Decades of research have shown that environmental exposures, including self-reports of trauma, are partly heritable. Heritable characteristics may influence exposure to and interpretations of environmental factors. Identifying heritable factors associated with self-reported trauma could improve our understanding of vulnerability to exposure and the interpretation of life events.N = 185,414 participants). We calculated genetic correlations (rg) between reported childhood maltreatment and 576 traits to identify phenotypes that might explain the heritability of reported childhood maltreatment, retaining those with |rg| > 0.25. We specified multiple regression models using genomic structural equation modeling to detect residual genetic variance in childhood maltreatment after accounting for genetically correlated traits.We used genome-wide association study summary statistics of childhood maltreatment, defined as reporting of abuse  and neglect  (2SNP]) of childhood maltreatment, respectively. Genetic influences on h2SNP of childhood maltreatment were generally accounted for by a shared genetic component across traits. The exceptions to this were general risk tolerance, subjective well-being, posttraumatic stress disorder, and autism spectrum disorder, identified as independent contributors to h2SNP of childhood maltreatment. These 4 traits alone were sufficient to explain 58% of h2SNP of childhood maltreatment.In 2 separate models, the shared genetic component of 12 health and behavioral traits and 7 psychiatric disorders accounted for 59% and 56% of heritability due to common genetic variants (single nucleotide polymorphism–based heritability [h2SNP of childhood maltreatment. Elucidating the mechanisms underlying these associations may improve trauma prevention and posttraumatic intervention strategies.We identified putative traits that reflect h PAGE 587SEE COMMENTARY ON Traumatic events, namely, events perceived as physically or emotionally threatening and violating, are associated with various adverse outcomes, including psychopathology , 2, 3, 4Heritable behavioral characteristics may contribute to the likelihood of experiencing certain events. Personality traits, such as openness to experience and antisocial behavior, are phenotypically and genetically correlated with reporting interpersonal assaultive trauma . Such paCorrelations between genetic factors and retrospective reports of trauma may also in part be driven by heritable characteristics influencing the subjective interpretation, willingness to disclose, and recollection of events ,22. Gene2SNP]) ranges from 6% to 9% for reported interpersonal trauma during childhood  summary statistics , 38. Thehildhood ,39 to 18hildhood . This achildhood , 11, 12.hildhood ,39,40. H2SNP of reported trauma using genomic multiple regression with the Genomic SEM R package  to examine the residual genetic variance of life event measures after accounting for genetically correlated traits ,42. To o package . Our prin = 169,766); however, a small proportion (8.5%) were reported prospectively by a parent or caregiver . The genetic correlation between retrospective and prospective childhood maltreatment was previously reported as 0.72   using linkage disequilibrium (LD) score regression  between reported trauma and a wide range of complex traits. We tested 576 traits from GWAS summary statistics for rg with reported trauma. We excluded the major histocompatibility complex region from our analyses , which was less stringent than our selected threshold rg |z| statistic ≥ 5 . The criteria were stringent to restrict the number of traits included in downstream analyses to well-powered GWASs with potentially larger genetic contributions to h2SNP of reported trauma.To identify traits associated with the genetic component of reported trauma, we used bivariate LD score regression ,52 to meanalyses ,53. We cvelopers ,55. All 2SNP of reported trauma, we used the Genomic SEM R package version 0.0.5 (https://github.com/MichelNivard/GenomicSEM/wiki)  . Genomicg). We selected explanatory variables based on results from bivariate LD score regression. We introduced one explanatory variable at a time, iteratively, from the most highly correlated trait with reported trauma to the least correlated trait. For all models, we used the default diagonally weighted least squares estimator, in which the precision of genetic covariances  is considered.We fitted fully saturated genomic multiple regression models. This approach simultaneously regressed the outcome  on various explanatory variables, which modeled genetic correlations between each explanatory variable. This was informative in two ways. First, we estimated the residual genetic variance of reported trauma not explained by the genetics of the explanatory variables. Second, we estimated the unique contribution of each explanatory variable to the genetic component of reported trauma independent of other explanatory variables . Therefore, we had to fit 2 models for categorically distinct traits identified in LD score regression analysis: 1) health and behavioral traits and 2) psychiatric disorders.2SNPz statistic = 18.7; mean 2 value = 1.27) and report our findings for reported lifetime trauma  in the Results from analyzing reported childhood maltreatment were highly similar to that of reported lifetime trauma. We therefore present results for the more highly powered GWAS of childhood maltreatment (power quantified by hrg| > 0.25 and rg |z| statistic ≥ 5). Genetic correlations with all 576 traits are summarized in rg| > 0.25 and rg |z| statistic ≥ 5 /SE]2 in R version 4.1.1) (stic ≥ 5 . The pain 4.1.1) ,56.Figur2SNP of childhood maltreatment .As noted above, as we were able to include a maximum of 11 explanatory variables at once, we specified separate models for health and behavioral traits and psychiatric disorders. The path diagram in p > .05) . However, 2 traits were uniquely genetically associated with childhood maltreatment, over and above their genetic correlations with the other traits: subjective well-being  and general risk tolerance . Models where each health trait was introduced iteratively are shown in When controlling for the genetic influences of the other explanatory variables, the majority of conditional genetic associations between reported childhood maltreatment and health and behavioral traits were nonsignificant (p = 9.23 × 10−9). Thus, 56%  of h2SNP of childhood maltreatment was explained by genetic components of these psychiatric disorders. In this model, most psychiatric disorders shared their genetic overlap with childhood maltreatment, as indicated by nonsignificant conditional associations after accounting for shared genetics (p > .05)  and posttraumatic stress disorder (PTSD) symptoms  had significant conditional associations with childhood maltreatment independent of other disorders. When taking into account the genetic influences of all 9 psychiatric disorders in a genomic multiple regression model , the resp > .05) . Autism p = 1.24 × 10−12). This means 58% of h2SNP of childhood maltreatment was explained by the genetic component of ASD, PTSD, general risk tolerance, and subjective well-being. In a model with 2 additional traits (attention-deficit/hyperactivity disorder and self-reported tiredness), the residual genetic variance of childhood maltreatment decreased by only approximately 2%  , as a sensitivity analysis, we specified the genetic component of these 4 traits as explanatory variables of the genetic component of reported childhood maltreatment simultaneously . The res× 10−12) .2SNP of reported trauma. Health and behavioral traits together accounted for 59% of h2SNP variance, while the model exploring psychiatric disorders explained 56%. In both models, a shared genetic component was observed across traits except for subjective well-being, general risk tolerance, PTSD symptoms, and ASD, which were independently associated with childhood maltreatment. Together, these latter 4 traits alone were sufficient to explain 58% of h2SNP of reported childhood maltreatment.Using genomic multiple regression in Genomic SEM, we identified traits that accounted for approximately 60% of hWe found similar results for retrospective lifetime trauma, which included adult trauma. We could not directly compare adulthood and childhood trauma as the lifetime trauma phenotype included both measures. Our findings suggest that the exact timing of trauma does not strongly affect the proportion of genetic variance accounted for by health and psychiatric traits. However, replication in nonoverlapping datasets and appropriate trauma measures are required to make strong conclusions about differences between adulthood and childhood trauma.Independently associated traits, in addition to the genetic components shared across health and psychiatric traits, may be involved in rGE and/or the reporting of such environments as traumatic. This raises the question of which processes explain these associations and could inform strategies to minimize risk and consequences of trauma.General risk tolerance is measured by endorsing a willingness to take risks, broadly capturing risk-taking behaviors . rGE maySubjective well-being captures an individual’s cognitive evaluation of life satisfaction and positive affectivity ,61. Our The independent genetic association between ASD and childhood maltreatment is supported by several previous studies ,64,65. FAs trauma exposure is necessary for a PTSD diagnosis, the unique genetic association between reported trauma and PTSD symptoms could be explained by trauma exposure increasing the risk of PTSD. However, there are plausible reverse or bidirectional mechanisms. This includes passive rGE, whereby parental genetic predisposition to PTSD may act to increase the risk of trauma exposure in the child, as suggested by studies of PTSD and parenting . However2SNP, estimated from summary statistics and may differ from results using more advanced methods or individual-level genetic data (Our modeling approach has several limitations. First, the model is fully saturated, and we could not objectively estimate which model best fits the data. Second, we were limited by the number of traits that could be fitted in one model. However, sensitivity analyses did not indicate that all of the residual genetic variance of childhood maltreatment could be explained if all available genetically correlated traits were accounted for in one model. Third, our estimates are based on lower bounds of the total genetic variance explained by common genetic variants that can be, as captured by htic data ,75.2SNP of prospective trauma is lower than retrospectively reported trauma (2SNP of trauma than traits involved in the exposure of events. The residual h2SNP of trauma may reflect traits involved in memory recall (Further research is needed to establish the role of traits in terms of whether they are associated with the risk of exposure or the interpretation and recollection of events. Preliminary evidence suggests that hd trauma . Thus, gy recall ,32 that y recall . Disenta2SNP of trauma. Potentially, indirect genetic effects regulating behavior and cognition are associated with trauma exposure and/or retrospectively self-reporting trauma. We emphasize that our findings do not suggest that an individual is ever at fault or responsible for their exposure to trauma. Furthermore, h2SNP of reported trauma does not mean that some individuals are genetically determined to experience trauma. Most of the phenotypic variance of reported trauma is explained by the environment, which is malleable and can be modified into a more supportive and protective environment to mitigate vulnerabilities. For example, if a genetic propensity for ASD, PTSD, general risk tolerance, and subjective well-being reflect genetic risk to reported trauma, more social support may protect such individuals and alleviate adverse posttraumatic effects. However, our findings are correlational, not necessarily causal, and better delineation of the processes involved is needed. Future studies could assess the specific role of these traits in large family-based datasets using within-family designs (In summary, we systematically examined traits genetically correlated with reported trauma, implicating possible mechanisms that partly explain h designs . Disenta designs ,76. Such


