Penalized Multiple Regression (PMR) can be used to discover novel disease associations in GWAS datasets. In practice, proposed PMR methods have not been able to identify well-supported associations in GWAS that are undetectable by standard association tests and thus these methods are not widely applied. Here, we present a combined algorithmic and heuristic framework for PUMA  analysis that solves the problems of previously proposed methods including computational speed, poor performance on genome-scale simulated data, and identification of too many associations for real data to be biologically plausible. The framework includes a new minorize-maximization (MM) algorithm for generalized linear models (GLM) combined with heuristic model selection and testing methods for identification of robust associations. The PUMA framework implements the penalized maximum likelihood penalties previously proposed for GWAS analysis , as well as a penalty that has not been previously applied to GWAS (i.e. LOG). Using simulations that closely mirror real GWAS data, we show that our framework has high performance and reliably increases power to detect weak associations, while existing PMR methods can perform worse than single marker testing in overall performance. To demonstrate the empirical value of PUMA, we analyzed GWAS data for type 1 diabetes, Crohns's disease, and rheumatoid arthritis, three autoimmune diseases from the original Wellcome Trust Case Control Consortium. Our analysis replicates known associations for these diseases and we discover novel etiologically relevant susceptibility loci that are invisible to standard single marker tests, including six novel associations implicating genes involved in pancreatic function, insulin pathways and immune-cell function in type 1 diabetes; three novel associations implicating genes in pro- and anti-inflammatory pathways in Crohn's disease; and one novel association implicating a gene involved in apoptosis pathways in rheumatoid arthritis. We provide software for applying our PUMA analysis framework. Genome-wide association studies (GWAS) have identified hundreds of regions of the human genome that are associated with susceptibility to common diseases. Yet many lines of evidence indicate that many susceptibility loci, which cannot be detected by standard statistical methods, remain to be discovered. We have developed PUMA, a framework for applying a family of penalized regression methods that simultaneously consider multiple susceptibility loci in the same statistical model. We demonstrate through simulations that our framework has increased power to detect weak associations compared to both standard GWAS analysis methods and previous applications of penalized methods. We applied PUMA to identify novel susceptibility loci for type 1 diabetes, Crohn's disease and rheumatoid arthritis, where the novel disease loci we identified have been previously associated with similar diseases or are known to function in relevant biological pathways. Genome-wide association studies (GWAS) have identified many susceptibility loci underlying the molecular etiology of complex diseases Here, we report a general framework for applying a family of GWAS analysis methods that is extremely promising for detection of weak associations yet has not been widely applied to learn novel biology from GWAS datasets: penalized multiple regression (PMR) methods. PMR methods work by simultaneously incorporating tens to hundreds of thousands of genetic markers in a single statistical model where a penalty is incorporated to force most marker regression coefficients to be exactly zero, so that only a small fraction are estimated to make a contribution to disease risk post hoc methods for assessing the rank of identified associations. Within PUMA, we implement all sparse feature selection, penalized regression approaches proposed for GWAS analysis to date, including four penalties implemented in a maximum likelihood framework , as well as theoretically justified penalties that have not been previously applied to GWAS (i.e. LOG)  analysis that optimizes these methods for reliable detection of weak associations when applied to large GWAS datasets. The complete PUMA framework includes an extremely efficient implementation of a new minorize-maximization (MM) algorithm .e. LOG) . We demoThe methods implemented in our PUMA framework are orders of magnitude faster than existing software when assigned identical computational tasks and no pre-screening of markers is performed . This suWhile pre-screening markers based on a p-value cutoff may initially seem to detract from the purpose of a multiple-locus analysis, it is supported by statistical theory, is necessary for large scale analysis and has almost no impact on the set of markers identified as associated. In a seminal paper, Fan and Lv We use a pre-screening p-value cutoff based on single marker analysis, because 1) it retains all relevant variables asymptotically We demonstrate this final and most important point in two complementary simulation studies. First we consider a simple two-step forward regression method, which is known to approximate penalized multiple regression We analyzed 960 simulated GWAS datasets to assess the performance of our PUMA framework compared to other published methods for PMR GWAS analysis. We note that these simulations, while far more extensive than other published works on PMR GWAS analysis We assessed the performance of PMR methods for which there is available software. We compared the performance of the Lasso penalty from Wu, et al. Simulations indicate that HyperLasso a priori. Furthermore, determining the appropriate cutoff for a desired eFPR for correlated high-dimensional data is the subject of current research We note that for perm-MCP, by setting the expected false positive rate (eFPR) and using permutations to obtain the value of the tuning parameter based on this rate, perm-MCP generates a single model with relatively few nonzero coefficients while explicitly addressing the multiple testing problem. Yet in practice this result indicates that perm-MCP may assign p-values to only a handful of markers so that the method may not identify any novel associations for a particular dataset. Since the number of nonzero coefficients is directly related to the specified eFPR and the pre-screening cutoff, we examined multiple eFPR values  performs a two dimensional search of the tuning parameter space 2) selects the number of nonzero coefficients based on both the fit to the data and the sample size, and 3) uses a heuristic methods to assess the significance of correlated markers. Conversely, perm-MCP fixes one of the tuning parameters, does not incorporate the sample size, and does not address the issues of testing the significance of correlated markers. Moreover, perm-MCP relies on setting the eFPR despite problem of determining an appropriate value For the 960 simulated GWAS datasets we analyzed, almost