Genomic imprinting is a phenomenon that arises when the expression of genes depends onthe parental origin of alleles. Epigenetic mechanisms may induce the full or partialsuppression of maternal or paternal alleles, thereby leading to different types ofimprinting. However, imprinting effects have received little consideration in animalbreeding programmes, although their relevance to some agricultural important traits hasbeen demonstrated. A recently proposed model (imprinting model) with twopath-of-transmission -specific breeding values for each animal accountsfor all types of imprinting simultaneously .Imprinting effects ) are determined bytaking the difference between the two genetic effects in each animal. However, thecomputation of their prediction error variance (PEV) is laborious; thus, we propose a newmodel that is equivalent to the aforementioned imprinting model, which facilitates thedirect estimation of imprinting effects instead of taking the differences and the PEV isreadily obtained. We applied the new model to slaughterhouse data for Brown Swiss cattle,among which imprinting has never been investigated previously. Data were available for upto 173 051 fattening bulls, where the pedigrees contained up to 428 710 animalsrepresenting the entire Brown Swiss population of Austria and Germany. The traits analysedcomprised the net BW gain, fat score, EUROP class and killing out percentage. The analysisdemonstrated that the net BW gain, fat score and EUROP class were influenced significantlyby POE. After estimating the POE, the new model yielded estimates with reliabilitiesranging between 0.4 and 0.9. On average, the imprinting variances accounted for 9.6% ofthe total genetic variance, where the maternal gamete was the main contributor. Moreover,our results agreed well with those obtained using linear models when the EUROP class andfat score were treated as categorical traits by applying a GLMM with a logit linkfunction. Genomic imprinting is an epigenetic phenomenon where the expression of genes depends on theparental origin of their alleles. Imprinting is known to affect a variety ofvalue-determining traits in agricultural species, and thus it should be considered in animalbreeding. However, the existing methods are still difficult in practice using standardstatistical software. Therefore, we propose a new statistical model that allows the directestimation of imprinting effects and their prediction error variances (PEVs). We appliedthis model to slaughterhouse data for Brown Swiss cattle, a breed in which imprinting hasnever been investigated previously.et al., etal., Genomic imprinting is known to be caused by allele-specific DNA methylation and histonemodifications during gametogenesis, which depend on the sex of an animal  led to theidentification of a polymorphism that causes a paternally expressed QTL in the, etal.  performeet al. ), carcassconformation, carcass fatness and killing out percentage (carcass weight divided by lifeweight (%)).etal., The carcass conformation was defined according to the European muscle conformation systemEUROP (E=excellent to P=poor). However, these EUROP grades were replaced by five monetaryvalues , which reflect the fact that although prices differ overtime, the price differences between classes remain stable (Engellandt Carcass fatness was available as scores ranging from 1 (lean) to 5 (very fat) where mostof the animals were classified with scores of 2 (23.27%) and 3 (71.9%).All of the fattening bulls with missing sires and/or dams, as well as all bulls belongingto a comparison group with less than five animals per group  were eliminated from the data set, which led to varying numberof observations. The highest number was available for net BW gain (173 051) and thesmallest for the killing out percentage (3226). A summary of the data is given in The number of pedigrees was 428 710 for net BW gain (up to 21 generations), 420 626 forcarcass conformation class and fat score (up to 21 generations) and 24 329 for the killingout percentage (up to 20 generations). The pedigree for net BW gain was pruned using theSECATEURS program Meyer, . This prAs suggested by Westell and Van Vleck ,unknownet al. a vector of random genetic effects under a paternal  expressionpattern, which corresponds to the vector of the transmitting ability (TA) for the sire(dam); X, Zs and Zd are the corresponding incidence matrices; and e a vector of random residuals. In terms of gametic variances, thevariance–covariance components of random effects can be written asTo investigate the role of imprinting effects, Neugebauer et al. developeλ coefficients is equivalenttoThe mixed model equations areA is the numerator relationship matrix and the diagonal matrix W has the elementsi=as−ad) and its variance defines the imprinting variance i can be derived easily asthe difference between both parental TAs using the imprinting model.However, determining their PEVs is demanding because the off-diagonal elements of theinverted coefficient matrices of the mixed model equations are necessary  of the imprinting effects as follows:In this study, we used the estimated variance–covariance components of theyijklmn is a beef trait record; SDi the fixed effect of the ith comparison group (combination offattening farm and date of slaughter); PNj the fixed effect of the jth parity number ; BTk the fixed effect of the kth birth type (singleton or twin);b the linear (b1), quadratic (b2) and cubic (b3) regression on slaughter age x; l; m; andeijklmn the random residual. It should be noted that carcass fatness is used as a fixedeffect in the routine genetic evaluation. However, we treated it as a trait because it isknown to be genetically influenced. Modified equations for an animal model were used toconsider missing parents within genetic groups, as described by Quaas and Pollak  are defined as described in the corresponding linear models.Most fattening bulls were assigned to conformation classes O and R (98%) and fat scores 2and 3 (95%), so both traits were also treated as ordered categorical traits with binomialdistributions. Thus, fattening bulls were classified either to class zero  or to class one . A logit link was chosen for the GLMM because there is an anecdotalevidence that logit GLMM converges better than probit GLMM when the variance componentsare estimated using the pseudo-likelihood approach of Gilmour et al.. The proet al. . The RLRT isasymptotically distributed as a mixture of two χ2 distributions with 1 and 2 DF  and verified usingsimulated data sets from a previous study . The incorporation of genetic groups had no noticeable impacton the estimates of genetic parameters for all of the traits analysed.The analysis yielded no significant results for the killing out percentage for all of the given slaughter traits, we first used linear animal models.The estimated values of h2 obtained from animal models are summarised in To estimate the heritability . High correlations were alsoobtained for the reliability of the POE, with values of 0.98 and 0.97. The clear linearrelationships between the TA from the GLMM and the TA from the LMM can be seen in We determined high correlations between the POE predicted using the et al. between the carcass fat score and carcassfat proportion in bulls, and thus it is plausible that the underlying continuous variablefor the fat class is generally identical to the carcass fatness. However, the approximatemonetary value of a 1 unit change in the TA on the underlying scale for the carcassconformation can be derived by assessing the associated changes in the average frequenciesfor all categories and in the average value of a carcass.The LMM yields estimates that can be interpreted directly in terms of monetarydifferences but this is not the case with the GLMM. Kempster et al. reportedet al. is not c(et al.  reportedIn this study, we developed a new model that facilitates the direct estimation ofimprinting effects and PEVs for a large number of animals using existing software.Furthermore, we determined significant imprinting variances for three of four beef traitsanalysed in Brown Swiss fattening bulls using LMM and GLMM. The imprinting variancesaccounted for ~10% of the total genetic variance, where the maternal gametes provided thelargest contributions. These findings highlight the importance of POE and support the needto incorporate them into selection decisions.


Populus is considered as a promising 2G feedstock and understanding the genetic basis of biomass yield and feedstock quality are a research priority in this model tree species.Second generation (2G) bioenergy from lignocellulosic feedstocks has the potential to develop as a sustainable source of renewable energy; however, significant hurdles still remain for large-scale commercialisation. Populus nigra L.), a native European tree, selected from 20 river populations ranging in latitude and longitude between 40.5 and 52.1°N and 1.0 and 16.4°E, respectively. When grown at a single site in southern UK, significant Site of Origin (SO) effects were seen for 14 of the 15 directly measured or derived traits including biomass yield, leaf area and stomatal index. There was significant correlation (p < 0.001) between biomass yield traits over 3 years of harvest which identified leaf size and cell production as strong predictors of biomass yield. A 12 K Illumina genotyping array  highlighted significant population genetic structure with pairwise FST showing strong differentiation (p < 0.001) between the Spanish and Italian subpopulations. Robust associations reaching genome-wide significance are reported for main stem height and cell number per leaf; two traits tightly linked to biomass yield. These genotyping and phenotypic data were also used to show the presence of significant isolation by distance (IBD) and isolation by adaption (IBA) within this population.We report the first coppiced biomass study for 714 members of a wide population of European black poplar  were found to reach putative significance and are also of interest for biomass yield, leaf area, epidermal cell expansion and stomatal patterning. This research on European P. nigra provides an important foundation for the development of commercial native trees for bioenergy and for advanced, molecular breeding in these species.The three associations identified reaching genome-wide significance at The online version of this article (doi:10.1186/s13068-016-0603-1) contains supplementary material, which is available to authorized users. Populus is widely considered as a promising lignocellulosic feedstock for second generation biofuel production [Populus species [P. trichocarpa genome, which at around 550 Mb is small for a forest tree [Populus became the first forest tree for which CRISPR/Cas genome editing has been successfully demonstrated [Short rotation coppice (SRC) or short rotation forestry (SRF) oduction , 2; beinoduction , widesproduction , geneticoduction , 6, readoduction  and alreoduction , 9. Mappoduction –13 exist species  and the est tree , has beeest tree . A numbeest tree  and POPaest tree . Most renstrated . This ofnstrated .Populus with much focus on mapping quantitative trait loci (QTL) for cell wall composition [2 [Populus, have been replaced with wide natural populations that are particularly beneficial for trees since they capture increased genetic variation [Populus commercialisation to be focussed on F1 hybrids originating outside Europe [Considerable research effort has been employed to elucidate the genetic basis of phenotypes of interest in position ; biomassposition , 21, 22;position ; droughtposition , 25; watposition ; pest reposition ; bud