Genomic selection has been successfully implemented in plant and animal breeding programs to shorten generation intervals and accelerate genetic progress per unit of time. In practice, genomic selection can be used to improve several correlated traits simultaneously via multiple-trait prediction, which exploits correlations between traits. However, few studies have explored multiple-trait genomic selection. Our aim was to infer genetic correlations between three traits measured in broiler chickens by exploring kinship matrices based on a linear combination of measures of pedigree and marker-based relatedness. A predictive assessment was used to gauge genetic correlations.K) was constructed as K = λG + (1 − λ)A, where A is the numerator relationship matrix, measuring pedigree-based relatedness, and G is a genomic relationship matrix. The weight (λ) assigned to each source of information varied over the grid λ = . Maximum likelihood estimates of heritability and genetic correlations were obtained at each λ, and the “optimum” λ was determined using cross-validation.A multivariate genomic best linear unbiased prediction model was designed to combine information from pedigree and genome-wide markers in order to assess genetic correlations between three complex traits in chickens, i.e. body weight at 35 days of age (BW), ultrasound area of breast meat (BM) and hen-house egg production (HHP). A dataset with 1351 birds that were genotyped with the 600 K Affymetrix platform was used. A kinship kernel  to 1 (only genomic information used). As λ increased, predictive correlations  increased and mean-squared predictive error decreased. However, the improvement in predictive ability was not monotonic, with an optimum found at some 0 < λ < 1, i.e., when both sources of information were used together.Estimates of genetic correlations were affected by the weight placed on the source of information used to build Our findings indicate that multiple-trait prediction may benefit from combining pedigree and marker information. Also, it appeared that expected correlated responses to selection computed from standard theory may differ from realized responses. The predictive assessment provided a metric for performance evaluation as well as a means for expressing uncertainty of outcomes of multiple-trait selection. The increasing availability of genome-wide dense molecular markers  has opened new avenues for obtaining additional genetic gain in breeding of elite animals and plants by exploiting “genomic selection” methods. These techniques have become important tools in modern breeding programs , 2. ManyMost prediction studies have been based on single-trait (uni-variate) statistical models. However, in practice, animals and plants often must be evaluated for several economically important traits. Multiple-trait model predictions have been typically regarded as better than uni-variate predictions . For exaMultiple-trait genomic selection models (MT-GS) have been explored and tested in research only to a limited extent . A genomThe objective of this study was to infer genetic and genomic correlations between three traits measured in broilers by exploring linear combinations of pedigree-based  and marker-based relationship matrices. As advocated by , a prediThe data consisted of records on 1351 birds from a commercial broiler chicken line that had undergone several generations of selection using the traditional multiple-trait genetic evaluations at the Aviagen Ltd Company . The traits considered were body weight at 35 days of age (BW), ultrasound area of breast meat (BM), and hen-house production . Some features of the dataset and pedigree information are in Table Prior to implementing the genome-enabled trivariate prediction model, we pre-corrected phenotypes to eliminate all known nuisance non-genetic sources of variation. This correction was based on uni-variate mixed effects models; BW and BM were corrected for a combined effect of sex, hatch week, contemporary group of parents, and pen in the growing farm. HHP was corrected for random hatch effects, with a general mean as the sole fixed effect. Figure The 1351 birds were genotyped using an 600 K Affymetrix SNP chip. SNPs with a minor allelic frequency (MAF) lower than 1% and a call frequency lower than 0.95 were filtered out. Missing genotypes were imputed locus by locus using the Beagle software version 3.3.2 . After qyt is a vector of m × 1 pre-corrected phenotypes for trait t (m = 1351); μt is a general constant and 1 is a vector of ones; Z is an incidence matrix  that allocates records to breeding values; gt is a vector of additive genetic effects or of direct genomic breeding values, and t. It was assumed that t, and K (m × m) reflects a covariance structure that results from the combined use of pedigree and marker information, as described later. Random residuals were assumed to follow a normal distribution It is an m × m identity matrix and t; this term represents variation of pre-corrected phenotypes that is not explained by additive genomic effects. The vectors gt and yt, μt, Zt, gt and K is a kinship or kernel matrix (described later) and Q is the (3 × 3) matrix of pedigree- or marker-based covariances among traits. The multivariate residual distribution was assumed to be R is the (3 × 3) residual covariance matrix among traits. The Kronecker product (⊗) notation applies to the residual covariance since all traits were measured on all birds.Tri-variate linear models were used for estimating (co)variance components and for predicting genomic breeding values. Such models were an extension of a typical single-trait model with random pedigree or genome-based effects, which can be represented as:G) computed from marker data replaces the pedigree-based matrix (A) of standard BLUP applications. The genomic relationship matrix intends to measure the realized fraction of alleles shared, rather than the expected fraction, as is the case for A [m × m matrix G analogous to the numerator relationship matrix A due to the denominator, 2Σpiqi. Here, W is a m × p centered matrix of SNP genotype codes 0, 1 and 2  and pi is the MAF at locus i. Second, Forni et al. [A when either the average level inbreeding is low or when the number of generations back to the base population is small.In a genomic best linear unbiased prediction model (GBLUP), a genomic relationship matrix  but heri et al.  suggesteG is to combine genomic and pedigree information into a single kinship “kernel” matrix A, where λ is a parameter (weight) bounded between 0 and 1, and G = GV or GF. For example, if λ = 0, pedigree information “dominates” in the model, which retrieves a traditional pedigree-based BLUP. Our expectation was that a specific combination of A and G matrices would provide the “best” estimates of parameters, as gauged by prediction of outcomes, as opposed to using either A or G alone or both, with (co)variance components estimated in training samples. To assess the best value of λ, we applied the grid λ =  and evaluated the ensuing predictive abilities over such a grid.An alternative to using any given sense of ). A “kerel ideas  and usedA, respectively. To render G on the same scale as A, we used the map minmax-function that is widely used in machine learning, e.g. [Gsij is a scaled element of the GV or GF matrix and Gij is typical element of GV or GF; Gsmax = 2 and Gsmin = 0 are the minimum and maximum values elements that the scaled matrix is allowed to take, respectively, and Gmin and Gmax are the maximum and minimum entries of the GV or GF matrix, respectively. While GV and GF may contain negative off-diagonals, this is not the case for the scaled matrices used here.When using marker- and pedigree-based relationship matrices together, scaling of genomic relationship matrices is needed for interpretation of parameters in the context of theory, e.g., in relation to a base population . Estimatng, e.g. , as follK = λG + (1 − λ)A was used as kinship matrix, where G was either the unscaled or scaled versions GV or GF.Variance and covariance components were estimated with multiple-trait restricted maximum likelihood (REML) via an average information algorithm (AI) implemented in the WOMBAT program . The sofλ values. We randomly partitioned the whole data into training (60%) and testing (40%) sets in each of the 20 repetitions. After a model was fitted to the training set data, we compared its predictions against realized values in the test set. Predictive ability was measured by mean squared error (MSE) and by the correlation between predicted and observed phenotypes in the testing set.We used a cross-validation scheme with 20 randomly constructed training and testing sets to assess predictive ability over the grid of λ = , we computed least-squares estimates of the regression of the phenotype for trait x on DGV for trait y, and vice versa, for each pair of traits for each of the 20 validation sets. These realized regressions were compared to expected genetic regressions deduced from REML (co)variance component estimates as:x and y, and λ.We also evaluated predictive relationships between pairs of traits, i.e., BW-BM, BW-HHP and BM-HHP, according to the cross-validation scheme described earlier. Over the predefined grid λ value, both for unscaled and scaled genomic relationship matrices. A low to moderate heritability was found for BW, BM and HHP. When using pedigree-based information only, heritability estimates (standard errors in parenthesis) were 0.187 (0.049), 0.244 (0.052) and 0.315 (0.074), respectively , 0.243 (0.04) and 0.174 (0.04) with an unscaled GV. Scaling the genomic relationship matrices increased heritability estimates relative to those obtained from unscaled matrices. Estimated heritabilities in the present study were lower than in [h2 would differ from those obtained using all available data, which would account for past selection.Table  than in , 30 usin than in , 30 estiG is A, then; E(K) = E(λG + (1 − λ)A) = A. However, if one uses a scaled GV, it follows from the scaling formula that E(Gsij) = 2E(Gij × Gmin/(Gmax − Gmin)). The latter expectation cannot be written in a closed form, because this requires knowledge of the distributions of Gmin and Gmax.Here, we used scaled kinship matrices to obtain “genetic parameters” which do not necessarily correspond to only those from standard pedigree-based additive genetic relationships or realized genomic pairwise similarities. Following VanRaden , if the λ grid. For example, the highest genomic heritability for BW was obtained at λ = 0.4(0.8), for unscaled  GF, and at λ = 0.4 for the two versions of GV. Scaling GF and GV always increased heritability estimates. For BM, higher heritabilities were obtained when scaling was applied. More specifically, the highest estimates were obtained at λ = 1 (GF) and λ = 0.6 (GV). With unscaled matrices, the highest heritabilities were obtained at λ = 0.4 and λ = 0.2. For HHP, the highest heritabilities were found at the extreme values of λ: λ = 0 for unscaled GF and GV  and λ = 1 for scaled GF. Adding genomic information had little impact on heritability estimates of HHP, except with scaled GF.Our multiple-trait GBLUP analysis indicated that the highest heritability estimates were not obtained at the extremes (0 or 1) of the G is constructed. Hence, inferences and comparisons between results from different studies must be done with care. In short, our results with a multiple-trait model indicated that a pedigree-marker based kernel (K) had an impact on heritability estimates and that scaling of the genomic relationship matrix led to higher “heritability” estimates, especially for GF.Our findings illustrate a fairly obvious point made by Legarra et al. : genomicλ than genetic correlations, so our discussion concentrates on the latter. All parameters were estimated for each λ and for each of the two genomic relationship matrices. When using a pedigree-marker based kinship matrix (K), estimates of genetic correlations for BW-HHP and BM-HHP changed gradually when λ increased from 0 to 1. Results are shown graphically in Figs. GF and GV, respectively. Changes were more pronounced for the genetic correlation between BW and HHP, which decreased in absolute value from −0.192 (λ = 0) to −0.02 , −0.019 , and 0.033  with λ = 1. Estimates of the genetic correlation between BM and HHP were always negative and tended to decrease in absolute value as λ increased. They decreased from about −0.206 when only pedigree-based information (λ = 0) was used to −0.154 when only genomic information (λ = 1) was used to construct K from scaled or unscaled versions of GF. BW and BM presented large positive genetic correlation estimates that ranged from 0.484 with the pedigree-based model to 0.497 (0.525) when only GF (GV) was used. It was insensitive to scaling of the G matrix. Standard errors of estimates for BM-BW (results not shown) tended to decrease when λ increased. There were no clear tendencies for the standard errors of estimates of the genetic correlation of BW with HHP and BM with HHP. In short, classical genetic correlations (based on A) and genomic correlations (based on G) were distinct, depending on the pairs of traits considered. However, varying λ from 0 to 1 produced very minor changes in estimates of the genetic correlation between BM and HHP, but large changes in estimates of the genetic correlation between BW and HHP. Estimates of the genetic correlations between BW and BM were insensitive to λ.Estimates of correlations are in Table The differences that were observed in estimates of genetic correlations depended on the type of information used. From theory, standard pedigree-based linear models capture expected genetic covariation, whereas marker-based models capture genetic covariation that is marked by SNPs. Our results are important from the perspective of multiple-trait genomic analysis because they indicate that estimates of genetic correlations between some traits may depend on the type of information used. This was clearly the case for the genetic correlation between BW and HHP.λ values, i.e., estimates of the genomic correlation and of the genetic correlation derived from the infinitesimal model were the same. On the other hand, when considering BW and HHP, the estimate of the pedigree-based genetic correlation was equal to 0.2, whereas the estimate of the genomic correlation was close to 0. This illustrates a situation where part of the covariance between a pair of traits was not detected by SNPs (“missing correlation”). Sources of genetic correlation may be lost in a multiple-trait marker-based analysis. In the case of BM and HHP, the classical genetic correlation was estimated at −0.20 and the genomic correlation at −0.15. The pedigree-based analysis suggested a stronger genetic correlation.Multiple-trait pedigree or marker-based prediction was designed to exploit genetic correlations between target characters and indicator traits , especiaCare should be exercised when interpreting and using genetic parameters that are assessed via molecular markers, as predictions for complex traits based on pedigree data may differ significantly from those based on SNP data. For this reason, we explored whether the two sources of information could be combined in some “optimal” manner.G and A as kinship kernel. For BW, the largest correlation and lowest MSE were obtained with unscaled GF and GV. In terms of the predictive correlation for BW, the largest values were obtained with scaled GV and unscaled GF, both at λ = 0.8. For BM, the largest predictive correlation was achieved with unscaled GV and scaled GF, at λ = 0.4 and 0.8, respectively. For HHP, both scaled GV and GF resulted in better performance, and the largest predictive correlations were obtained at λ = 0.2.The question of how to arrive at a “best” estimate of a genetic correlation  was examined and, to accomplish this objective, we used the predictive approach advocated by Lo et al. . Figure GF and scaled GV at λ = 0.6. For BM, the lowest MSE was obtained with λ close to 1 using scaled GV and GF. In addition, the scaled GV and GF produced the lowest MSE for HHP, with a slight superiority for values of λ close to 1. In terms of MSE, except for BW with GF, scaling of genomic relationship matrices yielded better results. Our findings are in agreement with Rodríguez-Ramilo et al. [A), the predictive correlation was lower than when assigning more weight to the genomic relationship matrix (G); a similar behavior was found for MSE. Rodríguez-Ramilo et al. [λ by using Bayesian methods and reported that the posterior mean of λ depended on training sample size and the trait.The lowest MSE for BW was achieved for unscaled o et al. , who repo et al.  estimateA and G to quantify kinship. This result may also hold when prediction involves multiple selection lines or crossbred animals. Combining kernels can be viewed as a form of model averaging [A informing about similarity by descent.Our results indicate that multiple-trait genome-enabled predictions may be improved in some cases by combining veraging , with maA and G.Our results using dense SNPs (600 K Affymetrix platform) indicate that GBLUP with scaled or unscaled relationship matrices typically performed better than pedigree-based BLUP. However, in most cases, the largest correlation and lowest MSE were achieved using a linear combination of λ value for the 20 cross-validation random samples and their medians are depicted as dark blue dotted lines on each plot. The REML regressions express the expected change in genetic value of trait i if the direct genomic value for trait j changes by one unit.Figures λ. In general, there was reasonable agreement between expected and realized regressions. However, for BW and HHP  varied around 0 for all λ values. There was some apparent inconsistency between the expectations based on REML estimates and the cross-validation regression.For BW and BM Fig. , the expHHP Fig. , the expλ was close to 0. The expected regressions based on pedigree information were negative, while the cross-validation regressions were positive. The expected regressions of HHP phenotypes on DGV of BM and variances tended towards 0 as λ tended to 1, i.e., when more weight was placed on SNPs. The cross-validation regressions were much more affected by the value of λ than the expected regressions based on REML estimates.Figure In genome-enabled prediction, there are different ways of incorporating molecular marker information into parametric and non-parametric models , 32. ResK) as a linear combination of pedigree and marker-based relationships between animals, defined as K = λG + (1 − λ)A. Predictive ability of the model and parameter estimates were obtained over a grid of values of λ that varied between 0 and 1, e.g., λ = 0 implied that all weight was assigned to pedigree, and none to SNPs.In order to explore a multiple-trait GBLUP model that also makes use of pedigree information, we constructed a pedigree-marker based kinship matrix . It remains to be seen whether genomic relationship measures can detect true ‘negative genomic correlations’ (if such correlations exist), which may be detectable using deep pedigree information and a definition of a base population. The genomic relationship matrices in our analyses were based on  population, as discussed in , 37, theOur results suggest that multiple-trait genetic predictions depended on the weight assigned to genomic data. Better predictions were often obtained when pedigree and SNP information were used simultaneously. Earlier studies using simulated or real data have explored the potential superiority of multiple-trait over single-trait genomic prediction with a focus on the relationship between traits in terms of differences in heritability, genetic correlations and number of indicator traits e.g., , 38, 39), 3938, 3A and G on estimates of the genomic correlation between three chicken traits and evaluated outcomes using a predictive framework. Some studies [A and G alone [Here, we examined the impact of combining  studies , 41 have G alone .λ. For example, on the one hand for BW and HHP, when using pedigree as the only measure of similarity (λ = 0), the genetic correlation was −0.20, but it shifted to near 0 or was even positive (GV) when only marker information was used. On the other hand, the estimate of the genetic correlation between BW and BM was stable with respect to λ, while the estimate of the genetic correlation between BM and HHP was only slightly affected, i.e. changing from −0.21 to −0.15 for GF, and from −0.22 to −0.20 for GV for λ = 0 and λ = 1, respectively. Clearly, genomic data provide a distinct measure of similarity between individuals, and this translates into differential capturing of genetic signals. For instance, most off-diagonal entries of A were zero but all entries of G were non-null.Our estimates of genetic correlations depended on the choice of K, with an impact on accuracy of prediction.In order to increase the accuracy of predictions by using pedigree and genomic information jointly, Legarra et al.  proposedA and G (with a specific weight on each one) that delivered the best predictive ability, which was found by searching the weight (λ) placed on genomic versus pedigree relationships. This type of predictive approach has been advocated in the statistical literature [In our study, predictive ability was measured using the correlation between predicted genetic values and observed phenotypic values, and mean squared error of these predictions. As shown in Fig. terature , 46, 47.A and G kernels yielded better predictions than when only G was used. In a GBLUP model, the entries of G reflect the actual extent of IBS relationships between individuals, but without making a clear reference to a base population [In general, combinations of pulation . This impulation , pedigreIn classical quantitative genetics, a genetic correlation between traits arises due to either genes that have an effect on both traits (pleiotropy), or due to LD between genes that affect different traits . When inEstimates of genetic correlations obtained from pedigree or from markers may differ either due to chance or other reasons, such as extent of LD between markers and the unknown QTL. One possible way of testing if such differences are systematic, is to examine pairs of estimates of pedigree- and marker-based correlations in re-samples from the dataset and constructing a paired comparison, by using either a parametric or a non-parametric approach. For example, the estimates of correlations could be z-transformed and a paired t test conducted.A and G matrices were different, but depended on the trait. This indicates that multiple-trait marker-based prediction may be enhanced by the combined use of genealogy and marker information in the models.In summary, combining pedigree- and marker-based information had an impact on predictive performance of multiple-trait models. Discerning the optimum weight placed on genomic and genealogical information is an important issue, and a grid-search scheme was used for that purpose. We found that estimates of genetic correlation obtained with To our knowledge, this is the first study with animal breeding data that explores how the weight placed on pedigree and marker information affects multiple-trait predictions. We designed a tri-variate genomic prediction model that exploited pedigree and marker information simultaneously. Use of a kinship matrix that is formed as a linear combination of pedigree- and marker-based relationships may enhance genome-enabled prediction, but the optimal weight placed on the two sources of information will differ between traits. Genetic correlation estimates from pedigree-based models may differ from those obtained from marker-based models, at least in some cases. Cross-validation was useful for gauging the genetic correlation in multiple-trait models.


