Sorghum bicolor as the model. This method combines the advantages of ample genetic diversity and the possibility of studying non-additive inheritance. Furthermore, this design enables dissecting the latter to identify specific intra-locus interactions. We identified three HTLs (3.5% of loci tested) with synergistic intra-locus effects on overdominant grain yield heterosis in 2 years of field trials. These loci account for 19.0% of the heterotic variation, including a significant interaction found between two of them. Moreover, analysis of one of these loci (hDPW4.1) in a consecutive F2 population confirmed a significant 21% increase in grain yield of heterozygous vs. homozygous plants in this locus. Notably, two of the three HTLs for grain yield are in synteny with previously reported overdominant quantitative trait loci for grain yield in maize. A mechanism for the reproductive heterosis found in this study is suggested, in which grain yield increase is achieved by releasing the compensatory tradeoffs between biomass and reproductive output, and between seed number and weight. These results highlight the power of analyzing a diverse set of inbreds and their hybrids for unraveling hitherto unknown allelic interactions mediating heterosis.Identifying intra-locus interactions underlying heterotic variation among whole-genome hybrids is a key to understanding mechanisms of heterosis and exploiting it for crop and livestock improvement. In this study, we present the development and first use of the heterotic trait locus (HTL) mapping approach to associate specific intra-locus interactions with an overdominant heterotic mode of inheritance in a diallel population using  Associating of causal polymorphism with complex phenotypes can provide a better understanding of the mechanisms underlying developmental and biochemical constraints, thus enabling accelerated crop improvement. Advances in genotyping technologies and computational approaches have reshaped the way genetic analysis is conducted and have allowed capturing a substantial proportion of the global genetic diversity for genome-wide association studies et al. et al. Solanum lycopersicum) by crossing 33 diverse fertile mutants with the matching non-mutagenized parent known as ‘M82’ to create isogenic mutant heterozygotes. Comparison of their yield traits identified six mutant heterozygotes that showed yield heterosis, with the individual effects ranging from 36% to 88%.Two recent reports illuminate this debate, although the final conclusion of both may still be linked to the type of plant system and phenotype analyzed, as well as to the genetic background (whole genome hybrids compared to isogenic homozygous background). Riedelsheimer et al. et al. To date, no individual overdominant locus has been isolated by unbiased QTL mapping and recent attempts to zoom in on genomic loci associated with heterosis have mostly made use of biparental populations. This is performed by estimating the heterosis phenotype through test-crossing introgression lines or recombinant inbred lines to the recurrent parent Sorghum bicolor, the fifth most important crop in the world (www.FAO.org), which exhibits a consistent yield increase in hybrids vs. varieties (up to more than double) under a wide range of growing and management conditions Previous studies have reported a high level of heterosis in S. bicolor is derived from 19 founder lines (FLs) selected from a wide gene pool. This population was phenotyped for 2 consecutive years and statistical and computational tools were integrated to test for association between specific intra-locus interactions and overdominant mode of inheritance. We discuss possible mechanisms underlying heterosis for grain yield in hybrids based on our experimental data and demonstrate that the results of this fast-track mapping are validated by the overdominant mode of inheritance of one HTL in the consecutive F2 population. Finally, we propose the incorporation of individual resequenced genomes of only diallel FLs to zoom in on hitherto unknown loci underlying heterosis, thereby paving the way for an improved understanding of molecular mechanisms underlying this elusive and important phenomenon.Here we present the first use of heterotic trait locus (HTL) mapping to identify intra-locus interactions mediating an over- or underdominant mode of inheritance. The wide diallel population of S. bicolor ssp. bicolor accessions from the Israeli Plant Gene Bank  was mined and an additional 100 accessions were added. All plants were grown in pots in a greenhouse for DNA extraction and seed collection. DNA was extracted as follows: young leaf samples were ground in tubes using a TissueLyser ; 0.7 mL nuclei lysis solution  was added to each sample before incubating at 65°C for 1 h, and then 800 µL chloroform:isoamyl alcohol  was added. Samples were shaken for 15 min and centrifuged for 15 min at 10,000 g; the supernatant was transferred to a new tube, and 2.5 µL RNase (Qiagen) was added before incubating at 37°C for 15 min. DNA was precipitated by centrifugation with 500 µL ice-cold isopropanol and the pellet was washed with 0.2 M sodium acetate (pH 5.2) in 76% ethanol at room temperature for 5 min before centrifugation for 5 min at 10,000 g. This was followed by an additional wash of the pellet with 10 mM ammonium acetate in 76% ethanol at room temperature for 5 min and centrifugation for 5 min at 10,000 g. DNA was dried and dissolved in 30 µL DDW.This study was initiated by obtaining 173 available Microsatellite [simple sequence repeat (SSR)] genotyping was conducted using multiplexes of three markers with primers labeled with FAM, HEX or TAMARA . PCR proAnalysis of genetic diversity and allele frequency, phylogenetic tree construction and genetic distances were calculated with PowerMarker version 3.25 et al. A crossing scheme was designed to allow continuous and synchronous flowering of the FLs. To perform crosses between all FLs, the panicles of the female plant were emasculated by hot-water treatment (45°C for 10 min) with dehiscence control using a plastic bag ; stem diameter (of the lower third of the stem); leaf weight, and stem weight. Panicles were oven-dried for 2 days at 65°C and dry panicle weight (DPW) was measured. Next, the panicle was dissected following Brown xy and P1xy are the high and low mean values of the two parents, respectively):The ODH parameter of the r progeny of a cross FLx X FLy was determined as follows /P2xy.If the phenotypic value of replicate r of the cross, F1xyr, is less than or equal to P1xy, then ODHxyr is calculated using the algebraic expression: ODHxyr = (F1xyr - P1xy)/P1xy.If the phenotypic value of the replicate r, F1xyr, is between P1xy and P2xy, then ODHxyr = 0.If the phenotypic value of the replicate r, F1xy for the cross was then calculated for all replicates of the cross using the algebraic expression The mean ODHJMP software  was used to perform multiple correlation analyses using the “stepwise” option under the “fit model” function. A forward direction was taken to select factors for the final model that correlate between traits or heterosis levels (this test was conducted using the hybrid means).ij = µ+αi+eijY, where µ is the mean ODH of the diallel population, iα is the effect of the genotypic group and ije is the random error, i.e. the variation between the ODH means of the different crosses of same genotypic group. The non-distribution-dependent, experiment-wise error level of α = 0.05 was computed based on 1000 permutations Data derived from each of the 2 years were analyzed separately. In the first stage, a general linear regression was implemented using TASSEL software http://www.r-project.org/) was used to compare the ODH distribution of the different hetero-genotypic groups to the homozygous group in these loci  − Fn’2,(x)], where supx is the supermum of the set of distances, and Fn1, and Fn’2, are the empirical ODH distribution function of a specific hetero-genotypic group and the homozygous allelic combinations, respectively. The null hypothesis is rejected at level α if The significant loci were then analyzed in the second step: A non-linear Kolmogorov-Smirnov pair-wise test  or N . JMP software  was used to perform two- and three-way ANOVA using the “Standard Least Squares” option under the “fit model” function with the EMS method. The two-way model was ijrk = µ+αi+γj+θr+αγij+βk+eijrkY, where µ is the mean ODH value of the diallel population, iα, jγ and rθ are the main fixed effects of the HTLs , ijαγ is the effect of interaction between HTLs hDPW1.1 and hDPW1.2; kβ is the random effect of the year, and ijrke is the random error.The three-way model was: A single validated hybrid between SB018 and SB153 that carries the 154 and 162 alleles of the Dsenhabm39 SSR marker was selfed to obtain the F2 population. One hundred plants were transplanted into the field during the 2011 trial and phenotyped with the diallel’s plants of this year. Linkage between the Dsenhabm39 locus and the different traits was tested by ANOVA under the “fit Y by X” function, and the “Compare with the best” option under the Compare means.http://www.symapdb.org/) was used to align the sorghum HTLs to the syntenic regions in the maize genome which were then assigned to the corresponding genomic bins (http://www.maizegdb.org/). Maize overdominant QTLs found on these bins were assembled to the synteny map by the physical location of the associated markers (http://www.maizegdb.org/).The ‘block view’ tool of Symap  found between DPW and total seed number within a subset of 60 different FLs and hybrids.The FLs selected for the heterosis