setposition , 28 and position , elevateition [2 , 31 and ition [2 . Recentlariation . This ine Europe  and becae Europe .r dropping to half its maximum value within 4 kb [Association mapping is a powerful technique for elucidating the genetic basis of qualitative and quantitative traits in species of interest, seeking statistical associations between genotypic markers  and defined phenotypic qualities within a population . Such ashin 4 kb .P. trichocarpa have made use of a 34 K array covering 3543 genes [P. trichocarpa across its North American range [Whilst association mapping can be performed within targeted areas of a genome; for example within candidate genes ; falling43 genes  in GWAS 43 genes , biomass43 genes , 47 and 43 genes  traits. an range .P.trichocarpa exceed those published in any other Populus species, however, in Europe, Populus nigra L. (black poplar) is the native cottonwood (Aigeiros); also found across North Africa and Central Asia [Studies in ral Asia , 51. It ral Asia –54; for ral Asia  used 433ral Asia  the studral Asia , 54. Undral Asia  and provral Asia , 58; as ral Asia , 60.P. nigra and with coverage of a far greater proportion of the genome. We focus on traits with moderate to high heritability and considered to be underpinning biomass production including leaf development, stomatal patterning, height and stem volume index [The aim of this research was to elucidate the links between biomass traits and their underlying genetic architecture. In particular we aim to unravel complex traits considered important for the development of the native black poplar as a sustainable source of lignocellulosics for the bioenergy industry, particularly across Europe where native species are likely to be preferred. This work describes the first use of phenotyping and genotyping data together from a 12K Illumina Infinium genotyping array which provides SNP markers an order of magnitude greater in number than previous studies in me index , 61 as wme index . These gP. nigra population [Populus, including response to drought stress [n) are provided in Table The pulation , 63, 64 pulation , 65. Cutt stress . In thist stress . 931 genTrichoderma reesei) and cellobiase (Aspergillus niger) enzymes  at 55 °C in a rotating thermomixer. Supernatant was assayed with GOD-POD  solution [As shown in Additional file mentclass2pt{minimsolution  which un® and mounted on glass slides as described previously [In August 2013 (1st year of growth post 2nd coppice) the first, mature leaf was sampled from the main stem for all genotypes in the course of a single week and imaged. Epidermal cell imprints were taken from the abaxial leaf surface using clear nail varnish and Sellotapeeviously . Slides eviously  was usedeviously , 72 and eviously , 73. Thei is the effect of site of origin i  and Bk are the effects of genotype j (nested within SO) and block k, respectively; both considered as random. In the case of saccharification potential where sample processing was completed in multiple runs over several weeks the factor ‘Run’ was additionally included as a random effect to account for laboratory drift. Individual genotypes (singlet genotypes not sampled from a defined river population) were excluded from this analysis but included in GWAS. In view of the significant block effect (Bk) found for all traits  for pairwise correlations between traits and with latitude and longitude of origin.For each trait only genotypes with measurements for at least two replicates and which had been genotyped on the Illumina array were considered in statistical analyses; this in view of the risk of undetected clonal duplication from nature among so-called ‘unique’ ungenotyped individuals in this species , 52, 54.mentclass2pt{minimP. nigra genotypes . SNPs selected for the array were drawn from 14 QTL regions and 2916 candidate genes (based on transcriptome studies and the literature) for biomass yield, bud phenology, wood quality, rust resistance and water-use efficiency traits as well as 1732 additional gene models spread throughout the genome [The genotyping data utilised in this work arises from a 12 K Illumina Infinium II Genotyping BeadChip array and full details of the DNA extraction, sequencing, design and quality testing for which have been recently reported . In summe genome . The pope genome ) were poe genome  to removr2 < 0.2 [The 7343 SNP marker set was further filtered for population genetic structure analysis. First, markers were filtered for Hardy–Weinberg equilibrium (HWE) in R using the function ‘HWChisqMat’ in the package ‘Hardy–Weinberg’ . This prr2 < 0.2 , 79 to pGenetic structure was investigated by three approaches:K, i.e. the number of subpopulations or clusters of genotypes within a population and to produce a Q-matrix in which individual genotypes are probabilistically assigned to K clusters with the proportional likelihood of membership of a given cluster expressed as a decimal between 0 and 1 and with individual probabilities summing to 1 across all clusters for a given genotype. In this instance STRUCTURE’s admixture model with correlated allele frequencies [K’s 1–10  with ten iterations for each value of K and 20,000 burn-in and 100,000 run-length for each iteration. The ‘Structure Harvester’ tool at UCLA [K according to the method of Evanno et al. [I. The reduced marker set (2390 markers) was entered in the program STRUCTURE  which emquencies  was used at UCLA  was theno et al. .II. Principal component analysis (PCA) of genetic variance in the R package ‘prcomp’  was perfST (genetic distance) estimates were calculated between the 20 represented sampled populations in the program Arlequin 3.5 [III. Pairwise Fquin 3.5 . A PCA wquin 3.5 . Simple quin 3.5 –90 were quin 3.5 .Meff) in the full 7343 marker set (accounting for non-independence between markers arising from LD) was calculated in the Genetic type 1 Error Calculator (GEC) which provides a robust estimation of the number of independent tests being performed for multiple test correction in GWAS; so as to control the genome-wide type 1 error rate at 0.05 [Meff. Meff was found to equal 5690 and thus the threshold was calculated as α = 8.79 × 10−6.Effective marker number  without correction for population genetic structure:2. GLM using significant PCs from reduced marker set PCA for genetic structure correction (P-model) with notation as for model I but β contains fixed effects for both genetic markers and population structure (PCs).K from STRUCTURE for genetic structure correction (Q-model) with notation as for model II but population fixed effects in β derived from Q-matrix instead of PCs.3. GLM using Q-matrix with optimal R package ‘GAPIT’ [Y is a vector of phenotypic values; β is an unknown vector containing fixed effects for genetic markers; u is an unknown vector of random additive genetic effects; X and Z are the known design matrices and e is the unobserved vector of random residuals.4. Mixed linear model (MLM) with a kinship matrix created from the reduced, 2390 marker set using the Efficient Mixed Model Association (EMMA) algorithm  in the R ‘GAPIT’  for gene5. The full animal model  MLM usin6. Full animal model MLM using significant PCs of genetic variation and EMMA kinship matrix for genetic structure correction (P + K-model) with notation as for model IV but β contains fixed effects for both genetic markers and population structure (PCs).To determine the most appropriate of the above models for identifying reliable trait-marker associations on a trait-specific basis the unified mixed model framework used by McKown et al.  was emplh2 for each phenotype using the individual observations for each genotypic replicate . The function ‘marker_h2′ was used to fit a mixed model using the EMMA kinship matrix and the seven significant principle components of the genetic variation as covariants. Narrow sense heritability is calculated according to the equation:g2 is the additive genetic variance and σr2 is residual (error) variance such that σg2 +σr2equates to the total model variance. Trait heritabilities were regressed against their absolute correlation coefficients with latitude and longitude in Minitab.The R package ‘heritability’  was emplp < 0.001) effect of genotype for all traits studied. Estimated biomass yield  was significant for all traits with the exception of saccharification potential for which the SO effect narrowly missed significance with the random factors block and run included in the GLM. The presence of a significant block effect necessitated the use of block adjusted marginal means in downstream analyses. This wide genetic variation displayed in traits, related to both genotype and SO, highlights the potential of this natural germplasm collection to provide diversity for future selection and breeding efforts for this native European tree species. Figure h2) shown across the matrix diagonal. Additional file r > 0.5) correlations within and where applicable between years as well as consistently significant, weak to moderate positive  correlations with longitude of origin. Biomass yield, height and basal area from 2013 also show a significant correlation with latitude. Leaf area (mature leaf size) 2013 shows a strong positive relationship with biomass yield from all years with the strongest correlation with EB-13 . It is also significantly positively correlated with both latitude  and longitude  of origin. By contrast specific leaf area (SLA-13) shows a moderate but significant negative correlation with EB-13  and with leaf area . Epidermal cell number per leaf (CNPL-13) is naturally very tightly correlated with leaf area  and in turn shows a strong positive correlation with EB-11, 12 and 13. Cell area (CA-13) shows a weak negative correlation with EB-13  and LA-13  and a strong negative correlation with stomatal density . Stomatal density and index (SD-13 and SI-13) show weak to moderate positive correlations with biomass traits in all years, leaf area and latitude and longitude of origin. Saccharification potential (SP-12) appears largely unrelated to the other traits measured with only very weak and in most cases non-significant correlations found. It shows no significant correlation with latitude and only a very weak relationship with longitude ; as might be expected in view of its lacking an effect for SO in the GLM analysis.Figure h2) ranged from 0.250 for SLA-13 to 0.497 for LA-13  for latitude of origin  but regressed strongly for longitude .Narrow-sense trait heritabilities  and Northern Italian (Ticino) genotypes are shown to belong to clearly distinct clusters with a degree of admixing in central Italy (Paglia). The German subpopulation (Kuhkopf) is strongly assigned to a unique cluster and is closely related to the more northerly Netherlands (NL) genotypes. Genotypes drawn from subpopulations on the France-Germany border  are also strongly assigned to this cluster but show some admixing with the Ticino subpopulation and with subpopulations in Southern and Central France as do the individuals from Dranse on the France-Switzerland border. The Central French subpopulations  are all predominantly assigned to their own cluster, whereas the Southern French (Drome and Ramieres) show more admixing; including with the distinctive Spanish populations (Ebro).STRUCTURE analysis after the method of Evanno et al. . found tt et al. . While i1, 710 = 41.5, p < 0.001, r2 = 0.055); PC1 with longitude ; PC2 with latitude ; PC2 with longitude ; PC3 with latitude ; PC3 with longitude   revealed 7 significant PCs according to a broken stick model  also showed 7 significant PCs cumulatively explaining 16.3 % of the variation. PCs 1 and 2 explained 6.78 and 