GWAS), has limited power to identify the genes responsible for variation in traits controlled by complex genetic architectures. In this study, we employ real‐world genotype datasets from four crop species with distinct minor allele frequency distributions, population structures and linkage disequilibrium patterns. We demonstrate that different GWAS statistical approaches provide favourable trade‐offs between power and accuracy for traits controlled by different types of genetic architectures. FarmCPU provides the most favourable outcomes for moderately complex traits while a Bayesian approach adopted from genomic prediction provides the most favourable outcomes for extremely complex traits. We assert that by estimating the complexity of genetic architectures for target traits and selecting an appropriate statistical approach for the degree of complexity detected, researchers can substantially improve the ability to dissect the genetic factors controlling complex traits such as flowering time, plant height and yield component.Association studies use statistical links between genetic markers and the phenotype variation across many individuals to identify genes controlling variation in the target phenotype. However, this approach, particularly conducted on a genome‐wide scale ( Association studies identify functionally variable alleles segregating in target species and these alleles can guide breeding efforts in crop and livestock species, as well as provide increasingly accurate predictions of disease risk factors in humans. Advances in genotyping technology have dramatically reduced the barriers to conducting association studies with genome‐wide genetic marker datasets across natural populations. Since becoming feasible in the mid‐2000s, genome‐wide association studies (GWAS) have been successfully used to identify thousands of single nucleotide polymorphisms (SNPs) associated with diseases in human  are widely employed in both plant and animal systems. MLM‐based approaches are able to control for confounding effects of both population structure and unequal relatedness among individuals, which are left uncontrolled in approaches based on generalised linear models (GLM), at the expense of greater run times. A wide range of different algorithms have been proposed and developed to improve the computational efficiency of MLM, including EMMAX  explicitly identify and control for the effects of large effect loci as fixed effects as these loci are identified by the model. Compared to GLM or MLM which only conduct tests on one marker at a time, the MLMM can test multiple markers simultaneously by fitting the supposed causal variants in the process called “forward‐backward stepwise linear mixed‐model regression” , foxtail millet , sorghum (Sorghum bicolor) and maize (Zea mays)  GWAS approaches across simulated trait datasets containing 2 to 1024 causal variants and different levels of heritability ranging from 0.1 to 1. To capture realistic patterns of minor allele frequency distributions, population structure and linkage disequilibrium, we employed real‐world genotype datasets from four widely studied crop species: rice  between genetic markers dropping to 0.25 around 100 kb, consistent with the original description of this dataset  with the causal SNP were identified by a given GWAS analysis. As expected, the power to detect true positives decreased in response to both increases in the number of simulated causal variants controlling the trait and decreases in simulated heritability , the BayesCπ approach outperforms FarmCPU on both power and false discovery rate metrics     . The downloaded genotype data included 916 diverse varieties and 726 080 SNPs with minor allele frequencies lower than 5% had been removed prior to the publication of the dataset. After downloading, SNPs without calls in >10% of samples were removed from the dataset. The sorghum GBS dataset which included 404 627 SNPs scored relative to the v1.4 of the sorghum reference genome  for the i‐th causal SNP of the j‐th plant; and ej is the residual error for j‐th plant extracted from a normal distribution with mean of 0 and standard deviation of Var∑Sijai1/h2−1, where h2 denotes the heritability.In the model, https://github.com/jyanglab/g3tools). For the results employed in this study, both the effect sizes of individual SNPs ai and the error term in measurements of individual genotypes ej were drawn from normal distributions. However, the software package developed to enable this study also provides the option to specify other effect size distribution models. Phenotype datasets were simulated for scenarios where the number of causal genetic loci ranged from 21 to 210 (2–1024 QTNs) and where the heritability of trait values ranged from 0.1 to 1.0 in steps of 0.1. For each combination of heritability and number of causal variants, 10 independent replicates with different randomly selected causal variants were generated.An R function ‘simcrop’ was implemented within the open source ‘g3tools’ R package  with the command “gemma ‐g [genotype mean file] ‐a [genotype annotation file] ‐p [phenotype file] ‐c [PCs file] ‐k [kinship file] ‐o [output file]” . The parameter method.bin = “optimum” allows the FarmCPU to selected optimized possible QTN window size and number of possible QTNs in the model  in R. Y, GD and GM represent phenotype, genotype and genotypic map data respectively. CV represents the principal components file. The kinship matrix was automatically estimated in FarmCPU. While kinship matrices were independently generated by GEMMA and FarmCPU, the correlation between these two matrices is over 0.9999  in each species in an MLM‐based GWAS.Figure S3 Relationship between the proportion of causal variants identified and the number of causal variants controlling a trait given different levels of heritability (0.1–1) in each species in an MLM‐based GWAS.Figure S4 Distribution of minor allele frequency and effect size for true positive and false negative causal variants in each species.Figure S5 Relationship between the proportion of causal variants identified and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 4, 8 and 32 causal variants.Figure S6 Relationship between the proportion of causal variants identified and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 128, 512 and 1024 causal variants.Figure S7 Relationship between false discovery rate and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 4, 8 and 32 causal variants.Figure S8 Relationship between false discovery rate and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 128, 512 and 1024 causal variants.Figure S9 Relationship between the proportion of causal variants identified and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 16, 64 and 256 causal variants.Figure S10 Relationship between the proportion of causal variants identified and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 16, 64 and 256 causal variants.Figure S11 Relationship between false discovery rate and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 16, 64 and 256 causal variants.Figure S12 Relationship between false discovery rate and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 16, 64 and 256 causal variants.Figure S13 Relationship between false‐positive rate (Type I error) and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 4, 8 and 32 causal variants.Figure S14 Relationship between false‐positive rate (Type I error) and the number of associated SNPs selected for MLM, FarmCPU and Bayesian analysis for 16, 64 and 256 causal variants.Figure S15 Differences in the characteristics of causal SNPs identified by BayesCπ and FarmCPU. Distribution of MAF (Left) and absolute effect size (Right) for causal variants identified by both BayesCπ and FarmCPU, only BayesCπ, only FarmCPU, or neither approach.Figure S16 Relationship between minor allele frequency and type I error rates for markers in the maize, sorghum and rice datasets for both FarmCPU and BayesCπ.Figure S17 Relationship between simulated heritability and heritability estimates generated by BayesCπ for traits controlled by different numbers of causal variants.Figure S18 Empirically determined effect sizes for loci control seven different traits in maize.Figure S19 Average run time of a single GWAS analysis using each of the three methods evaluation in each of the four populations tested.Figure S20 Average maximum memory use of a single GWAS analysis using each of the three methods evaluation in each of the four populations tested.Figure S21 The influence of different LD decay cut‐offs on apparent GWAS power. Data shown are from simulations where the number of causal variants is 32 and heritability is 0.7.Click here for additional data file.Table S1. Mann–Whitney U test between SNP groups detected and undetected by GEMMA. Data shown are from simulations where the number of causal variants is 64 and heritability is 0.7.Table S2. Mann–Whitney U test between SNP groups identified by FarmCPU, BayesCπ, both and neither. Number of causal SNPs is 256 and heritability is 0.5.Click here for additional data file.Appendix S1 The significant SNPs identified by MLM, FarmCPU and BayesCπ in real‐world maize flowering time dataset.Click here for additional data file.