analysis were intercrossed to achieve a diallel sufficient for two replicated field experiments in 2010 and 2011. The experiments were set up to achieve a reasonable compromise between gaining phenotypic and heterosis values from a large number of hybrids and growing plants under conditions resembling common practice for sorghum under dense planting conditions . In the P≤0.01). According to these results, the imprinting effect on heterosis was considered insignificant in our mapping populations.Different estimates of heterosis were computed for all traits: (1) mid parent heterosis, (2) BPH P value respectively), and a comparison of the effects of the different branching levels on DPW showed a stronger effect of SBN  relative to PBN  and TBN . Overall, this four-factor model explained 68% of the variation in grain yield (DPW). Next, a similar analysis between the heterosis values (BPH) of these traits showed that only SBN and PBN heterosis values are significantly and positively correlated with that of DPW , and together these two explained 35% of the DPW heterosis.Grain yield components such seed number and weight are known to be negatively correlated P = 0.0001 and 0.001, respectively; P = 0.003, P<0.0001, P = 0.02; A similar comparison of the relationships within the grain yield components, both on the trait per se and the heterosis values, showed significant differences in the direction of the correlations between the two levels. Multiple regression analysis between the panicle architecture traits and seed number showed that SBN and PBN explain 65% of the variation in seed number across all hybrids in the 2011 experiment, with SBN showing an approx. eightfold stronger effect  than PBN . There was no significant correlation between TBN and seed number. A correlation test between trait values of SDW and these significant contributors for seed number indicated negative correlations for both SBN and PBN to SDW  was significantly higher than those of both homozygous plants , with a mean effect of 21%  as a single factor, and hDPW1.1 and hDPW1.2 contributed 7% and 4% (P<0.0001 and P<0.0026), respectively, to this mode of inheritance. Next, two-way interactions were analyzed to test for epistatic relationships between the different loci. Of the three possible interactions, only that between the two HTLs on chromosome 1 was significant , and all other combinations were treated as a single neutral non-interacting combination (N). The search for the genetic architecture of quantitative and complex phenotypes in plants has experienced a quantum leap in the depth of genomic architecture descriptions hDPW4.1, the overdominant mode of inheritance is maintained in a consecutive F2 population , the HTL mapping results reflect the influence of inter-allelic interactions as well. Despite the fact that this genetic “background noise” may increase intra-genotypic-group variation , therebyet al. et al.’s Saccharomyces cerevisiae hybrids; Ben-Israel and Fridman, unpublished results).This study differs from the analysis of heterosis in a diallel population reported previously by Cho Arabidopsis thaliana, in order to test the prevalence of additional loci governing speciation.It should be noted that as a methodology, the HTL mapping approach can also be used to map the opposite trend in hybrids, i.e. to scan the genome for intra-locus interactions associated with hybrid inferiority. Whereas in our study, the general positive ODH values for all of the traits  directedDespite the fact that the HTL mapping was performed with a relatively small number of genetic markers, it allowed us to apply a novel mapping approach to study the relative contribution of intra-locus interactions to the heterotic variation in the gene pool. Overall, at this resolution, we identified three HTLs which were reproducibly associated with grain yield heterosis over 2 years, and additional loci which were not considered because the effect was only found in one growing season (data not shown). A comparison of our results to other studies shows that the number of loci with reproducible and significant overdominant effects on grain yield is comparable to that found in rice, for example. Although QTL studies show that heterosis is controlled by a large number of loci, and includes the involvement of complex epistasis, the number of true overdominant loci for grain yield with reproducible effects in more than 1 year sum to less than 4% of the markers used hDPW4.1 in an F2 population  with a similar genetic marker system showed the significant genetic bottleneck experienced by this crop during domestication, including reduction in allelic richness from 13.4 to 6 alleles per locus S. bicolor, on the other hand, the allelic richness–which is a prerequisite for testing multiple allelic interactions in a population structure such as the one presented in this study–is in fact comparable to that of H. spontaneum: more than 13 alleles per locus in the wide collection and 7 alleles per locus in the FLs of the diallel. In addition, while there is ample genetic heterogeneity in the wide collection, each of the accessions is, by itself, highly homozygous, reflecting the partial allogamous mode of reproduction in this plant There are several genetic and developmental attributes of hDPW4.1 was syntenic with two heterotic maize QTLs for yield that reside on bins 2.04 and 10.04  occurring early in ovary development lead to increases in cell number or total sugar yield in the mature fruit More specifically, the mechanism underlying such relaxation of metabolic flow or increase in growth potential may originate from changes in the activities of gene products with critical spatial and temporal distribution, at the cellular level, at early developmental stages or both. Such a sequential developmental pathway underlying naturally occurring variation, though not modulated by inter-allelic interactions, was exemplified in the previously characterized tomato QTLs Figure S1Scheme of the two mapping populations from A. 2010 and B. 2011 experiments. Dark and light purple blocks show crosses for which accessions indicated on the left or bottom, respectively, were used as females. Blue blocks show hybrids for which two reciprocal crosses were analyzed. Brown indicates hybrids whose two reciprocal crosses were field-trialed, but there were not enough replicates (n <3 for each) for statistical comparison between them. White blocks indicate missing hybrids.(TIF)Click here for additional data file.Figure S2Heterotic trait locus (HTL) mapping. Two-step genomic scan as performed with overdominant heterosis (ODH) values derived from the 2011 field experiment, shown for representative markers. A. Dsenhsbm99 showing similar ODH distributions for the different genotypic groups, i.e. did not pass the first mapping step (GLM). The line across each diamond and the vertical span represent the group mean and the 95% confidence interval for each group, respectively. B. Xcup64 showing significant difference  between ODH values of the different genotypic groups, albeit with no advantage for specific hetero-genotypic group as compared to the homo-genotypic group (H:H). This marker passed the first step and failed in the second (Kolmogorov-Smirnov). C. Dsenhsbm40 that passed the first step  and the second step with a significant advantage only for the hetero-genotypic groups 154∶156 and 154∶164 (in gray) vs. the homo-genotypic group . D. Cumulative distribution function plot showing the ODH values of the significant hetero-genotypic  and homo-genotypic groups (H:H) for the same marker (Dsenhsbm40). DPW, dry panicle weight.(TIF)Click here for additional data file.Figure S3Chromosomal physical map (in Mbp) of markers used in this study and the identified heterotic trait loci (HTLs) for grain yield . Position is only shown for HTLs that were mapped over 2 years–each HTL is marked with a black diamond. Black and white coloring indicate pericentric-heterochromatic and telomeric-euchromatic chromosomal regions, respectively. Gray indicates markers within pericentric-heterochromatic chromosomal regions.(TIF)Click here for additional data file.Figure S4Illustration of the allelic distribution in a diallel.A. Allelic distribution in founder lines (FLs) including the common A1 and A2 alleles shared by 4 and 3 parents, respectively, and the rare A3 allele found in FL18 and FL19. A rare allele is defined as one carried by less than three FLs. The genotype of each hybrid is projected from the two homozygous parents. B. Six homozygous hybrids derived from the four FLs that share the A1 allele (homo-genotypic group A1/A1). C. Eight heterozygous hybrids derived from four FLs that share the A1 allele and two FLs that share the A3 allele (hetero-genotypic group A1/A3). D. A rare homo-genotypic group (A3/A3) including a single hybrid derived from a cross between FLs sharing the rare A3 allele. This group cannot be compared to the corresponded hetero-genotypic groups (any groups that harbor one copy of A3).(EPS)Click here for additional data file.Figure S5Comparative heterosis mapping of sorghum and maize. For each sorghum heterotic trait locus , genomic intervals which are syntenic with the maize genome are shown. The locations of the maize overdominant QTL for yield-associated traits  on the maize bin map are drawn based on a combination of data from Tang et al. et al. (EPS)Click here for additional data file.Table S1List of the accessions included in the wide Sorghum bicolor sps. bicolor collection(XLSX)Click here for additional data file.Table S2SSR markers used in this study.(XLSX)Click here for additional data file.