2.60 %, respectively, and the individual marker eigenvalues reveal clusters of top loading SNPs for both PCs. For PC1 3 of the top loaded SNPs are within a tight cluster (73 kb) on chromosome 10; 3 are within a 15 kb region of chromosome 6 while a further 8 of the top 15 (0.2 %) are located within a 1.5Mbp region of chromosome 17. For PC2 a group of 6 top loaded SNPs are located within a 15 kb region on chromosome 6 with a further 3 located in a 62 kb region of chromosome 8. Additional file 3 SNPs alST  between subpopulations  to 0.159 (Kuhkopf) against all other groups excepting the Central Italian . As predicted from STRUCTURE the Spanish (Ebro) and Northern Italian (Ticino) are also more distantly related (FST range from 0.115 to 0.126). The German and Dutch subpopulations are again shown to be closely related (FST = 0.047). Within France FST is generally low with the greatest differentiation between Rhinau (France-Germany border) and the southerly Drome 1 (FST = 0.057).Pairwise Fons Fig.  shows thr2 = 0.107) and trivially with latitude (r2 = 0.031) , phenotypic and geographical distance matrices are shown in Table r = 0.844, p < 0.001) suggesting isolation by distance (IBD) and moderate positive correlation between genetic and phenotypic distance controlling for geographic distance  suggesting isolation by adaption (IBA).The results of full and partial Mantel tests on the genetic (FK = 2) from STRUCTURE (Q-model); (4) MLM with EMMA kinship matrix (K-model); (5) MLM with Q (K = 2) and kinship matrices (Q + K-model); (6) MLM with 7 PCs and kinship matrix (P + K model). The most appropriate model for each trait was then selected using BIC to compare log-likelihood values [−6. Table GWAS was conducted in TASSEL for all traits comparing 6 models: 1) a simple GLM with no population structure correction; (2) GLM with seven significant PCs from PCA of neutral genetic variance included as covariate (P-model); 3) GLM with Q-matrix ;  MLM with a simple1, 13 = 31.14, p < 0.001, r2 = 0.706 , Height-13 and CNPL-13  are located on chromosome 7 within an intron of the gene POPTR_0007s11900; chromosome 4 within the first exon of the gene POPTR_0004s10800 (synonymous) and 1 kb to the 3′ end of the gene POPTR_0013s00340, respectively. The bar plots in Fig. P. nigra association mapping population with greater than tenfold differences between genotypic extremes for many key traits  are encouraging since they imply that gains in biomass yield may be obtainable without negative impacts on the quality traits underpinning feedstock processing.The bioenergy trait data reported here demonstrates the extent of phenotypic variation within this priority , 101. Thr = 0.814) has been previously reported in Populus [h2 = 0.497) diagnostic indicator of biomass productivity [h2 = 0.480 and 0.270, respectively) and showed a far stronger correlation with total leaf area . Previous research [Populus they may prove valuable candidates for leaf development and biomass yield.The strong correlation between leaf area  and biomass yield in 2013  showing a strongly significant (p < 0.001) effect for Site of Origin (SO). Additionally, all traits show a weak to moderate correlation with longitude of origin and 9 (of 15) show a significant relationship with latitude of origin. Further evidence that phenotypic variation is more closely aligned with longitude than latitude (i.e. trait variation follows a predominantly east–west cline) is provided in Fig. r2 = 0.643) than latitude (r2 = 0.112). The first principal component of the PCA of phenotypic variance also showed a stronger regression with longitude (r2 = 0.104) than latitude (r2 = 0.032)  but a clear relationship with longitude   identified clusters of markers with highly weighted eigenvalues for the first 2 PCs  and between genetic and phenotypic distance when controlling for geographical distance . A good example of IBD is provided by contrasting the Basento  and Ebro (Spain) subpopulations which show high pairwise FST  whilst Germany and the Lowlands (including The Netherlands) were likely recolonized from the Italian and Balkan Peninsulas. This is supported by both microsatellite data [Table  maximum . Cottrel maximum  utilisedite data  and the Populus. Encouragingly, in a recent glasshouse trial of 3 diverse genotypes drawn from this population, POPTR_0004s10800 was shown to be differentially expressed in developing xylem  higher expression levels seen in the genotype possessing the “A” allele associated with greater height in this study . Its Arabidopsis ortholog AT4G30440 (known as GAE1) is a UDP-glucoronate 4-epimerase enzyme involved in pectin biosynthesis. When GAE1 expression was suppressed in conjunction with its homolog GAE6 in Arabidopsis the mutants displayed a mutant phenotype comprising slightly reduced size, leaf brittleness and suppressed immunity [Populus [Table immunity . POPTR_0immunity . Two linimmunity . POPTR_0immunity , 119. Inimmunity  does shoimmunity . Thus, w[Populus .P. trichocarpa [P. nigra association population is more highly structured than that for P. trichocarpa. McKown et al. [P. trichocarpa vastly exceed those reported here. Whilst this can be partly attributed to the superior numbers of SNPs on the 34 K chip and the greater numbers of traits phenotyped it is also likely that the lack of strong population structure in the P. trichocarpa association population is enormously beneficial in preventing over-correction by the application of more stringent models to control for stratification. Nevertheless, the associations provided above can be considered as robust for this out-breeding tree native to Europe and provide a firm basis for further proof of concept testing.The tendency for uncorrected population structure to cause inflated and false positive test statistics for trait-marker associations is well documented and much effort has been invested in developing robust methodologies for its control , 124. Suchocarpa . Publicachocarpa –48. Herechocarpa . We usedn et al.  found thOur research on native European black poplar provides a significant foundation for the development of commercial native trees for bioenergy and has identified important early diagnostic traits (leaf size and cell number) underpinning robust yield assessments over several years. We have been able to link these biomass traits to a set of candidate genes, varying from strong to putative but worthy of further investigation, that show differential expression in preliminary validation analysis. Although population structure; relatively low marker density and rapid decay of LD  have ren


In genetic association studies of rare variants, low statistical power and potential violations of established estimator properties are among the main challenges of association tests. Multi-marker tests (MMTs) have been proposed to target these challenges, but any comparison with single-marker tests (SMTs) has to consider that their aim is to identify causal genomic regions instead of variants. Valid power comparisons have been performed for the analysis of binary traits indicating that MMTs have higher power, but there is a lack of conclusive studies for quantitative traits. The aim of our study was therefore to fairly compare SMTs and MMTs in their empirical power to identify the same causal loci associated with a quantitative trait. The results of extensive simulation studies indicate that previous results for binary traits cannot be generalized. First, we show that for the analysis of quantitative traits, conventional estimation methods and test statistics of single-marker approaches have valid properties yielding association tests with valid type I error, even when investigating singletons or doubletons. Furthermore, SMTs lead to more powerful association tests for identifying causal genes than MMTs when the effect sizes of causal variants are large, and less powerful tests when causal variants have small effect sizes. For moderate effect sizes, whether SMTs or MMTs have higher power depends on the sample size and percentage of causal SNVs. For a more complete picture, we also compare the power in studies of quantitative and binary traits, and the power to identify causal genes with the power to identify causal rare variants. In a genetic association analysis of systolic blood pressure in the Genetic Analysis Workshop 19 data, SMTs yielded smaller p-values compared to MMTs for most of the investigated blood pressure genes, and were least influenced by the definition of gene regions. Candidate gene and genome-wide association studies have identified many common variants associated with a large number of complex traits, and explained some of the estimated heritability . The refWhile single-marker tests (SMTs) are often the method of choice for the analysis of common and low-frequency single nucleotide variants (SNVs) with a minor allele frequency (MAF) greater than 0.01 or 0.005, multi-marker tests (MMTs) have attracted much attention over the last years for the analysis of rare SNVs. Their development has been motivated by arguments that SMTs have inflated type I error and very low power when testing rare SNVs in the analysis of binary traits , and migFor the analysis of quantitative traits, however, extensive comparisons are lacking and few studies have compared SMTs with MMTs. Those studies that have investigated SMTs and MMTs for quantitative traits , 28–31 mAs a result of the inconclusive previous studies, the aim of this study is to provide a comparison of SMTs and MMTs for the analysis of quantitative traits based on a clear formalization of the tested hypotheses for each approach. Consequently, we compare an SMT  with popular MMTs  or any of the SNVs in a given gene (variance-component-type tests) is associated with the trait of interest, whereas SMTs are testing whether a given SNV is associated with the trait of interest. More formally, for a given gene including k SNVs, the tested hypotheses for SMTs areβi is the effect of the i-th SNV on the trait under consideration; and the tested hypotheses for MMTs areα is the effect of the gene on the trait of interest, which could be a single parameter in burden-type tests, or a vector of parameters for the k SNV effects in variance-component-type tests withSMTs and MMTs test different null hypotheses with a different focus. The unit under investigation in MMTs is a region of the genome such as a gene. Accordingly, MMTs are testing whether Hence, if SMTs and MMTs are compared by evaluating the power for identifying a given causal variant (SMT) and a given causal gene (MMT), respectively, any conclusion that one approach is more powerful than the other is questionable since different hypotheses are tested. In fact, within such a comparison of different hypotheses, SMTs are by design of the comparison disadvantaged. In order to compare both approaches fairly, we evaluate SMTs and MMTs in their power for identifying the same genetic locus, and choose a gene as locus. For the SMTs, we therefore test whether any of the rare SNVs within the gene shows a significant association with the trait, accounting for multiple testing, in order to declare that the gene is significantly associated.m replicates of a gene with multiple SNVs, gene-level power estimates are obtained withIn the simulation study including minP approach, which was also used in [−6 used in a genome-wide analysis of 20,000 genes. Empirical type I error estimates were obtained similarly for data generated from the null hypothesis. If not mentioned otherwise, all results reported in this study regarding type I error rates and power refer to this gene-level evaluation.For SMTs, this becomes used in  