The weight features of Alpine Merino Sheep, particularly their live weight in the 14th month (WT), are crucial in production and breeding, as they live at high altitudes and in highland areas where oxygen is scarce. Genome selection (GS) offers the advantages of minimizing breeding costs and generational intervals, and the main objective of genome selection breeding is the accuracy of GS. Genome-wide association studies (GWASs) were used in this study to extract the variation information related to the 14-month-old body weight trait of Alpine Merino Sheep, identify candidate genes associated with this trait, and employ GWAS results as prior information to conduct GS research on the trait to determine the most suitable GS breeding model for the target trait.FAM184B, NCAPG, MACF1, ANKRD44, DCAF16, FUK, LCORL, and SYN3 were candidate genes affecting live weight in the 14th month (WT), which regulated the growth of muscle and bone in sheep. In genome selection analysis, the heritability of GBLUP to calculate the WT was 0.335–0.374, the accuracy after five-fold cross-verification was 0.154–0.190, and after assigning different weights to the top 5%, top 10%, top 15%, and top 20% of the GWAS results in accordance with previous information to construct the G matrix, the accuracy of the WT in the GBLUP model was improved by 2.59–7.79%.Alpine Merino Sheep is a novel breed reared from Australian Merino Sheep as the father and Gansu Alpine Fine-Wool Sheep as the mother, living all year in cold and arid alpine areas with exceptional wool quality and meat performance. Body weight is an important economic trait of the Alpine Merino Sheep, but there is limited research on identifying the genes associated with live weight in the 14th month for improving the accuracy of the genomic prediction of this trait. Therefore, this study’s sample comprised 1310 Alpine Merino Sheep ewes, and the Fine Wool Sheep 50K Panel was used for genome-wide association study (GWAS) analysis to identify candidate genes. Moreover, the trial population (1310 ewes) in this study was randomly divided into two groups. One group was used as the population for GWAS analysis and screened for the most significant top 5%, top 10%, top 15%, and top 20% SNPs to obtain prior marker information. The other group was used to estimate the genetic parameters based on the weight assigned by heritability combined with different prior marker information. The aim of this study was to compare the accuracy of genomic breeding value estimation when combined with prior marker information from GWAS analysis with the optimal linear unbiased prediction method for genome selection (GBLUP) for the breeding value of target traits. Finally, the accuracy was evaluated using the five-fold cross-validation method. This research provides theoretical and technical support to improve the accuracy of sheep genome selection and better guide breeding. The results demonstrated that eight candidate genes were associated with GWAS analysis, and the gene function query and literature search results suggested that  Genomic selection (GS), a novel method for selective breeding using high-density markers covering the whole genome, was initially proposed by Meuwissen in 2001 ,4, and ihttps://github.com/xiaolei-lab/rMVP (accessed on 15 May 2023)) was used for analysis, which combines the advantages of the MLM and GLM and, through iteration, uses them to overcome their shortcomings. Eliminating the confusion between relatives and target trait genes in MLMs can reduce errors more effectively.Genome-wide association analysis (GWAS) is a method of identifying potential variants associated with target traits and the candidate genes associated with them, and it provides evidence-based breeding production theories. N. Risch and K. Merikangas first proposed GWAS while researching the genetics of complicated diseases. Various software packages and models are available to conduct GWAS, including the most commonly used general linear model (GLM), mixed linear model (MLM), FarmCPU model, etc. Each model has its advantages and disadvantages. In this study, the FarmCPU model in the rMVP package  were excluded from the analysis. The outcomes were systematically archived according to the documentation by proficient and experienced technicians. Outliers and extreme values were removed using the three standard deviations method, and all 1310 ewes had complete records of their phenotypic data. The entire population followed a the normal distribution. In this study, the weight phenotype was divided into two parts: (1) to identify candidate genes associated with live weight at 14 months, a total of 1310 Alpine Merino ewes were used for GWAS analysis. (2) To compare the genomic prediction accuracy between the GBLUP model and the GBLUP model incorporating GWAS information, the phenotypes of 1310 ewes were randomly divided into two groups, each containing 655 ewes, using the RAND function. These two groups were considered control groups for each other.p-value (HWE) of the Hardy–Weinberg balance was <10−6, and all the markers with a minor allele frequency (MAF) of <5% were eliminated. For sample individuals, all samples with an undetected rate > 10% were eliminated. To sum up, this study’s quality control criteria were as follows: SNP Call rate > 90%, MAF > 5%, HWE_p-value > 10−6, and Individual Call Rate > 90%. Beagle software (version 5.0) performs the self-filling of genotype data, since some models do not allow the presence of NA in genotype data. A total of 41,987 autosomal SNPs were isolated from the Fine Wool Sheep 50 K, and all 1310 samples passed the quality control criteria; then, they were retained for further GWAS and GS analysis following quality control and genotype data filling.Blood samples (of at least 3 mL) were collected from each sheep by puncturing the jugular vein. The sample were then immediately transferred to vacuum sampling vessel with ethylenediaminetetraacetic acid (EDTA) added . Afterward, blood samples were stored in the onboard refrigerator at 4 °C for subsequent DNA extraction. Genotyping was conducted using the Fine Wool Sheep 50K Panel . The reference genome used was the Oar v4.0 (GCF 000298735.2) version of sheep, as published on the NCBI. The PLINK (version: v1.9b4) conducted quality control on all SNPs. For SNP sites, the deletion rate was >10%, the test https://github.com/xiaolei-lab/rMVP, accessed on 15 May 2023) to perform GWAS analysis for live weight at 14 months. To eliminate the ambiguity of determining whether a relevant marker is in linkage disequilibrium (LD) with a detection marker, the FarmCPU model addresses kinship confusion by adopting a fixed-effect model. The approach removes the need to collect kinship information from all markers or related labels. Alternatively, the related marker is selected using the maximum likelihood approach based on kinship derived from the related marker. This method overfits the stepwise regression model. The FarmCPU model iterations utilize both a fixed-effect model and a random-effects model. In summary, the FarmCPU model is not only a statistically powerful method but also a computationally efficient GWAS approach [This study utilized the FarmCPU model in rMVP software (version 1.0.7) (approach . The modIn Equations (1) and (2), Equation (1) is a fixed-effect model, Equation (2) is a random-effects model, p-value of each SNP was obtained using a significance test, utilizing each SNP as a fixed factor for regression analysis. SNPs with smaller p-values were then selected and weighted according to their heritability as prior marker information for the subsequent GS analysis.The principal component analysis (PCA) results were evaluated using the BLINK model in the GAPIT software (version 3), and the FarmCPU model integrates both kinship relationships and population structure. The results of the GWAS analysis were corrected using the Bonferroni  correctiIn this study, the GBLUP  model inIn Equation (3), VanRaden , which iIn Equation (4), The kinship matrix construction method used by GS combined with GWAS prior information is as follows. The kinship matrix In Equation (5), The accuracy of genomic predictions was assessed using five-fold cross-validation . The 131In Equation (6), In this study, the weight traits of 1310 Alpine Merino Sheep ewes were recorded at 14 months of age by professional and experienced staff. As indicated by the pink line, most of the records were concentrated between 40 and 50 kg, as depicted in p-values from the GWAS analysis were sorted in descending order, and the top 5%, top 10%, top 15%, and top 20% of SNPs were selected as prior marker information. The top 5% contained 1908 SNPs, leaving 36,568 SNPs in the remaining 95%. The top 10% contained 3835 SNPs, leaving 34,642 SNPs in the remaining 90%. The top 15% contained 5726 SNPs, leaving 32,750 SNPs in the remaining 85%. The top 20% contained 7666 SNPs, leaving 30,810 SNPs in the remaining 80%. All of these SNPs were distributed across each chromosome.After quality control and genotype filling of the Fine Wool Sheep 50K data, a total of 41,987 SNPs were utilized for genome-wide association analysis and genomic selection. The All the trial populations used in this study came from five different core breeding farms. After quality control, a total of 41,987 autosomal SNPs were used for principal component analysis (PCA), The PCA diagram is exhibited in p-value in the GWAS result was corrected by the Bonferroni method. A total of 17 significant sites were associated with a significance threshold of 1, and the upstream and downstream 100 kb intervals of those associated significant loci were extracted to annotate the genes. The annotation tool used was the BEDTOOLS software, which offers a powerful genomic algorithm toolset satisfying the study’s gene annotation requirements, and the results of this study were annotated to a total of 22 adjacent genes (ANKRD44 (ankyrin repeat domain 44), MACF1 (microtubule actin crosslinking factor 1), SYN3 (synapsin III), DCAF16 (DDB1 and CUL4-associated factor 16), FAM184B (family with sequence similarity 184 member B), NCAPG (non-SMC condensing I complex subunit G), LCORL (ligand-dependent nuclear receptor corepressor like), and FUK (fucose kinase).The FarmCPU model was used to perform correlation analysis of the 14-month-old weight trait. The results of the Manhattan plot and QQ plot are shown in nt genes . In contThe GBLUP model is a representative of the direct method in GS prediction methods, which assumes that all SNPS have an effect. However, this assumption is obviously unreasonable. In this study, group 1 and group 2 were combined to verify the population. When the GBLUP model calculation was not based on the GWAS results, the genetic variance and environmental variance calculated by the G matrix were 5.427~6.176, 10.351 and 10.751, respectively. The heritability was estimated to be between 0.335 and 0.774, and the prediction accuracy, as assessed by five-fold cross-validation, ranged from 0.154 to 0.190. The genetic parameters for group 1 are presented in The GWAS results from trial group 2 were utilized as prior information to construct a G matrix, which was then used to validate trial group 1 and compare the accuracy of genome prediction. The most significant SNPs (top 5%) were selected to construct the kinship matrix G1. The genetic variance and environmental variance obtained were 2.702 and 13.308, respectively. The heritability was 0.169. The remaining 95% of SNPs were used to construct matrix G2. The genetic variance was 5.418 and environmental variance was 10.764. The heritability was 0.335, and the weighted values of G1 and G2 were 0.333 and 0.667, respectively. The G3 matrix was constructed with genetic variance and environmental variance of 4.840 and 11.229, respectively. The heritability was 0.158, and the prediction accuracy was 0.630, representing a 2.59% improvement in accuracy. The most significant SNPs (top 10%) were selected to construct the kinship matrix G1. The genetic variance and environmental variance obtained were 4.035 and 12.013, respectively. The heritability was 0.251. The remaining 90% of SNPs were used to construct the matrix G2. The genetic variance was 5.256 and the environmental variance was 10.915, resulting in a heritability of 0.325. The weighted values of G1 and G2 were 0.434 and 0.566, respectively. Additionally, the genetic variance was 5.331, the environmental variance was 10.767, the heritability was 0.331, and the prediction accuracy was 0.165, representing a 7.14% improvement in accuracy.The most significant SNPs (top 15%) were selected to construct