Despite ongoing reduction in genotyping costs, genomic studies involving large numbers of species with low economic value (such as Black Tiger prawns) remain cost prohibitive. In this scenario DNA pooling is an attractive option to reduce genotyping costs. However, genotyping of pooled samples comprising DNA from many individuals is challenging due to the presence of errors that exceed the allele frequency quantisation size and therefore cannot be simply corrected by clustering techniques. The solution to the calibration problem is a correction to the allele frequency to mitigate errors incurred in the measurement process. We highlight the limitations of the existing calibration solutions such as the fact they impose assumptions on the variation between allele frequencies 0, 0.5, and 1.0, and address a limited set of error types. We propose a novel machine learning method to address the limitations identified.The approach is tested on SNPs genotyped with the Sequenom iPLEX platform and compared to existing state of the art calibration methods. The new method is capable of reducing the mean square error in allele frequency to half that achievable with existing approaches. Furthermore for the first time we demonstrate the importance of carefully considering the choice of training data when using calibration approaches built from pooled data.This paper demonstrates that improvements in pooled allele frequency estimates result if the genotyping platform is characterised at allele frequencies other than the homozygous and heterozygous cases. Techniques capable of incorporating such information are described along with aspects of implementation. Recently the Illumina HiSeq X Ten  achievedAA,AB,BB with corresponding A-allele frequencies 1,1/2,0 and the ‘concentration’ is equivalent to the real valued A-allele frequency within the range .Pooling techniques date back to 1943 when blood from soldiers was pooled for testing of disease  and poolThe most significant drawback of the pooling approach is the error incurred in the process of measuring the pool’s allele frequency. The impact of this error is illustrated in the context of a bi-allelic quantitative trait linkage study.α and β) are identified exhibiting opposing extremes of the trait. From each sub-population a sub-set of individuals are selected, DNA acquired from each individual and combined in a single pooled sample representative of the respective subset. The two pooled samples are genotyped and their allele frequencies are compared. Both fixed and variable errors in the allele frequency measurement impact the power of such a study:Given a population and a single trait of interest, two sub-populations  is calculated from:where Z is the study test statistic, Es (due to the limited pool size), sample construction error: Ep  and allele frequency measurement error: Em (due to chemistry and detection errors in the genotyping process). If the true sub-population allele frequency is p, then these errors result in a measured allele frequency f=p+Es+Ep+Em. The variance introduced in f by approximating sub-population with N individuals is the expectation of the square error: τ is the standard deviation in the fractions of the pool contributed by the individuals. A thorough analyses of these errors under different sampling conditions is given in , or alternatively be only applied within the spread of allele frequencies on which the model was built. One alternative is to use smaller number of samples in constructing calibration pools, to increase spread. Another solution is to include a mixture of pools and individuals in the training of the algorithm such as the combined data set.In summary, whereas existing calibration approaches are trained using individual samples, machine learning approaches should not, and pooled samples are required. There is an advantage in including calibration pools when building calibration models. However care must be taken to avoid learning near the pool allele frequency values only. Models that achieved the best results (when tested on pools) were those trained only on the calibration pools and were not accurate elsewhere over the full allele frequency range. This is highlighted by the larger errors committed by all methods when trained on combined set was the SVR which achieved a MSE of 6.54 ×10−3 on pools with a variance of 2.55 ×10−3 on individuals. This is 33% larger than the duplicate values random error so although some scope still exists for improvement in reducing variation, any future substantial improvements would require investigation of the causes of variation in the platform response to duplicate samples. The best polynomial calibrator (2nd order Lagrange) achieved 12.34 ×10−3 MSE on pools only with much larger variance of 4 ×10−3×10−3 on individuals only. This is almost a factor of 2 in error reduction in MSE by the machine learning approach. The best approach for minimising variance on the individuals only set was the MLP which achieved a random squared error component 2.17 ×10−3 comparing with calibrated MSE of 3.75 ×10−3. This corresponds to an increase in increase in test statistic of 72% compared to standard calibration on the pools only data set. A comparison of the best performing ML approach with the existing methods is given in Table The most accurate method applied to pools, when trained with allele frequencies on the This is the first study of a machine learning approach to calibration of pooled SNP samples which has demonstrated the importance of training sample location on performance. The approach was tested on data generated by a Sequenom iPLEX SNP panel providing results for 61 SNPs on Tiger prawn individual and pooled samples. We showed that SNP to SNP variation is significant between the allele frequencies and different calibration polynomials are suitable for different SNPs. We introduced a machine learning technique to model each SNP separately and included data between the discrete allele frequencies of individuals by incorporating calibration pools into the model. The machine learning approach achieves significantly less error, by reducing error by a factor of 2 and improves study test statistic by 72% as a consequence of reduction in allele frequency variance.f, to become predictable in the additional dimension. In this situation variance causing error is converted to a bias error which can be corrected by calibration with a resulting reduction in variance. Here we have limited access to auxiliary data from the experiment and using allele frequency alone has allowed comparison of the techniques with the same input data.An additional advantage of the machine learning technique is the ability to calibration functions on higher dimensional inputs. The use of additional input information can allow errors which previously created variance in


The data set consisted of 55,825 probes and 228 samples.Association studies are an essential part of modern plant breeding, but are limited for polyploid crops. The increased number of possible genotype classes complicates the differentiation between them. Available methods are limited with respect to the ploidy level or data producing technologies. While genotype classification is an established noise reduction step in diploids, it gains complexity with increasing ploidy levels. Eventually, the errors produced by misclassifications exceed the benefits of genotype classes. Alternatively, continuous genotype values can be used for association analysis in higher polyploids. We associated continuous genotypes to three different traits and compared the results to the output of the genotype caller SuperMASSA. Linear, Bayesian and partial least squares regression were applied, to determine if the use of continuous genotypes is limited to a specific method. A disease, a flowering and a growth trait with We were able to detect associating probes using continuous genotypes for multiple traits, using different regression methods. The identified probe sets were overlapping, but not identical between the methods. Baysian regression was the most restrictive method, resulting in ten probes for one trait and none for the others. Linear and partial least squares regression led to numerous associating probes. Association based on genotype classes resulted in similar values, but missed several significant probes. A simulation study was used to successfully validate the number of associating markers.Association of various phenotypic traits with continuous genotypes is successful with both uni- and multivariate regression methods. Genotype calling does not improve the association and shows no advantages in this study. Instead, use of continuous genotypes simplifies the analysis, saves computational time and results more potential markers.The online version of this article (doi:10.1186/s12864-016-2926-5) contains supplementary material, which is available to authorized users. Many agriculturally and horticulturally important crops are polyploid , 2. PolyThe latter one is also referred to as genotype calling and is a challenging task for polyploids. While there are many methods available for diploids , only thGenerally, determination of genotype classes  reduces noise and leads to better associations. In polyploids, this task is not as straightforward and the advantage of noise reduction is reversed by the high risk of misclassification, i.e. assignment of wrong genotypes to samples. Therefore, we skipped genotype calling and used the continuous genotypic values  when we used the continuous values. We called the genotype classes with SuperMASSA and repeated the LR analysis leading to 2 significant probes. We compared the results to see which approach worked better. An example is shown in Fig. 3q-values of the LR of the continuous genotypes for the same probe were 9.97×10−7 and 0.0078, respectively  lay on one contig. Thus, it is unlikely to detect two or more significant SNPs from the same contig by chance. The fact that we found up to three SNPs from the same contig is a good indicator for real association. We detected 5 probes from one contig, coding for three different SNPs. The white area in the second bar in Fig. R2 values and explain only parts of the phenotypic variance. Table R2 values are obtained from the LR association.The PLSR and bayz associations detected 123 and 4 significant probes, respectively. The four probes, detected by bayz overlap with the LR and PLSR results. In addition there is an overlap of 89 probes between PLSR and LR. However, the associating probes have low θ range. Thus, we expect multiple genotype classes within that cloud of data points. However, they could neither be determined manually nor computationally. bayz did not detect any significant probes, either. In contrast, the PLSR association detected 62 significant probes. It includes low effect markers as well and is not limited to single loci. For polygenic traits PLSR is therefore advantageous.LR did not result in any significant probes for the growth trait. Growth is known to be a polygenic trait . Hence, 33We could have applied sparse partial least squares (SPLS) regression to deal with very high-dimensional data. The expected number of associating probes would be even higher than. We decided against it because the number of false positives and low impact probes  would have increased significantly. PLSR is less restrictive in the growing and disease trait but not in the flowering trait.EBVs are established metrics in breeding, but have been criticized for genome-wide association studies (GWAS) because their naïve usage reduces power, increases the false positive rate and misestimates effect sized of quantitative trait loci (QTL) . Hence, SuperMASSA misclassifies genotypes in some cases because it assumes clusters of equal distance at fixed positions. Instead, the data does not necessarily segregate into clusters Fig. g. If clu3θ needs to be upgraded to θi: Genotyping by sequencing (GBS) results in similar datasets, where the continuous genotypes are replaced by read counts. In general, our approach can be applied to this kind