The yak is a unique livestock species living in the Qinghai–Tibet Plateau. Investigating the morphological differences among different breeds of yaks is of paramount importance. However, due to the lack of effective communication of yak genetic information under natural and artificial selection, the genetic diversity of regional yaks is not effectively utilized for new breedings, and it is difficult for the existing analysis models to analyze such complex multi-species populations. Therefore, we extended the application scope of the current statistical model to perform whole-genome association analysis on multiple yak breeds and identified four genes significantly associated with body height. The findings of this study are of great significance for the development and improvement of yak morphological traits, as well as the expansion of statistical models.FXYD6, SOHLH2, ADGRB2, and OSBPL6, were identified. Our results show that when CMLM cannot identify optimal clustering groups, pCMLM can provide sufficient associated results based on population information. Moreover, this study provides basic information on the gene localization of quantitative traits of body size among yak breeds.Yaks have evolved several breeds or genetic resources owing to their geographical and ecological environment, and investigating the genetic construction of body size among breeds is key for breeding. Here, a genome-wide association study (GWAS) was performed for five body size traits in 31 yak breeds and genetic resources. The information from clustering individuals according to their habitats was used for kinship grouping in the compressed mixed linear model (CMLM). We named this approach the pCMLM method. A total of 3,584,464 high-quality single nucleotide polymorphisms (SNPs) were obtained, and six markers were found to be significantly associated with height by pCMLM. Four candidate genes, including  Bos grunniens), a unique large livestock species of the Qinghai–Tibet Plateau and surrounding Hengduan Mountains, provide a basic resource for the livelihood of plateau farmers and herders [Yak  distributed throughout the genome have become the genetic markers of choice. Genome-wide association study (GWAS) is a common experimental approach to study SNP markers associated with various economic traits in animal production by linking phenotypic and genotypic data and using statistical models to investigate genetic variant loci causally associated with the target trait . The GWAIn this study, we performed GWAS using yak datasets from different geographical areas in order to (1) detect SNP markers associated with body size among yak breeds, and (2) develop animal GWAS methods using the information provided on the populations.A total of 94 yaks were collected from different regions of the Qinghai–Tibet Plateau in China, including 17 Tibetan regions, 4 Qinghai regions, 4 Sichuan regions, 2 Gansu regions, 2 Xinjiang regions, 1 Yunnan region, and 4 wild yaks; in total, there were 31 yak breeds and genetic resources . Detaile−6. The Genome Associated Prediction Integrated Tool (GAPIT) [Data filtering was performed using the FASTP  software (GAPIT)  was usedhttps://itol.embl.de/, accessed on 3 October 2022), and principal component analysis (PCA) was performed and plotted using the GAPIT package in R. Population clustering analysis was performed using the Admixture [The neighbor-joining (NJ) tree was constructed using the P distance matrix calculated by the VCF2Dis  softwaredmixture .p-values were corrected with Bonferroni, and the cutoff was set to 0.05/number of all markers. Genome-wide association analysis was performed using a compressed mixed linear model (CMLM)  in the GThe general expressions of CMLM are consistent:https://github.com/liu-xinrui, accessed on 8 February 2023), which can provide a real or artificially defined grouping file for association study, as well as add grouping information to CMLM.Kinship in the model was calculated using all the markers. Combining test markers with kinship in MLM may lead to confusion between test markers and the genetic effects of individuals defined by kinship. In CMLM, Zhang et al.  introducBased on the physical location of the target trait association loci on the yak reference genome and combined with the LD decay distance of the yak genome (~20 kb), associated genes were screened on both sides of the SNP loci; we adjusted the LD decay distance to 100 kb when no linked genes were detected. If the gene on the reference genome had only an Ensembl ID, the sequence of the gene was extracted for Basic Local Alignment Search Tool (BLAST) comparison using the wild yak reference genome (BosGru_v2.0) for functional analysis. For multiple significant SNP loci, haploid block mapping was performed using LDBlockShow   between the body sizes of the domestic yaks and wild yaks. Among them, the body size trait of yaks in the Tibetan region was in the upper level among domestic yaks.We analyzed five body size traits of 94 adult yaks and summarized the descriptive statistics  for different body size traits . Most reA total of 47.15 million markers, including SNPs, indels, and other variants, were detected using the BWA-SAMtools-GATK pipeline  program In this study, yak populations were derived from 31 yak breeds and genetic resources from different regions of the Qinghai–Tibetan Plateau, and consisted of several yak populations from several provincial areas of China A; moreovp-value < 1.39 × 10−8) and these were associated with BH only in pCMLM  on chromosome 4, rs2659279  and rs2659285  on chromosome 13, rs310769  and rs477265  on chromosome 2, and rs2910497  on chromosome 15. The significant SNPs with their associated candidate genes did not have annotation information in the 100 kb linkage disequilibrium interval information either upstream or downstream. Therefore, we extracted the FASTA sequences of these candidate genes that were not annotated with gene names on the reference genome, for sequence alignment with the reference genome of wild yaks using BLAST. Except for the rs769892 locus, all the candidate loci obtained gene names with high similarity on the wild yak reference genome  of the two strategies for detecting BH traits, the results showed that the difference between pCMLM and CMLM was less than 10% of the mean value. Genotypic and phenotypic data of 94 individual yaks were analyzed using the GAPIT software with the first three principal components as fixed effects. Manhattan and quantile–quantile (QQ) plots are shown in in pCMLM A, whereain pCMLM . The QQ in pCMLM C of pCMLin pCMLM B. The QQin pCMLM C, which e genome .FXYD gene, rs310769 to ADGRB2, rs2910497 to SOHLH2, and rs477265 to OSBPL6 . The nearby LD block region was small, and the SNP was located on the outer side of the transcript. The analysis of allele haplotype based on this SNP showed that only GA and GG genotypes existed in 94 individuals, and no homozygous AA genotype was observed. In the results of the BH traits, yak individuals show higher body height A when tho OSBPL6 .Most GWAS models are effective in detecting populations, which is usually conducted by using genome-wide SNPs in a large number of individuals in the same population . They haVariation in body size traits is mainly based on distant cross-breeding among yak populations or genetic resources. In particular, to rejuvenate current domestic yak production performance, the wild yaks with superior traits were used for cross-breeding by local herders. These wild-blooded yaks (cross-breeding offspring of wild yaks and domestic yaks) tend to have a stronger body. Therefore, yak populations are more complex throughout the whole Qinghai–Tibet Plateau region. None of the 31 yak breeds and genetic resources in this study showed significant population clustering in multiple cluster analyses, with only the Tibetan breeds and genetics resources having a more similar genetic structure owing to their domesticated origins in Tibet . Such poFXYD6 (domain containing ion transport regulator 6), rs2910497 (chr15-57505237) with SOHLH2 (spermatogenesis- and oogenesis-specific basic helix-loop-helix 2), rs310769 (chr2-16165590) with ADGRB2 (adhesion G protein-coupled receptor B2), and rs477265 (chr2-129838648) with OSBPL6 (adhesion G protein-coupled receptor B2). Among these genes, the FXYD6 gene is a member of the FXYD family encoding a transmembrane protein, a specific protein encoding the hippocampus phosphate that has been shown in humans to be involved in mediating the Na/K ion pump [FXYD6 gene significantly accelerates Na+ deactivation and Na+ pump conversion rates [SOHLH2 gene belongs to the b-HLH (basic helix-loop-helix transcription factor) family, which encodes a testis-specific transcription factor essential for spermatogenesis, oogenesis, and folliculogenesis [SOHLH2 gene has also been shown to play an important regulatory role in the reproductive gonadal axis, pituitary, hypothalamus, ovary, and testis of buffalo [ADGRB2 gene acts as a transcriptional repressor through GA-binding protein, regulates vascular endothelial growth factor, and is significantly associated with its growth traits in grouper [OSBPL6 gene is a member of the family encoding hydroxysteroid-binding protein (OSBP), an intracellular lipid receptor [OSBPL6 gene contributes to the maintenance of cholesterol homeostasis in vivo by regulating cholesterol transport in humans through miR-33 and miR-27b [OSBPL6 in juvenile DePaul dwarf horses, it was shown that OSBPL6 is an essential factor affecting body height in DePaul dwarf horses [OSBPL6 and ADGRB2 genes are the most likely candidates to affect body height traits in yaks. However, whether and how the studied localized genes affect body height and size traits in yaks needs to be further explored, providing new directions and ideas for later validation studies.GWAS results based on pCMLM identified six SNP loci that were statistically significant in association with BH. Based on the annotation information provided by the 100 kb upstream and downstream of the yak reference genome, we obtained relevant annotation information on only four SNPs, but these contained only Ensembl ID. Probably because the yak reference genome is not yet complete, the sequences of these genes were compared to the wild yak reference genome by the BLAST tool. These candidate genes show association of rs2659279 (chr13-59118279) with ion pump . The FXYon rates  and alteon rates . The SOHogenesis . The b-Hchr2-1298648 with  buffalo , and mic buffalo ,40,41. T grouper . The OSBreceptor . The OSB miR-27b . In studf horses  by showif horses , and theFXYD6, SOHLH2, ADGRB2, and OSBPL6) were provided in association with yak’s body height. This study will help us to develop better biostatistical model optimization ideas and a deeper understanding of the relationship between genes and body height. These results may provide basic information for quantitative trait gene localization or candidate gene cloning in the yak body height formation mechanism.In conclusion, when traditional CMLM cannot provide effective compressed grouping by obtaining the best likelihood value, pCMLM can obtain better results by using the previous population clustering information provided. From the GWAS results of pCMLM and LD analysis, four candidate genes (


