Zea Mays) is one of the world’s most important crops. Hybrid maize lines resulted a major improvement in corn production in the previous and current centuries. Understanding the genetic mechanisms of the corn production associated traits greatly facilitate the development of superior hybrid varieties.Maize (log10P > 5), with an estimated total heritability of 37.31–62.34%, while large contributions to variations was due to dominance, dominance-related epistasis, and environmental interaction effects  population were analyzed using a full genetic model, and further, optimal genotype combinations and total genetic effects of current best lines, superior lines, and superior hybrids were predicted for each of the traits at four different locations. The analysis identified 21–34 highly significant SNPs (−Predictions of genetic breeding values showed that different genotype combinations in different geographical regions may be better, and hybrid-line variety breeding with homozygote and heterozygote genotype combinations may have a greater potential to improve ear traits.The online version contains supplementary material available at 10.1186/s12870-022-03913-1. The indigenous peoples of southern Mexico were the first to domesticate maize about 10,000 years ago, which has since become a staple food in many parts of the world . Maize iQTXNetwork  could provide insight for crop improvement along with the optimum homozygous genotypes  combination. Total genetic effect of the predicted SL had ear rank number 4.80, which is mostly like the existing BL (Z016E0164), suggesting that using only homozygous genotypes combination would have very little scope for further improvement. Difference between existing line Z016E0164 and SH was due to the genotypes of nine highly significant SNPs, whereas genotypes of four SNPs  had heterozygote for SH. For ear row number, the total genetic effect of the non-B73 allele homozygous (QQ) combinations was − 0.48, which varied − 0.38 ~ − 0.65 in four different locations. For ear row number existing line Z019E0115 revealed as the BL across environments and in Aurora. Z026E0166 line identified as BL in two locations, Clayton and Homestead, and Z019E0158 identified as BL in Urbana. Total genetic effects were large for Urbana, Aurora, and Clayton but smaller in Homestead. As similar to other ear traits, the total genetic effect of the SH was larger than existing lines for ear rank number, indicating that further improvement is possible with the optimum homozygous and heterozygous combinations.For ear rank number, overall total genetic effects of the non-B73 allele homozygous (Zea mays) is one of the important cereal crops. Since the release of the B73 reference genome, many GWASs of complex traits of maize have been performed to discover the genetic mechanism of complex traits for further breeding improvement [Maize . SNPs with MAF < 0.05 and call rate < 90% were discarded.The genotype (ZeaGBSv2.3) data was downloaded through CyVerse Discovery Environment (Data Store file path*: /iplant/home/shared/panzea/genotypes/GBS/v23/) and phenotypic data was downloaded from llinated , 36. EarXNetwork . Maize wQTXNetwork for dissecting genetic architecture of maize ear traits. Generalized multi-factor dimensionality reduction (GMDR) method was used to scan 472,469 SNPs by one dimensional (1D) for main effects, two dimensional (2D) and three dimensional (3D) for epistasis interactions using the GMDR-GPU module of QTXNetwork [QTXNetwork was used for association analysis on the detected SNPs. Genetic main effects  and epistasis effects  of SNPs are considered as fixed; environment (e) and gene × environment interaction effects  are considered as random. The phenotypic values of the k-th line in the h-th location (yhk) can be expressed by the following mixed linear full genetic model:μ is the population mean; chk is the cofactor of the model, e.g. principal component for adjusting population structure; ai is the additive effect of the i-th locus with coefficient QQ, 0 for Qq, − 1 for qq); di is the dominance effect of the i-th locus with coefficient Qq, 0 for QQ and qq); aaij, adij, daij, and ddij, are the digenic epistasis effects with coefficients QQ × QQ and qq × qq, − 1 for QQ × qq and qq × QQ, and 0 for others), QQ × Qq, − 1 for qq × Qq, and 0 for others), Qq × QQ, − 1 for Qq × qq, and 0 for others) and Qq ×Qq, and 0 for others); eh is the effect of the h-th location ; aeih is the additive × location interaction effect of the i-th locus in the h-th location with coefficient deih is the dominance × location interaction effect of the i-th locus in the h-th location with coefficient aaeijh, adeijh, daeijh, and ddeijh are the digenic epistasis × location interaction effects in the h-th location with coefficient εhk is the residual effect of the k-th individual in the h-th location. Both principal components adjusted and non-adjusted (base) models were analyzed in this study.Statistical analysis was implemented with XNetwork . SNPs deF-value to control the experiment-wise type I error (α < 0.05). The SNP effects were estimated by using the MCMC (Markov Chain Monte Carlo) algorithm with 20,000 Gibbs sample iterations [P value  was thus calculated for controlling the experiment-wise type I error (PEW < 0.05). More detail about the methodology is available in the supplementary text 1.Henderson method III  was usederations , 40–42. B73 maize genome reference sequence was used to identify putative candidate genes based on SNPs which significantly associated with the four ear traits. Candidate genes corresponding to the maize ear SNPs were collected from the GRAMENE database . The funThe method designing superior line and the superior hybrid was developed by . This apAdditional file 1: Text S1. Details about the statistical models used for analyses. Table S1. Highly significant SNPs identified by using the base model with no G × E effects for four maize ear traits Effect: a = additive effect, d = dominance effect,. aa = additive × additive interaction effect, dd = dominance × dominance interaction effect. SE: standard error of estimated effect/predicted effect. –Log10P: minus log10 , h2: estimated heritability. Bold underlined SNPs are strongly associated with family structure and were not identified in the principal component adjusted model. SNPs written in regular word were detected in both base and principal component adjusted model. Table S2. Highly significant SNPs identified by using the base model with G × E effects for four maize ear traits. Effect: a = additive effect, d = dominance effect, ae1 = additive by environment 1 (Urbana) specific effect, ae2 = additive by environment 2 (Aurora) specific effect, ae3 = additive by environment 3 (Clayton) specific effect, ae4 = additive by environment 4 (Homestead) specific effect. SE: standard error of predicted effect. –Log10P: minus log10 , h2: estimated heritability. Bold underlined SNPs are strongly associated with family structure and were not identified in the principal component adjusted model. SNPs written in regular word were detected in both base and principal component adjusted model. Table S3. Highly significant SNPs identified by using the PC adjusted model for four maize ear traits. Effect: a = additive effect, d = dominance effect, ae1 = additive by environment 1 (Urbana) specific effect, ae2 = additive by environment 2 (Aurora) specific effect, ae3 = additive by environment 3 (Clayton) specific effect, ae4 = additive by environment 4 (Homestead) specific effect. SE: standard error of predicted effect. –Log10P: minus log10 , h2: estimated heritability. Bold underlined SNPs were newly identified in the principal component adjusted models, which were not identified in the base model. SNPs written in regular word were detected in both base and principal component adjusted model. Table S4. Superior lines and hybrids predicted by using full genetic model for four ear traits of maize. GSL = general superior line for four locations, SL (+)1 = superior line for Urbana, SL (+)2 = superior line for Aurora, SL (+)3 = superior line for Clayton, SL (+)4 = superior line for Homestead; GSH = general superior hybrid line for four locations, SH (+)1 = superior hybrid for Urbana, SH (+)2 = superior hybrid for Aurora, SH (+)3 = superior hybrid for Clayton, SH (+)4 = superior hybrid four Homestead; (+) = positive genotypic value. Fig. S1. Tree map of gene ontology terms of the identified genes. Tree map was plotted using the generated R-script from Revigo. Different child terms were clustered into several parents’ gene ontology terms. Fig. S2. Expression data of the identified genes in Ear and Tassel retrieved from Maize inflorescence database. Tip of the ear (ear_tip), middle of the ear (ear_mid), base of the ear (ear_base), tassel at stage 1 (tassel_stg1), tassel at stage 2 (tassel_stg2), and tassel at stage 3 (tassel_stg3) from experiments in ear and tassel development series; wild type ear at 2 mm (wt_2mm_ear) from experiments in fascinated ear (fea4); and wild type ear 2–5 mm from experiments in knotted1. (A) Expression of a set of identified genes in Ear. We plotted heat map based on expression values of the genes with continuous color scale, where white color represents low expression, yellow represent mid-level expression and red color represents high expression And (B) Expression of a set of identified genes in Tassel. Here different color had same meaning as Fig. A.


