Scanning the genome with high density SNP markers has become a standard approach for identifying regions of the genome showing substantial between-population genetic differentiation, and thus evidence of diversifying selection. Such regions may contain genes of large phenotypic effect. However, few studies have attempted to address the power or efficacy of such an approach.In this study, the patterns of allele frequency differences between two cattle breeds based on the Bovine HapMap study were compared with statistical evidence for QTL based on a linkage mapping study of an experimental population formed by a cross between the same breeds. Concordance between the two datasets was seen for chromosomes carrying QTL with strong statistical support, such as BTA5 and BTA18, which carry genes associated with coat color. For these chromosomes, there was a correspondence between the strength of the QTL signal along the chromosome and the degree of genetic differentiation between breeds. However, such an association was not seen in a broader comparison that also included chromosomes carrying QTL with lower significance levels. In addition, other chromosomal regions with substantial QTL effects did not include markers showing extreme between-breed genetic differentiation. Furthermore, the overall consistency between the two studies was weak, with low genome-wide correlation between the statistical values obtained in the linkage mapping study and between-breed genetic differentiation from the HapMap study.These results suggest that genomic diversity scans are capable of detecting regions associated with qualitative traits but may be limited in their power to detect regions associated with quantitative phenotypic differences between populations, which may depend on the marker resolution of the study and the level of LD in the populations under investigation. With the development of dense genome-wide marker panels for many species, it is becoming common to use these markers to characterize genetic diversity across the genome. Such genomic scans are designed to identify regions where selection has acted and which therefore, may contain genes of large phenotypic effect. The rationale is that, even without phenotypic information, one can use patterns of genetic variation to highlight genomic regions under selection. However, the power and reliability of these studies has not been assessed because usually there is no independent data set against which the results can be compared. The current study was designed to address this point by examining the concordance between a genomic diversity dataset comprising genome-wide SNP data from two cattle breeds and a set of linkage mapping results from a study in an F2/Backcross population bred from founders of these same breeds.Using these datasets, an overall concordance between level of genetic differentiation and linkage mapping signal was evaluated. In addition, the more specific question to be addressed is whether regions with large allele frequency differences between the breeds are more likely to contain genes controlling phenotypes that differ between the breeds than regions with small allele frequency differences. However, because not all of the traits that might distinguish the breeds can be measured, the question was addressed in the converse direction in this study, i.e. whether regions of the genome where QTL have been identified are characterized by larger SNP allele frequency differences compared with other genomic regions.A three-generation Charolais x Holstein cattle herd was bred from seven founder Charolais sires, which were mated with Holstein cows to produce 137 F1 animals. From these, a total of 501 second generation cross-bred animals were produced, 315 were F2 individuals from crossing eight F1 sires with F1 cows, and 186 were reciprocal backcrosses of the F1 animals with the founder breeds . The second generation animals were measured for a wide variety of traits [A panel of 165 microsatellite markers were genotyped in the population; 139 of these were selected at random from across the autosomes and the other 26 were added later in regions on nine chromosomes where QTL were detected following initial analysis . Linkagehttp://www.ensembl.org/Bos_taurus) (88 markers) or by megaBLAST [Microsatellite markers used to derive the linkage maps were then mapped against the Baylor bovine genome assembly Btau_4.0  in orderegaBLAST  sequencemax) over all traits at each chromosomal position was used as the test statistic for the interval mapping results.The QTL analysis was performed using the QTL Express software , which iBos taurus breeds , plus sire-dam-offspring trios for data quality assessment, were collected and genotyped for 33,851 biallelic SNPs distributed across the genome (encompassing 3.2 Gb for Assembly Btau_4.0). The majority of SNPs were discovered by comparing shotgun genome sequence reads for cows from six breeds  to the Hereford reference genome sequence. SNP density was fairly uniform across the genome except that higher densities of markers were positioned on three chromosomes .Genome-wide SNP data was obtained from the Bovine HapMap Consortium  and is sOnly the genotype data for 49 Holstein and 20 Charolais individuals included in the HapMap project was considered . Loci with low minor allele frequencies, high error rates, evidence of deviation from Hardy-Weinberg Equilibrium or excessive missing data were removed from the data set , as werδ) was calculated at each SNP position  were calculated for each SNP [ST estimates were negative, they were set to 0 [ST was defined . Sequence positions for each marker were rounded to the nearest 100,000 bp and an average value of δ (or FST) was calculated for all markers with the same rounded position. Two smoothed statistics, MA_δ and MA_ FST, were calculated as moving averages of 11 δ or FST values, respectively, centered on each rounded position, i.e. including that position and its 10 flanking positions (excluding the first and last 5 positions of the chromosome).To calculate genetic differentiation from the HapMap data, the following protocol was followed. The frequency of one allele was calculated for each SNP for each of the two breeds. Two statistics were then used to characterize the differences between the two breeds. First the absolute value of the difference in allele frequencies between the Holstein and Charolais breed groups . Secondeach SNP ,15, adjueach SNP . If FST set to 0 . The datmax values from interval mapping and each of the four measures of SNP breed differences from the HapMap study  over the entire genome and for each chromosome. Then chromosomal positions were grouped according to whether their Fmax value was above (highF) or below (lowF) a given threshold. Three groupings were defined using the approximate cut-offs for chromosome-wise and genome-wide significance previously calculated by permutation testing for this data  were calculated for the highF and lowF groups on each chromosome. Numbers of chromosomes for which any Fmax values exceeded the thresholds decreased with threshold values . Wilcoxon signed rank tests were used to test whether the mean values of δ and FST (and their respective moving averages) for each chromosome differed for the highF and lowF groups, for each of the three F-thresholds. A one-tailed test was applied, i.e. the alternative hypothesis was that the highF group had greater δ or FST values than the lowF group.Correlation coefficients were calculated between F F = 10; ). For eaST and δ was high (0.8764) and results for both measures were generally similar. Thus, results are presented only for δ (and MA_δ) except where qualitative differences were seen between results for δ and FST. Visual inspection did not show a consistent trend between Fmax and δ across the genome, although such a trend was seen for some chromosomes. Figure max and MA_δ across the chromosomes with the largest QTL in the study, on BTA5, 6 and 18 . BTA5, 6 and 18 had positive correlations although the correlation coefficient was low for BTA6. For the chromosomes with a positive correlation between Fmax and δ, correlations were consistently higher between Fmax and MA_δ than between Fmax and δ . The highest chromosome-wide positive correlations between Fmax and δ were (in descending order) for BTA28, 18, 14, 5, 2 and 7 .The genome-wide correlation between Fδ was examined. This statistic was significantly higher (p < 0.001) for the SNPs detected in Holsteins (δ = 0.1565) than that detected in all other breeds (0.1372). The correlation coefficient between δ and Fmax values was recalculated as described above, for the 14,132 segregating SNPs that were detected in breeds other than Holsteins. For that subset of data, the overall correlation coefficient between Fmax and δ was 0.0427, lower than that calculated for all SNPs, thus the inclusion of the Holstein-derived SNPs did not reduce the overall correlation between Fmax and δ. However, for the non-Holstein SNP data, fewer chromosomes (13/29) had negative correlations between Fmax and δ (12/29 for MA_δ) than was found considering all SNPs (14/29).To test whether SNP ascertainment bias, and in particular the fact that the majority of SNPs were detected in Holsteins, may explain the lack of concordance between the interval mapping and SNP frequency, the effect of breed-of-origin on the value of δ and MA_δ distributions above and below Fmax thresholds revealed little difference between regions with high and low Fmax values for the lowest Fmax threshold (F = 5), but there were differences for the higher thresholds (F = 7 and F = 10). Wilcoxon signed rank tests revealed significant differences in the mean δ values between highF and lowF positions for Fmax thresholds of both 7 and 10 (p < 0.05), but not for the threshold of 5. The same results were seen for comparisons of mean MA_δ values between highF and lowF positions . These results are presented graphically in plots of the chromosome-wide mean MA_δ values for highF versus those for lowF positions , as well as BTA10 and 12 for which the highest Fmax values were between 10 and 12 .The comparison of s Figure . For F =δ distribution  covered 27 of the 29 autosomes. Of the 124 loci in the top 1% of the δ distribution, the greatest number of markers were found on BTA1 (9 positions), 5 (13 positions), 6 (10 positions) and 8 (9 positions). When positions were ranked by MA_δ values rather than by δ  were found on BTA5 , BTA6 , and BTA18 . The highest δ, MA_δ and MA_ FST values were found at 77.4 Mbp on BTA6. The highest FST value  was found at 63.6 Mbp on BTA5.With regard to extreme values of the genetic differentiation measures across the genome: the top 1% of the The objective of the analysis reported here was to assess if there was consistency between the pattern of allele frequency differences between two cattle breeds and the pattern of statistical evidence for QTL identified in a cross-bred population of the same breeds. The motivation for this was to test whether the current trend to look for signatures of selection in data from high density genome scans could detect the genomic regions controlling phenotypic