and othe used in , 20, 24. used in , but sin used in . We repol SNVs with the given MAF from all replicates. For a nominal α level of 0.05, this becomes:For the additional question investigated in this study, how the power of SMTs for identifying a causal gene compares to the power for identifying single causal rare variants, we also obtain SNV-level power estimates for detecting a causal rare SNV with a given MAF, based on the p-values of all Y was generated given causal SNVs  and two additional covariates. Then, different scenarios varying the percentage of causal variants, their effect sizes, and direction of effects were considered to evaluate the empirical type I error and power of the tests. The set-up of the simulation study is described in more detail in the following.In the simulation study, our aims were to investigate the properties of variant effect estimates obtained through single marker analysis and of the SMT , and to compare the empirical type I error and power estimates of the SMT with popular MMTs  in association studies of quantitative traits. A normally-distributed quantitative trait For the main study, we used the genetic dataset provided in the SKAT package in R , which cm = 10,000 replicates with genotypes of n = 1,000 individuals for the simulation study. With this, there were on average 33 non-monomorphic SNVs gi in each replicate , and in total 325,393 SNVs in all m = 10,000 replicates combined. Most of the SNVs were rare with MAF≤0.03. In detail, of the 325,393 SNVs, 132,797 SNVs had MAF = 0.0005 ; 41,341 SNVs had MAF = 0.001 (MAC = 2); 50,836 SNVs had 0.001<MAF≤0.005 (2<MAC≤10); 39,835 SNVs had 0.005<MAF≤0.03; and 60,584 SNVs had MAF>0.03.Similar to , we randY conditional on a binary covariate x1 and a normally distributed covariate x2 . We used the same model and parameter values as described in [x1∼Bin(0.5), x2∼N, ε∼N, βi = c ∙ |log10 (MAFi)|, where different values of c were considered in the simulation study.To evaluate the type I error and the power of the test statistics, we generated ribed in  with addm = 10,000,000 replicates were analyzed, and for the power comparisons, m = 10,000 replicates were used. We used the sample size of n = 1,000 individuals for all simulations. i in the gene [For the evaluation of type I error rates, the gene .Y,gi in a gene using the lm function in R, which provides the maximum likelihood estimate βi and its standard error estimate 2 [To evaluate the performance of SMTs, a linear regression model of te of σ2 . Then, tSKAT function in the SKAT package in R. The weights in the weighted kernels of SKAT and SKAT-O are a function of the MAF of SNVs. For the p-value estimation, the default “davies” setting was used for SKAT and “optimal.adj” for SKAT-O. Furthermore, a burden test was conducted by obtaining a gene score as the summation of the minor alleles of all SNVs in the gene  under the linear regression modellm function in R. All common and rare SNVs in the gene were included in the analysis of the SMT and each MMT for a fair comparison. Additional results from analyzing rare variants only are provided in the supplementary materials as a sensitivity analysis. All computations and visualizations were performed in R 2.15.0 and higher.With respect to multi-marker approaches, three different tests were conducted incorporating all SNVs in a replicate (i.e. gene). The SKAT and SKAT-O were computed using the default linear-weighted kernel (relating the genotypes to the phenotype) in the test statistics as it returned the highest power estimates among all possible options provided in the SBPadj for the analysis, which are adjusted for medication use and non-genetic covariates, as follows. First, we fitted a censored regression model conditional on the non-genetic covariates age, sex, and smoking status, with medication use as a censoring indicator. Then, for an untreated individual, SBPadj is defined as the difference between observed and fitted SBP from the censored regression model; for a treated individual, SBPadj is the difference between the estimated true and fitted SBP.For a comparison of the SMT and MMTs in a real data application, we performed a gene-level association analysis of systolic blood pressure (SBP) in the Genetic Analysis Workshop 19 data –41. The SBPadj. The SMT, SKAT, SKAT-O, and burden test were computed as described in the Simulation Study section. For SKAT and SKAT-O, the SKAT function in the SKAT R package was used with default settings. For the SMT, a Wald-type t-test was computed under the linear regression model for each SNV, the p-values in a gene were adjusted with the BH-correction, and the minimum adjusted p-value was extracted for each gene for the gene-level association test. First, all 2,779 common and rare SNVs were included leading to gene sizes between 59 and 1,395 SNVs with an average gene size of 309 SNVs. Second, the analysis was restricted to the 1,746 rare SNVs, which led to an average gene size of 194 SNVs.A query to the Ensembl database with reference genome GRCh37.p13 through BioMart was used to define gene regions as 5kb around the gene start and end positions for the gene-level testing. After basic standard quality checks and exclusion of SNVs with more than 5% missing base calls, this yielded 2,779 common (MAF>0.03) and rare (MAF≤0.03) SNVs in the 9 defined gene regions for the gene-level association tests with First, the coefficient estimates of SNVs in linear regression models (5) of quantitative traits and their corresponding standard error estimates were assessed under the null hypothesis  were investigated for different nominal levels, to assess whether they are well-controlled . The resAs a sensitivity check, misspecified distributions for the error term in model (5) were considered. Data was generated from the null model in (4) with error terms from the t-distribution with 4 and 8 degrees of freedom and from the standard log-normal distribution. Then, the SMT, SKAT, SKAT-O and burden tests were conducted to test the absence of genetic effects assuming normally-distributed errors as described in the Materials and Methods section. The results are shown in −6. The burden test had the lowest power among all tests in all scenarios when all rare and  common variants were included in the analysis. Regarding a comparison among the other MMTs, SKAT-O had generally similar power with SKAT and the only noticeable differences were in scenarios 11, 12  when the power of SKAT-O was 7–11.5% higher for α = 0.05 and 3.5–10% higher for α = 2.5∙10−6. These results are in line with the literature [terature .α = 2.5∙10−6), and more pronounced for candidate-gene testing (α = 0.05) when using a sample size of n = 1,000. The same tendencies held for both nominal significance levels, and the further most important determinants of which test has higher power were the effect size and the percentage of causal variants. As main results, the SMT had consistently the highest power when the effect sizes were higher (c = 0.6), for all percentages of causal SNVs and both nominal significance levels . When the effect sizes were moderate (c = 0.3) and small (c = 0.2), the power of SMTs and MMTs were very similar when there were 5% or 10% causal SNVs, SKAT/SKAT-O had slightly higher power when there were 20%, and larger power when there were 50% causal SNVs. For a given effect size, increasing the percentage of causal variants in a gene led to a power increase for each test. The direction of SNV effects within a gene did not seem to greatly influence the question which test has the highest power, illustrating the robustness of SKAT/SKAT-O.Regarding the comparison of the SMT with MMTs, a first observation was that the power differences between the SMT and MMTs were very small for a genome-wide scan , there was at least one rare SNV in a replicate (gene) with adjusted p-value smaller than 2.5∙10−6, which led to the identification of the gene as causal. In fact, 3,084 SNVs had adjusted p-value smaller than 2.5∙10−6 in the 2,629 replicates: 20  causal singletons were correctly identified, 14  causal doubletons were correctly identified, 341  causal SNVs with MAF between 0.001 and 0.005, 428  causal SNVs with MAF between 0.005 and 0.01, and 2,281  causal SNVs with MAF between 0.01 and 0.03. If singletons and doubletons had been excluded from the analysis of linear regression, the power would have been slightly elevated to 28.0% in this scenario. On the other hand, for the candidate-gene approach using a significance threshold of 0.05, the gene-level power of the SMT was 73.6% and substantially more very rare variants were identified and drove the high gene-level power. In more detail, 2,576  causal singletons were correctly identified, 1,551  causal doubletons were correctly identified, 3,757  causal SNVs with MAF between 0.001 and 0.005, 1,482  causal SNVs with MAF between 0.005 and 0.01, and 2,980  causal SNVs with MAF between 0.01 and 0.03. For this analysis, the power would have been substantially decreased to 62.4% by excluding singletons and doubletons.For an illustration and explanation of the performance of the SMT, we provide more details for the main results of scenario 4 in the following. Here, the SMT had a power of 26.3% to identify a causal gene in a genome-wide study under the nominal n = 5,000. Also, another genetic dataset (‘SKAT.example’ data in the SKAT R package) including 67 SNVs per gene was used to generate data under scenarios 1, 4, 7, 8, 12 with a sample size of n = 2,000. The power estimates are shown in n = 1,000 was analyzed in comparison to a gene with average size 58 SNVs with a sample size of n = 5,000, the increased sample size helped SMTs with a higher power increase compared to MMTs. For example, while the power of the SMT versus SKAT-O was 19.2% versus 19.9% (for α = 0.05) and 0.5% versus 0.7% (for α = 2.5∙10−6) in scenario 2 with n = 1,000 (α = 2.5∙10−6) for the larger sample and gene size. Hence, for larger sample sizes, SMTs are more powerful than all MMTs also for moderate effect sizes. These conclusions did not change when the same larger sample size  was analyzed with much larger genes including on average 572 SNVs  in a gene and disregarding the  common SNVs. The power of all approaches increased, but the conclusion which approach has the highest power in each scenario did not change, for both nominal levels see  Tables. In addition, the same simulation set-up was used to generate a case-control trait from a logistic regression model to compare the SMTs and MMTs for an analysis of a binary trait. Further details are given in After comparing the single-marker and multi-marker approaches in their ability to identify a causal gene, another important question for practical applications is: What is the power of the tests for identifying a causal variant for a quantitative trait, and how does it compare to the power for identifying a gene containing causal SNVs ? Importantly, this question should not be confused with a power comparison of SMTs  and MMTs . Obtaining SNV-level power estimates for SMTs is straightforward, and In the genetic association analysis of the adjusted SBP phenotype, gene-level hypothesis tests were performed using the SMT, SKAT, SKAT-O, and the burden test. The normal distribution assumption for the error terms in the linear regression of the adjusted SBP phenotype was satisfied. The p-values obtained under each test to assess the significance of the 9 candidate genes are shown in When the analysis was extended to test all 2,858 gene regions on chromosome 19 including 273,636 common and rare SNVs and 218,198 rare SNVs, the same above conclusions were reached but none of the approaches yielded a significant gene-level test for a nominal level of 0.05 corrected for multiple testing.