Disclosure of markers that are significantly associated with plant traits can help develop new varieties with desirable properties. This study determined the genome-wide associations based on DArTseq markers for six agronomic traits assessed in eight environments for wheat. Moreover, the association study for heterosis and analysis of the effects of markers grouped by linkage disequilibrium were performed based on mean values over all experiments. All results were validated using data from post-registration trials. GWAS revealed 1273 single nucleotide polymorphisms with biologically significant effects. Most polymorphisms were predicted to be modifiers of protein translation, with only two having a more pronounced effect. Markers significantly associated with the considered set of features were clustered within chromosomes based on linkage disequilibrium in 327 LD blocks. A GWAS for heterosis revealed 1261 markers with significant effects. Triticum aestivum L.) is an important source of calories and proteins for humans worldwide [Wheat  becauseorldwide ,7,8. Mororldwide .The availability of high-throughput genotyping techniques, such as genotyping by sequencing (GBS) or single nucleotide polymorphism (SNP) arrays, has accelerated global genetic analyses of large genome species, such as wheat ,12,13,14In addition to the agronomic performance of related traits, the condition of heterosis breeding success is the appropriate flowering biology of the parental components. Different elements of flowering biology determine the suitability of male and female wheat parents for hybrid breeding. Efficient anther extrusion and a high quantity of released pollen over an extended period are considered the most important traits desired in male candidates for the successful production of hybrid wheat seeds. For female parents as pollen recipients, more significant is the ability to open flowers in the time necessary to get pollinated for extended periods, coupled with hairy stigmas. Considering the plant height, it is recommended that the pollen parent be taller than the seed parent because the pollen of wheat is much less mobile than the pollen of typical wind-pollinated plants such as maize and rye ,21,22,23Despite several studies, the processes of flower opening and anther extrusion, a very complex and dynamic phenomenon combining anatomical, physiological, and biochemical parameters, are still not fully understood or defined ,25,26. NIn the presented work, we use the data presented in , which wTo verify this presumption, we set the following objectives: (1) to apply the genotyping data  consistip-value < 0.05; Six phenotypic traits were assessed in eight environments. The distributions of genotypic means . The variance components for random effects of genotypes (G) were much larger than those for G × Y and G × L interactions for traits HT, FT, and PH, which was reflected by the large heritability for these traits , localization (L), and Y × L interaction, were significant . The characteristics of the allelic substitution effects for these loci are shown in GWAS revealed 7603 SNPs with polymorphisms significantly associated with at least one phenotypic trait  with other SNPs in the region ±5 Mb was determined for significant SNPs. A detailed analysis of LD has been provided in  a heatm. The sigThe fraction of associations showing interaction with the environment was the lowest for PH and KN and the highest for KW. Associations were unevenly distributed in the wheat subgenomes. Most of the associated SNPs mapped to the A and B subgenomes , whereas only 14.14% were derived from D, and 2.44% remained unmapped ; howeverAllelic substitution effects for different traits were correlated . HoweverSNPs associated with traits were divided into three sets corresponding to plant phenology , PH (set 2), and kernel properties , with the numbers of associations in these sets being 592, 391, and 429, respectively. There were 26, 99, and 26 SNPs common to sets 1 and 2, 1 and 3, and 2 and 3, respectively, and the 12 SNPs common for all three sets . For paiOf the 26 markers that belonged to sets 1 and 2, 17 were assigned to genes, with 5 being modifiers and 4 substitutions having moderate effects . There wClusters of markers significantly associated with HT, FT (set 1), and with PH (set 2)  were conp-value < 0.05) revealed 1261 SNPs with significant effects , (PH),  based on heterosis effects contained 480, 324, and 83 markers, respectively. The latter (yield-related) set contained 52 markers assigned to genes; the heterosis effects in this set were: from −4.50 to 3.09 grains for KN, from −0.12 to 0.09 g for KW, and from −2.09 to 4.13 g for TKW. The highest negative effect for KN (−4.50 grains) was for marker 3024735|F|0-10|GA (TraesCS7B02G481400).The correlations of heterosis effects were similar to those of additive effects .Allelic effects were correlated with heterosis effects for markers with high heterozygosity . The ranOne marker, 1238701|F|0-16|GA (TraesCS2D02G127300), belonged to sets 1 and 2 with respect to additive effects , and to set 3 with respect to heterosis effects (effect 2.25 for TKW).GO terms  represented in sets of genes assigned to SNPs in association sets 1, 2, and 3 for allelic effects and heterosis effects are shown in p-value < 0.001; p-value < 0.001; Data from post-registration trials (PRT) were used to validate the GWAS results obtained in the HYBRE experiments. The general varietal means of HT, PH, and TKW from the two series of experiments were correlated  showed that, although a given genotype may be subjected to various degrees of environmental variance for various traits, some correlation exists among instability variances for traits related to hybrid component selection.However, our association analysis was performed assuming that SNP variant effects can also interact with environmental conditions. This aspect of GWAS analysis is often addressed by performing separate analyses for each environment cf. ,33,34), ,34, 33,3Validation of GWAS results can be done by an independent experimental study concerning another pool of genotypes. In our case, the pool covers most of the accessions that are practically interesting for project stakeholders. Another form of validation can be based on a real breeding process; this has been started by passing our results to breeders, who have already performed selected crosses and are currently assessing the value of hybrids by their standard procedures. In this report, to verify the results of GWAS, publicly available data from independent, post-registration trials performed in a wider set of environments were used. The mean BLUPs for genotypes from the HYBRE experiments were correlated with the general means from the PRT. Moreover, substantial correlations between allelic substitution effects obtained from GWAS on both datasets were obtained; the same was true for heterosis effects. The effects concerning plant height were found to be the most correlated. This means that the data obtained in the HYBRE experiment are representative, and it can be assumed that new breeding creations can be evaluated in limited field experiments rather than in large experimental systems.The expected female component of the hybrid should contain long stigmatic hairs that are fully extruded and receptive for long periods . Wheat sMarkers associated with flowering time are necessary to synchronize the flowering of hybrid wheat components. Eight QTLs for heading time have been reported . One of Searching Ensembl Plants for wheat orthologs of 204 Arabidopsis thaliana genes related to flowering  resultedSome Rht loci have been suggested to negatively affect anther extrusion ,45. The QTLs and candidate genes for PH were collected from the catalog of gene symbols for wheat  with upd. We founInformation on known genes responsible for wheat PH was used to search for homologous and paralogous genes (with identity to target > 50%). Sequences  corresponding to gibberellic acid insensitive (GAI) Rht-A1, Rht-B1, and Rht-D1 were mapped to the 4AL, 4BS, and 4DS chromosome arms ,55. ThesThe remaining Rht genes were sensitive to GA. Two known genes from this group are GA2-β-dioxygenase (GA2oxA9) and AP2-D (Q gene), which correspond to Rht18 and Rht23 loci, respectively ,56. Two We identified 224 genes (containing 313 SNPs) assigned to DNA sequences related to PH using the text search in the description of genes by GO terms and Interpro features for the texts “gibberellin,” “auxin,” “cytochrome,” “kaurene,” “kaurenoic,” and “DELLA.” Most detected hits were for “cytochrome,” as in . Of thesThe positions of significant SNPs for grain weight, number per spike, and TKW were compared with those reported in previous studies . MaintaiAmong the identified polymorphisms, two SNPs had high translational effects. The first identified polymorphism, 1090593|F|0-44|CT, was associated with TKW and located in the gene TraesCS4B02G086500, annotated with the GO term “polygalacturonase activity”. Polygalacturonases are hydrolyzing enzymes implicated in a wide range of plant developmental processes, such as cell elongation, organ abscission, fruit ripening, microspore release, and pollen tube growth ,64. MembThe second SNP (1130302|F|0-44|TG) was located in gene TraesCS6A02G085100 (Arabidopsis RPT3 ortholog) with a high translational effect and annotated with the GO term “protein ubiquitination” and was associated with FT. Protein ubiquitination is a sophisticated system of post-translational modification in all eukaryotes and has been demonstrated to play a key role in various plant developmental stages and processes, such as seed dormancy and germination, root growth, flowering time control, self-incompatibility, chloroplast development, and several abiotic stress responses . The SNPThe study was conducted using 509 wheat varieties and breeding lines. A set of 277 European varieties, registered mainly in Germany, Poland, and the United Kingdom, was used. Advanced breeding lines were represented by 232 accessions from the ongoing programs of the Plant Breeding Strzelce (STH) and Poznań Plant Breeding (PHR) companies. The genetic characteristics of the studied resources were provided by Tyrka et al. .2. Cultivation conditions in brief: Sowing rate: 250 kernels per m2. Fertilization: 45 kg ha−1 of P2O5 and 80 kg ha−1 of K2O prior sawing followed by 150 kg of N per hectare applied in 2 doses during the vegetation season. Plant protection: only herbicides and insecticides were applied (no treatments against fungi and lodging). The following traits were analyzed in the field experiments:Field experiments were conducted during two vegetation seasons, 2017/18 and 2018/19. Trials were established at four experimental stations of two breeding companies (STH and PHR) located in Strzelce , Kończewice , Nagradowice , and Leszno/Antoniny . Two replications of the studied objects were performed at each location. They were distributed within three randomized blocks. Each plot had an area of 1 mTime of heading (GS55)—HT (number of days since May 1)Time of flowering (GS65)—FT (number of days since May 1)Plant height—PH (average height of plants on a plot in cm)Number of kernels per spike—KN (assessed on 10 randomly collected spikes in each plot)Weight of kernels per spike—KW Thousand kernel weight—TKW www.coboru.gov.pl, accessed on 23 June 2019 [To validate the results obtained from the HYBRE experiments, publicly available data from Polish state post-registration trials (une 2019 ) from 20A detailed description of genotyping and genotypic data processing was provided by Tyrka et al. . Brieflyp-values for allelic substitution effects and heterosis effects were corrected for multiple testing using the Benjamini–Hochberg (BH) method. Only SNP data with more than five accessions present in both homozygous classes were used during the genome-wide association analyses. An SNP effect was considered statistically significant if the BH-corrected p-value was lower than 0.05.Phenotypic data were analyzed using a linear mixed model (LMM) with fixed effects of the year (Y), location (L), Y × L interaction, and random effects of genotypes (G), G × Y interaction, and G × L interaction. Broad-sense heritability was estimated by the method described by Cullis et al. . The addStatistical analyses were performed using Genstat for Windows 19th edition . VisualiIn conclusion, by employing an appropriate experimental and statistical approach, we generated a set of SNP markers that can be used in breeding practice to predict the earliness and height of plants to assess whether a given genotype will be particularly good as a maternal (early and short plant) or paternal form . The estimated heritability of phenological traits and plant height was relatively high; therefore, selection based on the markers indicated during this study may be successful. In contrast, the heritability of yield-related traits in our field trials was relatively low; nevertheless, it remained within the range reported by other authors ,83,84,85The successful parallel selection of homozygous parental genotypes (based on traits regulated by additive genes controlling phenology and plant height) and components revealing a high heterosis effect  using GWAS.Demonstrating that the application of clustered markers for the choice of genotypes in multi-feature processes may be more efficient than classic selection based on single marker polymorphism (SNP)Validation of the GWAS results using post-registration trial data.The main achievements of the presented work are:


A major challenge to enabling precision health at a global scale is the bias between those who enroll in state sponsored genomic research and those suffering from chronic disease. More than 30 million people have been genotyped by direct-to-consumer (DTC) companies such as 23andMe, Ancestry DNA, and MyHeritage, providing a potential mechanism for democratizing access to medical interventions and thus catalyzing improvements in patient outcomes as the cost of data acquisition drops. However, much of these data are sequestered in the initial provider network, without the ability for the scientific community to either access or validate. Here, we present a novel geno-pheno platform that integrates heterogeneous data sources and applies learnings to common chronic disease conditions including Type 2 diabetes (T2D) and hypertension.We collected genotyped data from a novel DTC platform where participants upload their genotype data files and were invited to answer general health questionnaires regarding cardiometabolic traits over a period of 6 months. Quality control, imputation, and genome-wide association studies were performed on this dataset, and polygenic risk scores were built in a case–control setting using the BASIL algorithm.N = 4,550  who reported being affected or previously affected for T2D and N = 4,528  for hypertension. We identified 164 out of 272 variants showing identical effect direction to previously reported genome-significant findings in Europeans. Performance metric of the PRS models was AUC = 0.68, which is comparable to previously published PRS models obtained with larger datasets including clinical biomarkers.We collected data on DTC platforms have the potential of inverting research models of genome sequencing and phenotypic data acquisition. Quality control (QC) mechanisms proved to successfully enable traditional GWAS and PRS analyses. The direct participation of individuals has shown the potential to generate rich datasets enabling the creation of PRS cardiometabolic models. More importantly, federated learning of PRS from reuse of DTC data provides a mechanism for scaling precision health care delivery beyond the small number of countries who can afford to finance these efforts directly.The genetics of T2D and hypertension have been studied extensively in controlled datasets, and various polygenic risk scores (PRS) have been developed. We developed predictive tools for both phenotypes trained with heterogeneous genotypic and phenotypic data generated outside of the clinical environment and show that our methods can recapitulate prior findings with fidelity. From these observations, we conclude that it is possible to leverage DTC genetic repositories to identify individuals at risk of debilitating diseases based on their unique genetic landscape so that informed, timely clinical interventions can be incorporated.The online version contains supplementary material available at 10.1186/s40246-022-00406-y. Early diagnosis and prevention of chronic modern diseases, including type 2 diabetes (T2D) and hypertension, have the potential to make a significant impact in patient outcomes. However, the Centers for Disease Control (CDC) estimated that over 20% of T2D cases are undiagnosed  and thatThe World Health Organization (WHO) reports a sustained increase in diabetes mellitus, with projections increasing to 3% of the world population by 2030, becoming the seventh leading cause of death globally . A sedenThe overlap between T2D and hypertension is common among the population . HyperteGenetics of T2D has been extensively studied –15, withDirect to consumer platforms are novel sources of information that have expanded quickly during the past decade. The earliest example in 2010 was the use of web-based self-reported questionnaires with complementary genetic testing, leading to the creation of a research database  which haThe rapid development of polygenic risk scores (PRS) in recent years stresses the importance of accurately assessing the ancestry makeup of participants in biomedical studies to avoid potential selection biases . PRS repEven though the need for ancestry-focused research has been highlighted by many , 47, theFurthermore, the validation of a DTC framework for validating and extending PRS provides a cost-effective means of enrolling understudied populations in complex disease genetics as 23andMe has done with their “Roots into the Future” effort. We aim to build on such successes by powering a public–private partnership that is collecting DTC data to be included in the Biobank Meta-analysis Network. The notion that DTC provided a “straight to mobile instead of landlines” opportunity is important to validate as most low- and middle-income countries are considering how to harness advances in genomics for the study of their own populations while building state-sponsored capacity is a fundamental challenge to many efforts.In this case–control retrospective observational study, adult participants from an international genetic platform were invited to self-report their health status and metabolic traits. Their genetic information was also previously uploaded in the same platform, which allowed us to explore their genetic susceptibility and to build polygenic risk scores (PRS) regarding these traits. Finally, we calculated ancestry estimation using Neural ADMIXTURE for all individuals. We were interested in evaluating ancestry-aware polygenic scores for type 2 diabetes and hypertension.https://www.wcgirb.com/) under IRB tracking ID 20,201,332.We used the research database where participants were drawn from Genomelink (genomelink.io) users, which offers a DTC genetic traits platform with more than 500,000 users globally. After uploading their genetic information, generated in other DTC platforms, users can be informed on their susceptibility to an extensive set of genetic traits. All participants created an account and agreed to a consent on the use of their data and legal agreement. Upon signing up, participants were invited to undertake a health online survey. Participants were redirected to the survey once they gave online consent to be a part of the research. The online consent is in compliance with the institutional review board (IRB) at WCG IRB . Individual quality control (QC) includes genotype call rates > 97%, matching between gender identification and chromosomal sex, and no excess ancestry-adjusted heterozygosity. Samples genetically related to other individuals in the cohort and duplicates were detected and removed, by applying the King algorithm . Principal component analysis was performed to identify global ancestry per individual using 1000 genomes as reference population with PLINK 2 [This study includes seven independent genotyping arrays, comprising a total of 12,424 unrelated individuals. Genotype-level data for each array were processed by applying identical quality control and imputation procedures. Briefly, variants with a call rate of < 95% and palindromic markers  were excluded. We performed an exact test for Hardy–Weinberg equilibrium for individuals of the largest ancestral group ( PLINK 2 . FurtherR2 > 0.30) from available datasets. Imputed makers with call rate > 0.95 in the merged data were selected for downstream analysis.Imputation was carried out using 1000 genomes as a reference panel with Beagle . Next, wN = 4,550; N = 4,528, respectively) using an additive genetic model with PLINK 2 (–glm). We include the top ten principal components (PC)s, age, sex, and the genotyping array as covariables in the model. The results were depicted using the qqman package in R.The GWAS was performed for T2D and hypertension phenotypes (The Batch Screening Iterative LASSO (BASIL) algorithm  is a metβ parameter are meant to be 0). This process is repeated until the optimum parameter λ0 is found, which is the one that minimizes (λ0). The BASIL algorithm guarantees to find the exact solution and not only an approximation, via the Karush–Kuhn–Tucker condition  [BASIL solves the Lasso solution path in an iterative fashion, starting with a sequence of candidate parameters. From these candidate solutions, each iteration discards the ones that do not meet the requirements to be a suitable solution. The set of variables who make it into the final set for a viable solution are those who were also screened satisfying a desired threshold requirement, while the others are discarded   which isTo address the confounding factor of population stratification in PRS estimations, various approaches have been taken , 54. HerWe first used descriptive statistics to understand the characteristics of this cohort, including the geographic distribution of participants, age, sex, and comorbidities. This can become useful in future replication studies. We built three PRS models using BASIL, a lasso-based linear model: a) one model included genotype features alone; b) another model used only the covariates of age, sex, and the first ten genetic principal components (PCs); c) and a final (full) model used both genotypes and covariates. We used the first 10 PCs to account for residual population micro-stratification as fixed effects. With the three models, we then calculate their predictive performances, as well as the performance of the full model against the covariate-only model (delta between models).The predictive ability of these PRS models was evaluated using the area under the curve (AUC) receiver operating characteristic (ROC) curves using the pROC package in R . To makeN = 4,550); and 2) 1,027 hypertension cases and 3,501 controls of European ancestry . We tested ~ 8 million variants for T2D and hypertension passing quality control and imputation filters . Both results showed low inflation of test statistics   389 T2D cases and 4,161 controls (p < 0.05) in this dataset. Among them, we identified variants closely associated with genes which have been previously linked to type 2 diabetes susceptibility , as well as variants in the FTO locus linked previously with both BMI and T2D. Overall, we identified 164 out of 272 variants showing identical effect direction to previously reported genome-significant findings in Europeans  was set to match the effect alleles in each study. We observed that the effect sizes of the genome-wide significant variants in the independent GWAS [We validated our GWAS using independent GWAS meta-analysis datasets from Mahajan et al. 2018   and Evanent GWAS , 60 wereOur observations highlight how carefully curated DTC repositories with ever increasing sample sizes and variant diversity can replicate previous findings and hold the potential of delivering enhanced discovery and single-variant resolution of causal T2D and hypertension risk and protection alleles. Additionally, our findings confirm the potential impact of DTC resources on mechanistic insights and clinical translation efforts.PRS models were built for each phenotype using the BASIL algorithm . The preThe European Bioinformatics Institute (EBI) developed the PGS Catalog , which iOur models are comparable to previously published PRS models. Figure In this study we generated PRS for T2D and hypertension from a heterogeneous dataset housing a combination of genetic data and self-reported information from a DTC genetics company. See Additional file Our study tested the possibility of inverting the model regarding genetic and phenotypic data acquisition in a research study. Individuals participating in our study shared their genetic array information from other DTC providers and were invited to take an online survey regarding their general health condition. We found no difference in predictive performance between our trained models that included respondents from all inferred ancestries and those models with respondents from European heritage, due to the fact that 86% of our database was of European origin. The genetics of our PRS models for T2D and hypertension are supported by our ability to replicate known variants from publicly available independent GWAS studies.Multiple array types were available in our database, and imputation across platforms (up-imputing) was necessary to harmonize these diverse datasets. The fact that individuals can self-report their genomic information could potentially corrupt the file being uploaded into our platform. However, applying appropriate quality control (QC) principles proved to successfully enable traditional GWAS and PRS analyses.DTC platforms can offer a wide range of information about personal wellness, ancestry, physical characteristics, and traits. Advances in genomic research have led the DTC genomics industry to flourish and make accurate yet easy to interpret genomic results. Strict privacy policies of many companies disallow them to share customers’ data without their consent. These platforms can serve as informative repositories giving actionable insights that aid traditional clinical approaches. The approach of subject recruitment for various complex phenotypes via online surveys is opening up multiple avenues to complement conventional research and clinical strategies. DTC platforms also provide convenience along with a wider reach to recruit participants from various locations. They surpass barriers of single-point data collection centers to language restrictions thus allowing the aggregation of data from places with different ancestries and demographics. Democratizing the access to these genetic platforms and prediction tools will likely boost progress in precision medicine. In the future, we plan to investigate how federated learning approaches can further improve the possibility to increase the power of studies in DTC genomic analysis, but also how meta-analysis can be done in combination with academic and clinical datasets (including those from large consortiums).We have shown that our DTC platform and research strategy has the potential to replicate the previously reported results with a very fast turnaround time. The participation of individual customers in our platform allowed the generation of a rich dataset that enabled the creation of PRS cardiometabolic models. The comparable predictive performance of our models also is a great indication of how we can quickly contribute more PRS models to the larger scientific community. As it stands right now, publicly available PRS models for T2D and hypertension have an AUC of 0.7 on average as shown in Fig. T2D and hypertension are multifactorial diseases that are impacted by genetic and environmental determinants, including lifestyle factors like nutrition and exercise habits. Nevertheless, the inherent limitation of PRS models to provide accurate disease predictions compels the need to interpret these findings with caution, especially when they come from DTC genetic services. The clinical actionability of PRS models has yet to be determined through pragmatic trials involving real-world data. We hope to provide a novel source of information that can shed light on this important issue. Therefore, providing personalized information about T2D and hypertension predisposition is poised to improve early diagnosis and prevention bringing precision medicine at scale for all.Additional file 1. Survey questionnaire.Additional file 2. Number of variants and Genotyping Call Rate.Additional file 3. Summary statistics for known D2T GWS signals in our dataset.Additional file 4. Predictive performance results by model.Additional file 5. PGS Catalog models for T2D and Hypertension.Additional file 6. PGS Catalog models for T2D and Hypertension.