the affinity matrix G1. The genetic variance and environmental variance obtained were 4.052 and 11.992, respectively. The heritability was 0.253, and the remaining 85% of the SNPs were used to construct matrix G2. The genetic variance and environmental variance were 5.236 and 10.93, respectively. The heritability was 0.324. The weighted values of G1 and G2 were 0.436 and 0.564, respectively. Additionally, the genetic variance and environmental variance were 5.301 and 10.800, respectively. The heritability was 0.329, and the prediction accuracy was 0.164, representing an improvement accuracy by 6.49%. The most significant SNPs (top 20%) were selected to construct a kinship matrix G1. The genetic variance and environmental variance obtained were 4.786 and 11.319, respectively, resulting in a heritability of 0.297. The remaining 80% of SNPs were used to construct matrix G2. The genetic variance and environmental variance were 5.129 and 11.033, respectively. The heritability was 0.317. The weighted values of G1 and G2 were 0.483 and 0.517, respectively. The G3 matrix was constructed with genetic variance and environmental variance of 5.493 and 10.626, respectively. The heritability was 0.341, and the prediction accuracy was 0.166, representing a 7.79% improvement in accuracy.The GWAS results from trial group 1 were utilized as prior information to construct a G matrix. This matrix was subsequently employed to validate trial group 2 and assess the accuracy of genome prediction. The most significant SNPs (top 5%) were selected to construct matrix G1. The genetic variance and environmental variance were 4.463 and 11.960, respectively, resulting in a heritability of 0.272. The remaining 95% SNPs were used to create matrix G2, which yielded a genetic variance of 5.968, an environmental variance of 10.542, and a heritability of 0.361. The weights of G1 and G2 were 0.428 and 0.572, respectively, which led to the construction of matrix G3. The genetic variance and environmental variance for G3 were 6.296 and 10.174, respectively, resulting in a heritability of 0.382. The prediction accuracy was 0.201, indicating a 5.79% improvement in accuracy. Furthermore, the most significant SNPs (top 10%) were selected to construct the matrix G1, resulting in a genetic variance of 4.688 and an environmental variance of 11.740. The heritability was estimated to be 0.285. The remaining 90% of SNPs were used to construct matrix G2, which had a genetic variance of 6.012, an environmental variance of 10.503, and a heritability of 0.364. The weights of G1 and G2 were 0.438 and 0.562, respectively. The genetic variance and environmental variance for matrix G3 were 6.057 and 10.340, respectively, resulting in a heritability of 0.368. The prediction accuracy was 0.188, representing a decrease in accuracy of 1.05%.The most significant SNPs (top 15%) were selected to construct matrix G1. The resulting genetic variance and environmental variance were 4.969 and 11.475, respectively, with a heritability of 0.302. The remaining 85% of SNPs were used to construct matrix G2, which had a genetic variance of 6.027, an environmental variance of 10.489, and a heritability of 0.365. The weights of G1 and G2 were 0.452 and 0.548, respectively. The genetic variance and environmental variance for G3 were 6.060 and 10.396, respectively, resulting in a heritability of 0.368. The prediction accuracy was 0.184, resulting in a decrease in accuracy of 3.15%. Similarly, the most significant SNPs (top 20%) were selected to construct matrix G1, resulting in a genetic variance of 5.288 and an environmental variance of 11.194. The heritability was estimated to be 0.321. The remaining 80% of SNPs were used to construct matrix G2, which had a genetic variance of 5.986, an environmental variance of 10.523, and a heritability of 0.363. The weights of G1 and G2 were 0.469 and 0.531, respectively. The G3 matrix was constructed with a genetic variance of 6.139 and an environmental variance of 10.330. The heritability was calculated to be 0.373. The prediction accuracy was 0.185, resulting in a decrease in accuracy by 2.63%.Alpine Merino Sheep is a new breed of Chinese sheep with exceptionally high-quality wool and great meat quality. These sheep thrive in cold, arid alpine areas throughout the year. Improving the breeding of Alpine Merino Sheep can have a positive impact on the local economy. Therefore, this study used the 14-month-old body weight trait of 1310 Alpine Merino ewes from the core breeding station of Huangcheng Sheep Breeding Extension Station in Gansu Province as the target trait for GWAS and GS analysis. The aim was to identify candidate genes associated with the target trait and determine the most suitable genomic prediction model for the trait. These phenotypic data were clean, well-documented, and free from outliers for research analysis. The genotype data used in this study was the Fine Wool Sheep 50K Panel data of the experimental animal for GWAS analysis. Following model correction, the Q-Q plot of GWAS results showed a good fit. The GBLUP model used in the GS analysis demonstrated a prediction accuracy ranging from 0.154 to 0.190. This was not significantly different from the results of genomic prediction accuracy studies on the carcass weight of the pig , the carCAPN6, which is associated with the birth weight of Hu Sheep, was identified using GWAS analysis [BMPR1B, HSD17B3, and TMEM63C) related to sheep production traits were identified [ANKRD44, MACF1, SYN3, DCAF16, FAM184B, NCAPG, LCORL, and FUK.Body weight traits are typical quantitative traits regulated by micro-efficacious polygenes, and GWAS is a powerful tool for identifying the genes underlying such traits. Many researchers have previously conducted GWAS analyses on livestock with a particular emphasis on body weight traits. For example, analysis . Additioentified . Furtherentified , body weentified , and musentified  in goatsFAM184B gene is located on sheep chromosome 6, and studies have demonstrated that it is not only associated with sheep meat quality, weight, and body shape traits [FAM184B gene has been identified as a gene strongly associated with body size and weight traits in livestock and poultry, including donkeys [NCAPG gene is located on sheep chromosome 6. Posbergh determined that this gene was associated with sheep size [NCAPG gene was abundant in the muscles of Qinchuan cattle. The analysis also identified that this gene plays a role in muscle growth and development. The NCAPG–LCORL loci were found to be significantly associated with feed intake and weight gain phenotypes in beef cattle [MACF1 gene is essential for regulating the actin and microtubule cytoskeleton network. The knockout function of mouse models revealed that MACF1 is associated with skin integrity and bone formation [SYN3 gene has been implicated in the body length asymmetry of goats and in the extracellular matrix of neuroregulatory processes [ANKRD44 gene has been found to have a significant association with birth weight in pigs. Additionally, it has been validated to be significantly associated with bone mineral density and whole-body lean mass [DCAF16 gene is significantly associated with the average daily gain of cattle, and the DCAF16-NCAPG region is a susceptible site for this trait [FUK gene [FAM184B, NCAPG, MACF1, SYN3, ANKRD44, DCAF16, FUK, and LCORL may be associated with body weight, body size, and muscle development in Alpine Merino Sheep. These genes and can be considered as potential candidates for target traits.The e traits  but alsoe traits . Additio donkeys , chicken donkeys ,38, and  donkeys . The NCAeep size , and Al-eep size ,42. Liu eep size  demonstrf cattle . Additiof cattle ,46, deerf cattle , and Korf cattle , the assf cattle . The LCOf cattle  in humanf cattle . NCAPG/Lf cattle . The MACormation . This geormation . The SYNrocesses . The ANKean mass ,55. Thisean mass . The DCAis trait . The stuFUK gene . These rFAM184B, NCAPG, MACF1, SYN3, ANKRD44, DCAF16, FUK, and LCORL genes, which have been reported as relevant genes in the body weight and body shape of sheep, cows and other domestic animals in many articles, the other genes reported in this study, SPRR4, ACTR2, SPRED2, TRNAC, TAB2, SF3B3, COG4, ST3GAL2, DDX19A, AARS, BDNF, FYB, CCND1, and DLGAP2, are considered to be equally important. These genes are potential genes for sheep growth and body weight. Specifically, the DDX19A, TAB2, ST3GAL2, and CCND1 genes are of particular interest. DDX19A is highly expressed in several mammalian tissues, including the brain smooth muscle, skeletal muscle, placenta, and fetal heart, with the highest expression observed in skeletal muscle [TAB2 gene is related to human developmental delay [In addition to l muscle . This inal delay . The ST3al delay , and theal delay . When mial delay . This inp-value. The SNPs with a significant impact on their phenotype were compared to traditional breeding methods. This improved the G matrix. SNPs associated with the target traits have been partially screened out, and as a result, the study finding are consistent with expectations. Compared to the GBLUP model, this method can significantly enhance prediction accuracy.In this study, the prediction accuracy of the GBLUP model for the two groups ranged from 0.154 to 0.190. However, when the G matrix was constructed by combining the results of GWAS as prior information, the prediction accuracy of genomic selection ranged from 0.158 to 0.201. We used the GWAS results from group 1 to predict GS in group 2 and vice versa, which helped prevent overfitting. The construction of the G matrix with GWAS results as prior information in GS is different from other genome selection prediction models. This is because GWAS analysis has already identified SNP loci that are associated with target traits, and these loci will have higher heritability when constructing the G matrix. The higher the heritability, the greater the prediction accuracy. However the prediction accuracy does not continue to increase with higher heritability. There is a limit to the increase, which is consistent with the hypothesis and findings of this study. However, in this study, when the GWAS results of group 2 were used as prior information to predict the genome prediction accuracy of group 1, there were varying degrees of improvement, specifically for the top 5%, top 10%, top 15%, and top 20%, respectively. On the other hand, when the GWAS results of group 1 were used as prior information to predict group 2, only the accuracy of the top 5% SNPs improved, while the other parts showed a decline. It could be due to the following reasons: (1) the site effect screened by group 2 is larger than that of group 1, and (2) the sample size of this study is relatively small. Despite the interference of other factors, the accuracy of genome prediction is improved by constructing a G matrix based on GWAS prior information compared to traditional breeding methods. This improvement has a positive impact on enhancing the accuracy of genome prediction. It is unreasonable to assume that all SNPs in the GBLUP model have the same effect and follow the same distribution. Some researchers have integrated the GS model with prior information and made various advancements, including the use of genomic feature BLUP  and BayeFAM184B, NCAPG, MACF1, ANKRD44, DCAF16, FUK, LCORL, and SYN3. Additionally, SNPs representing the top 5% to top 20% based on the p-value in the GWAS analysis were selected as prior information. The G matrix was then constructed using the GBLUP model in GS analysis. The results of genetic parameter estimation and prediction accuracy analysis for the WT trait demonstrated that the accuracy of breeding values improved by 7.79% when the top 20% SNPs were used as prior information. Consequently, based on the results of the GWAS analysis used as prior information, the accuracy of genomic prediction achieved by constructing the G matrix in GS analysis was higher than that of the GBLUP model. This suggests that this method is suitable for selecting weight traits at 14 months of age in this population.In this study, Alpine Merino Sheep ewes were used as the research group, and the target trait was initially analyzed using a GWAS at 14 months of age. Subsequently, the accuracy of estimating genomic breeding values, when combined with prior information from GWASs, was compared to the GBLUP model for estimating the breeding values of target traits. The GWAS analysis using the FarmCPU model identified eight candidate genes for the target trait:


Polygenic risk scores (PRSs) have been studied for predicting human diseases, and various methods for PRS calculation have been developed. Most PRS studies to date have focused on European ancestry, and the performance of PRS has not been sufficiently assessed in East Asia. Herein, we evaluated the predictive performance of PRSs for East Asian populations under various conditions. Simulation studies using data from the Korean cohort, Health Examinees (HEXA), demonstrated that SBayesRC and PRS-CS outperformed other PRS methods  in high fixed heritability (0.3 and 0.7). In addition, we generated PRSs using real-world data from HEXA for ten diseases: asthma, breast cancer, cataract, coronary artery disease, gastric cancer, glaucoma, hyperthyroidism, hypothyroidism, osteoporosis, and type 2 diabetes (T2D). We utilized the five previous PRS methods and genome-wide association study (GWAS) data from two biobank-scale datasets [European (UK Biobank) and East Asian (BioBank Japan) ancestry]. Additionally, we employed PRS-CSx, a PRS method that combines GWAS data from both ancestries, to generate a total of 110 PRS for ten diseases. Similar to the simulation results, SBayesRC showed better predictive performance for disease risk than the other methods. Furthermore, the East Asian GWAS data outperformed those from European ancestry for breast cancer, cataract, gastric cancer, and T2D, but neither of the two GWAS ancestries showed a significant advantage on PRS performance for the remaining six diseases. Based on simulation data and real data studies, it is expected that SBayesRC will offer superior performance for East Asian populations, and PRS generated using GWAS from non-East Asian may also yield good results. In addition, evidence for the clinical utility of PRS in diseases such as coronary artery disease (CAD)2, breast cancer3, and diabetes4 is currently increasing5, and the possibility of applying PRS for early detection, risk stratification, and personalized treatment of complex diseases has been suggested7.Genome-wide association studies (GWAS) have provided information on a large number of genetic variants that contribute to the risk of complex diseases. The genetic susceptibility of individuals to disease can be estimated by calculating the polygenic risk score (PRS) using the associated genetic variants. There has been considerable interest in PRS and the field is growing rapidly, with more than 2700 PRS algorithms presented in the open resource catalog8, which employs linkage disequilibrium (LD) clumping and P-value thresholding (P + T), LDpred9, SBayesR10, and PRS-CS11, which utilize Bayesian regression frameworks; and LDpred-funct12 and SBayesRC13, which incorporate additional functional annotations. These methods differ in two key criteria: which genetic variants are included in the study, and how to apply weights for genetic variants. Frequently, comparisons between these methods are conducted using simulated data and real-world examples14.PRSs are calculated from the number of alleles of genetic variants, typically weighted by the effect of the variants, estimated from GWAS data. In recent years, various methods for calculating Polygenic Risk Scores (PRS) have been developed. These methods include PRSice15. When selecting a GWAS, the ancestry of the study population is a key factor, since the transferability of PRSs across populations is poor owing to differences in allele frequencies and LD patterns of genetic variants17. Although the number of GWAS has been increasing in non-European ancestries18, most are still performed in European ancestry19. This imbalance in GWAS results has led to twice as many PRS studies for European than non-European ancestries17. Moreover, the performance of PRS when applying data from GWAS conducted in European ancestry to populations with non-European is unclear.Choosing an appropriate GWAS is one of the most important considerations to optimize PRS performance20. We employed five PRS methods based on single GWAS data: lassosum21, LDpred-funct, PRSice, PRS-CS, and SBayesRC. The predictive performance of the five PRS methods was assessed using simulated data representing different genetic architectures. In addition, we generated PRSs for ten diseases: asthma, breast cancer, CAD, cataract, gastric cancer, glaucoma, hyperthyroidism, hypothyroidism, osteoporosis, and type 2 diabetes (T2D), using the five PRS methods, and PRS-CSx, which allows for the integration of GWAS data from multiple populations. Biobank-scale GWAS summary statistics from European and East Asian cohorts, UK Biobank (UKB) and BioBank Japan (BBJ)23 were used, and each PRS method and GWAS population were compared using two predictive performance metrics. Our results can provide guidance in selecting an appropriate PRS method and its corresponding GWAS for a specific population of interest.To explore the performance of PRS for those of non-European ancestry, we tested PRSs under various conditions in a South Korean cohort, Health Examinees (HEXA) of the Korean Genome and Epidemiology Study (KoGES)24. Table P < 0.05, Student’s t-test). For asthma, hyperthyroidism, hypothyroidism, and osteoporosis, there was a significantly higher proportion of women in the disease cases and these diseases are known to affect women more frequently27. For T2D, CAD, and gastric cancer, the incidence in men was higher, which is in accordance with previous research30. In the disease groups for asthma, CAD, and T2D, for which body mass index (BMI) is a risk factor33, the average BMI was higher than that in the control groups. The SNP-heritability of the diseases in HEXA was varies from 0.08 to 0.48 . The prediction accuracy for all methods was assessed by calculating Nagelkerke’s RFigure We calculated PRSs for ten diseases using GWAS summary statistics obtained from UKB for the European population and BBJ for the East Asian population. Five PRS methods, including lassosum, LDpred-funct, PRSice, PRS-CS, and SBayesRC, were implemented using single GWAS summary statistics. Furthermore, the PRS-CSx was employed to integrate GWAS summary statistics from UKB and BBJ. A total of 110 PRSs, including 11 PRSs for each disease, were generated. The association between each PRS method and the target diseases through logistic regression is summarized in Table 2 and area under the curve (AUC)  Table . In the e 2 Fig. . The oth2  that using a single set of GWAS summary statistics in Koreans. Afterwards, we applied the five PRS methods to the ten diseases using GWAS summary statistics from both East Asian and European ancestries, respectively. Furthermore, we applied PRS-CSx as an algorithm utilizing GWAS summary statistics from multiple populations, resulting in a total of 110 PRS being generated. The performance of each PRS was compared using metrics such as RAmong the various PRS methods, SBayesRC showed the best performance in simulation data with high fixed heritability of 0.3 and 0.7 Fig. . Consist17. In breast cancer, cataract, gastric cancer, and T2D, the BBJ GWAS summary statistics from the same ancestry with HEXA showed better predictive performance compared to the UKB summary statistics  as a reference panel41. For quality control, SNPs with minor allele frequency less than 0.01 or Hardy–Weinberg equilibrium P-values less than 10–6 or missing data > 0.05 were excluded. A total of 7,915,509 SNPs remained.The genotype data were produced by the Korea BioBank Array, which is optimized for the Korean population and includes 833,535 single nucleotide polymorphisms (SNPs)The number of disease cases ≥ 300 in HEXA.The SNP-heritability of the disease > 0 in HEXA.GWAS summary statistics for the disease are available from both BBJ and UKB.For the PRS analysis, we selected the disease based on the following criteria:As a results, ten diseases  passed the criteria.Participants who constituted the T2D case and control groups were identified by their answers to the questionnaire on T2D diagnostic history and fasting glucose level. Those who replied ‘Yes’ to the questionnaire or had a fasting glucose level above 126 mg/dL were classified into the case group, and those who answered ‘No’ to the questionnaire and had a fasting glucose level less than 126 mg/dL constituted the control group.We identified case groups for breast cancer and gastric cancer from participants who responded 'yes' to the questionnaire on cancer diagnosis. Among these participants, those who indicated “breast cancer” in response to the question on cancer type were classified as the breast cancer case group, while those who indicated “gastric cancer” were classified as the gastric cancer case group. The cancer control group was defined as those who answered ‘No’ to the questionnaire on cancer diagnosis.For the other diseases , the participants were classified using a diagnostic history questionnaire for each disease. Those who answered ‘Yes’ were defined as disease cases, and those who answered ‘No’ were defined as controls. The case group for all the diseases comprised more than 300 individuals. The characteristics of the samples are listed in Table www.ebi.ac.uk/gwas) and JENGER (jenger.riken.jp/result)42. The information of GWAS data is shown in Table For the PRS calculation, GWAS summary statistics from the UKB and BBJ were selected. We used a total of 20 summary statistics. GWAS summary statistics were obtained from the NHGRI-EBI GWAS Catalog  and other parameters  with default setting. The PT value that maximizes the prediction accuracy in the validation dataset is selected, and the performance of the optimized PRS was assessed in an independent testing dataset.PRSice, is a P + T method that tests PRS at a large number of thresholds and applies the best-fit PRS to the study samples. PRS is calculated as the sum of the remaining independent SNPs with a GWAS association PRS-CS is Bayesian method that leverages GWAS summary statistics and LD information to estimate the effect size of each variant on a trait. It employs a continuous shrinkage prior to SNP effect sizes, which reduces the influence of noisy SNPs and improving the accuracy of the PRS. In the analysis, we used default parameter settings, along with an LD reference panel based on external European and East Asian samples from the 1 KG, considering the ancestry of the GWAS summary statistics.SBayesRC is a Bayesian method that assumes a multi-normal mixture distribution for SNP effects. It assumes that the effects of standardized SNPs follow a mixture of normal distributions with different variances , with each SNP explaining genetic variance ranging from zero to 1%. Also, SBayesRC utilizes annotation data that can influence the probability of a SNP being considered causal, as well as the magnitude of its causal effect size. We utilized the provided genomic annotation data and LD reference of EAS and EUR from UKB.Additionally, we applied PRS-CSx, which an extension of PRS-CS that enables the integration of GWAS summary statistics from various populations. PRS-CSx leverages the correlation among genetic effects while considering the allele frequency and LD information that are unique to each population. We applied the 1 KG LD reference panel in accordance with ancestry.44 with varying levels of polygenicity , heritability , and a default prevalence of 0.1. The sample was divided into a training set and a test set at a ratio of 4:1. GWAS was performed on the training set, and PRS was calculated for the test set using the five PRS methods. The simulation was repeated 10 times.We performed simulation studies using real genetic data on chromosome 1 of 6000 individuals form the HEXA. Synthetic phenotypes were generated using GCTA45. GWAS analysis was performed using SAIGE46. The SNP-heritability was estimated using LDSC43, which utilized pre-calculated LD scores, regression weights, and allele frequencies from the 1 KG in a relevant ancestral population. We excluded variants in the HLA region  for the calculation of heritability. For the evaluation of PRS performance, AUC was calculated by applying five-fold cross-validation for each subject of the disease47. Student’s t-tests and regression analyses were performed using basic packages of R version 4.05. Nagelkerke’s R2 was calculated using R package ‘lrm’. The bar plot and box plot were created using the R package ‘ggplot2’.SNP quality control, sample filtering, and PRS calculation were performed using PLINKv.1.9.0Supplementary Information 1.Supplementary Information 2.