The investigation of associations between rare genetic variants and diseases or phenotypes has two goals. Firstly, the identification of which genes or genomic regions are associated, and secondly, discrimination of associated variants from background noise within each region. Over the last few years, many new methods have been developed which associate genomic regions with phenotypes. However, classical methods for high-dimensional data have received little attention. Here we investigate whether several classical statistical methods for high-dimensional data: ridge regression (RR), principal components regression (PCR), partial least squares regression (PLS), a sparse version of PLS (SPLS), and the LASSO are able to detect associations with rare genetic variants. These approaches have been extensively used in statistics to identify the true associations in data sets containing many predictor variables. Using genetic variants identified in three genes that were Sanger sequenced in 1998 individuals, we simulated continuous phenotypes under several different models, and we show that these feature selection and feature extraction methods can substantially outperform several popular methods for rare variant analysis. Furthermore, these approaches can identify which variants are contributing most to the model fit, and therefore both goals of rare variant analysis can be achieved simultaneously with the use of regression regularization methods. These methods are briefly illustrated with an analysis of adiponectin levels and variants in the ADIPOQ gene. New methods for the analysis of rare genetic variants are appearing rapidly. Resequencing efforts are identifying numerous new variants but the majority of the new variants are seen only in a very small number of individuals Hoffman Usually there are very few individuals carrying the minor allele at the majority of the identified variants, and therefore it is extremely challenging to estimate the parameters Conceptually, the problem of how best to model the relationship between a phenotype and a large set of rare genetic variants is a problem of variable selection (or feature selection) and/or dimension reduction (or feature extraction) in a sparse covariate space. There are many well-studied statistical methods for feature selection and extraction when the number of predictor variables is large. However, for the analysis of rare genetic variation, such approaches have only recently been explored. There were several groups at the GAW17 workshop in 2010 who implemented feature extraction or penalization methods, using a wide variety of different approaches In this paper, we explore whether several classic approaches for feature selection or extraction (ridge regression (RR) n method . PCR andSince the extreme rarity of most resequencing variants could lead to computational and inferential challenges with feature selection and extraction methods, we also implemented and investigated adaptations of these methods specifically for rare variant analysis. Each method is implemented using two different model choice criteria, both with and without our rare variant adaptation. Using genetic variants identified by Sanger sequencing on three genes in 1998 individuals, we simulated phenotypes under a range of models, and then compared the ability to identify the causal variants using these regression regularization methods. We have also compared performance with three popular methods recently developed for rare variant analysis: the weighted count of Madsen and Browning (WE) In fact, we show that RR, PLS, LASSO and sparse PLS usually outperform WE, VT and SKAT as long as the causal variants are not singletons or extremely rare. Our comparison is timely, since there is great interest in methods for rare variant detection. One additional advantage of feature selection methods is that they can not only identify associations, but can also point towards which variants are likely the truly-associated ones.Commonly-used methods for rare variants often pool rare alleles and fit simple regression models relating the phenotype to rare allele counts. However, the choice of threshold below which a variant is pooled or collapsed for rare-variant analysis is, of course, arbitrary. Although a 1% threshold is the traditional standard for differentiating between a polymorphism and a mutation In contrast, we are using multiple regression methods to look for rare variant associations. The five statistical models for feature selection and extraction were fit using well-known R packages To combine our chosen multiple regression methods with the concepts of pooling and collapsing, we propose an approach motivated by the variable threshold idea For our evaluations, we used genotype data on three genes where the exons and flanking regions were Sanger sequenced in 1,998 individuals (courtesy of GlaxoSmithKline (GSK)) Continuous phenotypes were generated assuming a normal distribution When fitting the models, a single measure of model fit was chosen for each method, after choosing all the parameters of the model see . EmpiricEach of our five chosen methods was used to analyze 1000 simulated data sets, and the results are used to calculate empirical power at significance level Methods are colour coded and labelled across the top of each figure. Several different options were used for fitting each of the multiple regression methods. For PCR and PLS, models with one component are denoted “Comp1”. The label “Compk” denotes models with With a few exceptions, any of the 5 multiple regression methods had better power than the three approaches developed specifically for rare variant analysis , and furthermore, performance was often very similar across different variants of the multiple regression methods.Consider first two situations where causal variants had clear large effects , the relative performances of the multiple regression methods were similar to Scenario set I; we saw very little alteration in the relative performances of the various algorithms. The multiple regression methods continued to perform well in comparison with VT, WE and SKAT. However, all methods had excellent power for the models with a mixture of rare and common variants (I.2 and II.2). This is due to the definition of the effect sizes in this scenario, where the average effect size was defined across all causal variants see .In scenario I.6 and II.6, only variants with frequency less than 1/1000 were selected as causal. Power is substantially lower in this situation for all methods and the patterns of performance differ. In Scenario set I  and S2, The addition of pooled variables to the predictor space did not seem to alter power in the simulations using Scenario set I. However as previously noted, PCR with one component and pooled predictor variables performed better than other approaches in scenario I.6:VeryRare, and is presumable capturing the causal rare variants through one or more of the pooled variables. Since in most cases, the pooled predictors made no difference, the figures for Scenario set II do not include pooled predictors.When effects could act in both directions (I.4) VT and WE did very poorly, but these approaches are known to look only for variants acting in one direction Gene B contains only 28 variant sites, and as a result the power for detecting association is low for all methods  with only one component tended to perform poorly. In fact, this could probably be expected. These methods are normally used together with a rule for determining the best number of components, and so choosing only one component is not the normal implementation. Multiple regression methods also performed poorly in a simulation where the causal variants were very rare; in that situation there was a large discrepancy between the frequency of the causal variants (0.001) and the largest threshold we used for pooling rare alleles (0.05). Therefore, refining our combined regression and pooling approach may improve performance in this case. For example, we could reduce the number of MAF thresholds that we included, or use counts weighted by the inverse of MAF.It is difficult to understand why some models would include multiple pooled variables with different thresholds, as was seen in Since permutations are required, the computational overhead of some of these regression approaches can be quite high. Supplemental It is interesting to speculate on why these methods work. Some of the rare causal variants in our simulations could have been observed in up to 20 individuals out of the 2000 in the sample, and hence there would be adequate power to identify these variants. It is also possible that the presence of long-range correlation between variants could provide information to PCR or PLS methods. Long-range correlation between common and rare variants can occur due to patterns of ancestral recombinations and co-occurrence of rare variants in some parts of a gene genealogy Nevertheless, these multiple regression methods were not designed for data as sparse as data from resequencing studies. We therefore proposed augmenting the variable space with new variables defined by pooling rare variants together. Instead of choosing a single threshold, we augmented the predictor space by a set of pooled counts based on a range of thresholds. These variables would, of course, be highly correlated with each other. We did not find an improvement in power in most situations when we added the pooled variables, and we believe that this is due to the increase in the parameter space, so that the models had more difficulty identifying the best predictors.Any division of genetic variants into “common” and “rare” is arbitrary. Our choice of 5% for the upper threshold of rarity for pooling may also have an impact on the performance of the models including pooled variable sets. It would be interesting to investigate whether considerations of population history could be used to set more appropriate thresholds distinguishing rare variants from common ones.Simulations can be designed to favour one analytic strategy over another. When we modelled a constant effect of the causal variants (Scenario set I), as expected the VT method usually outperformed the WE method. In contrast, in Scenario set II where the effect depended on MAF, performance of WE was improved. Our simulations did not explicitly select correlated genetic variants to be causal, and therefore the dimension reduction approaches of PCR and PLS would not necessarily be expected to outperform other approaches. However, the idea that a small percentage of the rare genetic variants in a gene are causal underlies most of the methods developed for rare variant analysis, and therefore the better performance of multiple regression methods is a pleasant surprise.All simulations were based on the genotype data from three Sanger sequenced genes. The variants chosen as causal were randomly selected for each simulated data set and therefore there was variability across the simulations in the rarity of the causal variants. However, evaluation of performance on a larger set of genotypes may provide additional insight into performance of these methods.Predictions of changes in amino acids in proteins, or predictions of sequence conservation have been used with success to distinguish potentially causal variation from variation that is unlikely to be causal Theoretically, such methods could simultaneously model all the genetic variants in more than one gene, such as all variants in a pathway, or conceivably all exome-identified variants. Genome-wide simultaneous modeling has been suggested by several authors, in particular using Bayesian methods We obtained excellent power over a variety of simulation scenarios with many of our implementations of these multiple regression methods. Therefore, the choice of best method may be partially the preference of the data analyst. PLS or SPLS methods may be beneficial for modelling jointly covariates and genotypes. We like ridge regression since it is computationally fast, but where computation time is less of a concern or the variable selection aspect is of importance, the LASSO could be an excellent choice since the power is often slightly better.Methods developed for high-dimensional data may outperform other approaches for rare variant analysis. These methods will simultaneously model the effects of all genetic variants in a gene, common or rare. Furthermore, unlike collapsing, counting, or variance-based methods for rare variant association analysis, some of these regression methods can identify the most likely causal variants.The genotype data used for our simulations represents a re-use of data and no new human interventions were conducted. No additional IRB approvals were sought for the simulation studies. The Committee on Ethics in Clinical Research, CHUV, Lausanne University, Lausanne, Switzerland approved the original protocols for sample collection for the genotype data used in simulations. All participants in Twins UK provided informed written consent, and the research protocol was approved by institutional ethics review committees at Kings College London. Again, the data used for our analyses represents a re-use of data that has been previously analyzed and no further IRB approvals were sought.www.mcgill.ca/statisticalgenetics/.Suppose we have a sample of In PCR In PLS The fitted values for PCR and PLS depend on the number of components, Parameters in RR models The penalty parameter in LASSO To evaluate model performance for LASSO and SPLS, we used the selected final model F-test p-value as the score measuring model performance. The R-package ‘glmnet’ was used for LASSO Let The subjects used in this paper are a subset of the CoLaus study, a population-based study of 6,188 Lausanne residents aged 35 to 75 years Sanger sequence data for the exons and flanking regions of three genes from 1,998 individuals were provided by GlaxoSmithKline (GSK) Within each simulation, a proportion of the rare variants was randomly selected to be causal, depending on the simulation scenario . The thrFor each simulated data set, the phenotype data was permuted relative to all the genotype data and the analysis was repeated. For each permutation, the analysis included all model fitting steps, so that variable selection or identification of the best model as a function of AIC or BIC was repeated for each permutation step. Using the chosen measure of model fit for each method (described above), we then compared this statistic between the permuted data sets and the original simulated data set, and counted the number of permutations where the model fit statistic was more extreme than in the original data.An R package, RVtests, that uses these approaches to test for rare variant associations, is available from the authors or from cran-r.project.org.Figure S1Power for Scenario set I for gene B.(PDF)Click here for additional data file.Figure S2Power for Scenario set I for gene C.(PDF)Click here for additional data file.Figure S3Power for Scenario set II for gene A.(PDF)Click here for additional data file.Figure S4Power for Scenario set II for gene B.(PDF)Click here for additional data file.Figure S5Power for the LASSO method as a function of the penalty parameter.(PDF)Click here for additional data file.Figure S6QQ plot of empirical p-values for gene C under the null hypothesis.(PDF)Click here for additional data file.Table S1Test power of WE, VT, SKAT, PCR, PLS, RR, LASSO, and SPLS for three genes and for scenario set I where variant effects do not vary with the minor allele frequency.(PDF)Click here for additional data file.Table S2Test power of WE, VT, SKAT, PCR, PLS, RR, LASSO, and SPLS for three genes and for scenario set II where variant effects vary with the minor allele frequency.(PDF)Click here for additional data file.Table S3Simulation run time for three genes and six scenarios.(PDF)Click here for additional data file.