Potential functional variants (PFVs) can be defined as genetic variants responsible for a given phenotype. Ultimately, these are the best DNA markers for animal breeding and selection, especially for polygenic and complex phenotypes. Herein, we described the identification of PFVs for complex phenotypes  using a systems-biology driven approach based on RNA-seq data from physiologically relevant organs.The systems-biology coupled with deep molecular phenotyping by RNA-seq of liver, muscle, hypothalamus, pituitary, and adrenal glands of animals with high and low feed efficiency (FE) measured by residual feed intake (RFI) identified 2,000,936 uniquely variants. Among them, 9986 variants were significantly associated with FE and only 78 had a high impact on protein expression and were considered as PFVs. A set of 169 significant uniquely variants were expressed in all five organs, however, only 27 variants had a moderate impact and none of them a had high impact on protein expression. These results provide evidence of tissue-specific effects of high-impact PFVs. The PFVs were enriched (FDR < 0.05) for processing and presentation of MHC Class I and II mediated antigens, which are an important part of the adaptive immune response. The experimental validation of these PFVs was demonstrated by the increased prediction accuracy for RFI using the weighted G matrix  obtained in the ssGWAS in comparison to the unweighted G matrix .Here we identified PFVs for FE in beef cattle using a strategy based on systems-biology and deep molecular phenotyping. This approach has great potential to be used in genetic prediction programs, especially for polygenic phenotypes.The online version contains supplementary material available at 10.1186/s12864-022-08958-y. Potential functional variants (PFVs) can be defined as genetic variants responsible for a given phenotype. Ultimately, these are the DNA markers needed for animal breeding and selection specially for polygenic and complex phenotypes . One posFeed efficiency (FE) in beef cattle is one of the most important traits in livestock . While bOur research group was the first to describe a pathophysiological mechanism associated with FE in beef cattle: liver inflammation due to altered metabolism and/or bacterial translocation/infection , which wn = 227,225 unique variants) was used for statistical analysis, in which 4,39% (n = 9986 variants) were significantly associated with FE. Next, we classified the PFVs according to their impact on protein function, in which 20,0% (n = 1995 variants) were classified with moderate impact and only 0.78% (n = 78 variants) with high impact on protein function  first with all the genes carrying the PFVs grouped, disregarding which tissues they came from, and second (ii) by considering the PFVs separately for each tissue. In the first scenario, all enriched terms were related to the processing and presentation of MHC Class I and MHC class II mediated antigens (major histocompatibility complex), which are an essential mechanism of the adaptive immune response. In addition to the innate immunity system enriched terms, vesicle-mediated transport, cell signaling, ubiquitination, double-strand break repair, and nucleotide excision were also reported.The tissue-specific enrichment analysis mainly described terms related to the processing and presentation of MHC Class I and MHC class II antigens, innate immune system, vesicle-mediated transport, cell signaling, ubiquitination, and DNA double-strand break repair. It should be highlighted that the RNA polymerase III transcription pathway was also indicated in the adrenal glands, muscle, hypothalamus, and liver. The simple DNA strand repair pathway was enriched in the muscle and the nucleotide excision pathway was over-represented in the adrenal glands, hypothalamus, and liver tissues , respectively. To carry out the validation and genomic predictions for the validation set, SNP markers adjacent to the PFVs were differentially weighted based on the results obtained with the ssGWAS using the training dataset. The genomic prediction ability for the RFI in the validation dataset when the PFVs information is not included in the analyses is shown in Table The prediction ability for each tissue improved in comparison to the ssGBLUP+wG by adding the information of the PFVs with differentially weighted SNPs Table . The preDetermination of the PFVs of complex phenotypes in livestock species is scarce and imperative. Some research groups have been trying to find the best way to identify PFVs, but they weren’t able to state whether these variants were causal or not and what were their full biological consequences for the phenotype –28. HereThe strategy used in this study consists of two major stages. The first is the identification of the PFVs using a systems biology approach, and the second is their validation through genomic selection. In the first stage, the GATK was used to call the variants: it compares the case RNA sequencing data with the control (bovine reference genome) using powerful filtering and statistical tools. This tool is widely used in several research to identify variants –32, and expression quantitative trait loci (eQTL) mapping can help identify causal variants and also in the distinction between pleiotropic and binding effects [The second stage, on the other hand, involves validating the results obtained in the first stage using the genomic prediction in an independent population by including differential weighting in genomic regions harboring such PFVs on the prediction accuracy and inflation for RFI. The GWAS is generally used to find DNA variants associated with phenotypic variation of complex traits, however, it does not identify whether the variant is causal or not. Studies –39 point effects . It shou effects , 41 and  effects , 24 cattGains in prediction accuracy are expected when widely known candidate regions identified by the GWAS are included and weighted in the prediction models : (i) a tOur analysis also allowed us to perform a functional enrichment analysis encompassing the genes with the PFVs. Over-represented terms for Class I MHC mediated antigen processing and presentation were described for all organs, along with the DNA double-strand break response specifically in the hypothalamus. An overrepresentation of the BOLA family genes and its polymorphisms , JPS.1 , and BOLA-NC1) was found. These genes are mainly involved in the MHCclass I , and BOLA-NC1) and class II . The MHC is a fundamental mechanism of the immune system, which has several functions and the response against infectious diseases is the most important , 47. TheAn increasing number of studies have demonstrated the link between the immune system and FE in different livestock species. In one of our previous studies , the traIn conclusion, the identification of PFVs by a systems biology based on multi-organ deep phenotyping by RNA-seq data increased the accuracy of the prediction for young animals without phenotypic records. The study also identified that variants existent in the liver and muscle have more impact on genomic predictions for young animals, highlighting the importance of these two organs for feed efficiency. The PFVs identified herein were found to be mainly involved in the processing and presentation of MHC class I and II mediated antigens, an important mechanism of the innate immune system. It did not escape our attention that this strategy for detecting PFVs for genetic selection can be used for other livestock species since the main biological pathways of feed efficiency are similar for other species, such as pigs, poultry, and dairy cows.Bos taurus indicus) (16 up to 20 months of age and 376 ± 29 kg BW) were evaluated in a feeding trial which comprised 21 days of adaptation to the feedlot diet followed by a 70-day period of data collection. Total mixed feed was offered ad libitum and daily dry matter intake (DMI) was individually measured. Animals were weighted at the beginning, at the end, and every 2 weeks during the experiment period. Feed efficiency was estimated by residual feed intake (RFI) [All animal protocols were approved by the Institutional Animal Care and Use Committee of Faculty of Food Engineering and Animal Sciences, University of São Paulo (FZEA-USP – protocol number 14.1.636.74.1). All procedures to collect the phenotypes and biological samples were carried out at FZEA-USP . Ninety-eight Nellore bulls (ke (RFI) . Forty ake (RFI) .http://www.bioinformatics.babraham.ac.uk/projects/fastqc/) was used to visualize the sequencing quality. The removal of Poly A/T tails and adapters was carried out using the Seqyclean software , and bases with quality ≥20 and complete reads with at least 50 bp were considered for subsequent analysis. Alignment of the reads was done using the STAR software version 2.7 [Bos taurus ARS-UCD1.2 , allowing two mismatches per read.Samples of nine animals from each FE group (high and low) were selected for RNA-seq using RFI . The totsion 2.7  with theP < 0.05.Genome Analysis Toolkit (GATK) software version 4.0.11.0  was usedThe PFVs were analyzed in the Variant Effect Predictor (VEP) online tool release 98 , which pn = 5857) with PFVs identified from the RNA-seq of the five selected tissues . For the statistical analysis, the bonferroni, benjamini and False Discovery Rate (FDR) test was carried out. Significant pathways were considered when FDR < 0.05.The functional enrichment analysis was carried out using DAVID version 6.8  to identThe validation of the PFVs for the RFI obtained in different five tissues was performed in an independent Nellore cattle population. The influence of differential weighting in genomic regions harboring the PFVs on the prediction accuracy and inflation for the RFI was evaluated. The validation of the PFVs was performed by including differential weighting in genomic regions associated with RFI identified by the weighted single-step GWAS (WssGWAS) analysis, together with candidate regions harboring PFVs obtained in this study. To calculate the genetic merit and the SNP effects, the SNPs weights were estimated by performing a WssGWAS. In this methodology, the SNP weights are obtained iteratively. The iterative process increases the weights of the SNP with large effects and decrease those with small effects, essentially regressing them to the mean . Such meRecords for RFI were obtained from the Nellore Brazil breeding program coordinated by the National Association of Breeders and Researchers  from feed efficiency tests carried out between 2011 and 2018. A total of 4653 phenotyped and 5117 genotyped animals collected in 60 feed efficiency tests in the feedlot system using the same protocol as described by  were useThe animals were evaluated under similar management and environmental conditions in the feedlot with an average of 423 ± 122 days of age at the beginning of the tests. During the tests, the animals were exposed to a feeding trial which comprised 21 days of adaptation to the feedlot diet followed by 70 days of data collection. The average weight of each animal was obtained by periodic manual weighing or by automated weighing platforms (GrowSafe® or Intergado®).yi is the weight of the ith animal on the jth day; α is the intercept of the regression equation which represents the initial weight; β is the linear regression coefficient which represents the ADG; DITi is the day in the performance test of the ith observation; and ε is the error associated with each observation.The following feed intake records were not considered in the analyses: days when the animals were handled outside the facilities for several hours, equipment failure, and when no refusals were found. The dry matter percentage was determined from weekly samples of the offered diet and refusals. The average daily gain (ADG) in each test was considered as the linear regression coefficient of