Our knowledge of non-linear genetic effects on complex traits remains limited, in part, due to the modest power to detect such effects. While kernel-based tests offer a versatile approach to test for non-linear relationships between sets of genetic variants and traits, current approaches cannot be applied to Biobank-scale datasets containing hundreds of thousands of individuals. We propose, FastKAST, a kernel-based approach that can test for non-linear effects of a set of variants on a quantitative trait. FastKAST provides calibrated hypothesis tests while enabling analysis of Biobank-scale datasets with hundreds of thousands of unrelated individuals from a homogeneous population. We apply FastKAST to 53 quantitative traits measured across ≈ 300 K unrelated white British individuals in the UK Biobank to detect sets of variants with non-linear effects at genome-wide significance. We have developed FastKAST, a highly-scalable algorithm to identify non-linear genetic effects on complex traits in large datasets. Applied to 300K UK Biobank individuals, we successfully detected significant non-linear effects across 53 traits. A powerful approach to identify such effects relies on grouping genetic variants into “sets” and testing their aggregated effect13. The mixed model framework offers a versatile approach to test such effects: capable of testing a wide range of linear and nonlinear relationships between genotype and trait by employing a kernel function that measures similarity between pairs of genotypes13. In practice, testing within the mixed model framework is computationally impractical for large datasets, so current approaches typically restrict their focus to linear additive models11. While biobank-scale datasets containing genetic and phenotypic data over hundreds of thousands of individuals provide the large sample sizes needed to identify nonlinear effects16, computational challenges have limited these efforts.Understanding the contribution of nonlinear genetic effects on complex traits is an important question in human genetics17 within a score test, obtaining calibrated p values by fitting a distribution to genome-wide statistics obtained from a small number of permuted phenotypes18. As a result, FastKAST can efficiently test nonlinear associations in biobank-scale data.We propose Fast nonlinear Kernel-based ASsociation Test (FastKAST), a scalable approach to test for nonlinear effects of a set of variants on a trait in a mixed model framework. Specifically, FastKAST permits the fitting of a wide class of kernel functions that model nonlinear effects of genetic variants on a trait  kernel). FastKAST combines a low-dimensional approximation to the kernel function21) but no nonlinear dependencies, we find that FastKAST provides calibrated p values. On small-scale datasets that permit exact computation, FastKAST is highly concordant with exact tests. To illustrate its utility, we applied FastKAST to 53 quantitative traits measured across N ≈ 300K unrelated white British individuals in the UK Biobank (UKBB). Performing a genome-wide scan of nonlinear effects of genotypes measured on common SNPs with MAF ≥ 0.01 on the UKBB SNP array grouped into non-overlapping 100 kb windows, we found 75 windows with statistically significant nonlinear effects across 25 traits  and a phenotype. The vector of phenotypes y, measured on N individuals, is modeled as:FastKAST tests for nonlinear effects between genotypes measured on a set of X denotes fixed effects. K is a N × N kernel matrix obtained by applying a kernel function k to every pair of genotypes over the M SNPs to be tested, i.e., entry  in the matrix K, Ki,j = k where zi (zj) denotes the genotype of individual i (j). Here 11. While p values for the score test can be computed efficiently when testing linear effects (as implemented in the SKAT software11), these approaches are computationally impractical for testing nonlinear effects in large samples.Testing for a genetic contribution in this model involves testing the null hypothesis: 17 where the number of random features D (termed the approximation dimension) determines the quality of the approximation. Combining the idea that an approximation dimension D substantially smaller than the sample size N is sufficient for approximating the kernel function with efficient linear algebra implementations allows FastKAST to efficiently compute p values. While these p value computations assume that the kernel hyperparameters are known , the more common setting is one in which the hyperparameter is unknown. In this more general setting (which is the setting that we focus on in this work), FastKAST adaptively selects the hyperparameter and obtains calibrated p values by fitting a distribution to genome-wide statistics18 (see Methods for details).FastKAST approximates the kernel function by transforming the input genotypes to a randomized feature spaceN = 337,205 individuals and M = 593,300 SNPs on the UK Biobank Axiom array; see Methods for details on the dataset). We performed simulations under four genetic architectures: infinitesimal model , where causal variant ratio refers to the proportion of variants that are causal to the outcome trait; non-infinitesimal model  with a different range of minor allele frequencies (MAF) for the causal variants:  (RARE), [0.05–0.5] (COMMON),  (ALL). The trait heritability was set to h2 = 0.50 in all settings.To assess the calibration of FastKAST, we performed simulations of quantitative traits with linear additive effects but no nonlinear effects. We simulated phenotypes based on whole-genome genotypes from unrelated white British individuals in the UK Biobank (UKBB)  across SNPs  kernel in non-overlapping 100 kb windows to a sub-sample of N = 50,000 individuals with phenotypes simulated above. We approximated the RBF kernel with approximation dimension p values obtained by FastKAST to an exact test. In the first set of experiments, we analyzed the correlation in p values between an exact test using the RBF kernel with hyperparameter γ = 0.1 and the approximate kernel used by FastKAST in a simulation with causal variant ratio = 0.001 with h2 = 0.5. We limited our sample size to 8000 individuals due to the limitations of computing the exact kernel. Since the approximation accuracy depends on the approximation dimension D, we explored the correlation between exact test p values and FastKAST p values by varying D. We found that values of D ≥ 50M, where M is the number of SNPs in the set, resulted in consistently high correlation (≥0.9)  with FastKAST (D = 50M) on two real traits: Body mass index (BMI) and blood Mean Platelet Volume (MPV). Applying both tests to assess nonlinear effects within 100 kb windows across 5000 unrelated white British individuals, p values obtained by FastKAST are highly correlated with those obtained by the exact test , the kernel variance component D  and D = 50M. For each setting , we randomly subsampled N individuals from UKBB and M consecutive SNPs and reported the average runtime across 100 runs (10 replicates for sample sizes larger than 30K).We compared the runtime of FastKAST to the exact test with increasing sample size with the number of SNPs set to N = 50K , FastKAST requires less than 5 min to analyze a single set . We also found that the runtime of FastKAST scales quadratically as a function of the number of SNPs and approximation dimension, so that FastKAST is best suited for analyzing relatively small sets of SNPs . In the second stage, all the trait-set pairs were tested using a larger approximation dimension D = 50M, and only the trait-set pairs that are significant after Bonferroni correction for both the number of traits and sets tested  to test for nonlinear effects using the RBF kernel and each of 53 quantitative traits (see Methods for details on data processing). For each window tested, we regressed out the linear effect of genotypes using a superwindow of size five. We included sex, age, and the top 20 genetic principal components (PCs) as covariates in all our analyses. We adopted a two-stage testing strategy. In the first stage, we used a small approximation dimension p < 3.27 × 10−8) for 25 traits ” in Supplementary Table We performed additional analyses to investigate the nature of the nonlinear effects at these loci. First, we repeated our analysis by regressing out linear and quadratic effects and repeated the test using FastKAST  in men and women using FastKAST. We obtain a p value of 6.8 × 10−4 in men and 5.2 × 10−7 in women even though the number of men and women is comparable in our analyses . Overall, these results suggest that many of the loci that we detect as showing strong evidence of nonlinear effects harbor variants with significant marginal additive effects.Many of the regions with significant epistatic signals have been detected in previous association studies that typically focus on linear additive effects. The locus associated with MPV (12:122.3-122.4 Mb) overlaps the gene α = 0.05/, where 53 is the number of traits tested. In the first experiment, we aimed to compare the tests for nonlinear effects as realized in FastKAST to a test for linear effects implemented in SKAT11. We applied FastKAST to windows defined by protein-coding genes. We also tested the same regions using SKAT with its default settings. FastKAST detected 48 trait-gene pairs as significant, with 35/48 regions overlapping with the windows detected using the genome-wide scan. Among the 48 significant trait-gene pairs, nine were not detected as statistically significant when analyzed using SKAT  on the UKBB genotyping array grouped into non-overlapping 100 kb windows and 53 quantitative traits measured across ≈300K unrelated white British individuals in UKBB, we discovered 75 nonlinear associations across 25 traits. We additionally analyzed these associations after regressing out pairwise interactions and on imputed genotypes in UKBB to find eight associations that remain significant for Alkaline phosphatase, Lipoprotein-A, and Urate. We also applied FastKAST to the UKBB array SNPs grouped into protein-coding genes to detect 48 significant trait-gene pairs of which 35 associations overlapped with the associations detected in our genome-wide scan. In this setting, we also compared the results of FastKAST to those from the linear model underlying SKAT to find that 9/48 significant trait-gene pairs were not detected by SKAT. Finally, we compared FastKAST to SKAT in a general set-based association test setting that aims to detect either a linear or a non-linear association at a set of genetic variants and found 7522 trait gene-pairs that were detected as significant by FastKAST but not by SKAT while SKAT detected 421 trait-gene pairs that were missed by FastKAST.13. We leave a systematic evaluation of this extension to future work. Second, nonlinear interactions are represented in FastKAST using the class of shift-invariant kernels (which include the widely-used RBF kernel). In this work, all the experiments utilized the RBF kernel due to its popularity. FastKAST has the potential to be extended for a wider class of kernels (including kernels that are not shift-invariant) using other randomized approximations, e.g., Nyström kernel approximation35. For example, polynomial kernels might provide more interpretable insights into the basis of epistasis. In general, the optimal kernel remains unknown due to our limited understanding of the nature of epistasis. Indeed, the type of kernel that is appropriate is likely to depend on the trait and the set of genetic variants analyzed. We leave a more detailed exploration of alternative kernels and approximations for future work. Third, our results are localized to fairly broad windows of size 100 kb. While the application to disjoint windows of size 100 kb was motivated by computational and statistical considerations, we can apply FastKAST to other choices of windows. We have provided an alternative approach to define windows based on protein-coding genes annotation that can lead to more interpretable signals of epistasis. While the choice of windows could affect power when the underlying interaction effects are not confined to the window, we emphasize that FastKAST is consistently calibrated across all the null settings leading to high confidence in our