traits identified by traditional linkage mapping techniques. The results suggest that genomic differentiation patterns can pick up very large, qualitative phenotypic effects, but may have limitations as predictors of genomic regions associated with smaller, quantitative phenotypic differences.SILV gene, 61.9 Mbp) causes complete dilution of coat pigmentation and gives this breed its characteristic white coat [MC1R locus (13.8 Mbp), which is the main regulator of the switch between red and black coat color pigments [MC1R, although it is not visible in the coat because of the dilution effect, whereas black and white Holsteins are predominantly homozygous for the black allele, with a low frequency of heterozygotes [max and MA_δ were 0.421 on BTA5 and 0.651 on BTA18, and as seen in Figure MA_δ graphs. Furthermore, the positions of the known pigmentation genes are very close to the peak MA_δ values, particularly for the SILV gene on BTA5. However, there was only a weak positive correlation on BTA6 (0.075), where the third highest F-ratio in the linkage mapping study was found. The QTL corresponding to the high F-ratio was associated with birth weight and carcass-related traits [MA_δ although this was not in the top 1% of the distribution. The chromosome-wide correlation on BTA6 was reduced, however, because there are other regions further downstream with even higher values of MA_δ but where there is only weak evidence of QTLs, for bone weight and average feed intake. The regions of high MA_δ may be associated with traits that were not measured in the linkage mapping study or the linkage mapping study may not have been powerful enough to detect associations in this region. In the 2-Mbp region centered at 77.4 Mbp (the peak δ and MA_δ position), there are no annotated genes in the bovine genome, although there is homology to some expressed genes in the human genome (http://genome.ucsc.edu). The KIT gene, which is associated with the level of white spotting in Holstein cattle and other mammals [δ and MA_δ peak. While the level of spotting was not analyzed in the linkage mapping population, variation in this trait was observed in the F2/Backcross generation.In the comparison of genomic data from two cattle breeds carried out in the present study, allelic differentiation was amplified in regions where the largest genetic effects were detected by QTL mapping BTA5 and 18), however, overall, there was low correlation between the test statistics from the two analyses. The BTA5 and 18 QTL were associated with Mendelian loci influencing coat colour: the Charolais-derived allele in a region of BTA5  value was higher for the lowF group. There were several QTL on this chromosome for carcass traits, but the MA_δ graph did not follow the QTL pattern. While the difference between the highF and lowF groups for the Fmax = 7 threshold was also statistically significant, the effect was not as pronounced as for the Fmax = 10 threshold; for 4 out of 13 chromosomes, MA_δ was greater in the lowF than the highF group.Interpretation of correlation coefficients calculated across the genome is made difficult because not all traits that differ between the breeds were measured in the interval mapping study. Indeed some loci under divergent selection in these two breeds may not have phenotypically obvious effects and will not have been analysed. However, this problem is avoided by the analysis where differentiation levels were compared at positions with low F-ratios versus high F-ratios. Where there is a positive association between the two analyses, there should be higher allele frequency differences for the high F-ratio group than the low F-ratio group, even if there are other QTL that were not detected. For the most extreme comparison of FST or related statistics. This has been demonstrated in recent empirical studies: e.g. Sutter et al. [IGF1 locus, a gene that is associated with body size, a trait which has been under strong selection in the development of dog breeds. In this region, they found a very narrow peak (< 0.2 Mbp) in extreme values of FST . In contrast, Akey et al. [ST values between Shar-Pei and Dachshund dogs  in a region containing a strong candidate locus for skin wrinkling (a characteristic of the Shar-Pei breed). The extensive region of inflated FST in this case compared to the narrower region surrounding IGF1 may reflect the more limited region of LD shared by several breeds compared to a broader LD region that may be shared by two breeds. The power of an approach based on allelic differentiation for identification of genes of large effect will depend, in part, on the levels of linkage disequilibrium in the genome. Further studies are required to quantify this relationship and to determine the marker density required to detect loci associated with selected traits in a given population.While approaches based on allelic differentiation are currently being used for QTL mapping in some model species e.g. in Drosophila, Arabidopsis and maize -27, the r et al.  looked ay et al.  identifimax for these regions (e.g. BTA6). However, this was not observed in the analysis. In addition, performing interval mapping using genome sequence positions may also have influenced the scale of the Fmax values as there is not a one-to-one correspondence between the linkage map and the genome sequence due, in part, to variation in recombination rates across the genome. This should not, however, have had a substantial impact on the results pertaining to the moving average measures, which were spatially averaged. Finally, although the linkage mapping experiment was designed to detect QTL fixed for alternative alleles in the founder breeds, it may still have picked up large effects for which the QTL was segregating within breeds. In that case, allelic differentiation between breeds would be reduced compared to the case where alternative alleles were fixed in the two breeds.Factors in addition to LD levels may have influenced the results of the present study, for example, the interval mapping data was based on small numbers of individuals measured for some of the phenotypic traits . This may have increased the rates of both false positive and false negative linkage associations. Furthermore, the density of markers in the linkage study was relatively low such that QTL positions were not very precise and in many cases 95% confidence intervals covered most of the chromosome. However, marker density was enhanced in regions where QTL were detected in preliminary analysis , which iIn addition to the inherent limitations of the individual datasets, there may be problems in combining them: the QTL mapping study used British Charolais and Holstein animals as founders for the experimental crossbred population, while the HapMap SNP diversity study sampled North American Charolais and Holsteins. This should not have been a problem for the Holstein breed, which is very similar worldwide due to large-scale use of artificial insemination in the global dairy industry and the worldwide predominance of North American sire lines. However, there may be genetic differences between UK and North American Charolais due to genetic drift or different selection pressures in Europe and North America. Such differences are most likely to occur in regions associated with quantitative traits rather than highly-visible, categorical traits like coat colour which are key for breed identification.MA_δ values on BTA5, 6 and 18 discussed above, there were extreme values (> 0.3) on BTA13 (11.3 Mbp) and BTA20 (28.5-28.6 Mbp). The BTA13 region could not be associated with a gene known to be involved in any of the traits considered or with QTL for these traits from this study or others. On BTA20, a QTL for growth was detected slightly upstream of the Fmax peak  gene, located at 33.9 Mbp on this chromosome, is associated with growth in cattle [KIT on BTA6, however, this gene is several Mbp downstream of the MA_δ peak.In addition to the high n cattle ,32 as weST reported by Flori et al. [MA_δ positions reported in the current study. These included regions of BTA3, 4, 5, 6, 18 (near MC1R), 20 (near GHR) and 26. In a study of allele frequency differences between Holstein and Angus (another beef breed) cattle [p < 0.001) sliding window average differences (their Table two), three were within 2 Mbp of the top 1% MA_δ positions identified in the current study: on BTA14 (two positions) and BTA20, within 5 Mbp of GHR. There was less concordance between data reported here and results from Barendse et al. [ST values for both the original HapMap dataset (19 beef and dairy breeds) and a set of 20 beef and dairy breeds from Australia . Only 4 out of the 95 significant markers identified by Barendse et al. [ST reported in the original HapMap study [KIT gene.  The correspondence between the current study and those of Flori et al. [et al. [http://www.ncbi.nlm.nih.gov/sites/entrez?db=omia) whereas many meat and dairy traits are quantitative traits and thus under the control of multiple genes, which may fix more slowly than single genes [Several of the regions with high levels of genetic differentiation were detected in previous studies to identify signatures of selection in cattle. Seven of the 13 regions of high Fi et al.  in three) cattle , of the e et al. , which re et al.  were witap study  , this approach may not have sufficient power to detect smaller, quantitative effects, depending on the marker resolution used in the study and the levels of linkage disequilibrium in the populations under investigation.PW planned the study, performed some of the data analyses and drafted the manuscript, MAE wrote and executed scripts to extract and manipulate the data, positioned the markers used in the linkage mapping study on the genome sequence, and performed some of the data analyses, JLW conceived and managed the study from which the linkage mapping results derived, was part of the Bovine HapMap Consortium and participated in writing the manuscript, DW advised on and assisted with the statistical analyses, AL wrote and executed scripts to extract and manipulate the data, JAW advised on the statistical analyses and was part of the Bovine HapMap Consortium, and BGG provided the linkage mapping data, assisted with positioning the markers on the genome sequence and helped prepare the manuscript. All authors approved the manuscript.Table S1: List of traits analyzed from F2/Backcross linkage mapping experiment.Click here for fileMA_δ, represented by diamonds) and the maximum F-ratio of the linkage mapping study with Holstein and Charolais founders  across the bovine autosomal genome (BTA1 - BTA29).Click here for fileTable S2: Top 1% MA_δ values, sorted by chromosome.Click here for file