the body weight on days in the test (DIT):The DMI (kg/day) was obtained by calculating the average daily intake values during the test period. In individual stalls, this parameter was calculated as the difference between the dry matter offered and the refusal. In group pens, the DMI was calculated from the amount of individually consumed feed automatically recorded by the electronic systems.0.75) was retrieved from the liveweight and ADG as follows:Metabolic weight MW  was estimated within each contemporary group (CG) by the residual of the DMI regression as a function of ADG and MW, using a multiple regression model regressing DMI on ADG and MW, in the following model:yi is the individual DMI of the ith animal; β1, β2, and β3 are the linear regression coefficient of ADG, MW and CG, respectively; and εi is the residual error of the ith animal .where The relationship matrix used in the WssGWAS and prediction analyses was calculated based on pedigree information from 19,507 animals with 1809 sires and 9147 dams through nine generations, provided by the Nellore Brazil Breeding Program, coordinated by the ANCP. More information regarding the set of animals used in this study can be found elsewhere .A total of 963 animals were genotyped using the Illumina BovineHD BeadChip , which contains 777,962 SNP markers of an independent population. These animals were used as a reference population to impute genotypes of 5117 animals, previously genotyped with a low-density panel (CLARIFIDE® Nelore 3.1) encompassing over 27,000 SNP markers. Genotype imputation was carried out using the FImpute 2.2 software . Qualityn = 3253 animals) and validation  subsets. The validation dataset was composed of young animals without progeny records with genotypic and phenotypic information. The training dataset was composed of genotyped and phenotypes sires with phenotyped progenies. In the training population, a total of 201 genotyped and phenotyped animals and 2588 ungenotyped and phenotyped animals were described. The phenotypes and genotypes of the validation subset were omitted in the GWAS. The GWAS analysis was carried out using the training subset and applying the weighted single-step GWAS (WssGWAS) methodology [n = 2).To carry out the GWAS, the dataset was split into training  and its inverse is the same as in BLUP [𝐆 is genomic relationship matrix.The animal linear model included the fixed effects of contemporary group (CG) and the animal age as covariable, and the random direct additive genetic effect. The CG were composed of farm, management group, sex, feed efficiency test, year, and birth season. Records within ±3.5 standard deviations from the CG mean were considered in the analysis, and the CG that had at least four animals were also considered in the analysis. The animal model used was: in BLUP :\documenG matrix was obtained following [M is an allele-sharing matrix with m columns  and n rows , and P is a matrix containing the frequency of the second allele (pj), expressed as 2pj. Mij was 0 if the genotype of individual i for SNP j was homozygous AA, was 1 if heterozygous, or 2 if the genotype was homozygous BB. To account for heterogeneous SNP weights, a matrix of weights should be included in the formula for constructing G, in which var(s) is the vector containing the variance of the individual SNP effects, and di is the ith diagonal element of D, accounting for the ith SNP weight:The ollowing :\documenBased on that, a weighted relationship matrix can be defined as:𝜆 is a ratio of variances or normalization constant :𝒊 is the allele frequency of the second allele of the i-th SNP. According to Stranden & Garrick [û) can be obtained as follows:The  Garrick , the SNPEstimates of the SNP effects can be used to estimate the individual variance of each SNP effect  looping through steps 2–6.The SNP weights were calculated iteratively  of the validation subset was calculated considering the whole population  by applying the weighted single-step genomic BLUP procedure (WssGBLUP). The WssGBLUP is a weighted adaptation proposed to predict the genomic values , which iD matrix updates the model, in which these regions exhibit higher influence for the trait compared to other genomic regions. Hence, three levels of weight for SNPs neighboring the PFVs were tested, 1-fold, 2-fold, and 3-fold the maximum weighted  obtained in the ssGWAS after two iterations. The prediction analyses were performed using the BLUPF90 software family [To evaluate the impact of the causative PFVs on RFI genomic predictions, the G matrix was constructed using different combinations of SNPs and weights: (a) Unweighted G matrix with 460,992 SNPs; (b) weights in D calculated based on genome-wide association studies (ssGWAS) using iterative WssGBLUP as in , updatine family  includine family .i the inbreeding coefficient. The regressions coefficient between the GEBV obtained using the complete dataset considering the unweighted G and the GEBV estimated for different weighted G scenarios with or without PFVs was used to evaluate the prediction inflation.The prediction accuracies were calculated according to the Beef Improvement Federation (BIF)  as folloAdditional file 1: Table S1. Mean and standard deviation (SD) of tissue alignment results.Additional file 2: Table. Biological pathways enriched from potential functional variants associated with feed efficiency by tissue.


With the advent of high throughput genetic data, there have been attempts to estimate heritability from genome-wide SNP data on a cohort of distantly related individuals using linear mixed model (LMM). Fitting such an LMM in a large scale cohort study, however, is tremendously challenging due to its high dimensional linear algebraic operations. In this paper, we propose a new method named PredLMM approximating the aforementioned LMM motivated by the concepts of genetic coalescence and Gaussian predictive process. PredLMM has substantially better computational complexity than most of the existing LMM based methods and thus, provides a fast alternative for estimating heritability in large scale cohort studies. Theoretically, we show that under a model of genetic coalescence, the limiting form of our approximation is the celebrated predictive process approximation of large Gaussian process likelihoods that has well-established accuracy standards. We illustrate our approach with extensive simulation studies and use it to estimate the heritability of multiple quantitative traits from the UK Biobank cohort. In recent years, there is an increased interest of estimating heritability from genome-wide SNP data in large scale cohort studies. Here, we propose the PredLMM, a computationally rapid and memory-efficient linear mixed model for heritability estimation. The proposed approach can estimate SNP heritability on Biobank-scale datasets in a fraction of time compared to the existing mixed model based approaches. Along with the extensive simulations illustrating the precision and robustness of the PredLMM, we have also estimated heritability of several anthropometric traits from the UK Biobank cohort. In the past few decades, genome-wide association studies (GWASs) have identified hundreds of single nucleotide polymorphisms (SNPs) influencing the genetic architecture of complex diseases and traits. For majority of the traits, however, the associated SNPs from a GWAS only explain a small fraction of the heritability estimated using twin and family studies. In search of this so called “missing heritability”, there were attempts to capture even infinitesimal SNP effects by taking into account genome-wide variants in a linear mixed model (LMM) framework –4. This In recent years, advances in genome sequencing have generated huge amount of genetic data on large scale cohort studies, such as UK Biobank , PrecisiN be the number of individuals and M be the number of SNPs, the first step of computing the GRM, takes complexity of O(MN2) FLOPS (floating point operations). And, the next step i.e., fitting the REML to estimate heritability, requires inverting the GRM matrix which uses per iteration complexity of O(N3) FLOPS. When N is extremely large , this step becomes computationally intractable. It should be noted that the first step (computing the GRM) is also very demanding in terms of both computation and memory requirements . In large biobank-scale studies, where the interest is to estimate heritability of a large number of traits, implementing these approaches becomes computationally very demanding.Programs such as genome-wide complex trait analysis (GCTA) , genome-O(MN1.5) per iteration which is better than the previous methods in terms of N. The software is well optimized and in our analysis of UK Biobank data, it performed much better compared to the other approaches in terms of computational time. However, the complexity of Bolt-REML is not linear in N which makes it challenging to use for larger N . Additionally, the computational complexity also increases linearly with M per iteration. Thus, in a large cohort with millions of SNPs, it would be immensely intensive to use Bolt-REML for estimating heritability of all the traits one by one. On the other hand, methods like GCTA, GEMMA estimate the GRM only once ) and after that, the complexity of analyzing any trait does not depend on M.Recently, an approximate method named Bolt-REML , 13, 14 Alternative to the REML estimation approaches, there are other ways of estimating heritability from the LMM framework that can be computationally much faster but cost significant efficiency –17. TherN × N) at every iteration. It reduces per iteration computational complexity from O(N3) FLOPS (floating point operations) to O(Nr2) + O(r3) FLOPS where r is much smaller than N. Theoretically, we show that under a model of genetic coalescence, the limiting form of our approximation is the celebrated predictive process approximation of large Gaussian process likelihoods [O(N2) storage and cost a significant amount of time. Our approach stores only a few blocks of the GRM and requires only a storage space of O(Nr + r2). We have demonstrated that the proposed approach achieves accuracy close to the GREML methods through extensive simulation studies replicating many possible realistic scenarios. We have analyzed the UK Biobank cohort data  to estimate the heritability of Standing Height, Weight, BMI, Systolic and Diastolic blood pressure, Hip and Waist circumference. We have implemented PredLMM in an efficient Python module available at this link, . It is worth pointing out that in the developed module, we allow users to incorporate SNP-based weights, such as LD-based weights proposed by Speed et. al. (2012) [In this paper, we approximate the likelihood of the standard LMM framework to develop a rapid algorithm for estimating heritability. The approximation is motivated by the concepts of genetic coalescence , 23 and elihoods  that has. (2012) , into thY denote the N × 1 vector of phenotype corresponding to N individuals, X denote the N × p matrix of covariates, and W denote the N × M matrix of mean and variance scaled genotype for the N individuals and M SNPs, i.e., E(wij) = 0 and Var(wij) = 1. Consider the following LMM,Let A is formally known as the Genetic Relationship Matrix (GRM) and I is the identity matrix. Heritability is calculated as And, the corresponding marginal model can be written as,h2, different REML algorithms are generally used. The entire framework is referred to as genome-based restricted maximum likelihood (GREML) approach. There are two types of programs implementing the GREML approach: a) Exact Methods (methods that converge to the REML optimum) and b) Approximate Methods (methods that approximate the REML optimum).To estimate the variance parameters Exact Methods: Programs such as GCTA [A in the marginal model from h2 using different REML algorithms. These REML algorithms are