Ppd-D1 for maturity and Rht-D1 for plant height and seven of those were detected with both methods. We identified one locus for yield per se in 2014 on chromosome 6B with QTCAT and three in 2015, on chromosomes 4B and 5A with GAPIT and 6B with QTCAT. The 6B loci corresponded to the same region in both years. The favorable haplotypes for yield at the 5A and 6B loci are widespread in Australian accessions with 112 out of 153 carrying the favorable haplotype at the 5A locus and 136 out of 146 carrying the favorable haplotype at the 6A locus, while the favorable haplotype at 4B is only present in 65 out of 149 Australian accessions. The low number of yield QTL in our study corroborate with other GWAS for yield in wheat, where most of the identified loci have very small effects.Wheat landraces, wild relatives and other ‘exotic’ accessions are important sources of new favorable alleles. The use of those exotic alleles is facilitated by having access to information on the association of specific genomic regions with desirable traits. Here, we conducted a genome-wide association study (GWAS) using a wheat panel that includes landraces, synthetic hexaploids and other exotic wheat accessions to identify loci that contribute to increases in grain yield in southern Australia. The 568 accessions were grown in the field during the 2014 and 2015 seasons and measured for plant height, maturity, spike length, spike number, grain yield, plant biomass, HI and TGW. We used the 90K SNP array and two GWAS approaches (GAPIT and QTCAT) to identify loci associated with the different traits. We identified 17 loci with GAPIT and 25 with QTCAT. Ten of these loci were associated with known genes that are routinely employed in marker assisted selection such as  Wheat is the second most important cereal crop worldwide . It is ae.g. a 5-year mean of around 2 t/ha in the state of South Australia [In southern Australia, spring-habit wheat is sown in early autumn (often in May) so that the crop can rely upon autumn and winter rainfall. In spring, rainfall becomes more sporadic and heat waves often occur. This can lead to drought and heat stress at flowering and during grain filling and significant yield losses (reviewed by ). This kustralia . DespiteThe genetic improvement of crop plants is achieved by increasing the frequency of favorable alleles  within gene pools. For wheat, the primary gene pool consists of modern cultivars, landraces, synthetic hexaploids and some of wheat’s wild relatives . Althouge.g. [Considerable research has been conducted to detect and map quantitative trait loci (QTL) for yield and yield components using mapping populations derived from crosses between Australian varieties e.g. –15) and  and e.g.Genome-wide association studies explore historical recombination events by associating genotypes with phenotypes . They reDue to the diverse origins and genetic history of accessions that may be used for GWAS, statistical models are used to account for population structure and avoid the detection of false-positive associations –18. CommIn GWAS, the power of QTL detection can be low. To address this limitation, a quantitative trait cluster association test (QTCAT) was proposed , which gHere we describe the detection of genotype: phenotype associations for traits that were measured in a panel of over five hundred bread wheat accessions grown in southern Australia. We applied and compared linear mixed models and QTCAT approaches for the detection of these associations.The germplasm evaluated here consisted of a panel of 568 accessions of spring wheat originating from 36 countries. This panel included advanced cultivars, landraces and synthetic hexaploids. Seeds were obtained from INRA, CIMMYT and the Australian Grains Genebank (AGG) .o S, 138.772695o E). Management of pests and diseases and fertilizer applications followed local practices. Rainfall data were collected from a station located less than 5 km from the field site. Temperature data were collected from a station at Roseworthy, South Australia, around 30 km from the field site. Plots were six rows wide by 4 m long, with 22.5 cm spacing between rows within plots.Two field trials were grown during the 2014 and 2015 seasons under rainfed conditions at Tarlee, South Australia  in a partially replicated (p-rep) design . Of the In both 2014 and 2015, plant height  was measured for three randomly chosen plants per plot, from the soil surface to the tip of the spike excluding awns. In 2014, plant growth stages were recorded using the Zadoks scale  at 104 , Reduced Height gene  and Photoperiod genes  were obtained from the CerealsDB website  technology. KASP assays for aGW2-6B,  were desPopulation structure was estimated using a model-based approach implemented in the software ADMIXTURE version 1.23 . Accessi2) was estimated using a secondary model with accession as a random effect using the method of [Ppd-B1, Ppd-D1, Rht-B1 and Rht-D1) as fixed effects were also estimated.Before GWAS analysis, the phenotypic data from both trials for each trait were checked and spatially analyzed using the ASReml  package ethod of , for allTwo GWAS methods were used: the compressed mixed linear model (CMLM)  implemen2) was calculated as the difference between the R2 of the GAPIT model with and without the strongest associated SNP.In the GAPIT analysis, we accounted for population structure (Q) through a principal component (PC) analysis and for relationships among individuals through a kinship (K) matrix , both usIn QTCAT, the first step of the analysis was to generate a hierarchical clustering of all markers based on their correlations. Secondly, these clusters were tested for significant associations for each trait along this hierarchy, using a family-wise error rate threshold of α = 0.05. This step was repeated for all clusters showing significant association until none of the clusters of the next lower level was significantly associated anymore or until the single marker level was reached.−40 in order to find their putative locations on the wheat genome. DAWN  Chinese Spring (CS) RefSeq v1.0  using BLgeNomes, ) was usegeNomes, .In 2014, rainfall at the trial site was higher than average early in the year  but less than average later in the year (from August through December) . In 201510.25909/5becfa45c176f). Heritability estimates were quite high for most traits, including grain yield for which heritability was estimated at 70% and 85% in 2014 and 2015, respectively. This is not surprising, given the wide range of genetic material used. As expected in a dry and hot climate, grain yield was positively correlated with Zadoks scores, above ground biomass and HI and negatively correlated with plant height (A summary of the phenotypic traits is given in t height . Correlat height .10.25909/5becfa45c176f).A total of 30,548 SNP markers were polymorphic across the diversity panel, with 6,510 of these identical to other markers in the dataset, leaving 24,038 unique markers. Map positions were available for 24,982 markers , from whThe evaluation of cross-validation errors calculated for varying numbers of ancestral population K in the ADMIXTURE analysis showed that the error levelled off at K = 4 but continued to decrease somewhat for values of K > 4. The ancestral fractions estimated in ADMIXTURE for the number of ancestral populations K = 4 are shown in Pairs of accessions that showed very high levels of genetic similarity  were checked against pedigree information, and other known information about the background of the accessions. For example, two CIMMYT lines with very similar pedigrees differed at only 10 out of 23,833 markers indicating that they are almost certainly the same accession. Due to uncertainty about the true identity of these lines, both members of such pairs were removed from the GWAS analysis. This left subsets of 458 and 502 accessions for the 2014 and 2015 analyses, respectively.2) for significant associations found by GAPIT. We also show GAPIT’s allelic effect for associations found with QTCAT for which the GAPIT p-value was below 0.15. When an MTA was found with both methods, the p-value is given for both. A list of all significant markers is given in We tested the commonly used CMLM approach implemented in GAPIT and the recently developed QTCAT approach. In GAPIT, we accounted for population structure through PC analysis and model selection to determine the optimal number of PCs to include for each trait. A kinship matrix was also included in the GAPIT model to account for the relationships among individuals. No preference was given to a single method, so Markers that showed significant associations with traits were aligned to the Chinese Spring reference sequence (RefSeq v1.0) and BLASTN results are shown in Ppd-D1 locus on chromosome 2D was associated with Zadoks score and yield in both trials, and with harvest index (Qhi.aww-2D) in 2014, while the Rht-D1 locus on chromosome 4D was associated with plant height in both trials  and 4B (QSn.aww-4B), respectively (QSl.aww-4D (at 455 Mbp on chromosome 4D) and QSn.aww-4B (at 447 Mbp on chromosome 4B) suggest that these regions might be homeologous , 3B (QHi.aww-3B) and 6B (QHi.aww-6B)  . AlthougThe marker wsnp_Ex_c6129_10723211, which was not included in the consensus map of Wang et al. (2014), was significantly associated with harvest index and yield in 2015. The BLAST results for this marker show two possible positions on the physical map on chromosomes 3B and 4B, with very similar e-values.Ppd-D1 on chromosome 2D (per se (i.e. not related to phenology) are on chromosomes 4B (QYld.aww-4B), 5A (QYld.aww-5A) and 6B (QYld.aww-6B.1 and QYld.aww-6B.2). We used DAWN [Overall, we found five yield QTL, of which one was linked to osome 2D . The othsed DAWN  to visuased DAWN . DAWN [3sed DAWN  aligns rsed DAWN  onto theQYld.aww-4B peak is located in a 2 cM interval on the genetic map [The etic map  that is QYld.aww-4B, in contrast with Gladius and Wyalkatchem which carry the haplotype II  confirmed that Yitpi carries the favorable allele only at BS00023152_51, Xioyan-54 carries the favorable allele only at BS00066653_51 and that AC Barrie carries only unfavorable alleles . Using the six markers, we detected four haplotypes  yielded as much as those containing the favorable allele at all three yield QTL. The comparison of the effect of the individual QTL is complicated by the fact that only two accessions carry only QYld.aww-4A. QYld.aww-6B in isolation had an effect larger than that of QYld.aww-5A , and thMost GWAS methods use correction for genetic structure to reduce false marker-trait associations. The standard correction for genetic structure is a very stringent restriction on a GWAS analysis that often leads to a reduction of power in detecting true association. If a trait is highly correlated with genetic structure, then the significance of true positive decreases . This isHere, we studied a panel of around 550 diverse wheat accessions in two field trials and identified a total of 25 MTA using QTCAT and 17 MTA using the GAPIT approach. These results are more consistent with the comparison between methods in a simulation study . This stPpd-D1 on chromosome 2D. This gene has been shown to affect grain yield, especially in hot and dry environments where plants can escape the stress by flowering earlier in the season [Rht-D1 in both trials. Although Rht-B1 was also segregating in our panel, it was not significantly associated with plant height after correcting for structure; as the panel is structured in clusters that differ at Rht-B1, correction for structure removed Rht-B1 effects. We also found a locus associated with plant height on chromosome arm 6AS. QPh.aww-6A is located around 95 Mbp from the recently identified Rht25 locus, which affects plant height, heading time and spike development [QPh.aww-6A and the Rht-25 regions  but we could not locate this QTL on the physical map because the BLAST results only returned hits on chromosomes 4A, 4D and unassigned contigs  or the favorable alleles at QYld.aww-4B (47%). A previous study using 192 wheat accessions from southwest China found four loci associated with TGW on chromosome 4B [QTgw.aww-4B and the other three loci  were located less than 1 cM from our QSn.aww-4B. A QTL affecting the number of spikes could also affect TGW because of the negative correlation between grain number and grain size. So QSn.aww-4B may be the same as one of the TGW loci reported [We also found a QTL for TGW on chromosome 4B . In maize, a previous study could identify QTL of grain yield explaining 79% of the genetic variance with a dataset of 244 hybrids, 515k polymorphic SNP and 29 field trials across Europe  and the Ppd, Vrn and Rht as core genes. Because regulatory networks are highly interconnected, any expressed gene is likely to affect the regulation of core genes with a small effect size.An “omnigenic” model was proposed to explain the missing heritability in GWAS for complex traits . In humaThe omnigenic model raises questions about current methods for handling the multiple testing issue (such as FDR) which have arisen from the assumption that the majority of loci have an effect size of zero, with only a small number of non-zero effects. Hence new statistical approaches that move away from the paradigm of hypothesis testing may be needed if the majority of genes contribute small non-zero effects .Multiparent populations such as MAGIC (Multi-parent Advanced Generation Intercrosses) and NAM (Nested Association Mapping) populations might be a good alternative to GWAS in the case of grain yield especially in a crop like wheat in which genetic architecture of grain yield may be too complex explained by highly connected regulatory networks. These populations allow to explore more genetic diversity than the traditional biparental populations and have a higher power to detect QTL than GWAS –56. FutuS1 FigA) Rainfall in 2014 and 2015 as compared with the historical data (grey boxplot). B) Maximum average temperature in 2014 and 2015 as compared with historical data (grey boxplot).(PDF)Click here for additional data file.S2 FigPpd-D1 insensitive allele, the red dots represent accessions carrying the Ppd-D1 sensitive allele, the black dots represent negative controls and the pink dots represent accessions for which we were not able to make a confident call.The three panels represent different accessions. The blue dots represent accessions carrying the (JPG)Click here for additional data file.S3 FigThe red line represents the FDR corrected p-value of 0.04318, which is the closest to the threshold of FDR corrected p-value = 0.05 obtained in 2014.(JPEG)Click here for additional data file.S4 FigThe red line represents the FDR corrected p-value of 0.04433, which is the closest to the threshold of FDR corrected p-value = 0.05 obtained in 2015.(JPEG)Click here for additional data file.S5 Fig(PDF)Click here for additional data file.S6 Fig(PDF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table* Position based on BLAST results.(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 TableAlleles increasing yield are highlighted in blue and alleles decreasing yield are highlighted in yellow. Markers are ordered from left to right based on their position on the CS IWGSC RefSeq v 1.0.(XLSX)Click here for additional data file.S8 Table(XLSX)Click here for additional data file.S9 TableAlleles increasing yield are highlighted in blue and alleles decreasing yield are highlighted in yellow. Markers are ordered from left to right based on their position on the CS IWGSC RefSeq v 1.0.(XLSX)Click here for additional data file.S10 Table(XLSX)Click here for additional data file.S11 TableAlleles increasing yield are highlighted in blue and alleles decreasing yield are highlighted in yellow. Markers are ordered from left to right based on their position on the CS IWGSC RefSeq v 1.0.(XLSX)Click here for additional data file.S12 Table(XLSX)Click here for additional data file.


Data from genome-wide association studies (GWASs) have been used to estimate the heritability of human complex traits in recent years. Existing methods are based on the linear mixed model, with the assumption that the genetic effects are random variables, which is opposite to the fixed effect assumption embedded in the framework of quantitative genetics theory. Moreover, heritability estimators provided by existing methods may have large standard errors, which calls for the development of reliable and accurate methods to estimate heritability.In this paper, we first investigate the influences of the fixed and random effect assumption on heritability estimation, and prove that these two assumptions are equivalent under mild conditions in the theoretical aspect. Second, we propose a two-stage strategy by first performing sparse regularization via cross-validated elastic net, and then applying variance estimation methods to construct reliable heritability estimations. Results on both simulated data and real data show that our strategy achieves a considerable reduction in the standard error while reserving the accuracy.The proposed strategy allows for a reliable and accurate heritability estimation using GWAS data. It shows the promising future that reliable estimations can still be obtained with even a relatively restricted sample size, and should be especially useful for large-scale heritability analyses in the genomics era.The online version of this article (10.1186/s12859-019-2792-7) contains supplementary material, which is available to authorized users. Heritability measures how much the variation of a phenotypic trait in a population is caused by the genetic variation among individuals in that population. It has two specific types of definition: the broad sense and the narrow sense. The narrow-sense heritability is of more importance in genetic applications, which is defined as the ratio of the additive genetic variance to the total phenotypic variance . With thTraditional approaches to estimating narrow-sense heritability are based on twin or pedigree studies, in which genetic variance can be estimated from phenotypic similarity between relatives; see, e.g., , 3 and r3), though the whole number of SNPs is usually very large  [However, from the framework of quantitative genetics theory, the effects of genetic markers on a trait are fixed quantities, and genetic variance stems from variation at quantitative trait locus (QTL) genotypes , 14. Wha105∼106) , 19. In q<+∞, the ℓq norm of a vector u=0 if ui=0 for all i=1,2,⋯,n. For m≥1, let m×m identity matrix. For a matrix Wij  to denote its ij-th entry, Wi·  to denote its i-th row, and Wj·  to denote its j-th column. For any index set M⊆{1,2,⋯,n}, we use uM to denote the subvector containing the components of the vector u that are indexed by M, and WM to denote the submatrix containing the columns of the matrix W that are indexed by M.We begin this section by first introducing some definitions and notations for future reference. For 0<In this paper, we consider the following sparse linear model to approximate the true underlying model in GWASs, W is an m×n (m≪n) design matrix storing the SNP information, s (s≤n) nonzero entries, and e is a vector of residual effects with M0|=s represents the number of causal SNPs of a given trait. The sparsity level is defined as γ:=s/n, which may be high or low according to the trait studied. When there are other covariates  to be considered, we simply apply the method proposed in [where posed in , which pThen we state two assumptions regarding the model Eq. Fixed Effect Assumption. This assumption is consistent with the quantitative genetics paradigm. We now specify it in the sparse scenario as follows: (i). The rows of the design matrix W1·,W2·,⋯,Wm· are independent and identically distributed random vectors with mean n×n positive definite covariance matrix Σ=Cov(W1·); (ii). The residuals e1,e2,⋯,em are independent of the design matrix W; (iii). The vector u consists of fixed quantities with supp(u∗)=M0. Here the assumed covariance structure of Wi· is used to characterize the correlations between the n SNPs.Random Effect Assumption. Recently, researchers in [i∈{1,2,·,m} and j∈M0, ei is independent of W is made up with fixed entries.chers in , 10 madeW in detail under the context of genetics. Noting from the facts that in GWAS each SNP is regarded as a binomial random variable with two trials, and that the success probability is defined as “reference allele frequency”, the entries of the design matrix W can be formulated by another matrix Z in the following way: We now describe Z stores the original genetic information in a population. Concretely speaking, the genotype of each SNP is coded in this way: Zij=0  if the genotype of the ith individual at locus j is bb , and pj is the frequency of the reference allele at locus j. After being constructed as above, W is the standard genotype matrix with each column/row standardized to have zero mean and unit variance.where the matrix Then we are at the stage to define heritability under the two assumptions on the model Eq. mentclass2pt{minimFor the random effect assumption, which has been investigated by many authors , 21, theτ2 is still a fixed quantity, we make a slight modification to take expectation over the distribution of u∗, that is, The following proposition tells us that Eq. i∈{1,2,⋯,m}, u∗ are independent. Then Suppose that the nonzero genetic effects i∈{1,2,⋯,m} fixed, the total genetic variance attributed to causal SNPs is □For any u∗ are independent that where the third equality is from the fixed effect assumption (i) that j∈M0, By the assumption that for Wij:j∈M0} are a set of centralized and normalized random variables with zero mean and unit variance by Eq. Since {In this subsection, we introduce our two-stage strategy to estimate heritability, which consists of a sparse regularization step followed by a variance estimation step.m is even for simplicity. Then the original data set  is randomly split into two disjoint data sets (y(1),W(1)) and (y(2),W(2)) with equal samples. Without loss of generality, the following sparse regularization step is performed on (y(1),W(1)) to reduce the model, while the variance estimation step is applied on (y(2),W(2)). In doing so, it is guaranteed that sparse regularization and variance estimation are performed on independent samples. We explain the reason for using independent samples at the end of this section.Before a detailed description of the strategy, let us assume that the sample size Recall the model Eq. Since in reality, one has no prior knowledge on the amount of each effect, the sparse regularization technique is required to be flexible to