The availability of high-dimensional genomic data and advancements in genome-based prediction models (GP) have revolutionized and contributed to accelerated genetic gains in soybean breeding programs. GP-based sparse testing is a promising concept that allows increasing the testing capacity of genotypes in environments, of genotypes or environments at a fixed cost, or a substantial reduction of costs at a fixed testing capacity. This study represents the first attempt to implement GP-based sparse testing in soybeans by evaluating different training set compositions going from non-overlapped RILs until almost the other extreme of having same set of genotypes observed across environments for different training set sizes. A total of 1,755 recombinant inbred lines (RILs) tested in nine environments were used in this study. RILs were derived from 39 bi-parental populations of the Soybean Nested Association Mapping (NAM) project. The predictive abilities of various models and training set sizes and compositions were investigated. Training compositions included a range of ratios of overlapping (O-RILs) and non-overlapping (NO-RILs) RILs across environments, as well as a methodology to maximize or minimize the genetic diversity in a fixed-size sample. Reducing the training set size compromised predictive ability in most training set compositions. Overall, maximizing the genetic diversity within the training set and the inclusion of O-RILs increased prediction accuracy given a fixed training set size; however, the most complex model was less affected by these factors. More testing environments in the early stages of the breeding pipeline can provide a more comprehensive assessment of genotype stability and adaptation which are fundamental for the precise selection of superior genotypes adapted to a wide range of environments. Glycine max (L.) Merr.] delivers the highest amount of protein per hectare than any crop and accounts for over 60% of total global oilseed production  data sets from the International Maize and Wheat Improvement Center (CIMMYT)’s breeding program in eastern Africa, Triticum L.) (Arachis hypogaea L.) (Oryza sativa L.) (Using two maize (icum L.) , maize (icum L.) , groundngaea L.) , and rictiva L.) . To datetiva L.) . Two difhttps://www.soybase.org/SoyNAM/) were used in this study. Briefly, the SoyNAM data is comprised of 5,600 recombinant inbred lines (RILs) derived from 40 bi-parental populations (140 RILs per population) corresponding to 40 founders belonging to three different genetic backgrounds  crossed with a common hub parent (IA3023) (ca. 4 m long) and phenotyped for nine agronomic traits including grain yield (kg ha-1), plant height (cm), seed protein and oil (% dry weight), days to maturity , seed size (100 seeds weight in grams), fiber content (percentage in the grain), lodging (score from 1–5), and shattering (score from 1 to 5). Initially, the RILs from each family were split in four sets of 35 and each set was augmented with the two parents of the family and three check cultivars selected for adaptation to the field environment; however, if there was not enough seed available for a RIL, the plot was completed with a check variety. RILs were genotyped using the Illumina Infinium BARCSoySNP6K BeadChip (Phenotypic and genomic data from the Soybean Nested Association Mapping (SoyNAM) experiment ((IA3023) . The comBeadChip . After fBalanced multi-environment field experiments where all genotypes are observed in all testing environments are essential to assess the efficacy and advantages of the sparse testing design. For this, environments with less than 1,500 overlapping RILs across all testing environments were discarded. After applying this criterion to the phenotypic data, a total of 1,775 RILs derived from 39 bi-parental families  remained for analyses . The nine environments considered in this study were located across five States  in 2012 and 2013. These included Iowa 2012 (IA_2012), Iowa 2013 (IA_2013), Illinois 2012 (IL_2012), Illinois 2013 (IL_2013), Indiana 2012 (IN_2012), Indiana 2013 (IN_2013), Kansas 2012 (KS_2012), Kansas 2013 (KS_2013), and Nebraska 2012 (NE_2012).Two different selection methods were considered to compose calibration sets. The first method (S1) is based on randomly selecting (for each replicate) sets of 195 RILs  and assigning non-overlapped to each one of the nine environments . In this case, the 1,755 phenotypic observations measured across nine environments correspond to roughly 11% of all the total potential RILs-in-environment combinations . The objective is to predict the remaining 1,560 non-observed RILs  in each environment for a total of 14,040  missing combinations across all environments. In addition, different training set sizes were considered by systematically reducing the training set size by groups of 10 RILs from 195 to 95 RILs within each environment. For instance, by reducing the initial training set size (195) by 10 RILs, the training set size across environments was reduced to 1,665 . By reducing the training set by 100 RILs, the training set size across environments was reduced to 855 . The different within environments training set sizes varied from 195 to 95 RILs .In addition, for each of the training set sizes , different training compositions consisting of non-overlapping (NO-RILs) and overlapping (O-RILs) genotypes across environments were considered under the S1 selection method . To compThe second method (S2) implemented to select RILs and compose training sets is an alternative to the ramdom method and it is based on the genetic diversity of the RILs using genomic information. It focuses mainly on the maximization/minimization of the genetic diversity. For this, the Super Saturated Design (SSD) method was implement to select samples of fixed size (selected from a large pool of genotypes) increasing (SSD.max) or decreasing (SSD.min) the genetic diversity in the sample . Here, tj = 1,2, … , 1,560) from the E(S2) is computed, where E(S2) is computed is 304,200  and the objective is to identify the lth  RIL in the mth  RIL of the lth RIL in mth RIL in kth iteration Systematically, for each iteration, each RIL (one at a time) from the selected set of 195 RILs ith genotype at the jth environment, and it is composed of the sum of a common effect (μ) plus an environmental random effect , a genetic random effect corresponding to the ith RIL , a genomic random effect , and a random error term X is the centered and standardized (by columns) matrix of SNPs, Consider that ith genotype and the jth environment. The previous interaction effect can be modeled as a random effect following a multivariate normal distribution centered on zero and a covariance structure given by The previous M1 returns a singular genomic effect for each genotype observed in different environments. Thus, the resulting predicted genomic effect might not be accurate when considering all tested environments. To allow specific genomic effects at each environment, a model incorporating the genotype-by-environment GE interaction was considered. The reaction norm model conceptually allows the inclusion of the interaction between each molecular marker and each environmental factor in a convenient way via covariance structures . Let gEkth family such that Predictive ability was measured on a trial basis, thus the Pearson correlation coefficient between predicted and observed values was computed within environments. The overall predictive ability was computed as the average Pearson’s correlation coefficient across the nine environments. As mentioned before, despite the training set size or its composition (NO-RILs and O-RILs), the testing set size (prediction set) was the same for all cases. Within each environment, between 95 and 195 RILs were used as the training set for a constant prediction set size of 1,560 RILs.Since the RILs belong to families with different genetic backgrounds , the Pearson’s correlation coefficient was also calculated considering only the RILs within each one of the different groups at each environment. In this case, in each environment, the Pearson’s correlation coefficient between predicted and observed values was computed three times, one for each genetic background group. The objective of considering the different groups of families when computing the correlations was to assess the effects on predictive ability when blocking for population structure although that was not the main goal of this research.1) compared to the average of all other sampling methods of  and a significantly lower coefficient of variation among samples  for a total of 15,795 records available for analysis. No statistically significant differences were observed for yield across the seven different initial samples of size 195 RILs selected with the S1 (five replications based on random selections) or S2 (two for maximizing/minimizing the genetic diversity) selection methods. However, the sampling method minimizing genetic diversity resulted in higher average yield  observed across all nine environments. The total number of correlation values among the nine environments was 36  (0.123) .A total of 4,100 SNPs were included in the analysis after filtering the original set of 5,400 SNPs. Among the 1,755 RILs, no clear association patterns regarding population structure were observed across different genetic background groups  (left panel in The highest mean average correlation was obtained with model M3 (∼0.57), which was roughly 33% and 90% higher than M2 (∼0.40) and M1 (∼0.30), respectively . A slighConsidering the largest training set size (195 RILs), the training composition did not have a significant impact on the model performance, particularly in model M3 which performance was stable across all training compositions. Consequently, model M3 has advantages since high predictive ability does not require testing a large set of common RILs across environments which could be challenging due to constraints on the land and seed availability, especially