iterative and compute analytically exact solutions. For example, GEMMA uses a modified version of Newton-Raphson method (considers exact Hessian), GCTA uses average information (AI) method . The second step involves computing the inverse and determinant of the N × N dense matrix O(N3) FLOPS, making these exact methods computationally intractable as N increases. as GCTA , GEMMA [ as GCTA  operate Approximate Methods: Unlike the above methods, Bolt-REML [A. It directly uses with the SNP data matrix W and follows a Monte Carlo REML approach that uses random sampling to approximate the derivatives of the log likelihood corresponding to the marginal model from O(MN1.5) per iteration which is better than the previous methods in terms of N. The software is well optimized and in our analysis of UK Biobank data, unlike the previous methods, it would successfully converge for moderately large N  in a reasonable amount of time. However, the per iteration computational complexity of Bolt-REML still increases linearly with M. Thus, in a cohort study where M is closer to a million , it will become computationally much more challenging to use Bolt-REML. On the other hand, methods like GCTA, GEMMA estimate the GRM only once ) and after that, the complexity of analyzing any trait does not depend on M.olt-REML , 13, 14 N increases, an alternative would be to utilize a sub-sample based approach. Choose a random sub-sample of small size r from the pool of all N individuals and use a standard GREML based program, such as GCTA to estimate heritability .In our simulation studies and real data analysis, we assess the performance of this method for varying values of M goes to infinity, the likelihood corresponding to the marginal model from : We assume that each individual i = 1, 2, …, N can be represented by a point (location) si in an abstract spatial manifold d. The correlation between the genotypes of individuals i and i′ at the jth SNP is given by Cov = Cj where Cj is a valid covariance function in genetic coalescence [time to coalescence, i.e., number of ancestral generations till the most recent common ancestor. Hence, the MRCAs of different pairs of individuals in a sample can be assigned to nodes of a genealogical tree. Trees are equipped with a valid distance metric (shortest distance between nodes) and models for tree-structured objects commonly specify the correlation as decreasing function of the distance [This assumption is rooted in the theory of lescence , 23. Thelescence . Under cdistance .h2 from : We assume that the centered and scaled genotype process j = 1, 2, …. Stationarity translates to j, j′ implying that the covariance functions Cj = C for all j = 1, 2, … Ergodicity implies that as the number of SNPs grows, we haveAR(p)), moving average (MA(q)) or ARMA [The simplest setting where this assumption is satisfied is when the scaled and centered genotype processes timation  but indetimation , the paitimation  like autMA  will satMA .NN denotes the N-variate normal likelihood for a realization Y with mean μ and variance Σ. Thus the marginal GREML likelihood converges to the likelihood of a Gaussian process where NNO(N3) FLOPS. However, over the last two decades a series of increasingly sophisticated algorithms have been proposed for fast approximate GP likelihoods )i∈A,i′∈B. The predictive process approximation of C is given byOur approach uses predictive process (PP) , 25 whicC using the knots S*. [r ≪ N, inference from the predictive process likelihood provides an excellent approximation to that from the full GP likelihood. Computationally, predictive process only requires O(Nr2 + r3) FLOPS and as r ≪ N, the approximation results in massive gains in run times. Consequently, predictive processes is one of the most popular approximations of the full GP likelihood and is widely adopted in many spatial applications.The first term is a low-rank factorization as the number of knots is much less than the sample size.  showed tnots S*.  proposedsi are unknown to us. Hence, CPP can only be calculated using approximate locations like a vector of the top few PC scores. The impact of such choices of locations is less clear. Second, covariance functions usually involve additional spatial parameters θ, thereby increasing the number of unknown parameters to be estimated.In our setting, direct usage of predictive process likelihood is not recommended for two reasons. First, the locations A as,Instead, we consider the following strategy. We choose A that is explained by the information about the subset of individuals A asThe decomposition is inspired by the concept of conditional variance . The firA and M → ∞, while for a well chosen set of knots S*, the predictive process approximation C (since C is a decreasing function of the distance as postulated in Assumption 1). Hence the middle term will also be small. This justifies why for large M, A.We propose using the likelihood ius norm . Under aIn our empirical studies detailed later, the predictive process approximation consistently and substantially outperforms the subsample-based method when both uses the same set of knots (sub-sample) A based on the genetic information only from the individuals in subset h2. This thus ignores the genetic correlation of these sub-sampled inviduals with those not sub-sampled  to O(Nr + r2)—a substantial gain for biobank-scale studies with large N as r ≪ N.Evaluation of our PredLMM likelihood O(Nr2 + r3) FLOPS, as r ≪ N, the computation is thus becomes linear in N—a drastic reduction from the O(N3) FLOPS required for evaluating the true likelihood.Subsequently, the nice low-rank plus diagonal structure of identity , while tidentity  is leversi are observed. Hence, the knots need not coincide with the data locations. Recommended choices for the knot-set include space-filling designs and lattices [A. However, our practice has precedence even in conventional spatial settings. Using some of the data locations has been shown to improve performance of predictive process [A. Next, we ordered the set of indices, r individuals as the set of knots. Note that a large value of row-sum indicates that the particular individual shares significant genetic relationship with one or more other individuals and would be a more fitting choice as a knot than an individual sharing little to no correlation with the rest of the individuals. The reasoning becomes more apprehensible if we look at A, are the ones corresponding to the sub-matrix In traditional applications of Gaussian processes in spatial statistics, the domain lattices . In our  process , while rr to be used for PredLMM is more nuanced. Performance of predictive process is generally more sensitive to the number than the design of the knots [r improves the quality of the approximation, with A when r = N and r, use of a very large r would defeat the purpose of the approximation. Parallel computing resources, if available, can be heavily deployed for this step.Choice of the the number of sub-samples he knots , 39. IncWe have derived the expression of the asymptotic variance (standard error) of the PredLMM estimator. Since it is extremely time consuming to perform the matrix multiplications needed for the exact computation of the variance expression, we make some reasonable approximations. The details of the derivation can be found in The following simulation study replicated a scenario where Assumption 1 from Section Asymptotic limit of the GRM approximately held i.e., every individual originated from a common ancestor and individuals in the same sub-population shared a more recent ancestor than the individuals in different sub-populations. Such an evolutionary tree-like structure with four generations has been depicted in j , the allele frequency j-th SNP of the i-th individual from the k-th sub-population : pijk was simulated from a beta distribution with parameters N/4 resulting in a total population of size N. Next, we simulated the SNP genotype: wijk from a binomial distribution: Bin assuming Hardy-Weinberg equilibrium. Once the genotypes of M SNPs for N individuals are simulated, we randomly selected mcausal causal SNPs (out of M) to create a N × mcausal causal SNP genotype matrix denoted by Wcausal. Fixed effect of m-th causal SNP: um was simulated from N, and the residual effect e was simulated from NNIN). Finally, the N-dimensional phenotype vector (Y) was generated as, m-th column of Wcausal.The generation procedure was as follows. For each SNP ls model , 41. In h2 (low and high) and two different combinations of the number of individuals N and the number of SNPs M. We considered case (1.1): h2 = 0.2, N = 5000, M = 8000, case (1.2): h2 = 0.2, N = 8000, M = 13000, case (1.3): h2 = 0.8, N = 5000, M = 8000 and case (1.4): h2 = 0.8, N = 8000, M = 13000 to study the influence of M and N on heritability estimation. In this simulation study and also in the subsequent ones we considered 100 replications. r) 500 and 2000 respectively. We noticed that GREML (500) had the largest empirical RMSE in all the cases with the largest being in case (1.4). PredLMM (500) showed RMSE values close to GREML (2000), whereas PredLMM (2000) achieved RMSE close to the full GREML based methods, such as GCTA, GEMMA and Bolt-REML. Therefore, we could conclude that when the genetic data were simulated using the Balding-Nichols model, the quality of the PredLMM estimator would be much superior compared to the sub-sample based GREML and even close to the full GREML based methods for a moderately large knot-size. Refer to We considered two different values of the true heritability: To replicate more realistic scenarios, we next considered simulations using the UK Biobank cohort data . UK Biobh2 = 0.2, (b) h2 = 0.4, and (c) h2 = 0.6. Next, we simulated the trait as Y100,000 ∼ N100,000I100,000) where A100,000 was the corresponding GRM. We compared PredLMM with GREML (sub) for four different sub-sample (knot) sizes, r = 2000, 4000, 8000, and 16, 000.After standard quality control steps as advised in   and (2.2) are respectively shown in Figs The huge time advantage of PredLMM has already been illustrated in O(Nr2 + r3) i.e., the complexity is cubic with respect to the knot size r which justifies the leap. One may argue that it would be wise to use just 8000 knots since it can yield a reasonable estimate in a very reasonable time. We should also mention that we used a pre-computed GRM (using GCTA) in all our analyses (we computed the GRM for the entire population and used its sub-matrices as necessary in Simulation Study 2). Computing the GRM is an arduous task that can take multiple hours depending upon the number of SNPs and the number of individuals. It has computational complexity of O(MN2). But, it is usually less concerning since the computation needs to be performed only once and the computed GRM then can be used in multiple analyses. Bolt-REML does not use a pre-computed GRM and uses the genetic data every time for each of the traits which makes it very time consuming to perform a heritability analysis with multiple traits.According to Standing Height, Weight, BMI, Diastolic and Systolic blood pressure, Hip and Waist circumference using the British population of size 286,000 and 566,000 SNPs [We estimated heritability of a number of quantitative traits: 000 SNPs . We took000 SNPs , 14. TheA had a very small proportion of elements significantly non-zero and even those were very small in magnitude. In a dataset with more genetic relatedness, PredLMM would arguably achieve adequate accuracy even with a small knot-size.The heritability estimates from all the methods generally agreed with the findings from other studies based on the UK Biobank cohort –48. We nN) is too large. In this paper, we have developed a rapid algorithm for estimating heritability in large scale cohort studies. Our proposed approach PredLMM approximates the likelihood of a GREML