of data, but it is limited to bi-allelic SNPs and requires an extension to account for multi-allelic SNPs. Assuming an additive genetic effect  and a muG is the set of alleles and Gi is the read count of allele i. Alternatives to the log-transformations might be more effective and need to be investigated [where stigated .n we expect up to 2n+1 clusters on a similar range, because the overall signal strength is limited by the used technology . Consequently the distances between clusters decrease and the correction accounts for smaller proportions of the signal. In addition, the risk of misclassifications increases, because there is less tolerance for variation in the signal intensity or clusters overlap. Further, the distribution of genotype values approximates a continuous distribution with increasing ploidy levels. Figure θ and provide genotypic information. From a biological perspective, continuous genotypes are difficult to interpret, because the number of alleles is discrete and should fall in one of the genotype classes. One explanation are tri- and tetra-allelic SNPs, where more than two nucleotides are present at the same position [The higher the ploidy level, the smaller is the advantage of genotype classes over the continuous values. With increasing numbers of genotype classes, the effect of noise reduction declines. For instance, in a diploid we expect the clusters AA, AB and BB at around 2, 0 and −2, respectively. A value of 1.2 would be assigned to cluster AA, so we correct for a large proportion of the signal. For any ploidy level position , 30. If position . Both reSkipping genotype calling leads to further challenges with current linkage mapping and haplotype phasing methods, because they require genotype classes. Nevertheless, the choice of tools that work for polyploids is very limited anyways and new solutions need to be developed. Further, low-coverage sequencing and imputations of genotypes add more difficulties .We showed that continuous genotype data can be used successfully in an association study of a polyploid crop and validated our findings in a simulation study. Application of different regression tools show that our approach is not limited to a specific method, but the results vary to a large extend.Genotype calling leads to misclassification and false association results in some cases, where significant markers could not be detected. However, the majority of markers lead to similar results with genotype classes and continuous values, indicating that genotype calling is not adversely in general. In this study genotype calling has no advantage and can be skipped unless better methods are developed. Instead, use of continuous genotypes simplifies the analysis, saves computational time and results more potential markers. Nevertheless, the overlapping clusters of the given data set remain a challenge and the use of continuous genotypes is a successful solution to that problem.A hexaploid chrysanthemum population consisting of 228 F1 offspring was used for our study. The cultivated plant material was provided by Dümmen Orange and all experiments have been performed according to legal guidelines.Three different traits have been used, as shown in Table The estimation of the breeding values (EBVs) was performed using ASReml-R . The EBVyi is the observed trait value, α is the population mean, gi is the random accession effect, where ei is the random error of the observed trait value, where Where k et al. , the preWith and i and where k probes for hexaploid chrysanthemum. We filtered out probes with a θ range below 2, because association requires segregation. The final data set consists of 55,825 probes. Each SNP is represented by two probes, upstream and downstream, respectively. We genotyped 228 samples and preprocessed them with Affymetrix Power Tools [A and B are transformed into difference values θ, where The genotypes were measured with a customized Affymetrix Axiom™ microarray. It provides ∼100er Tools . This ins where and a signal strength θ, the difference between the two alleles A and B. The values span the whole range of potential genotypes and represent seven different genotype classes. The leftmost samples are homozygous A, while the rightmost ones are homozygous B. The intermediates are heterozygous in varying proportions. The y-axis shows the mean signal strength s. The homozygous s values are lower, because logarithmic values are used.An example of a bi-allelic probe from a hexaploid chrysanthemum data set is shown in Fig. http://statgen.esalq.usp.br/SuperMASSA/) [The genotype calling was done with the web application of SuperMASSA without population-level information (rMASSA/) . The ploThree different methods to associate the continuous genotypic values with the phenotypes were used: LR, bayz and partial least squares regression (PLSR). The model to calculate the LR for all three traits was Yi are the DEBV s, α is the population mean, β is the regression coefficient, xi the mean-centered, continuous genotype value and εi the residual error. The function lm from the R package stats (Version 3.1.3) with the default parameters was used for the regression [q-values with the function qvalue of the R-package qvalue (Version 1.43.0) with default parameters [where gression . The resrameters , 37. We BayesCπ method [π was changed from a uniform distribution to a slightly informative prior distribution ∼Beta. In bayz, shrinkage of allele effects was done by applying a mixture distribution. Many SNP effects were shrunk to nearly zero to obtain high sparsity in SNP effects and only a small part of the SNP effects were less severely shrunken, thereby identifying SNPs with important associations. The prior mixture distribution was The effect of each SNP was estimated using Bayesian Variable Selection method as implemented in the bayz software , 22 and π method , except π0=0.99 and π1=0.01 and Beta.Where the ‘null’ distribution modeled the majority of SNP with  no effect using prior settings pls functions of the R package caret (version 6.0-47) [For the PLSR analysis we used the most significant probes of the LR analysis, based on F-statistic values ≥4. The numbers of probes were 4517, 4546 and 4957 for the disease, flowering and growth trait, respectively. We used the  6.0-47) . The assn is the number of samples, γi is the observed and varImp function from the R-package caret [Where old of 2 , 42. Thege caret . The calYi for each offspring i with an adapted formular by Günter et al. [We simulated 228 F1 offspring genotypes  based on the parental genotypes with PedigreeSim . We seler et al.  11\docuπj is the explained variance fj is the allele frequency and aij is the genotype of sample i for probe j. The heritability was set to 0.78 as for the flowering trait. Afterwards, we associated the simulated phenotypes with the genotypes using LR. This simulation procedure was repeated 100 times for each parameter combination.where BF, Bayes factor; PLSR, partial least squares regression; DEBV, deregressed estimated breeding value; GBS, genotyping by sequencing; LR, linear regression; MCMC, Monte Carlo Markov Chain; PEV, predictive error variance; REML, residual maximum likelihood; SNP, single nucleotide polymorphism; SPLS, sparse partial least squares


For all ages, YWs exhibited moderate single nucleotide polymorphism (SNP)-based heritability estimates (0.25–0.38), while the estimates for FW (0.16) and OW (0.20) were relatively low. Independent univariate genome-wide screens for each trait identified 12, 3, and 31 novel significant associations with YW, FW, and OW, respectively. A list of candidate genes such as ZAR1, STARD13, ACER1b, ACSBG2, and DHRS12 were identified for having a plausible function in yolk and follicle development. These genes are important to the initiation of embryogenesis, lipid transport, lipoprotein synthesis, lipid droplet promotion, and steroid hormone metabolism, respectively. Our study provides for the first time a genome-wide association (GWA) analysis for follicle and ovary weight. Identification of the promising loci as well as potential candidate genes will greatly advance our understanding of the genetic basis underlying dynamic yolk weight and ovarian follicle development and has practical significance in breeding programs for the alteration of yolk weight at different age points.Because it serves as the cytoplasm of the oocyte and provides a large amount of reserves, the egg yolk has biological significance for developing embryos. The ovary and its hierarchy of follicles are the main reproductive organs responsible for yolk deposition in chickens. However, the genetic architecture underlying the yolk and ovarian follicle weights remains elusive. Here, we measured the yolk weight (YW) at 11 age points from onset of egg laying to 72 weeks of age and measured the follicle weight (FW) and ovary weight (OW) at 73 weeks as part of a comprehensive genome-wide association study (GWAS) in 1,534 F Chicken egg yolk is an emulsion of water 48%), lipids 33%), and proteins 17%) [7% [1]. B3%, and p8%, lipidThe central area of the chicken ovary is composed of a vascularized medulla and a cortex containing the small follicles that are oocytes covered by follicular epithelium , and egghttp://www.animalgenome.org/cgi-bin/QTLdb/index). In recent years, genome-wide association studies (GWASs) have been utilized to identify the associations between genomic loci and phenotypes with relatively high-density single nucleotide polymorphism (SNP) arrays in chickens [Due to the wide utilization of egg yolk, many efforts have been performed to alter egg yolk weight . Howeverchickens . Recentlchickens . The dev2 chicken population to explore the associated genomic loci and genes that contribute to the dynamic change in the yolk weight with the aging process. Furthermore, the GWA analysis was also performed on ovary and follicle weights at 73weeksof age to detect the causal genes related to follicle and ovary development. This study lays the foundation for an investigation into the genetic control of yolk and follicle development.In the current study, we conducted GWA analysis on the yolk weight at 11 time points from the onset of egg laying to 72 weeks utilizing 600K high-density SNP arrays in an FAll protocols and procedures involving animals were performed in accordance with the Guidelines for the Care and Use of Experimental Animals established by the Ministry of Agriculture of China . All animal work was approved by the Animal Welfare Committee of China Agricultural University (permit number: SYXK 2007–0023).2 resource population. For parents, six WL and six DX males were initially mated with 133 DX and 80 WL females, generating 1,029 and 552 chicks for the F1 generation, respectively. Then 25 males and 407 females from the WL/DX cross and 24 males and 235 females from the DX/WL cross in the F1 generation were used to produce the F2 population, which consisted of 3,749 chicks in a single hatch, originating from 49 half-sib and 590 full-sib families. The hens were kept in individual cages of the same environment with food and water adlibitum at the Jiangsu Institute of Poultry Sciences. Finally, 1,534 hens from 49 half-sib families and 550 full-sib families with sufficient phenotypic and pedigree information were selected for SNP genotyping. All layers were caged individually and subjected to a light/dark cycle of 16h of light and 8h of darkness (16L:8D)and raised in the same environment with feed and water adlibitum.Reciprocal crosses between standard breed White Leghorns (WL) and Dongxiang chickens (DX), an indigenous Chinese strain, were utilized to develop an FYolk weight (YW) was measured for the first egg of each hen and again at 32, 36, 40, 44, 48, 52, 56, 60, 66, and 72 weeks of age, consisting of 11 age points. Except for the first egg, fresh eggs were collected for four successive days to ensure two eggs per hen at each age point. Eggs were broken to obtain the internal contents, and then the yolk was separated from the albumen and weighed by electronic scale. All hens were humanely sacrificed by 