Gasterosteus aculeatus). We found that both the number of vertebrae (2h = 0.36) and body size (2h = 0.42) were moderately heritable, whereas the influence of maternal effects was estimated to be negligible. While the number of vertebrae had a positive effect on body size, no evidence for a genetic correlation between body size and vertebral number was detected. However, there was a significant positive environmental correlation between these two traits. Our results support the generalization-in accordance with results from a review of heritability estimates for vertebral number in fish, reptiles and mammals-that the number of vertebrae appears to be moderately to highly heritable in a wide array of species. In the case of the three-spined stickleback, independent evolution of body size and number of vertebrae should be possible given the low genetic correlation between the two traits.Intraspecific variation in the number of vertebrae is taxonomically widespread, and both genetic and environmental factors are known to contribute to this variation. However, the relative importance of genetic versus environmental influences on variation in vertebral number has seldom been investigated with study designs that minimize bias due to non-additive genetic and maternal influences. We used a paternal half-sib design and animal model analysis to estimate heritability and causal components of variance in vertebral number in three-spined sticklebacks ( Jordan The three-spined stickleback has become an important model organism in evolutionary biology and developmental research The aim of this study was to investigate the relative roles of genetic, environmental and maternal effects on the number of vertebrae in three-spined sticklebacks, as well as to estimate heritability of this trait. To this end, we performed a large number of half-sib crosses on marine sticklebacks and subjected the data to ‘animal model’ analyses. In addition, we investigated the relationship between body size and the number of vertebrae, and tested whether the increase in vertebral number results in the increase of body size. Additionally, the genetic and environmental correlations between body size and number of vertebrae were estimated.In all three cases-univariate analyses of vertebral number and body size, and multivariate analysis of both traits-only the models that included the additive effects received the strongest support . Hence, 2h = 0.357 , and there was no difference in the mean number of vertebrae between the sexes . There was significant additive genetic variation in vertebral number , and the = 0.357 .2h = 0.445 , but other effects in the model remained qualitatively unaffected.The mean body size was 40.62 mm , but there was significant sexual size dimorphism, with females  being on average larger than males . There was significant additive genetic variance also for body size , with he = 0.445 . Fittinggr = −0.324 [95% HPDI:−0.793–0.162]). However, environmental correlation between the traits was positive and significant (er = 0.424 [0.116–0.760]). Since phenotypic correlation is a sum of genetic and environmental correlations pr = 0.104) observed above is largely driven by environmental effects.Genetic correlation between number of vertebrae and body size was negative but not significant  that largely agreed with the animal model estimates. The slightly lower estimate for vertebral number in this alternative approach could be due to the fact that animal model estimates did not account for maternal  effects. Although non-significant, they accounted in the standard generalized mixed model analysis for 2.9% (95% HPDI: −11.8–17.4%) and 6.4% (95% HPDI: −9.7–18.3%) of the total phenotypic variance in body size and vertebral number, respectively. The estimate of genetic correlation in this alternative approach was gr = 0.071 (95% HPDI: −0.517–0.626), the correlation of maternal (or common environment) effects mr = −0.316 (95% HPDI: −0.782–0.195), and environmental  correlation er = 0.211 (95% HPDI: 0.101–0.331). These estimates indicate that the non-significant negative genetic correlation observed with the animal model might in fact stem from maternal or common environment effects.Standard generalized mixed model analysis produced estimates of heritabilities  from 2h≈0.36) could owe to methodological differences. This is also suggested by the fact that regression estimates of heritabilites in the Hermida et al. Although subject to much research over decades e.g. , relativ2h = 0.36) and standard generalized mixed model (2h = 0.29) estimates of heritability for vertebral number could be due to unaccounted maternal effects (m = 0.06) in the animal model estimate.Depending on study design, maternal and non-additive genetic effects can confound estimates of additive genetic variance and heritability. The breeding design we have employed in this study should be robust in respect to both of these factors. In our design, most non-additive effects should end up in residual variance, whereas maternal effects could either increase or decrease additive genetic variance. We did take maternal effects into account in the model selection-fitting models that included them–but since no evidence for them was found, maternal effect terms were excluded from final parameter estimation. Also, the standard generalized mixed model analyses–in which the dam effects were explicitly fitted into the model–suggested that maternal effect influences were small  relative to additive genetic effects. However, these analyses also suggest that the small discrepancy between animal model .The parents for the fish used in this study were collected in June 2006 from the Baltic Sea near Helsinki  for the purpose of a large genetic experiment 19,20>3630.99, P<0.001). Hence, counting (measurement) error was zero. All the counts were made by the same person. No distinction was made between abdominal and caudal vertebrae, but all vertebrae were counted. Fused vertebrae were counted as two.The vertebrae were counted under dissection microscope after the whole vertebral column from one side was exposed with the aid of a scalpel. To determine the repeatability of vertebral number counts, 20 individuals were counted twice and blind with respect to the first count. Repeatability (R) was estimated following Sex of the individuals was identified by amplifying a part of 3′UTR of the IDH gene as explained in iy is the observed trait value, j the sex, k the block and d the dam of individual i, μ the intercept, js fixed effect of sex, kb fixed effect of block, ia the random additive genetic effect, dm the random effect of maternal identity estimating maternal effects influences, and ie the residual or environmental effect. Apart from fitting this model, in the case of body size we also fitted a model in which vertebral number was added as a covariate. The rationale behind this was to see whether any of variance in the body size could be explained by variation in vertebral number. Also a multivariate model was fitted to estimate genetic and environmental correlations between body size and vertebral number. Normal distribution was assumed for all random effects in all models, and commonly used prior specification for variance components  was used for univariate and (V = diag(2) * 0.02, nu = 3) for multivariate models. For each model, one chain with 600,000 iterations–first 100,000 of which discarded as burnin–was run. The chain was thinned by 100, resulting in 5,000 samples from posterior distribution.Contributions of genetic and environmental effects on vertebral number and body size were estimated for individuals measured for both traits (on average 3.98 [median = 4] fish from each of the 84 families) using animal model analyses as implemented in MCMCglmm package In all three cases–univariate analyses of vertebral number and body size, and multivariate analysis of both traits–we used model selection procedure based on deviance information criterion (DIC) to choose the most parsimonious model: the smaller the DIC-value, the more parsimonious the model. The set of candidate models in each case included models with both additive and maternal effects included and excluded. In order for a more complex model to be favored over a more parsimonious one, the difference between DIC-values of the two models (ΔDIC) should not exceed 10 A ( = additive genetic variance) and the variance component attributable to dam is the sum of ¼ VA, ¼ VD ( = dominance variance) and VM  effect component. Genetic correlation was estimated following equation 19.3 in Falconer and Mackay For comparative purposes we also report heritability estimates and genetic, maternal and environmental correlations between body size and vertebral number as obtained from standard generalized mixed model analysis implemented in the MCMCglmm package. Sire and dam (nested within sire) effects were treated as random effects, and sex and block as fixed effects. A single multivariate model was fitted, and again commonly used prior specification for variance components (V = diag(2) * 0.02, nu = 3) was used. One chain with 600,000 iterations–first 100,000 of which discarded as burnin–was run. The chain was thinned by 100, resulting in 5,000 samples from posterior distribution. In this analysis the variance component attributable to sire effect is ¼ V