both small and large effects. In this paper, we adopt the elastic net  as our sα∈, which is designed for Lasso or elastic net regularization of linear models. Specifically, we first define a set Ω corresponding to the domain of α. Then for each α∈Ω fixed and a set of regularization parameters λ predefined, we perform 10-fold cross-validation and choose the smallest λ that is within one standard error of minimum prediction mean squared error (MSE), as is shown for instance in blue dashed line in Fig. α to be the one that meets the minimum prediction MSE across the set Ω. After the parameters α and λ have been determined, the selected model is denoted as In practice, we fit the optimization problem Eq. m/2.Now some certain variance estimation methods are applied to 2∼103) to large , the method must be stable with respect to the sparsity level. Moreover, as it is realistic that different SNPs are usually not independent, the method should also be capable of handling the case where there exist correlations between the SNPs. Therefore, we choose to use the method proposed in [τ2 and For the fixed effect assumption, as le works –28 consiposed in , which iNote that when For the random effect assumption, we simply apply the widely-used software GCTA , which iOLT-REML  or MEGHAOLT-REML  are of cSince the true heritability always belongs to , once λ is chosen to be the smallest one that is within one standard error of minimum MSE in section 2.2.1, as is shown in blue dashed line in Fig. λ is too small and the selected model contains many redundant variables, though the heritability estimator is almost unbiased, its variance is large. Our choice of λ guarantees that the heritability estimator is not only almost unbiased but also with a smaller variance. The performance of our strategy will be demonstrated in detail in the next section.To understand the behavior of the heritability estimator produced by our two-stage strategy, we make a decomposition of the bias and variance of the estimator. We only use mentclass2pt{minimmentclass2pt{minimmentclass2pt{minimλ which represents the model selection process. We only use λ becomes larger, the selected model becomes more sparse, and the generalization ability of the selected model increases. Therefore, using samples independent of those used in model selection to estimate variance guarantees that even if the selected model is not sparse enough, the heritability won’t be overestimated. Otherwise, if model selection and variance estimation are done on the same sample set, the heritability is more likely to be overestimated. Hence, we suggest that model selection and variance estimation should be performed on independent samples to reduce overestimation.Now let us turn to illustrate the reason for using independent samples in the proposed two-stage strategy. Assume that we are in the case where there are 10 causal SNPs out of total 10000 SNPs. Then Fig. https://github.com/hruffieux/echoseq) [W is generated with correlated columns based on generally accepted principles of population genetics . The sparse effect vector s indices at random according to a s being chosen for given n. The noise vector e is set as Gaussian with mean 0 and covariance matrix y are then obtained via the model Eq. The simulated genotype data are generated via the R package “echoseq” (echoseq) . Specifimentclass2pt{minimhttp://imagen-europe.com) using a standardised 3T, T1-weighted gradient echo protocol in eight European centres [https://www.cog-genomics.org/plink2) [%, minor allele frequency ≥1%, and Hardy-Weinberg equilibrium P≥1×10−6. After quality control, we finally used 225139 SNPs across the 22 autosomes genotyped on 1765 participants.Brain imaging scans were obtained from a cohort of 2089 adolescents  from the IMAGEN project ( centres . Genotyp/plink2) . We exclThe purpose of this section is to carry out several experiments and demonstrate results on the heritability estimation problem for both simulated data and real data from the IMAGEN project. All experiments are performed in MATLAB R2014b and executed on a computer with the following configuration: Intel(R) Xeon(R) CPU E5-2630 v2, 12×2.60 GHz, 126 GB of RAM. The runtime for model selection is about 10 minutes and the required memory is about 8GB, with a data set including 1000 samples and 100000 SNPs, whose scale is close to that of real data. The following variance estimation step takes only a few seconds.s=n and M0={1,2,⋯,n}.To compare the influences of the fixed and random effect assumptions, the estimators The corresponding boxplot is displayed in Fig. s=n and M0={1,2,⋯,n}. The noise level To simplify our expositions, the following simulations are carried out under the case in which all the SNPs have nonzero effects, that is m∈{300,1000,3000}. The corresponding boxplot is displayed in Fig. Firstly, we illustrate the performance of both estimators entclass1pt{miniman∈{1000,3000,10000}. The corresponding boxplot is displayed in Fig. Secondly, we illustrate the performance of both estimators entclass1pt{minimas∈{100,1000,10000}. We use the oracle estimators corresponding to the fixed and random effect assumptions for comparisons, whose values are calculated via To elucidate the importance of sparsity, both estimators s=100,1000. On the other hand, we can see from the oracle estimators that when the sparsity of u∗ is taken into consideration, the corresponding standard errors have been greatly reduced, resulting in more reliable estimations. In practice, since the set of causal SNPs is usually unknown, it is necessary to approximate the sparsity pattern of the effect vector M0 as close as possible before variance estimation.The corresponding boxplot is displayed in Fig. To illustrate the performance of the proposed two-stage strategy, both estimators n is high , the performance of the estimator W, and can be applied to the cases where LD exists.We can see from Fig. We apply our two-stage strategy to estimate the heritability of height and the volume of neuroanatomical structures, specifically, the nucleus accumbens (Acc), amygdala (Amy), caudate nucleus (Ca), hippocampus (Hip), globus pallidus (Pa), putamen (Pu), and thalamus (Th).α∈{3×10−5,10−4,3×10−4,10−3} in Eq. As is widely-acknowledged that most human complex traits are generally polygenic and the corresponding heritability is largely captured by common SNPs , 32, theWe can see from Tab. In addition to demonstrating the performance of our strategy, we analyse the heritability of average cortical thickness measures in 68 regions of interest  defined by the Desikan-Killiany atlas [n is high , the performance of the estimator In this paper, we compared the fixed and random effect assumption in detail from both theoretical and practical aspects. In the theoretical aspect, we proved that the definitions of heritability are equivalent under mild conditions for both the fixed and random effect assumptions. In the practical aspect, our results demonstrated that both assumptions worked well, and produced similar estimators. However, when there exist correlations between the SNPs and the problem dimension In modern GWASs, it has been pointed out in , 19, 35 We proposed a two-stage strategy by first performing sparse regularization using cross-validated elastic net to select the model, and then applying certain variance estimation methods on the reduced model. Due to the fact that in the context of GWASs, there always exists a strong correlation between the explanatory variables  , attentiResults from simulated data implied that our strategy produced estimators with considerably smaller standard errors than those obtained via methods without considering the sparsity Fig. , leadingWhile we are working on this paper, we became aware of an independent work . Our conWe have considered the potential sparse structure of GWAS data, and proposed a two-stage strategy to produce reliable heritability estimations. Results on simulated data and real data demonstrate the promising future of our strategy for ultrahigh dimensional heritability analyses with even a relatively restricted sample size. Due to the fact that model selection consistency cannot be achieved unless certain strong conditions are satisfied , thAdditional file 1Additional estimation results using the proposed strategy. (PDF 242 kb)


ReliefF is a nearest-neighbor based feature selection algorithm that efficiently detects variants that are important due to statistical interactions or epistasis. For categorical predictors, like genotypes, the standard metric used in ReliefF has been a simple (binary) mismatch difference. In this study, we develop new metrics of varying complexity that incorporate allele sharing, adjustment for allele frequency heterogeneity via the genetic relationship matrix (GRM), and physicochemical differences of variants via a new transition/transversion encoding.We introduce a new two-dimensional transition/transversion genotype encoding for ReliefF, and we implement three ReliefF attribute metrics: 1.) genotype mismatch (GM), which is the ReliefF standard, 2.) allele mismatch (AM), which accounts for heterozygous differences and has not been used previously in ReliefF, and 3.) the new transition/transversion metric. We incorporate these attribute metrics into the ReliefF nearest neighbor calculation with a Manhattan metric, and we introduce GRM as a new ReliefF nearest-neighbor metric to adjust for allele frequency heterogeneity.We apply ReliefF with each metric to a GWAS of major depressive disorder and compare the detection of genes in pathways implicated in depression, including Axon Guidance, Neuronal System, and G Protein-Coupled Receptor Signaling. We also compare with detection by Random Forest and Lasso as well as random/null selection to assess pathway size bias.Our results suggest that using more genetically motivated encodings, such as transition/transversion, and metrics that adjust for allele frequency heterogeneity, such as GRM, lead to ReliefF attribute scores with improved pathway enrichment.The online version of this article (10.1186/s13040-018-0186-4) contains supplementary material, which is available to authorized users. ReliefF is a nearest-neighbors feature selection algorithm that is known for its ability to identify statistical interactions in high dimensional data , 2. SpecWhile ReliefF analysis of GWAS data depends critically on its ability to measure the degree of dissimilarity between genotype states, the diff function used up to this point has been extremely simple. For example, the standard ReliefF genotype diff between two subjects is binary: the diff is 0 when the genotypes of the two subjects at a SNP are identical and 1 if their genotypes are not identical. The distance between a pair of subjects is obtained by summing the diff values in a city-block (Manhattan) metric across all SNPs. The binary nature of this standard diff is likely an oversimplification that misses information because there are degrees of difference between genotypes. In addition to a metric based on allele-sharing differences, we develop a transition/transversion (Ti/Tv) metric that accounts for physicochemical differences of nucleotides and a Genetic Relationship Matrix (GRM)  metric tThe main goal of the current study is to develop and compare combinations of metrics between SNPs and subjects in ReliefF