60%–70% carbon dioxide at 73weeks of age, the follicles and ovaries were then separated and weighted for follicle-active hens. FW includes the weight of all follicles that were contained in the ovary, and OW indicates the weight of the follicle-free ovary, which consisted of a highly vascularized central area (medulla) and a peripheral area (cortex). Descriptive statistics were calculated with R project (R version 3.1.2) using all available records. The function of ‘rntransform’ in the GenABEL package of R project was used for the rank-based inverse normal transformations .P< 1 × 10−6 were removed from the downstream analysis. Some sporadic missing genotypes were imputed using the BEAGLE v4.0 procedure [R2>0.5 were retained. Ultimately, up to 1,512 individuals and 435,867 SNPs were valid for the GWA analysis.Genomic DNA was extracted by the standard phenol/chloroform method and genotyped with the Affymetrix 600K Axiom Chicken Genotyping Array . Affymetrix Power Tools v1.16.0 (APT) software was then used for quality control (QC) and genotype calling. Specifically, only samples with dish quality control (DQC) >0.82 and a call rate>97% were included in the subsequent analyses. An R script supplied by Affymetrix was run to compute the SNP QC metrics and filter out individual SNPs falling below given thresholds. After these QC steps, 1,512 individuals and 532,299 SNPs remained valid. Because the current statistical methods are more powerful for the detection of the associations between phenotypes and autosomal genotypes, all SNPs on sex chromosomes were excluded in the QC process. The PLINK v1.90 package  was thenrocedure , and onlh2snp). We also quantified the pair-wise genetic and phenotypic correlations for each trait at multiple time points with a bivariate mixed model [A univariate restricted maximum likelihood (REML) estimation was implemented in the GCTA v1.24 program [ed model . A genetP values were 8.43 × 10−7  and 1.69 × 10−5 , respectively.The principal component analysis (PCA) implemented in the PLINK package was conducted prior to genome-wide association (GWA) analysis to eliminate spurious associations resulting from the presence of cryptic relatedness or hidden population stratification. To properly decide the thresholds for genome-wide significant/suggestive associations, we used the simpleM method  to correP value was calculated for the significance level between the SNPs and phenotypes. The univariate linear mixed model as follows:A univariate association test equipped with an exact mixed model approach in GEMMA v0.94 software  was perfy is an n × 1 vector of phenotypic values for n individuals, W is an n × 5 matrix of covariates  including a column vector of 1, α is a 5 × 1 vector of corresponding coefficients including the intercept, x is an n × 1 vector of marker genotypes at the locus tested, β is the corresponding effect size of the marker and all effects are reported for the minor allele in each marker, u is an n × 1 vector of random polygenic effects with a covariance structure as u~ N, where K represents a known n × ngenetic relatedness matrix derived from SNP markers and Vg is the polygenic additive variance, and ε is an n × 1 vector of random residuals with ε ~ N, where I is an n × n identity matrix, and Ve is the residual variance component. We used the Wald test statistic β = 0, where the best linear unbiased estimate (BLUE) of β and the corresponding sampling variance g and Ve.For the equation, The Manhattan plots and quantile—quantile (QQ) plots were drawn by the “gap” packages  in R proNotably, many SNPs maybe passively significantly associated with target traits, resulting from their linkage to a strongly causal mutant. In general, GWAS does not distinguish a genuine causal locus from those that are statistically significant loci within a strong linkage disequilibrium (LD) region. Therefore, in order to characterize the potential candidate genes responsible for a trait, we conducted an LD analysis and inferred the haplotype blocks containing peak SNPs by Haploview v4.2 . A blockVariant Effect Predictor (VEP) and BioMart tools based on the galGal4 assembly supported by Ensembl were used for the identification of candidate genes in which significant loci were located  and for Descriptive statistics for egg yolk weights at 11 age points and follicle and ovary weights at 73 weeks were presented in h2 = 0.38). Moreover, bivariate GCTA analyses indicated that yolk weights at the various ages exhibited highly and positively correlation, especially for yolk weights at neighboring time points. At the beginning of the entire laying stage, the yolk weight of the first egg (FYW) showed slightly lower genetic correlations with the yolk weights at the following ages (rg<0.60), compared with those among yolk weights from 32 to 72 weeks of age (rg>0.80). Notably, the follicle weight at 73 weeks had low phenotypic (0.02 to 0.17) and genetic (-0.003 to 0.52) correlation with yolk weights at the 11 age points. Similarly, the ovary weight also poorly correlated with yolk weights, and the phenotypic and genetic correlation coefficients ranged from 0.02 to 0.13 and -0.02 to 0.40, respectively. However, the genetic correlation between ovary weight and follicle weight was relatively high (0.86).We quantified the additive genetic variation in liability to yolk weights at the different ages captured by eligible GWAS markers. Univariate GCTA analyses revealed that all yolk weights had moderate heritable patterns , and theWe conducted separate association tests using a univariate model for egg weights at each age point and follicles and ovary weight at 73weeks. The Manhattan plots and the Quantile-Quantile (Q-Q) plots of the yolk weight of first eggs (FYW) are shown as an example in DOT1L, STON2, GALC, RPA2, BRCA2, ZAR1, EML4, KCNG3, ELL, ENSGALG00000028314 and RGS3F were detected as harboring or being near these significant loci  and 40, 48, 56, 66,and 72 weeks of age . Eleven ant loci .DCLK1) gene, and rs313140585 was identified in the neurobeachin (NBEA) gene. In addition, two other genes, spastic paraplegia 20 (SPG20) and StAR-related lipid transfer domain containing 13 (STARD13), were found near the significant SNPs.Three SNPs located on chromosome 1 (GGA1) were significantly associated with follicle weight (FW). Detailed SNP messages are presented in NEK5), NIMA-related kinase 3(NEK3), and cytoskeleton associated protein 2 (CKAP2). Twelve of the 24 SNPs in GGA28 were located in known genes, and the remainders were located 0.4 to 10 kb away from the nearest known genes, which included 19 annotated genes  in a narrow region (800kb) in GGA28, we speculated that strong LD exists in this region. Hence, the LD analysis was performed in the genomic region from 1.60 to 2.40 Mb, which contained 744 SNPs, and 76 small scale blocks were observed in this region . Eight o2 cross population, which could maximize the differences of the traits and increase the power to identify the QTLs for traits that differed between the breeds. Compared with previous association analyses in chickens, our analysis used a higher density (600K) SNP array covering chromosomes 1–28 and two unassigned linkage groups. In addition, this F2 population consisted of 1,512 hens, which is the largest population used for GWA analysis of egg traits so far, and therefore, the novel genomic region and loci revealed by the current study should be accurate and reliable. Several previous studies detected causal genomic regions or genes that controlled yolk weight using GWA analysis [The population used for this study was anFanalysis , 18. HowP<8.33 × 10−7). These significant loci, which occurred on GGA 1, 3, 5, 17, and 28, had no overlap with previously reported QTLs. This might due to the specially designed F2crosses used in this study. In addition, the significant loci for each age point varied completely, which was notable because it indicated that the genetic control for yolk weight was age-dependent. However, the genetic correlations among yolk weights at each age points were relatively high , which is downstream  of rs313116098, an SNP significantly associated with YW48.ZAR1 is considered to be an oocyte-specific maternal-effect gene [One candidate gene with a biologically plausible function is zygote arrest 1(ect gene  and is tect gene . Michailect gene . This geSTON2), galactosylceramidase(GALC), and potassium channel, voltage-gated modifier subfamily G, member 3 (KCNG3) have functions related to nerve regulation. In fact, nerve networks have close relationships with ovarian follicle development. Specifically, the maturity and ovulation of the yolky follicle is profusely innervated by both adrenergic and cholinergic fibers [STON2encodes a protein that participates in synaptic vesicle recycling through interaction with synaptotagmin 1, which is required for neurotransmission [GALC encodes galactosylceramidase, which is related to globoid cell leukodystrophy in humans [KCNG3encodes for the voltage-gated potassium (Kv) channels, which regulate neurotransmitter release, insulin secretion, and neuronal excitability [Three genes, stonin 2  domain and can cause protein translocation to the plasma membrane when stimulated with epidermal growth factor (EGF) [STARD13 encodes a protein possessing C-terminal STAR-related lipid transfer domain, which is a classical type of lipid transporter [STARD1-STARD15, possess a START domain, and cholesterol, 25-hydroxycholesterol, phosphatidylcholine, phosphatidylethanolamine, and ceramides are ligands for STARD1/STARD3/STARD5, STARD5, STARD2/STARD10, STARD10, and STARD11, respectively [STARD13 gene was identified with follicle weight, indicating its crucial role in lipid metabolism in the process of yolk deposition, an association that needs further investigation.Three loci  in GGA1 were significantly associated with follicle weight, and two candidate genes, or (EGF) , 42. STAnsporter , 44. In ectively . In the DHRS12, a gene that encodes the enzyme of the short-chain dehydrogenases/reductases (SDR) family, which metabolizes many different compounds, including steroid hormones [DHRS12is closely related to ovarian development.The SNPs that were significantly associated with the follicle-free ovary weight were distributed on two chromosomes, GGA1 and GGA28. The loci on GGA1 (169.01–169.70Mb) were upstream from and only 3 Mb away from the loci (172.06–172.45Mb), which were related to follicle weight, whereas the candidate genes in these two regions were completely different. Six genes containing these loci of interest or located near these loci in GGA1 were identified. However, only one gene hasa function plausible for ovarian development. This gene is P = 1.7 × s3-10), was located in two genes, including alkaline ceramidase 1 (ACER1b) andacyl-CoA synthetase bubblegum family member 2 (ACSBG2). These two genes are closely related to the biological process of yolk formation, such as lipoprotein synthesis, lipid droplet promotion, and lipid carrier. ACER1can catalyze the hydrolysis of very long chain ceramides to sphingosine, while sphingosine is absorbed and converted to palmitic acid and then acylated into chylomicron triglycerides (TGs), the materials needed for the synthesis of lipoproteins [ACSBG2,encodes proteins belonging to the acyl-CoA synthetase family, which can channel lipids into nascent lipid droplets in mammals [ACSBG2 gene is significantly associated with abdominal fat deposition and exhibited functions related to lipid metabolism in chickens [For the loci in GGA 28, the most significant SNP, rs316105069Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(TIF)Click here for additional data file.S4 Fig(TIF)Click here for additional data file.S5 Fig(TIF)Click here for additional data file.S6 Fig(TIF)Click here for additional data file.S7 Fig(TIF)Click here for additional data file.S8 Fig(TIF)Click here for additional data file.S9 Fig(TIF)Click here for additional data file.S10 Fig(TIF)Click here for additional data file.S11 Fig(TIF)Click here for additional data file.S12 Fig(TIF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.