Association of NMR-derived quantities with genetic variants can uncover biologically relevant metabolic traits. Using NMR data of plasma samples from 1,757 individuals from the KORA study together with 655,658 genetic variants, we show that ratios between NMR intensities at two chemical shift positions can provide informative and robust biomarkers. We report seven loci of genetic association with NMR-derived traits  and characterize these traits biochemically using mass spectrometry. These ratios may now be used in clinical studies.Nuclear magnetic resonance spectroscopy (NMR) provides robust readouts of many metabolic parameters in one experiment. However, identification of clinically relevant markers in  Identification of the genetic and environmental determinants of human metabolism is key to the understanding of complex disorders. Metabolic profiling of blood samples from cohort studies is a major tool in the discovery of new disease relevant biomarkers and the metabolic individuality in the general population. Two major techniques are generally used: mass spectrometry (MS) and nuclear magnetic resonance spectroscopy (NMR). At the basis, both platforms are complementary in many regards. For instance, MS is more sensitive and allows obtaining more detailed information while using small sample volume, but is also quite sensitive to changing experimental conditions, and sample preparation is more demanding. NMR-based measurements, on the other hand, require higher sample volumes and the interpretation of the raw spectra is not always straightforward. Still, the strongest advantages of NMR are simplicity of sample preparation and excellent reproducibility of quantitative metabolic readouts. It has previously been shown that the stability of NMR measurements is to some extend independent of the NMR platforms and laboratory practices ,2. TherePreviously, we and others have shown the potential of MS-based and NMR-based metabolomics in discovery studies such as the KORA study -7. UsingUp to now, GWAS using metabolic traits mainly focused on metabolites that were identified by the annotation of MS and NMR spectra using reference spectra in existing databases.Here, we address the question of whether known clinically relevant GIMs can be derived from raw NMR spectra in blood plasma without prior annotation. We take a hypothesis-free approach to identify genetically influenced NMR features and investigate whether specific ratios between NMR intensities at two chemical shifts can provide informative and robust biomarkers. Finally, we interpret our findings using correlations to MS determined metabolite concentrations.With the KORA F4 study cohort, we have unique access to a large number of samples of the general population, which are metabolically deeply characterized both using MS and NMR methods. In previous studies based on these data, we showed that using ratios between metabolite concentrations can strengthen genotype-metabotype associations. In such cases, the ratios often reflect educt-product pairs of enzymatic reactions . Based oThe KORA study is an independent population-based survey from the general population living in the region of Augsburg, Germany. The KORA S4 study was conducted in 1999-2001 and comprises a total of 4,261 participants . BetweenBlood samples for metabolic analysis and DNA extraction were collected as part of the KORA F4 follow-up study. To avoid variation due to circadian rhythm, blood was drawn in the morning between 08:00 and 10:30 after overnight fasting. A part of the blood was drawn into serum gel tubes, gently inverted twice, and then allowed to rest for 30 min at room temperature (18-25°C) to obtain complete coagulation. The material was then centrifuged for 10 min . Serum was divided into aliquots and kept for a maximum of 6 h at 4°C, after which it was frozen at -80°C until final analysis. Another part of the blood was drawn into ethylene diaminetetraacetic acid (EDTA) tubes, gently inverted twice, and left on the Sarstedt Universal mixer <5 min to avoid mechanical hemolysis, followed by centrifugation at 15°C for 10 min at 2,750 g. Thereafter, plasma was separated, divided into 200 mL aliquots and kept at 4°C, after which it was deep-frozen to -80°C. Within 2 weeks, plasma was stored in the gaseous phase of liquid nitrogen at -196°C.-6 were applied as filters. In total, 655,658 autosomal SNPs satisfied these criteria.For all individuals profiled from the KORA study, genome-wide single nucleotide polymorphism (SNP) data were already available. These data have been used and described extensively in the past in the context of several GWAS . TherMetabolic analyses were conducted using clinical biochemistry methods, two distinct MS-based platforms (targeted and non-targeted), and NMR spectrometry . For the joint analysis, metabolomics and genotype data were available for a total of 1,757 individuals. All metabolite measurements have been reported before. We therefore only summarize here the points that are essential for the present study.The following serum lipids were measured on fresh samples using the Dimension RxL (Dade Behring). TC was determined by cholesterol esterase method , HDL-C using the AHDL Flex , LDL-C using the ALDL Flex , and TG was measured using a TGL Flex .The Biocrates AbsoluteIDQ p150 kit was used for absolute quantification of a defined set of serum metabolites. Sample analyses were done on an API 4000 Q TRAP LC/MS/MS system (Applied Biosystems) equipped with a Schimadzu Prominence LC20AD pump and a SIL-20AC autosampler. The complete analytical process was performed using the MetIQ software package, which is an integral part of the AbsoluteIDQ kit. In total, we detected 163 different metabolites. The metabolomics dataset contains 14 amino acids, hexose (H1), free carnitine (C0), 40 acylcarnitines (Cx:y), hydroxylacylcarnitines (C(OH)x:y), and dicarboxylacylcarnitines (Cx:y-DC), 15 sphingomyelins (SM Cx:y) and N-hydroxylacyloylsphingosylphosphocholine (SM(OH) Cx:y), 77 phosphatidylcholines  and 15 lyso-phosphatidylcholines. Lipid side chain composition is abbreviated as Cx:y, where x denotes the number of carbons in the side chain and y the number of double bonds. For further details on this dataset and the coefficients of variation (CVs) of metabolite quantification see [2 data were searched against a standard library generated by Metabolon that included retention time, molecular mass to charge ratio (m/z), preferred adducts and in-source fragments as well as their associated MS/MS spectra for all molecules in the library. The library allowed for the identification of the experimentally detected molecules on the basis of a multiparameter match without the need for additional analyses. For further details on this dataset and the coefficients of variation (CVs) of the metabolite measurements see [Metabolon, a commercial supplier of metabolic analyses, developed a platform that integrates the chemical analysis, including identification and relative quantification, data-reduction, and quality-assurance components of the process. The analytical platform incorporates two separate ultrahigh-performance liquid chromatography/tandem mass spectrometry (UHPLC/MS/MS2) injections and one gas chromatography/mass spectrometry (GC/MS) injection per sample. The UHPLC injections were optimized for basic and acidic species. The LC/MS portion of the platform was based on a Waters ACQUITY UPLC and a Thermo-Finnigan LTQ mass spectrometer, which consisted of an electrospray ionization (ESI) source and a linear ion-trap (LIT) mass analyzer. For GC/MS, the samples were analyzed on a Thermo-Finnigan Trace DSQ fast-scanning single-quadrupole mass spectrometer using electron impact ionization. A total of 295 serum metabolites were measured, spanning several relevant classes . The detection of the entire panel was carried out with 24 min of instrument analysis time (two injections at 12-min each), while maintaining low median process variability . The resulting MS/MSNMR spectra measurements were carried out at numares (formerly LipoFIT), Regensburg. The blood plasma spectra were recorded on a Bruker 600 MHz Avance IIplus spectrometer. The spectra were phased and baseline corrected. Since no reference compound was added, all spectra were horizontally aligned to the prominent lactate signals at 1.36 and 1.37 ppm. Based on a proprietary approach that uses complex deconvolution algorithms on the spectral regions between 0.6 and 1.5 ppm, a set of 15 lipoprotein subfractions was derived from the spectra. These fractions correspond to HDL , LDL , IDL (L10), VLDL , remnants L13), and chylomicrons . For further details on this dataset see [, and chy10-transformed prior to analysis. To diminish the effect of outliers, for each bin individual intensity values more than three times the standard deviation away from the mean were excluded. Also, the spectral region affected by the water peak (δ = 4.6-5 ppm) was excluded from further analysis.For the purpose of this study, the spectra were limited to a range from 0 to 9 ppm and divided into 10,000 bins of equal width (0.001 ppm). Spectral binning is a standard procedure in NMR-based metabolomics studies that reduces the data complexity and compensates for slight jitter of the signals' chemical shifts . The intvs. strength of association) resulting from the first GWAS run to pick the positions on the spectra which show the strongest associations. We then used the 500 best-scoring NMR signal positions to compute pair wise ratios . As before, we used age- and gender-adjusted linear additive models in PLINK to test for associations.To test for associations between genetic polymorphisms and individual NMR signal bins, we created age- and gender-adjusted linear additive models using PLINK (Version 1.07) . TestingP value of 0.05/655,658/133,350 = 5.72 × 10-13.We applied a conservative Bonferroni correction to control for false-positive error rates resulting from multiple testing. We corrected for tests on 655,658 SNPs and 133,350 NMR features at a nominal significance level of 5%, thus obtaining an adjusted Spearman correlations between biochemically and MS determined metabolite concentrations and NMR signal intensities were calculated using the statistical analysis system R (Version 2.15.1). To avoid false-positive associations due to small sample sizes, only metabolic traits with at least 300 non-missing values were included. Furthermore, metabolite concentrations that were more than three times the standard deviation away from the mean were excluded.1H-NMR spectra from 1,757 plasma samples. To this end, we binned the spectral region ranging from 0 to 9 ppm at a high resolution of 0.001 ppm. The region surrounding the water peak (δ = 4.6-5 ppm) was discarded. NMR intensities were log10-scaled and extreme outliers were removed (see Methods). Usually, NMR-based GWAS either use a selection of chemical shifts or perform spectral annotation to reduce the NMR data to the underlying metabolite concentrations . In conP value was selected. In a second GWAS, we then tested all possible ratios between the intensities at these 500 chemical shift positions for associations with all genetic variants. To our knowledge, this is the first GWAS that uses a ratio-based, hypothesis-free approach with raw NMR spectral data as a phenotype. For both GWAS, age and gender were used as covariates. In the subsequent analysis, we considered only robust associations of frequent SNPs with minor allele frequencies (MAF) >10%.In the second step, we selected the 500 bins in the NMR spectrum that exhibited the strongest signal of association. In cases where neighboring bins all displayed associations of comparable strength to the same single nucleotide polymorphism (SNP), the bin with the lowest P <5.72 × 10-13) after Bonferroni correction for 655,658 tested SNPs and 133,350 NMR traits . Table et al. in 2011 [In total, seven loci  displayed a signal of association that attained the genome-wide level of significance  in association with NMR intensities at single chemical shift positions (NMR bins) in our genome-wide approach. Note that in comparison, the strength of association is generally weaker when testing NMR