in the earlier stages of the soybean breeding pipeline.Since the RILs were derived from families with different groups of ancestry , the effects of ancestry groups on the predictive ability were assessed by computing the correlation between predicted and observed values of similar families within each environment. For this, a post-stratification of the vector of predicted values of size 1,560 in the three different groups was conducted. Then, the within environments predictive ability for each group of families were computed despite the training set composition.Similar to A more detailed dissection of the model’s predictive ability at the group/family  level is displayed in Different patterns were observed for each one of the ancestry groups. For the G1 group , the meak+1)th iteration is larger than the previous one. On the other hand, a total of 182 iterations were needed to meet the stopping criteria in SSD.min. The corresponding Besides the method that randomly selects RILs to compose the training set, the SSD algorithm that chooses RILs maximizing/minimizing the genetic diversity  for a fixed sample size that was also considered. vice versa. In general, across groups of ancestry, equivalent results between the random and SSD.max were observed for all sample sizes. On the other hand, the random sample method outperformed SSD.min in all groups of ancestry and sample sizes  investigated the potential of incorporating soil texture information and its interaction with molecular markers via covariance structures for enhancing predictive ability across breeding scenarios. The obtained results were more stable when predicting trait performance in novel environments compared to the conventional reaction norm model.The expression of a phenotype is a function of the genotype, the environment, and the interaction between the genotype and environment (G×E) across different environments . Grain yIn soybean breeding, this is particularly important in the early stages of yield trials  where seed availability and the excessive number of testing genotypes are major constraints . In the In this study, different prediction models, as well as multiple training set sizes and compositions , were investigated. The most comprehensive model, including the interaction between families and the environment (M3), yielded the highest prediction accuracies independent of training set sizes and composition. The ability to borrow information between genotypes derived from the same families likely contributed to the superior performance of M3 because half of the cross was already observed a considerable number of times in other crosses and environments . In GP-bThe results and trends in predictive ability obtained with models M1 (main effects only) and M2 (reaction norm considering the interaction between markers and environments) were similar to those obtained by S2) . The method successfully created two fixed-size sample groups with contrasting genetic diversity. This was further observed in the population structure of each group, where SSD.max samples showed wider distribution and minimal clustering as compared to the SSD.min samples  and minimizing (SSD.min) genetic diversity was also investigated. The Super Saturated Design (SSD) methodology was implemented to identify the set of 195 RILs that either decreased or increased E yielded stable prediction accuracies across various training set sizes and compositions. Like the SSD.max observation, this could be attributed to the higher availability of diverse stress resilient-alleles and therefore require a smaller number of samples, as well as reduced O-RILs to achieve maximum prediction accuracy. These observations are fundamental to the establishment of a successful GP-based sparse testing design and should be further explored across populations with various genetic backgrounds, including high-yielding bi-parental populations.Similarly to the analysis of the different genetic backgrounds, a more detailed analysis can be done by considering the model’s predictive ability at the family level. As expected, a significant reduction in predictive ability was obtained ; howeverGenomic prediction-based sparse testing design is a promising approach to further maximize the applications of high-dimensional genomic data and predictive models toward improving cultivar development. The increase of testing environments in the early stages of the breeding pipeline can provide a more comprehensive assessment of genotype stability and adaptation which are fundamental for the precise selection of superior genotypes widely adapted to various environments. Various training set sizes and compositions, as well as prediction models, have been investigated. Overall, the training set size and the inclusion of O-RILs appear to be the main factors impacting prediction accuracy given a fixed training set size while the genetic diversity seems to be a secondary factor, except when it was minimized returning the worse results. Additional studies investigating the real-world effectiveness of prediction accuracy based on genotype ranking and advancement breeding decisions can help determine the ideal protocols for GP-based sparse testing in soybean. In summary, GP-based sparse testing can either improve/increase testing capacity (represented as the number of genotypes and environments) at a fixed cost or substantially decrease the cost of a breeding pipeline at a fixed testing capacity.


Estimating the FDR significance threshold in genome-wide association studies remains a major challenge in distinguishing true positive hypotheses from false positive and negative errors. Several comparative methods for multiple testing comparison have been developed to determine the significance threshold; however, these methods may be overly conservative and lead to an increase in false negative results. The local FDR approach is suitable for testing many associations simultaneously based on the empirical Bayes perspective. In the local FDR, the maximum likelihood estimator is sensitive to bias when the GWAS model contains two or more explanatory variables as genetic parameters simultaneously. The main criticism of local FDR is that it focuses only locally on the effects of single nucleotide polymorphism (SNP) in tails of distribution, whereas the signal associations are distributed across the whole genome. The advantage of the Bayesian perspective is that knowledge of prior distribution comes from other genetic parameters included in the GWAS model, such as linkage disequilibrium (LD) analysis, minor allele frequency (MAF) and call rate of significant associations. We also proposed Bayesian survival FDR to solve the multi-collinearity and large-scale problems, respectively, in grain yield (GY) vector in bread wheat with large-scale SNP information. The objective of this study was to obtain a short list of SNPs that are reliably associated with GY under low and high levels of nitrogen (N) in the population. The five top significant SNPs were compared with different Bayesian models. Based on the time to events in the Bayesian survival analysis, the differentiation between minor and major alleles within the association panel can be identified. Triticum aestivum L.) is among one of the major crops for food security worldwide which alone contributes 20% of the protein and calories in our daily diet. Increasing Grain yield (GY) is the main goal of wheat breeding programs. GY is a complex trait controlled by many genes with small effects. Under field conditions, both genetic and environmental factors, and interaction between genotype and environment (G × E) affect GY [p-value-small effects. However, the Bayesian whole genome regression model based on prior and posterior probability distributions is a convenient algorithm to deal with these difficulties [p-values [p-value for ranking significant associations [Bread wheat  techniques. When multiple pairwise association tests are performed between case and control individuals, it becomes difficult to minimize type I error  in hypothesis testing simultaneously. Some efforts to control the family wise error rate (FWER) versus multiple pairwise errors were proposed by Bonferroni, then Benjamini , who prop-value . Large-sp-value . The loclocFDR) is then defined as:In the local FDR framework, the FDR is a measurement of posterior signal SNPs with rule:locFDR, maximum likelihood estimator is sensitive to bias when the GWAS model includes two or more explanatory variables as genetic parameters. The results are based on maximum likelihood of marker effects, which is only a point estimation and there is no further information about prior distribution of the signal and followers of the signal associations.Thus in 1,…, SNPp when pairwise comparisons between censored and relapsed observations, are conditionally independent, However, the advantage of the Bayesian perspective is that the knowledge of prior distribution comes from other genetic parameters included in the GWAS model, such as linkage disequilibrium (LD) analysis, MAF and call rate of significant associations. In the current study, we propose to solve the multicollinearity and large-scale problems in the GY vector as a complex trait in bread wheat and large-scale SNP information with Bayesian survival analysis. The aim of this study is to obtain a short list of SNPs that are reliably associated to GY vector among three levels of N. The hypothesis to test, for each SNP = SNP0: i is not significantly associated with GY among population.Ha: i is significantly associated with GY among population.HIn Bayesian survival framework, the FDR is a measurement of posterior signal SNPs with rule:Where The Bayesian survival FDR (bsFDR) is then defined:Estimating a significant FDR threshold in GWAS is still a major challenge to distinguish true positive hypotheses from false positives and negative errors. Several comparative methods for multiple testing have been developed to determine the significance threshold; however, these methods may be overly conservative and lead to an increase in false negative errors. Here, we developed two empirical methods to determine the statistical significance threshold based on SNP- heritability of GY as a target trait. To test the locFDR and bsFDR methods for significance threshold under different distinguished GWAS models, we used the mean of results from three years of field experiments on GY vector in bread wheat under low N (LN) and high N (HN) applications.2). In the histogram plot, the Shapiro p-value = 0.0891, which indicates the GY vector follows a normal distribution. However, we considered this test inadequate, so to