Accurate prediction of genomic breeding values (GEBVs) requires numerous markers. However, predictive accuracy can be enhanced by excluding markers with no effects or with inconsistent effects among crosses that can adversely affect the prediction of GEBVs.We present three different approaches for pre-selecting markers prior to predicting GEBVs using four different BLUP methods, including ridge regression and three spatial models. Performances of the models were evaluated using 5-fold cross-validation.Ridge regression and the spatial models gave essentially similar fits. Pre-selecting markers was evidently beneficial since excluding markers with inconsistent effects among crosses increased the correlation between GEBVs and true breeding values of the non-phenotyped individuals from 0.607  to 0.625 (using pre-selected markers). Moreover, extension of the ridge regression model to allow for heterogeneous variances between the most significant subset and the complementary subset of pre-selected markers increased predictive accuracy (from 0.625 to 0.648) for the simulated dataset for the QTL-MAS 2010 workshop. Genomic selection (GS) is a method for predicting breeding values on the basis of a large number of molecular markers . HoweverWe compare different methods for selecting the most relevant markers for GS. Genomic breeding values (GEBVs) were estimated using different BLUP methods and number of pre-selected markers. Besides ridge regression (RR), spatial models were also used. The best model was selected using cross-validation (CV).A simulated dataset of 3226 individuals in five generations generated for the QTL-MAS 2010 workshop was analysed. A total of 2326 individuals belonging to the first four generations were phenotyped and genotyped with 10031 SNP markers. Moreover, 900 individuals in the fifth generation were genotyped but had no phenotypic records. We focus here only on the quantitative trait. A SNP was included in the analysis only if its minor allele frequency exceeded 2.5%. This resulted in the exclusion of 461 SNPs.ikz for the i-th individual  and the k-th marker  for biallelic SNP markers with alleles A1 and A2 was set to 1 for A1A1, -1 for A2A2 and 0 for A1A2. Covariates were stored in a matrix Z = {ikz}.The marker covariate We tested the effect of each SNP on the quantitative trait using three different methods.Each SNP was tested using a linear regression, like in Macciotta et al. , given biy = μ + kziku + ie,iy is the phenotypic record for the i-th individual, μ is the intercept, ikz is the genotype of the i-th individual for the k-th marker, ku is the slope of the linear regression on the k-th marker and ie is the residual error where Each SNP was analysed for consistency among crosses using the modelicy = μ + kziku + cCross + ckzikγ + ice,cCross is the random effect of the c-th cross and ckγ is the slope of the random linear regression of the c-th cross on the k-th marker. The variance-covariance structure for the random regression was assumed to be unstructured and bivariate-normal (BVN), i.e. Σ is an unstructured 2×2 variance-covariance matrix. The random interaction effect (ckγ) served as the error term for the test of the SNP main effect (ku). If the SNP main effect is highly consistent, the interaction will be small, and so the F-value will be relatively large. Conversely, if the SNP is inconsistent, the main effect will be small and the interaction large, yielding small F-values.where Each SNP was analysed for consistency among generations using the modeligy = μ + kziku + gGeneration + gkzikγ + ige,gGeneration is the random effect of the g-th generation and gkγ is the slope of the random linear regression of the g-th generation on the k-th marker. Similarly to method 2, the SNP main effect (ku) is tested against the random interaction term (gkγ).where n  most significant markers  were included in the GS model.The The genotypic effect was estimated using the following linear mixed model:iy = μ + ig + ie,iy is the phenotypic record for the i-th individual, μ is the intercept, ig is the genotypic effect of the i-th individual, and e is a random residual where g) was predicted by regression on the maker types:The genotypic value  most significant markers and the remaining n-a  pre-selected markers, similar to model MIXTURE in [This model was extended to incorporate heterogeneous variances between the m=1 denotes the a most significant and m=2 the remaining n-a pre-selected markers.where μ + ig corresponding to GEBVs.The regression coefficients were predicted by best linear unbiased prediction (BLUP) and the variance components estimated by restricted maximum likelihood (REML). For each fitted model we obtained BLUPs for g′ = , conditionally on the markers Z = {ikz}, where G is the number of genotypes. All conditional models were of the form Γ that is a function of Z and Γ = {f(dii′)}, where dii′ is the Euclidean distance of genotypes i and i′, defined as iid′ = ||iz – iz′||, with i-th row of Z, and f(d) is some monotonically decreasing function of d. Some examples of the function f(d) are shown in Figure We considered different models for the variance of  used in ,7. The gg′ = g,g2,…,gG,A 5-fold cross-validation (CV) was performed to evaluate model performance. All phenotyped individuals were included in the CV, except those in the first generation. Overall 75 crosses (full sib families) were included. The dataset was randomly split into 5 subsamples each of which contained 15 crosses. In each CV round the phenotypic records for one of the five subsamples was held out and used as a validation set. Each subsample was held out and used as a validation set only once.The mean Pearson correlations between the GEBVs and observed values in the 5 replicates of the validation sets and between the true breeding values (TBVs) of the non-phenotyped individuals of the fifth generation and GEBVs were used as measures of accuracy.All mixed models were fitted using the REML method in the SAS MIXED procedure and the theoretical semivariograms in the SAS NLIN procedure.A high correlation was established between the semivariance and the genetic distance between pairs of individuals Fig. , suggestPre-selection of markers was evidently beneficial, with methods 1 and 2 achieving similar predictive accuracies and outperforming method 3 (Fig. Moreover, the extended model with heterogeneous variances between lowly and highly significant markers increased accuracy Table .Overall, RR with 2000 markers selected by method 2 and allowing for heterogeneous variances among the 100 most significant and the remaining 1900 markers gave the most accurate prediction of GEBVs for the fifth generation.We have evaluated how pre-selection of markers influences predictive accuracy in GS using RR and its spatial extensions via genetic distances. The spatial models differed in terms of the theoretical models used to model the empirical semivariogram among the genotypes as a function of their genetic distances of separation. All the fitted theoretical semivariogram models were remarkably similar within the range of the observed semivariogram values, and so were their predictions. This suggests that further study is needed to decide if modelling genetic covariances using non-linear spatial models is beneficial compared to RR, especially for non-additive genetic effects.Our results reinforce findings of other studies suggesting that pre-selecting markers may enhance predictive accuracy . For exaThe extended model with two variance components for the markers increased predictive accuracy because it better approximated the simulated genetic model with a few QTLs with different variances. Heterogeneous variance models may, however, not always exhibit superior performance. In particular, simulating many QTLs with small effects may lower the performance of models allowing for heterogeneous variances among individual markers .Pre-selection of markers was beneficial and increased predictive accuracy from 0.607 to 0.625. Partitioning markers into two groups with heterogeneous variances further increased accuracy up to 0.648 for the simulated dataset.The authors declare no competing interests.TSS participated in the design of the study, performed all analyses and drafted the manuscript. JOO helped draft the manuscript and interpret the results. HPP conceived the study, participated in its design, and helped in the final editing of the manuscript.


Genomic selection is an effective tool for animal and plant breeding, allowing effective individual selection without phenotypic records through the prediction of genomic breeding value (GBV). To date, genomic selection has focused on a single trait. However, actual breeding often targets multiple correlated traits, and, therefore, joint analysis taking into consideration the correlation between traits, which might result in more accurate GBV prediction than analyzing each trait separately, is suitable for multi-trait genomic selection. This would require an extension of the prediction model for single-trait GBV to multi-trait case. As the computational burden of multi-trait analysis is even higher than that of single-trait analysis, an effective computational method for constructing a multi-trait prediction model is also needed.We described a Bayesian regression model incorporating variable selection for jointly predicting GBVs of multiple traits and devised both an MCMC iteration and variational approximation for Bayesian estimation of parameters in this multi-trait model. The proposed Bayesian procedures with MCMC iteration and variational approximation were referred to as MCBayes and varBayes, respectively. Using simulated datasets of SNP genotypes and phenotypes for three traits with high and low heritabilities, we compared the accuracy in predicting GBVs between multi-trait and single-trait analyses as well as between MCBayes and varBayes. The results showed that, compared to single-trait analysis, multi-trait analysis enabled much more accurate GBV prediction for low-heritability traits correlated with high-heritability traits, by utilizing the correlation structure between traits, while the prediction accuracy for uncorrelated low-heritability traits was comparable or less with multi-trait analysis in comparison with single-trait analysis depending on the setting for prior probability that a SNP has zero effect. Although the prediction accuracy with varBayes was generally lower than with MCBayes, the loss in accuracy was slight. The computational time was greatly reduced with varBayes.In genomic selection for multiple correlated traits, multi-trait analysis was more beneficial than single-trait analysis and varBayes was much advantageous over MCBayes in computational time, which would outweigh the loss of prediction accuracy caused by the approximation procedure, and is thus considered a practical method of choice. A huge number of genome-wide polymorphisms have recently been elucidated in livestock and crops with the development of sequencing technologies. High-throughput genotyping systems, such as high-density SNP chips containing several tens or hundreds of thousands of genome-wide SNP markers and GBS (genotyping by sequence), have beπ, that a SNP has zero effect and is removed from the model was considered in the model fitting to obtain the best model explaining the phenotypes with a small number of SNP effects. A normal distribution with mean 0 and SNP-specific variance is assumed for the prior distribution of SNP effects in BayesB, as in BayesA, if SNPs are included in the model with probability 1-π and, otherwise, both the mean and variance