α levels, different proportions of SNVs with positive/negative effect on the trait, and different corrections for multiple testing of SNVs in a gene (Bonferroni and BH correction) with SMTs. In the data application, the SMT provided the smallest p-values in the testing of previously identified candidate blood pressure genes.In this study, we focused on the association analysis of rare variants with quantitative traits and first showed that standard restricted maximum likelihood estimation in a single-marker approach does provide unbiased estimates and single-marker Wald-type t-tests allow valid statistical inference even for very rare SNVs. In the following main analysis, we compared the power of the SMT and MMTs for identifying a gene that includes causal rare variants, and demonstrated that SMTs or MMTs can be more powerful depending on the scenario. More specifically, SMTs lead to more powerful association tests for identifying causal genes than MMTs when the effect sizes of causal variants in the gene are large, and less powerful tests when causal variants have small effect sizes. For moderate effect sizes, whether SMTs or MMTs have higher power depends on the sample size and percentage of causal SNVs. In our opinion, the most realistic scenarios are that at most 5% or 10% rare SNVs in a gene are causal. Then, for moderate effect sizes, the SMT has higher power when the sample size is larger, and slightly less power for a smaller sample size. These results seem to hold consistently for different gene sizes, different nominal For any gene-level investigation, a very important question is which SNVs should be grouped together in a test. Including more true causal SNVs by extending the region under consideration or by analyzing both common and rare SNVs can increase the power. At the same time, including more non-causal SNVs adds noise and decreases the power. Accordingly, in the simulation study, the power of all approaches increased when the analysis was restricted to rare SNVs, since only rare SNVs were chosen as causal SNVs in the data generation. The same was observed in the real data association study–but only consistently for the SMT–where the reason might have been as well that there were not any common causal SNVs. In the presence of causal common SNVs, including them in gene-level tests should increase the power. The data application also showed that while the SMT, SKAT, and SKAT-O are quite robust against which sets of SNVs are investigated, the burden test is highly sensitive and can lead to vastly different results.It should be noted that in the simulation study, the data was generated from the same model as in  where thOur proposition to use SMTs for the analysis of rare variants is based on the fact that maximum likelihood estimation returns valid estimates under the linear regression model, even for the analysis of singletons and doubletons. Importantly, as described in the Results section, the strategy to include singletons and doubletons in the analysis can substantially improve the power of SMTs. Of course, this does not alleviate the need to check for genotyping errors and other biases, which are especially relevant to singletons and doubletons. Also, while all investigated approaches rely on normality assumptions, the Wald-type t-test (SMT) was much more vulnerable to a distribution misspecification than the MMTs. When the residuals in the genetic association test are not normally distributed for one or multiple SNVs (or when effects follow another genetic model), adapting the test statistic is warranted. Further analyses of our study (data not shown) confirmed that for binary outcomes, standard statistical tests such as Fisher’s exact test, logistic regression likelihood ratio tests, Wald tests, and Score tests, should not be directly used for testing singletons and doubletons since they do not allow valid inference. Therefore, for each test, all assumptions including the (asymptotic) distribution assumptions and empirical type I errors have to be assessed before the analysis, and significant test results have to be cautiously investigated, especially if they are based on singletons or doubletons.Secondary results of our study provide suggestions regarding the study design of rare variant association studies. We observed that the power to identify causal low-frequency SNVs is almost always much smaller compared to the power to identify gene regions encompassing causal rare SNVs . CompariOur results add more details and shed a light on the comparison of single-marker and multi-marker tests for quantitative traits, and provide clear suggestions under which assumptions MMTs should be used, and when a simple SMT is favorable. In contrast to popular practice in epidemiological and medical studies, our additional results also highlight that quantitative traits should be analyzed whenever possible instead of binary traits to maximize the power of association tests. It will be interesting to observe if using more powerful tests can help to identify a larger number of functional rare variants in future studies.S1 Text(PDF)Click here for additional data file.S2 Text(PDF)Click here for additional data file.S1 Tablen = 1,000 for m = 10,000,000 replicates. The table shows the mean and standard deviation of the SNV effect estimates and the mean of the corresponding standard error estimates, for the 132,797,000 singletons in all replicates, the 41,341,000 doubletons in all replicates, and the 2,985,000 SNVs with 10 observed minor alleles .Datasets were generated from the null model described in scenario 0 in (PDF)Click here for additional data file.S2 Tablen = 1,000 for m = 10,000,000 replicates, with the error distribution of the phenotype given covariates chosen to be from a standard normal  common SNVs in a gene, as well as restricting the analysis to SNVs with at least 2 (MAC>1) or 3 (MAC>2) observed minor alleles for the SMT. For other nominal levels Click here for additional data file.S3 Tablen = 1,000 for m = 10,000 replicates. The nominal α level was set to 0.05. Adjustments for multiple testing of all SNVs in a gene with the SMT were done using the BH correction. The power results are provided for analyses using all rare and  common SNVs in a gene, and for using all rare SNVs in a gene by excluding the common SNVs from the analysis.Data was generated under the alternative-hypothesis model described in scenarios 1–36 in (PDF)Click here for additional data file.S4 Tablen = 1,000 for m = 10,000 replicates. The nominal α level was set to 2.5∙10−6. Adjustments for multiple testing of all SNVs in a gene with the SMT were done using the BH correction. Power results are provided for analyses using all rare and  common SNVs in a gene, and for using all rare SNVs in a gene by excluding the common SNVs from the analysis.Data was generated under the alternative-hypothesis model described in scenarios 1–36 in (PDF)Click here for additional data file.S5 Tablen = 5,000 for m = 10,000 replicates. The genes analyzed in the replicates included on average 58 SNVs. The nominal α level was set to 2.5∙10−6. Adjustments for multiple testing of all SNVs in a gene with the SMT were done using the BH correction. Power results are provided for analyses using all rare and  common SNVs in a gene, and for using all rare SNVs in a gene by excluding the common SNVs from the analysis.Data was generated under the alternative-hypothesis model described in scenarios 1–12 in (PDF)Click here for additional data file.S6 Tablen = 5,000 for m = 10,000 replicates. The genes analyzed in the replicates included on average 572 SNVs. The nominal α level was set to 2.5∙10−6. Adjustments for multiple testing of all SNVs in a gene with the SMT were done using the BH correction. Power results are provided for analyses using all rare and  common SNVs in a gene, and for using all rare SNVs in a gene by excluding the common SNVs from the analysis.Data was generated under the alternative-hypothesis model described in scenarios 1–12 in (PDF)Click here for additional data file.S7 Tablen = 2,000 individuals in the ‘SKAT.example’ data in the SKAT R package were used in each replicate. Data was generated under the alternative-hypothesis model described in scenarios 1, 4, 7, 8, 12 in n = 2,000 for m = 10,000 replicates. The nominal α level was set to 2.5∙10−6. Adjustments for multiple testing of all SNVs in a gene with the SMT were done using the BH correction. Power results are provided for analyses using all rare and  common SNVs in a gene.As genetic data, the available genotypes of the 67 SNVs of (PDF)Click here for additional data file.S8 Tablen = 1,000 for m = 10,000 replicates. The nominal α level was set to 2.5∙10−6. Adjustments for multiple testing of all SNVs in a gene with the SMT were done using the BH or the Bonferroni correction. Power results are provided for analyses using all rare and  common SNVs in a gene.Data was generated under the alternative-hypothesis model described in scenarios 1–12 in (PDF)Click here for additional data file.S9 Tablen = 1,000 for m = 10,000 replicates. The nominal α level was set to 0.05. Adjustments for multiple testing of all SNVs in a gene with the SMT were done using the BH correction. All rare and  common SNVs were incorporated in the analysis.Case-control data was generated under the alternative-hypothesis model described in scenarios 1, 4, 7, 8, 12 in (PDF)Click here for additional data file.S10 Tablen = 1,000 for m = 10,000 replicates for a binary trait. The nominal α level was set to 2.5∙10−6. Adjustments for multiple testing of all SNVs in a gene with the SMT were done using the BH correction. All rare and  common SNVs were incorporated in the analysis.Case-control data was generated under the alternative-hypothesis model described in scenarios 1, 4, 7, 8, 12 in (PDF)Click here for additional data file.S11 Tablen = 1,000 for m = 10,000 replicates. The nominal α was set to 2.5∙10−6 for the gene-level evaluation of SMT and SKAT-O , cf. −7 for the SNV-level evaluation of SMT . Adjustments for multiple testing of all SNVs in a gene were done using the BH-correction. The power of the SMT for identifying a causal SNV with a given MAF is based on all causal SNVs in the m = 10,000 replicates with the specified MAF. It is estimated by the number of significant causal SNVs Click here for additional data file.S12 Tablen = 1,000 for m = 10,000 replicates. The nominal α level was set to 0.002, representing the Bonferroni-correction for testing 25 SNVs in a gene . The power of the SMT for identifying a causal SNV with a given MAF is based on all causal SNVs in the m = 10,000 replicates with the specified MAF. It is estimated by the number of significant causal SNVs  divided by the total number of causal SNVs with the specified MAF.Data was generated under an alternative-hypothesis model described in scenarios 13–24 in (PDF)Click here for additional data file.S1 Fign = 1,000 for m = 10,000,000 replicates. The histograms and provided descriptive statistics  are based on the 132,797,000 t-test statistics of all singletons in all replicates (left panel), on the 41,341,000 t-test statistics of all doubletons in all replicates (middle panel), and on the 325,393,000 t-test statistics of all SNVs in all replicates (right panel). Overlaid in a blue line is the empirical estimate of the density function. The theoretical mean and standard deviation (SD) of the t1000-4 distribution are 0 and 996/994 = 1.001.Datasets were generated from the null model described in scenario 0 in (PDF)Click here for additional data file.