bins instead of lipid subclasses, as one would expect when using a less aggregated parameter. However, in the GWAS with ratios of chemical shift pairs (NMR ratios), we observe a strong increase in the strength of association for four loci , resulting in P values that are between 9 and 89 orders of magnitude lower than the values reported by Petersen et al. for the associations with lipid subclasses  were performed on blood samples from the same draw and subject. Correlation spectra thus link the chemical identity of the metabolites detected by other platforms to chemical shifts in the NMR spectra, where the chemical shifts may correspond to the same metabolite, but also to a metabolite on a related biochemical pathway. As an example, Figure A s2) up to 0.61. In most cases, we can verify the validity of the correlations using experimental spectra of pure compounds from HMDB [In the case of correlation with lipid-related parameters, the correlation spectra generally show wider areas of the NMR spectrum corresponding to these metabolites  and the chemical shift where the correlation coefficient is highest. The corresponding correlation spectra are provided in Additional file Additional file For all associations between NMR bins and genetic loci, we report the best correlating biochemically or MS-determined metabolite at the given chemical shift position Table . In caseIn this study, we perform a GWAS with binned NMR spectra and ratios between pairs of chemical shifts in a hypothesis-free approach without prior annotation of NMR features. In total, we identify seven genetic loci. Four of these associations  only reach a genome-wide significance level when ratios between the signal intensities at two different chemical shift positions are tested. Five of the seven loci  are also known lipid risk loci, and all have previously been identified in GWAS with metabolic traits. There is thus no doubt about the functional role of these genetic loci in inducing a metabolic phenotype. Moreover, correlating NMR features to known metabolic phenotypes determined on other platforms can help in the interpretation of the observed genetic associations for various loci and the characterization of the associated NMR trait, as shown in this study for the CPS1, FADS1, and GCKR loci.Given the fact that these loci have already been largely studied for their interest from a biomedical point of view, we focus here on aspects that highlight NMR-specific features of the associations. The features presented in this work may now be used in future studies with clinical disease endpoints or may potentially be established as biomarkers. In the following, we focus on four of the loci, each of them highlighting a different situation.et al. report two mutations of the CPS1 gene that contribute to the onset of CPS1 deficiency, an inborn error of metabolism that causes hyperammonemia [et al. reported an association of SNP rs2216405 with glycine concentrations at a nominal P value of 2.59×10-26 [et al. presented a genetically influenced metabotype that might represent a mild form of CPS1 deficiency.The carbamoyl-phosphate synthase 1 (CPS1) controls the first step in the urea cycle. Klaus mmonemia . In 2010P = 4.46×10-14). The correlation between MS determined glycine and the NMR signals at that chemical shift is rs2 = 0.22. Although this correlation is modest, the correlation spectrum for glycine shows a distinct peak at δ = 3.599 ppm  gene product catalyzes the desaturation reaction of 8,11,14-eicosatrienoyl-CoA to arachidonoyl-CoA C20:3 → C20:4). Genetic variants in this locus have been linked to Crohn's disease . Recentl → C20:4. [et al. .P = 3.96×10-35). Interestingly, when using ratios between the NMR intensities at δ = 2.801 ppm and 2.017 ppm, the strength of association increases by nearly 60 orders of magnitude (P = 1.1×10-94), similar to the MS-based case. The NMR ratio δ = 2.801 ppm/δ = 2.017 ppm is therefore a likely proxy for the ratio between three- and four-fold desaturated long chain fatty acids. As a metabolic marker, this ratio might be a readout for the efficacy of the FADS1 enzymatic reaction in the context of dietary intake of PUFAs.In our data, the correlation spectra for glycerophospholipid levels show distinct differences depending on whether the degree of saturation of the side chains is below four double bonds (precursor of substrates of FADS1 enzymatic reaction) or equal or above four double bonds (products downstream of FADS1) Figure . When teThe product of the glucokinase regulator (GCKR) gene both transports and regulates glucokinase, a key enzyme of glucose metabolism . GCKR iss2 = 0.61) . When testing ratios for association, the strength of association increases by five orders of magnitude, with a P value of 2.8×10-15 for the association of SNP rs780094 to the NMR ratio δ = 1.370 ppm/δ = 3.286 ppm. The correlation spectrum with glucose shows a distinct signal at δ = 3.286 ppm (rs2 = 0.28). This chemical shift is indeed located within a known glucose-related spectral region. Furthermore, this NMR ratio correlates with the triglyceride/glucose ratio (rs2 = 0.42). Interestingly, GCKR is a diabetes risk locus that inversely modulates triglyceride and fasting glucose levels [In our study, SNP rs780094 (intronic region of GCKR) associates with NMR intensities at δ = 1.370 ppm. At this spectral position, we observe a high correlation between NMR signals and TG levels . However, as opposed to the FADS1 locus, the ratio here is between two chemical shift positions in direct neighborhood (δ = 2.757 ppm and 2.755 ppm). An inspection of the detailed spectrum differentiated by genotype reveals that only the signal at δ = 2.757 ppm actually shows clear genotype dependence, with a peak only detected in the major allele homozygote group x:y: Hydroxylacylcarnitine ; C0: Free carnitine; CETP: Cholesterylester transfer protein; CEU: Utah Residents with Northern and Western European Ancestry; CHR: Chromosome; CPS1: Carbamoyl-phosphate synthetase 1; CV: Coefficient of variation; Cx:y: Acylcarnitine ; Cx:y-DC: Dicarboxylacylcarnitine ; DNA: Deoxyribonucleic acid; DSS: 4,4-dimethyl-4-silapentane-1-sulfonic acid; EDTA: Ethylene diaminetetraacetic acid; ESI: Electro spray ionization; FADS1: Delta-5 fatty acid desaturase 1; FID: Free induction decay; GC: Gas chromatography; GCKR: Glucokinase regulator; GIM: Genetically influenced metabotype; GWAS: Genome-wide association study; H1: Hexose; HLD-C: High-density lipoprotein cholesterol; HMDB: Human Metabolome Database; IDL: Intermediate-density lipoprotein; KORA: Kooperative Gesundheitsforschung in der Region Augsburg ; LC: Liquid chromatography; LD: Linkage disequilibrium; LDL-C: Low-density lipoprotein cholesterol; LIPC: Hepatic lipase; LIT: Linear ion trap; m/z: Mass-to-charge ratio; MAF: Minor allele frequency; MS: Mass spectrometry; NCBI: National Center for Biotechnology Information; NMR: Nuclar magnetic resonance spectroscopy; PC aa Cx:y: Diacyl phosphatidylcholine ; PC ae Cx:y: Acyl-alkyl phosphatidylcholine; POS: Position; ppm: Parts per million; PUFA: Polyunsaturated fatty acid; PYROXD2: Pyridine nucleotide-disulphide oxidoreductase domain 2; Q-Q: Quantile-quantile; SM(OH) Cx:y: N-hydroxylacyloylsphingosylphosphocholine ; SM Cx:y: Sphingomyelin ; SNP: Single nucleotide polymorphism; TC: Total cholesterol; TG: Triglyceride; UHPLC: Ultrahigh performance liquid chromatography; VLDL: Very low-density lipoprotein.FB and PP are employed by numares GmbH. They contributed only to logistics, optimization of NMR spectroscopy, and to NMR data interpretation. numares was not involved in the design of the study, statistical analyses, or interpretation of the results. All other authors declare that they have no competing interests.Designed the study and wrote the paper: GK, JR, WR, KSu Contributed to data analysis and/or interpretation: JA, FB, CG, CH, TI, CM, AP, PP, KSt, HW Provided material and/or data: JA, CG, CH, TI, CM, HW All authors read and approved the final manuscript.Regional association plots, box plots, histograms, and quantile-quantile plots for the genetic associations and NMR traits reported in Table 1. Top: Regional association plots based on the SNPs that were used in our GWAS. Gene annotations and SNP positions are based on human genome hg18 (NCBI 36.1); linkage equilibrium correlation coefficients (r2) are based on Hapmap, release 21. Bottom left: Box plots of NMR signal intensities or NMR ratios for each genotype . The number of samples per group is indicated below the plot. Data are presented on a log10-normal scale. Bottom center: Histograms for NMR signal intensities or NMR ratios. The blue line and blue boxes indicate the distribution of the log10-scaled data, the red line indicates a normal distribution with the same mean and standard deviation as found in the log10-scaled data. Bottom right: Q-Q plots showing the observed versus the theoretically expected distribution of the associations' P values for all tested SNPs to the given NMR bin or NMR ratio.Click here for fileSpearman correlation plots between NMR chemical shifts and metabolite concentrations. The plots correspond to the correlations between metabolites and chemical shifts reported in Additional file Click here for fileTable S1. Spearman correlations between NMR intensities and metabolite concentrations measured on different platforms. The 'Chemical Shift' column lists the position of the signal intensities that show the best correlation (for rs2≥0.20) with the chemical compound noted in the 'Metabolite' column. '▲' 'indicates positive correlation, '▼' anticorrelation. 'N' is the number of samples used for calculating the correlations where valid NMR data points and metabolite concentrations were jointly available.'CV' gives the coefficient of variation in the quality control samples, where available. Chemical shifts are reported in parts per million (ppm).Table S2. Non-parametric tests for genetic associations with NMR bins and NMR ratios. All associations listed in Table 1 were tested separately using a non-parametric test. To test for associations between a SNP and an NMR trait , Spearman's rho statistic was used; the resulting P values are given as ps. For comparison, the P values of the age- and gender-corrected linear models are given as plm. Chemical shifts are reported in parts per million (ppm). See Table 1 for details about the SNPs and the number of tested traits for each variant.Click here for file