are fixed at 0 with probability π.In the original study of genomic selection by Meuwissen et al., two Bayν and scale parameter S is adopted as the prior distribution of the variance. However, only the information of the relevant single SNP can be used for the posterior inference of this SNP-specific variance regardless of the number of genotypes or phenotypes. Due to the insufficient Bayesian learning for the variance, the degree of shrinkage for the estimates of SNP effects is largely influenced by the prior setting for ν and S in BayesA and BayesB indicates the expectations of parameters other than θk that are calculated with respect to every other parameter’s variational posteriors except qk(θk)  4] to muIn the simultaneous analysis of multiple traits for constructing a GBV prediction model, the computational burden greatly increases depending on the number of analyzed traits in comparison with single-trait analysis. We developed a variational approximation procedure, varBayes, for MCBayes to reduce the computational time for multi-trait analysis. In varBayes, the joint posterior distribution of parameters was approximated by a factorized function, each component of which approximated marginal posterior distribution of each parameter and was referred to as a variational posterior. Variational posteriors were shown to be well-known distribution functions such as normal or inverse Wishart that could be derived by simple non-MCMC based numerical iteration.In genomic selection, it is important to construct a model that enables accurate prediction for GVBs. Therefore, precise point estimation of the model parameters is more relevant rather than the construction of their posterior distributions. Accordingly, the evaluation of loss of prediction accuracy with varBayes in comparison with MCBayes would be suitable for the evaluation of approximation accuracy of varBayes. Using simulation experiments, we investigated the performance of the prediction model constructed with multi-trait analysis compared with single-trait analysis as well as the model constructed using variational approximation. Moreover, the performance of multi-trait analysis in the case of missing phenotypic records commonly occurring in the treatment of the actual data of multiple traits were evaluated based on the results of simulations. These points are discussed below including the computational time and the possible extension of prediction model considering polygenic effects.ρGAB = 0.72), prediction accuracy was increased with multi-trait analysis. As trait C was not genetically correlated with trait A, the accuracy of predicting the GBV of C was not improved with multi-trait MCBayes analysis. The accuracy of predicted GBV of trait B was also increased with multi-trait varBayes analysis in Data I and Data II in comparison with single-trait MCBayes analysis while the prediction accuracy of trait C was lower with multi-trait varBayes analysis . In Data I, where 100 replicates of datasets each including genotypes of 1010 SNPs for 1000 individuals were simulated, varBayes took only 12 minutes with Taking computational time and prediction accuracy into account, varBayes is considered a useful method for multi-trait genomic selection, which can rapidly construct a prediction model that is less accurate than that with the MCMC-based method for multi-trait analysis, but is more accurate than that with single-trait analysis for correlated traits. The usefulness of varBayes would be more remarkable for simultaneous prediction of GBVs of a large number of traits based on a huge number of SNPs where the application of an MCMC-based method might be prohibited.ρEAB = 0.1, ρEAC = 0.2, ρEBC = 0.3), the loss of prediction accuracy caused by missing phenotypes was anticipated to be less with multi-trait analysis than with single-trait analysis. We expected that, in Data III, the prediction accuracy of trait C, environmentally correlated with trait A (ρEAC = 0.2), was maintained higher in the presence of missing records for some phenotypes using multi-trait analysis in comparison with single-trait analysis. However, the rate of loss for the prediction accuracy for trait C was similar between multi-trait and single-trait analyses as seen in the comparison of the prediction accuracies between Data I and Data III , which indicates that residual effects of missing phenotypes can be restored from those of observed phenotypes. When the model fitting is successful for observed phenotypes, the residual effects of the phenotypes are well estimated by subtracting SNP effects and other fixed effects from the phenotypic effects, and those of missing phenotypes are suitably obtained by (18) utilizing the environmental correlation (covariance) between observed and missing phenotypes. Therefore, by assuming non-zero environmental correlation between traits (We can modify the Bayesian model (1) by including polygenic effects as follows;vi is a vector of polygenic effects for multiple traits and assumed to follow a multivariate normal distribution, vi ~ N with Σv being a variance-covariance matrix of polygenic effects. The polygenic effects for all individuals of a training population and a test population are collectively denoted by V, then the variance-covariance matrix of V can be expressed as A ⊗ Σv, where A is additive genetic relationship matrix for analyzed individuals, computed from the information of pedigree or markers. When the low-density markers are used for the analysis, a considerable portion of genetic effects could not be captured by markers. Accordingly, if pedigree information is available, inclusion of polygenic effects estimated based on pedigree is beneficial in predicting breeding values for genomic selection. The revised model (19) can be similarly treated by MCBayes and varBayes as the model (1), where estimation steps for additional covariates and parameters, V and Σv, can be easily implemented in the procedures of Bayesian multi-trait model construction using MCMC iteration and variational approximation. When no pedigree information is available, A is computed from marker information as a genomic relationship matrix. However, the model (19) includes all available markers as covariates, resulting in redundantly using the same marker information in the model fitting. In the availability of high-density SNP markers, which is the case for some species of animals and plants currently, the genetic relationships between individuals can be well captured by markers themselves in the multi-locus model (1), the benefit from the inclusion of the polygenic effects in the model would be subtle[where e subtle.In this study, we described a statistical model for Bayesian simultaneous prediction of GBVs in genomic selection targeting multiple traits and devised an MCMC-based method and a computationally cost-effective method utilizing the variational approximation procedure, referred to as MCBayes and varBayes, respectively, to estimate parameters included in the model. The results of simulation experiments showed that the multi-trait analysis that could utilize the correlation structure between traits allowed more accurate prediction of GBVs for correlated traits compared to single-trait analysis that treated each trait separately, where, for low-heritability traits correlated with high-heritability traits, the prediction accuracy for GBVs was remarkably improved with multi-trait analysis. Although the prediction accuracy with varBayes was lower than that with MCBayes in multi-trait analysis, the rate of loss in accuracy was moderate and the accuracy for correlated low-heritability traits was still higher with varBayes analysis compared to single-trait analysis. Considering the benefit of greatly reduced computational time, varBayes was considered to be a practical method for predicting GBVs in multi-trait genomic selection.The authors declare that they have no competing interests.TH devised Bayesian prediction methods for the genomic selection of multiple traits, developed a program for simulations and drafted the manuscript. HI assisted in developing a program and drafted the final manuscript. Both authors read and approved the final manuscript.Derivation of full conditional posterior distributions of parameters in a statistical model.Click here for fileDerivation of variational posteriors for parameters in a statistical model.Click here for file


FIN = 11 266) not selected for IA, to assess the association of previously identified IA candidate loci (n = 19) with BP. We defined systolic BP (SBP), diastolic BP, mean arterial pressure, and pulse pressure as quantitative outcome variables. The most significant result was further tested for association in the ICBP-GWAS cohort of 200 000 individuals. We found that the suggestive IA locus at 5q23.2 in PRDM6 was significantly associated with SBP in individuals of European descent . The risk allele of IA was associated with higher SBP. PRDM6 encodes a protein predominantly expressed in vascular smooth muscle cells. Our study connects a complex disease (IA) locus with a common risk factor for the disease (SBP). We hypothesize that common variants in PRDM6 can contribute to altered vascular wall structure, hence increasing SBP and predisposing to IA. True positive associations often fail to reach genome-wide significance in GWAS. Our findings show that analysis of traditional risk factors as intermediate phenotypes is an effective tool for deciphering hidden heritability. Further, we demonstrate that common disease loci identified in a population isolate may bear wider significance.Although genome-wide association studies (GWAS) have identified hundreds of complex trait loci, the pathomechanisms of most remain elusive. Studying the genetics of risk factors predisposing to disease is an attractive approach to identify targets for functional studies. Intracranial aneurysms (IA) are rupture-prone pouches at cerebral artery branching sites. IA is a complex disease for which GWAS have identified five loci with strong association and a further 14 loci with suggestive association. To decipher potential underlying disease mechanisms, we tested whether there are IA loci that convey their effect through elevating blood pressure (BP), a strong risk factor of IA. We performed a meta-analysis of four population-based Finnish cohorts  aim to detect common genetic variations that associate with complex traits or diseases. Although GWAS have been successful in identifying strongly associated genetic loci, they lack the means to point out true, but less strong, associations. Studying conditions that are related to the disease of interest can help sort out less strong associations. Intracranial aneurysms (IA) are berry-like dilations in cerebral arteries. Most IAs do not give symptoms until they bleed, causing a highly fatal form of stroke. Half of the people who suffer bleeding of an IA die. IA is a complex disease. Both inherited risk and environmental factors contribute to the risk of developing IA. Women, smokers, those with high alcohol intake or high blood pressure are more prone to develop IA and bleeding. GWAS found 19 genetic regions increasing the risk of IA. Here we show that one of these loci, on the long arm of chromosome 5, in addition to raising IA risk also increases systolic blood pressure. We speculate that the cause is modified vascular wall structure. Intracranial aneurysms (IA) are berry-shaped pouches at the branching sites of cerebral arteries. 