feature selection. We also compare with statistical learning feature selection methods Random Forest  and LassIn the current study, we use enrichment of pathways related to major depressive disorder (MDD) to compare feature selection methods. Early GWAS studies of MDD had limited success at finding significant variants due to the contribution of many loci with small effect sizes as well as the heterogeneous characteristics of MDD and the complex interaction between genetic variation and environmental factors . In receThe current study is organized as follows. We describe the overall strategy, briefly review the relevant components of ReliefF, describe a new allele sharing ReliefF diff, develop a new 2d transition/transversion genotype encoding and accompanying new ReliefF diff. We also introduce the first use of GRM to compute nearest hits and misses in ReliefF. We apply ReliefF using combinations of diffs and metrics with other statistical learning methods to 463 cases of MDD and 459 controls, and we test the top selected SNPs and their corresponding genes for overlap with biological pathways related to mental disorders. Our results suggest that using more genetically motivated metrics  and metrics that adjust for allelic heterogeneity  lead to ReliefF scores that improve enrichment of biologically relevant pathways.The goal of this study is to develop new ReliefF metrics for GWAS and compare them based on their ability to enrich for genes in pathways that have prior evidence for relevance to a phenotype. Our overall strategy Fig.  is to coFor ReliefF, we implement four methods for computing the nearest-neighbor distance matrix in our inbix software with --snp-metric-nn flag Fig.  and threi (i=1…m) as another instance that has the same class label (case or control) as that of Ri, and a miss is another instance with a different class label from Ri. Once a distance matrix, D, is computed between all instances (discussed more below), the reformulated ReliefF score for SNP gν (ν =1…N) can be written as:The goal of the Relief algorithm  is to eswhere the quantitiesandgν of all subjects Ri (i=1…m) from their k-nearest-neighbor misses  and hit) in Eq. ]. The k We introduce three diff functions for measuring the genetic dissimilarity between pairs of individuals at a single locus. The first diff is the standard used in ReliefF for categorical variables, which we refer to as genotype mismatch (GM). The second metric accounts for allele sharing, which we refer to as allele mismatch (AM). The third diff further accounts for mutation type through transition/transversion differences (Ti/Tv). These first three diffs will be used to compute attribute importance and to compute city-block (Manhattan) distances between subjects. We will discuss these nearest-neighbor metrics and the genetic relationship matrix (GRM) in a later subsection.R1, R2) for a SNP, gν, based on the individuals’ genotypes. The diff function isThe standard metric used by ReliefF for categorical variables uses a binary mismatch diff. For SNPs, the genotype mismatch (GM) is a 0 or 1 difference between two individuals  is the genotype for individual R1 for SNP gν. In other words, two individuals have zero diff if they have identical genotypes and they have unit diff if they have different genotypes.where genotype diff accounts for the difference in the number of alleles for a SNP when computing the difference between two individuals. The difference of two individuals can be calculated by the following formulagiν is the number of copies of the reference allele for the νth SNP of the ith individual. In other words, the value of gν1 is the number of minor alleles in the genotype: 0, 1 or 2. Then the return value of diffAM  is 0, 0.5 or 1 when the two individual have 2, 1 or 0 alleles in common, respectively.where The AM diff increases the sensitivity over the GM diff because with AM a heterozygous state is half the distance between either homozygous state. Next our goal is to incorporate additional physicochemical information into the diff based on transition and transversion mutations. A transition is a point mutation  and ey = . Below we use Dirac bra-ket notation, where | x〉 represents a column vector and 〈x| represents a row vector. An example of this encoding that is appropriate for transversion genotypes or an additive encoding  to each other: | aa〉Tv = ex on the horizontal axis and | AA〉Tv = ey on the vertical axis. And then the heterozygous state is an equal mixture (θ = π/4) of the homozygous states: Before constructing the Ti/Tv diff, we first introduce a 2d Ti/Tv genotype encoding Fig.  in whichθ = π/4) like transversions, but instead of being orthogonal, the homozygous states are contracted toward the diagonal with an angle of separation θ = π/6.For transition mutations, we want our encoding to contract the distance (relative to transversion encoding) between two homozygous states and between a homozygous state and the heterozygous state 〉 to represent the six possible 2d Ti/Tv genotypes  for SNP gν is the squared dot product of the individuals’ Ti/Tv encoding (| ψ1(gν)〉 and | ψ2(gν)〉):We use | pes Fig.  for indiwhere orgν is a transversion and individual R1 has homozygous genotype 2 has heterozygous genotype If For two individuals at a transversion SNP that are opposite homozygotes  to be smaller than diffs between Tv homozygous states (1 difference) because transition mutations stay in the same biochemical family (purine to purine or pyrimidine to pyrimidine). Similarly, the encoding causes diffs between heterozygous and homozygous Ti genotypes (1/4 difference) to be smaller than the corresponding Tv diffs (1/2 difference).We catalog the output of the GM, AM, and Ti/Tv diff functions for all combinations of genotypes and for the cases when the SNP is a transition or transversion Table . The GM i and Rj for all genetic variants gν (ν = 1…N) in a city-block metric  Eqs. , 5, 8 batric Eq.  below. T. GM Eq.  in the fAM  from GCTA. The GRM is used to calculate the genetic relatedness between pairs of individuals in the space of N SNPs , 20. We wheregiν is the number of copies of the reference allele for the νth SNP of the ith individual and pν is the frequency of the reference allele [3]. Each genotype in the summand is standardized by pν to account for the differences in allele frequency between SNPs. In addition to comparing diff functions  is a widely used machine learning classifier and feature selector that grows an ensemble of classification trees in bagged samples with random attribute selection . To meas2 = 0.5 as the estimate of the heritability to calibrate the regression and we used λmin = 0.001 for the L1 penalty parameter. Finally, we generated lists of random genes as a null comparison list that shows the effect of pathway size on enrichment. A random set of 500 genes is randomly sampled 100 times and the average overlap of the 500 genes is computed for each pathway. Estimating the expected number of overlapping genes by chance helps to calibrate the overlaps of each pathway for the non-random feature selection methods.We used the PLINK software to perform Lasso (--lasso). We adjusted for the first five principal components, and the PCs were not subject to model selection. The top Lasso variants were chosen by top regression coefficients. We used hInteraction-Network BIonformatics ToolboX (inbix) software for machine learning and epistasis network analysis for high-dimensional data. Inbix is a free, open-source, command-line bioinformatics tool, written in C++ and designed to perform a range of large-scale analyses with computational efficiency. The source is publicly available from our website and github (http://insilico.utulsa.edu/index.php/inbix/ and https://github.com/insilico/inbix) [./inbix --bfile <bed-file> --relieff --pheno <pheno-file> --snp-metric-nn <nn-metric> --snp-metric-diff <diff-metric> --out <results-file>where <diff-metric> can take on values gm, am, or ti/tv and <nn-metric> can also take on values gm, am, or titv with manhattan or Euclidean for combining the individual SNP diffs. The user may alternatively select grm in <nn-metric>, which uses GRM as the nearest-neighbor metric and does not use the diffs. Any combination of <diff-metric> or <nn-metric> is allowed. For the MDD GWAS with 922 individuals and 281,648 SNPs (after filtering), the GRM metric takes approximately 8 hours and the other metrics take approximately 12 hours of CPU time  , 25, 26.o/inbix)  along wik = ⌊m/6⌋ = 138 nearest neighbors.In this study we compare ReliefF metrics with each other and with other analysis methods based on enrichment of selected features in functional pathways for MDD. We used a recent GWAS of MDD  that incAdditional details of data processing and analysis, including command line scripts, is provided in the Additional file A list of ranked SNPs for each method is obtained from the algorithms to be compared   to identWe evaluate feature selection methods based on the number of genes found in pathways that have been implicated in mood disorders Figs. , 6 and 7We compare combinations of ReliefF attribute diff functions for use in the average miss and hit calculations Eqs.  and 3 anWe first note that for random gene selection  was calculated. Our results provide evidence that using either AM Eq.  diffs inThe GRM method for finding nearest neighbors has the useful property of adjusting for alleleic heterogeneity. Using GRM to compute nearest neighbors results in the best enrichment for two of the three pathways: GPCR Signaling with GRM-TiTv . However, we note that no single analysis method can extract all information from a whole-genome association study  and each method finds unique gene signatures that can contribute to the overall picture of the pathway or phenotype. Thus, combining metrics and feature selection methods may be a good strategy for maximizing the detection of relevant genes. There are opportunities to improve these methods by incorporating additional information about the biological properties of the data, similar to phylogenetic substitution matrices or using coding/non-coding information. One may also assess the false discovery rate of different metrics using the STIR approach for determining the statistical significance of Relief scores .Additional file 1:Command line details to use inbix to perform GWAS filtering and pathway enrichment and feature selection by random forest, lasso, and ReliefF with new transition-transversion diff and genetic relationship metric. (DOCX 35 kb)