Z = 3.44, p = 0.0006). Here we describe replication results from 22 independent schizophrenia case-control datasets from the Psychiatric Genomics Consortium . Using the same ROH calling thresholds and procedures as Keller et al. (2012), we were unable to replicate the significant association between ROH burden and schizophrenia in the independent PGC phase II data, although the effect was in the predicted direction, and the combined  dataset yielded an attenuated but significant relationship between Froh and schizophrenia  = ,Z = 2.40,p = 0.02). Since Keller et al. (2012), several studies reported inconsistent association of ROH burden with complex traits, particularly in case-control data. These conflicting results might suggest that the effects of autozygosity are confounded by various factors, such as socioeconomic status, education, urbanicity, and religiosity, which may be associated with both real inbreeding and the outcome measures of interest.It is well known that inbreeding increases the risk of recessive monogenic diseases, but it is less certain whether it contributes to the etiology of complex diseases such as schizophrenia. One way to estimate the effects of inbreeding is to examine the association between disease diagnosis and genome-wide autozygosity estimated using runs of homozygosity (ROH) in genome-wide single nucleotide polymorphism arrays. Using data for schizophrenia from the Psychiatric Genomics Consortium , Keller et al. (2012) estimated that the odds of developing schizophrenia increased by approximately 17% for every additional percent of the genome that is autozygous  = ,  It is well known that mating between relatives increases the risk that a child will have a rare recessive genetic disease, but there has also been increasing interest and inconsistent findings on whether inbreeding is a risk factor for common, complex psychiatric disorders such as schizophrenia. The best powered study to date investigating this theory predicted that the odds of developing schizophrenia increase by approximately 17% for every additional percent of the genome that shows evidence of inbreeding. In this replication, we used genome-wide single nucleotide polymorphism data from 18,562 schizophrenia cases and 21,268 controls to quantify the degree to which they were inbred and to test the hypothesis that schizophrenia cases show higher mean levels of inbreeding. Contrary to the original study, we did not find evidence for distant inbreeding to play a role in schizophrenia risk. There are various confounding factors that could explain the discrepancy in results from the original study and our replication, and this should serve as a cautionary note–careful attention should be paid to issues like ascertainment when using the data from genome-wide case-control association studies for secondary analyses for which the data may not have originally been intended. Close inbreeding  is known to decrease fitness in animals and to iFroh, can then be used to predict complex traits, p = 6x10-4.) This was by far the largest study to that date examining the association between Froh and any psychiatric disorder, and the significant relationship between Froh and case-control status remained robust through secondary analyses of various covariate combinations, common vs. rare IBD haplotypes, and SNP thresholds used to define ROHs. These results are consistent with the hypothesis that autozygosity causally increases the risk of schizophrenia. Nevertheless, because various confounding factors may increase likelihood of distant inbreeding as well as the probability of having offspring with schizophrenia, these results do not imply a causal relationship. For example, parents higher on schizophrenia liability may pass their higher liability to offspring and mate with more genetically similar partners .In 2012, Keller et al.. Im the PGC to furthn = 21,868 after QC), and the “replication” dataset contained all subjects  in the PGC SCZ2, Z = 0.08, p = 0.94) or for ROHs defined as ≥ 2.3 Mb  = , Z = 0.31, p = 0.76). The results from analyses on ROHs called from imputed rather than raw SNP data were also non-significant  = , Z = 1.78, p = 0.07).For each dataset, we regressed case-control status on ip matrix and two ous SNPs  or ROH lous SNPs . The ovenificant . As in KFroh-schizophrenia relationship remained non-significant in these follow-up analyses , reran our baseline analysis , but still observed a non-significant Froh-schizophrenia relationship  = , Z = 0.42, p = 0.68) in the predicted direction. Therefore, this post-hoc analysis does not lend support to the possibility that small samples in the replication set added noise to our analysis, obscuring an Froh-schizophrenia relationship.We noticed that there was greater variability in Froh associations based on ROH thresholds greater than 60 consecutive homozygous SNPs or longer than 1 Mb were significant  = , Z = 2.40, p = 0.02). In this combined dataset, we also used a replication status-by-Froh interaction to conclude that the Froh-schizophrenia association was only marginally higher in the original compared to the replication datasets  for ROHs defined as at least 110 consecutive homozygous SNPs.Although results from the replication analysis were not significant, they were in the same direction as the original analysis. It could therefore be argued that the best estimate of the association between ROHs and schizophrenia is obtained by combining the two datasets. When we reran our analyses on the combined original + replication data , all ant Figs  and 5. FFroh variances, calculating Froh_short as the proportion of the genome contained in ROHs < 8 Mb long, and Froh_long as the proportion of the genome contained in ROHs > 8 Mb long. Although neither association was significant, the effect of Froh_short  = , Z = −1.42, p = 0.16), caused by autozygosity arising from more ancient common ancestors, was negative (“protective”) and in the opposite direction of effect of Froh_long  = , Z = 0.40, p = 0.69), caused by autozygosity arising from more recent common ancestors, which predicted increased risk for schizophrenia  and the statistical power in the replication study to detect the observed effect size in the original study was nearly 100%, it is possible that the estimated effects of the original analysis could have been over-estimated and/or those of the replication analysis under-estimated, due to sampling variability. There is some support for this interpretation, as there was not a significant difference in results between replication versus original datasets (interaction p = 0.07).Perhaps the simplest explanation for this pattern of results is that the conclusions about distant inbreeding from the original data represent a type-I error or that the lack of replication in the current report was a type-II error. Despite the fact that the effect in the original study was highly significant (Froh and risk for major depressive disorder (MDD) in the Dutch population. However, the authors found that religiosity was significantly associated with both higher autozygosity and lower MDD in this population. When religiosity was accounted for in their regression model, the original association between MDD and Froh disappeared. A similar effect was detected for educational attainment: highly educated individuals were more likely to migrate and mate with highly educated and more diverse partners, making highly educated spouse pairs share less ancestry and leading to their offspring having lower Froh[Froh associations, potentially affecting results in ways that can be difficult to account for. For example, an observed Froh-schizophrenia relationship could be due to parents with a higher schizophrenia liability mating with less genetically diverse mates due to, e.g., fewer educational opportunities or lower migration rates. Thus, the causation may be reversed: schizophrenia liability in parents could cause not only higher schizophrenia risk, but also higher Froh, in offspring rather than Froh in offspring increasing their schizophrenia liability. Such reverse and third variable causation possibilities can only be tested if relevant socio-demographic variables in subjects and  their parents are collected.An alternative explanation for the overall pattern of results has to do with the potential influence of unmeasured confounding factors in both the original and replication analyses. Unlike genotype frequencies, which change very slowly and are unaffected by inbreeding, ROH levels can change substantially after even a single generation of inbreeding, making ROH analyses highly susceptible to confounding factors associated with both disease risk and the degree of inbreeding/outbreeding. For example, contrary to initial predictions, Abdellaoui et al. identifiower Froh. Thus, aFroh-disorder relationships seems particularly likely in analyses conducted on ascertained samples. Ascertainment of cases and controls not perfectly matched on socio-demographic factors that might affect degree of outbreeding  can mask any true Froh association and bias the observed association in either direction. Such a scenario might explain otherwise contradictory findings in previous ROH case-control analyses[n = 3,400 and 11,244 respectively) were substantially smaller than the current one . . We then calculated the overall Froh ~ schizophrenia relationship with the same logistic regression model and using the same covariates as in the original analysis. Across 1,000 permutations, 183 p-values were significant (p < 0.05), implying a type-I error rate of 0.18 and demonstrating how false conclusions about Froh relationships can be reached even when ascertainment biases are random across multiple sites.It is important to recognize that even ascertainment biases that differ at random across sites would substantially inflate type-I error rates because the proper degrees of freedom for the test should be closer to the number of independent sites rather than the number of independent cases and controls. To demonstrate this, we permuted data under the null hypothesis of no relationship between Given concerns about the false discovery rate in science, there hOur study used 37 datasets from the Psychiatric Genomics Consortium’s SCZ2 data–these data included 28,985 schizophrenia cases and 35,017 controls, collected from 37 sites in 13 countries. Data collection and ascertainment details are described elsewhere.Keller et al. used 17 −6; b) had missingness >0.02; or c) had a missingness difference between cases and controls >0.02.We followed the same QC procedures as Keller et al.. We remo2 > .90 across all datasets, as was done in the original study[Early in the analysis process, we found that only including SNPs with imputation dosage rnal study, left usnal study was more2 had to be > .90 in each individual datasets. We excluded any imputed SNPs that had a dosage r2<0.98 or >1.02 in the overall sample  or that had MAF<0.15 within each sample , leaving 340,084 high-quality imputed SNPs .SNPs were imputed using the 1000 Genomes reference panel; imputat2 > 0.90 between the focal SNP and the 50 surrounding SNPs.Again, we followed the same ROH calling procedures as in Keller et al. As recoWe called ROHs using PLINK’s—homozyg flags, defining initial ROHs as being ≥40 homozygous SNPs in a row with no heterozygote calls allowed. We required that ROHs have a density greater than 1 SNP per 200 kb, and split an ROH into two if a gap >500 kb existed between consecutive homozygous SNPs. We then post-processed the initial ROH calls by altering the SNPs-in-a-row threshold and the Mb length threshold; specifically, we looked at ROH calls with a minimum of 40 to 200 consecutive homozygous SNPs in increments of 10, and ROH calls with minimum lengths ranging from 1 to 20 Mb by increments of 1 Mb. We varied ROH thresholds this widely to ensure that no potential effects of autozygosity were missed, but the primary results presented here are based on two replication attempts in the unimputed data: (a) using the same SNP thresholds that gave the most straightforward comparison with the original report , and (b) using the physical length threshold (2.3 Mb) that corresponded to the average Mb length for 110 SNPs-in-a row in the original report.9 bases) to calculate Froh. Froh, the proportion of the genome contained in long homozygous regions, was used as the predictor of schizophrenia case-control status in analyses described below. As confounding factors such as population stratification, SNP missingness, call quality, and plate effects can influence Froh, we included the first 20 principle components , percentage of missing SNP calls in the raw data, and excess heterozygosity in all regression models[Froh using a mixed linear effects logistic regression model (available in the lme4 package in R version 3.1.0), treating dataset as a random factor, to assess the overall effect of Froh on schizophrenia across all sites. Some of the models with random effects did not converge; thus, for consistency, we modeled dataset as a fixed factor for all analyses. The results from mixed linear effects models that converged were very similar to fixed effects models, giving us confidence that the fixed effects results of this analysis and the random effect results from the original Keller et al. (2012) study are commensurate. We also ran logistic regressions in each of the 22 datasets separately.After calling ROHs, we summed the total length of all autosomal ROHs for each individual and divided that by the total SNP-mappable distance Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S1 FigZ = 0.31, p = 0.76).Boxes are proportional to the square root of sample sizes . Dataset names are on the x-axis. Only one of the individual estimated odds ratios significantly differs from one (“clm2” dataset), and the overall effect (black) is not significant Click here for additional data file.S2 Figp = 0.000357.)Boxes are proportional to the square root of sample sizes . Dataset names are on the x-axis.  Only one of the individual estimated odds ratios significantly differ from one (the “muc” dataset), but the overall effect (black) is significant Click here for additional data file.S3 FigAll SNP homozygosity thresholds above 40 SNPs-in-a-row were significant.(TIFF)Click here for additional data file.S4 FigAll ROH Mb thresholds equal to and longer than 1 Mb were significant.(TIFF)Click here for additional data file.S5 Fignot significant .Boxes are proportional to the square root of sample sizes . Dataset names are on the x-axis. Only one of the individual estimated odds ratios significantly differs from one (“clm2” dataset), and the overall effect (black) is (TIFF)Click here for additional data file.S6 FigNo SNP homozygosity thresholds were significant.(TIFF)Click here for additional data file.S7 FigNo ROH Mb thresholds were significant.(TIFF)Click here for additional data file.S8 Figindividuals but within the PGC’s SCZ2 data, where some of the original individuals were divided among several new datasets. This is why some of the dataset names are slightly different from those in the original unimputed PGC SCZ1 data in Z = 2.43, p = 0.02.)Boxes are proportional to the square root of sample sizes . Dataset names are on the x-axis—note that this imputed analysis was performed on the original SCZ1 (TIFF)Click here for additional data file.S9 FigAll SNP length thresholds were significant.(TIFF)Click here for additional data file.S10 FigAll ROH Mb thresholds were significant.(TIFF)Click here for additional data file.S11 FigSNP thresholds of 120 homozygous SNPs-in-a-row and above were significant.(TIFF)Click here for additional data file.S12 FigAll Mb thresholds ≥ 3 Mb were significant(TIFF)Click here for additional data file.