2–5% of the world population is estimated to harbor IA Our understanding of the environmental and genetic background of IA formation is limited. Positive family history of IA or SAH, older age and female sex increase the risk of developing IA Multiple factors, such as familial aggregation of the disease, make a genetic contribution likely to the risk of IA. A minority of IAs show familial aggregation (under 10%) Despite the success of GWAS in identifying IA susceptibility loci, the pathomechanism by which they contribute to IA formation remains elusive. We hypothesize that hypertension, a strong modifiable risk factor of IA, may possess an overlapping genetic background with IA. To test this hypothesis, we analyzed the IA loci so far identified, in well-characterized population-based cohorts consisting of more than 210 000 individuals with blood pressure measurements.41 SNPs from 19 independent IA loci rs570682 = 4.80E-05, prs2287696 = 6.81E-05, prs335206 = 3.01E-05) , had on average 1.3 Hgmm higher SBP compared to those who were homozygous for the protective allele, and 0.9 Hgmm higher than those with the heterozygous genotype. This effect size is comparable to those of most blood pressure loci identified by The International Consortium for Blood Pressure Genome-wide Association Studies (ICBP-GWAS) consortium rs570682 = 0.02, prs2287696 = 0.04, prs335206 = 0.03) and MAP  showed a reduction of significance when results were combined from all cohorts  . Compari.01E-05) . Study p cohorts .rs570682 = 0.0065, prs2287696 = 0.00079, prs335206 = 0.0014) in the ICBP-GWAS cohort of 200 000 individuals of European descent. The risk allele for elevated SBP in the ICBP-GWAS cohort was the same as in our meta-analysis of four Finnish population-based cohorts. When the results from the four Finnish cohorts were combined with the ICBP-GWAS results in a fixed effect meta-analysis, the strength of the association increased with all three SNPs tested (ALL = 8.13E-07). This suggests that the variant at 5q23.2 is a common risk factor present in multiple populations of European descent. Further loci or results for DBP or MAP were not tested for association in ICBP-GWAS, since they failed to show significant association in our replication cohorts.To test whether the association at the 5q23.2 locus is unique to the Finnish cohorts, we attempted to replicate the association with the three SNPs in the multinational cohort ICBP-GWAS s tested . The strPR domain containing 6 (short form: PRDM6) and showed comparable p-values. To further explore the associated region in an attempt to pinpoint the causative variant, we examined all 1000 Genomes variants around PRDM6 in the four Finnish cohorts  is just downstream from the region of association . In our two tier approach, the discovery cohort (ndiscovery = 1581) was a subsample of the H2000 replication = 8312) consisted of the YFS (n = 1874) Four Finnish population-based cohorts were included in our study . These cThe ICBP-GWAS represents a union of numerous prior blood pressure GWAS consortia to create a discovery meta-analysis of over 200 000 individuals of European ancestry. NFBC1966 is part of the ICBP-GWAS; however, this overlap does not represent a significant risk for bias, due to the small relative contribution of NFBC1966 to the ICBP-GWAS results.All Finnish cohorts were genotyped using Illumina arrays : Illumina Infinium HD Human610-Quad BeadChip for H2000, Illumina HumanCNV370-Duo BeadChip for NFBC1966, and Illumina Human670K custom BeadChip for YFS and HBCS. For SNPs to be successfully genotyped, a per individual and per marker success rate minimum of 95% was defined as default. 36 out of 41 candidate SNPs were successfully genotyped in all cohorts. For SNPs with no directly genotyped data available, we imputed genotypes with MACH PRDM6 was tested for association in the ICBP-GWAS Candidate loci were selected based on IA GWAS results PRDM6. We took uncertainty of imputation into account by using the maximum likelihood estimates of the reference allele counts as genotypes . Fine mapping of the 5q23.2 region was performed with 1000G+HM3 imputed data. Results were plotted with LocusZoom To further investigate the strongest associated locus, we analyzed all 1000 Genomes variants, with minor allele frequency greater than 1%, in and around Figure S1Suggestive association with IA at 5q23.2 in GWAS  (PDF)Click here for additional data file.Figure S2Age distributions in the Finnish cohorts. In the NFBC1966 all were of the same age, since data utilized here were collected when the participants of the birth cohort were 31 years old. HBCS participants were older than the rest. (X-axis density = number of cohort participants).(PDF)Click here for additional data file.Figure S3Comparing causality and pleiotropy as possible explanations of the overlapping association between IA and SBP.(PDF)Click here for additional data file.Table S1Association results in the discovery cohort (H2000) of representative SNPs from the 19 regions tested. Association with systolic blood pressure (SBP), diastolic blood pressure (DBP), mean arterial pressure (MAP) and pulse pressure (PP) were tested with the ROBUST model (age and gender as covariates).(DOC)Click here for additional data file.Table S22q33.1 and 5q23.2 loci cohort-wise ADVANCED model effect estimates and meta-analysis results with diastolic blood pressure (DBP) and mean arterial pressure (MAP).(DOC)Click here for additional data file.Text S1Full list of The International Consortium for Blood Pressure Genome-Wide Association Studies (ICBP-GWAS) co-authors, with affiliations.(DOC)Click here for additional data file.


Mastitis is the most costly disease for dairy production, and control of the disease is often difficult, due to its multi-factorial nature. Susceptibility to mastitis is under partial genetic control and the industry uses indirect selection for decreased concentrations of somatic cells in milk to reduce mastitis.A genome-wide scan was performed to identify genomic regions associated with deregressed estimated breeding values (EBVs) for somatic cell counts (SCC) in Holstein bulls. In total 1183 proven bulls of the Italian of Holstein population, were genotyped with the BovineSNP50 BeadChip  and a whole genome association analysis was performed using the R package GenABEL.-6) and a region on chromosome 6 with moderate significance (P < 5x10-5).Two chromosomal regions showed association with SCC, a region on chromosome 14 with high significance (P < 5x10Two regions with effects on SCC have been identified with good statistical support. A further study of these candidate regions will be performed to verify the results and identify the causal mutations. Mastitis, an inflammation of the mammary gland caused by an infection with a range of bacteria, is the most costly disease for dairy production. Control of mastitis is difficult due to its multi-factorial nature. Susceptibility to mastitis is under partial genetic control and the industry uses selection on a correlated trait (somatic cells score in milk), to reduce mastitis incidence in the population. Over the last few years, several studies have identified genetic loci putatively associated with somatic cell counts or clinical mastitis ,2. The aThe bulls chosen for the genome wide association study were selected from among the 3155 animals progeny tested in Italy with DNA samples available. All these bulls will be used by the Italian National breeders association of Holstein Frisian Cattle (ANAFI) to perform national genomic evaluations.Selection criteria used for association studies were intended to obtain: i) bulls with high selection index reliability (PFT > 0.75%); and ii) as low relationships between animals in the dataset as possible by trying to keep as many families (father – son couples) as possible. Among the 3155 bulls with biological material available 2109 bulls had appropriate criteria to be included in the study, 1183 of which had been already genotyped with the Bovine 50K SNP chip .The EBV for SCC had a mean of 98.73 ± 5.3 for the 2109 bulls, and a mean 98.77 ± 6.3 in the cohort of 1183 animals included in the study. Furthermore, deregressed EBVs (DR-EBVs) had mean of 0 and a standard deviation of 5. The DR-EBVs and reliabilities for somatic cell counts were derived from a reduced animal model for single records on a single trait. The strategy used to estimate the deregressed estimates was a simplified version of the algorithm of Jamrozik et al. [-7 were accepted to represent very strong proof of genome-wide association, while p-values between 5 x 10-7 and 5 x 10-5 were considered as moderately significant associations.Genome-wide association analysis was performed with the GenABEL package in R using a three step GRAMMAR-CG approach, (Genome wide Association using Mixed Model and Regression - Genomic Control) ,5. UncorA total of 1183 progeny tested bulls were genotyped with the BovineSNP50 BeadChip . Genotype quality assurance was performed within the R statistical environment using the GenABEL package (“check.marker” function) . SNPs weFollowing quality control checks, 641 markers were excluded because of low call rate and 11404 markers were excluded because of low minor allele frequency. Furthermore, markers on the sex chromosomes were removed from the analysis. A total of 8 samples were removed because of low call rate and other 2 were eliminated because of high autosomal heterozygosity (FDR < 1%). Mean heterozygosity of the dataset after quality check was 0.33 ± 0.01, while the samples removed had heterozygosity higher than 0.63, indicating possible sample contamination. No samples were removed due to high IBS (Identity By State). Mean IBS was 0.70 ± 0.01, based on 2000 autosomal markers, while the threshold for IBS was set to > 0.95. No outliers were identified by Classical Multi Dimension Scaling (MDS).After quality controls, the final dataset used in the following association analysis contained 1173 samples and 41209 Genome wide SNPs.-6) and a region on chromosome 6 with moderate significance (P < 5x10-5). These two chromosome regions should be further tested to confirm these associations and to potentially identify the causative variations that affect this trait.Two chromosomal regions showed associations with SCC, a region on chromosome 14 with high significance (P < 5x10A recent review of QTL reported on chromosome 14  identifiFurthermore Nilsen et al,  characteThe authors declare that they have no competing interests.GM and JLW wrote the manuscript. JLW and PAM conceived the study. ELN extracted the phenotypic and pedigree information and defined the selection criteria. RN coordinated the sample collection and DNA preparation. GM performed statistical analysis. AS and FS contributed to the data analysis. All authors revised the paper, and approved the final manuscript.