Using SNP genotypes to apply genomic selection in breeding programs is becoming common practice. Tools to edit and check the quality of genotype data are required. Checking for Mendelian inconsistencies makes it possible to identify animals for which pedigree information and genotype information are not in agreement.Straightforward tests to detect Mendelian inconsistencies exist that count the number of opposing homozygous marker (e.g. SNP) genotypes between parent and offspring (PAR-OFF). Here, we develop two tests to identify Mendelian inconsistencies between sibs. The first test counts SNP with opposing homozygous genotypes between sib pairs (SIBCOUNT). The second test compares pedigree and SNP-based relationships (SIBREL). All tests iteratively remove animals based on decreasing numbers of inconsistent parents and offspring or sibs. The PAR-OFF test, followed by either SIB test, was applied to a dataset comprising 2,078 genotyped cows and 211 genotyped sires. Theoretical expectations for distributions of test statistics of all three tests were calculated and compared to empirically derived values. Type I and II error rates were calculated after applying the tests to the edited data, while Mendelian inconsistencies were introduced by permuting pedigree against genotype data for various proportions of animals.Both SIB tests identified animal pairs for which pedigree and genomic relationships could be considered as inconsistent by visual inspection of a scatter plot of pairwise pedigree and SNP-based relationships. After removal of 235 animals with the PAR-OFF test, SIBCOUNT (SIBREL) identified 18 (22) additional inconsistent animals.Seventeen animals were identified by both methods. The numbers of incorrectly deleted animals (Type I error), were equally low for both methods, while the numbers of incorrectly non-deleted animals (Type II error), were considerably higher for SIBREL compared to SIBCOUNT.Tests to remove Mendelian inconsistencies between sibs should be preceded by a test for parent-offspring inconsistencies. This parent-offspring test should not only consider parent-offspring pairs based on pedigree data, but also those based on SNP information. Both SIB tests could identify pairs of sibs with Mendelian inconsistencies. Based on type I and II error rates, counting opposing homozygotes between sibs (SIBCOUNT) appears slightly more precise than comparing genomic and pedigree relationships (SIBREL) to detect Mendelian inconsistencies between sibs. Use of many SNP genotypes to apply genomic selection in breeding programs is becoming common practice. With the increasing importance of this new information source, the need for tools to edit and check the quality of this data increases as well. One of the common editing steps for marker (e.g. SNP) data, is to check for Mendelian inconsistencies . A MendeMendelian inconsistencies are usually identified by comparing the genotypes of one or both parents to the genotypes of their offspring. This comparison is straightforward, since it only involves checking for each locus whether one of the two alleles that the individual has could have been inherited from one of its parents. The expected number of inconsistencies between a genotyped parent-offspring pair and the variance of this expected number is very low when opposing homozygotes only result from genotyping errors . When twTherefore, the objective of this paper was to develop and demonstrate two tests, both comprising a set of rules that allow for the fast identification of sibs with conflicting genotype and pedigree information. The first test identifies sibs for which the number of contrasting homozygous genotypes does not match the expectation. The second test identifies sibs for which the pedigree and genomic relationships do not match. The performance of both tests was demonstrated on a dairy cattle dataset comprising predominantly genotyped cows. In addition, we derived the theoretical expectations and variance of the number of inconsistencies for unrelated animals, half-sibs and full-sibs, using observed allele frequencies.In this study, we compared two statistical tests to detect inconsistencies between pedigree and genotype information of supposed sib pairs. In both tests, the data was first checked for inconsistent parent-offspring pairs. Animals that were inconsistent with a supposed parent or offspring were detected, and problematic animals were iteratively removed, as described directly hereafter.Parent-offspring inconsistencies were detected by considering all pairs of animals that were supposed parent-offspring based either on the pedigree or the SNP information. For each genotyped pair of animals that were parent-offspring according to the pedigree, the number of opposing homozygous loci was counted. Two animals have opposing homozygous loci when one animal is homozygous for one allele, and the other animal is homozygous for the other allele. The realized distribution of the number of opposing homozygotes was used to define the threshold for declaring a parent-offspring pair inconsistent. Based on this distribution, we also identified all pairs of animals that were not parent-offspring pairs according to the pedigree, but that had a number of opposing homozygotes smaller than the threshold used for PAR-OFF similar to Hayes . To avoiInconsistent parent-offspring pairs were removed as follows.st degree genotyped relatives.1. Both animals from inconsistent parent-offspring pairs were removed when both animals in the pair had no other 12. If the parent was already removed, due to inconsistency with its genotyped parent(s), then the offspring was left in the data.3. When a parent had multiple genotyped offspring, it was removed only if it was inconsistent with more than 80% of its offspring. In all other cases, the inconsistent offspring were removed.After removing animals, locus-specific inconsistent genotypes of remaining parent-offspring pairs were set to missing for both animals. Then, the Beagle software  was usedAn iterative approach was used to discard animals from the dataset that caused inconsistencies between pairs of sibs. In the first step, all inconsistent pairs were identified and in subsequent steps, the animal with the highest number of inconsistencies was iteratively removed from the dataset until no inconsistencies remained. Detection of inconsistent pairs of sibs was either based on differences between pedigree and genomic relationships (SIBREL), or on the number of opposing homozygous genotypes (SIBCOUNT) between them.For each pair of genotyped animals for which pedigree records indicated that they were unrelated , half-sibs, or full-sibs, the number of opposing homozygous loci was counted. Empirical distributions of the number of opposing homozygous loci were used to define minimum thresholds for declaring inconsistent pairs of unrelated animals, half-sibs, and full-sibs. Animal pairs that had the same genotype for  all loci were also identified. This last category was expected to contain pairs of monozygotic twins based on the SNP information, but may have been caused by samples being mixed up . In other datasets, this category could also include split embryos used in embryo transfer and clones from nuclear transfer.n bi-allelic loci with allele frequencies i pand iq. Likewise, the expected number of opposing homozygous loci between two full-sibs is The empirical distributions of the number of opposing homozygotes were also compared to theoretically predicted distributions. The latter may be used when the number of observed relationships in a population for a given class is too low to obtain a proper empirical distribution. The expected number of opposing homozygous loci between two half-sibs is equal to Empirical distributions of pedigree and genomic relationships were first compared to expected distributions of relationships, which were derived in Appendix B. An algorithm was developed to efficiently compare pedigree and genomic relationships to identify inconsistent sib pairs. This algorithm comprises the following main steps that are explained in more detail below:1. calculate the pedigree relationship matrix for all genotyped animals with consideration of inbreeding using the complete pedigree information,2. calculate the genomic relationship matrix for all genotyped animals using genotype information,3. rescale the genomic relationship matrix such that the average genomic inbreeding coefficient is the same as in the pedigree relationship matrix,4. empirically derive the threshold for inconsistent pairs of half- and full-sibs, by identifying differences (i.e. lack of overlap) between distributions for different relationship classes,5. identify half- and full-sib pairs that are inconsistent based on the threshold defined under 4.A was calculated using the algorithm of Meuwissen and Luo [The pedigree-based relationship matrix  and Luo . Genomic and Luo :i pis the frequency of the second allele at locus i, and Z is an incidence matrix that stores the genotypes of all animals at all loci. Z is calculated as matrix M - 2(i p- 0.5). Matrix M contains elements -1, 0, and 1 for the three possible genotypes, where 1 codes for the genotype that is homozygous for the second allele. Note that G contains identical-by-state relationships, rather than identical-by-descent relationships. This means that the generation in which the allele frequencies i pare calculated, is considered to be the base generation, assuming that animals in that generation are unrelated. One way to put G and A on the same scale, is to estimate i pfor the considered base generation in A (i.e. the first generation of the available pedigree). For simplicity, i pwere calculated across all genotyped animals, meaning that the current population is the base generation, which implies that the genomic relationships were somewhat underestimated. To deal with this underestimation, G was rescaled as follows. The pedigree inbreeding coefficient was calculated for all animals, and averaged  was randomly shuffled amongst the permuted animals. This permutation simulated a situation in which possibly existing sib relationships based on the pedigree were not supported by the genotype information and vice versa. Pedigree relationships between all pairs of animals were compared before and after permutation. For all animals with a permuted pedigree, we checked if there was at least one other animal that was either a half- or full-sib, both before and after permuting the pedigree information. Such animals were deleted in this replicate to make sure that permuted animals really had inconsistent SNP and pedigree information. Finally, the type I error rate was calculated as the proportion of animals that were removed although their pedigree was correct (i.e. not permuted) and the type II error rate as the proportion of animals not removed although their pedigree was permuted. This whole process was done twice, once preceded by the PAR-OFF test, and once without doing the PAR-OFF test. When the PAR-OFF test was performed, type I and II error rates for SIBCOUNT and