all PMR GWAS approaches implemented in PUMA except NEG and adaptive Lasso outperformed single marker analysis under simulation conditions with sufficient sample size , S9, S10While the penalized methods implemented in our PUMA framework consistently had higher power than single marker analysis as a function of FDR under most simulation conditions, none of the penalties consistently stood out as the most powerful. However, our PUMA framework, which includes a fast novel algorithm for penalized maximum likelihood estimation in generalized linear models, data-adaptive tuning of tuning parameters, heuristics for model selection and novel method of assigning p-values see  increasepost hoc analysis and discussion.In our re-analysis of type 1 diabetes, Crohn's disease and rheumatoid arthritis datasets, we applied a single-marker analysis and all PMR analysis approaches  using all the recommended components of our framework. We included sex and the first two principal components as unpenalized covariates, applied a pre-screening cutoff of 0.01 on the p-values from the single marker test, and ran 100 reorderings for the non-convex penalties. Quantile-Quantile (QQ) plots of p-values from a standard single marker analysis indicate that the effects of any remaining population structure is minimal. Moreover, including the subset of significantly associated markers identified by the PMR methods as covariates in a single marker analysis of remaining markers does not yield an inflation of the QQ plots and thus indicates that the PMR methods are not overfitting the data . We alsoOur single-marker re-analysis of type 1 diabetes, Crohn's disease and rheumatoid arthritis datasets reproduced the same associations as reported in the original analysis . Our PMRA critical point to note about the performance of our PUMA framework for PMR analysis of GWAS data is that these methods not only result in the correct identification of more loci than a single marker testing analysis , but also lead to re-orderings of the rank of markers that are considered the most significant when compared to a single marker analysis . As a co−7.The associations identified by PUMA generally recapitulate associations identified by single marker analysis, and the PUMA hits have perfect concordance for strong associations. Overall 2D-MCP recapitulates the largest number of associations, while the union of the other PMR methods  had a lower degree of concordance with the single marker analysis . Of the We compared associations identified by our PUMA methods that were not detected by single marker tests in the WTCCC dataset to markers identified by independent studies in the HuGE database of published GWAS While all PUMA methods and a single marker test are able to replicate associations from independent studies, LOG, NEG and 1D-MCP, stood out in terms of identifying associations replicated by non-independent studies, but not detected in the WTCCC dataset by a single marker analysis. These counts reflect the results when the number of markers considered as ‘hits’ was set to be equal across methods so that they reflect the ordering of markers by PMR methods rather than the number of associations. When comparing the total number of significant hits from each method to associations identified in either independent studies or non-independent external studies that incorporated WTCCC data, 2D-MCP is the only PMR method to identify as many total replicated associations as a single marker test , S19. HoRe-analysis of type 1 diabetes, Crohn's disease and rheumatoid arthritis datasets from the original WTCCC PUMA methods identified novel susceptibility loci for type 1 diabetes involved in pancreatic function, insulin pathways and immune cell function and for Crohn's disease that are involved in pro- and anti-inflammatory pathways . 2D-MCP Each GWAS discovery that has a well supported association produces valuable information for understanding the etiology of the disease phenotype and such discoveries are regularly used as the foundation for studies that use the locus as a starting point A critical property of our PUMA framework is it does not return the same ordering of significant markers produced by a standard single marker analysis. By simultaneously accounting for the associations of multiple loci and better reflecting the underlying polygenic architecture of complex phenotypes, PUMA can find strong statistical support for associations deemed non-significant by a single marker analysis and places these among the top list of associations. A prime example is marker rs613232 which had a p-value of 6.51 of 6.96 , Table 5was 3.78 , Table 5The PUMA framework and software that we present here is immediately applicable to a large number of existing GWAS and we are currently exploring extensions of the framework to address additional challenges in GWAS experimental designs and GWAS analysis. For example, GWAS discoveries are regularly being produced by consortia that combine several independently executed GWAS experiments. Such combined data introduce a number of complexities including complex batch effects, population structure, relatedness, and latent environmental variables. While meta-analysis techniques for combining p-values across studies are a good approach to normalizing for many of these issues post hoc model fitting approaches for ranking associated markers.Our framework is a combination of algorithms and heuristic approaches designed for robust and efficient analysis of GWAS datasets when the desired output is a ranked list of genetic markers that individually tag disease loci. The value of the framework is that tag genetic markers, which are too weak to be reliably identified by a single marker analysis, can be identified while preserving a conservative FDR genome-wide. To solve issues that have limited the value of existing PMR GWAS software for this purpose, we designed our framework to have the following properties: 1) the versatility to handle a diversity of penalties for simultaneous analysis of thousands to millions of genetic markers while incorporating unpenalized covariates, 2) the efficiency to analyze up to millions of markers after pre-screening on a standard desktop, 3) the sensitivity to tune the strength of penalties and to perform model selection when the fraction of variation accounted for by disease loci identifiable with tag markers is small , and 4) the capability to return a ranked list of p-values where each of the top markers identifies an independent disease association. We outline the components of our framework responsible for each of these properties in the next four sections, followed by a description of our software PUMA that implements our recommended practices and options for implementation. We note that in its entirety, this framework is a new GWAS analysis approach that incorporates novel components including (but not limited to): application of penalties not previously applied to GWAS, a new