Sorghum bicolor lines and landraces and S. bicolor × S. halepense recombinant inbred lines. One key breeding problem modelled was predicting the performance in the antioxidant production of new and unphenotyped sorghum genotypes . The population was weakly structured , showed a significant genetic diversity and expressed antioxidant traits with a good level of variability and high correlation. The S. bicolor × S. halepense lines outperformed Sorghum bicolor populations for all the antioxidants. The four GS models implemented in this work performed comparably across traits, with accuracy ranging from 0.49 to 0.58, and are considered high enough to sustain sorghum breeding for antioxidants production and allow important genetic gains per unit of time and cost. The results presented in this work are expected to contribute to GS implementation and the genetic improvement of sorghum grain antioxidants for different purposes, including the manufacture of health-promoting and specialty foods.The purpose of this work was to assess the performance of four genomic selection (GS) models  in 4 sorghum grain antioxidant traits  using whole-genome SNP markers in a novel diversity panel of  Sorghum bicolor (L.) Moench) (2n = 2x = 20 chromosomes) is one of the world’s most important cereals grown for food, feed and biofuel )ith individual at the jth marker, jth marker covariate. The residual was assumed to follow normal distribution with constant variance i.e., Descriptively, the genomic selection models assumed that the phenotypic outcomes ested by . To evalested by ,54 was aThe model parameters were estimated in the training set and the models validated in the testing set. The performance of the models (accuracy) was measured as the Pearson correlation coefficient  in all the traits. The pairwise Pearson correlation coefficients among the four antioxidant traits  were posThe next generation sequencing and genotyping of the panel of 114 sorghum lines evaluated in this work yielded an unfiltered matrix of 1,252,091 SNP marker loci which, after quality control, resulted in a final working matrix consisting of 61,976 high-quality SNPs. The physical maps of the 61,976 discovered high-quality markers covered the 10 chromosomes (Chr) of Sorghum bicolor . The relSorghum bicolor × S. halepense recombinant lines, cluster B (vivid orange color) included 37 Sorghum bicolor breeding lines developed mainly from Southern and Eastern African Sorghum bicolor lines and landraces, while in cluster C (dark-cyan color) 58 Sorghum bicolor breeding lines developed mainly from Asian Sorghum bicolor lines and landraces were grouped. As shown by the neighbor joining algorithm, these main clusters included several sub-clusters and the model-based structure algorithm showed that most of the lines included different levels of admixture coefficients values. The analysis of molecular variance (AMOVA) resulted in highly significant effects (p = 0.001) of the clusters on the molecular variance observed in the GBS SNP dataset (2) was calculated to assess how well the three-cluster model explained the variability in the data set. In this work, R2 was low (9%), meaning that the AMOVA model based on the three clusters did not fully account for the diversity that existed in the population.The 114 sorghum genotypes evaluated in this work clustered in three main groups using neighbor joining  and mode dataset . The coeThe main feature of the genomic selection approach is represented by the possibility to compute the genomic estimated breeding value  upon which superior strains are selected without conventional trials and phenotyping. Four GS models were implemented in this work to evaluate their performance in predicting the genetic merit for the production of polyphenols, flavonoids, total antioxidants and condensed tannins in 114 sorghum genotypes. The predicting ability as represented by the respective GS model accuracy is presented in Compared to other grains, sorghum contains high levels of antioxidants, which can help prevent cell and DNA damage and play a role in degenerative disease prevention . SorghumSorghum bicolor landraces and a progeny derived from S. bicolor × S. halepense (SBxSH) hybridizations. To the best of the authors’ knowledge, it is the first time GS approach is performed to predict antioxidants in sorghum grains. The different metrics used in this work highlighted the important diversity that existed in the evaluated sorghum materials. Using a quantile approach and the Bayesian regression model with Stan revealed a good level of phenotypic variability that was significantly explained by the differences between the evaluated sorghum lines (2 = 9%) genetic differentiation. The lower coefficient of determination (R2) meant that much of the variance and the structure observed in the population could be attributed to other sources, such as differences between individuals within clusters and/or between individuals, and admixture, all of which can be associated with different levels of pairwise kinships. This work aimed at conducting GS for sorghum grain antioxidants using SNP markers in a novel diversity panel consisting of a combination of um lines , Table 1S. halepense genome constitute a good source of antioxidants [S. halepense represents an untapped reservoir and a good source of genetic diversity that can be used in conventional and molecular breeding. On the other hand, the S. bicolor genotypes were derived from African and Asian landraces and are expected to harbor a high level of genetic diversity for breeding purposes inasmuch as Africa and Asia represent, respectively, the primary and secondary sorghum centers of diversity [S. bicolor landraces evaluated have a long history spanning, respectively, more than 6 and 20 years in our breeding program. They have accumulated cycles of meiotic and recombination events that brought about genetic diversity, which qualify the sample size used herein for investigations in genomic prediction [The observed diversity is associated with the intrinsic genetic properties of the plant materials used in this work. The landraces and, particularly, the oxidants . In SBxSiversity . Furtherediction ,61,62. The broad-sense heritability of the traits  evaluated in this work was very high, indicating that the phenotypic variations of the measured antioxidant metrics are mainly affected by genetic factors and therefore this panel can be used for genomic prediction and selection. On the other hand, the pairwise correlation among the four antioxidant traits  was posiSorghum bicolor landraces and S. bicolor × S. halepense recombinant inbred lines. To the best of the authors’ knowledge, it is the first time GS prediction modelling is implemented in sorghum antioxidants. Sorghum halepense is mostly used in hybridizations with domesticated S. bicolor with the aim of introgressing perenniality into the genetic background of S. bicolor but, it can also be used for genetic improvement of several other traits [S. halepense × S. bicolor lines statistically (at the 0.05 probability level) outperformed S. bicolor populations in terms of total antioxidant capacity  and the contents of tannins (7358.57 versus 3053.25 μg CE g−1 dm−1), phenols (6.56 versus 3.93 g GAE kg−1 dm−1) and flavonoids (6738.39 versus 3869.66 μg CE g−1 dm−1). The S. halepense × S. bicolor lines evaluated in this work can therefore be considered as a good source of antioxidants variability in addition to the possibility of using them to breed for perennial grain sorghum fortified with antioxidants. Nonetheless, the genomic selection for grain quality and production in a population derived from the hybridization Sorghum bicolor × Sorghum halepense is expected to be challenging particularly due to the necessity to eliminate negative wild-related traits such as loose panicle, tiny seeds and seed chattering. The different breeding strategies can be applied, including combining different traits in an index of selection with appropriate weights or applying a breeding scheme  to cull the undesired traits first, before proceeding with breeding for antioxidant production. The purpose of this work was to conduct GS of sorghum grain antioxidants using SNPs in a novel diversity panel of r traits , such asr traits  in whichMarker density resulted in a physical map length comparable to the sizes of the chromosomes of the sorghum reference genome (Sorghum_bicolor NCBIv3) . The denThree major factors that affect the GS accuracy are the training set size, marker density and population structure . In thiss . In adds e.g., ,39). . ntrn= 8The available empirical evidence for GS efficiency in plant breeding is set to 0.5, the baseline for GS prediction accuracy in plant breeding ,67. In h


HLA play an important role in the acute and chronic allogeneic immune response against the graft. Perfect matching at clinically relevant HLA loci does not obviate the need for immunosuppression, suggesting that additional genetic variation plays a critical role in both short‐ and long‐term graft outcomes. By combining patient data and samples from supranational cohorts across the United Kingdom and European Union, we performed the first large‐scale genome‐wide association study analyzing both donor and recipient DNA in 2094 complete renal transplant‐pairs with replication in 5866 complete pairs. We studied deceased‐donor grafts allocated on the basis of preferential HLA matching, which provided some control for HLA genetic effects. No strong donor or recipient genetic effects contributing to long‐ or short‐term allograft survival were found outside the HLA region. We discuss the implications for future research and clinical application.Improvements in immunosuppression have modified short‐term survival of deceased‐donor allografts, but not their rate of long‐term failure. Mismatches between donor and recipient  The largest multicenter genome‐wide association study to date on short‐ and long‐term renal transplantation outcomes finds no loci outside the HLA region, highlighting challenges in phenotypic heterogeneity and sample size while also providing a reference dataset for future meta‐analyses. NIHRThe National Institute for Health ResearchUKIRTCThe United Kingdom and Ireland Renal Transplant ConsortiumWTCCC3Wellcome Trust Case Control Consortium 31Kidney transplantation is a highly successful treatment for end‐stage renal failure, with significant benefits for recipients both in survival and quality of life. Early outcomes have steadily improved over the last 10 years,The importance of genetic factors in transplantation has been clear since the inception of the technique, with the first successful kidney transplant having been performed between identical twins in 1954. Renal transplantation between identical twins continues to show excellent long‐term outcomes,HLA genes are highly polymorphic, and demonstrate the importance of genetic variation in donor‐recipient pairing that impacts on long‐term outcomes. However, over recent decades, our ability to assay human genetic variation beyond the HLA region has increased considerably.A number of studies have been published over recent years exploring the association between genotypes of interest and renal transplant outcomes.CAV1 (caveolin‐1),APOL1 (apolipoprotein‐L1),ABCB1  genes CAV1.More recently, attention has also focused on non‐immune‐related genetic risk variants. Donor genetic variation in In general, candidate gene studies in renal transplantation have so far failed to provide consistent and reproducible results. Some of the reasons for this may include small sample sizes, variations in genotyping methodology and strategy, and, perhaps most importantly, a lack of consistency in clinical phenotyping.http://www.wtccc.org.uk/ccc3) has led the deployment of GWAS in a wide range of conditions. As part of WTCCC‐3, all renal transplant centers in the United Kingdom and Ireland formed the United Kingdom and Ireland Renal Transplant Consortium . Collaborative initiatives such as these are essential for the collection of adequate sample numbers, for the sharing of expertise, standardization of techniques, and building consensus on accurate