Genome-wide association studies (GWAS) have been successful in identifying loci associated with a wide range of complex human traits and diseases. Up to now, the majority of GWAS have focused on European populations. However, the inclusion of other ethnic groups as well as admixed populations in GWAS studies is rapidly rising following the pressing need to extrapolate findings to non-European populations and to increase statistical power. In this paper, we describe the methodological steps surrounding genetic data generation, quality control, study design and analytical procedures needed to run GWAS in the multiethnic and highly admixed Generation R Study, a large prospective birth cohort in Rotterdam, the Netherlands. Furthermore, we highlight a number of practical considerations and alternatives pertinent to the quality control and analysis of admixed GWAS data.The online version of this article (doi:10.1007/s10654-015-9998-4) contains supplementary material, which is available to authorized users. Genome-wide association studies (GWAS) analyze a large number of single nucleotide polymorphism (SNPs) across the genome in a large number of samples, aiming to identify loci associated with complex traits at the population level. Since 2007, well-designed studies have been able to comprehensively test common genetic variation across the genome . Up to nVariants discovered by GWAS typically have small effects which is why minor sources of systematic or random error can lead to false positive associations or can mask real effects . In order to avoid bias, it is necessary to closely control the processes underlying the production of GWAS data, extending from laboratory processes (data generation) to imputation. It is also necessary to conduct statistical analyses, which incorporate factors into the models known to influence the trait of interest, as well as being appropriate to the characteristics of the study design.Ethnicity is a confounder of epidemiological studies which incorporates cultural, geographical and biological dimensions. In the GWAS context spurious associations between genetic variants and a trait of interest occur when both allele frequencies and differences in trait distributions , vary across ethnicities. From this perspective, adequate correction for potential population stratification is required for successful identification of genetics determinants of complex traits and diseases.UBE2E2 and KCNQ1 that have higher frequencies in East Asians  as compared with Europeans   were derived from this IBS matrix by multi-dimensional scaling (MDS), to characterize the variability present in the data using few variables (PLINK –cluster –mds-plot). Participants were defined as being of non- Northwestern European ancestry when deviating more than 4 standard deviations (SDs) from the CEU panel mean value in any of the first four genomic components.To characterize the genetic ancestry of the children in the Generation R Study, all samples passing QC procedures were merged with the three genotyped panels from the HapMap Phase II release 22 build 36 including: Northwestern Europeans (CEPH collection or CEU), Sub-saharan West Africans (Yoruba or YRI) and Asians  , 15 usinTo identify cryptic family relationships within the Generation R samples, we first removed the HapMap samples, recalculated the IBS matrix including only participants of the Generation R Study and then determined pairwise, the proportion of shared IBS alleles. By using this information and the population allele frequency, PLINK is able to estimate the number of these alleles coming from the same ancestor, known as IBD (identity-by-descent), using the methods of moments . These fhttp://genome.sph.umich.edu/wiki/Minimac) consisting of 20 iterations of the Markov sampler and 200 states . Parallelization was achieved by splitting jobs on chunks across chromosomes. The window size was 2100 markers, of which 100 were flanking markers, when using assembly build 36, and a window size of 2500 markers, using 500 as flanking markers when using assembly build 37. Imputations were performed following the same chunking strategy of parallelization as mentioned for the phasing step. To evaluate genotype imputation quality we used the MACH r-squared (Rsq), metric based on the ratio of the empirically observed variance of the allele dosage to the expected binomial variance p(1 − p), assuming Hardy–Weinberg equilibrium, where p is the observed allele frequency. When imputations hold adequate information for predicting the unobserved genotypes from the observed haplotype backgrounds, this ratio should be distributed around unity . The 1.6 % of samples not genotyped were discarded either for low quantity and/or low concentration of DNA in the stock solution as well as possible unresolved sample swaps. The extra 320 DNA samples in Generation R-2, were genotyped with the Illumina HumanHap 660 Quad chip . The genotype data were exported on forward strand for both collections. A total of 178 samples with genotyping rates lower than 97.5 % , likely arising due to low DNA quality, array problems or poor performance of agents, were excluded from the final projects (Generation R-1 and Generation R-2 sets).P < 1 × 10−7). While other causes of deviation exist, failure of this test is highly indicative of genotyping errors at a given marker [CNVs reported in the manifests of the arrays, together with SNPs which could not be called in at least 95 % of the samples or with a MAF ≤ 0.001, were eliminated (Online Resources 1 and 2) before merging the Generation R-1 and Generation R-2 sets. The combined dataset, merged using only SNPs common to both platforms (n = 5809), consisted of 549,511 SNPs. No SNP was excluded in any of the two call-rate inspections. One hundred and ninety-five SNPs were removed due to differential missingness, addressing possible bias induced by batch effects between the sets. Improvements to our quality control pipeline could be implemented, as to have more stringent standards. For example, although PLINK will report alleles incompatibilities when merging datasets, these would not be detectable in case of palindromic SNPs (A/T and G/C). Therefore, since strand issues would not be detected for these type of SNPs checking allele frequencies before merging is strongly recommended. In addition, 30,971 SNPs were excluded for deviations from Hardy–Weinberg equilibrium (HWE) proportions . Sex inconsistencies were flagged by PLINK in 60 samples. Ten of them had incompatible sex data while the others were assessed as ambiguous. After revision of Genome Studio plots (Online Resource 4), we identified discrepancies for 15 of those samples. In total, 25 samples were excluded during this sex check. A sample genotyped call rate test, based on the remaining SNPs after merging projects, resulted in no samples exclusion. We found no individual samples with excess of heterozygosity of more than 4 SDs above the mean heterozygosity value of all samples, thus the presence of sample cross-contamination was unlikely. However, reduced heterozygosity (−4 SDs) was identified in 34 samples, possibly as result of the multiethnic background of the samples. Excess of homozygosity is typically seen in individuals from genetic isolates with large stretches of linkage disequilibrium (LD) or in populations with substructure, in which there is partial admixture as result of non-random mating, as is the case in the Generation R Study , 25.Generation R and the three HapMap panels were merged based on a common set of 36,845 independent (LD-pruned) autosomal SNPs. After calculation of pairwise IBS genetic distances between all individuals, we derived genomic components, summarizing the structure of the data into main genomic components explaining the genetic variation Fig. . ApproxiTwo-hundred and eighty-nine possible pairwise sib-ships were found by IBS-sharing using PLINK (0.35 < PI_HAT < 1). Sixteen pairs of individuals shared two alleles at every locus corresponding either to monozygotic twins or a single sample processed twice. Twelve of these relations were conflicting with the registry, and thus most likely correspond to the same sample being processed twice. In these cases both samples were removed from the dataset. The four remaining pairs were twins when traced back to registries. For these true twin pairs, the sample with a lower call rate was removed from the dataset. First-degree relationships discrepant with registry (13 samples) identified using PLINK were not initially excluded. Nevertheless, they were excluded after confirmation by REAP. Visualization of kinship coefficients obtained from REAP revealed that Generation R participants are (to a large extent) unrelated. Sibling pairs are represented by the small peak around a kinship coefficient of 0.25. Yet another peak (0.025< kinship coefficient <0.0635) evidence the presence of third and fourth degree related individuals (Online Resource 5). Related individuals were not removed from the dataset to allow exclusion/inclusion in association analyses to be done specifically by phenotype availability. In addition, one more individual was recently removed for retracted informed consent. In summary, the current GWAS collection for the Generation R Study consists of samples from 5732 children.Using the three HapMap panels combined 3,021,329 SNPs were imputed. The MAF distribution of imputed SNPs is shown in Fig. --merge-mode 7 option).We were able to impute 30,072,738 autosomal variants using the 1KG reference panel, in which 28,681,763 are SNPs and 1,390,975 are insertion/deletions. The mean Rsq for all variants was 0.574 ; when markers with MAF < 0.01 were excluded , the mean Rsq increased to 0.815 . Figure The socio-demographic ethnic definition in the Generation R Study is based on country of birth of the parents of the participants. To evaluate the degree of potential misclassification between definitions, we assessed the agreement of the questionnaire definition with that of genetic ancestry, using genomic components (Online Resource 7). Groups classified as being of European and Dutch origin have historically undergone high waves of migration during the 1960s, 1970s or early 1980s. As a consequence, a scattered distribution across the genomic components axes was observed instead of a uniform one. A similar pattern was also observed for participants of Surinamese origin, arising from two clearly differentiated ethnic groups, the Hindustani and the Creoles.p value distribution) and genomic inflation factors (GIF) close to unity for both EMMAX (GIF = 0.994) and genomic components correction (GIF = 0.999). In contrast, when no adjustment for population stratification was employed, very early  deviation was seen in the QQ plot, erroneously indicating that the vast majority of markers across the genome were associated with red hair pigmentation . There is no evidence of major degrees of residual population stratification in the GWAS results for red hair color . We compared the association results for rs13223036 in this locus. The frequency of the effect allele in Europeans was 0.622, while it was 0.695 in non-Europeans. The effect size differed by ~27 % of the effect size in the European group , being stronger and more significant in the non-European set .Skull BMD analysis for equal sets of European and Non-European children shows a GWS signal in the In summary, we have described the methodology used to genotype, impute, and analyze data for association with phenotypes in the multiethnic Generation R Study, addressing a number of practical issues that arise in implementing imputation-based association for a multiethnic cohort.Our genome-wide genotyped data, ready for analysis after quality control (QC), comprises information for 518,245 markers in 5732 individuals of different ethnic backgrounds, which is available in the most common genome builds (i.e. 36 and 37). Enrichment by imputation of our genotypes, following a cosmopolitan approach, resulted in an increment of the number of markers of about 5.7 times for the HapMap imputed data and 46 times for the 1KG imputed data (Rsq > 0.3).The Generation R Study withholds a special setting determined by the admixed nature of its population confined within a restricted area. This encompasses analytical challenges as well as opportunities to design genetic studies, which take advantage of such characteristics. A joint