signals. Fourth, we used only unrelated white British individuals across all our analyses. Analysis of related individuals or multiple ancestries will need to account for the possibility of population stratification . Further information from identity-by-descent (IBD), in addition to genetic ancestry, may be needed in these settings, which we leave for future work. Finally, we note that though we have shown strong evidence for the potential existence of higher-order feature interactions, our results must be interpreted with caution. The interpretation of genetic interactions is conditioned on the number and quality of SNPs analyzed. It has been shown that apparent interactions in the data can be explained by linearity with missing SNPs36. We have attempted to address this issue by replicating the loci discovered on the imputed genotypes in UKBB. While the imputed genotypes contain the vast majority of SNPs with minor allele frequency >1%, it is likely to be missing low-frequency SNPs. The availability of whole-exome and whole-genome sequencing data in the UK Biobank (and other biobanks) will allow a more thorough investigation of these effects.We end with a discussion of the limitations of our approach and directions for future work. First, FastKAST is designed to analyze quantitative traits. FastKAST could potentially be extended to binary traits using a generalized linear mixed model with a logistic link functiony denote the vector of phenotypes measured on N individuals and Z denote the design matrix of genotypes over M SNPs that are desired to be tested. The goal is to test for association between the set of M SNPs and the phenotype.Let y, as:We model the distribution of phenotypes, M SNPs, and Here The above model assumes that the genotype has a linear and additive effect on phenotype. To model nonlinear effects, we transform the genotype using a nonlinear function Φ is the design matrix obtained by applying ϕ(z) to each individual genotype z. ϕ(z) is assumed to lie in a Hilbert space endowed with a reproducing kernel function k37. Equivalently, we can write this model as:Here K is the N × N kernel matrix where Ki,j = k, i, j ∈ {1, …, N}. For example, a common kernel is the radial basis function (RBF) kernel: Here 11. Under the null hypothesis, the score statistic PKP and 39 have characterized the sampling distribution of the score statistic in finite samples enabling the computation of exact p values for the score test.Testing for a genetic contribution to the phenotype in Equation  involvesp values for the score statistic is the computation of all the eigenvalues of PKP. If we want to compute the p values for the exact score test, we need to construct the kernel , permit efficient computation. However, these approaches are not applicable to kernels that model general nonlinear effects (like the RBF kernel), so that the computational complexity of testing for such effects scales as Weighted linear kernels, 17. For the class of shift-invariant kernel functions f) that include the popular RBF kernel, the kernel function can be approximated by projecting each input z onto a random direction ω drawn from the Fourier transform of k. Specifically, we approximate D denotes the number of random features (which we term the approximation dimension), p(ω) denotes the Fourier transform of k, γ = 1: FastKAST relies on the observation that the kernel function can be approximated by mapping the input features to a randomized low-dimensional feature spaceN × D approximate feature matrix k for a sufficiently large number of features D17 . A key computational advantage of this approximation is that the approximate design matrix Given the P is the projection matrix. We show that, under the null hypothesis, the approximate score statistic is distributed as ρn denotes the nth eigenvalue of the matrix p values for the approximate score statistic p values using FastKAST is We use a score statistic to test the null hypothesis that γ. First, we note that the hypothesis test remains calibrated for any choice of hyperparameter. However, the choice of hyperparameter can influence power. A naive approach to perform hypothesis tests while integrating over choices of the hyperparameter would involve selecting a set of hyperparameter values {γ1, . . . , γH} followed by computation of p values ph for each hyperparameter h (using the process described above). We then choose the minimum p value: p* = min{p1, . . . , pH} as the statistic. If the null hypotheses associated with the H tests are all true, each of the p values is calibrated under the null, and the p values are independent, then it is well-known that p* ~ Beta, where α = 1 and β = H, i.e., the minimum of H independent uniform random variables is distributed as a Beta random variable with density p* by a beta distribution whose parameters we estimate using one of two approaches.α and β. This approach assumes that the null hypothesis is true across most windows.Learn the distribution from observed data. In this approach, we fit a single beta distribution to the observed p-values to learn the parameters Learn the distribution from p-values computed from permuted phenotypes. In this approach, we fit a single beta distribution to the p-values computed on permuted phenotypes across all the windows. This approach relaxes the assumption that the null hypothesis is true across most windows.Applying FastKAST typically requires choosing a value for the kernel hyperparameter We adopted the first approach for all the tests of epistasis on real data as well as in simulations where the signals of epistasis were assumed to be sparse. On the other hand, for the general association test on real data, we adopted the second approach by permuting ten times to generate the null distribution.N = 337,205 unrelated white British individuals measured at M = 593,300 common SNPs (MAF > 1%) genotyped on the UK Biobank Axiom array to use in simulations by extracting individuals that are >3rd-degree relatives and excluding individuals with putative sex chromosome aneuploidy. This dataset was used for all simulations except for Supplementary Table We obtained a set of Ps MAF > % genotyp−7 were removed. We restricted our study to self-reported British white ancestry individuals, which are >3rd-degree relatives that is defined as pairs of individuals with kinship coefficient <1/2(9/2)40. Furthermore, we removed individuals who are outliers for genotype heterozygosity and/or missingness. Finally, we obtained a set of N = 291,273 individuals and M = 459,792 SNPs to use in the real data analyses. We further excluded the MHC region in all our analyses (chr6: 25–35 Mb). For our analysis of fixed 100 kb windows, the number of SNPs per window has a mean of 17.5, a median of 16, and a range between 3 and 199. For our analysis of protein-coding genes, the distribution of the number of SNPs per gene has a mean of 15.6, a median of 7, and a range between 3 and 916. For both analyses, windows with SNPs number smaller than 3 were excluded from our analyses.For analysis of real traits, we restricted our analysis to SNPs that were presented in the UK Biobank Axiom array used to genotype the UK Biobank. SNPs with greater than 1% missingness and minor allele frequency smaller than 1% were removed. Moreover, SNPs that fail the Hardy–Weinberg test at significance threshold 10N = 291,273 unrelated white British individuals. We removed SNPs with greater than 1% missingness, minor allele frequency smaller than 1%, SNPs that fail the Hardy–Weinberg test at significance threshold 10−7, as well as SNPs that lie within the MHC region (Chr6: 25–35 Mb) to obtain 4,824,392 SNPs.We also analyzed imputed genotypes across We selected 53 quantitative traits in the UKBB, which we processed using inverse rank-normalization. We included sex, age, and the top 20 genetic principal components (PCs) as covariates in our analysis for all phenotypes. We used PCs computed in the UKBB from a superset of 488,295 individuals. Extra covariates were added for diastolic/systolic blood pressure .Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


R) and root mean square errors (RMSEs). Results of PCVs among all the traits show importance of multidimensional traits, as seed volume (22.4%), cardioid-derived area (16.97%), and maximum projection area (14.67%). ANOVA shows a highly significance difference among all accessions. The results of GVF innovatively reflect the connection between genotypic variance and phenotypic traits from parents to offspring. Our results confirmed that extracting multidimensional traits from digital images is a promising high-throughput and cost-efficient pathway that can be included as a valuable approach in genetic variation assessment, and it can provide useful information for genetic improvement, preservation, and evaluation of wheat germplasm.In this paper, a new pathway was proposed to assess the germplasm genetic variation by multidimensional traits of wheat seeds generated from digital images. A machine vision platform was first established to reconstruct wheat germplasm 3D model from omnidirectional image sequences of wheat seeds. Then, multidimensional traits were conducted from the wheat germplasm 3D model, including seed length, width, thickness, surface area, volume, maximum projection area, roundness, and 2 new defined traits called cardioid-derived area and the index of adjustment (J index). To assess genetic variation of wheat germplasm, phenotypic coefficients of variation (PCVs), analysis of variance (ANOVA), clustering, and the defined genetic variation factor (GVF) were calculated using the extracted morphological traits of 15 wheat accessions comprising 13 offspring and 2 parents. The measurement accuracy of 3D reconstruction model is demonstrated by the correlation coefficient ( Germplasm resources represent a critical foundation for crop breeding ,2. The aThe genetic variation in crop germplasm is shaped by both natural genetic drift and human-directed selection, endowing crops with the capacity to adapt to diverse environmental conditions ,7. PhenoPhenomics has made significant strides in the study of genetic variation in crop germplasm in recent years. He et al.  delved iWith the evolution of digital imaging methodologies, phenomics has entered a new phase in the study of genetic variation. Image analysis can be considered a measurement tool, where automated image processing techniques allow for higher throughput, reliability, and repeatability at various scales, ranging from microscopic to field levels. Typically, 2-dimensional (2D) images are used to calculate parameters such as width, length, and area –22, whil3D reconstruction technology, with its capability to capture an expansive range of multidimensional traits, has heralded a new revolution in agricultural breeding research. Methods based on active light, employing tools like x-ray computed tomography (CT) and laser scanners, boast high precision but come at a greater cost and complexity. Studies by Li , Huang eThis research presents a pathway for assessing genetic variation in wheat germplasm using multidimensional traits derived from digital images. The specific objectives were to (a) construct a machine vision platform to acquire images of wheat seeds; (b) perform a 3D reconstruction of wheat seeds within the modeling of the rotational axis, using a voxel reconstruction method that requires only one calibration for high-precision 3D reconstruction; (c) extract multidimensional phenotypic traits from the reconstructed model; and (d) evaluate genetic variation using phenotypic coefficients of variation (PCVs), analysis of variance (ANOVA), and the defined genetic variation factor (GVF). This research aims to provide useful information for the genetic improvement, preservation, and evaluation of wheat germplasm.•Construction of a machine vision platform: Composing with a nozzle to attach wheat seeds and a checkerboard, a high-precision rotation step motor, and a control system to capture images, allowing us to obtain images of the wheat seeds and checkerboard from different angles.