Such a dimension reduction is able to group highly correlated predictors and allows for collinear or nearly collinear markers. Different from BayesB, which predetermines hyperparameters, POCRE uses an empirical Bayes thresholding method to obtain data-driven optimal hyperparameters and effectively select important markers when constructing each component. Demonstrated through simulation studies, POCRE greatly reduces the computing time compared with BayesB. On the other hand, unlike fBayesB which slightly sacrifices prediction accuracy for fast computation, POCRE provides similar or even better accuracy of predicting breeding values than BayesB in both simulation studies and real data analyses.Recent advances in high-throughput genotyping have motivated genomic selection using high-density markers. However, an increasingly large number of markers brings up both statistical and computational issues and makes it difficult to estimate the breeding values. We propose to apply the penalized orthogonal-components regression (POCRE) method to estimate breeding values. As a supervised dimension reduction method, POCRE sequentially constructs linear combinations of markers,  The advantages of using genome-wide genetic markers to estimate the breeding values have been widely recognized . Recent A variety of methods have been proposed to estimate the total breeding value, for example, least squares (LS) approach, best linear unbiased prediction (BLUP), and Bayesian methods . With a L1 penalty function can enable variable selection has recently motivated many penalized least squares methods to fit high-dimensional linear regression models, such as lasso proposed by The fact that an Here we propose to apply the penalized orthogonal-components regression (POCRE) to estimate/predict breeding values and therefore enforce genomic selection. POCRE was proposed by On the basis of simulation studies, p markers genotyped from a total of n individuals, the classical regression model can be written asYn×1 collects the phenotypic value of all individuals, Xn×p represents the genotype information of all individuals, μ is an overall mean of polygenic effects, pβ×1 corresponds to the effect of each marker, and ε is the error term. Because typical genomic selection presents many more markers than individuals, in other words, p ≫ n, special algorithms are needed to estimate β. p ≫ n data.With Y and X are centralized, and accordingly, assume μ = 0 in k ≥ 2, are iteratively built to be orthogonal to kω, k ≥ 1, is obtained as α minimizesλg(γ) is a penalty function defined by a proper regularization on γ with tuning parameter λ.Assume that both λg(γ) ≡ 0, the optimal γ solving λg(γ). While POCRE0 directly applies the empirical Bayes thresholding method, POCRE applies it to the statistics from Fisher’s z-transformation. Such penalty helps estimating covariance between phenotype and genotypes, and it provides adaptively sparse loadings of orthogonal components. The empirical Bayes implementation is also computationally efficient. The tuning parameter λ can be appropriately set to account for possible dependence structure among different markers.When γ solving Y. Then regressing Y on the orthogonal components, i.e.β1,…, pβ in Model 1. Since non-zero loadings in jω, j = 1, 2,…, are sparse, most of the estimated β1,…, pβ are therefore zero, reflecting the fact that most markers do not (significantly) contribute to predicting phenotypic values, as discussed in the literature, e.g.λg(γ) ≡ 0 in The sequential construction of the orthogonal components stops when the optimal λ is used to account for possible dependence structure among different markers, it can be chosen on the basis of previous experience with similar studies. In the case of no experience with similar studies, a simulation study may be designed to utilize the available genotypic values and to reveal an appropriate choice of the tuning parameter. We will discuss several strategies on the basis of cross-validation (CV) to elicit a data-driven optimal value for the tuning parameter in the simulation studies.While the tuning parameter −5 and 2.5 × 10−3 for QTL and marker SNP, respectively, per locus per generation. On the basis of the genetic variance, environmental effects were generated from a Gaussian distribution with mean zero and variance calculated to meet the required heritability, which is 0.5 in the simulation. To establish mutation drift equilibrium, a population of 100  were allowed to randomly mate for 1000 generations. Each family produced 2 offspring. The population was expanded by twice in the next generation  and then by a factor of 10 in the following generations . The 2200 individuals at generations 1001 and 1002 were genotyped and phenotyped, respectively  were used in the analyses. Here we applied BayesB and compared it with POCRE and POCRE0 in terms of the computation time and the prediction accuracy, which is defined as the correlation between the estimated and true breeding values. For BayesB, the probability π that a SNP has zero effect is assessed empirically from the data, and the other hyperparameters were chosen following POCRE and POCREA striking nature of BayesB is that it employs a mixture prior for each regression coefficient in 0 methods provided better estimates of breeding values for generations 1001 and 1002 than BayesB. For POCRE and POCRE0 methods, their predictions of breeding values for generation 1003 were not only more accurate but also more robust than those of BayesB. Indeed, except for generation 1004 with POCRE0 (CV0), all POCRE implementations provided more robust predictions of breeding values than BayesB.As shown in 0, we observe that CV0 was the worst strategy as it always provided the lowest accuracy in predicting breeding values among all three strategies for both POCRE and POCRE0. For POCRE, CV1 performed the best by providing better prediction accuracy than the other two. However, for POCRE0, CV2 provided the best prediction accuracy in generations 1003–1005, whereas CV1 provided the best prediction accuracy in generations 1006 and 1007. In general, prediction accuracy between CV1 and CV2 was only slightly different for both POCRE and POCRE0. All cross-validation strategies were similarly robust in predicting breeding values. Therefore, we suggest using either CV1 or CV2 scheme for cross-validation to choose the tuning parameters for both POCRE and POCRE0.When comparing the three different strategies of cross-validation for both POCRE and POCREβ, can be used to evaluate the bias of genomic selection methods. With β = 1, the method provides unbiased prediction of the breeding values; β < 1 implies an overestimated breeding value, and β > 1 implies an underestimated breeding value. β of all methods across different generations. The predictions of all methods alternated between overestimate and underestimate from generations 1003 to 1007. That is, these methods all overestimated/overpredicted the breeding values in generations 1001/1002, 1004, and 1006, but they underpredicted the breeding values in generations 1003, 1005, and 1007. In general, all methods performed quite well in predicting the breeding values in terms of bias.It is well known that the coefficient in a non-intercept simple regression of TBV against EBV, denoted as 0 were similar and both took much less time than BayesB. Specifically, BayesB took 14,685.12 sec for one dataset based on 5,000 burn-ins and another 5000 iterations for inference.As one of the primary goals of this study was to propose a fast approach for genomic selection, we compared the computing time of BayesB with POCRE. All methods were programmed in MATLAB, and all simulated data were analyzed on a Linux server with dual Intel Xeon Quad-Core 5410 2.33 GHz processors without taking advantage of parallel computation. We witnessed that the computing times for POCRE and POCRE0 need to be elicited through cross-validation, the computation time relies on the number of folds for cross-validation and the number of candidate values searched for the tuning parameter. For example, when a 10-fold cross-validation is utilized to search the tuning parameter from the pool {0.7, 0.71,…, 0.8}, 101 datasets need to be analyzed by either POCRE or POCRE0 for choosing the tuning parameter; therefore, it took about 1010 sec to search for the optimal tuning parameter and another 10 sec to fit the model. Hence, the computation time is about 1/14 of that of BayesB. To further reduce the computation time of POCRE and POCRE0, some strategies (discussed later) can be designed to search for a much smaller number of candidate tuning parameter values during cross-validation, and the number of folds can be reduced when a large number of individuals is available. Indeed, available multiple processors in many computers imply that parallel computation can greatly shorten the computing time of POCRE and POCRE0.When the tuning parameters of POCRE and POCREAlthough genomic selection emerged from dairy cattle breeding programs, it is also useful to plant breeding programs . To furtThe pine dataset consists of 850 individuals and 4698 SNPs. Missing genotypes were imputed by sampling alleles from a Bernoulli distribution with variance equal to locus allele frequency. Individuals and SNPs having more than 20% missing values were removed from the data before the analysis. Diameter at breast height (DBH) and height (HT) were collected for pine trees in Nassau that were used in our analysis. Details of this data are referred to in 0 to evaluate their performance with 10-fold cross-validation because independent validation population is not available. As shown in 0 yielded similar accuracies. Indeed, POCRE provided more robust accuracies for both DBH and HT traits. Accuracies of estimated breeding values for POCRE were also better than POCRE0, except in the training data of HT trait. The results of POCRE and POCRE0 were similar in terms of the bias as shown in Here we applied POCRE and POCREThis data were collected from a maize study on flowering time  to fill corr, was estimated to assess the accuracy of genomic selection. Indeed, h2 referring to the heritability.We randomly split the data into training and test sets of sizes 3500 and 1392, respectively, to evaluate the performance of our method. Five replicates were carried out to test the accuracy, which results in five pairs of training and test sets. Without the true breeding values (TBV), we can estimate them using either the original phenotypic values (termed PEBV hereafter) or genotypic values (termed GEBV hereafter) with BayesB or POCRE. The correlation between PEBV and GEBV, that is, 0 to analyze the whole-genome dataset, with 5-fold cross-validation to elicit the tuning parameters. corr averaged at 0.9381, and POCRE0 at 0.9426; both are very close to the estimated heritability 94%. Both methods are robust in estimating the breeding values of the training datasets. For the test datasets, both methods provided robust estimates of breeding values, with estimated standard deviations 0.0045 and 0.0039 for POCRE and POCRE0, respectively, without the first replicate. With the large number of SNPs included in this example, it was computationally intensive to run the Markov chain Monte Carlo for BayesB. Therefore, we only applied POCRE and POCRE0, we chose 2000 SNPs based on univariate tests performed for each SNP separately. From the SNPs with P-values less than 0.0001, we randomly selected 200 SNPs, and we chose 1800 SNPs from those with P-values greater than 0.0001. With the selected 2000 SNPs, we applied all methods to re-analyze the five replicates. Five-fold cross-validation was employed to elicit the tuning parameter for POCRE and POCRE0. The results are summarized in 0 provided the larger estimate of corr for the training datasets, and they predicted the breeding values with better accuracy and more robustly than BayesB. Note that with only 2000 SNPs, corr estimated from the test datasets are smaller than those presented in To compare BayesB, POCRE, and POCRE0 are comparable to that of BayesB in simulation studies, and their performance is much better than BayesB in analyzing maize flowering time data. Second, POCRE and POCRE0 enjoy enormous computational advantage over BayesB. Finally, POCRE and POCRE0 make it feasible to analyze data with a huge number of markers. For example, both POCRE and POCRE0  took about 36 hr to analyze the maize flowering time data, which includes a total of 284,025 SNPs for each of the 5000 genetic lines. This is promising because current high-throughput biotechnologies routinely genotype millions of markers. Our proposed method has the potential to take advantage of such high-dimensional data that may challenge the genomic selection.Here we present alternative approaches for genomic selection that provide competitive prediction of breeding values and also significantly reduce the computing time. First, note that the prediction accuracy of both POCRE and POCRE0. While cross-validation is a popular method to select the tuning parameter, it may not be optimum as shown in our simulation studies and others (Results from both simulation studies and real data analysis showed the importance of the tuning parameter for the performance of POCRE and POCREAs evidenced in the simulation studies, selecting the tuning parameter using cross-validation should also consider the possible population structure in the data. The time usage for cross-validation relies on the number of folds and number of potential tuning parameter values under investigation. Parallel computation can significantly reduce the computation time of cross-validation. As genomic selection datasets usually include a large number of individuals, we can choose the number of folds as small as two. We have considered a grid search of the optimal tuning parameter in the simulation studies and real data analysis. For a strategic thorough search, we may first take a coarse grid to search and then look into a finer interval suggested from the initial coarse grid search. On the other hand, some targeted simulation studies may be designed to shed light on the optimal tuning parameter for a specific study.