analysis including all Generation R participants represents a considerable increase in power of the design, as about half of the study population is of non-Northwestern European background. While, increment in sample size will in principle boost the power of the study, differences in allele frequency or LD relationships between the variants merit further interpretation, as shown in the example of skull BMD with equal number of individuals for both European and non-European sets. Decrease in power due to the use of an admixed population can appear when the association is confined to one of the subpopulations  either because of differential tagging or due to the effect of secondary signals .GWAS meta-analyses are expanding to include Non-European populations  with adequate methodology lagging behind due to scarce available software for the processing and analysis of multiethnic data. For example, as the most used software, PLINK , relies Choosing the optimal panel to impute the GWAS data of a multiethnic population is critical. For the Generation R Study, we have employed the so-called “cosmopolitan approach”, which has become the preferred approach after the release of the 1000 Genomes Project panel . NotablyNew denser reference panels for imputation are becoming available achieving a better characterization of human genetic variation , 19, 34.Ethnic background, as assessed by questionnaire did not match the distribution of the samples in the genomic components, mainly because it does not allow for the identification of the third generation participants, i.e. the grand children of those who originally migrated to the country, and thus groups together children that are genetically divergent as shown in Online Resource 7. This comparison together with analysis of different traits, indicate that the genetic structure of studies, such as the Generation R Study, cannot be accounted for by considering the ethnic group definitions based on questionnaire data alone. Another practical advantage when using genomic components to adjust GWAS, is the possibility to include participants even when no information of the parents’ country of origin is available. Although in other studies this percentage might be larger, in the population under study, <7 % of the information on ethnicity from the questionnaire was missing. The ethnic distribution of the remaining children is in agreement with the ethnic demography of the city of Rotterdam  and thusWe chose red hair pigmentation as an example of a highly stratified trait since it is more common in countries in the north of Europe and selected against in Africa due to higher sensitivity of its carriers to UV rays. As shown in Fig. It is important to emphasize possible drawbacks of both association strategies. Those of using EMMAX include: (1) for discrete traits obtained betas cannot be translated to odd ratios, given the statistical model applied and (2) its requirement for PLINK files, prevents the use of allelic dosages for analysis. On the other hand, since genomic components are calculated based on the variability of the input data, it is important to generate specific sets of components for particular subsets of the data when working with structured populations. Moreover, while using between two and four genomic components is common practice, the number of genomic components needed to control for population stratification is trait-specific  . The GIFAlthough the general problem of stratification, differential ethnic allele frequencies, has been successfully addressed in our cohort by the use of genomic components or linear mixed models, the ethnic differences in patterns of correlation between the underlying casual variant and the surrounding SNPs which are under study (LD), can still induce to false-negative findings .As single-center GWAS are usually underpowered, the standard strategy in the field is meta-analysis, the combination of results from multiple independent studies, increasing sample size and reducing false-positive findings. Frequently, pooling studies from ethnically diverse populations within a single transethnic meta-analysis can be challenging. To cope with this, specialized software such as MANTRA, which allows effect size to vary across different populations, has been developed . The samThe complex structure of the Generation R Study, where admixture of individuals cannot be easily discerned just by assessing the combination of two ancestral populations, constrains the application of admixture mapping, which is an important limitation of our study. Further, in the current setting of the Generation R Study, the small sample size resulting from defining well characterized ethnic groups (of non-European background) is insufficient to allow fine mapping of variants underlying complex traits, typically withholding weak genetic effects. Yet, with new approaches being developed , this anThe Generation R Study is unusual in the international arena due to its size, age range, quality of data and longitudinal study design, but particularly due to its multiethnic nature. These characteristics represent the main strengths of the cohort, allowing among others, the generalizability of findings and ethnic comparisons in epidemiological research, although complex routines might be required for genetic association analysis.In summary, we have described the methods used for generating the GWAS data of the Generation R Study, as well as general strategies for imputation and analysis within a multiethnic setting. Such strategies have allowed the Generation R Study to take part in several consortia and collaborations, which have successfully identified genetic factors underlying an ample range of complex traits.Supplementary material 1 (PDF 90 kb)Supplementary material 2 (PDF 127 kb)Supplementary material 3 (PDF 79 kb)Supplementary material 4 (PDF 101 kb)Supplementary material 5 (PDF 94 kb)Supplementary material 6 (PDF 65 kb)Supplementary material 7 (PDF 83 kb)Supplementary material 8 (PDF 35 kb)Supplementary material 9 (PDF 54 kb)Supplementary material 10 (PDF 51 kb)Supplementary material 11 (PDF 76 kb)Supplementary material 12 (TIFF 171 kb)Below is the link to the electronic supplementary material.


Non-additive interaction between genetic variants, or epistasis, is a possible explanation for the gap between heritability of complex traits and the variation explained by identified genetic loci. Interactions give rise to genotype dependent variance, and therefore the identification of variance quantitative trait loci can be an intermediate step to discover both epistasis and gene by environment effects (GxE). Using RNA-sequence data from lymphoblastoid cell lines (LCLs) from the TwinsUK cohort, we identify a candidate set of 508 variance associated SNPs. Exploiting the twin design we show that GxE plays a role in ∼70% of these associations. Further investigation of these loci reveals 57 epistatic interactions that replicated in a smaller dataset, explaining on average 4.3% of phenotypic variance. In 24 cases, more variance is explained by the interaction than their additive contributions. Using molecular phenotypes in this way may provide a route to uncovering genetic interactions underlying more complex traits.DOI:http://dx.doi.org/10.7554/eLife.01381.001 Every person has two copies of each gene: one is inherited from their mother and the other from their father. These two copies are often not identical because there can be many different variants of the same gene in the human population. Traits  vary from one person to the next—and for many traits this variation depends in part on the different gene variants that each person has inherited. Studies seeking to find the differences in DNA that can predict this variation have often assumed that the changes in DNA act on traits independently of the effect of environment and of other genetic variants.In contrast, studies with animals have shown that some genetic variants can interact to produce a bigger  effect than would be expected from simply ‘adding together’ their individual effects—a phenomenon called epistasis. But how much does epistasis contribute to variation in human traits, if at all? This question has been much disputed, and is difficult to test, not least because of the sheer number of interactions to assess: tens of millions of changes in DNA have been observed in the human genome, and so there are many more than billions of possible combinations of these changes to investigate.Here, Brown et al. have examined the sequences of all the genes that were expressed in cells taken from a cohort of twins and searched for genetic variants that show these epistatic interactions. By studying gene expression, which can be greatly affected by small changes in the DNA code, Brown et al. were able to identify 508 variants that had a bigger than expected effect on the level of gene expression. This may be a sign that these variants act in combinations: if within one genome a variant increased expression and in another it decreased expression, then this would cause greater variation in gene expression. Further investigation of these 508 variants led to the discovery of 256 examples of epistasis, and 57 of these were replicated in samples from another cohort. Brown et al. calculated that these epistatic interactions explained up to 16% of the variation in gene expression. Furthermore, as well as being involved in epistatic interactions, about 70% of the genetic variants that had an effect on the variation in gene expression were also involved in interactions between genes and the environment.In addition to showing that epistasis contributes to variation in human traits, the work of Brown et al. could help to uncover interactions behind complex traits—beyond the expression level of a gene—that could not previously be investigated.DOI:http://dx.doi.org/10.7554/eLife.01381.002 The discrepancy between the contribution of known genetic factors to variation of a trait and the estimated total contribution of all genetic variants has become known as ‘missing heritability’ . Some ofDrosophila populations and found very little concordance between the results. They postulated that this could be because the effect of genetic variants was dependent on the genetic background, and found frequent evidence of genetic interactions between one or more variants and the originally associated SNPs. Annotating these interacting SNPs to genes revealed common networks of highly connected genes across both populations. In a study of sources of variation in yeast crosses, On long time frames, epistasis plays an important role in evolution , and hasHowever, epistasis has proved harder to identify in human genome-wide association studies. In particular, with classical complex traits there has not been evidence of epistasis on the scale seen in model organisms. This may be in part because of the large number of possible interactions to test in the human genome, and possibly because the genetic architecture is different in a homogeneous outbred population from that of a cross between inbred lines.We therefore adopt the following two step strategy for uncovering epistasis affecting gene expression. We search for: (1) SNPs affecting the variance of expression (v-eQTL) within the 2 Mbp region around the transcription start site (TSS) of the gene, and then (2) SNPs in epistasis with these v-eQTL. Previous work that looked for variance QTL for height and BMI in ∼150,000 samples identified one replicated locus . Wang etTwo papers have also looked at producing a phenotype related to variance, in both cases using the coefficient of variance (CV) within inbred lines to map variants which control the stochastic influence in phenotypic variation . In sing2 with the eQTL, but high D′) could be observed as variance effects of a single SNP. This could also by mistaken for epistasis between two variants which jointly tag the eQTL. We control for this possibility by explicitly considering all possible explanatory eQTL in the full sequence data available for our replication sample.There are two other mechanisms by which genotype dependent variance can be induced. Firstly, as −10). Many of the FDR defined v-eQTL cluster close to the TSS (9.3% are within 10 kb) but they are found at all positions in the window  twin pairs and 192 dizygotic (DZ) pairs. The same samples from this cohort have previously been used for eQTL analysis, with expression quantified using microarrays . The leve window . Of the e window .