By combining individual-level whole genome sequenced data from the UK10K study, and imputed genome-wide genetic data on individuals from the Study of Osteoporotic Fractures (SOF) and the Osteoporotic Fractures in Men Study (MrOS), a data set of 8810 individuals was assembled; tests of association were performed between autosomal gene-sets of genetic variants and BMD measured at lumbar spine and femoral neck. Distributions of p-values obtained from analyses of a single BMD phenotype are compared to those from the multivariate tests, across several region definitions and variant weightings. There is evidence of increased power with the multivariate test, although no new loci for BMD were identified. Among 17 genes highlighted either because there were significant  Many different set-based methods have been proposed, such as burden tests3, variance component score test4, the combination of these two types of tests6, and many others7.The massive advances and cost decreases in sequencing technologies have led to identification of millions of rare minor alleles  less than 0.05). However, power to detect associations between complex traits and such genetic variants is low, due to the small number of individuals who carry such variants. Set-based tests have been proposed to try and improve power by jointly testing association with multiple rare variants in a pre-defined set. In set-based analyses, SNPs are assigned to SNP sets by forming linkage disequilibrium (LD) blocks, using sliding windows or on the basis of some meaningful biological criteria (genomic features); e.g., genes or pathways9, and also because picking the genomic set for the test is quite challenging since it is usually unclear which variants should be included. The best way to improve power is, of course, to enlarge sample sizes, and for feasibility reasons, this is often achieved by combining participants from different studies together, either directly or through the use of meta-analysis10. Improvements in power can also be achieved through using imputation: ungenotyped variants can often be accurately estimated when the genotyped variants are used as a skeleton framework for imputation against a large panel of individuals who have been sequenced11.Despite the potential for improved power of set-based methods, statistical power is often limited due to the complex way that genotypes map to the phenotypes, to the complex networking among factors that influence the etiology of diseases14, and these authors have shown that multivariate tests are generally more powerful than the univariate ones by accounting for existing pleiotropic effects15 as well as the correlations among multiple phenotypes.Most currently used rare-variant tests analyze one phenotype—that is, they focus on the association between a set of rare variants and a single phenotype. However, multiple correlated phenotypes are often collected. Therefore, there is also potential for increasing power by capturing phenotypic correlations and their relationships to associated genetic variants. Recently, several multivariate rare-variant association tests have been developed17, to investigate the potential benefits associated with a multivariate-phenotype analysis of correlated BMD phenotypes and associations with genetic variation using set-based methods. To create a data set with reasonable power for rare-variant analyses, a single data set was created by combining individual-level data from three large cohorts: whole-genome sequencing data from a subset of the UK10K project18 (http://www.uk10k.org/ and www.gefos.org), and genome-wide genotyping data that had undergone imputation from the Study of Osteoporotic Fractures (SOF)19 (http://sof.ucsf.edu/interface/) and Osteoporotic Fractures in Men (MrOS) Study21. Tests of association between genetic variation in the genetic regions and BMD are performed with a recently developed multivariate rare-variant set-based association test (MURAT)12 that is built on a mixed effect model, and the well-known single phenotype Sequence Kernel Association Test (SKAT) test4, which is derived similarly from a mixed effect model. We first perform an exome-wide gene-based analysis, and then study more intensively some selected candidate genes.In this paper, we use a well-studied phenotype, bone mineral density (BMD)To assess the impact on power in a genome-wide analysis, we applied region-based tests of association for all genes using SKAT, for the BMD phenotypes at two positions: lumbar spine (LS) and femoral neck (FN), separately, as well as using MURAT for a joint analysis of both phenotypes. Analysis was performed on 19,052 genes, but since some genes were extremely large (greater than 150 kb), we divided the large genes into smaller pieces , leading to a total of 24,333 regions for analysis ), where MAFj is the MAF for the jth variant, and beta is the probability density function for a random variable, x, coming from beta distribution with parameters α and β. Then a third weight was defined by assuming the MAF follows a Beta  distribution  distribution of the MAF Fig. , i.e. thion Fig. , where BNear the top of Fig. p-values from SKAT need to be adjusted for the fact that two phenotypes were analyzed separately. However, the two single-phenotype test results can be expected to be correlated since the two phenotypes in the combined data set are quite correlated (r = 0.64). We performed permutation analysis of the phenotypes versus the genotypes and repeated the region-based analyses on chromosome 9 with different weightings. Using the extrapolation method in Xu et al.25, we estimated the genome-wide significance threshold at 7.51 × 10−7 for MURAT and 1.12 × 10−7 for the minimum of the two SKAT tests across all three weights  are seen at RUNX2, ESR1, WNT16, DKK1, SOX6, LRP5, SP7, TNFSF11 and SOST for at least one gene piece and weighting scheme. Certainly, however, their p-values would not stand out in a genome-wide analysis.This region-based analysis of gene pieces did not identify many of the genes well-known to contain variants influencing bone mineral densityNevertheless, our gene pieces contain as many as 2800 variants, and the effects of a small number of causal variants could be overwhelmed in such regions. Therefore, we undertook a second set of analyses of candidate genes using smaller windows containing a maximum of 30 variants, to further compare multivariate and univariate region-based test performance.To investigate MURAT’s performance in more depth at known BMD genes, we selected 17 genes for analysis with smaller non-overlapping windows containing no more than 30 variants. This list contains the 3 genes in Table −7 and 7.51 × 10−7 as the SKAT and MURAT thresholds for statistical significance  weight, some of the small segments in its gene did show significance with this weight. Finally, we note that for most of the significant segments, the MURAT p-values are smaller than the minimum of two SKAT p-values obtained by testing LS and FN separately, no matter which weights are chosen.If we retain 3.42 × 10We also ran a series of single variant analyses for these 17 selected genes . In total, 19,325 SNPs are contained in these 17 genes, but at some SNPs, only a few individuals carry the minor allele among the 8810 subjects. Considering the robustness of single variant analysis, we removed SNPs where the minor allele was carried by less than 4 individuals, leaving 19,071 variants for analysis , Osteoporotic Fractures in Men (MrOS) Study, and the UK10K project, we investigated the performance of a newly proposed multivariate rare-variant association test (MURAT) through analyses of bone mineral density (BMD). In our investigations, we compared the multivariate test, MURAT, with single-phenotype test, SKAT, by testing BMD at femoral neck (FN) and lumbar spine (LS) jointly and separately for each gene-based variant set. In addition, genes identified via our gene-based analysis and reported from previous literature were further examined by small window and single variant analyses. We also compared performance of three different MAF-based weighting schemes in both MURAT and SKAT with sets of SNPs. Although there is an increasingly large literature on how to best prioritize genetic variants for analysis using external annotation information, particularly in the context of region based tests17. MURAT provides a modest increase in power which cannot compete with the power gain associated with an over 6-fold increase in sample size. To identify new genes where rare genetic variation is associated with BMD, including subjects with more extreme bone phenotypes could be useful. However, MURAT may be of assistance for increasing power for studies involving other phenotypes where it is more challenging to increase the sample size.Despite the potential for improved power associated with multivariate phenotype analysis, all of the genes that we identified as associated with BMD had been previously reported. Indeed, the recent meta-analyses including over 50,000 individuals has identified genetic variants in more than 20 genes as associated with BMD27. However, not all analyses can be achieved by sharing only summary statistics; in this collaboration, we were able to create a data set containing individual phenotypes and genotypes for 8810 people, thereby increasing our power as much as is often reasonably possible simply through increased sample sizes for individual-level data. However, since the genetic signals can be very subtle, potential additional power improvements through multivariate analysis are of great interest.Currently, individual level data are required for the calculations in MURAT. Assembling extremely large sample sizes for single variant analysis is sometimes feasible through meta-analysis, where only summary level statistics need to be shared; an extension of SKAT has also been developed that requires only sharing of a set of summary statisticsHowever, it must be acknowledged that a single analysis of all the individual-level data from three studies may be susceptible to bias from confounding arising from different BMD distributions across the cohorts, in conjunction with subtle genetic variation. For example, Table p-values obtained via MURAT are generally smaller than the ones calculated from adjusted SKAT . Tukey’s test for multiple comparisons showed that groups having more variants generally had larger p-values. The box plots for p-values within each group, and plots of 95% family-wise confidence levels for Tukey’s multiple comparison procedure are shown in Supplemental Figures To further investigate the relationship between p-values obtained via two models, with or without study covariates, are almost the same .34, there is no strong consensus on ideal weight choice, and of course it will depend on the true genetic architecture at the locus. It may be worth additional investigation to understand which weights retain the most power even when the true genetic model is incorrectly modelled. In addition, similar to other set-based association studies, here we have only provided an overall p-value for the association between a group of variants and the phenotypes. We note also that a nonparametric multiple-trait set-based test has recently been developed based on generalized similarity U-statistics35, and it would be worth comparing its performance with MURAT.In our analyses, we used three different weights, and the identical weight showed better results. The choice of weighting scheme is critical to improve test power. Although there are a few publications that have evaluated multiple weights in different study designs through simulation36 and follow-up replication studies8 are usually needed to achieve these goals. Nevertheless, a few methods for variable selection or adaptive combinations of p-values have been proposed to fill the gap between SNP set analysis and fine mapping of individual variants39. Investigations of how such techniques perform for a multivariate test such as MURAT would be worthwhile.Once a new association is found, it becomes interesting to ask which individual variants drive the association and to estimate corresponding genetic parameters. Careful fine-mappingIn the analyses, we combined individual level autosomal data from three studies.19 (http://sof.ucsf.edu/interface/) is a prospective multicentre study that enrolled 9704 women over age 6542, and the Osteoporotic Fractures in Men study (MrOS) is a multicentre study of musculoskeletal health in men 65 and older21 that enrolled 5,994 participants. In both studies, participants were required to be able to walk without assistance at study entry. Written informed consents were obtained for both studies, and Institutional Review Boards at each enrollment site approved these studies. Genotyping for both SOF and MrOS samples was performed with the Illumina HumanOmni1_Quad_v1-0 H array. Samples with call rate under 97% were excluded, as were samples with evidence for non-European global ancestry or showing unusual heterozygosity or relatedness16. Genotypes with MAF < 0.01 or Hardy-Weinberg disequilibrium (at p < 1e-4) were excluded, and the remaining genotypes were subsequently imputed against the combined UK10K/1000Genomes reference panel. Singletons were excluded from the reference panels prior to merging, and variants missing from one