MM algorithm for GLMs, heuristics for penalty strength and model selection, and Our framework makes use of a generalized linear modeling (GLM) framework to construct the likelihood objective function. We can therefore model phenotypes measured on a large diversity of scales by implementing an appropriate link function For marker selection, we use the penalized maximum likelihood estimate (pMLE) of the regression coefficients:The Lasso penalty The Adaptive Lasso penalty The NEG penalty grpregThe MCP penalty We also implement the LOG penalty and apply it to GWAS for the first time. The LOG penalty Our framework implements a highly efficient algorithm and optimized coding practices to allow fast simultaneous analysis of genetic markers in the range of hundreds of thousands to millions. We implement a new minorize-maximization (MM) algorithm for finding pMLE by using a coordinate-wise ascent approach with an upper bound on the second derivative of the likelihood function Critical to the performance of our framework is preserving a conservative control of the FDR for identified markers. To accomplish this, we employ a strategy that allows our PMR methods to automatically adapt, not only to the sample size of the dataset, but also to the number and magnitude of the non-zero regression coefficients for relevant markers associated with the phenotype. Our approach includes an adaptive tuning of penalty strength in combination with model selection and assessment of model fit.Statistical theory considering linear regression has shown that for a sample size of Once sets of markers with nonzero coefficients are identified for each value of the tuning parameters for a given penalty, the optimal set is determined. We assessed the overall appropriateness of the fit of a selected model based on a QQ plot by fitting an unpenalized model with selected markers, and calculating p-values for each marker in the dataset by regressing it against the residuals from the first step  [79].A slight inflation of The most valuable final output of a PMR GWAS analysis is a ranked list of markers in decreasing order of highest confidence. Standard methods for producing such ranked lists in a PMR framework assess significance by conducting variable selection on a subset of the data and assessing significance on another subset We deal with the problem of producing an informative ranked list of selected markers in our framework by initially fitting an unpenalized regression model with all markers selected by a given PMR and including relevant covariates, and calculating p-values for each marker using a standard likelihood ratio test by comparing the full model to null models where each marker is omitted in turn. The correlation between all pairs of selected markers is then evaluated, the pair of markers with the largest correlation is identified, the marker with the smallest absolute regression coefficient of the two is dropped, and p-values are then recalculated for the remaining markers. This process is repeated until no pairwise correlation between remaining markers exceeds 0.1 and each marker is finally assigned the smallest p-value produced for it during this processes. This heuristic procedure means that the values cannot be interpreted strictly as asymptotic p-values http://mezeylab.cb.bscb.cornell.edu/Software.aspx.PUMA implements both linear and logistic models for PMR methods, as well as single marker analysis, a conditional regression analysis, and the variational Bayes multiple regression method VBAY For the single marker analysis, p-values are calculated using a standard F-test or likelihood ratio test The default settings of PUMA are our recommended settings for a GWAS analysis, which are the same procedures we followed for our analysis of the WTCCC data here:Marker imputation: Beagle Inclusion of fixed covariates: Identify relevant covariates and principal components and perform single marker analysis so that the corresponding QQ plot and Marker filtering: We applied a pre-screening filter based on p-values from single marker analysis using a cutoff of Number of restarts: The penalized likelihood for the 1D-MCP, 2D-MCP, NEG and LOG penalties is non-convex so 100 reorderings were used to explore the multimodal surface for each setting of the tuning parameters.Performance assessment: We recommend assessing the fit of a PMR model by including the selected markers as covariates in a subsequent single marker analysis. Too much inflation or deflation of the p-values indicates that the PMR method may be overfitting the data.Threshold determination: We have demonstrated that the reported p-value score statistics are valuable at prioritizing the top hits as well as novel weak associations, so assessing the list in rank order is the suggested strategy for minimizing false positives. For example, in our current analyses we examined at most the top 30 hits for each method combined across the three diseases, which limited our focus to markers with a p-value score of Our approach was to simulate different sized GWAS experiments where we used the real genetic markers for unrelated European individuals from the Multi-Ethnic Study of Atherosclerosis (MESA) Following the performance evaluation of previous studies To run the data analysis we used the same quality control filters as in the Wellcome Trust Case Control Consortium, first by excluding 809 individuals because of poor sample quality, non-Caucasian ancestry, or a high degree of relatedness In order to explore the biological function, relevant pathways and possible disease implications of each gene near a significantly associated marker, we mined public databases including GenBank Figure S1Assessing p-value cutoff in two-step forward regression. Plots show (PDF)Click here for additional data file.Figure S2Effect of pre-screening on performance. (a) 100 replicate simulations with 500 K markers, 50 causal markers, heritability of 50% and 1000 or 2000 individuals using Lasso and MCP methods show that using a pre-screening p-value cutoff of 1, 0.10 and 0.01 has no noticeable effect of performance of PUMA. Note that the performance was so similar for all cutoffs that the curves are overlapping. (b) Running times for simulations in (a) show that pre-screening substantually reduces computational time. We note that simulations with 5000 individuals were not possible due to the very high memory requirements of running PUMA without prescreening.