated with grain yield and yield stability indices. The common MTAs between different traits and yield stability coefficient have already been reported50. The low number of MTAs identified for PH is probably due to the fact that this trait is controlled by a small number of genes compared to other traits. However, the above results for yield and its components show that they are controlled by several genes that interact with each other and the environment. Stability-associated genes can also be stress-responsive genes50. Therefore, GO results could be well described, given that two of the six environments are under rain-fed conditions. Proteins phosphorylation, especially in wheat grains, play an important role in drought stress60. Jasmonic acid biosynthetic modulates drought stress in wheat61. Markers related to mean GY and SW were annotated with antioxidant activity. Reducing the effects of drought stress by such activity with various enzymes in wheat was demonstrated by previous researchers62. The Synthesis of fatty acids is useful in counteracting the drought stress in oats63. Transmembrane transport, DNA-binding transcription factor activity, DNA repair, and peptidase activity were other examples that were annotated and possibly involved in response to drought stress. These results are similar to the previous reports64. Earlier efforts have been made to interpret GWAS results and understand GEI using gene annotation33. KOBAS is a useful tool for genome annotation65. It has been shown that ubiquinone and other terpenoid-quinone biosynthesis are metabolic pathways of response to drought stress in plants66. In addition, carotenoid biosynthesis is involved as one of the KEGG pathways in drought stress tolerance67. Such an important role for the biosynthesis of secondary metabolites has been proven68.The multi-trait loci controlling performance and stability were located on chromosomes 1B, 3B, and 7B. Furthermore, chromosomes 2A and 4A in all three cultivars, landraces, and the sum of these two had multi-trait control loci. All chromosomes, except for chromosome 3B, were reported in a similar studyIn the current study, GWAS was performed for some important agronomic traits and different static and dynamic stability indices based on those traits were calculated in a diverse panel of 268 Iranian wheat cultivars and landraces. The highest number of marker pairs and lowest LD decay distance in both cultivars and landraces was observed on the B genome, whereas the D genome had the least number of marker pairs and most significant LD decay distance. A total of 846, 653, and 1023 significant MTAs were identified for the traits and their related stability indices in cultivars, landraces, and total genotypes datasets, respectively. The chromosomes 6B and 4D had the highest and lowest number of MTAs, respectively. The multi-trait loci controlling mean traits and stability were located on chromosomes 1B, 3B, and 7B, and GO results for highly significant MTAs almost confirmed the accuracy of the identified markers. The identified markers in this study could provide valuable genetic resources to initiate marker-assisted selection, fine mapping, and cloning the underlying genes and QTLs.-1) were traits that were measured based on ten randomly selected samples from each plot. Plant height was recorded from ground level to tip of the spike, excluding awns, at maturity stage. After harvesting, all spikes were hand-threshed to determine the GY, SW, and GN. Then, stability parameters  GBS pipeline was used for SNPs calling, where reads with a low-quality score (< 15) were discarded. Imputation was performed in BEAGLE v3.3.273 using w7984 reference genome74. Finally, SNPs with heterozygotes < 10%, and minor allele frequency > 5% were used for further analysis.The development and genetic material studied was previously described based on genotyping by sequencing of a GBS library for the Iranian wheat samples have been by Alipour et al.75 software and GAPIT R-package76. The results of GLM was adjusted using the first three principal components (PCA) and population structure (Q) and MLM was corrected using kinship-matrix with the first three principal components (PCA + K) and population structure (Q + K). Results of all approaches from both TASSEL and GAPIT were evaluated based on the Q-Q plot and significance of associated loci using t-tests. In general, the results of the MLM approach of the first three principal components and kinship-matrix (PCA + K) obtained from GAPIT provided a more robust control of confounding effects. We, therefore, only reported the results MLM obtained from GAPIT. In the MLM model, individuals are considered random effects, and the relatedness among individuals is conveyed through a kinship matrix. A threshold of –log10 (p) > 3 was used to state statistically significant MTAs78. Confidence intervals (CIs) for MTAs were calculated for each chromosome using the linkage disequilibrium (LD) decay. Circular Manhattan plots were performed using the CMplot R-package79.Both general linear model (GLM) and mixed linear model (MLM) were employed to obtain the unbiased estimation of marker effects using TASSEL 5.0http://plants.ensembl.org/index.html) to assess gene annotation using Gramene (http://www.gramene.org/) by aligning them to the IWGSC RefSeq v1.0 annotation (https://wheat-urgi.versailles.inra.fr/Seq-Repository/Annotations). After aligning SNPs sequences to the reference genome, we selected overlapping genes with the highest identity percentage and blast score for further processing. The gene ontology of each selected gene, including molecular function and biological process, was extracted from the ensemble-gramene database (http://ensembl.gramene.org). In addition, the sequences of significant SNPs were used for GO enrichment analyses using KOBAS (KEGG Orthology-Based Annotation System) software80 to test for statistically enriched pathways in the Kyoto Encyclopedia of Genes and Genomes  database.Sequences surrounding all significantly associated SNPs were obtained from the blast tools in EnsemblPlants database (Supplementary Information 1.Supplementary Table 4.Supplementary Table 5.