reference were imputed into the other before creating the combined reference. Genotypes were pre-phased without using the reference panel, and then variants from the reference were imputed into the best-guess haplotypes. Variants with INFO score less than 0.4 were excluded. Full details of the imputation pipeline can be found in16.The Study of Osteoporotic Fractures (SOF)18 (http://www.uk10k.org/ and www.gefos.org). These individuals were selected from participants in the TwinsUK study (http://www.twinsuk.ac.uk/) or the ALSPAC study  and had previously been assessed for BMD45. Whole genome sequencing was performed with the Illumina HiSeq platform with an average read depth of 6.7. Identified variants were quality filtered with a VQSLOD score of −0.6804, Hardy-Weinberg equilibrium p-value < 1e-6, or evidence of batch effects16. Imputation was performed against a combined reference panel formed by merging the 1000 Genome haplotypes with UK10K haplotypes, removing singletons, and imputing missing variants from each of the two studies into the other16. Data were pre-phased without a reference panel, and then imputed with IMPUTE2 using an info score of 0.4 to remove poorly imputed variants18.There were 3,781 individuals who underwent whole genome sequencing in the UK10K studyIn the MrOS study, BMD at the femoral neck and lumbar spine was measured using dual-energy X-ray absorptiometry (DXA) with Hologic QDR‐4500 W scanners  at the baseline clinic visit. A central quality‐control laboratory, certification of DXA technicians, and standardized procedures for scanning were implemented to ensure reproducibility of DXA measurements. At baseline, a hip phantom was circulated and scanned at the six clinical centers. Cross‐calibration studies indicated no linear differences across scanners, and the interscanner coefficient of variation (CV) was 0.9%. Height was measured using a Harpenden stadiometer, and weight was measured by a standard balance beam or an electric scale. Two consecutive height measurements were taken, and the average of these measurements was used in the analysis. If the two height measurements differed by >5 mm, a third measurement was performed, and the average of the two values with the smallest difference was used in the analysis.42. Briefly, paired initial and follow up hip scans were analyzed using the automated “compare” feature of the Hologic software. Quality control center technicians reviewed a random sample. In addition, all scans identified by the technicians for certain problems such as changes in positioning between the initial and follow up scans or difficulty defining bone edges were reviewed at the quality control center. An anthropometric spine phantom was scanned daily, and a hip phantom was scanned once per week at each clinic to assess longitudinal performance of the scanners. Weight was measured using a standard balance beam scale, and height was measured using a Harpenden stadiometer.In the SOF, BMD of the proximal femur and spine was measured using DXA  during a follow up visit between 1989 and 1990. Densitometry quality control methods have been previously publishedIn the UK10K study, lumbar spine and femoral neck BMD measurements were obtained from the available measurements taken in the ALSPAC and Twins UK studies. Specifically, BMD was measured using DXA with Hologic QDR 4500 W for TwinsUK participants, and in ALSPAC, TB-DXA scans were performed on all participants, using a Lunar Prodigy scanner  with paediatric scanning software . In ALSPAC, all DXA scans were subsequently reviewed by a trained researcher, and re-analysed as necessary, to ensure that borders between adjacent ROI’s were placed correctly by the automated software. Data were standardized within the two source studies prior to combining. Both TwinsUK and ALSPAC use Harpenden stadiometer to measure height.For 3256 women in SOF and 4550 men from MrOS with imputed genotype data, and 1004 sequenced women from the UK10K study, BMD measures were also available. With these 3 cohorts together, there are 8810 subjects included in our analyses.2, gender, and weight were used as covariates. In addition, the first five principal components (PCs), obtained using a subset of genotype data that were randomly selected from our analyzed variants with large MAF (>0.48) and low LD (r2 < 0.1) based on all 8810 subjects, were also included as covariates to adjust for population structure.We considered two correlated bone density phenotypes, BMD at femoral neck (FN) and lumbar spine (LS). A log transformation was applied to these two phenotypes before the analyses so that they have bell-shaped distributions, and after the log transformation the correlation between the phenotypes in combined data set is 0.6775. In all analyses, variables age, ageDescriptive statistics for BMD and covariate measurements are listed in Table et al.16). Hence, we used only the rare variants in or near genes on the autosomes (excluding chromosomes X and Y) analyzed in Zheng et al.16, where rare variants were defined as SNPs with MAF <0.05, and the MAFs were estimated based on the 21 cohorts used in their paper. However, since only three out of the 21 cohorts are being analyzed here, some of the variants we used may have larger MAF than 0.05. The majority of analyzed variants are still rare: 76.67% have MAF <0.05 and 81.58% have estimated MAF <0.10.Many previous studies related with BMD association have focused on common variants (MAF >0.05), and have insufficiently assessed the role of low frequency (MAF 0.01–0.05) and rare (MAF <0.01) genetic variation  a1 = 1 and a2 = 25, (the parameters suggested by SKAT4). These choices allow higher weights for the rare variants (with MAF <1%) and give modest weights for low frequency variants with MAF 1–5%. (ii) a1 = a2 = 0.5, which is equivalent to jth variant. This choice puts more weight onto the very rare variants and almost zero weights to variants with MAF >1%46.For a univariate method that tests the two BMD phenotypes separately, we used SKAT to identify association. For a joint multivariate analysis of the two BMD phenotypes simultaneously, we used MURATet al.12. The method performs a joint analysis of more than one phenotype, and tests for association simultaneously for all phenotypes and all variants in a region.A description of this method is found in more detail in Sun i th subject, i = 1, …, N, we observe K correlated continuous phenotypes, Yi = T; m covariates, Xi = T; and genotype values for a group of v variants, Gi = T, where gij for j = 1, …, v are coded as 0, 1, or 2, representing the number of minor alleles that individual i carries for the j th variant. Similar to SKAT4, a single phenotype, Yik, is linked with Gi and Xi via a linear mixed modelαk0 is a scalar for intercept; αk and βk are corresponding coefficient vectors, and βk ~ N is a vector of random effects, such that τ2 is an unknown variance component, W = diag{w1, …, wv} is a weight matrix with wj representing the weight for the j th variant; and εik is random error following a standard normal distribution.Suppose for the K phenotypes are correlated, in MURAT, a multivariate linear mixed model is used to jointly model these phenotypes,α0 = T, εi = T, 1K is a K-dimensional vector of ones, and ⊗ represents Kronecker product. In this multivariate model, the variant effect, β, is assumed to follow a multivariate normal distribution, N. In addition, to account for trait pleiotropy effects, βk and k ≠ k′, are assumed to be correlated, such that ρ unknown, and Σβ = τ2R⊗W, where εI is assumed to independently follow a multivariate normal distribution N, where Σ is an arbitrary symmetric and positive definite matrix.However, since β equals zero in MURAT. By using a data-adaptive procedure to manage unknown correlation, ρ, among variant effects, βk’s, MURAT can obtain p-values analytically via a one dimensional numerical integration. It has been shown12 that by incorporating arbitrary correlations among multiple phenotypes and considering the existence of trait pleiotropy effects, the proposed MURAT has the potential to increase test power compared with other univariate tests. In addition, since MURAT calculated p-values analytically without permutation or resampling, MURAT can be used for a genome-wide analysis.In order to test the association between genotype and multiple phenotypes, a score type statistic was derived to test whether Supplemental Material


Emerging evidence suggests that the basis for variation in late-life mobility is attributable, in part, to genetic factors, which may become increasingly important with age. Our objective was to systematically assess the contribution of genetic variation to gait speed in older individuals. We conducted a meta-analysis of gait speed GWASs in 31,478 older adults from 17 cohorts of the CHARGE consortium, and validated our results in 2,588 older adults from 4 independent studies. We followed our initial discoveries with network and eQTL analysis of candidate signals in tissues. The meta-analysis resulted in a list of 536 suggestive genome wide significant SNPs in or near 69 genes. Further interrogation with Pathway Analysis placed gait speed as a polygenic complex trait in five major networks. Subsequent eQTL analysis revealed several SNPs significantly associated with the expression of PRSS16, WDSUB1 and PTPRT, which in addition to the meta-analysis and pathway suggested that genetic effects on gait speed may occur through synaptic function and neuronal development pathways. No genome-wide significant signals for gait speed were identified from this moderately large sample of older adults, suggesting that more refined physical function phenotypes will be needed to identify the genetic basis of gait speed in aging. Despite promising results from candidate gene studies, a systematic and comprehensive examination of genetic determinants of gait speed in a large sample of older adults has been lacking. Furthermore, previous study samples have been too small to detect the expected modest genetic effects especially in such complex and polygenic encoded traits. To address these limitations, we conducted a meta-analysis of GWAS of gait speed in 31,478 older adults and validate our candidate signal in a cohort of 2588 older adults. Close to 600 candidate genetic variants have been linked to gait speed. Such efforts have provided us with an increased knowledge of the biological systems which impact on gait speed; this may contribute to improved treatment strategies and drug development to promote aging with grace.Gait speed has been described as the “sixth vital sign” because it is a core indicator of health and function in aging and disease . DeclineMany genetic and non-genetic factors (environment and disease) are likely to affect quantitative complex traits such as gait speed. There are individual differences in rates of decline in physical function, and genetic epidemiological studies provide a method for decomposing that variance into genetic and environmental sources. Twin studies suggest that genetic factors account for 15-51% of the variance of gait speed in older adults , 12. Mor(ACE) gene have been linked to better mobility response to exercise. The R577X polymorphism in the alpha-actinin-3 encoding gene (ACTN3) was associated with elite athletic performance, and muscle strength and power in the general population, especially in women  and Gothenburg [MrOSGBG] studies Table . Togethe2>0.9) between the different methods of measuring gait speed [The different methods of assessing gait speed in individual cohorts are described in Table it speed , 67. The2 or oevar_imp < 0.3); and for the meta-analysis, SNPs with average MAF ≤ 0.01 and total N < 15,000.A structured, pre-specified analytical plan was applied to each of the 17 cohorts included in the screening sample. Genome-wide analysis of imputed genotypes, summarized in Multiple linear regression of imputed SNP dosages on gait speed was performed using an additive model, i.e. as a count of the number of variant alleles present (1 degree of freedom). Sex-combined analysis was performed. Adjustment for age (at time of exam), sex, study site (for cohorts with multiple sites), principal components to control for population stratification, height, and presence of osteoarthritis (yes/no) if available were included. For cohorts with osteoarthritis data available, the analysis was done excluding participants with osteoarthritis .−8 was used to indicate genome-wide statistical significance.Inverse variance weighted meta-analysis was performed on summary statistics of the cohort-level association analyses. Meta-analysis of gait speed ) was performed using METAL  with a f−4) with gait speed. This list resulted in 67 candidate genes  and SeattleSeqAnnotation) being identified which were used in the IPA analysis (www.ingenuity.com). The resulting classification of networks, pathways, biological processes and molecular functions are represented in tables and graphic format  that were highly suggestively associated  to further explore their biological and functional relevance to gait speed (We examined existing eQTL resources for the candidate suggestive list of 536 SNPs (p<10it speed . We querit speed  containiFurther we applied the HaploReg v4.1 annotation tool for TF analysis of 536 SNPs suggestively associated with gait speed.