focus more on the quality of observations, the random vectors were repeated 2000 times with replacement from original GY vector was generated and Bayesian bootstrap p-value = 0.00325, which shows the Shapiro p-value is accurate (r = 0.814), showing that the effects of genotypes are distributed randomly and the quality of GY vector is acceptable to use in GWAS and GP models. Moreover, under LN treatment after removing outliers the Bayesian bootstrap p-value = 0.3048, which shows the Shapiro p-value = 0.2462 follows a normal distribution and is ready to apply in GWAS models  the standard error is minimum (sigma = 0.048), but Bayesian whole genome regression (NAM) exhibits the highest Delta (0) = 0.625, which shows that the false positive rate to reject H0 via sommer under LN treatment is not high, so this minimum sigma = 0.048 is not reliable. For all GWAS models, the local FDR plot was revealed in one tail.In NAM) the standard error is minimum (sigma = 0.062), the Delta is highest (0) = 1.034, in front in variance component model, sigma = 0.664 is highest and the higher sigma with lower Delta (0) = 0.433, representing lower model accuracy, so the sommer model was removed from further analysis.In rrBLUP and NAM, the local FDR plot was one tail but in mlmm model the two tails of significant SNPs was revealed. To check the performance of the remaining three GWAS models, the Bayesian survival analysis based on highest significant association was performed for GY vector under LN and HN treatments separately, and the mean and standard error of survived SNPs (iS(SNP)) were calculated. To measure the accuracy of each model, Akaike information criterion (AIC) and Bayesian information criterion (BIC) were calculated and the results are shown in rrBLUP and mlmm models was the only major allele that survived with mean of S(iSNP) 0.547 and 0.481. However, in the NAM model both major and minor alleles during survival analysis have remained. Moreover, the NAM displayed the minimum standard error (SE S(iSNP) = 0.189) in comparison to the other two models. The AIC and BIC were 150,408 and 150,867, respectively, which are lower than rrBLUP and mlmm. For GY vector under HN condition, the bootstrapping method was applied and in the mlmm model only the major allele survived with mean of S(iSNP) 0.597. However, in the rrBLUP both major and minor alleles and in the NAM all major, minor, heterozygous and missing (NA) alleles during survival analysis remained. In addition, the NAM exhibited minimum SE S(iSNP) = 0.104 in comparison to the other two models. Here, the AIC and BIC values were also less than those against rrBLUP and mlmm. Therefore, both local FDR and Bayesian survival analyses have confirmed NAM to be the best GWAS model with minimum residual errors on the SNPs. The Manhattan and QQ-plots for NAM model for GY vector under HN are shown in For −log10 (p = 4), the continuous points on chromosome region 3A specify the reliable SNPs, which show association with investigated trait  of length 150,000 iterations was considered after a burning bootstrap period of 2000 iterations. The p-values generated from all prior distributions were converted to z-values for easier interpretation and minimizing the effect of the SNP dimension. By comparing the box plots of the SNP Z-scores generated from six different Bayesian prior distributions  is still high. The main criticism of this approach is that it locally focuses only on SNP effects in tails, whereas signaling associations were distributed throughout the genome. Moreover, the magnitude of SNP effects alone may be insufficient to inform a conclusion about the performance of the model. For example, the degree of freedom (df) to fit the estimated density among SNPs is affected by the MAF and the quality of SNP chip . A larger df is required for sharper tails in mlmm model df is low, and consequently the sigma is partially low, which may lead to underestimation or overestimation of the model. With this limitation, we also considered whether we should use this approach because the proportion of false rejection hypotheses is larger in this approach than in the family wise error rate (FWER) approach. The most interesting result of this approach is that in the variance component GWAS model, proportion of H0 (sigma/mean) = 1.034 is the highest due to the highest sigma (SNP standard error), thus this model can clearly be removed due to its very low power. In the Bayesian whole genome regression with a low proportion of H0 (sigma/mean) = 0.633, the putative signal SNPs in the tails were very well covered and the model produced the lowest error (sigma = 0.062).Local FDR as frequentist inference with Fisher information background was applied to check the distribution of SNPs especially in the tails as critical regions of the distribution. This method, based on maximum likelihood estimation, is more precise for determining the effect size and strength of a large-scale genomic file. As can be observed in the results, the expected mean likelihoods based on SNP information are acceptable, but the standard error in the models with a scale of NAM model were both minor and major alleles revealed in the results with the highest AIC and BIC criteria versus two models. In GWAS with SNP simulation, all allelic effects including major, minor, heterozygous and missing were revealed in the same model, which may present good evidence supporting this model as the best performing. Thus, we found that this is in good agreement with [NAM model was lower than the others. To compare the performance of the Bayesian survival model with other commonly used Bayesian platforms, we proposed p-value and Bayes factor with a smaller comparison interval. The five top significant SNPs were compared with different Bayesian models. Only Bayesian survival analysis can identify the difference between minor and major alleles based on time to events. In Bayesian survival FDR analysis as a modern inference based on posterior estimation of SNP effects is commonly used for large-scale genomic data with small effects. In the survival part with the ent with  to minimsults of ,33. Binaaneously . It seemaneously  of the ibootstrap, and then Bayesian bootstrap p-value was calculated. To also control genotype random effect, the EBVs and BLUPs were based on broad sense heritability [In this study, a set of 221 bread wheat genotypes from Breeding Innovations In Wheat for resilient Cropping Systems (BRIWECS) project were cultivated as split-plots design, in three cropping seasons 2018, 2019 and 2020 at the agricultural research station Campus Klein-Altendorf, University of Bonn, Germany. We recorded the GY value of each genotype under high and low N fertilizer annually. Then, the average GY values of the genotypes were used as GY vector for subsequent analysis. The outliers in the GY vector were checked. To deal with outliers, they were kept since they reflected the actual field values across all years. The distribution of the residuals was checked using Shapiro normality test. To improve the quality of the vector, 2000 repeated random samples with replacement were generated from the original GY vector using R/tability  plotted.A platform of 150 K affymetrix SNP Chip was used to apply the GY vector in the GWAS and GP models. The SNPs with MAF ≤ 0.05 were removed due to monomorphism in the marker. After checking SNPs that deviated from the Hardy–Weinberg equilibrium (HWE), only 22,489 polymorphic SNP markers remained, which were used in GWAS and GP analyses.adegenet for assessing the population structure. To determine the actual number of PCs retained in the DAPC, cross validation (CV) was performed to simulate the low and high numbers of PCs in the model. To control outliers in the population clusters, information from the identical-by-state (IBS), which measures differences in allelic states, and the fixation index , which minimizes genetic variation within clusters, was also conducted using R/timation . To deteBasically, the GRM as kinship matrix is used in GWAS and GP models. Based on the method suggested by , the corrBLUP [mlmm.gwas [sommer [NAM [−log  is above the FDR threshold line, A total of four different GWAS models, including single-locus association with R/rrBLUP , multi-llmm.gwas , varianc [sommer  and Bayemer [NAM  at low aGP models were performed with Bayesian whole genome regression based on the following model: ual term . Bayesiap-value, for each GWAS model under low and high N levels, zz vector was created under the null hypothesis N , which is necessary, when SNPs p-value is very far from normal distribution. To fit the density of f (zz) with heavy tails, degree of freedom (df) was determined based on SNP sample size. Then, empirical null hypotheses were used to estimate the parameters of f (zz) by maximum likelihood, indicating the accuracy of each GWAS model, and the results were visualized using R/locfdr [survival [p-value distribution and the peaks, while there were no other observations in the bottom of distribution To check the distribution of SNPs R/locfdr . Based osurvival , SSNPi=e