-value <1.98 × 10−8; To search for epistasis, we scanned the cis windows for a second variant statistically interacting with each of the peak v-eQTL. A forward stepwise analysis identified independent examples of epistasis, not induced by linkage disequilibrium; a statistical test was applied to remove signals related to dominance . This identified 256 independent SNPs in apparent epistasis with the peak v-eQTL for 173 genes , with 202 of the 246 interactions sharing the same direction of effect   .−5, ‘Materials and methods’). The aim was for good characterisation of eQTL down to low frequency variants, though this is complicated by power and poorer imputation accuracy at such frequencies. We then tested whether the epistatic interaction was still significant in models incorporating each eQTL individually at the same threshold as previously applied. Fifty seven epistasis signals remain significant. TRIT1, As discussed in the introduction, it is possible that an observed statistical interaction between two SNPs can be caused by a single true eQTL in linkage disequilibrium with them. For example, a particular combination of alleles across the pair of SNPs could tag a rare causative eQTL. To rule out this possibility, we took advantage of the full sequence for the GEUVADIS replication samples obtained by the 1000 Genomes Project . For theTRIT1  in epistasis with the v-eQTL yielded no hits that replicated in the GEUVADIS cohort. However, using the twin design we were able to address the contribution of long range epistasis by a heritability analysis. Assuming no recombination in the cis region, the proportion of the cis window that dizygotic twins (DZ) inherited identically by descent is either 0, 0.5 or 1 and this allows us to perform a linkage analysis to estimate the proportion of variance explained by variants in the cis region, the trans region (5 Mbp away from the TSS) and interactions between the two. We had information about the IBD sharing around 273 of the 508 v-eQTL genes. For 15 of these, interactions between the cis and trans regions explain more than 10% of the variance in expression. For all of these there is greater evidence of cis-trans epistasis affecting expression than an influence of common environment, and for 9 of the 15 the interaction effect was more than the estimated combined direct genetic contribution of both cis and trans variants .The presence of v-eQTL can be induced by gene–environment interactions, as well as epistasis or haplotype effects. Because our data come from a twin cohort, which includes monozygotic (MZ) twin pairs, we have another measure of variability within the dataset: the discordance in expression between MZ twins. Genotype dependent differences in expression within MZ pairs cannot be induced by epistasis or haplotype effects, as both twins share the same genetic background. Therefore, evidence that v-eQTL are also discordant eQTL (d-eQTL) would suggest that v-eQTL could also have a GxE explanation, including possibly interactions between the genome and the epigenome . Using oArabidopsis and S. cerevisiae.By looking at variance between individuals and discordance between monozygotic twins, we mirror an approach which looked at robustness of phenotypes to genetic and environmental influences . In thisThe importance of non-additive variation to explaining missing heritability has been much debated . Here, wSpecifically in gene expression, progress has recently been made to move beyond a solely additive view of variation. The majority of the interactions are close to each other and to the TSS , consistA recent paper has also looked for evidence of epistasis affecting transcription in humans , using aIn conclusion, we report 26 replicated variance eQTL and 57 replicated cis epistatic interactions, which explain up to 16% of the variance of our phenotypes. In almost a half of cases, more variance is explained by the interaction than by single additive effects. Furthermore, we have also shown substantial evidence for gene by environment interactions. We have shown that a proportion of variation of molecular phenotypes can be ascribed to genetic interactions, and that v-eQTL are a valid way of discovering them. Densely phenotyped cohorts are now commonly collecting such molecular data, and therefore there is considerable scope to look both for more of this type of interactions, and for the particular environments involved in GxE. The ability to find genetic interactions affecting molecular phenotypes also suggests a hypothesis driven path by which genetic interactions underlying more complex traits may be identified.Samples were genotyped on a combination of the HumanHap300, HumanHap610Q, 1 M-Duo and 1.2MDuo 1M Illumnia arrays. Samples were pre-phased using IMPUTE2  with no Samples were prepared for sequencing with the Illumina TruSeq sample preparation kit  according to manufacturer's instructions and were sequenced on a HiSeq2000 machine. Afterwards, the 49-bp sequenced paired-end reads were mapped to the GRCh37 reference genome  with BWAGRAMMAR  was usedK = 0), conditioned on all previously discovered interactions. If the most significant SNP was Bonferroni significant (p<1.98 × 10−8), the SNP was added to the list and the process continued, otherwise the list was considered complete. This revealed 275 examples of epistasis, affecting expression of 178 genes. To exclude the possibility that significant interactions could be explained by a non-additive genetic effect of the original v-eQTL appearing as epistasis between the v-eQTL and another variant in tight linkage disequilibrium, a further conditional analysis tested the epistasis term conditional on the model it was discovered in and a non-additive effect of the v-eQTL . SNPs which were not Bonferroni significant at the same threshold (p<1.98 × 10−8) were removed, leaving 256 epistatic interactions affecting 173 genes. Proportion of variance for linear mixed models was calculated as described in The R package lme4  was usedi, expression by yi, dosage of v-eQTL by Siv, dosage of the kth discovered epistatic SNPs by Sik, probability that the v-eQTL is a heterozygote by Denoting individual βi= βj when i and j are twins, and γi= γj when i and j are MZ twins (capturing the increased genetic correlation of MZ twins).To correctly model the twin structure we require that A variance components model was fitted in the program solar  where thFor comparison, the model without cis-trans interactions but with a common environment term was fitted, and the two models compared using likelihood.Maximum expression of the two twins was regressed on minimum expression of the twin pair and genotype of the twin pair to detect whether the relationship between max and min expression was conditional on genotype.−5 in the GEUVADIS dataset. A t test for each reported eQTL assessed significance of the interaction conditional on the v-eQTL, epistasis SNP and the eQTL. If the greatest p value, over all possible eQTL, did not meet the FDR cut-off the SNP was removed from the list of interactions. FDR was calculated using the qvalue package  to control for population effects. Epistasis was assessed for each SNP individually, as LD induced multiple signals and dominance effects had been removed in the TwinsUK sample. To ensure that our results are not caused by heteroskedasticity, we have considered various transformations to remove this issue and found the results to be robust. In particular, of the 131 statistically significant interactions in the GEUVADIS cohort, 126 are also significant when log transformed data is analysed . To eliminate confounding with eQTL variants, an identical forward stepwise cis eQTL scan to that used in  package  in R  under accession number EGAS00001000805.Sequence data has been deposited at the European Genome-phenome Archive . Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.eLife posts the editorial decision letter and author response on a selection of the published articles . An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent  contributing non-additively to genotype-specific variance is direct evidence of epistasis. There are also presumably specific assumptions in the models, such as the dependence of variance on scale, the type of interaction, or the complex effects of LD, and these should be made clearer.– does imputation uncertainty matter here? Please also clarify why the influence of a second eQTL doesn't have an impact on the result.In terms of methodology, Step 1, the identification of v-eQTL, does not appear to leverage the twin design  and this should be explained more clearly. Step 2, “Epistasis” does use the twin structure and is based on a LRT comparing linear mixed models with and without an interaction term. What is the form of the interaction term? There are many ways to encode it which can involve more than one parameter for SNPs not in D'=1. Why use a non-parametric test for v-eQTL discovery and then a LMM for interaction? Although the data are quartile normalised, are the squared residuals and what is the effect of outliers? The conditional analysis presumably includes SNPs one-by-one to check the association holds In the main text: after identification of v-eQTL “to search for epistasis we scanned the cis windows for a second variant statistically interacting with each of the peak v-eQTL”. It would be helpful to include a mathematical description of the model. Many of the comments were about a lack of clarity in the methods and explanation: we have in response expanded the paper and included a more detailed motivation for following our path from variance to epistasis.In the course of expanding the Methods section and replying to the reviewers we re-examined some of the analysis. In particular, we realised that a forward stepwise procedure based on Bonferroni significance would be preferable to the backwards stepwise algorithm we originally used to remove non-independent signals. There are two reasons for this:1) The backward procedure we applied looked at whether there was sufficient evidence to remove the alternative hypothesis. A forward stepwise procedure asks whether there is sufficient evidence to reject the null hypothesis, the standard approach in statistical inference.2) The forward stepwise approach has been commonly applied in the literature, e.g., Compared to the previous approach, which yielded no genes with multiple examples of epistasis, we now have identified 83. That is, we were able to find 83 genes where more than one independent SNP showed evidence of an interaction with the v-eQTL, accounting for LD. Details on the methodology and new results have been included in the manuscript.While implementing these changes, we also became aware of two coding mistakes made during the analysis. Correcting these has improved our results dramatically. Firstly, we corrected a mistake while converting the GEUVADIS dataset genotype information; in combination with the new approach to detect more than one epistatic interaction, this resulted in substantially more replicated examples of both v-eQTL and epistasis in the GEUVADIS cohort. Secondly, there was a mistake in defining the location of the TSS on the negative strand for the TwinsUK analysis. Within the properly defined cis-window we found 7 new v-eQTL, bringing the total to 508.Because we were able to replicate more examples of epistasis, we have expanded our discussion of the relative impact of interacting and additive effects on variance, including new figures.Finally, since we submitted the paper the GEUVADIS consortium have reported their results and made the replication data publicly available. We would therefore like to make the processed replication data available as supplemental data for the paper, in an R dataset which also includes functions which will repeat the analysis. This will allow anyone to easily repeat the analysis and check the methodology. We also make available the R scripts used to analyse the TwinsUK sample to allow the methods applied to this dataset to be inspected. We are in the process of depositing the RNA-seq data in EBI-EGA for controlled access, with release on publication.Below we address each of the reviewers’ concerns:The only substantive concern is that the paper should be re-written because the concepts and methods need to be