Linear regression modeling was used to estimate the effect of gene-environment interactions on BMI for 131 lifestyle factors related to: dietary habits, smoking and alcohol consumption, physical activity, socioeconomic status, mental health, sleeping patterns, as well as female-specific factors such as menopause and childbirth. In total, 15 lifestyle factors were observed to interact with GSBMI, of which alcohol intake frequency, usual walking pace, and Townsend deprivation index, a measure of socioeconomic status, were all highly significant . Interestingly, the frequency of alcohol consumption, rather than the total weekly amount resulted in a significant interaction. The FTO locus was the strongest single locus interacting with any of the lifestyle factors. However, 13 significant interactions were also observed after omitting the FTO locus from the genetic score. Our analyses indicate that many lifestyle factors modify the genetic effects on BMI with some groups of individuals having more than double the effect of the genetic score. However, the underlying causal mechanisms of gene-environmental interactions are difficult to deduce from cross-sectional data alone and controlled experiments are required to fully characterise the causal factors.Previous genome-wide association studies (GWAS) have identified hundreds of genetic loci to be associated with body mass index (BMI) and risk of obesity. Genetic effects can differ between individuals depending on lifestyle or environmental factors due to gene-environment interactions. In this study, we examine gene-environment interactions in 362,496 unrelated participants with Caucasian ancestry from the UK Biobank resource. A total of 94 BMI-associated SNPs, selected from a previous GWAS on BMI, were used to construct weighted genetic scores for BMI  Genome-wide association studies (GWAS) have identified hundreds of genes as being associated with body mass index (BMI). How these genetic effects are modulated by lifestyle factors has not been extensively investigated previously. Here we utilise data from approximately 360,000 participants from the UK Biobank, aged 40–69 years old, to identify interactions between genetic and lifestyle factors in relation to BMI. We investigated 131 lifestyle factors, of which 15 influence the genetic effects on BMI. The most significant factors were those related to physical activity, alcohol consumption, and socioeconomic status. For example, the effect of a genetic score for BMI was almost twice as high in participants who reported never drinking alcohol compared to every-day drinkers. Similarly, the effect of the genetic score for BMI was 2.5 times higher in participants who reported having a slow walking pace compared to participants who reported having a brisk walking pace. Our results show that many lifestyle factors influence the genetic effects, which suggests that changing our lifestyle may be a way to influence our genetic risk for obesity and other common human disorders. Gene-environment interactions result from individuals responding differently to environmental stimuli depending on their genotype, or from genetic effects that vary between groups of individuals depending on their lifestyles. In humans, the most famous examples include skin color and risk of melanoma in response to ultra-violet rays, and phenylketonuria (PKU) in response to foods containing phenylalanine in individuals who carry mutations that lead to phenylalanine hydroxylase deficiency . Gene-enth century and up to the present day [FTO locus [Obesity and being overweight are serious public health issues due to their strong associations with diseases such as cardiovascular disease, type 2 diabetes and cancer. In addition, their global prevalence has increased dramatically over the latter part of the 20sent day –5. Recensent day . HoweverTO locus –9. IdentTO locus , and difFTO locus variant, rs1421085, interacts with several lifestyle risk factors such as alcohol consumption, sleep patterns, diet and physical activity [Initiatives such as the UK Biobank provide a unique opportunity to study interactions between genetic and lifestyle factors. Data collection in UK Biobank has been performed in a standardised manner and data include a large number of lifestyle and environmental factors collected from approximately half a million UK citizens, as well as comprehensive, genome-wide genotyping . Recent activity . Anotheractivity .GSBMI) which was composed of 94 single-nucleotide polymorphisms (SNPs) that have previously been associated with BMI in a GWAS [Here, we study the effects of gene-environment interactions on BMI, by analysing 131 lifestyle factors assessed by touchscreen questionnaires. These factors include diet, smoking, alcohol consumption habits, physical activity, socioeconomic status, mental health, sleep, general health as well as factors that are specific to females such as number of live births. For the purpose of our analyses, we constructed a genetic score for BMI (http://www.ukbiobank.ac.uk/about-biobank-uk/) [rd degree relatives = kinship coefficient > 0.044). In addition, only people who self-identified as white British (Data-Field 21000) and that were classified as Caucasians based on the genetic principal components (Data-Field 22006) were included. After filtering, 116,138 individuals remained for the analysis in the discovery cohort. The same filtering was applied to the replication cohort, leaving 246,358 participants for the replication.We utilised data from the UK Biobank Resource (ank-uk/)  for all ank-uk/)  using a ank-uk/)  haplotypank-uk/) . We utilhttp://www.hra.nhs.uk/), which lets applicants conduct research on UK Biobank data without obtaining separate ethical approvals. Access to UK Biobank genetic and phenotypic data was granted under application no. 15152: “Interaction between diet, food preference and lifestyle with genetic factors influencing body mass, body adiposity and obesity”. Written consent was obtained from all participants.All participants had provided signed consent to participate in UK Biobank . UK BiobParticipants’ weights were assessed by a variety of means during the initial UK Biobank assessment centre visit. For weight, we utilised data-field 21002, which is an amalgate of all weight values into a single item. Standing height was measured on a SECA 240 Height Measure. BMI was constructed from height and weight measurements during participants’ initial visit to assessment centers. For most analyses, BMI was transformed using rank-based inverse normal transformation.Lifestyle factors have primarily been collected via self-report touchscreen questionnaire. All lifestyle variables that had been assessed in more than 20,000 of the participants were included for analyses. This resulted in 131 quantitative, ordinal and categorical measurements of lifestyle factors representing dietary habits, general health, sleep, smoking and alcohol consumption, physical activity, mental health and socioeconomic status .th percentile of quantitative phenotypic variables, such as, for example: “Average weekly red wine intake” in number of glasses, and “Duration of moderate physical activity” in minutes, to reduce the effect of outliers. We analysed ordinal phenotypic data as quantitative variables. For example, data-field 1558—frequency of alcohol intake: which is coded as: 1 = “Daily or almost daily”, 2 = “Three or four times a week”, 3 = “Once or twice a week”, 4 = “One to three times a month”, 5 = “special occasions only”, 6 = “Never”.We aimed to use linear regression models to test for interaction between lifestyle factors and genetic factors on BMI. To this end, “Prefer not to answer” and “I don’t know” were set to “missing” in our analyses. We removed the 99Data field 20126 represents bipolar and major depression status among participants. This variable was derived from self-report questionnaire data . Very fe2 = 0.99, D’ = 1). Three SNPs were removed due to deviation form Hardy Weinberg equilibrium, which left 94 SNPs for the analyses. Since many of these variants have not been replicated in an independent cohort, we first tested for association in the initial release of genotype data from the UK Biobank cohort. This was done using linear regression models with BMI as a response variable. BMI was first transformed using a rank-based inverse normal transformation similar to the discovery study [2 and the first 15 genetic principal components (PCs). Some of the SNPs were identified as being associated with BMI in females or males separately in the previous study [Genotype data for 97 SNPs that have previously been identified to be associated with BMI  were conGSBMI, regression coefficients (β-estimates) were retrieved from the GIANT consortium meta-analysis for BMI for the European populations with males and females combined [GSBMI were then calculated for each individual by multiplying the number of effective alleles for each of the 94 SNPs  with the respective β-estimates  on BMI, for 131 lifestyle factors (E) separately. In addition to the GSBMI× E interaction term, each of the 131 models was adjusted for covariates: age, age2, sex, PCs, and genotyping array (batch). Interaction terms for GSBMI with age, age2, and sex as well as interaction terms for the lifestyle factor with age, age2, and sex were also included in order to properly control for possible confounding effects of these interactions, in accordance with previously published recommendations [Linear regression modeling was used to estimate the effect of gene-environment interaction . The models also included 15 principal components (PCs) to account for effects of population stratification in UK Biobank. In the primary analyses, models for each of the 131 lifestyle factors were analysed separately. The aim of this study was to investigate the effect of the interaction term GSBMI×E on BMI. For this purpose, we focused our attention on the estimate of the coefficient β3 in (2), and more specifically whether this estimate significantly deviated from zero. The null hypothesis H0: β3= 0 was either accepted or rejected, depending on the outcome of a two-sided marginal student’s t-test, which in this case  is equivalent to a likelihood-ratio test of the hypothesis H0: β3= 0. P-values lower than the significance level α = 0.05/131 ≈ 3.82*10−4 were considered significant to account for the family-wise error rate using the Bonferroni method. Interaction effects that were considered significant in the discovery cohort were then tested in the replication cohort using the same covariates as well as 15 PCs. Calculations were performed in R version 3.3.0 [We assume that the error term on 3.3.0  using thGSBMI and of individual SNPs on BMI in different subgroups with regards to lifestyles, e.g., the genetic effect in participants with different frequencies of alcohol consumption. In these analyses, linear regression was performed in the subgroups using the same covariates as above, but with untransformed BMI values as a response variable, for easier interpretability of the regression coefficients (presented in kg/m2). Here the differences in effect between the subgroups reflect the interaction term from the previous analyses. Interactions were visualised with bar graphs using the ggplot2 package in R. We also used the plot3D R package to visualise interactions in 3D-plots.In order to visualise and make it easier to interpret the significant interactions, we also estimated the effect of FTO have consistently been shown to be the strongest genetic factors associated with BMI [FTO-linked SNP rs1558902 (GSBMI’), and performed linear regression modeling in exactly the same manner as previously. We