Currently, meat cut traits are integrated in pig breeding objectives to gain extra profit. However, little is known about the heritability of meat cut proportions (MCP) and their correlations with other traits. The aims of this study were to assess the heritability and genetic correlation of MCP with carcass and meat quality traits using single nucleotide polymorphism chips and conduct a genome-wide association study (GWAS) to identify candidate genes for MCP.HMGA1 may be the strongest candidate gene affecting forelimb bone development. Moreover, as previously shown, VRTN is a causal gene affecting vertebra number, and BMP2 may be the strongest candidate gene affecting hindlimb bone development.Seventeen MCP, 12 carcass, and seven meat quality traits were measured in 2012 pigs from four populations . Estimates of the heritability for MCP ranged from 0.10 to 0.55, with most estimates being moderate to high and highly consistent across populations. In the combined population, the heritability estimates for the proportions of scapula bone, loin, back fat, leg bones, and boneless picnic shoulder were 0.44 ± 0.04, 0.36 ± 0.04, 0.44 ± 0.04, 0.38 ± 0.04, and 0.39 ± 0.04, respectively. Proportion of middle cuts was genetically significantly positively correlated with intramuscular fat content and backfat depth. Proportion of ribs was genetically positively correlated with carcass oblique length and straight length (0.35 ± 0.08 to 0.45 ± 0.07) and negatively correlated with backfat depth (− 0.26 ± 0.10 to − 0.45 ± 0.10). However, weak or nonsignificant genetic correlations were observed between most MCP, indicating their independence. Twenty-eight quantitative trait loci (QTL) for MCP were detected by GWAS, and 24 new candidate genes related to MCP were identified, which are involved with growth, height, and skeletal development. Most importantly, we found that the development of the bones in different parts of the body may be regulated by different genes, among which Our results indicate that breeding programs for MCP have the potential to enhance carcass composition by increasing the proportion of expensive cuts and decreasing the proportion of inexpensive cuts. Since MCP are post-slaughter traits, the QTL and candidate genes related to these traits can be used for marker-assisted and genomic selection.The online version contains supplementary material available at 10.1186/s12711-023-00817-y. For a long time, the traditional pork sales model in China consisted in cutting the carcass into pieces following customers’ preferences , 2. HoweAs early as the 1970s, Whiteker et al. , 6 had aIn this study, we compared the heritability estimates for meat cuts between different breeds and crossbred populations and investigated their genetic correlations with carcass and meat quality traits, which will benefit decision-making in breeding programs for meat cut traits. Finally, we also performed a genome-wide association study (GWAS) to identify quantitative trait loci (QTL) for meat cut traits and, for the first time, the associated genes.All procedures involving animals followed the guidelines for the care and use of experimental animals approved by the State Council of the People’s Republic of China. The ethics committee of Jiangxi Agricultural University specifically approved this study., which were formulated to meet the recommendations of the Chinese National Feeding Standard  at different growth phases. After 180 days of age, they were centrally slaughtered following standard pig slaughtering processes.In total, 2012 pigs from Muyuan Food Co., Ltd.  were randomly sampled for the meat cut evaluation experiment, as described in Lei et al. . In brielongissimus dorsi muscle between the 11th rib and the first lumbar vertebra.In the slaughterhouse, 12 carcass traits were measured, including carcass straight length (CSL), carcass oblique length (COL), thoracic length (THL), lumbar length (LUL), thoracic number (THN), lumbar number (LUN), single lumbar length (SLUL), shoulder backfat depth (SBD), 6th to 7th rib backfat depth (RBD), waist backfat depth (WBD), hip backfat depth (HBD), and mean of backfat depth (MBD). These traits were measured on the complete carcass, which was hung vertically by fixing the hind legs. Backfat depth refers to the thickness of the subcutaneous fat on the back of the carcass. After 24 h of acid excretion, the carcass was divided into three primal cuts , and 14 commercial meat cuts . The three primal and 14 commercial meat cuts obtained by dissecting the carcass in accordance with the processing standard GB/T 9959) are called carcass cuts or meat cuts. Details of the carcass cutting process and the appearance of the meat cuts are described in our previous study 959 are c, 14. At As pedigree information was not available for most individuals, all individuals were genotyped. Genomic DNA was isolated from the muscle tissue of each animal using the routine phenol/chloroform extraction method. The CC1 PorcineSNP50 BeadChip  was used to genotype individuals in accordance with the manufacturer’s protocol. Our previous study  provided1 and 2 are the vectors of residuals, which were assumed to follow the multivariate normal distribution The following two-trait animal model was used in the analyses:The variance–covariance matrix of The genomic relationship matrix  methodology using the GCTA software (version 1.93.1beta) . EstimatGenome-wide association studies (GWAS) were performed using the GEMMA software  and the p value thresholds of 1.25 × 10–6 and 2.50 × 10–5, respectively.For GWAS, statistical significance was set using the Bonferroni correction method. The genome-wide significance threshold was set at 0.05/N, with 1/N indicating a suggestive significance threshold , 22, wheBased on our previous results, carcass weight, sex, and breed composition had significant effects on the majority of the meat cut, meat quality, and carcass traits . The coeThe estimates of heritability (± SE) for MCP ranged from 0.13 ± 0.04 for TPB to 0.44 ± 0.04 for SB in the combined population  but negative genetic correlations were estimated for these traits with BF, BE, BPS, and BL [Fig. p value > 0.05). In addition, the majority of the meat cut traits had low or nonsignificant genetic correlations with carcass and meat quality traits. This is consistent with previously reported results [As shown in Fig.  results  of low oP = 1.25 × 10–6).Based on 40,016 SNPs and 2012 individuals, we identified 28 QTL that were associated with 15 carcass cut traits and reached the suggestive significance threshold (Table –5) SNPs were identified to be associated with the proportion of BBS, BPS, AB and SC. Among the SNPs in the region between 29.99 and 30.57 Mb on the Sus scrofa chromosome (SSC) 7, two genome-wide significant SNPs were identified to be associated with the proportion of AB  with SNP rs0700777  at this locus . Student’s t-test was performed between each pair of the three classes  in the VRTN gene located within this region that affects thoracic vertebrae number and performed a series of functional validation experiments [p value of 2.02 × 10–107, and this locus corresponded exactly to the causal mutation g.19034 A > C. The most significant SNP for THL (P = 1.77 × 10–46), located within the VRTN gene at position 97,618,073 bp (rs0702038), was also the most significant SNP for CB  on SSC7 that included 12, 4, and 10 genome-wide significant SNPs were identified to be associated with RI, CB, and MC proportions, respectively (Table eriments . The numP < 1.25 × 10–6) associated with LB proportion  family, which is a candidate gene for LB proportion. Abnormal expression of BMP2 results in failure of some chondrogenic condensates to form in the limbs, which affects vertebrate limb development and skeletogenesis [p value of 2.67 × 10–14, explaining 2.7% of the phenotypic variation. The other top SNP associated with LBP on SSC5 was located at position 66,103,958 bp (rs0501167) with a p value of 5.84 × 10–8, and was within the CCND2 gene. In previous studies, the CCND2 gene has been shown to regulate the cell cycle progression of hematopoietic stem cells [CCND2 have been found to be significantly associated with human height [. [CCND2 as a candidate gene for hip height, body height, and body length in Chinese Wagyu beef cattle, while Le et al. [CCND2 participates in growth-related processes and regulates conformational traits in pigs. These results suggest that BMP2 and CCND2 are candidate genes for LB.For leg cut traits, we identified nine genome-wide significant SNPs and 14 suggestive significant SNPs that are associated with the proportion of BL, TL, LB, and LC  in the VRTN gene that is associated with thoracic vertebrae number [BMP2, GRM4, HMGA1, CCND2, HAO1, and NUDT3, have all been found to be associated with skeletal development [Meat cuts are post-slaughter carcass composition traits that are challenging to evaluate in vivo. Therefore, marker-assisted selection and genomic selection would be optimal methods to select for carcass cuts, as these strategies can shorten the generation interval through early selection and increase the accuracy of the predicted breeding values, especially for complex traits with a low heritability and traits that are difficult to measure –39. Howee number  is also elopment , 30, 32 elopment , 27, 32,elopment , 25, 34.HMGA1, VRTN, and BMP2 [HMGA1 may be the strongest candidate gene for forelimb bone development, VRTN is a causal gene for vertebra number, as we have previously shown, and BMP2 may be the strongest candidate gene for hindlimb bone development. Therefore, it seems that bone development in different parts of the body is regulated by different genes. Analysis of the genetic architecture of meat cut traits will help analyze the molecular mechanism that underlies bone development of the forelimbs, spine and hindlimbs and lays a research foundation for the selection of the best shapes in different parts of the body.The body shape of pigs includes two dimensions: body length (spine) and body height (forelimbs and hindlimbs). The carcass cuts in this study were divided based on the pig’s bone structure and commercial value, including the three types of bones: arm bones (forelimb), chine bones (spine), and leg bones (hindlimbs). We identified three candidate genes that are significantly associated with these three types of skeletal development, namely and BMP2 –30, 32. This study evaluated the genetic parameters of 17 carcass cut traits, 12 carcass traits, and six meat quality traits in four populations of pigs. Genetic parameters for some of these novel meat cut traits have not been reported before. We found that some high economic value meat cuts, such as ribs, belly, loin, and tenderloin, have moderate to high heritabilities, which indicates that improvement of these traits through breeding programs is possible. This could increase the market price of the carcass by selecting on key meat cut traits. Estimates of genetic correlations revealed weak or nonsignificant correlations between many meat cut, carcass, and meat quality traits. Rib proportion was favorably correlated with carcass oblique length, straight length, thoracic number, and thoracic length, and negatively correlated with backfat depth. In addition, the GWAS identified 28 QTL and several candidate genes for meat cut traits for the first time. These findings provide a key reference for marker-assisted selection and genomic selection for meat cut traits.Additional file 1: Table S1. Estimates of genetic correlations between carcass cut proportions with carcass traits and meat quality traits.Additional file 2:Figure S1. Q-Q plot and lambda values of genome-wide association study (GWAS) of meat cut traits and carcass traits. Lambda values are normally used to characterize population stratification in multibreed GWAS.Additional file 3: Figure S2. Genome-wide association study (GWAS) for thoracic number and thoracic length. a, b The Manhattan plots show the associations of 40,016 SNPs with thoracic number and thoracic length, respectively, in the combined population. c A haplotype view of all polymorphic sites within the 500-kb interval before and after the top significant SNP (rs0702038).