Genome-wide association studies (GWAS) are now used routinely to identify SNPs associated with complex human phenotypes. In several cases, multiple variants within a gene contribute independently to disease risk. Here we introduce a novel Gene-Wide Significance (GWiS) test that uses greedy Bayesian model selection to identify the independent effects within a gene, which are combined to generate a stronger statistical signal. Permutation tests provide p-values that correct for the number of independent tests genome-wide and within each genetic locus. When applied to a dataset comprising 2.5 million SNPs in up to 8,000 individuals measured for various electrocardiography (ECG) parameters, this method identifies more validated associations than conventional GWAS approaches. The method also provides, for the first time, systematic assessments of the number of independent effects within a gene and the fraction of disease-associated genes housing multiple independent effects, observed at 35%–50% of loci in our study. This method can be generalized to other study designs, retains power for low-frequency alleles, and provides gene-based p-values that are directly compatible for pathway-based meta-analysis. Genome-wide association studies (GWAS) have successfully identified genetic variants associated with complex human phenotypes. Despite a proliferation of analysis methods, most studies rely on simple, robust SNP–by–SNP univariate tests with ever-larger population sizes. Here we introduce a new test motivated by the biological hypothesis that a single gene may contain multiple variants that contribute independently to a trait. Applied to simulated phenotypes with real genotypes, our new method, Gene-Wide Significance (GWiS), has better power to identify true associations than traditional univariate methods, previous Bayesian methods, popular L1 regularized (LASSO) multivariate regression, and other approaches. GWiS retains power for low-frequency alleles that are increasingly important for personal genetics, and it is the only method tested that accurately estimates the number of independent effects within a gene. When applied to human data for multiple ECG traits, GWiS identifies more genome-wide significant loci  than any other method. We estimate that 35%–50% of ECG trait loci are likely to have multiple independent effects, suggesting that our method will reveal previously unidentified associations when applied to existing data and will improve power for future association studies. Traditional single-SNP GWAS methods have been remarkably successful in identifying genetic associations, including those for various ECG parameters in recent studies of PR interval  One analytical approach, gene-based tests proposed during the initial development of GWAS Despite these appealing properties, gene-based and related multi-marker association tests have generally under-performed single-locus tests when assessed with real data Multi-locus tests often have the additional practical drawback of being highly CPU and memory intensive. Several methods use Bayesian statistics to drive a brute-force sum or Monte Carlo sample over models ad hoc follow-up analyses to identify additional independent association signals in loci with genome-wide significant primary associations.The Gene-Wide Significance (GWiS) test addresses these problems by performing model selection simultaneously with parameter estimation and significance testing in a computational framework that is feasible for genome-wide SNP data (see Methods). Model selection, defined as identifying the best tagging SNP for each independent effect within a gene, uses the Bayesian model likelihood as the test statistic The ECG parameters PR interval, QRS interval and QT interval are ideal test cases because recent large-scale GWAS studies have established known positive associations. These traits are all clinically relevant, with increased PR interval associated with increased risk of atrial fibrillation and stroke Homo sapiens genome build 35.1 reference assembly The SNPs were assigned to genes based on the NCBI The “gold standard” known positives rely on previously published meta-analyses of PR interval L1 regularized regression, is a multivariate method that combines sparse model selection and parameter optimzation The minSNP test uses the p-value for the best single SNP within a gene. The minSNP-P test converts this SNP-based p-value to a gene-based p-value by performing permutation tests within each gene. BIMBAM averages the Bayes Factors for subsets of SNPs within a gene, with restriction to single-SNP models recommended for genome-wide applications Power calculations used genotypes from the ARIC population to ensure realistic LD. Phenotypes were then simulated for genetic models with one or more causal variants within a gene. GWiS was the best-performing method, with an advantage growing as more independent effects are present . TheoretOf the other methods, minSNP-P and BIMBAM had similar performance that degraded as the true model included more SNPs. The VEGAS test did not perform well, presumably because the sum over all SNPs creates a bias to find causal variants in LD blocks represented by many SNPs and to miss variants in LD blocks with few SNPs. In the absence of LD, with genotypes and phenotype simulated using PLINK The advantage of GWiS arises in part from better power to detect associations with low-frequency alleles . GWiS, mThe model size selected by GWiS and LASSO was evaluated by simulation . These sGWiS provides a better estimate of the true model size than LASSO, assessed from the ow power  and 0.81ow power . GWiS alow power .Removing a causal SNP results in GWiS predicting a smaller model, with the ratio of estimated to true These results demonstrate that the model size returned by GWiS is conservative for causal variants with small effects, and approaches the true model size for causal variants with large effects.We then obtained p-values from GWiS, minSNP, minSNP-P, BIMBAM, VEGAS, and LASSO for the ARIC data. Permutations of phenotype data holding genotypes fixed GWiS out-performed all other methods in the comparison . GWiS idDue to the limited size of the ARIC cohort relative to the studies that generated the known positives, no method was expected to find all 38 known loci to be genome-wide significant. Nevertheless, known positives should still rank high among the top predictions of each method, assessed by the ranks of the known positives at 40% recall . We founinterval , S4, S5.While our conclusions are based on cardiovascular phenotypes, the results suggest that GWiS will have an advantage when causal genes have multiple effects. When an association is sufficiently strong to be found by a univariate test, GWiS is generally able to identify it. Beyond these association, GWiS is also able to detect genes that are genome-wide significant, but where no single effect is large enough to be significant by univariate tests. The association of QRS interval with SCN5A-SCN10A is a striking example: 4 independent effects are found by GWiS  . A commoinSNP-P)  demonstrOf the 38 known positives, 20 have GWiS models with at least one SNP (regardless of genome-wide significance), and 7 of these are predicted to have multiple independent effects . These rIn summary, we describe a new method for gene-based tests of association. By gathering multiple independent effects into a single test, GWiS has greater power than conventional tests to identify genes with multiple causal variants. GWiS also retains power for low-frequency minor alleles that are increasingly important for personal genetics, a feature not shared by other multi-SNP tests.Furthermore, GWiS provides an accurate, conservative estimate for the number of independent effects within a gene or region. Currently there are no standard criteria for establishing the genome-wide significance of a weak second association in a gene whose strongest effect is genome-wide significant. While the number of effects can be provided by existing Bayesian methods The test we describe includes a prior on models designed to be unaffected by SNP density, in particular by the number of SNPs that are well-correlated with a causal variant. The priors on regression parameters are essentially uniform, with the benefit of eliminating any user-adjustable parameters. A theoretical drawback is that the priors are improper Bayesian methods can be computationally expensive. GWiS minimizes computation by evaluating only the locally optimal models of increasing size in a greedy forward search. This appears to be an approximation compared to previous Bayesian methods that sum over all models. Previous Bayesian methods entail their own approximations, however, because the search space must either be truncated at 1 or 2 SNPs, heavily pruned, or lightly sampled using Monte Carlo. Our results demonstrate that the approximations used by GWiS provide greater computational efficiency than approximations used in previous Bayesian frameworks, with no loss of statistical power. GWiS currently calculates p-values, rather than Bayesian evidence provided by other Bayesian methods. If Bayesian evidence is desired, an intriguing alternative to Bayesian post-processing of candidate loci might be to use the Bayes Factor from the most likely alternative model identified by GWiS as a proxy for the sum over all alternatives to the null model. This may be an accurate approximation because, in practice, the Bayes Factor for the most likely model from GWiS dominates all other Bayes Factors in the sum.The GWiS framework, using gene annotations to structure Bayesian model selection, may be applied to case-control data by encoding phenotypes as 1 (case) versus 0 (control), a reasonable approach when effects are small. More fundamental extensions to logistic regression, Transmission Disequilibrium Tests (TDTs), and other tests and designs should be possible and may yield further improvements. Moreover, similar gene-based structured searches can be applied to genetic models to include explicit interaction terms This research involves only the study of existing data with information recorded in such a manner that the subjects cannot be identified directly or through identifiers linked to the subjects.Known positive associations are taken from published genome-wide significant SNP associations  enrolled in 1987-89 and prospectively followed Y for N individuals is an X has N rows and P columns, one for each of P genotyped markers assumed to be biallelic SNPs. For simplicity, the vector Y and each column of X are standardized to have zero mean. A standard regression model estimates the phenotype vector as b is a vector of regression coefficients and e is a vector of residuals assumed to be independent and normally distributed with mean 0 and variance The phenotype vector The maximum likelihood estimators (MLEs) are F-statistic to decide whether adding a new SNP improves the model significantly,K SNPs, distributed as M total SNPs, because the A conventional multiple regression approach uses the M is defined as the subset of P total SNPs that are permitted to have non-zero regression coefficients. For each gene, GWiS attempts to find the subset that maximizes the model probability P columns of X corresponds to a SNP assigned to the gene. In the absence of association, the null model with A model The factor P SNPs within the gene has an identical probability of being associated with the trait. This probability, denoted f, is unknown, and is integrated out with a uniform prior. The prior is also designed to make the model probability insensitive to SNP density: it should be unaffected if an existing SNP is replicated to create a new SNP marker with identical genotypes. We do this by replacing the number of SNPs within a gene with an effective number of tests, The prior probability of the model, The remaining factor in Eq. 4 isThe integration limits and prefactor The log-likelihood is thenAs in the BIC approximation, we retain only terms that depend on the model