also performed additional analyses to assess how individual SNPs interacted with lifestyle factors. SNP-interactions that were considered significant in the discovery cohort were further tested in the replication cohort. We also performed sensitivity analyses by including TDI and its interactions with age, age2, sex, GSBMI, as well as each of the lifestyle factors in the model, in addition to the variables described in Eq  using the ‘step’ function included in the ‘stats’ package in R . This fuy Keller .GSBMI. No differences in effect size between males and females were observed for any of the 94 SNPs . Basic characteristics are provided in  94 SNPs  and we t83 kg/m2 . GSBMI eGSBMI to interact with 19 lifestyle factors related to physical activity, alcohol consumption, smoking, socioeconomic status, sleep, mental health and number of live births (p < 3.8*10−4). Of these, interactions with 15 factors were replicated using the second release of genotype data from the UK Biobank cohort  revealed e births  Tables, k cohort . If we ik cohort  Tables.GSBMI was seen for alcohol intake frequency (p = 1.45*10−29) with larger effect of GSBMI in infrequent drinkers .Strong evidence for interaction with drinkers . The effdrinkers . The intdrinkers . In addiIn contrast to alcohol frequency, we were unable to observe significant interactions with the number of alcoholic beverages per week or total weekly alcohol intake (gram/week). An interaction was observed with total weekly intake of red wine in the discovery cohort, where higher genetic effects were associated with low weekly consumption of red wine . Howeverp = 3.38*10−26, GSBMI, no significant interactions were identified for durations of physical activity , as well as number of vehicles in household and total household income . Interactions were also observed for factors related to sleeping patterns with higher genetic effects in the group that often take a nap during the day and in the group that often felt tired or reported having low energy. Significant interactions were also identified for smoking status . These analyses resulted in large number of statistical tests , which reduces the statistical power. Adjusting for all tests performed using Bonferroni or FDR resulted in only one significant interaction between rs1558902 at the FTO locus and usual walking pace  interactions were found for eleven lifestyle factors in the discovery cohort, of which three interactions with the FTO SNP rs1558902 could be replicated . In the discovery analysis, all Bonferroni significant interaction terms from the previous analyses remained significant when we used GSBMI’, except for smoking status and number of treatments/medications taken . Including TDI as a covariate led to a general slight decrease in effect sizes of interaction terms. The largest decreases were seen for factors related to socioeconomic status , so that a single-standard-unit increase in the GSBMI_UKBB results in an exactly 1.00 unit increase in the rank-transformed BMI, which is 22% higher compared to 0.82 for GSBMI. The interaction results were also strongly correlated between using GSBMI_UKBB or GSBMI , usual walking pace (p = 1.55*10−14), frequency of 10+ minute walks (p = 6.26*10−4), smoking status (p = 1.45*10−3), frequency of vigorous exercise (p = 2.28*10−3), number of vehicles in household (p = 1.03*10−2), TDI (p = 3.02*10−2) and frequency of tiredness/lethargy (p = 3.87*10−2) and. The adjusted R2 value for the final model was 0.1957.Several of the exposures that were found to interact with  another . In ordeplicated . This reIn this study, we performed a gene-environment interaction study using genetic variants and self-reported lifestyle data. We identified several lifestyle factors that influence the effect of genetic variants on BMI. Interactions were observed for factors related to alcohol intake, physical activity, socioeconomic status, mental health and sleeping patterns. Interactions were seen for factors related to physical activity, where a more active lifestyle attenuated the genetic effects, which is consistent with previous reports –9. InterStrong evidence was also observed for an interaction with frequency of alcohol intake. The genetic effect was attenuated with higher frequency of alcohol intake in an almost dose-dependent manner with twice as large effects in non-drinkers compared to daily drinkers. Alcohol consumption is common in western societies, where also most previous GWAS have been performed. Our results indicate that the interaction associated with alcohol intake frequency may have partially attenuated the full effect of BMI-associated genetic variants observed in previous association studies.In vitro and in vivo experiments have also shown ethanol exposure to increase lipolysis and reduce white adipose tissue mass [GSBMI.Alcohol intake frequency was also associated with lower average BMI. This is consistent with clinical reports of lower BMI and fat mass in severely alcoholic patients –24. In vsue mass ,26. Thissue mass , which ssue mass . In addisue mass . Unfortuet al. used a genetic score composed of 69 BMI-associated variants to study interactions with measurements of the obesogenic environment, with focus on physical activity, diet and socioeconomic status [et al. study contrasts the current in the selection of twelve obesogenic factors. The current study instead utilised a hypothesis-free approach to test interactions between GSBMI and 131 factors, which allows us to contrast aspects of the same behaviour, e.g., between amounts of physical activity and frequency and also gives us the potential to identify new gene-environment interactions. A drawback to this approach is the increased statistical power required in order to correct for the family-wise error rate.In a previous study on gene-environment interactions in the UK Biobank, Tyrrell c status . Interacc status  which weFTO-linked SNP rs1558902, in addition to interacting with alcohol intake frequency, also interacts with average total household income and physical activity.In our primary analyses, we have investigated interactions between lifestyle factors and a genetic score composed by 94 independent SNPs, located in different loci. SNPs were combined into genetic scores that explain a greater amount of the variation in BMI compared to the individual SNPs, in order to gain statistical power . These SFTO variant, rs1558902, is associated with the expression of two upstream genes (IRX3 and IRX5) which affect adipocyte “browning”, i.e. the occurrence of thermogenic ‘beige’ adipocytes in white adipose tissue depots. This may partly explain the observed interaction between rs1558902 and frequency of alcohol intake, as in vitro experiments have shown that ethanol exposure interferes with mobilization of glucose transporters to the adipocyte cellular membrane in response to insulin [For BMI, as well as for other complex traits, knowledge on the biological implications of associated genetic variation is limited, which impedes deduction of causal mechanisms underlying gene-environment interactions. The  insulin . Beige a insulin . The altGSBMI.Enrichment analyses from previous GWAS have also implicated central nervous system processes to play an important role in BMI ,5. The cA possible limitation to our study is responder bias in the self-report questionnaire data. This may be more likely for factors pertaining to self-image such as alcohol, tobacco use and physical activity. The lack of an interviewing person, and assuring participants of the confidentiality and anonymity of their data aim to reduce the likelihood of responder bias . We testGSBMI as covariates in all analyses, which resulted in very little effect on the main results. To identify factors with the highest predictive value, we also performed SLR, which showed evidence for interactions between GSBMI and alcohol consumption frequency, physical activity, smoking, and socioeconomic status all contributed independently to a predictive model for BMI.In this study, we primarily investigated associations, and the underlying causal mechanisms behind gene-environment interactions are difficult to deduce from cross-sectional data alone. We constructed separate models for each environmental exposure or lifestyle factor. As such, it is important to be aware that confounding effects of factors that are not included in the models, or that are unknown, may be present in the results from these tests. In order to fully correct for confounding factors and correctly characterise causal factors, controlled experiments such as clinical trials in controlled settings serve as the gold standard. We have attempted to correct for confounding by including TDI and the interaction term TDI*GSBMI and frequency of alcohol intake, frequency of physical activity and socioeconomic status. Previous studies have reported interactions between genetic variants at the FTO locus and environmental factors [FTO locus was excluded from the genetic score, which indicates that the individual interactions are not solely dependent on FTO variants. We can therefore conclude that the presence of genetic interactions is more general and will be identified to a higher degree for individual SNPs once the sample size increases even more and reaches sufficient power.In conclusion, the standardised collection of genetic and lifestyle data in UK Biobank has enabled us to identify several factors that modify the effect of BMI-associated genetic variants. The most significant interactions were observed between  factors –9. HowevS1 Fig(PDF)Click here for additional data file.S2 Fig(A) Histogram of BMI for the 116,138 participants from the UK Biobank Resource. (B) BMI was normalized by rank transformation.(PDF)Click here for additional data file.S3 Fig(PDF)Click here for additional data file.S1 TableQuantitative variables are described by average ± standard deviation. Ordinal variables are described by the number and percentage of individuals in each category.(DOCX)Click here for additional data file.S2 Tableβ: estimated β-values from linear regression models. β_se: standard error for estimated beta-values. p: p-values for association tests. *p-adj: p-values corrected for multiple testing using the Bonferroni method. Power indicates the power to replicate, with Bonferroni adjusted p-value < 0.05, the in UK biobank considering the effect size and allele frequency of each SNP in GIANT.Three SNPs deviated from HWE and were excluded from further analysis. HWE: p-values from tests for deviation from hardy Weinberg equilibrium. (DOCX)Click here for additional data file.S3 Tableβ is the effect size estimate of the SNP, SE β is the standard error of the effect size estimate, and p is the corresponding p-value from association tests between SNPs and BMI. p#—p-values from student’s two-sample t-tests to compare means between males and females. p-adj*—p values adjusted for multiple testing using the Bonferroni method.