•Establishment of a 3D seed model: Composing of 3D model reconstruction of wheat seed, modeling of the rotational axis, and parameter traits extracted from the model.The evaluation of genetic variation in wheat germplasm was comprehensively assessed using a combination of phenotypic coefficient of variation (PCV), variance analysis (ANOVA), clustering, and a newly defined GVF. The validity of these results was contingent upon the accuracy of the extracted phenotypic traits. To obtain multidimensional phenotypic traits of wheat seeds, a phenotyping system utilizing omnidirectional images was developed, as shown in Fig. Fifteen wheat seed varieties were selected for the assessment of genetic variation. The chosen varieties comprise 2 parental strains, Xinmai 26 and Xinong 294, and 13 offspring varieties derived from them. The parental strains, cultivated over several years, are excellent varieties that cover a broad spectrum of seed traits. Their hybrid offspring bear significance for the study of genetic variation. The offspring varieties are divided into 2 batches. The first batch contains 6 varieties derived from a crossbreed between Xinmai 26 and Xinong 294. The second batch consists of 7 varieties, which were obtained by first crossbreeding Xinong 20 and 02Ta, followed by a crossbreed with Xinong 585. A total of 450 wheat seeds, with 30 seeds randomly selected from each variety, were subjected to the experiment. The detailed information of the varieties is shown in Extended Table The assessment of genetic variation was based solely on digital images. Prior to the experiment, 8 to 12 checkerboard images were acquired and utilized to calibrate the camera poses in the system. A 9 × 9 checkerboard was utilized with a corner-to-corner distance of 0.5 mm, and the camera pose calibration was performed only once. During the experiment, omnidirectional image sequences of 450 wheat seeds were acquired at 9-degree intervals, totaling 40 images per seed. The acquired calibrated images and 450 × 40 images of the wheat seeds were analyzed and processed to assess the genetic variation in wheat germplasm. The data from these images served as the sole input for the entire method.To obtain a complete sequence of wheat seed images, a machine vision platform has been constructed that incorporates a precision rotating mechanism and a clever suction device, as shown in Fig. Wheat seeds or a checkerboard were stably adsorbed on the suction nozzle after activating the air pump. The stepper motor drove the suction nozzle to rotate in 9° increments, collecting a total of 40 omnidirectional image sequences of the wheat seed at different angles. The contact surface between the suction nozzle and wheat seed was minimal, ensuring the completeness of the captured images. Before capturing wheat seed images, images of a checkerboard were also obtained for calculating the virtual angle of views. It was ensured that the interval between each rotation was 9° or 4.5°, and 9 checkerboard image sequences were collected. Accordingly, software was designed to automate this process. After fixing the machine vision platform, it was only necessary to capture images once with the checkerboard attached to the suction. Then, the number was input and the first wheat seed was placed onto the machine vision platform. Once it was finished, the next one was placed on. These were all the operations that needed to be performed manually. Each time the nozzle rotated, the CCD camera took a picture and saved it, which was all executed automatically by the software.In order to study the genetic variation more thoroughly in wheat germplasm, it is necessary to comprehensively and multidimensionally characterize the traits of wheat seeds. However, due to the small size of wheat seeds, manual nondestructive measurement methods and image processing-based methods are prone to large errors. Therefore, this study proposes a method to build 3D models of wheat seeds considering the machine vision platform. The method is based on IBVH , which cMATLAB R2018b is used to calculate the virtual view, C++ OpenCV library is used to process digital images, and C++ PCL (Point Cloud Library)  and VTK A method was proposed for building 3D models of wheat seeds using a machine vision platform. The 3D reconstruction process involved 3 main steps: image processing, projection matrix calculation, and face slice reconstruction.First, images obtained from the vision platform were processed using image binarization, background removal, and silhouette extraction to get high-quality contour images of wheat seeds from 40 different viewpoints. Background removal is a crucial step in the contour extraction process. A method was utilized that segments the suction nozzle background by identifying the horizontal intersection line between the suction nozzle and the wheat seeds when the total number of white pixel points in the same row changes more than a certain percentage compared to the previous view. Additionally, an algorithm based on a localized Radon transform  was emplf , dx and dy , uα and vα , and uvs (distortion factor). The rotation matrix R and the translation vector T are used to describe the rigid body transformation relationship between the camera coordinate system and the world coordinate system, forming a 4 × 4 matrix to determine the camera’s pose, which are the external parameters of the camera. These internal and external parameters are then combined to form a 3 × 4 projection matrix P, which represents the geometric relationship between a 3D point in space and its projection to a 2D point in the imaging plane. A calibration method based on the rotation axis model was proposed to calculate the camera’s external parameters.Second, the calculation of the projection matrix, as shown in Eq. 1, was performed. This involves determining the camera’s internal and external parameters using the classical linear camera model (the pinhole model) for the conversion of the world coordinate system to the pixel coordinate system. The camera internal parameters are represented by the matrix K, which includes 5 parameters: lgorithm  was utilCXCYCZCO extracted, the circle centers of space are solved. These circle centers are located on different positions of the rotation axis. The 3D spatial straight line where the set of circle center points is located is fitted, which is the requested rotation axis. In order to obtain more robust calculation results, multiple corner points are used to participate in the estimation.Based on the constructed rotational visual platform, an accurate method for modeling the rotational axis has been designed. In the whole process of virtual view construction, the calculation of camera internal parameters and the establishment of the final projection matrix are the basic steps in the 3D reconstruction process. In the middle, the calculation method of the rotation axis is the key of the experiment, and its accuracy directly affects the accuracy of the reconstruction results. According to the spatial arc coordinates of each corner point in the camera coordinate system iP were set to constitute the data set P, and the circle center O and radius R were obtained by fitting the spatial sphere, that is, to findOi, i = 1, …N. The average value of N is:iO, as shown in Eq. 4.n corresponding to the largest eigenvalue of λ is obtained, namely, the rotation axis.The corner points By referring to the related research on wheat seed phenotypic identification , we deteR2) was employed to reflect the regression relationship between manual and 3D reconstruction measurements, while the root mean square error (RMSE) was used to quantify the errors. In the manual measurements, a vernier caliper was utilized to hold the wheat seeds, providing precise length measurements. However, it should be noted that the measurements for width and thickness may exhibit slight deviations at the millimeter scale.Following the extraction of phenotypic traits, a comparison between manual measurements and 3D reconstruction measurements was conducted. The coefficient of determination  was employed to assess the genetic variation in wheat seeds, using the 3D model derived from images taken at different angles, as shown in Fig. δj(i) is the effective value of the jth individual of the ith germplasm and Pσ is the standard deviation (SD) of phenotypic traits.The coefficient of variation (CV) is a useful metric for quantifying data dispersion, controlling for measurement scale and dimension. In the agricultural sector, the use of phenotypic coefficient of variation (PCV), genetic coefficient of variation (GCV), and environmental coefficient of variation (ECV) is commonplace in the assessment of crop character diversity in response to various factors ,38. WhenTo gain a deeper understanding of genetic variation in multidimensional traits, it is imperative to accurately determine the CV (PCV) for each trait within the germplasm. This process involves calculating the SD of the phenotypic traits and then dividing that value by the average effective value of each sample in the germplasm set. Through this methodology, we can assess the degree to which diversity in each germplasm variety is influenced by elements like genetics and environmental factors. A lower PCV indicates that a trait is relatively stable, with only subtle differences between seeds or varieties. Conversely, when PCV is higher, it signifies that there is a notable variance in trait expression. Such traits are of higher value in genetic research since they can be more effectively associated and analyzed. This foundational step is essential for understanding the genetic variability in wheat and other crops.Statistical measures were calculated for all wheat grain samples from 15 varieties, including the mean, minimum, maximum, SD, and phenotypic CV for nine traits. Following the calculation of SD, PCVs for each trait were computed. These PCVs were then ranked to identify traits exhibiting the greatest variability. Finally, to further analyze the genetic variation of traits based on phenotypic data, violin plots  were draF value, calculated for each ANOVA, and the differences observed between groups.ANOVA and cluster were utilized to analysis genetic variation between different offspring. The ANOVA analysis was used to assess the variation between 2 groups of progeny, including those produced via binary hybridization between Xinmai 26 and Xinong 294, and those resulting from ternary hybridization between Xinong 2002Ta and Xinong 585. Individual ANOVAs were conducted for both within and across germplasm, evaluating the differences among the 6 variants of the first progeny, as well as comparing both the first and second progeny to the parental plants. Analysis focused on the K means, hierarchical, and DBSCAN  were utilized to categorize 390 wheat germplasm into 2 classes. Varieties derived from binary hybridization (Xinmai 26 and Xinong 294) were designated as category 0, while those from ternary hybridization  were classified as category 1. The clustering analysis took place after measuring wheat seed trait parameters using a 3D reconstruction method. The purpose of this analysis was to assess the reliability of the clustering-based variety analysis approach by comparing the outcomes yielded through clustering.Subsequently, clustering was employed to classify the data into distinct groups. Three different clustering methods, namely The final results of the ANOVA and clustering are presented in the form of graphs and charts. The ANOVA is conducted using R programming language for data processing, with the ultimate results presented in tabular format. The outcomes of clustering are visualized through scatter plots generated in 3 different ways, accompanied by histograms that display the various evaluation metrics of the clusters. MATLAB R2018b software is employed for the clustering analysis and plotting, incorporating the Statistics and Machine Learning Toolbox.The calculation of the PCV among parents and offspring, as well as the difference analysis between varieties of parents and offspring, can reflect the genetic variety to a certain extent. However, the changes of phenotypic traits not only include the value of genetic variation but also environmental variation to a large extent. In fact, the calculation of the former cannot exclude the influence of environment on the phenotypic variation. In order to reduce the interference of environmental error variance as much as possible and evaluate the genetic variation of