(PDF)Click here for additional data file.Figure S3Power vs sample size. Simulation results showing power for our PMR methods, current PMR methods, an approximate Bayesian method, single marker analysis and conditional regression methods at an FDR of 5% as a function of sample size as in (PDF)Click here for additional data file.Figure S4Power vs number of causal markers. Simulation results showing power for our PMR methods, current PMR methods, an approximate Bayesian method, single marker analysis and conditional regression methods at an FDR of 5% as a function of the number of susceptibility loci. (PDF)Click here for additional data file.Figure S5Power vs marginal heritability for 1000 samples. Simulation results showing power a sample size of 1000 for our PMR methods, current PMR methods, an approximate Bayesian method, single marker analysis and conditional regression methods at an FDR of 5% as a function of the marginal heritability of each causal marker as in (PDF)Click here for additional data file.Figure S6Power vs marginal heritability for 2000 samples. Simulation results showing power a sample size of 2000 for our PMR methods, current PMR methods, an approximate Bayesian method, single marker analysis and conditional regression methods at an FDR of 5% as a function of the marginal heritability of each causal marker as in (PDF)Click here for additional data file.Figure S7Power vs marginal heritability for 5000 samples. Simulation results showing power a sample size of 5000 for our PMR methods, current PMR methods, an approximate Bayesian method, single marker analysis and conditional regression methods at an FDR of 5% as a function of the marginal heritability of each causal marker as in (PDF)Click here for additional data file.Figure S8Precision-Recall curves for 1000 samples. Simulation results showing precision-recall curves for a sample size of 1000. (PDF)Click here for additional data file.Figure S9Precision-Recall curves for 2000 samples. Simulation results showing precision-recall curves for a sample size of 2000. (PDF)Click here for additional data file.Figure S10Precision-Recall curves for 5000 samples. Simulation results showing precision-recall curves for a sample size of 5000. (PDF)Click here for additional data file.Figure S11Precision-Recall curves for perm-MCP for multiple values of eFPR and pre-screening p-value cutoff. Simulations for 5000 samples, 20 causal markers and heritability of 50% using eFPR values (1(PDF)Click here for additional data file.Figure S12a) Crohn's disease, b) Rheumatoid arthritis and c) Type 1 diabetes. Quantile-Quantile plots for each disease and method. Plots are shown for (PDF)Click here for additional data file.Figure S13a) Crohn's disease, b) Rheumatoid arthritis, and c) Type 1 diabetes datasets from our re-analysis. Shown are Manhattan plots of single marker analysis for three disease datasets. Manhattan plots showing results of single marker analysis for (PDF)Click here for additional data file.Figure S14a) Crohn's disease, b) rheumatoid arthritis and c) type 1 diabetes using PMR methods, conditional regression, and single marker analysis. External associations from independent datasets (which do not include WTCCC data) and non-independent datasets (which include WTCCC data) of the same disease are indicated with pink boxes and diamonds, respectively. Markers that are considered associations only when the p-value threshold for the single marker analysis is relaxed to match the same number of associations (with hits in the MHC region excluded) as the union of all PMR methods are indicated with black circles. Arrows indicate novel associations that are biologically interpretable.Genome-wide plots of hits found by each method. Genome-wide plot of associations identified by analyzing the WTCCC data for (PDF)Click here for additional data file.Figure S15Local manhattan plots of hits replicated from an independent study of Crohn's disease.(PDF)Click here for additional data file.Figure S16Local manhattan plots of hits replicated from an independent study of rheumatoid arthritis.(PDF)Click here for additional data file.Figure S17Local manhattan plots of hits replicated from an independent study of type 1 diabetes.(PDF)Click here for additional data file.Figure S18Local manhattan plots hits replicated from a non-independent study of Crohn's disease.(PDF)Click here for additional data file.Figure S19Local manhattan plots of hits replicated from a non-independent study of type 1 diabetes.(PDF)Click here for additional data file.Figure S20Local manhattan plots of biologically relevant hits for Crohn's disease.(PDF)Click here for additional data file.Figure S21Local manhattan plots of biologically relevant hits for rheumatoid arthritis.(PDF)Click here for additional data file.Figure S22Local manhattan plots of biologically relevant hits for type 1 diabetes.(PDF)Click here for additional data file.Table S1Concordance of PMR hits with single marker analysis. Number of regions identified by a single marker analysis with a p-value(PDF)Click here for additional data file.Table S2Regions identified only by single marker analysis. Regions identified by single marker analysis with a p-value(PDF)Click here for additional data file.Table S3Associations recapitulated in independent studies. Regions which are significant either by single marker analysis, conditional regression, or a PMR method and which recapitulate a known association to the same disease in an independent study that does not include data from the WTCCC. The table includes all regions with a VBAY posterior probability(PDF)Click here for additional data file.Table S4Associations recapitulated in non-independent studies. Regions which are significant either by single marker analysis, conditional regression, or a PMR method and which recapitulate a known association to the same disease in a non-independent study that includes data from the WTCCC. The table includes all regions with a VBAY posterior probability (PDF)Click here for additional data file.Table S5a) independent (not including WTCC data) and b) non-independent (including WTCC data) datasets, where the number of markers considered as ‘hits’ is set to be equal across methods. For each method the number of hits is set to a given value and the number of replications is reported. Numbers in parentheses indicate the number of hits that are distinct from those found by the single marker analysis.Replication counts for equal numbers of hits. For each method, the number of associations in this re-analysis that replicate associations identified in (PDF)Click here for additional data file.Table S6Additional associations for Crohn's disease. Additional associations for Crohn's disease identified by PMR methods but not a single marker analysis.(PDF)Click here for additional data file.Table S7Additional associations for rheumatoid arthritis. Additional associations for rheumatoid arthritis identified by PMR methods but not a single marker analysis.(PDF)Click here for additional data file.Table S8Additional associations for type 1 diabetes. Additional associations for type 1 diabetes identified by PMR methods but not a single marker analysis.(PDF)Click here for additional data file.Text S1Parameters for running HyperLasso.(PDF)Click here for additional data file.Text S2Efficient coordinate-wise gradient descent algorithms for high-dimensional penalized generalized linear models with convex or nonconvex penalties.(PDF)Click here for additional data file.