SIBREL were calculated based on the permuted animals that were not removed by PAR-OFF. Average type I and II error rates were calculated across 50 replicates of the permutation.2 less than 600 [In total, 2,359 animals with known pedigree were genotyped using the Illumina BovineSNP50 BeadChip . This data comprised Holstein-Friesian cows from experimental farms in Ireland, the UK, the Netherlands and Sweden, as well as sires of some of the genotyped cows. The quality control criteria for selecting the final set of SNP were a call rate of > 95%, a GenCall score > 0.2, and a GenTrain score > 0.55 , a minor allele frequency greater than 1% for each country, and a lack of deviation from Hardy-Weinberg equilibrium based on a χThe number of SNP loci with opposing homozygotes was first calculated between all pairs of animals Figure . Based oRelationships were calculated for pairs of half- and full-sibs, using either pedigree or SNP information Figure . The expTo visualize the relationship between the number of opposing homozygotes and the difference between pedigree and genomic relationships, both these variables were plotted against each other across all half- and full-sib pairs Figure . Based oDue to parent-offspring inconsistencies, 235 animals were removed from the data, of which 12 animals were part of a parent-offspring pair based on the SNP data but which was not supported by the pedigree data. Deleting the 235 animals with parent offspring inconsistencies removed many inconsistencies between the genomic and pedigree-based relationships, as can be seen by comparing Figures Type I and II error rates for SIBCOUNT and SIBREL were evaluated using the permuted data Table . Both meThe type II error rate, i.e. the proportion of incorrectly non-deleted animals, was considerably higher for SIBREL than for SIBCOUNT. Not performing PAR-OFF first, substantially decreased the type II error rates for both SIBCOUNT and SIBREL when 1% of the data was permuted, while they remained similar when 25% of the data was permuted. Type II error rates were quite high when only 1% of the animals was permuted. And for PAR-OFF they were only slightly affected by the percentage of pedigree permuted.To further gain insight on the performance of both tests, the absolute numbers of correctly deleted animals, and the number of type I and II errors were calculated Table . The resThe objective of this paper was to present two tests that comprise a set of rules for fast identification of supposed sib pairs for which genotype and pedigree information are inconsistent, either based on counting opposing homozygotes (SIBCOUNT), or based on comparing pedigree and genomic relationships (SIBREL). Both algorithms performed similar in terms of type I error rate, but the SIBCOUNT algorithm performed better based on realized type II error rate. Both algorithms can be applied to edit SNP data that are obtained in an experiment or in a practical breeding program. Although we applied the methods to a dataset with relatively large  families, both methods are expected to work equally well in populations with smaller  families, judging from the clear distributions of the test statistics Figure .In the first steps, when removing parent-offspring inconsistencies (PAR-OFF), the derived threshold of 250 inconsistent SNP was close to the value of 200 used by Wiggans et al.  and moreGenerally, SIBCOUNT and SIBREL performed similarly, as expected because the threshold for SIBREL was determined based on the corresponding count of opposing homozygotes Figure . Our resThe type II error rate for PAR-OFF was between 0.297 and 0.341. Of all genotyped animals that were included to calculate type II error rates, 16% had no genotyped offspring or parent. Thus, those animals could not fail the PAR-OFF test and when permuted automatically contributed to the type II error rate. Therefore, it appears that the 'true' type II error rate for PAR-OFF for this data was ~0.14 to 0.18. Given the very high accuracy to detect inconsistent parent-offspring pairs, or to assign animals to parents using 50k SNP [st degree genotyped relatives are available. For the SIBCOUNT algorithm, the formula presented in this study can be extended to predict the expected numbers of opposing homozygotes between two animals with a particular relationship between them. For the SIBREL algorithm, general formulae that predict variances of a range of relationships have been presented by Hill and Weir [In this study, we limited the detection of Mendelian inconsistencies to parent-offspring, half-sib or full-sib relationships. Both algorithms presented can, however, be extended to check for Mendelian inconsistencies for other relationships, such as half cousins, double cousins, or uncle-nephew relationships. Extensions with other relationships may help to avoid deleting animals incorrectly, when limited numbers of 1and Weir .Depending on the structure of the genotyped population, many animals may have e.g. several genotyped male ancestors that can be used instead. Wiggans et al.  presenteIn our data, we removed ~10% of the genotyped animals, which is in line with reported values of misidentification in commercial herds of 5 to 13% -18. An iThis study shows that tests for opposing homozygotes and comparison of genomic and pedigree-based relationships are powerful tools to detect sib pairs with inconsistent SNP and pedigree information. Counting the number of opposing homozygotes between pairs of sibs was slightly better at detecting inconsistent animals than comparing genomic and pedigree-based relationships, while both methods were equally likely to remove animals that in reality were consistent. Our results showed that tests to remove Mendelian inconsistencies between sibs should be preceded by a test for parent-offspring inconsistencies. These should be detected in two directions: 1) assuming that the pedigree is correct and test whether the SNP data of considered parent-offspring pairs is in agreement with the pedigree, and 2) assuming that the SNP data is correct and test whether the pedigree of considered parent-offspring pairs is in agreement with the SNP data.The authors declare that they have no competing interests.MPLC wrote the algorithms, performed the analyses and drafted the first version of the manuscript. HAM participated in discussions on the rules used in the described algorithm and critically contributed to the final version of the manuscript. JWMB performed the initial quality control steps on the SNP data and critically contributed to the final version of the manuscript. All authors read and approved the final manuscript.i between any two animals is equal to the probability that the first animal is homozygous for the first allele and the second animal is homozygous for the second allele, or vice versa. This is hereafter referred to as the probability that two animals have opposing homozygous genotypes.In all derivations below, we assume that animals are not inbred. The probability that an inconsistency occurs on SNP locus i (qi) pof the first (second) allele at locus i, this probability is: For two unrelated individuals in a population, given a frequency of n loci for two unrelated animals, regardless whether any of the loci are linked to each other, therefore is: The number of expected opposing homozygotes across iqip), both half-sibs receive different alleles from the common parent (2 × 1/2 × 1/2), and both half-sibs are homozygous, i.e. receive the same allele from the other parent as from the common parent (iqip). This probability therefore is: For two half-sibs in a population, the probability that they have opposing homozygous genotypes is equal to the probability that the common parent is heterozygous  = x(1 - x)The variance of the expected number of opposing homozygous genotypes at locus x is equal to the probability that two animals have opposing homozygous genotypes at locus i. This probability is derived above for pairs of unrelated animals, half-sibs and full-sibs. The variance of the expected number of opposing homozygotes across n loci, involves both the variance at each of the loci, but also the covariance between any pair of loci. The covariance of the expected number of opposing homozygotes between loci i and j is equal to the probability that two animals have opposing homozygotes both at locus i and j. Considering bi-allelic loci, with alleles 1 and 2 segregating at each locus, there are four possible haplotypes for loci i and j: 11, 12, 21, and 22, with probabilities ij f(11), ij f(12), ij f(21), and ij f(22). The probability that two unrelated animals have opposing homozygotes at both locus i and j is equal to the probability that the first (second) animal has two haplotypes 11 (22), or vice versa, plus the probability that the first (second) animal has two haplotypes 12 (21), or vice versa. The covariance in opposing homozygotes between locus i and j for two unrelated animals is equal to this probability, minus the probability that those animals are inconsistent between locus i and j due to chance rather than linkage disequilibrium between the loci . For full-sibs, this covariance reduces by a factor 4, because animals need to receive a different haplotype from the common parent (which is only the case in one out of four possible scenarios).ij f(11), ij f(12), ij f(21), and ij f(22) are simply the frequency of the haplotypes in the population. For unlinked loci, i.e. loci with an (expected) recombination rate of 0.5, E(ij f(11)) = ipjp, E(ij f(22)) = iqjq, E(ij f(12)) = iqjp, E(ij f(21)) = ipjq, and therefore the expected covariance in opposing homozygotes between unlinked loci i and j is equal to zero. Therefore, we consider only covariances between pairs of loci that are located on the same chromosome.Ignoring recombination for closely linked loci, and assuming linkage equilibrium for non-linked loci, n loci):Thus, the total variance of the number of opposing homozygotes between two unrelated animals is  = ip, ii f(22) = iq, and ii f(12) = ii f(21) = 0, the formula can be more generally written as:And, realizing that Similarly, for two half-sibs, the total variance of the number of opposing homozygotes isAnd, for two full-sibs, the total variance of the number of opposing homozygotes isThe variance of the total number of opposing homozygous loci across the whole genome is the sum of the above variances for all chromosomes.The expected variance of half-sib relationships was calculated using the following formula :L is the genome size, v is the number of chromosomes, and j lis the length of chromosome j. In this study we considered all 29 bovine autosomes. Therefore, L was considered to be 30.14 M, using the values for j las reported by Ihara et al. [2V(HSP) [where a et al. . For ful[2V(PHS) .