The two hemispheres of the human brain differ functionally and structurally. Despite over a century of research, the extent to which brain asymmetry is influenced by sex, handedness, age, and genetic factors is still controversial. Here we present the largest ever analysis of subcortical brain asymmetries, in a harmonized multi-site study using meta-analysis methods. Volumetric asymmetry of seven subcortical structures was assessed in 15,847 MRI scans from 52 datasets worldwide. There were sex differences in the asymmetry of the globus pallidus and putamen. Heritability estimates, derived from 1170 subjects belonging to 71 extended pedigrees, revealed that additive genetic factors influenced the asymmetry of these two structures and that of the hippocampus and thalamus. Handedness had no detectable effect on subcortical asymmetries, even in this unprecedented sample size, but the asymmetry of the putamen varied with age. Genetic drivers of asymmetry in the hippocampus, thalamus and basal ganglia may affect variability in human cognition, including susceptibility to psychiatric disorders.The online version of this article (doi:10.1007/s11682-016-9629-z) contains supplementary material, which is available to authorized users. Regarding sexual dimorphisms, a sex difference in asymmetry of the amygdala has been reported  Consortium . Specifically, image pre-processing and subcortical segmentation were done with FreeSurfer versions 4.3 through to 5.3 . The protocol consisted of visually checking individual images, plotted from a set of axial slices. Volume estimates derived from poorly segmented structures (i.e. where tissue labels were assigned incorrectly) were excluded from each site’s datasets and subsequent analyses. In addition, a number of checks were performed to assess potential errors in the left-right orientation of the data  depending on each dataset’s sample size . Statistical tests were run on the seven subcortical AIs separately. Differences between sexes or handedness groups were assessed by Welch’s two-sample t-test, to avoid assuming balanced group sizes and equal variances , on table-formatted data. Asymmetry Indices (AI) were defined as the relative volume difference between the left and right structure in relation to its total bilateral volume: (Left - Right)/(Left + Right). To exclude possible outliers in volumes or AIs we used an adaptive SD threshold , i.e., the percentage of the total variance explained by each factor. Given that individual sites ran their analyses on one version of FreeSurfer only, we computed main effects but not their potential interactions.For each of the seven AIs we assessed heterogeneity due to dataset differences through analyses of variance, with ‘dataset’ and ‘FreeSurfer version’ as the main factors. For this analysis we re-computed the total AI variance for a given structure and partitioned it into between-and within-'dataset’ contributions, and between- and within-'FreeSurfer version’ contributions. This allowed us to calculate estimates of eta-squared . The method used was Rosenberg’s . Furthermore, effect heterogeneity was assessed by Cochran’s Q and the complementary Higgins’ I2, which both assess the contribution of dataset differences to the observed pooled effect. All tests were performed in R using the ‘metafor’ library  were included.To assess the pattern of statistically significant age effects across the lifespan, we performed a post-hoc weighted meta-regression of the age coefficients from each dataset on the corresponding median ages. Datasets were weighted by the square root of their corresponding sample size. The same criterion for dataset inclusion was used as described above.T-scores and corresponding P-values were calculated for the difference between the mean AI and zero (i.e. the point of volumetric symmetry) for each structure and dataset, separately by sex. These were combined to assess population-level lateralizations for each structure, separately for each sex.We estimated the heritability of volumetric asymmetries using the Genetics of Brain Structure (GOBS) dataset  of the total observed variance per structure. Likewise, heterogeneity attributable to different versions of FreeSurfer was also substantial, with η2 > 0.1 for AI’s of the nucleus accumbens, globus pallidus and thalamus.We observed notable heterogeneity in the AI distributions across datasets Table . Except 2within*100), was 7.8 % for the nucleus accumbens and 2.5 % for the caudate nucleus. All structures showed highly significant mean lateralization, as well as consistency in mean direction of lateralization between the sexes  was also found for the hippocampus. Meta-analyses of handedness effects on AIs showed no significant group differences .After adjusting the significance threshold to en Table , correcten Table , indicatP = 0.007 for multiple testing over seven structures, meta-analysis revealed a significant effect of age on the AI of the putamen (see Table n = 85) suggested that a biasing influence of study heterogeneity on the results was unlikely.After adjusting the significance threshold to In our post-hoc analysis of age effects, by means of weighted meta-regressions, the putamen showed effects that changed across the median ages of our samples. We found larger effects of age in the younger datasets, compared to the older datasets see Fig. .2 = 0.15 to 0.27  in the presence of a significant phenotypic correlation . In other words, there may be genetic variability which affects these two AIs in opposite directions.Pairwise phenotypic and genetic correlations, assessed in the GOBS sample, are shown in Supplemental Information There is an inconsistent literature regarding basic biological factors that may affect subcortical and hippocampal asymmetries, including age, handedness, and sex. Subcortical asymmetries are subtle compared to some cerebral cortical asymmetries, and have so far only been assessed in small sample sizes, often with different analysis methods across studies (see Introduction). Compared to prior reports on subcortical asymmetries, our study analyzed a large number of datasets worldwide using a harmonized protocol and meta-analysis methods. To our knowledge, this was by far the largest ever study of healthy variation in any aspect of human brain asymmetry. The 52 datasets had technical and demographic differences, which appeared to influence the levels of asymmetry measured, but in this respect were representative of the heterogeneity that exists across cohorts worldwide. Given the scale of our study, and in contrast to literature-based meta-analyses, ours was not affected by publication bias nor by spurious results from underpowered studies. For future genome-wide screens, we also revealed significant heritabilities of asymmetries in a family sample.We found reliable sex differences in asymmetries of the globus pallidus and putamen which, together with the hippocampus and thalamus, were also the most strongly heritable asymmetries among the seven structures analyzed. With increasing age, there were changes in the mean asymmetry of the putamen. Handedness was not detectably related to any subcortical asymmetry. The ENIGMA Consortium  that results in differential innervation of the bilateral epithalamus into the surrounding tissue, which later affects other brain regions


The task of identifying genomic regions conferring yield stability is challenging in any crop and requires large experimental data sets in conjunction with complex analytical approaches. We report findings of a first attempt to identify genomic regions with stable expression and their individual epistatic interactions for grain yield and yield stability in a large elite panel of wheat under multiple environments via a genome wide association mapping (GWAM) approach. Seven hundred and twenty lines were genotyped using genotyping-by-sequencing technology and phenotyped for grain yield and phenological traits. High gene diversity (0.250) and a moderate genetic structure (five groups) in the panel provided an excellent base for GWAM. The mixed linear model and multi-locus mixed model analyses identified key genomic regions on chromosomes 2B, 3A, 4A, 5B, 7A and 7B. Further, significant epistatic interactions were observed among loci with and without main effects that contributed to additional variation of up to 10%. Simple stepwise regression provided the most significant main effect and epistatic markers resulting in up to 20% variation for yield stability and up to 17% gain in yield with the best allelic combination. The projected global demand for wheat by 205025The advances in next generation sequencing technologies and high-throughput genotyping systems have revolutionized the field of plant genomics, offering a range of modern tools and methods to scientists to characterize their populations. Genotyping-by-sequencing (GBS), which simultaneously performs SNP discovery and genotyping, has taken marker technologies to a next level providing breeders with a cost-effective genome scan of their breeding linesSince its first application for milling quality in wheat121314151617Despite the increasing awareness that epistasis forms the genetic basis of complex traits, the significance of epistasis in the genetics of grain yield has been rarely investigated in a wheat GWAM panelOur GWAM panel contained a large (720 entries) set of candidate wheat lines  from the11181422A comprehensive phenotypic data set was collected on our panel under multiple irrigated (favorable) and stress environments  which allowed us to quantify yield stability by meta-analysis of all environments. Additionally, the size of the panel made the study of multi-locus epistatic interactions feasible as reasonable statistical power could be obtained with such a large experimental data set, the lack of which has often been a limitation in GWAM studiesh2 = 0.54) was witnessed for grain yield across environments which further raised the scope of obtaining stable MTA. However, days to heading (DH) also showed a wide variation in the panel (The panel showed a wide range of variation for grain yield (GY) , suscepthe panel  and its he panel ; positivThe average gene diversity  