(DOCX)Click here for additional data file.S4 TableE: the results, with corresponding estimates (β) and p-values (p) for the linear models testing for the effect on each lifestyle variable on BMI without including the interaction term. GSBMI× E: Results for the interaction term from linear models for association with the genetic score for BMI composed of the effects of 94 SNPs associated with BMI. β2: Estimated effect sizes of the interaction. p2: p-value for tests of the estimated effect size deviating from zero. GSBMI' × E is the genetic score for BMI excluding the FTO SNP rs1558902 with corresponding estimates (β3) and p-values (p3) for the interaction terms.N: number of individuals included in the respective analyses. (DOCX)Click here for additional data file.S5 TableE: the results, with corresponding estimates (β) and p-values (p) for the linear models testing for the effect on each lifestyle variable on BMI without including the interaction term. GSBMI× E: Results for the interaction term from linear models for association with the genetic score for BMI composed of the effects of 94 SNPs associated with BMI. β2: Estimated effect sizes of the interaction. p2: p-value for tests of the estimated effect size deviating from zero. GSBMI' × E is the genetic score for BMI excluding the FTO SNP rs1558902 with corresponding estimates (β3) and p-values (p3) for the interaction terms.N: number of individuals included in the respective analyses. (DOCX)Click here for additional data file.S6 TableE: the results, with corresponding estimates (β) and p-values (p) for the linear models testing for the effect on each lifestyle variable on BMI without including the interaction term. GSBMI× E: Results for the interaction term from linear models for association with the genetic score for BMI composed of the effects of 94 SNPs associated with BMI. β2: Estimated effect sizes of the interaction. p2: p-value for tests of the estimated effect size deviating from zero. GSBMI' × E is the genetic score for BMI excluding the FTO SNP rs1558902 with corresponding estimates (β3) and p-values (p3) for the interaction terms.N: number of individuals included in the respective analyses. (DOCX)Click here for additional data file.S7 TableN: number of individuals included in the respective analyses.E: the results, with corresponding estimates (β) and p-values (p) for the linear models testing for the effect on each lifestyle variable on BMI without including the interaction term. GSBMI× E: Results for the interaction term from linear models for association with the genetic score for BMI composed of the effects of 94 SNPs associated with BMI. β2: Estimated effect sizes of the interaction. p2: p-value for tests of the estimated effect size deviating from zero. GSBMI' × E is the genetic score for BMI excluding the FTO SNP rs1558902 with corresponding estimates (β3) and p-values (p3) for the interaction terms.(DOCX)Click here for additional data file.S8 TableN: number of individuals included in the respective analyses.E: the results, with corresponding estimates (β) and p-values (p) for the linear models testing for the effect on each lifestyle variable on BMI without including the interaction term. GSBMI× E: Results for the interaction term from linear models for association with the genetic score for BMI composed of the effects of 94 SNPs associated with BMI. β2: Estimated effect sizes of the interaction. p2: p-value for tests of the estimated effect size deviating from zero. GSBMI' × E is the genetic score for BMI excluding the FTO SNP rs1558902 with corresponding estimates (β3) and p-values (p3) for the interaction terms.(DOCX)Click here for additional data file.S9 TableE: the results, with corresponding estimates (β) and p-values (p) for the linear models testing for the effect on each lifestyle variable on BMI without including the interaction term. GSBMI× E: Results for the interaction term from linear models for association with the genetic score for BMI composed of the effects of 94 SNPs associated with BMI. β2: Estimated effect sizes of the interaction. p2: p-value for tests of the estimated effect size deviating from zero. GSBMI' × E is the genetic score for BMI excluding the FTO SNP rs1558902 with corresponding estimates (β3) and p-values (p3) for the interaction terms.N: number of individuals included in the respective analyses. (DOCX)Click here for additional data file.S10 TableGSBMI and environmental factors are shown. Results for the full model are available in the supplementary Data. Stepwise linear regression was performed as was described in the methods section. Age, age2 and sex were included as covariates. Interaction terms for all secondary interactions were included to control for potential confounding. The model also included a batch variable for the two genotyping platforms used in the UK Biobank, as well as 15 principal components. p-values < 0.05 were considered significant.Results for interactions between (DOCX)Click here for additional data file.S11 Tableβ1–3: Estimated effect sizes of the interaction terms. p1-3: p-value for tests of the estimated effect size deviating from zero.N: number of individuals included in the respective analyses. (DOCX)Click here for additional data file.S12 Tableτ). Values in the upper diagonal represent p-values.Values in the bottom diagonal represent Kendall tau coefficients ((DOCX)Click here for additional data file.S1 DataTests for SNP-environment interactions were performed for each individual SNP and environmental factor according to Eq  see met. Each ta(XLSX)Click here for additional data file.S1 Supporting Information(DOCX)Click here for additional data file.S2 Supporting Information(DOCX)Click here for additional data file.


Ostreid herpesvirus (OsHV) can cause mass mortality events in Pacific oyster aquaculture. While various factors impact on the severity of outbreaks, it is clear that genetic resistance of the host is an important determinant of mortality levels. This raises the possibility of selective breeding strategies to improve the genetic resistance of farmed oyster stocks, thereby contributing to disease control. Traditional selective breeding can be augmented by use of genetic markers, either via marker-assisted or genomic selection. The aim of the current study was to investigate the genetic architecture of resistance to OsHV in Pacific oyster, to identify genomic regions containing putative resistance genes, and to inform the use of genomics to enhance efforts to breed for resistance. To achieve this, a population of ∼1,000 juvenile oysters were experimentally challenged with a virulent form of OsHV, with samples taken from mortalities and survivors for genotyping and qPCR measurement of viral load. The samples were genotyped using a recently-developed SNP array, and the genotype data were used to reconstruct the pedigree. Using these pedigree and genotype data, the first high density linkage map was constructed for Pacific oyster, containing 20,353 SNPs mapped to the ten pairs of chromosomes. Genetic parameters for resistance to OsHV were estimated, indicating a significant but low heritability for the binary trait of survival and also for viral load measures (h2 0.12 – 0.25). A genome-wide association study highlighted a region of linkage group 6 containing a significant QTL affecting host resistance. These results are an important step toward identification of genes underlying resistance to OsHV in oyster, and a step toward applying genomic data to enhance selective breeding for disease resistance in oyster aquaculture. Crassostrea gigas) worldwide  improving host resistance to OsHV-1 via selective breeding has become a major target.A specific variant of the ostreid herpesvirus (OsHV-1-μvar) has been suggested to be the main cause of periodic mass mortality events in farmed Pacific oysters  facilitate development of high density linkage maps and high resolution genome-wide association studies into the genetic architecture of traits of economic interest. In addition, these arrays enable testing of genomic selection approaches which are increasingly common in aquaculture breeding, with encouraging empirical data supporting the advantage over pedigree-based approaches  to identify loci associated with the trait, and the relative contribution of these loci to the heritability of the trait.The aim of this study was to investigate the genetic architecture of resistance to OsHV-1 infection in Isocrysis, Tetraselmis, Chaetoceros, Pavlova sp., and ‘Shellfish Diet 1800’ until they reached an appropriate size (>5 mm) at approximately eight months of age. A subsample of approximately 1,000 oysters were then transferred to the challenge tank at 20 +/− 2° for two days for acclimation.Oysters used in this study were obtained from multiple crosses of parents provided by Guernsey Sea Farms (UK) and reared at Cefas facilities. The oysters comprised three pair crosses that were created at Cefas (from 3 sires and 2 dams) and each reared separately, while the rest of the crosses (from 14 sires and 14 dams) were obtained as spat from Guernsey Sea Farms and combined into a mixed culture tank at Cefas. Oysters were held at 20 +/− 2 C during post-settlement and fed with a combination of 7 copies /ml  with continuous flow. Mortalities were checked every three hours by visual and manual inspection, morbid or dead animals were removed, snap frozen, and stored at -80°. The challenge lasted for 21 days, by which time mortality rate had returned to baseline levels, and all remaining mortalities and survivors were snap-frozen and stored for DNA extraction.OsHV-1 µVar was isolated from an individual oyster sampled during a 2015 disease outbreak in Poole harbor (UK). Briefly, the gill and mantle were isolated from the diseased oyster, homogenized in filtered sea water, and filtered sequentially through 1.2, 0.8, 0.45 and 0.2 µm filters. Purified virus was then passaged twice by injection through susceptible oysters for proliferation as per previous protocols  or 1 . The viral count of all samples was determined by qPCR according to  using the RealPure genomic DNA extraction kit , quantified on Qubit and the DNA integrity was checked on a 1% agarose gel.. After considering available DNA quality and quantity, only 897 samples were retained for genotyping . Genotyping was carried out at Edinburgh Genomics using the recently developed Affymetrix SNP array for oysters variance structure for the genetic effect was calculated either using pedigree (A) or genomic (G) matrices  or N), where G is the genomic kinship matrix and σ2 is the genetic variance. Hence, the narrow sense heritability was estimated by the additive genetic variance and total phenotypic variance, as follows:2a is the additive genetic variance and σ2p is the total phenotypic variance which is a sum of 2aσ  2e+ σ  . Heritability on the observed binary scale obtained for survival was converted to the underlying liability scale according to Genetic parameters for the resistance traits were estimated using a linear mixed model approach fitting animal as a random effect using ASReml 4  using the mmscore function (−6 as determined by Bonferroni correction (0.05 / N), where N represents the number of QC-filtered SNPs across the genome, while the suggestive threshold was set as 3.08 × 10−5 (0.5 / N), i.e., allowing 0.5 false positive per genome scan.The GWAS was performed using the GenABEL package (function  with theC. gigas genome v9 assembly (GCA_000297895.1)  from the NCBI database.To identify candidate genes potentially underlying the identified QTL for further study, the location of the most significant SNPs on individual contigs and scaffolds was recorded on the File S1. Genotype data corresponding to all informative markers for all the individuals involved in this study is given in File S5.Linkage map including all mapped markers and their position is given in 5, s.e 2.2 x104), than survivors .At the end of the 21 day disease challenge, 749 oysters had survived while 251 had died during the experiment. From the latter, 71 oysters had no body tissue at the moment of their removal, leaving 181 mortalities suitable for downstream analyses. Therefore, overall mortality was approximately 25%, but in the subset of oysters available for genotyping the mortality was ∼18%. Viral load calculations (copies/mg) showed that mortalities had a higher average viral load . Making use of the pedigree information, the