A GLM that accounts for population structure (Q) or standard mixed linear model that accounts for kinship (K) can identify tan1-a, whereas a compressed mixed linear model performs worse than the naive GLM. Interestingly, a simple loss-of-function genome scan, for genotype-phenotype covariation only in the putative loss-of-function allele, is able to precisely identify the Tannin1 gene without considering relatedness. We also find that the tan1-a allele can be mapped with gene resolution in a biparental recombinant inbred line family (n = 263) using genotyping-by-sequencing markers but lower precision in the mapping of vegetative pigmentation traits suggest that consistent gene-level resolution will likely require larger families or multiple recombinant inbred lines. These findings highlight that complex association signals can emerge from even the simplest traits given epistasis and structured alleles, but that gene-resolution mapping of these traits is possible with high marker density and appropriate models.Genome-wide association studies are a powerful method to dissect the genetic basis of traits, although in practice the effects of complex genetic architecture and population structure remain poorly understood. To compare mapping strategies we dissected the genetic control of flavonoid pigmentation traits in the cereal grass sorghum by using high-resolution genotyping-by-sequencing single-nucleotide polymorphism markers. Studying the grain tannin trait, we find that general linear models (GLMs) are not able to precisely map  FRIGIDA expression in Arabidopsis (Genome-wide association studies (GWAS) have been used to dissect the genetic basis of complex traits in humans , and crovs. structured models, further empirical studies of validated functional variants are needed to inform investigations of novel trait loci. Moreover, it has been argued that the impact and prevalence of synthetic associations will only be determined empirically , will yield inflated association signals when used for structured traits . Given tirically .Supporting Information, Table S1). Although the core components of the flavonoid network are relatively well-understood, there are a number of areas that remain to be elucidated, including the polymerization and transport of tannins  Moench] there is abundant natural variation for flavonoid pigmentation, which underlies a number of agronomic traits, such as grain mold  and anti-inflammatory properties (B1 and B2), pericarp , coleoptile , and adult vegetative leaf and stem (P and Q) , which controls pericarp pigmentation and phytoalexin production (Tannin1), which controls the presence of tannins in the testa  and complementary dominance between at least two loss-of-function loci  . In addia priori candidate gene set for comparison with mapping results, we conducted a systematic survey of flavonoid-related gene families in the reference sorghum genome  that were developed as a stem borer resistance mapping population but also segregate flavonoid pigmentation phenotypes (http://sourceforge.net/projects/tassel/).Genotypes for this study were generated with genotyping-by-sequencing  were previously published (http://www.ars-grin.gov). The presence or absence of a pigmented testa on the grains was visually assessed (three seeds per accession) after removal of the pericarp on the dorsal side and scored as 1 and 0, respectively (File S2). Eleven accessions that showed a segregating phenotype were dropped from the analysis. Pericarp pigmentation was visually assessed for three seeds per accession, scored as 0 for white and 1 for red or yellow (File S2). Brown pericarp accessions were dropped from the analysis because this phenotype is known to be caused by the spread of tannin from the testa and masks the expression of the R and Y genes  in world sorghum collections from the Germplasm Resource Information Network. For the RIL family, phenotyping was performed in the 2007 and 2008 kharif (rainy) season in Patancheru, India, with presence/absence of pigmentation scored for 10-wk-old seedlings (coleoptile color) or physiologically mature plants , or compressed mixed linear model (CMLM) with population parameters previously determined . GeneticP-value for a given SNP  is calculated with binomial tests in R , respectively, W1 and W2 are the counts of the wild-type phenotype for alleles 1 and 2 (“failures”), respectively, and P is the overall proportion of loss-of-function phenotypes given by P = (L1+ L2)/(L1+ L2+ W1+ W2).Loss-of-function genome scan sts in R  as follon = 142) global diversity panel (Tannin1 coding region (S4_61667908) that is 218 bp upstream of, and in perfect linkage disequilibrium with, the G-deletion that is causative for the tan1-a null allele (n = 161) (tan1-a SNP) as a positive control to compare mapping approaches. Using a simple model without statistical control for population structure  we find that, as expected, the most significant association signals lies at ~61 Mb on chromosome 4 colocalized with the Tannin1 locus . Instead, the most significant association peaks are found in the ~1-Mb region surrounding Tannin1, at 61.1 Mb , 61.2 Mb , and 61.8 Mb . Including the Tannin1 locus, we observe at least 13 peaks of association that are significant at a nominal Bonferroni-corrected P-value of 0.01 (P < 2 × 10−7), among which are additional candidate loci for genetic control of tannin pigmentation (File S3).To identify loci underlying natural variation in grain tannin pigmentation, we first characterized associations between published tannin (presence/absence) phenotypes from a small  does not improve the mapping resolution at the Tannin1 locus, as the tan1-a SNP remains less significant (P < 10−4) than several other SNPs in the ~1 Mb region surrounding Tannin1 (P < 10−6).Given the extensive population structure in sorghum, as well as kinship among elite sorghum lines, we also carried out GWAS using MLMs that take into account population structure (Q) and/or kinship (K) . We fit Tannin1 in the small association panel is caused by a small sample size, then increasing the size of the association panel should improve the mapping resolution. Therefore, we phenotyped testa presence/absence in the sorghum association panel , but is still not the top association. Adding control for population structure and kinship using