better explained for non-specialist readers. In particular, it should be made clearer why showing that two loci (SNPs) contributing non-additively to genotype-specific variance is direct evidence of epistasis. There are also presumably specific assumptions in the models, such as the dependence of variance on scale, the type of interaction, or the complex effects of LD, and these should be made clearer.We have added two new paragraphs to the Introduction (fourth and seventh), which we hope suitably summarise our motivations and the possible causes of genotype dependent variance, as well as modelling assumptions.In terms of methodology, Step 1, the identification of v-eQTL, does not appear to leverage the twin design  and this should be explained more clearly. Step 2, “Epistasis” does use the twin structure and is based on a LRT comparing linear mixed models with and without an interaction term.The justification for using GRAMMAR is purely computational, a full scan of all cis windows for v-eQTL involves ∼65 000 000 tests. Ideally we would like to construct residuals which control out twin structure and general SNP effect simultaneously for every SNP as currently this is assumed to maximise power (as argued in Zhou and Stephens (2012)). However, this is computationally infeasible. Instead we adopted a two stage procedure, the twin structure is removed from the phenotype, then each SNP effect can be removed separately using a much faster linear model. The epistasis scan was limited to a small set of genes and it was feasible to run the full linear mixed model, therefore twin structure was modelled simultaneously with SNP effects to maximise power.We have added the following sentence to the Methods: “This two stage procedure where relatedness was regressed out separately from v-eQTL mapping was adopted to make the full scan for v-eQTL computationally feasible.”What is the form of the interaction term? There are many ways to encode it which can involve more than one parameter for SNPs not in D'=1.We modelled epistasis as a multiplicative term in the dosages rather than a more general model, which would include factors such as recessive epistasis. This was for two reasons:1) The interacting dosage model is consistent with expected expression under the assumption that cis interacting variants must share the same haplotype (recessive and dominant epistasis would require departures from what we expect is a reasonable model of a cis molecular interaction), and2) Certain more general models of epistasis could manifest as an effect based on highly infrequent combinations of genotypes  which could produce significant findings based on very small numbers.Why use a non-parametric test for v-eQTL discovery and then a LMM for interaction? Although the data are quartile normalised, are the squared residuals and what is the effect of outliers?The squared residuals are not rank normalized: this is why a non-parametric test was applied as there are often departures from normality. An alternative would be to normalise the squared residuals and then apply linear regression, but we believe these two alternatives to be equivalent , where a stepwise equivalent to the Spearman correlation test was required). When testing interactions, our approach is to follow the standard statistical methodology. Our solution to avoid false positives due to outlier effects is to use replication.We also face the issue of heteroskedasticity, where the genotype dependent variance means that the axioms of linear regression do not hold. To ensure that our results are not caused by heteroskedasticity, we have considered various transformations to remove this issue and found the results to be robust. In particular, of the 131 statistically significant interactions in the GEUVADIS cohort, 126 are also significant when log transformed data is analysed . We now refer to this test in the Methods section.The conditional analysis presumably includes SNPs one-by-one to check the association holds – does imputation uncertainty matter here? Please also clarify why the influence of a second eQTL doesn't have an impact on the result.We assume the reviewers are discussing the analysis that investigated confounding by haplotype effects using the GEUVADIS dataset.Although there is imputation uncertainty in the 1000 Genomes dataset, this is greatest for low frequency (below 1%) variants, whereas to explain away our observed epistatic interactions we would most likely require variants of higher allele frequency. Also, good haplotyping tagging is directly related to good imputation quality, thus we would expect such causative variants to have better imputation quality. However, we do recognise this as an issue and so have added the following caveat:“The aim was for good characterisation of eQTL down to low frequency variants, though this is complicated by power and poorer imputation accuracy at such frequencies.”-5 . Of the 131 genes, 103 had at least one eQTL, with numbers of eQTL ranging from 1 to 5. To discard haplotype effects as an explanation for the observed interaction we test each eQTL individually. If when controlling for any of the eQTL, the interaction is no longer significant, we discard this interaction. We believe this to be a conservative criterion for keeping interactions: in total 57 out of 131 survive this correction.With respect to the identification of eQTL, we have changed the manuscript. We now identify eQTL affecting expression in GEUVADIS by a forward stepwise scan with a threshold of 10In the main text: after identification of v-eQTL “to search for epistasis we scanned the cis windows for a second variant statistically interacting with each of the peak v-eQTL”. It would be helpful to include a mathematical description of the model.We have rewritten the Methods to give explicit mathematical formulae, which we agree gives greater clarity. In addition, we have made all code available so that the methodology can be implemented by anyone interested in doing so .The epistasis section of the Methods has therefore been much enlarged, and a new Methods section “Equations” presents all linear mixed models used in this paper. Supplementary material has been uploaded where it is simple to repeat the replication analysis, and the TwinsUK scripts are provided so the methodology can be examined.


Many disease phenotypes are outcomes of the complicated interplay between multiple genes, and multiple phenotypes are affected by a single or multiple genotypes. Therefore, joint analysis of multiple phenotypes and multiple markers has been considered as an efficient strategy for genome-wide association analysis, and in this work we propose an omnibus family-based association test for the joint analysis of multiple genotypes and multiple phenotypes.The proposed test can be applied for both quantitative and dichotomous phenotypes, and it is robust under the presence of population substructure, as long as large-scale genomic data is available. Using simulated data, we showed that our method is statistically more efficient than the existing methods, and the practical relevance is illustrated by application of the approach to obesity-related phenotypes.http://healthstat.snu.ac.kr/software/mfqls/.The proposed method may be more statistically efficient than the existing methods. The application was developed in C++ and is available at the following URL:  During the last decade, more than a hundred genome-wide association studies (GWAS) have been initiated, and GWAS have been successful in identifying many susceptibility loci involved in human disease. However, phenotypic variance explained by significant findings has often been small, even for most heritable phenotypes ,2. For eIt has been found that analysis with secondary phenotypes -9 reduceThe family-based design has been considered to be an important strategy in genetic association analysis. However the parameter estimations for the analysis of family data is numerically complicated, and few methods other than the linear mixed model for quantitative phenotypes have been available for family-based samples. In particular, FBAT statistics , based oIn this report, we propose a new statistical method for the joint analysis of multiple phenotypes and genotypes with family-based samples. Our method can be utilized for both quantitative and dichotomous phenotypes, and is robust against the population substructure if the correlation matrix between individuals can be estimated from large-scale genetic data. The proposed method consists of two steps. First, phenotypes are adjusted with the offset based on the best linear unbiased predictor (BLUP)  or diseaQ phenotypes is considered. We assume that there are n families and ni individuals in family i. If we denote the sample size by N, N is equal to xijm and yijq denote the coded genotype of individual j in family i at variant m and the qth phenotype respectively, where m = 1, …, M and q = 1, …, Q. We letThe genetic association between M variants and N × M matrix and Y is a N × Q matrix. We also defineHere X is a Zij, which affects the phenotype, is observed for individual j in family i, and the intercept is included in Zij. We letWe assume that covariate column vector, bijq is a random effect for an additive polygenic effect for the qth phenotype and the variable eijq is a random error. We letIn addition, we assume that bijq, and the variance-covariance matrix for Bq can be parameterized by the function of kinship coefficient matrix Ф. If we let πij,i'j' be the kinship coefficient between individual i in family j and individual i' in family j', and dij be the inbreeding coefficient for individual j in family i, Фi is denoted byCovariances between individuals are explained by the random effect Ф should be replaced with the genetic relationship matrix estimated with large-scale genetic data to provide the robustness of the proposed method [Under the presence of population substructure, d method ,27. Howed method ,28. In sd method ,29 are uq be βmq, the null and alternative hypotheses areIf we let the effect of variant m on phenotype ijq for qth phenotype of individual j in family i at variant m to improve the efficiency of the proposed score test. We setEither prospective or retrospective analysis for this hypothesis testing can be selected depending on the sampling scheme. While prospective analysis assumes that phenotypes are response variable and compares the phenotype distributions between each genotype group, retrospective analysis assumed that individuals were selected based on their phenotypes, and compares genotype distributions between affected and unaffected individuals. In particular large numbers of genotypes enables the estimation of genotypic correlations between individuals, and analysis robust against nonnormality of phenotypes can be conducted with retrospective analysis. As a result, we focus on the retrospective analysis which compares genotype frequencies according to disease phenotypes. When comparing the genotype distribution, it has been shown that the statistical efficiency of the test statistic can be improved by adjusting phenotype , and we 1w be the w × 1 column vector that consisted of 1 and Iw be the w × w identity matrix. We denoted an MAF of variant m in unaffected individuals by pm, and p = t. We assumed [γm,q,pm + γm,q < 1. If we let V be the working correlation matrix for Xm, the score for a variant m can be defined byFor any positive integer w, we let  assumed  that forV and μ were incorporated to generalize the quasi-likelihood score function and can be estimated by maximizing the efficiency of the score statistics. Their incorporation is a main difference from the assumptions for WQLS and MQLS statistics [Here atistics ,32. The atistics , and we ij be an N × 1 vector where the If we let eTherefore,Thus if we defineV and μ [V, the identity matrix maximizes the statistical efficiency of the quasi-likelihood [V. The most efficient choice of μ may be related with the sampling scheme, and either BLUP or the prevalence were shown to be the most efficient [μ. The linear mixed model [Statistical efficiency depends on the choices of V and μ ,33,34, afficient ,33. In ted model  for quanΣB by ΣB and Here, we denote the qth diagonal element for el exist -38, and el exist  has ofteTq estimated by the same way for quantitative phenotypes was recommended for dichotomous phenotypes when individuals were randomly selected [V and BLUP for μ for both quantitative and dichotomous.For a dichotomous phenotype, the generalized linear mixed model  might beselected . TherefoXij) by Ψ and we assume thatWe denote var isThe proposed statistic will be denoted as MFQLS in the remainder of this report.