estimated heritability on observed scale was 0.13 (0.06), corresponding to a value of 0.25 on the underlying liability scale . These eP < 0.001) in at least one family with at least ten progenies, leaving 21,087 maternally informative markers and 20,528 paternally informative markers for map construction (Table S1).The linkage mapping was performed using the 23 full sibling families comprising 809 progenies and 31 parents. On average, 10% of the markers showed evidence of segregation distortion (C. gigas karyotype) as shown in File S1). These scaffolds and contigs containing mapped SNPs covered approximately 87% of the reference genome length.The linkage map contains 20,353 SNPs distributed on 10 LGs (in accordance with the C.gigas linkage maps. Our medium density oyster array contains 464 of the SNPs mapped by File S2). Likewise, we observed that approximately 38%  of the scaffolds with informative markers show evidence of errors in the assembly, due to assignment to at least two distinct LGs in our map (File S3). As expected, the number of LGs associated with scaffolds was positively correlated with scaffold length .Linkage groups were labeled according to File S4. Of the ten markers showing the most significant association in the two approaches, four markers are linked to LG 6 but they do not map to the same scaffold, nor are they close together on the linkage map. The proportion of phenotypic variation explained by the top ten markers ranged between 0.019 and 0.047, which implies a polygenic architecture to host resistance, albeit the LG 6 QTL potentially explains a large proportion of the genetic variance given the low heritability estimates.The GWAS for the binary survival trait using the FASTA approach identified two markers showing a genome-wide significant association with the trait , as shown in File S4). The SNP showing the most significant association is located in LG 8, however, no other markers are located in the same LG. While most of the markers significantly associated with the trait were not mapped, the nearest mapped SNPs according to their position on the genome scaffolds suggests that three SNPs are located on LG 6. Therefore, it is plausible that there is at least one QTL on LG 6, and this QTL may affect both viral load and the binary trait of survival. The proportion of phenotypic variation in viral load explained by the top ten markers ranged between 0.0209 and 0.037.The GWAS for the trait of viral load detected two markers showing significant genome-wide association with both FASTA and EMMAX, with an addition eight SNPs identified as significant using EMMAX only  in comparison to other recent studies that have analyzed resistance to OsHV-1, where estimates have ranged from 0.21 to 0.63  (Table S1). Moderate levels of segregation distortion have been commonly observed in oysters (Family assignments were rigorously tested to avoid pedigree errors in the construction of the linkage maps. Distortions from the expected Mendelian segregation were found in ∼10% of the SNPs in the larger families ( oysters . In the File S1). This linkage map should be able to provide a good base for the identification of assembly errors and the potential re-assembly of the genome, which seems like a requirement to maximize its utility for future genomics research in this species.A measure of the quality of the linkage map was given by overlap with a previous linkage map described by File S4). For the trait of viral load, markers showing a genome-wide significant association were located in LG 8, LG 6LG 10 & LG 4, and suggestive association found in LG 1 & LG 7(File S4). The only previously published study describing genomic regions associated to summer mortality resistance found significant QTL in LG V, VI, VII & IX  in different families , these genes may represent candidates for future validation, resequencing and functional testing. The SNP showing an association with both survival and viral load (AX-169210119) was located in the RAN Binding Protein 9-like gene which has recently been linked to the interferon gamma signaling pathway (Numerous genes were identified from the genomic regions flanking the most significant SNPs impacting the resistance traits. While the limits defined for screening flanking regions of significant SNPs were defined practically (Nevertheless, validation studies are required in independent populations to assess the robustness of the observed association between the significant SNPs and OsHV-1 resistance in oysters, particularly given the unusually low mortality observed in the challenged population. A higher mortality level could potentially provide a higher power of detection for the association analyses that could help confirm any putative QTL.C. gigas, and the GWAS identified numerous markers showing a genome-wide significant association with the traits. The most encouraging QTL was located on LG 6, reaching genome-wide significance for the binary trait of survival, with some evidence of a significant association with viral load. Future analyses will test candidate genes identified by the GWAS, verify trait-associated SNPs in independent populations, and test genomic selection as a tool to enhance host resistance to this problematic pathogen for oyster aquaculture.This is the first GWAS using the a high density SNP panel Pacific oysters, and was enabled by the recent development of a SNP array (www.g3journal.org/lookup/suppl/doi:10.1534/g3.118.200113/-/DC1.Supplemental Material is available online at Click here for additional data file.Click here for additional data file.Click here for additional data file.Click here for additional data file.Click here for additional data file.Click here for additional data file.Click here for additional data file.


VA), providing the basis for claims that non-additive gene actions are unimportant. In this study, we show that arbitrarily defined parameterizations of genetic effects seemingly consistent with non-additive gene actions can also capture the majority of genetic variation. This reveals a logical flaw in using the relative magnitudes of variance components to indicate the relative importance of additive and non-additive gene actions. We discuss the implications and propose that variance component analyses should not be used to infer the genetic architecture of quantitative traits.Classical quantitative genetic analyses estimate additive and non-additive genetic and environmental components of variance from phenotypes of related individuals without knowing the identities of quantitative trait loci (QTLs). Many studies have found a large proportion of quantitative trait variation can be attributed to the additive genetic variance ( There has been a great amount of debate over the relative importance of additivity and non-additivity in quantitative trait variation. The main argument supporting the importance of additivity is the observation that the additive component of genetic variance is much greater than non-additive variance components, while the main argument supporting the importance of non-additivity is the identification of many non-additive effects in genetic mapping studies. By recapitulating many classical results and introducing new alternative parameterizations of genetic effects, we point out some of the common mistakes and misleading arguments in using variance component analyses to infer genetic architecture, specifically the gene actions of QTLs. Because of the wide applications of variance component analyses, our study has profound implications and clarifies some of the most confusing concepts in quantitative genetics in the genomics era. VA), dominance (VD), and inter-locus interaction (epistatic) variance (VI) components .pqd2  [2]xA as:Alternatively, we can define a random variable xA is equal to the number of A alleles. It is easy to show that the allele substitution effect α as defined above is the slope of the least squares regression of genotypic value y on xA in an idealized population with random mating (VA = Var(ŷ) = Var(αxA) = α2Var(xA) = 2pqα2 and the dominance genetic variance VD is the residual variance. It is easy to see that the least squares solution for this regression seeks to maximize VA and minimize VD. This least squares interpretation is not new and dates back to the early days of quantitative genetics [This parameterization has the convenient interpretation that m mating . The addgenetics .x or more than one of them and fit a linear model of form y = βx + ϵ, we can partition genetic variance due to the assumed genetic model Var(ŷ) = Var(βx) and residual variance Var(ϵ).By extension of this least squares regression interpretation of genetic variation, if we arbitrarily define any one random variable Now we illustrate the idea of using least squares regression to partition genetic variance due to dominant gene action and the remaining genetic variance. We define the random variable VA and VD, we define the residual variance as an “additive deviation” variance The least square solution for the linear model qd+11+qa . Therefox and finding the solution is not always easy. However, it is computationally trivial to find. For example, to numerically estimate the additive by additive variance Extending the least squares regression interpretation of genetic variance to any arbitrary random variable y onto x. The proportion of genetic variation explained by this parameterization is then just the R2 of the regression.Then, p = 1,000 loci were randomly assigned according to their Hardy-Weinberg frequencies to n = 5,000 individuals. Genetic values were then assigned to the 5,000 individuals using this general formula g = Xβ. Each of the columns of the n × p matrix X was coded by the additive parameterization xA as defined above for the additive genetic model, β was drawn from standard normal distribution. The phenotypic value y for each individual was then simulated by adding random noise such that Y = g + ϵ, where ϵ was normally distributed with zero mean and variance equal to H2 was the broad sense heritability and was always set to 0.5.To extend the single- and two-locus models to polygenic models, we used mixed model analysis to partition phenotypic variation in simulated and real data. To simulate phenotypic data with pre-defined genetic models, we first drew 1,000 realizations from the U-shaped distribution  f(p)∝1pqX and computed the covariance matrix as XXT, which was further scaled by the mean of its diagonal values. A linear mixed model Y = μ1 + uZ + ϵ was fitted to the data, where μ was the population mean, Z was the incidence matrix and in all cases in this study the identity matrix, u was a random effect with variance covariance matrix Gσ2, where G was simply the scaled XXT above and σ2 was the part of genetic variance due to the specific parameterization. We fitted this model using the GCTA software[2 as h2/H2, where H2 was the simulated broad sense heritability.We standardized columns of  software with REMa priori, we downloaded genotype and phenotype data from dbGaP for the GENEVA Genes and Environment Initiatives in Type 2 Diabetes study (phs000091.v2.p1). We pruned the data set to contain 5,497 unrelated  individuals with European ancestry based on both self-reported ethnicity and principal component analysis. We then computed genetic covariance matrices as defined above using autosomal SNPs and partitioned phenotypic variance using GCTA where sex was fitted as a fixed effect in the model. We used the parameterization (VA, VD, and Ve. We also partitioned phenotypic variance into Ve, where To analyze real data where the genetic architecture cannot be known rization  as definy phs00001.v2.p1. able xA′ , wherex