phenotyping of clinical data. Through this consortium, 3936 samples comprising 2094 complete donor‐recipient pairs were tested in the GWAS discovery phase, and an additional 5866 complete donor‐recipient pairs in the replication phase, making this the largest GWAS conducted to date in renal transplantation outcomes.The Wellcome Trust Case Control Consortium (22.1http://www.UKIRTC.org), coordinated by King's College London in partnership with the WTCCC‐3 and the National Health Service Blood and Transplant database (NHS‐BT), sourced all available good‐quality stored DNA samples and pre‐existing GWAS data from both recipients and their corresponding donors from all renal transplantation centers in the United Kingdom and the Republic of Ireland , there were 2689 unique recipients, 2204 unique donors, and 2094 complete donor‐recipient transplantation pairs available for analysis. Figure Inclusion criteria for the study were as follows: (1) deceased donor kidney transplants only; (2) recipient is an adult (>16 years old); (3) reported European ancestry for recipients; and (4) graft survival time >3 months. Donor‐recipient allocation followed NHS‐BT standard UK‐protocols during the study period.2.2A cohort of 5866 complete donor‐recipient pairs, with similar ethnicity to that of the discovery study, were obtained from the Collaborative Transplant Study DNA Biobank held at the University of Heidelberg, Germany Table .Clinical variables, datasets, and analysis are described in Supplementary Methods.2.3A whole genome amplification step was undertaken  for samples containing 5‐40 μL of DNA (n = 990 samples). Samples were assayed via Illumina 670 Quad Custom GWAS chips, and subjected to standard postgenotyping quality control procedures before being imputed to the 1000‐genomes reference dataset. Imputation of HLA alleles from SNP genotype data was undertaken using HLA*IMP software2.4P value (<10−6) from the discovery phase, plus good support of association signals from SNPs in local linkage disequilibrium (LD), or on prior candidature from previous association studies. SNPs were tested according to the same model as motivated their inclusion in the replication panel . Meta‐analysis of discovery and replication results was carried out using inverse variance meta‐analysis.Replication DNA samples were received at King's College London and sent to the Wellcome Trust Sanger Institute for replication analysis. A replication panel of 139 SNPs  was tested based on a combination of low For further details see Figure 2.5The funding sources did not participate in the study design, collection, analysis or interpretation of the data, nor did they have a role in writing the report or the decision to submit for publication.33.1P ≤ 5 × 10−8). We also performed a partitioned heritability analysis via stratified LD score regression,Despite the large size of our study Table , none ofP value from the discovery phase plus LD support or on prior candidature from previous association studies. In general, the distribution of replication P values for all the tests did not depart appreciably from that expected under a global null hypothesis  did not reach genome‐wide significance (P ≤ 5 × 10−8). The single SNP with strongest evidence for association was rs2289887  were tested, based either on a low is Table . There w7 Figure , which hWe collated all previously published association signals for early graft rejection and long‐term allograft survival and none of these replicated in our study Table .3.2P = .022) and HLA‐DRB (P = .00049) mismatches using the recorded data.We took advantage of recorded serological information to check for known associations with donor‐recipient mismatch levels and to compare recorded information with imputed mismatches based on SNP genotype information Figure . As expeOn the other hand, the imputed mismatch results did not reproduce the expected associations. We attribute this to 2 factors: (1) the true mismatch = 2 frequency was low, due to donor selection; (2) as with any statistical noise, the imputation inaccuracy tended to act with disproportionate effect in the extremes of the distribution , resulting in higher relative errors in that group. Thus, although the overall imputation accuracy was high Tables  and S6, 4In this article, we report the results of the first large‐scale GWAS in renal transplantation. Despite our considerable sample size, we did not replicate any proposed findings from previous candidate gene studies nor did we discover any convincing new variants in our own analyses. There are a number of plausible reasons that may explain this.Firstly, although this was a study involving thousands of individuals, by GWAS standards it was at the lower end of the range of sample sizes that have been employed for other human traits.Secondly, part of our study sought to look for recipient‐donor genetic interactions. Interaction effects require even larger sample sizes to be reliably discovered. With a few notable exceptions,Thirdly, and perhaps most importantly, the transplantation outcomes we considered were relatively crude measures obtained retrospectively from national registry data, collected over many years for reasons other than for acting as endpoints in a genome‐wide association study. Our outcomes were therefore heterogeneous, subject to missingness, and subject to environmental factors that likely weakened the genetic signals. Graft survival time is expected to be subject to a range of factors including graft quality, drug regimen, patient compliance, changes in standard‐of‐care over time, between‐center differences, and underlying biological causes of renal dysfunction. Additionally, a substantial proportion of the survival time data were right‐censored , reducing the power for this endpoint.Acute graft rejection is also a heterogeneous phenotype arising from various immune and nonimmune biological causes. Furthermore, this phenotype was derived from a field that in many records was left blank, resulting in a high degree of missingness . The high missingness rate reduced the power of our study, and nonrandom missingness would complicate the interpretation of any positive association signals we might have found .Batch effects are also a concern. Both the discovery and replication data were obtained from multiple different collection points in different countries over many years, and thus our phenotypes may be subject to batch effects, for example, arising from different treatment protocols over time and space. Genetic data can also be subject to batch effects, for example, arising from differences in sample collection protocols and unknown differences in population structure. We applied both covariate selection and genetically derived principal component axes to try to mitigate such effects. We also note that, as with nonrandom missingness, the batch effect structure would need to be the same in both the discovery and replication cohorts in order for false‐positive association signals to be replicated. Nevertheless, together these extraneous factors may well have increased the noise in our data, and so reduced (and made less detectible) the genetic effects in our data.HLA imputation from chip‐based genetic data might in time be of value as an adjunct to serological typing. However, our investigations found that the additional noise introduced by imputation uncertainty prevented the imputed data from picking up the well‐known mismatch signals at HLA‐A and HLA‐DRB. This suggests that the accuracy of HLA imputation will need to be improved before it can be used reliably as an alternative to serotyping.In contrast, our serological data successfully detected the HLA‐A and HLA‐DRB mismatch signals, despite the reduced power to do so resulting from HLA‐matching of deceased donor allografts. This indicates that, despite the various shortcomings of our study, strong HLA signals were detectable in our data. The implication therefore, at least as far as our primary graft survival endpoint is concerned, is that signals outside the HLA region are weaker than those already established in the HLA region. We therefore anticipate that genetic effects outside of the HLA region are more likely to be of value in elucidating biological pathways than in direct clinical prediction.−8, power = 0.8, minor allele frequency>0.05), and to detect main‐effect acute rejection association signals with allelic odds ratios in the range 1.7‐2.9. We emphasize that these effect sizes are applicable to the traits investigated in this study, but that larger effects might be found in future studies under more precise phenotyping.We explored this last point further via formal power calculations. These indicated that we were well powered to detect any main effect graft survival association signals involving causal SNPs with allelic hazard ratios in the range 1.4‐1.9 (log‐additive risk model, alpha = 5 × 10In summary, while our study was able to replicate known mismatch signals in the HLA region, we failed to find convincing association signals outside of the HLA region. Both phenotype heterogeneity and sample size may have contributed to this result. Looking ahead, we note that the general lessons from GWAS applied to multiple human traits over more than a decade have brought home 3 clear messages.M.P.H. conducted a literature search, did data and sample collection, manuscript preparation and review, and grant provision and supervision. C.F. and I.R.M. conducted a literature search, did data analysis and interpretation, manuscript preparation and review, and grant provision and supervision. J.M. conducted a literature search. F.D. did data and sample collection. E.P. conducted a literature search, did data and sample collection, did data analysis and interpretation, and manuscript preparation and review. C.S. did data analysis and interpretation. R.B., C.B., B.C., M.C., J.F., S.F., S.G., A.H., R.H., A.J., M.K., T.L., I.Mc., P.B.M., J.M., P.M., W.McK., A.McL., C.H., T.A., P.P., S.P., P.R., H.S., R.T., P.T., did data and sample collection and data analysis and interpretation. N.S. and E.S. did grant provision and supervision. R.T. did study design and grant provision and supervision. R.V. and S.S. did study design, data and sample collection, and data analysis and interpretation. G.C. and P.C. conducted a literature search, did the study design, data and sample collection, manuscript preparation and review, and grant provision and supervision. G.O. did data sample and collection. N.S. did manuscript preparation and review and grant provision and supervision. M.W. did study design, data analysis and interpretation, manuscript preparation and review, and grant provision and supervision. G.L. did study design, manuscript preparation and review, and grant provision and supervision.American Journal of Transplantation. M.E.W. is an employee of Genomics plc, a company providing genomic analysis services to the pharmaceutical and health care sectors. M.H.F. and I.R.B. are employees of UCB Celltech, a pharmaceutical company. Their involvement in the conduct of this research was solely in their capacity as academics at King's College London.The authors of this article have conflicts of interest to disclose as described by the  Click here for additional data file. Click here for additional data file. Click here for additional data file.