approach. The approximation is achieved by unifying the concepts of genetic coalescence and Gaussian Predictive Process models. The algorithm reduces the usual per iteration computational complexity from O(N3) to O(Nr2 + r3) where r (knot size) is much smaller than N.Genome-based restricted maximum likelihood (GREML) approaches for estimating heritability have become widely popular with the availability of large scale cohort studies. However, majority of the existing approaches such as GEMMA, GCTA, Bolt-REML implementing GREML, either become computationally very demanding or even intractable when the number of individuals (r). To replicate more realistic scenarios, next we have performed simulation studies using the real genetic data from the UK Biobank cohort study. We have checked the performance of PredLMM in two cases, a highly homogeneous sub-population and a heterogeneous sub-population (see Simulation Study 2) for a varied range of heritability values. We have observed that even with a very small knot size (say 4% or 8% of the entire population size), PredLMM can produce an extremely precise estimate of heritability at a fraction of time taken by existing softwares like Bolt-REML. Finally, we have estimated the heritability of a number of quantitative traits like Standing Height, Weight, BMI, Diastolic and Systolic blood pressure, Hip and Waist circumference using the entirety of the British population from UK Biobank data. For all the traits, estimates by PredLMM for varying knot-sizes come out to be very close and also, very similar to other methods like Bolt-REML (Pseudo).In different simulation studies, we have compared the empirical root mean-squared error (RMSE) of PredLMM for different knot-sizes with existing methods. From the Simulation Study 1, we have seen that under the presence of genetic pattern (a tree like structure) among the individuals, PredLMM yields highly robust estimate of heritability even with a small knot size  etc. from the UK Biobank data. It would be slightly more challenging since those traits often tend to be skewed and deviate from the usual normality assumption. A very efficient module implementing PredLMM in Python is available here, https://github.com/sealx017/PredLMM. Recall that, PredLMM does not use the full GRM but only a few particular blocks of it. In the module we provide a function for computing the GRM-blocks necessary for fitting the PredLMM algorithm.Our next goal would be to analyze behavioral traits like S1 FigA and its blocks that are used in computing r of the total of N individuals are in the set of knots We look at the full GRM (TIF)Click here for additional data file.S2 FigBox-plots of the estimates are shown for varying sub-sample sizes (knot-sizes) in four different cases.(TIF)Click here for additional data file.S3 FigBox-plots of the estimates are shown for varying sub-sample sizes (knot-sizes) in three different cases.(TIF)Click here for additional data file.S4 FigBox-plots of the estimates are shown for varying sub-sample sizes (knot-sizes) in three different cases.(TIF)Click here for additional data file.S1 AppendixWe derive an approximate estimate of the asymptotic variance of the PredLMM estimator. Using the proposed variance formula, we present two tables that list coverage probability of PredLMM under different simulation setups. We also provide the details on the efficient matrix operations that PredLMM makes use of.(PDF)Click here for additional data file.


Identifying the genetic components underlying yield-related traits in soybean is crucial for improving its production and productivity. Here, 211 soybean genotypes were evaluated across six environments for four yield-related traits, including seed yield per plant (SYP), number of pods per plant number of seeds per plant and 100-seed weight (HSW). Genome-wide association study (GWAS) and genomic prediction (GP) analyses were performed using 12,617 single nucleotide polymorphism markers from NJAU 355K SoySNP Array. A total of 57 SNPs were significantly associated with four traits across six environments and a combined environment using five Genome-wide association study models. Out of these, six significant SNPs were consistently identified in more than three environments using multiple GWAS models. The genomic regions (±670 kb) flanking these six consistent SNPs were considered stable QTL regions. Gene annotation and in silico expression analysis revealed 15 putative genes underlying the stable QTLs that might regulate soybean yield. Haplotype analysis using six significant SNPs revealed various allelic combinations regulating diverse phenotypes for the studied traits. Furthermore, the GP analysis revealed that accurate breeding values for the studied soybean traits is attainable at an earlier generation. Our study paved the way for increasing soybean yield performance within a short breeding cycle. Glycine max L. Merr.) is one of the most important food legume crops cultivated globally . All these studies have validated the role of linkage mapping as an efficient approach to dissecting the genetic basis of quantitative traits , number of pods per plant (PPP), number of seeds per plant (SPP), and 100-seed weight (HSW). Based on the phenotypic performance, genome-wide association analysis was conducted to identify QTLs associated with the studied traits using five different models. The genes underlying the identified QTLs were validated based on RNA-seq data for soybean tissues. Furthermore, superior haplotypes and alleles were identified within the genomic regions associated with the studied traits. Also, genetic values of individual genotypes were estimated based on the studied yield-related traits to facilitate the selection of soybean for improved yield performance.The GWAS panel of soybean used in the current study consists of 211 diverse genotypes; which include 201 genotypes originating from 25 provinces of China that represents all three ecological habitats of China  and ten lme4 – an r-package implemented in PBTools v1.4 . BLUPs were generated for GWAS by setting the genotype as random. Pearson correlation coefficient between traits was determined at p < 0.05 and visualized using MVApp , number of pods per plant (PPP), number of seeds per plant (SPP), and 100-seed weight (HSW). The phenotypic data were subjected to analysis of variance with the mixed linear model using ng MVApp .r2) between SNP markers with known genomic positions were calculated using Trait Analysis by Association, Evolution, and Linkage (TASSEL) v5.72  v5.72  with 1001) General linear model (GLM) with principal component analysis (PCA) to reduce false positive association due to population structure  based onWhere Si = testing marker, and Q = Population structure.2) The compressed mixed linear model (CMLM) , has incWhere Si = testing marker, Q = Population structure, and K = Kinship by group.3) The multiple-locus mixed linear model (MLMM)  incorporWhere Si = testing marker, Q = Population structure, K = Kinship of individuals, and S = Pseudo QTN.4) The fixed and random model circulating probability unification (FarmCPU)  iterativWhere K = kinship derived from only the associated markers or Pseudo QTN (S) using maximum likelihood method.5) Bayesian-information and linkage-disequilibrium iteratively nested keyway (BLINK)  is an imThe GWAS was performed using the following five models:S = pseudo QTNs that are not in LD with each other selected in two FEMs and one filtering process and optimization using Bayesian information criterion (BIC).R environment. To correct for the population structure, PCA was employed using BIC to estimate the optimal numbers of PCA . Furthermore, only SNPs that were commonly detected across a minimum of two models were considered for further analysis.Among the five GWAS models used, GLM and CMLM are single locus models; whereas, MLMM, FarmCPU, and BLINK are the multi-locus models. All of the models were implemented using GAPIT v3 package  in an R s of PCA . The popGAPIT v3  as the nhttps://www.soybase.org). Functional descriptions of these genes were also obtained, manually screened, and presented in a heatmap.The genes lying upstream and downstream of each stable SNP (within the LD decay distance of the studied population) were obtained from the freely available online RNA-seq data for different soybean tissues on SoyBase website . Also, the contribution of each haplotype to the observed phenotypic variance across the environments was estimated using the "--hap-assoc” command  and the ridge regression best linear unbiased prediction (rrBLUP) based on the mixed-model:The gBLUP was implemented in TASSEL v5.72 . Cross-vp < 0.0001) was observed for the genotype, environment, and G × E interaction in all the studied traits. However, the estimates of variance components varied across different traits (h2) was observed, ranging from 0.61 (SYP) to 0.99 (HSW) in individual environments  and lowest (352) number of markers present on Chr.06 and Chr.05, respectively . Heatmapr2 value of the genome was 0.12, and the LD decay was found to initiate at an r2 value of 0.47 and reached half-decay at 0.24. The LD decay curve intersected with the half-decay at 670 Kbp, which represents the genome-wide critical distance to detect linkage. Hence, markers associated with the same trait within this distance were considered as a single QTL.The graphical representation of the linkage disequilibrium characteristics of the 211 soybean genotypes is presented in A total of 57 SNPs detected using five different GWAS models were found to possess significant association with four studied traits across six different environments ; Table 2Furthermore, three significant SNPs  on Chr.20, Chr.04, and Chr.18, respectively, were consistently detected in the combined environment using three different models  and showed association with two of the three traits viz., HSW, PPP, and SPP. The SNP (AX-93922099) was detected in the combined environment using two different models (BLINK and FarmCPU) and was associated with HSW. Few significant SNPs such as AX-93792,964, AX-94034,566, AX-93797,890, and AX-94104,132, present on Chr.11, Chr.07, Chr.12, and Chr.13, respectively, were found to be associated with two of the four studied traits, using up to three GWAS models in one or two individual environments and a combined environment. Moreover, eight SNPs  were detected in one or two individual environment(s) and a combined environment. Each of these eight SNPs was associated with only one trait and identified using up to four different GWAS models. The SNPs  were found to be associated with two traits (PPP and SPP) and were identified using two GWAS models (BLINK and GLM), but were identified in only one individual environment. The remaining 37 significant SNPs were found to be associated with only one trait and environment, and most of them were identified using two or three GWAS models.qHSW-SPP13, qHSW-SPP11, qPPP-SPP20, qHSW5, qPPP-SPP4, and qHSW-PPP18, respectively  on Chr.4, Chr.5, Chr.11, Chr.13, Chr.18, and Chr.20, respectively, consistently in three or more than three environments and using multiple models , 3. Of tectively . These QqPPP-SPP4), Chr.05 (qHSW5), Chr.11 (qHSW-SPP11), Chr.13 (qHSW-SPP13), Chr.18 (qHSW-PPP18), and Chr.20 (qPPP-SPP20) were further used to identify putative genes regulating yield-related traits in soybean. The gene models and their annotations underlying the physical intervals of these six QTL regions were downloaded from the SoyBase database to predict putative candidates  was downloaded and analyzed for identifying putative genes underlying the QTL intervals , showing stable MTAs with yield-related traits were further used to determine the effects of their individual alleles on the studied traits . The allMoreover, three alleles of SNP marker AX-94199992, including AX-94199992-AA, AX-94199992-AG, and AX-94199992-GG, were