and are of order The strategy of GWiS is therefore to find the model that maximizes the objective functionThe terms involving GWiS is designed to select a single model for each gene. An alternative related approach would be to test for the posterior probability of the null model, The effective number of tests is an established concept in GWAS to provide a multiple-testing correction for correlated markers. While the exact correction can be established by permutation tests, faster approximate methods can perform well i is standardized to have zero mean. Correlations between all pairs of SNPs i and j are initialized as T is initialized to 0. The SNP i with maximum weight is identified, and the following updates are executed:The method we adopt is based on multiple linear regression of SNPs on SNPs. The genotype vector T. Model selection may therefore have a conservative bias. The p-values are not affected, however, because they are calculated by permutation tests as described below.This process continues until all weights are equal to zero. When SNPs with maximum weight are tied (as occurs for the first SNP processed), the SNP with lowest genomic coordinate is selected to ensure reproducibility; we have ensured that this method is robust to other methods for breaking ties, including random selection. For simplicity, the correlations are not updated , that does not affect the test statistic. Letting We use two stages of permutation tests: the first stage converts the GWiS test statistic into a p-value that is uniform under the null; the second stage establishes the p-value threshold for genome-wide significance.S successes  out of Q permutations, the empirical p-value is S/Q. To save computation, permutations are ended when Q = 1 million trials, regardless of S. In these cases, for purposes of ranking, a parametric p-value is estimated for GWiS asThe first stage is conducted gene-by-gene. We permute the trait array using the Fisher-Yates shuffle algorithm F statistic from the MLE fit, and the second term is the combinatorial factor for the number of possible models of the same size.The first factor is the parametric p-value for the While these p-values are uniform under the null, the threshold for genome-wide significance requires a second set of permutations. To establish genome-wide significance thresholds, in the second stage we permuted the ARIC phenotype for each trait 100 times, ran GWiS for the permuted phenotypes on the entire genome, and recorded the best genome-wide p-value from each of the 100 permutations. We then combined the results from each trait to obtain an empirical distribution of the best genome-wide p-value under the null. We then estimated the p = 0.05 genome-wide significance threshold as the 15th best p-value of the 300. This procedure was performed for GWiS, minSNP, minSNP-P, LASSO, and VEGAS to obtain genome-wide significance thresholds for each. Since minSNP-P and BIMBAM are both uniform under the null, we used the genome-wide significance threshold calculated for minSNP-P, nal cost . The thrIn a region with a strong association and LD, GWiS can generate significant p-values for multiple genes in a region. A hierarchical version of GWiS is used to distinguish between two possibilities. First, through LD, a strong association in one gene may cause a weaker association signal in a second gene. In this case, only the strong association should be reported. Second, the causal variant may not be localized in a single gene; for example, the best SNP tags are assigned to multiple genes. In this case, the individual genes should be merged into a single associated locus. The hierarchical procedure is as follows.Identify all genes with GWiS Run GWiS on the merged locus  and identify the SNPs selected by the GWiS model. If genes at either end of the locus have no GWiS SNPs, trim these genes from the locus. Repeat this step until no more trimming is possible. If only a single gene remains, accept it with its original p-value as the only association in the region. Otherwise, proceed to step 3.Use a permutation test to calculate the p-value for the merged locus from step 2. Assign it a p-value equal to the minimum of the p-values from the individual genes, and the p-value from its own permutation. Regardless of the p-value used, retain the entire trimmed region as an associated locus.The trimming in step 2 handles the first possibility, a strong association in one gene that causes a weaker association in a neighbor. The rationale for accepting the smallest p-value in step 3 is the case of a single SNP assigned to multiple genes. The merged region will have a less significant p-value than any single gene, and it does not seem reasonable to incur such a drastic penalty for gene overlap.F-statistic as the test statistic, with empirical p-values from permutation to ensure correct p-values for SNPs with low minor allele frequencies. The minSNP method assigns a gene the p-value of its best SNP. Selection of the best p-value out of many leads to non-uniform p-values under the null. It is standard to reduce this bias by scaling p-values by a Bonferroni correction based on the number of SNPs or number of estimated tests. Instead, we perform gene-by-gene permutation tests using the best F statistic for SNPs within the gene as the test statistic. As with GWiS, if 1 million permutations do not lead to one success, the association is clearly genome-wide significant and we use the Bonferroni-corrected p-value for ranking purposes.For these tests, SNPs are assigned to gene regions as before. The p-value for each SNP is then calculated using the The Bayesian Imputation-based Association Mapping (BIMBAM) is a Bayesian gene-based method The design matrix The sufficient statistics used by BIMBAM are identical to minSNP and minSNP-P, yet we found that the runtime of the public implementation was much slower, taking 270 sec for 1000 permutations of a gene with 135 SNPs across 8000 individuals. By improving memory management and optimizing computations, we improved the timing to 14 sec per 1000 permutations, a 19-fold speed-up. This implementation is included in our Supplementary Materials.The Versatile Gene-Based Test for Genome-wide Association (VEGAS) L1 regularized regression onto a computationally tractable quadratic optimization problem LASSO regression is a recent method for combined model selection and parameter estimation that maps To reduce computational cost, univariate p-values are estimated from parametric tests, and gene-based SNPs with As suggested previously, we used the Selection Index to rank genes and as the test statistic for a permutation p-value For each true model size of We attempted to distribute the total population variance explained, The power was calculated as (number of genes that are genome-wide significant)/1000, and the error of the estimate was calculated using 95% exact binomial confidence intervals. The p-value thresholds were taken directly from genome-wide permutations .Phenotypes that were used to estimate the model size were generated by assigning each “causal” SNP the same power of 0.1 and 0.8. The population variance explained for each SNP was calculated as Only GWiS and LASSO give model size estimates. GWiS directly reports the model size as the number of independent effects within a gene and LASSO reports the model size as the number of selected SNPs within a gene. We ran both methods using the simulated data with LD. We also tested both scenarios when the causal SNPs were kept or removed from gene.Gene associations were scored as true positives if the gene (or merged locus) overlapped with a known association, and as false positives if no overlap exists. Only the first hit to a known association spanning several genes was counted.The primary evaluation criterion is the ability to identify known positive associations at genome-wide significance. The genome-wide significance threshold was determined separately for each method (see above), and no method gave any false positives at its appropriate threshold.A secondary criterion was the ability to enrich highly ranked loci for known associations, regardless of genome-wide significance. This criterion was assessed through precision-recall curves, with precision  =  TP/(TP+FP), recall  =  TP/(TP+FN), and true positives (TP), false positives (FP), and false negatives (FN) defined as a function of the number of predictions considered.Small differences in precision and recall may not be statistically significant. To estimate statistical significance, we performed a Mann-Whitney rank sum test for the ranks of the known associations at 40% recall for GWiS, minSNP, minSNP-P, and LASSO.www.baderzone.org), and is being incorporated into PLINK GWiS runs efficiently in memory and CPU time, roughly equivalent to other genome-wide tests that require permutations . ComputaFigure S1Estimated power at genome-wide significance for genotypes simulated without LD. Simulation tests were performed for true models in which a single gene housed one to eight independent causal variants. Genotypes were simulated with 20 SNPs per gene, no LD between SNPs, and minor allele frequencies selected uniformly between 0.05 and 0.5. Power estimates are provided for VEGAS (green), GWiS (black), minSNP-P (blue), BimBam (blue dashed), and LASSO (red). While VEGAS performs well in the absence of LD, its performance degrades under realistic LD Click here for additional data file.Figure S2Number of SNPs and effective number of tests per gene. The number of SNPs and effective tests per gene are displayed as a density plot for (a) chromosome 1 and (b) the autosomal genome. While on average genes have 70 SNPs and 9 tests, large genes can have over 1000 SNPs and 100 tests.(TIF)Click here for additional data file.Figure S3Precision-recall curves for recovery of known associations. Precision and recall for recovery of 38 known associations are shown for GWiS (black), minSNP (thin blue), minSNP-P (thick blue), BIMBAM (dashed blue), LASSO (red), and VEGAS (green). Ranking is by p-value for GWiS, minSNP, minSNP-P, and VEGAS, and by Selection Index for LASSO. The tails of the curves for GWiS and LASSO are truncated when remaining loci have no SNPs entered into models, which occurs close to 50% recall. Triangles indicated the last genome-wide significant finding from each method.(TIF)Click here for additional data file.Table S1Number of identified genome-wide significant loci. Results are reported for 20 kb and 100 kb flanking transcription boundaries. G: GWiS, S: minSNP, SP: minSNP-P, B: BIMBAM, V:VEGAS, L: LASSO. *BIMBAM was only tested for 20 kb. **VEGAS is hard-coded to use (PDF)Click here for additional data file.Table S2Genome-wide significance thresholds calculated by permutation. Results are reported for 20 kb and 100 kb flanking transcription boundaries. Thresholds for GWiS, minSNP, minSNP-P and VEGAS are for p-values. Threshold for LASSO are for the selection index. The thresholds for minSNP and LASSO decrease because the larger threshold implies more tests. GWiS and minSNP-P already include a correction for the number of tests within a gene, and thresholds are somewhat less stringent for longer gene boundaries. *BIMBAM uses the threshold from minSNP-P because both tests provide gene-based p-values with identical uniform distributions under the null. **VEGAS is hard-coded to use (PDF)Click here for additional data file.Table S3Top associations for PR interval. The top 100 associations are reported for GWiS, minSNP, minSNP-P, BIMBAM, VEGAS, and LASSO. The locus name concatenates the named genes within the start and end positions indicated. Additional columns provide the number of SNPs, the effective number of tests, the number of independent associations within the region ((XLS)Click here for additional data file.Table S4Top associations for QRS interval. The column information is the same as for (XLS)Click here for additional data file.Table S5Top associations for QT interval. The column information is the same as for (XLS)Click here for additional data file.