Ψ. For individuals with missing genotypes and nonmissing phenotypes, the missing genotypes can be replaced with the conditional expectations for the association analysis [U and O indicate individuals with missing genotypes and individuals with nonmissing genotypes, respectively. We assume that NO (NU) indicates the numbers of individuals with nonmissing (missing) genotypes, and in a similar way we defineIndividuals with missing genotypes and nonmissing phenotypes, or vice versa, can be utilized for genetic association analysis. For individuals with missing phenotypes and nonmissing genotypes, tijq are assumed to be 0 and these individuals are utilized for the proposed analysis. These individuals are informative only for enhancing the accuracy of the estimated variance–covariance matrix of genotypes analysis . We let m by pm, the conditional mean vector of the missing genotypes for multiple variants isThen, if we denote the minor allele frequency for variant stimator  to pm maThis is an extension of the conditional expectation for a single variant . TherefoA(a) and B(b), respectively. If we denote the minor allele frequencies as pA and pB, and the linkage disequilibrium between these two loci by d, the haplotype frequencies for AB, Ab, aB, and ab were calculated byIn our simulation studies, we considered large families with 10 subjects that extended over three generations , and the average of maternal and paternal polygenic effects was combined with values independently sampled from MVN for the polygenic effects of offspring. The random errors for Q phenotypes were assumed to be independent and were independently sampled from MVN. We assume that if Q = 2,The quantitative phenotypes were defined by summing the phenotypic mean, polygenic effect, main genetic effect, and random error. We assumed that and if Q = 5, they wereHere ρ indicates the correlation between different phenotypes.Q phenotypes in both populations differed by 0.2. The amounts of linkage disequilibrium for both populations were assumed to be same and the allele frequencies for each marker in two subpopulations were generated by the Balding–Nichols model [qA and qB, in an ancestral population was generated from U and if we let FST be the fixation index by Wright [pk(1 – FST)/FST, (1– pk)(1 – FST)/FST). The value for Wright’s FST was assumed to be 0.01, and 0.05.Furthermore, the robustness of the proposed statistic in the presence of population substructure was evaluated with simulated data. We assumed that there were two subpopulations and each founder was assigned to one of the two subpopulations with 0.5 probability. Means of ls model . The ally Wright , the marQ = 2, and it was 0.1, 0.1, 0.2, 0.2, and 0.3 if Q = 5. The statistical validity of the proposed method for dichotomous phenotypes was also evaluated under the presence of population substructure. Genotypes and liability scores were generated under the same model as used for the quantitative traits with the Balding–Nichols model, and liabilities for each individual were transformed to either being affected or unaffected, respectively.Last, the simulations of the dichotomous phenotypes were performed using the liability threshold model. Once the quantitative phenotypes with polygenic effect and random error were generated, they were transformed to being affected if quantitative phenotypes are larger than the threshold, but to unaffected when not. The threshold was chosen to preserve the assumed prevalence. We assumed that prevalence was 0.1 and 0.2 if For the evaluation of statistical validity, the empirical type-1 error estimates for extended families were calculated at the various significance levels from 10,000 replicates for both dichotomous and quantitative phenotypes. One hundred extended families were generated in each replicate, and we assume that ρ = 0.2. Table V and μ were compared, and they were with an omnibus family-based association test (MFBAT) [Y1), …, var(YQ)) be the block diagonal matrix that consists of submatrices, var(Y1), …, and var(YQ). Then it is a NQ × NQ dimensional matrix. If diag(var(Y1), …, var(YQ)) and BLUP are utilized for V and μ, respectively, the proposed method for quantitative phenotypes becomes an extension of the mixed-model association score test on related individuals (MASTOR) [INM and the prevalence are utilized for V and μ, respectively, our score is an extension of the more powerful quasi-likelihood score test (MQLS) [For comparison of power with existing methods, the empirical power estimates were calculated from 2,000 replicates at the 0.005 significance level for quantitative and dichotomous phenotypes. We assumed that ρ were 0.2 and 0.5. For the proposed method, results from different choices of  (MFBAT) . We let (MASTOR)  for the t (MQLS) ,31 for tQ and D', but inversely related with ρ. This result is reminiscent of the analysis of repeated measures, even though results may vary depending on the situation. For the analysis of repeated measurements, it has been shown that power improvement is proportionally related with the number of observations for each individual, but inversely related with the correlation between different measurements [D' leads to reduced standard deviation of the statistics, while the larger ρ may induce sample size reduction.Table urements . This maST indicates the level of population substructure and we assumed that FST = 0.01 and 0.05. Robustness of the proposed method to population substructure is provided if the genetic relationship matrix is estimated with large-scale genetic information and replace the kinship coefficient matrix [Φ in the proposed methods. The empirical type-1 error rates were calculated from 10,000 replicates at the 0.005, 0.01, and 0.05 significance levels. Table ST was assumed to be 0.01 and ρ was 0.2. The QQ plots showed that the statistical validities for both dichotomous and quantitative phenotypes were preserved at various significance levels.The proposed methods for both dichotomous and quantitative phenotypes were evaluated in the presence of population substructure. Wright’s Ft matrix . In our t matrix , which wThe empirical power estimates for quantitative and dichotomous phenotypes are shown in Tables –5 or MAF less than 0.01, leaving 516,610 SNPs for subsequent analysis. The proportion of genotypes identical between individuals in each family was calculated and individuals with inconsistency between the genetic and reported relationship (n = 58) were excluded. At the same time, individuals with coding error about type of twin status were excluded, and in total genotypes for 1801 individuals were used for analysis.The HTK cohort which consisted of families ascertained with healthy twins was initiated to identify genetic variation responsible for complex traits and the role of the environment in the etiology of complex diseases. HTK cohort consists of 2,473 individuals including 900 monozygotic (MZ) twins and 234 dizygotic (DZ) twins. In particular, MZ twins have same genotypes, and a single individual from each twin was randomly selected for genotyping. 1861 individuals were genotyped with Affymetrix Genome-Wide Human SNP array 6.0. We discarded SNPs with p-values for Hardy–Weinberg equilibrium (HWE) less than 10The body mass index (BMI) is defined as individuals’ body mass divided by the square of their height and the waist-hip ratio (WHR) is the ratio of the circumference of the waist to that of the hips. The triglyceride (TG) is an ester derived from glycerol and three fatty acids, and we took a logarithm to TG. With these three phenotypes we performed joint analysis to identify the disease susceptibility loci for obesity-related phenotypes. Age and sex were included as covariates for the linear mixed model and BLUP was utilized as offset for MFQLS. The number of individuals with missing phenotypes for BMI, WHR, and TG were 4, 1, and 28, respectively, and their tijq were assumed to be 0. For comparison, EMMAX  based on–8 and Table –7 for EMMAX or MFQLS. rs651821 is an unique genome-wide significant result and the p-value of rs651821 derived by MFQLS was markedly less than those derived by EMMAX. P-values of rs17119975 and rs4417316 were larger than the significance level by Bonferroni correction but they are still expected to be promising candidate disease susceptible loci. In particular, the genetic positions of these three SNPs were similar, and we checked the linkage disequilibrium between theses SNPs with pairwise r2 from the Chinese and Japanese data in the HapMap Release 3. rs17119975 and rs4417316 were in linkage disequilibrium with r2 = 0.823, but r2 between rs651821 and the others are less than 0.01. Small p-values of rs17119975 and rs4417316 may be generated with the same genetic component even though both are located in different genes, and it should be noticed that the smallest p-value for rs17119975 and rs4417316 was found with MFQLS.The QQ plots in Figure Q = 3 and M = 1 for APOA5, and Q = 3 and M = 3 for BUD13 and ZNF259. Table M = 1 identified only a single genome-wide significant SNP. Therefore, the analyses of multiple genotypes provided more genome-wide significant results, and seem to be efficient strategy for association analysis.Based on those results, we conducted the gene-based analysis with MFQLS for those three genes. All SNPs in each gene were utilized for the joint analysis of multiple phenotypes and multiple genotypes. Single SNP is located in APOA5, and three SNPs are in BUD13 and ZNF259. The result for APOA5 is same as results for rs651821. Thus, our MQLS statistics assumes that M = 1 and Q = 3 required 13 minutes and 26 seconds. The pedigree structure does not affect the computational intensity and thus we can conclude that the proposed method is computationally efficient enough to complete genome-wide association analysis using a few thousand individuals within a few hours. The software for the proposed method is downloadable from http://healthstat.snu.ac.kr/software/mfqls/.In this report, we have extended a score test based on the quasi-likelihood to joint analysis of multiple phenotypes and genotypes. The proposed method can be applied to dichotomous and quantitative phenotypes, and it is statistically valid even in the presence of population substructure. With extensive simulation studies, we found that the proposed method is statistically more efficient than existing methods. The genome-wide association analysis of the HTK cohort with V and μ. For instance, if M and Q are 1, the MASTOR statistic [V and μ, respectively. If an identity matrix and prevalence are used, our method is equivalent to MQLS [The proposed method is based on quasi-likelihood -33,44 an to MQLS . We empi to MQLS ,33. Our The proposed methods test the homogeneity of genotype distribution along the phenotypes, but this retrospective analysis is expected to be less efficient than the prospective analysis of random samples. However, it has recently been shown that power loss for retrospective analysis is often negligible , and theEven though GWAS have successfully identified many genetic variants for diseases in the past decade, our experience has revealed that further investigation of the analysis strategies for reducing false negative findings is necessary. The significant results from our analysis with simulated data and real data for obesity indicated that joint analysis with multiple phenotypes and genotypes may provide a breakthrough in genetic association analysis.We proposed a new method for the joint analysis of multiple phenotypes and genotypes. There is no uniformly most powerful method for the joint analysis and the statistically most efficient method depends on the unknown disease model. The proposed method assumes that multiple genes have a causal effect on multiple phenotypes, and the genotype-phenotype models are multidimensional, multivariate analyses. In such a scenario, our method is expected to be an efficient strategy. The proposed method is implemented with C++ and the computationally efficient at the genome-wide scale. We feel the current methods open new ways to identify the disease susceptibility loci.