CMLM (K or Q+K), we find the rank and significance of the tan1-a SNP is actually reduced compared with the results using a GLM (P = 0.09). Finally, a GLM with population term (Q) or a standard MLM .If the inability to precisely map n = 336; . Fitting K only;  that tretan1-a SNP? To better understand the population structure of natural variation in tannins, we characterized the distribution of pigmented testa phenotype in worldwide sorghum collections. The tannin trait segregates in all the botanical races of sorghum but shows modest population structure, with durra and guinea types having the lowest proportion of tannin accessions (15%) and caudatum and guinea-caudatum accessions having the greatest proportion . However, with respect to model selection in GWAS, the structuring of the trait itself may be less important than structuring of the alleles underlying the trait. The tan1-a allele is found at high frequency in African and Indian durra accessions and at low frequency in Chinese and southern African accessions  perform worse than a naive model (GLM), generating a false-negative result for the cessions . The tantan1-a in an association population difficult, we considered whether the reduced genetic and allelic heterogeneity of a biparental family would allow precise mapping of Tannin1 using linear models. We phenotyped testa pigmentation (tannin presence) in a population of 263 RILs that we genotyped at 265,487 SNPs. There is a single locus associated with the pigmented testa in this family that is precisely colocalized with Tannin1 on chromosome 4, with the most significant SNP being the tan1-a SNP . This peak colocalizes with the classical Rs1 locus and a priori candidate gene Sb06g025060, a putative basic helix-loop-helix (bHLH) transcription factor, and a sorghum co-ortholog of Arabidopsis TRANSPARENT TESTA8 and maize B1/R1 anthocyanin regulators (File S3). However, the most significant SNP (S6_53849573) is 220 kb upstream of Sb06g025060, and no promising a posteriori candidate genes are found at S6_53849573, suggesting gene resolution was not achieved in this case. Adult plant color maps to 58 Mb on chromosome 6, colocalized with the classical P locus (TRANSPARENT TESTA3 and BANYULS and maize ANTHOCYANINLESS1 (File S1). Here again, the most significant SNP (S6_57865283) is not colocalized precisely with the a priori candidates (TT3/BANYULS cluster) but 260 kb upstream .Given that complex association signals made the precise mapping of n1-a SNP . To dete P locus  and a latan1-a allele in association panels, even though it is common and highly penetrant? A comparison of the 2 × 2 contingency tables for the tan1-a SNP vs. the more significant SNPs provides some insight here  but little signal of covariation for the wild-type allele . Although this lack of covariation for the wild-type allele is to be expected , it reduces the significance of a linear model fitting the genotype-phenotype association. In contrast, the other more significant SNPs near Tannin1 show covariation for both alleles (in opposite directions), with the wild-type allele more often found with the wild-type phenotype . We identified SNPs with alleles that are often found in individuals with the loss-of-function phenotype (testa absent) and rarely or never found in individuals with the wild-type phenotype (testa present). In effect, the phenotypes at the putative wild-type allele at each SNP is ignored. With this loss-of-function genome scan approach, the tan1-a SNP is precisely identified whereas other SNPs near the Tannin1 locus that had strong indirect associations with linear modeling have reduced association signals . Thus, in this case we find that a simple heuristic scan that considers the underlying genetics of the trait outperforms more sophisticated models.To investigate an approach that may be appropriate for loss-of-function alleles we used a simple heuristic genome scan based on a binomial test  but the most significant association are ~0.5 Mb from Y1 (S1_61717652). Because white pericarp represents loss-of-function phenotype, we also used the loss-of-function genome scan approach for the pericarp pigmentation trait. In this case, the loss-of-function genome scan does not improve the mapping resolution as compared to the linear models.Although we found that gene-resolution mapping was possible with s exists . As expes exists . As was B1 and B2) that have been mapped to chromosome 2 and chromosome 4, and one of these was cloned as WD40 gene Tannin1 , there is evidence that the gene underlying B1 is the putative bHLH transcription factor Sb02g006390. This study is based on qualitative tannin phenotypes (presence/absence) so quantitative phenotyping may reveal additional loci underlying the observed variation among intermediate and high tannin varieties , as the major locus underlying testa presence/absence, but the precise identification of the Tannin1 gene was not consistently obtained. Increasing the panel size increased the significance of the tan1-a SNP relative to the indirect associations. Given that minor allele frequencies (MAFs) of indirect associations  are greater (MAF = 0.3 – 0.45) than the tan1-a SNP (MAF = 0.2), these indirect associations fit the expectation for synthetic associations: older, more widespread SNPs that tag a haplotype block on which multiple loss-of-function alleles of Tannin1 have arisen  while the wild-type allele can easily be found in an individual that harbors an independent loss-of-function allele at a different locus .Loss-of-function variants are a common source of natural variation, and recently methods have been developed to identify multiple, low-frequency loss-of-function alleles at the same gene in GWAS (Tannin1 in a modest-sized (n = 263) RIL family with simple phenotyping (field-based scoring of testa presence/absence) demonstrates that the combination of advanced mapping populations with high-resolution genotyping is an effective strategy for trait dissection , are represented in the genotyping data. A lack of a causative or perfectly linked SNP for pericarp pigmentation would explain why both the linear model and loss-of-function genome scan approaches achieved just Mb resolution for this trait. Similarly in the RIL mapping, had the tan1-a SNP not been represented the other SNPs in the data set would not have precisely