The trait of participating in a genetic study probably has a genetic component. Identifying this component is difficult as we cannot compare genetic information of participants with nonparticipants directly, the latter being unavailable. Here, we show that alleles that are more common in participants than nonparticipants would be further enriched in genetic segments shared by two related participants. Genome-wide analysis was performed by comparing allele frequencies in shared and not-shared genetic segments of first-degree relative pairs of the UK Biobank. In nonoverlapping samples, a polygenic score constructed from that analysis is significantly associated with educational attainment, body mass index and being invited to a dietary study. The estimated correlation between the genetic components underlying participation in UK Biobank and educational attainment is estimated to be 36.6%—substantial but far from total. Taking participation behaviour into account would improve the analyses of the study data, including those of health traits. A new methodology to study participation genetics via analyzing shared and unshared genotypes is applied to the UK Biobank, suggesting that participating in genetic studies is a complex trait with a meaningful genetic component. By its very nature, ascertainment bias usually cannot be evaluated based on the sample alone3. Typically, other variables (covariates) that have known distributions for both sample and population are needed for adjustments3. Such adjustments are inherently imperfect as the covariates are unlikely to fully capture the underlying bias3. For genetic studies, among participants of the primary study who have contributed DNA, further engagement in optional components of the study has been demonstrated to have associations with genotypes and phenotypes7. That, however, does not address the genotypic difference between the primary study participants and the target population. Thus, it is striking that one can investigate how the sampled genotypes are biased based on themselves alone. A recent study identified single nucleotide polymorphisms (SNPs) that had significant allele frequency differences between the sampled males and females, and proposed that those variants have differential participation effects for the sexes8. This approach, however, cannot identify variants that affect primary study participation of both sexes in a similar manner. Here, we show how to do so.For all sample surveys, ascertainment bias, meaning that the sample is not representative of the target population, could lead to seriously misleading conclusions10, and are unaffected by population stratification11.All individuals are genetically related to some degree. Furthermore, each individual has two copies of genetic segments on autosomal chromosomes, and some of these segments are identical by descent (IBD), that is inherited from a recent common ancestor, with genetic segments in a relative. Instead of comparing individuals, we compare genetic segments. The key idea is that an allele that has higher frequency in participants than nonparticipants would also have higher frequency in segments that are in two participants than in segments that are in only one. Following this observation, we present below three principles of genetic induced participation bias, and show how to use only the sampled genetic data to perform genome-wide association scans (GWAS) for study participation that capture only direct genetic effectsOn average, between two ascertained individuals, genetic segments shared IBD, relative to segments that are not, are enriched with alleles that have positive direct effects on ascertainment probability. Figure T), the parental allele not transmitted to the offspring (NT) and the allele inherited by the offspring from the other parent (O). The T allele is shared, and the other two are not-shared. The NT and T alleles are perfectly matched as both are in the ascertained parent. Mendelian inheritance dictates that each would have the same chance to be transmitted to the offspring to become the shared allele. The principle is similar to that underlying the transmission disequilibrium test12. The O allele is not as perfectly matched and is currently not used. For the ascertained parent–offspring pairs, with alleles coded as 0/1, and FT and FNT denoting the frequency of 1s among the T and NT alleles respectively, the differenceFor an ascertained parent–offspring pair Fig.  where thtainment . We callAt a specific locus, assuming random Mendelian transmission, a sib-pair has probability 1/2 of inheriting the same allele IBD from the father, and the same independently from the mother. Consequentially, a sib-pair shares 2, 1 or 0 alleles IBD with probabilities 1/4, 1/2 and 1/4, respectively. With dense SNPs, the IBD state of a locus can usually be determined with high accuracy. For a specific SNP, based on the sib-pairs with known IBD states, two comparisons are made.S) and two distinct not-shared alleles (NS1 and NS2). Let FIBD1S and FIBD1NS denote the frequency of allele 1 among the S alleles and the NS (NS1 and NS2 combined) alleles, respectively. The differenceS allele is paternally inherited, then the two NS alleles are maternally inherited, and vice versa. Despite that, conditional on the genotypes of the two parents, without ascertainment bias, the frequency difference has expectation 0. Assuming random transmissions, the shared allele is equally likely to be paternal or maternal  participated and went through baseline assessments that took place from 2006 to 2010 (ref. 14). In addition to phenotypic details collected at the baseline visit, information continued to be added, including follow-up studies for large subsets of the cohort16. It is known that the UKBB sample is not fully representative of the UK population17. Participants were more likely to be female, less likely to smoke, older, taller, had lower body mass index (BMI)14 and more educated17.The UK Biobank (UKBB) is a large-scale database with genetic and phenotypic information of individuals from across the UK13. For each SNP, t-statistics for TNTC, WSPC and BSPC were computed by dividing each of the frequency difference, equations (1) to (3), by its standard error (s.e.) . We discarded SNPs from the MHC and other extended LD regions20 and applied other quality control filtering , and some were invited to a physical activity study in 2013–2015 that required wearing an accelerometer for a week15. Not everybody was invited  and only a subset of those invited actually participated. We call participation in these follow-up studies ‘secondary participation’. For the dietary study, the estimated effect of the combined pPGS on being invited, in loge odds-ratio Some UKBB participants were invited to answer a dietary study questionnaire in 2011–2012  has average value for the second half of the sibling pairs that is 0.044 s.d. higher than that of the unrelateds  test. For example, results that are significantly different between WSPC and BSPC at the MHC region would indicate data or data-processing problems. Furthermore, note that the genotyping-error induced bias also affects the transmission disequilibrium test—a test usually considered as fully robust.There can be a common genetic component underlying many different participation events, for example, the pPGS constructed for primary participation associates with both the passive (being invited) and active (deciding to participate when invited) phases of the secondary participation events. Thus, the effect of a genetic component associated with participation could accumulate through many participation events of a person’s lifespan, or it can be magnified through nested participation, for example, the participants in the dietary and physical activity studies have higher average genetic propensity to participate than the other UKBB participants, who have higher average propensities than the population. Instead of thinking of participation as a consequence of other characteristics and established traits, we propose that the propensity to participate in a wide range of events is a behavioral trait in its own right. While our method exploits information previously not utilized, even more could be achieved by combining it with other available information.13. We filtered out individuals that had withdrawn consent, were not in the kinship inference and phasing input, had a duplicate/twin in sample, with excess of third degree relatives, with missing rate above 2% as well as heterozygosity and missingness outliers and those who showed potential sex chromosome aneuploidy or potential sex mismatch.The UKBB has a Research Tissue Bank approval (Research Ethics Committee reference 21/NW/0157) from the North West Multicenter Research Ethics Committee, and all participants gave informed consent. For our data application, we used the UKBB 500K data release previously described by Bycroft et al.13. We refer to them as SNPs even though a very small fraction are short indels. Compared with standard GWAS, some of our analyses are more sensitive to data artefacts. Thus, we applied a number of filters to the SNPs in addition to those applied by Bycroft et al.13  = 1951.3). Those are referred to as the ‘unrelateds’ here.Using kinship coefficients from the UKBB data release, we identified 16,668 White British sib-pairs ) = 1950.8), and 4,427 White British parent–offspring pairs  = 1941.7; offsprings: 38.9% male, mean (YOB) = 1965.0, Supplementary Note section 9, a program designed for sib-pairs. Compared with KING18 (v.2.2.4) a program not tailored for sib-pairs, snipar entails a substantial improvement in IBD estimation , and BSPC were treated as a two-sample t-test. Specific equations are given in Supplementary Note section For each SNP, we computed separate quations  to 3), , t-statit-statistics showed a tendency towards favouring the major allele as having higher frequency in the shared alleles. We identified three sources to this bias:When the initial results for all the SNPs were examined together, the 18 program by snipar9, as noted above. Together with the trimming noted above, the impact of IBD estimation errors seems to be mostly eliminated , t-statistics of WSPC and TNTC, respectively. This adjustment avoids artificial association with other GWASs that are also subject to a major-allele bias, but resulting from a different mechanism. If the other GWASs exhibit major-allele biases for the same reasons, this adjustment would reduce, but not eliminate, an artificial association.For WSPC and TNTC, separately, we made a simple adjustment by regressing the t-statistics would also inflate the average values of the t-statistic adjustment