found to govern three diverse phenotypes of SPP and PPP . BesidesThe six stable markers mentioned above were used as a reference for the identification of haplotypes for yield-related traits. These stable markers were located on Chr.04 , Chr.05 (AX-93922099), Chr.11 , Chr.13 , Chr.18 (AX-94176727), and Chr.20 (AX-94199992). All the markers that were in strong LD (within ±670 kbp) with these six SNP markers, represented a haplotype block/locus . These tp < 0.05) in their associated traits across all six environments. The phenotypic variance contributed by the alleles of different haplotype blocks to the associated traits across six environments is shown in Eight SNP markers were associated with AX-93807,406 , which represented a haplotype block and constituted six haplotype alleles. All the six alleles identified within this haplotype block showed significant differences in the phenotypes of HSW and SPP . SimilarThe genome-wide prediction accuracy values obtained from the gBLUP and rrBLUP approaches for the studied yield-related traits are presented in Yield-related traits are important characters associated with yield and directly govern the productivity and quality of crops . They alIn the present study, 211 soybean germplasm accessions were characterized in six field trials for four yield-related traits. The genotypic performance of the soybean germplasm based on all these traits varied significantly, indicating the possibility of genetic improvement. Moreover, the medium to high broad-sense heritability observed for these traits across environments is an indication that the same phenotypic performance is achievable if grown in the same environment. However, the significant environmental variations observed for all the four yield-related traits studied suggest possible complexity in their inheritance pattern which may lead to difficulty in breeding efforts. These findings corroborate many earlier reports on these yield-related traits in soybean germplasm . MoreoveBased on the high genetic variability observed, the studied yield-related traits were subjected to further analysis to unravel their genetic basis and pave the way for their improvement through marker-assisted breeding (MAB). MAB involves the identification of genetic markers that are associated with the trait of interest in a defined germplasm collection, such as bi-parental population or a panel of diverse accessions as used in this study. Marker-trait association using a panel of diverse accessions is often confounded by several factors, including genotyping error, population structure, and linkage disequilibrium. These factors are responsible for the high rate of false associations that are not useful in MAB. In this study, the discovery of false association was reduced by ensuring only quality markers which included a total of 12.617 SNPs at genotyping rate of 99%, which were retained for further analysis. Although the population structure of the germplasm collection used in this study appears continuous with no definite stratification, the LD decay distance of 670 kb within which significant association may be defined as relatively large. In self-pollinating plants such as soybean, LD may range over several hundred Kbp leading to the inclusion of many candidate genes in a single LD block exhibiting a significant signal . MoreoveHundreds of QTLs for yield and yield-related traits have been reported in soybean mainly by using the low-resolution approach of linkage mapping. Rarely any of these QTLs have been used for breeding high-yielding soybean varieties . In thisqHSW-SPP11 was found to co-locate with the same physical interval. Therefore, qHSW-SPP11 might be similar to Seed weight 35–9, as reported earlier by Seed weight 35–9, the physical interval of qHSW-SPP11 has been considerably decreased in the present study. Furthermore, qHSW5 identified in the present study was found to co-locate with two previously identified QTLs viz., Seed weight 34–9  and Seed-yield 22–10  on Chr.05  identified in the current study represented novel QTLs. The physical intervals of qHSW-SPP11 and qHSW5 were considerably reduced in the present study. This ability of the GWAS allows for its increased utility in crop breeding programs for developing high-yielding stress-tolerant soybean varieties  were intermediate between two homozygous alleles which control the extreme phenotypes of yield-related traits. However, two homozygous alleles identified for the remaining three SNP markers  regulate contrasting/extreme trait values of the corresponding traits. As a result, the SNP alleles with higher trait effect, i.e., which increase the target trait, were defined as “favourable alleles”; whereas, SNP alleles regulating the lowest trait value were defined as “unfavourable alleles”. However, the heterozygous alleles possessing trait effect between favourable and unfavourable alleles were referred to as “intermediate alleles”. This classification assisted in the use of these alleles for yield modulation in soybean. To date, the effectiveness of marker-based gene pyramiding strategies in soybean has been demonstrated for soybean mosaic virus , PhytophPP2C-1 . In the Recent studies have documented desirable haplotype alleles for important traits such as salinity tolerance in soybean , grain qGenomic Prediction (GP) is a modern breeding approach that involves the use of genome-wide markers to estimate the breeding value of the genotypes at the genomic level . For theThe range of moderate to high GP accuracy of 100-seed weight and seed yield observed in our study is similar to the observation of qPPP-SPP4, qHSW5, qHSW-SPP11, qHSW-SPP13, qHSW-PPP18, and qPPP-SPP20). Among these six QTLs, four QTLs  were novel; whereas, the remaining two QTLs (qHSW5 and qHSW-SPP11) were reported previously. Besides, a total of 15 genes underlying these six QTLs were prioritized as putative candidates. Allele-effect analysis of the six significant SNPs showed the presence of two or three alleles within each of these SNPs that regulated contrasting phenotypes of the associated traits. Moreover, multiple haplotype alleles detected within each of the six haplotype blocks regulated a diverse range of phenotypic variation for yield and yield-related traits. The GP analysis for four studied traits showed moderate to high accuracy using two methods (gBLUP and rrBLUP). The stable QTLs as well as the desirable SNP alleles and haplotype alleles (underlying these stable QTLs) identified for the yield-related traits can serve as potential resource for the improvement of soybean yield. After proper validation of these QTLs and alleles/haplotypes in different genetic backgrounds of soybean, they can be introduced into marker-assisted breeding programs for developing high-yielding soybean varieties. Besides, the putative candidate genes underlying these stable QTLs, after proper functional validation using overexpression or gene knockout studies, can be deployed in the development of high-yielding soybean varieties. Our study provided critical analyses of cultivated soybean genetic resources and identified novel genomic resources  for soybean yield improvement programs.The present study used GWAS, haplotype analysis, and GP for studying the genetic architecture of four yield and yield-related traits in soybean. GWAS identified a total of 57 significant SNPs and six stable QTL regions (


Eucommia ulmoides Oliver has been used extensively in many fields. To satisfy increasing demand, great efforts must be made to further improve its traits. However, limited information is available on these traits, which is a factor that restricts their improvement. To improve traits directionally, nine clones were assigned to six sites to analyze the effect of different variation sources  on the phenotypic trait. In addition, a mixed linear model was used to assess the contribution of variations. In general, for most traits, the site effect accounted for a larger proportion of the variance, followed by the genotype and genotype × environment interaction effects. All the studied genotypes and sites had a significant effect, indicating that they could be improved by selecting preferable genotypes or cultivation areas, respectively. Interestingly, growth traits or economic traits could be improved simultaneously. Trait performance and stability are necessary when selecting genotypes. Moreover, the discriminating ability of genotypes should be considered in selecting cultivation areas. Annual mean temperature and annual sunshine duration proved to be crucial factors that affected the traits. They were correlated positively with economic traits and leaf yield and correlated negatively with growth traits. These findings contributed to selecting a wider range of cultivation areas. Regarding the genotype × environment interaction effect, there were significant differences only in the gutta-percha content, the total number of leaves, and the chlorogenic acid content. These traits could also be improved by choosing appropriate genotypes for the local environment. The research has provided preliminary data on the main factors that affect the traits of E. ulmoides and offered solutions for trait improvement. This information could be a reference for the trait improvement of other plants. Eucommia ulmoides Oliver is an economically important tree native to China  interaction effects   Du, . HoweverE. ulmoides improvement  were collected from all the seedlings in each block in September 2020. The samples were mixed fully and placed in a drying oven at 60°C. Then, they were stored hermetically at room temperature for later use. Growth traits were measured after the leaves fell in 2020. Tree height was measured by using a box staff. A Vernier caliper  was used to measure ground diameter and diameter at breast height. The presented phenotypic trait values are the averages of the three blocks.The samples were ground into powder by using a tissue grinder apparatus  before measuring economic traits.The extraction and determination of gutta-percha were performed according to the description of Ma et al. . In brievia a high-performance liquid chromatography (HPLC) system . Chlorogenic acid and rutin were detected at 320 and 360 nm, respectively. The 1260 DAD-chemstation (off-line) software was used for data analysis. Chlorogenic acid and rutin concentrations were calculated based on external calibration by peak areas. They are presented as the average of the contents in three blocks. Chlorogenic acid (HPLC ≥ 98%) and rutin (HPLC ≥ 98%) standards were purchased from Shanghai Yuanye Bio-Technology Co., Ltd.Extraction of effective medicinal components (chlorogenic acid and rutin) was conducted according to the study by Dong et al. . The comhttp://data.cma.cn/en).The longitude, latitude, and altitude were obtained using a handheld GPS locator . The environmental factor data  were obtThe chlorogenic acid and rutin content were determined from the following standard curves:x is the peak area and y is the content.In Equations (1) and (2), The universal mixed linear model was as follows:Si is the site effect, Gj is the genotype effect, SGij is the interaction effect between the site and genotype, and eijk is the error effect. All the effects were random.In Equation (3), μ is the overall average, F-test of variance analysis in R was used to test for the significance of the effects. Multiple comparisons were conducted using Duncan's test. The ASReml-R V4.0 statistical analysis package  correlation coefficient between trait i and j, Vij is the covariance between trait i and j, and Vi and Vj are the genetic (phenotypic) variance estimated for trait i and j, respectively.The genetic (phenotypic) correlation among traits was obtained by using the ASReml-R version 4.0 statistical analysis package  Program (2019NY-012).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.