tagged the Tannin1 gene. Although the identification of a priori candidates through comparative genomics provides some guidance, there are typically many reasonable candidates within Mb-scale mapping intervals; for example, around 60−63 Mb on chromosome 4, there are four other homologs of tannin genes that would have been equally promising candidates. As genomic coverage increases, imputation methods improve, and mapping populations are refined and expanded, genome-wide mapping approaches will increasingly need to be optimized to identify causative variants as opposed to tagging SNPs (vs. the high cost of candidate gene validation efforts, the use of whole-genome resequencing to increase the resolution of mapping studies is likely to be cost effective. Although this study of relatively simple pigmentation traits highlights the trade-offs between population- and family-based mapping approaches because of the complexity of association signals, in either approach high density genotyping can facilitate gene resolution mapping of traits.It is worth noting that if the


Increasing awareness of limitations to natural resources has set high expectations for plant science to deliver efficient crops with increased yields, improved stress tolerance, and tailored composition. Collections of representative varieties are a valuable resource for compiling broad breeding germplasms that can satisfy these diverse needs.Here we show that the untargeted high-coverage metabolomic characterization of such core collections is a powerful approach for studying the molecular backgrounds of quality traits and for constructing predictive metabolome-trait models. We profiled the metabolic composition of kernels from field-grown plants of the rice diversity research set using 4 complementary analytical platforms. We found that the metabolite profiles were correlated with both the overall population structure and fine-grained genetic diversity. Multivariate regression analysis showed that 10 of the 17 studied quality traits could be predicted from the metabolic composition independently of the population structure. Furthermore, the model of amylose ratio could be validated using external varieties grown in an independent experiment.Our results demonstrate the utility of metabolomics for linking traits with quantitative molecular data. This opens up new opportunities for trait prediction and construction of tailored germplasms to support modern plant breeding. Modern crop breeding techniques such as wide crossing and marker-assisted selection have been highly successful in improving the quality traits of rice ,2. HowevWhile the germplasm that is actively used for rice breeding may be narrow, the total number of rice varieties is enormous due to its very long domestication history . The broOryza sativa L.); yet with only 67 varieties, it is small enough to allow comprehensive molecular profiling.Genetic core collections of relatively small size have been developed in several rice genebanks to obtain manageable but still representative selections, e.g., the Rice Germplasm Core Set (RGCS) from the International Rice Research Institute (623 accessions) , the GCoArabidopsis thaliana using both recombinant inbred lines [Direct relationships between metabolic composition and genotype and phenotype have been shown for the model plant ed lines  and natued lines ,13. Metaed lines .1H-NMR did not reveal any relationship between metabolomic and overall genetic diversity [With these considerations in mind, we aimed to (i) chart the metabolic diversity of kernels from the RDRS and (ii) investigate the covariance between metabolite profiles and quantitative quality traits. A previous study of 18 of the RDRS varieties using iversity . As thisiversity , we chosiversity . The resiversity , ear emeiversity , and amyssIIIa) with white-core phenotypes had very high amylose ratios without the accompanying expected fatty acid/lipid composition, suggesting an important role of fatty acids in starch packing. Taken together, our results demonstrate the usefulness of metabolomic profiling of genetically diverse varieties for linking quality traits with molecular features.Starch composition is a major determinant of the taste and texture of cooked rice . The pacRice plants from the 67 RDRS varieties plus Nipponbare (reference Japonica variety), Kasalath (reference Indica variety), and the Pokkari variety were grown in a field in Tsukuba in 2005 and harvested after maturation . Brown rExamining the genetic population structure of the RDRS using principal coordinates analysis on the matching coefficient-based genetic distance matrix Figure  and the Using analysis of variance (ANOVA) to extract the metabolites that were differentially abundant among the different subtypes we noted that Indica I was characterized by a relatively low abundance of several metabolites including most amino acids and 5 of the detected phosphatidylcholines Figure . Indica P = 0.0001) but Japonica (P = 0.0047), Indica I (P = 0.0064), and Indica II (P = 0.0001) were also significant on their own, indicating the presence of a fine-grained correlation between genetic diversity and metabolite abundances . In particular, the models of amylose ratio and ear emergence day were remarkably accurate with While yielding a good metabolomic coverage  and the variance of the observed sampling distribution of CP. To address this problem we define a probabilistic statistic for feature selection, log B; it scores how many times more likely the alternative hypothesis is over the null-hypothesis.The OPLS regression framework, and therefore also MB-OPLS, provide correlation loadings, B statistic and the nominal Spearman's correlation, Sρ, as a complementary bivariate method. We extracted the annotated metabolites with log B >0 and S ρwith an associated false discovery rate (FDR) less than 0.05. We visualized the correlation loadings for all annotated metabolites as word clouds, and listed the top 10 selected metabolites in Additional file When screening for trait-associated metabolites we used both the model-based log P <0.001) for the 10 significant models and the germination rate since this trait had border-line significance with PCV <0.1 for all 4 independent datasets. The resulting graph  e1, an ssIIIa mutant (Nipponbare background) and the