the traits from parent to offspring, a method of calculating genetic coefficient is proposed.Calculating the GVF, which reflects genetic diversity from parent to offspring, assists in understanding trait inheritance and species or population genetic makeup. The complexity of this calculation arises from the influence of both genetic and environmental factors on phenotypic traits. Truncation error estimation helps mitigate the impact of environmental variables.P1 and P2 denoting parent varieties and iF referring to the ith offspring variety resulting from parental breeding.Cumulative mean values of parent varieties are computed, and differences between offspring varieties are determined. The square root of the parent–offspring difference is calculated using the principle of covariance, obtaining the change value of the trait under the response gene’s influence. Dividing the change value by the mathematical expectation value of the parent traits yields the genetic coefficient. This coefficient indicates genetic variation from parent to offspring and the extent to which offspring traits resemble those of the parent. Considering both genetic and environmental factors provides a comprehensive understanding of species or population genetic makeup. Equation 6 presents the genetic coefficient calculation, with Fifteen wheat varieties were employed to reconstruct 3D models, comprising 2 parental and 13 offspring lines. A total of 450 seed samples were collected by randomly selecting 30 seeds from each variety. These samples facilitated the successful reconstruction of the wheat grain’s complete 3D shape and extraction of 9 desired phenotypic traits.The duration was measured across 3 phases of the 3D modeling process: image capturing, 3D modeling, and trait measurement. During image capturing, photographs were taken at intervals of 9 degrees, each followed by a pause of 300 ms to facilitate camera shooting. This phase, which involved manual placement and image capturing of the seeds, took an average of 40 s per seed. 3D reconstruction, facilitated by CUDA on a GTX 1650, allowed the reconstruction of approximately 450 wheat seeds at a voxel resolution of 128 × 128 × 128 within roughly 13 h. During trait measurement, calculation of surface area and volume through meshing required 40 to 60 s per seed, while other traits could be calculated in less than 1 s per seed. Given that these 3 processes can be executed simultaneously on a single computer, the average time for complete trait measurement of wheat seeds was approximately 100 s per seed. The method, which necessitates only a low-cost industrial camera, turntable, and stepper motor, facilitates multidimensional trait measurement of wheat seeds. It presents a significantly more cost-effective solution than active light reconstruction technologies, such as CT and laser scanners, and outperforms CT reconstruction and manual measurement in terms of time efficiency. Further comparison of results can be found in Extended Table To verify the reliability of the experimental results, 120 seed samples from 4 varieties  underwent analysis. Several manually measurable phenotypic traits were assessed and compared to the model-derived values. Out of the 9 traits, only length, thickness, and width could be easily measured manually. An electronic caliper with a precision of 0.01 mm was employed for these measurements. For wheat grain length, the top and bottom of the seed were clamped, yielding a relatively accurate value. Each seed’s length was measured thrice, with the average value recorded. Given the potential for larger inaccuracies in manual measurements of wheat seed thickness and width, RMSEs are used to reflect measurement discrepancies. The seed surface is uneven and the thickness is nonuniform, necessitating the division of each wheat grain into 3 groups. Each group was measured thrice, with the maximum value selected. The average of these 3 measurements provided the final manual measurement result. To effectively compare manual measurements with 3D model results, a scatter plot was constructed and a line was fitted, as depicted in Fig. The RMSE for length, thickness, and width was 0.15, 0.19, and 0.26, respectively, all falling within 0.3, as depicted in Extended Fig. Table Furthermore, regarding the furrow phenotype of the wheat grain, 2 associated traits have been identified: the heart-shaped area and the heart-shaped derivative index. Among the 9 traits, the heart-shaped area’s PCV ranks second, suggesting its potential significance in genetic variation research, while the J index has the smallest PCV, indicating its stability across different grain varieties.Three traits with the highest PCV rankings were selected, and the resulting violin plots are presented. As depicted in Fig. P value less than 0.01, which applied to both within and among germplasm. Nevertheless, the extent of these differences varied, as demonstrated by the F values. Excluding the 3 traits of length, surface area, and volume, F values for the remaining 6 traits were higher among germplasm than within germplasm. Consequently, ANOVA results suggest that variability among different offspring is somewhat greater than within the same offspring. However, these results cannot directly determine the classification of seeds originating from distinct offspring.ANOVA revealed significant differences in both intraspecific and intermediate traits, with interspecific differences being more substantial than intraspecific differences, as displayed in Table K-means clusterer is 70%, as demonstrated in Fig. According to the ANOVA results, various methods can effectively cluster wheat seeds into 2 categories, as illustrated in Fig. The devised GVF quantitatively reflects genetic changes from parent to offspring. The “Genetic variation expressed from multidimensional traits” and “Variance and clustering among diverse offspring” sections demonstrate that seed phenotypic traits can respond to genetic variation to a certain degree, albeit heavily influenced by environmental factors. GVF calculations aim to minimize the impact of environmental errors. GVF values for 9 traits of the second offspring variety, corresponding to the 2 parents, were computed and are presented in Table F1, F2, F7, F4, F5, F3, F6. Accordingly, F1, F2, and F7 exhibit superior genetic variations and can be utilized in agricultural breeding hybrid experiments. Thus, the GVF definition could impact breeding processes.In the “Genetic variation expressed from multidimensional traits” section, the coefficient of phenotypic variation was calculated, and it was hypothesized that multidimensionality might better reflect genetic variation. However, since phenotypic variation encompasses both genetic variation and environmental error, minor environmental errors may be amplified in multidimensional traits. Consequently, it is not possible to directly confirm that top-ranked traits possess larger genetic variations through the coefficient of phenotypic variation. Nevertheless, GVF effectively mitigates the influence of environmental error through straightforward differential analysis, under the assumption of an unchanging environment, and thereby illustrates the relationship between multidimensional phenotypic traits and genetic variation. Results indicate that the average coefficient of genetic variation for the 9 traits of these 7 offspring is as follows: volume, cardioid area, thickness, largest area, surface area, roundness, width, J index, and length. Except for thickness, 2D and 3D trait values remain larger. This outcome provides stronger evidence that the 3D model better represents and evaluates genetic variation. Finally, the average GVFs corresponding to all traits of 7 varieties were calculated. The ranked GVFs for each variety, from largest to smallest, are In recent years, 3D reconstruction methods, such as SFM- and MVS-based algorithms, have gained popularity due to their reliance on multi-view feature extraction and matching –42. HoweHowever, it all became easier when a set of adsorption, rotation, and image capture platforms for wheat seeds was built. With the platform completely fixed, it was only necessary to capture a set of calibration chessboard images, eliminating the need for additional work. A custom rotation model based on platform rotation was designed, ensuring accurate calibration. A critical aspect of the 3D reconstruction process is the fitting of the rotation axis, as illustrated in Fig. It is well established that phenotypic variance can be decomposed into genetic variance and environmental error variance. The goal of this study is to obtain a concise formula that captures a factor of genetic variance associated with the presence of parent and offspring while excluding environmental error variance. By applying an engineering treatment of truncation error, the mean phenotypic variance of the 2 parents was calculated and subsequently subtracted from the phenotypic variance of the offspring. The resulting value represents the difference that can be observed from parents to offspring. To eliminate the effects of measurement units, the result was further divided by the mean value of the 2 parents.Existing parameters that respond to genetic characteristics, such as heritability and combining ability, are available but often require integration with molecular marker techniques for analyzing genotypically distinctive features ,48. In oWheat seeds are small, and their phenotypic traits are not easily accessible, resulting in limited measurable traits through manual methods. Traditionally, grain traits were assessed by measuring protein content after crushing, which is a destructive and irreversible measurement. In recent years, valid traits have been obtained through spectroscopic analysis, though these methods entail high costs and require extensive analysis or training of spectral data ,50. In cR value for length  and the RMSE for length, width, and thickness hold referential significance. The results corroborate the feasibility of the 3D reconstruction model. In the future, more precise yet time-consuming and costly 3D measurement methods, such as CT scanning, can be used for accurate evaluation of the multidimensional traits of wheat seeds, thereby serving as a basis for comparison with the model outcomes developed in this study. It is believed that multidimensional traits will play an increasingly prominent role in the assessment of seed genetic variation.Undoubtedly, the accuracy of multidimensional traits measurement is directly related to the assessment of genetic variation. Nonetheless, due to the difficulty in measuring phenotypic traits of wheat seeds, the accuracy assessment of the model poses a challenge. In this study, manual measurements of length, width, and thickness were employed to evaluate model precision. Given the substantial error associated with manual measurements, only the A reference pathway was presented that uses image-based 3D reconstruction for multidimensional traits measurement and genetic variation assessment with 40 wheat seed image sequences and less than 12 checkerboard images. Rotary axis calibration algorithm was used for seed 3D reconstruction, and 9 traits including length, width, thickness, roundness, surface area, volume, projection area, cardioid area, and J index, were extracted from the 3D model. For accuracy assessment, the correlation coefficient of length is 0.91, and the RMSEs of length, width, and thickness are all less than 0.3 mm. For genetic variation assessment, PCVs among all the traits show significance of multidimensional traits, as seed volume (22.4%), cardioid-derived area (16.97%), and maximum projection area (14.67%). ANOVA shows a highly significance difference among all accessions. The results of GVF innovatively reflect the connection between genotypic variance and phenotypic traits from parents to offspring. These results demonstrate the feasibility of image-based reconstruction for measuring multidimensional traits and assessing genetic variation for wheat seeds without any manual intervention or environmental error. Future studies can apply image-based 3D reconstruction algorithms to genetic variation analysis of other crops and traits, and combine them with genotyping studies to better serve agricultural breeding.