Genetic variants can influence the expression of mRNA and protein. Genetic regulatory loci such as expression quantitative trait loci (eQTLs) and protein quantitative trait loci (pQTLs) exist in several species. However, it remains unclear how human genetic variants regulate mRNA and protein expression. Here, we characterized six mechanistic models for the genetic regulatory patterns of single-nucleotide polymorphisms (SNPs) and their actions on post-transcriptional expression. Data from Yoruba HapMap lymphoblastoid cell lines were analyzed to identify human cis-eQTLs and pQTLs, as well as protein-specific QTLs (psQTLs). Our results indicated that genetic regulatory loci primarily affected mRNA and protein abundance in patterns where the two were well-correlated. While this finding was observed in both humans and mice , the genetic regulatory patterns differed between species, implying evolutionary differences. Mouse SNPs generally targeted changes in transcript expression (51%), whereas in humans, they largely regulated protein abundance, independent of transcription levels (55.9%). The latter independent function can be explained by psQTLs. Our analysis suggests that local functional genetic variants in the human genome mainly modulate protein abundance independent of mRNA levels through post-transcriptional mechanisms. These findings clarify the impact of genetic variation on phenotype, which is of particular relevance to disease risk and treatment response. Single-nucleotide polymorphisms (SNPs) play an important role in the regulation of transcription and translation . The cenDuring the past decade, genome-wide association studies (GWAS) have identified thousands of regulatory genetic variants not only in humans but also in many other species, for varieties of complex traits ranging from disease to quantitative traits and including mRNA or protein levels . Like maIn the present study, we assessed six regulatory relationship models in humans. The correlations between genotype, transcript levels, and protein abundance were quantified from lymphoblastoid cell lines (LCLs) of 62 unrelated HapMap Yoruba individuals from Ibadan, Nigeria (YRI). Our results show that genetic regulatory patterns in which transcription levels directly affected protein abundance were predominant in both humans and mice; however, one specific pattern was enriched in humans. Additionally, the regulatory loci underlying the human-enriched regulatory pattern were enriched in psQTLs that were predicted to independently affect protein abundance. This may be associated with a differential regulatory mechanism, with possible biological functional diversity between human and mice.http://eqtl.uchicago.edu/dsQTL_data/GENOTYPES/.Genome-wide genotypes and mRNA and protein quantification data from 62 YRI HapMap human LCLs were obtained from a recent study . We seleWe also downloaded local pQTLs from the study by QTLs were identified in human YRI HapMap individuals using R software. Prior to QTL mapping analysis, we used standardization, quantile normalization, and principal components analysis to ensure that the data (mRNA and protein abundance) followed a standard normal distribution with no unidentified confounders .p value in linear regression, regardless of whether the p values were significant. In the second round, all eQTLs and pQTLs were mapped through linear regression analysis using the “lm” R package; psQTLs were identified using likelihood ratio test (LRT) with the following two linear models performed by the ”lrtest” function in “lmtest” R packages:In the first round of identification of regulatory patterns, we used only one pQTL for each gene corresponding to the smallest Sx is the genotype, Rx is the level of mRNA expression, and y is the level of protein expression. The p value was recorded as significant evidence. We filtered eQTLs, pQTLs, and psQTLs using a cutoff p value (4.8 × 10−4) that was determined at a false discovery rate (FDR) of 0.1 after multiple hypothesis corrections  value. BIC values and corresponding weight values were calculated using the “bbmle” package of R.It was assumed that the models of regulatory patterns were established based on a Markov chain. The maximum likelihood estimation for these models can be performed using joint probability distributions as follows:where S is the SNP genotype, R is the mRNA level, and N is the protein level. P(R|S) and P(N|S) mean that the phenotype (mRNA and protein level) is associated with an SNP; P(N|R) in model #4 means that N is associated with R; and P in model #5 means that N is associated with R, which may be affected by other SNPs or other common factors, but is unrelated to S. However, P in model #6 means that N is associated with R, which may be influenced by other SNPs or other common factors as well as S.It was assumed that mRNA and protein levels follow a normal distribution of N . We further assumed that traits R and N are normally distributed under each genotypic mean of a SNP, so that the likelihoods corresponding to each of the joint probability distributions were based on a normal probability density function.j) is the probability of genotype Sj  and was derived from the prior probability of the population, and p(Ri) and p(Ni) are from the normal probability density function. Other conditional probabilities were based on the normal conditional probability density function with means and variances for each component given by the following equations:where i is the individual from 1 to m, p. In total, 15 chromatin states were annotated and used to segment the genome. We calculated the relative ratio showing whether a particular chromatin state of QTLs was enriched in the regulatory pattern by the formula Annotation of human LCL GM12878 chromatin states were obtained from: https://david.ncifcrf.gov/summary.jsp). The gene list of each regulatory pattern was submitted to run the functional annotation tool. The Benjamini method was chosen to perform multiple test correction. Modified Fisher’s exact p values were recorded for significantly enriched annotation terms.Gene functional enrichment analysis was performed by Database for Annotation, Visualization, and Integrated Discovery (DAVID) Bioinformatics Resources 6.8 . All pQTLs were identified by QTL mapping analysis based on a linear regression model. One of the six possible regulatory patterns between SNP, mRNA, and protein was determined for each pQTL using a maximum likelihood model and BIC scoring. The model with the smallest BIC value was considered to be the most probable regulatory relationship explained by the observed data.To explore whether a predominant regulatory pattern exists in human cells, we selected 4,340 genes for which both mRNA and protein levels were measured in at least half of 62 unrelated HapMap Yoruba individuals for pQTLs identification. We only considered local SNPs  as candidate regulatory variants, which mapped to the target gene within a ±20-kb window. In our initial analysis, we used the same strategy published by Chick and colleagues  to selecn = 2554, By comparing the proportion of six models derived from human data in this study with those from mice summarized by Chick et al., we can better understand if there is a general relationship pattern through which local pQTLs affect protein expression, regardless of species. A similar distribution of regulatory patterns was observed in humans and mice Figure 2.If protein abundance is regulated by pQTLs through a post-transcriptional mechanism, it would also correlate with transcriptional changes, so protein abundance may appear unchanged and potential regulatory pQTLs will not be found. To overcome this, we analyzed SNPs that were significantly associated with protein abundance while including the mediation of their coding mRNA levels, i.e., psQTLs. Given that protein abundance may be indirectly affected by eQTLs through changing mRNA levels, candidate datasets for model testing were extended to include all significant eQTLs, pQTLs, and psQTLs, rather than limiting them to the best pQTLs as above. Significant psQTLs were identified using the LRT; eQTLs and pQTLs were identified using QTL mapping analysis. All QTLs were filtered at an FDR threshold of 0.1. The regulatory patterns were then re-identified with extended QTL sets by the maximum likelihood estimation, where the aim was to find parameter values that made the observed data most likely to be in accordance with the statistical model. The best model was also determined by the minimum BIC score.p value = 4.8 × 10−4; In total, we identified 16,726 eQTLs, 8,364 pQTLs, and 5,475 psQTLs after multiple hypotheses correction , we analyzed the functional annotation enrichment according to Gene Ontology Biological Process terms using DAVID. Whole genome-wide genes were used as background for enrichment calculation. The significantly enriched terms of biological processes are shown in In this study, we examined human genetic variants that affect transcription levels and/or protein levels. Overall, our results show that human pQTLs near a gene primarily affect protein levels independently of transcription levels. These findings are supported by the fact that the mutant phenotype caused by the same genetic variants is also susceptible to gene expression , indicattrans-acting SNPs and/or co-regulated genes ,.Publicly available datasets were analyzed in this study. This data can be found here: WF, YL, and YW designed the work program and drafted the manuscript. YW wrote the code and implemented the analysis. YW, BH, YZ, JR, SC, ES, WF, and YL participated in the writing of the paper and revising the manuscript. All authors read and approved the final manuscript.This research was funded by the National Natural Science Foundation of China (grant number 61471139), the Natural Science Foundation of Heilongjiang Province of China (grant number F2016006), and the HEU Fundamental Research Funds for the Central University .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.eQTL, expression quantitative trait loci; pQTL, protein quantitative trait loci; SNPs, single-nucleotide polymorphisms; psQTLs, protein-specific quantitative trait loci; LCLs, lymphoblastoid cell lines; GWAS, genome-wide association studies; YRI, Yoruba in Ibadan, Nigeria; BIC, Bayesian information criterion; LRT, likelihood ratio test; FDR, false discovery rate; GO, gene ontology; BP, biological process; DAVID, Database for Annotation, Visualization, and Integrated Discovery; MAF, minor allele frequency; PCA, principal components analysis.