above will reduce, but not eliminate, this inflation. This is because the adjustment is based on allele frequency, that is, it removes the average bias of alleles with similar frequency. As SNPs with similar allele frequency will have biases that vary around the average, the variation of the adjusted t-statistics would still be inflated, and through that inflate the average value of the t-statistic adjustment, and 1.074, 1.029 and 1.086, respectively, after adjustment. With t-statistic adjustment, the average r = 0.006), the t-statistic adjustment, have a larger but negative correlation with MAF (r = −0.021). The latter is because the major-allele bias of an SNP increases as t-statistics on polynomial of MAF up to the third power. The fitted values of the χ2 values as a function of MAF are displayed in Extended Data Fig. t-statistics gave the ‘final’ z-(or t-) scores of the WSPC GWAS. The same method was used for the TNTC GWAS. These z-scores were used to evaluate the significance of individual SNPs and to compute the polygenic scores used for Table The errors underlying the major-allele bias of the mentclass2pt{minimt-statistics, with or without adjustments, has very similar predictive power as the polygenic score constructed from the BSPC t-statistics  by summing over the weighted genotypes of the 500,632 SNPs fulfilling quality control, using the z- (or t-) statistics from the primary participation GWASs as weights. The relationship between the pPGS, standardized to have a variance of 1, and the phenotypes in Table P value for each pPGS-phenotype association was adjusted through dividing the squared test statistic (t-test for quantitative phenotypes and z-test for binary phenotypes) by the LD score regression intercept estimated from GWAS summary statistics for the corresponding phenotype (see below).The pPGS was computed with PLINK 1.90 (ref. 19) using the European Ancestry LD scores computed by the Pan-UKB team23 (downloaded on 7 April 2021). Analyses were based on the 500,632 SNPs used to compute the pPGS.We performed LD score regression with the program LDSC (v.1.0.1) (ref. 25). For quantitative phenotypes, which had been adjusted for sex, age, YOB and 40 PCs and transformed to have variance of 1 as described in Supplementary Note section P values, P_LINREG, from the BOLT output. Heritability of participation traits was estimated for a liability-threshold model (see below).LD score regression intercepts and genetic correlations were estimated for the primary participation test statistics described above and the phenotypes shown in Table The liability-threshold model assumes that a liability score, denoted here by g, the liability of sibling ij is modeled asBij are standard normal variables. The variables Ai, Bi1 and Bi2 are assumed to be independent of gi1 and gi2, and each other. Ai captures effects from shared environment as well as shared genetic factors other than g. We assume Xij) = 1. Because cor = 1/2, Xij is not exactly normally distributed because of gij, but it is close if For wA are chosen so that 13.Results in Fig. gij in the liability score definition is taken as the standardized version of a 0/1 variable, which is 1 if the actual genotype is 1 or 2, and 0 otherwise. For the recessive model, gij is the standardized version of a 0/1 variable, which is 1 if the actual genotype is 2.Simulations for dominant and recessive models were performed similarly. For the dominant model, the Here, we show how the heritability of the participation traits were estimated, starting with secondary participation. When the LDSC program is given the E stands for expectation. Consider the Dietary Study invitation event. Feeding the LDSC program the Heritability of The heritability of the liability scores of the other secondary participation events are similarly estimated. The With primary participation, heritability estimation requires the adjustment step above plus two others because the BSPC results are not direct comparisons of genotypes of participants and nonparticipants. Let As variance here is inversely proportional to efficiency, this leads to the adjustment factor, for arbitrary There is a third adjustment because the allele frequency difference between the IBD2 sibs and the IBD0 sibs is smaller than the frequency difference between the participants and nonparticipants. Specifically, for Since 2, the adjustment factor isBecause efficiency is proportional to effectWith the three adjustments, the estimated heritability of primary participation isFurther information on research design is available in the Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41588-023-01439-2.Supplementary InformationSupplementary Tables 1–3 and Note.Reporting SummaryPeer Review File


Climate change across the globe has an impact on the occurrence, prevalence, and severity of plant diseases. About 30% of yield losses in major crops are due to plant diseases; emerging diseases are likely to worsen the sustainable production in the coming years. Plant diseases have led to increased hunger and mass migration of human populations in the past, thus a serious threat to global food security. Equipping the modern varieties/hybrids with enhanced genetic resistance is the most economic, sustainable and environmentally friendly solution. Plant geneticists have done tremendous work in identifying stable resistance in primary genepools and many times other than primary genepools to breed resistant varieties in different major crops. Over the last two decades, the availability of crop and pathogen genomes due to advances in next generation sequencing technologies improved our understanding of trait genetics using different approaches. Genome-wide association studies have been effectively used to identify candidate genes and map loci associated with different diseases in crop plants. In this review, we highlight successful examples for the discovery of resistance genes to many important diseases. In addition, major developments in association studies, statistical models and bioinformatic tools that improve the power, resolution and the efficiency of identifying marker-trait associations. Overall this review provides comprehensive insights into the two decades of advances in GWAS studies and discusses the challenges and opportunities this research area provides for breeding resistant varieties. Helminthosporium oryzae) resulted in the Bengal famine that took lives of millions of people , which does not require genotyping of a large number of individuals, and which further reduces the cost, labor and time involved. The statistical basis of genome screening is the most important part of GWAS, as statistical tools are used to predict the correct association of outcomes by calculating a large amount of data. Power and resolution are the two important factors that can alter the genome-wide association. Power represents the ability to detect an association, and resolution regards the proximity of the association between a marker and quantitative trait locus . In multAssociation mapping is widely used to check marker associations with a specific trait based on the difference in allele frequency across the genomes . More prZea mays) is one of the widely cultivated major crops across the globe. Despite wide investigations and availability of genome sequences, very few studies deployed candidate gene-based GWAS to identify candidate genes for disease resistance in maize. In the seminal study, 18 novel genes associated with head smut resistance were identified (ZmFBL41 gene encoding F-box protein that confirms resistance to sheath blight and banded leaves was reported using GWAS (GRMZM2G006745) and LRR receptor-like serine/threonine-protein kinase (GRMZM2G141288)  . A totalG141288) . In totasistance . A totalsistance . Fumonissistance  (Table Oryza sativa) is staple food for more than half of the global population, and second most important cereal after Maize. In the case of rice, fungal diseases like blast, sheath blight and sheath-rot, bacterial diseases like bacterial blight (BB) and the viral disease like rice tungro disease, are major diseases. GWAS approach has been deployed to identify and validate genomic regions for tolerance to BB  were identified that had no relationship with previously identified genes or QTLs. In rice, high nitrogen input levels are conducive to disease development, a phenomenon called nitrogen-induced susceptibility. Two important QTLs include NIS2 and RRobN1 were identified that may play an important role in the blast disease response to nitrogen fertilizer (qLN11 and qMLL11) controlling sheath blight resistance was investigated recently (OsRSR1) and protein kinase domain-containing protein (OsRLCK5)  . Transges oryzae . This shrecently Triticum aestivum), genetic loci for disease resistance to yellow rust , rusts and PM diseases that have a major effect on yield. Based on phenotyping of 431 European barley accessions for two seasons and genotyping using DArT-seq, 78 MTAs for PM and rusts adult plant resistance were reported (In case of barley (reported . In casereported . Using mreported .Sorghum bicolor) using association analysis genetic loci linked to various disease resistances including anthracnose, head smut, downy mildew, and target leaf spot, were reported  is adversely affected by a wide range of pathogens like fungi, bacteria, viruses, and nematodes. MTAs identified for various diseases are comprehensively reviewed recently by Rsv1, Rsv4, and Rsv5 (Yield in soybean (and Rsv5 .Arachis hypogaea) is an important oilseed crop with a large and complex genome, is one of the most nutritious food. A comprehensive GWAS study based on 300 genotypes peanut from 48 countries identified 1 MTA for Aspergillus flavus resistance, 6 MTAs for early leaf spot, 31 MTAs for groundnut rosette disease and 1 MTA identified for late leaf spot of peanut (Aspergillus flavus (Peanut (f peanut . Early lf peanut . Similarf peanut . Most caf peanut . In GWASs flavus .Brassica napus) using GWAS analysis, Rlm12 locus was reported to be associated with adult plant resistance to blackleg disease caused by Leptosphaeria maculans  is second most important grain legume cultivated in more than 150 countries across the globe. Fusarium wilt, Ascochyta blight (AB), and Botrytis grey mould are major diseases that lead to yield losses in chickpea growing regions. Association mapping approach was extensively deployed in case of abiotic stress (AB4.1) on chromosome 4 with 12 predicted genes  significantly associated with AB resistance was reported (Chickpea (c stress . Very fec stress . In addireported . Recentlreported .Gossypium hirsutum), genomic regions, NBS-LRR and enriched with resistance gene analog (RGA) clusters (RGA1 and RGA3) associated with two different strains causing wilt disease (Solanum tuberosum), 16 QTLs associated with resistance to late blight were reported, with PVE between 13.7% and 50.9%. Of 15 candidate genes found in the study, ten for stem resistance and five for leaf resistance were reported (Lycopersicum esculentum), eight genomic regions associated with bacterial wilt resistance and their corresponding QTLs (Bwr-4 and Bwr-12) explaining 8.36–18.28% PVE were identified  associated with shoot and blossom blight resistance, respectively  and the alternative hypothesis (H1). Under H0, the marker under evaluation is not associated with the trait, whereas the alternative hypothesis rejects H0. The consensus metric of association is the p value, defined as the probability of observing the association informed by the data given that the null hypothesis is true. Thus, lower values support the rejection of H0. The preferred scale for p value is -log10, so that stronger associations are displayed as higher values. The genome-wide plot where the markers are ordered according to their physical position on the x-axis with associations presented on the y-axis in terms of -log10  is referred to as the Manhattan plot.In mathematical terms, GWAS analysis consists a series of statistical testing, screening the genome with one marker at a time, one region at a time, or the whole genome at once. The hypotheses under evaluation consist of the null hypothesis . A standard procedure is the Bonferroni correction, which consists of dividing α by the number of markers, creating a more stringent threshold to define an association. The Bonferroni threshold may be too stringent with sequence-level data involving millions of markers. A threshold relaxation is attained through an acceptable false discovery rate (FDR), referred to as Benjamini–Hochberg, which consists of dividing α by (1-FDR) × m. Other alternatives include replacing the total number of markers by the effective number of segments (m*), which accounts for marker collinearity associated with linkage disequilibrium.When a single marker is tested, the target p value to assert an association is equal to or lower than Linear models represent the main framework to test marker-QTL associations on complex traits. At its simplest form, the linear model that defines the alternative hypothesis, ergo fitting a marker, isy is the vector of phenotypes, μ is the intercept, x is the vector containing the marker information, b is the marker effect, and e is the vector of residuals. The marker information is normally coded as {0,1,2} corresponding to {AA,Aa, aa} to capture the additive effect of an allele substitution. The null hypothesis model does not contain a marker term and is defined aswhere In both cases, the residuals are assumed to be normally and identically distributed as b is a vector of fixed effect coefficients, including the intercept and the marker, and V is the variance-covariance matrix, which for this simple model where v) dictated by the difference in degrees of freedom from models H0 and H1; thus, LRT ~x2(v). For the simple case presented above that corresponds to one degree of freedom because there is one additional parameter in the alternative model, that is, the marker effect (b). When the single marker association jointly tests for additive and dominant effects, the LRT is tested with two degrees of freedom, which may reduce the statistical power.The p value is obtained from LRT from chi-squared density with the number of degrees of freedom  at the marker density that captures all linkage blocks; (2) with a population that has enough diversity to display nucleotide segregation across the genome; and (3) sufficient recombination between segregant markers to enable the detection of the marker to the causative locus.In genetics, structure is the term reserved to define the existence of stratifications in a population, where a subpopulation may differ with respect to its origin, evolutionary history, and allele frequency. Association studies in structured populations are likely to provide spurious results if the structure is not accounted for in the statistical model. Without a structure term, the model is incapable of differentiating a signal from a marker in LD to a QTL and a marker that displays higher frequency in subpopulations with higher (or lower) phenotypic means. The latter is the case when the marker tracks population structure instead of the true associations.Key parametrizations of population structure include (1) model-based terms as derived from STRUCTURE software ; (2) redM is the genotypic matrix where rows are individuals and columns are markers, U is the matrix of orthogonal eigenvectors (U′U = I) that correspond to the principal components, D is a diagonal matrix with the eigenvalues, which inform how much variation of M is explained by each principal component, and S is the rotation matrix. The alternative model for genome-wide association containing either principal components or model-based covariates is commonly defined aswhere y is the vector of phenotypes, X is the design matrix of fixed effects containing a vector of ones and the structure term , corresponding to the principal components or model-based covariates, b is a vector of fixed effect coefficients including the intercept and the regression coefficients of the structure term, m is the vector with marker genotype information, a is the allele substitution effect, and e is the vector of residuals.where G. There are various methods to build the G matrix, which may entail the use of marker information, pedigree information, or a combination of both  is normalized by the sum of allele variances under Hardy-Weinberg equilibrium, defined for the jth marker as Var(mj) = pj(1-pj). The genomic relationship matrix enters the genome-wide model as the covariance of the random term that describes the polygenic effect (u), which is assumed to be normally distributed as where the cross product of the genotypic information matrix -1X′ V-1. The variance components needed to estimate V, namely, via Expectation-Maximization . Measurements of variable importance can be generated for support vector regressions, random forests, gradient boosting machines, and neural networks. However, there is no gold standard method to measure variable importance across machine learning methods. The use of variable importance as a genome-wide association statistic often relies on an empirical significance threshold that can be estimated from permutations  is a function that represents a tree built with a random subset of markers (p ∈ P) from the genotypic matrix M whereas the number of trees NT is at times considered a tuning parameter, higher counts provide more stable measurements of variable importance. The common metric for variable importance in random forests is the mean decrease impurity, or simply “impurity”, which corresponds to the reduction in variance for regression problems and the Gini index for classification problems.where NDistinct GWAS approaches often provide different association results; hence, the deployment of various methods may lead to the discovery of more signals across the genome. Stronger signals are likely to be captured by multiple methods, whereas minor QTLs may be found by a specific methodology that best reflects the role of any given marker under the general architecture of the trait. Presence of population structure and genetic relatedness lead to detection of false positives in association studies. To overcome these limitations, general linear model (GLM) and mixed linear model (MLM) were used. MLM has been the most flexible and strong statistical tool for managing population structure and family relatedness kinship; . During k-mers, meta data and transcriptomes that improved the efficiency and power of identification of significant MTAs in crop species or animal systems  compare to SNPs based analysis   . More thed lines . Scoary ed lines . Roary ied lines .Pi5(t), Pi28(t), and Pi30(t) genes were identified for blast resistance (Peronospora effuse has been fine mapped in case of spinach (Spinacia oleracea) and the most promising candidate genes Spo12784 and Spo12903 near the RPF1 locus were reported ; MAGIC plus ; japonica MAGIC (8 japonica parents); and Global MAGIC (16 parents - 8 indica and 8 japonica) were created to directly and indirectly employ the highly recombined lines in breeding programs, for studying the interactions of genome introgressions and chromosomal recombination and to fine map the QTLs for several characteristics , structural variants  are ignored in GWAS studies and the rare variant associated with phenotype might be ignored. To overcome these limitations GWAS can be use sequences of nucleotide residues called it as ing data  to find iciently . In anotentation . CollectMeta GWAS analysis is a method of utilizing the results of previous studies to improve the power and resolution of association increasing sample size and by examining more variants . StatistFusarium verticillioides were identified using GWAS and validated by comparing the transcriptomes (Zm00001d050283, Zm00001d050284, and Zm00001d050293 (Pseudomonas syringae and plant growth in Arabidopsis (Transcriptome based GWAS association approach investigates associations between genetically regulated gene expression and complex diseases or traits using the genes/transcripts. TWAS has gained popularity during last five years due to its ability to reduce multiple testing burden and has been extensively used in fine mapping different traits in humans. With the advent of single-cell sequencing, chromosome conformation capture, gene editing technologies, and multiplexing reporter assays, we are expecting a more comprehensive understanding of genomic regulation and genetically regulated genes underlying complex diseases and traits in the future. Recently, in cotton a combinatorial approach of GWAS, QTL-seq and transcriptome-wide association studies was used to discover candidate genes and developed KASP marker for verticillium wilt resistance in cotton . 69 candriptomes . Transcr1d050293 . A transbidopsis .Identification of genetic loci or candidate genes is key to trait improvement in breeding programs Figure 3Meta-GWAS has emerged as a major strategy of dissecting traits to improve the strength of single-marker GWAS and enables to find the most effective stable loci spanning space and time while eliminating false positives . In addiMT and CZ conceived the idea; SG, AX, YD, UJ, SK, RK, MR, SC, DE, RM, RZ, LC, HS, MP, SP, VM, UR, BG, NG, VS, XW, CZ, and MT – contributed to writing the review; All authors read and approved the review article.