of the p2526The principal component analysis (PCA) showed five groups in the panel . The fir1317The decay of linkage disequilibrium (LD) over physical/genetic distance in a population determines the density of marker coverage needed to perform GWAM. A faster LD decay indicates that a higher marker density is required to capture the markers close enough to the causal loci172126P-values for all traits and indices  and a modest effect on DH (4.1 to 7.0%) and GY (6.3 to 9.2%) . A mixedThirty seven MTA for GY, delineating into 27 quantitative trait loci (QTL), were identified considering all environments. Of these, 16 MTA belonging to 11 QTL were shared between at least two or more environments. A comparison with previously published studies is summarized in For yield stability coefficient, 15 MTA delineating into 11 QTL were identified on chromosomes 2B, 3A, 3B, 4A, 5B, 7A and 7B . The GBS32Two genomic regions were identified on chromosome 4A associated with yield stability coefficient , of whic1317351317Two novel QTL for yield stability were identified on chromosome 7B; the first QTL identified by marker M7175 with higher allelic effects in irrigated and heat stress environments as compared to drought environments is within ~12 and 15 cM from a major QTL identified for heat toleranceVrn-B1a  and Ppd-D1a  alleles with DH and GY  epistatic interactions and so were 50% of the markers associated with yield stability coefficient  for yield stability coefficient, and including more markers did not result in any further significant increase  having a proven role under stress43To extract the best from our GWAM and epistatic interaction analyses, the nine most stable markers with main and epistatic effects  were selected for a forward stepwise regression analysis to identify possible marker combinations resulting in higher mean GY across environments. The results of the analysis revealed that the combination of four markers  resulted in the highest Rincrease . The R2 as 17.5% . The allas 17.5% . FurtherHere we identified both, known associations (previously reported QTLs for grain yield) and new candidate genomic regions for grain yield and yield stability coefficient. The coincidence of the QTLs for yield stability coefficient in the same genomic regions as QTLs reported for GY under drought and heat stress and/or for DSI and HSI in previous studies, specifically on chromosomes 3A, 3B and 4A, suggests that many “stability-associated genes” could simply be “stress-responsive genes”. We successfully demonstrated a way to use the results of exhaustive association and epistatic scans in molecular breeding of complex traits such as grain yield and yield stability. Combining GWAM and the study of epistasis have clear potential for optimizing molecular marker based selection strategies for GY and yield stability.th IBWSN in 2012 in CIMMYT’s spring bread wheat program  were applied with the total amount of water available for the plant equaling 180 mm. For environment IV, two irrigations (at germination and 40 days after the first irrigation) were applied using furrow irrigation with a total water supply of 280 mm. Six irrigations  were applied in environment VI using furrow irrigation. The experimental design was an alpha lattice design with three replications. Each experiment included 28 lines and two checks. For each of the trials conducted in beds, the plots comprised of two 0.80 m raised beds of 2.8 meters long with three planting rows on the top of each bed. The ZT management was different from the bed trials in complete absence of tilling for three consecutive years. For the flat plot trial, experimental plots were 1.3 by 4.5 m.The panel was evaluated at the Borlaug experimental research station in Ciudad Obregon, Mexico, during the 2009–2010 and 2010–2011 growing seasons in six contrasting environments in combination with three management conditions . Optimum environments included three well-irrigated treatments with five irrigations in different management conditions . The five irrigations were applied at germination and 40, 70, 95 and 115 days after the first irrigation with a total water supply of 550 mm in optimum environments. Stress environments included two drought stress treatments [(B-2IR 2010–2011 (IV) and B-drip 2010–2011(V)] and one high temperature treatment due to a 90 day delay in the planting date [(B-heat 2010–2011 (VI); average TThe phenotypic traits evaluated in this study were grain yield (GY), days to heading (DH) and plant height (PH) for all environments except V for which PH was not recorded. DH was recorded as the number of days from planting until 50% of the spikes in each plot had completely emerged above the flag leaves. PH was recorded as the average of three values for each plot measured in centimeter from the soil surface to the tip of the spike excluding awns.ij − Yi) + Yall trials, where Yij is value of the entry for a trial, Yi is mean of checks of that trial and Yall trials is the mean of checks of all trials.For each environment, the adjusted entry mean of the genotypes were calculated for GY relative to the performance of the two check cultivars Roelfs F2007 and RSM NORMAN F2008 in SAS 9.4 using PROC GLM. The traits for which single replications (DH and PH) were measured, the adjusted mean was calculated by the formula Y = (Yh2) was calculated across environments from variance components obtained from REML analysis in GenStat edition 14th using formula h2 = Vg/((Vg + Vge/n) + (Verr/nr)) where, Vg = genotypic variance, Vge = genotype x environment variance, Verr = error variance, n = number of environments and r = replicates. Pearson phenotypic correlation coefficients among traits were obtained in Minitab 15 (http://www.minitab.com/en-IT/products/minitab/).Broad sense heritability (Yd/Yi)/S, where Yd = yield of each line in drought stress environment (B-drip 2010–2011), Yi = yield of each line under fully irrigated conditions (II) and S = 1 − (Ydm/Yim) where Ydm and Yim are the mean yield over all genotypes evaluated under drought stress and irrigated conditions, respectively. Similarly, HSI was calculated as (1 − Yh/Yi)/S, where Yh = yield of each line under high temperature conditions (VI), and S = 1 − (Yhm/Yim) where Yhm is the mean yield over all genotypes evaluated under high temperature conditions. These susceptibility indices indicate tolerance of genotypes under drought and heat stress environments. DSI and HSI values greater than 1 indicate above average susceptibility to drought and heat stress, respectively.A drought and heat susceptibility index  was calculated as described by Fisher and MaurerPi)th. This index determines the mean squared distance between genotype i and the genotype with the maximum yield within each environment as a genotypic superiority measure (Pi) with following expression:A yield stability coefficient was calculated for all entries using Lin and Binn’s superiority index . Genotyping was accomplished using GBS developed by DArT Pty. Ltd., Yarralumla, Australia. The detailed methodology is described elsewherehttp://www.diversityarrays.com/sequence-maps) was provided as a part of the service which contained ~64 K GBS markers and 4000 DArTs as anchored markers.Genomic DNA was extracted from dried leaves collected from five plants per line using a modified CTAB method described in CIMMYT laboratory protocols , photoperiod sensitivity (Ppd-1) and plant height . SNP marker genotyping was performed using the LGC Genomics KASP chemistry (www.lgcgenomics.com). The detailed protocols used for PCR reaction mixtures and thermal cycling conditions for amplifying SNP and STS markers are described elsewhereThe GWAM panel was also genotyped with 22 allele-specific markers  for major2 (squared correlation coefficient) was calculated among all pairs of loci using TASSEL version 4.0 (http://www.maizegenetics.net) and were plotted against the genetic distance in centiMorgans to determine the pattern of LD decay across the three sub-genomes and whole genome. A cut off of r2 = 0.1 was considered as the critical distance up to which a QTL region extends.Out of a total of 11,221 GBS SNP markers, 6,040 markers with known map positions, filtered with minor allele frequency >0.05 and missing data points <30% were used for diversity and LD analyses. The two diversity parameters, gene diversityP-values threshold for declaring significant MTA. However, due to high stringency of FDR-adjusted P-values and the potential risk of type II error, the criterion of selecting the P-values obtained within the bottom 0.1 percentile of the distribution was utilizedGWAM was conducted using two models; the mixed linear model (MLM) in the “EMMAX” (Efficient Mixed Model Association-Expedited) package and multi-locus mixed model (MLMM) designed for mapping complex traits in structured populationsr2 values ≥ 0.5).Adjacent co-segregating markers of a MTA were assigned to a unique QTL region upon meeting the following conditions: ≤5 cM of inter-marker genetic distance (based on LD decay across genome) and presence of strong LD among markers . A significant threshold of P < 0.001 was used to declare significant marker-marker interactions.The genotypic and phenotypic data, PCA and kinship matrices were used to analyze epistatic interactions. A linear regression model was used to calculate th Edition. All possible combinations of the selected markers were utilized and drawn against the adjusted R2 for yield stability and mean adjusted grain yield across environments.To discover the best allelic combination for yield stability and highest yield across environments, a stepwise regression analysis was conducted in GenStat 14http://www.ensembl.org/info/docs/tools/vep/index.html was used to determine the functional consequences of the variant within 5 kb of the SNP location.GBS sequences of the markers were aligned to Synthetic W7984/Opata M85 PopSeq contigs and wheat genome assembly IWGSC1.0 using Bowtie2 version 2.2.2.9How to cite this article: Sehgal, D. et al. Identification of genomic regions for grain yield and yield stability and their epistatic interactions. Sci. Rep.7, 41578; doi: 10.1038/srep41578 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.