ssIIIa/starch branching enzyme (be) double mutant 4019 (Nipponbare/Kinmaze background) [e1 mutant manifested a white-core phenotype [4019 mutant was almost completely opaque , middle- (Kinmaze), and low amylose ratios Soft158). Additionally, we included the 2 amylose hyper-accumulating knock-out lines (kground) . Rice kekground) . The selhenotype  and the e Figure . The amy8. Additia Figure . Of the a Figure . The preArabidopsis thaliana grown under tightly controlled conditions [We profiled the metabolomic composition of kernels from the RDRS and investigated trait-metabolite correlations by means of a multi-platform approach. Using our multi-block extension of the OPLS algorithm we found a population structure-independent correlation between metabolite abundances and 10 of the 17 examined traits. With the majority of these traits being only weakly dependent on each other Figure , this innditions ,12, for The MB-OPLS model for amylose ratio indicated very strong negative correlations between the amylose ratio and the abundances of palmitic acid, linoleic acid, glycerol, and putrescine, and positive correlations with 18:2 and 14:0 lysoPC  had increased levels of tryptophan and indole-3-acetate as well as other amino acids in kernels without a significant difference in the ear emergence day [The model for the ear emergence day was also very accurate Figure  and gaveence day .Arabidopsis photosynthetic tissues, it has been shown that biomass is negatively correlated with glucose-6-phosphate and succinate levels [For e levels . Keepinge levels . In a brPCV = 0.024. However, nicotianamine, known to be involved in iron metabolism [B >0 -associated loci. This concept is similar to the current advancements in plant phenomics. There, complex high-level traits are being modeled using sets of simpler traits that have tighter relationships with genetic determinants than the high-level trait itself . With mee1 and 4019) were used for this study. Plant growth and harvesting were carried out as described in Additional File The RDRS and an external set of rice varieties as well as two knockout mutants e and 40192 transformed and scaled to unit-variance prior to further data analysis. All peaks with more than 30% missing values were excluded.All data was loghttp://prime.psc.riken.jp/?action=drop_index and as Additional File The multi-platform data was summarized by unifying metabolite identifiers to a common referencing scheme using the MetMask tool . The fouAll data analyses were performed using R v2.12.1. Network visualization was done using Cytoscape and the GOlorize plug-in . MissingjZ, was compensated for the differences arising from the different sub-populations by settingEach column trait data vector, Q is the estimated population membership matrix from the STRUCTURE program and B is the vector of coefficients estimated by least-squares regression.where i and pre-processed trait vector j Yare formed where the nsamples × ni peaks,metabolite data matrix, Xi, is decomposed into a jY-correlated part, jY-uncorrelated part, E asThe MB-OPLS regression method consists of two steps. In the first, OPLS models of each block Xj Top,for each trait j are formed by concatenation:and new regressor matrices Xj Top,and jY. MB-OPLS for a single block is equivalent to ordinary OPLS.Top-level models are then estimated by ordinary OPLS regression between j + 1 parameters corresponding to the number of orthogonal components  used for the block-, and top-level models respectively. We optimize these parameters by seven-fold internal cross-validation (CV).Each MB-OPLS model has jY. In order to test the significance of the model, we shuffle j Yone-thousand times, calculate n0, when P-value estimate PCV = (n0 + 1)/(1000 + 1). This CV approach is computationally intensive and was therefore computed on in parallel using the multicore package [The diagnostical statistic  package . Since td(Cp), by bootstrapping the regression model, and the density distribution under the null-hypothesis (X and j Yare independent), d(C|Hp0), by randomization of jY. We then calculate a score for the relevance for each metabolite asWe assess how informative each metabolite is in each model by estimating the density of the sampling distributions for its correlation loading, a priori expected probability of H0 to 0.95. Our statistic log H0 was true.setting the HR and MK analyzed the data, designed experiments and wrote the manuscript. MK performed GC-MS analysis. KE provided plant material and designed the study. AO performed CE-MS analysis. FM performed LC-MS analysis. YO performed IT-MS analysis. NF provided plant material. MA and KS conceived of and designed the study. All authors read and approved the final manuscript.Supplementary methods, tables metabolomics meta-data.Click here for fileSupplementary datasets.Click here for fileInfluential metabolites. Correlation loading, PC, indicate proximity between the metabolite and the trait-correlated variance. log B indicates how many times more likely the alternative hypothesis  is than the null-hypothesis (no association). Spearman's correlation S ρwith associated FDR indicates the direct bivariate correlation. Word clouds are ordered alphabetically and have font sizes proportional to the corresponding correlation loading (PC). Green and red indicate apositive and negative correlation with the trait, respectively. The spatial layout is abitrary. Where present, initial capital letters of the metabolite abbreviations indicate type of molecule Click here for fileThe summarized metabolomics data of the RDRS.Click here for file


It is thought that a proportion of the genetic susceptibility to complex diseases is due to low-frequency and rare variants. Next-generation sequencing in large populations facilitates the detection of rare variant associations to disease risk. In order to achieve adequate power to detect association at low-frequency and rare variants, locus-specific statistical methods are being developed that combine information across variants within a functional unit and test for association with this enriched signal through so-called burden tests.We propose a hierarchical clustering approach and a similarity kernel-based association test for continuous phenotypes. This method clusters individuals into groups, within which samples are assumed to be genetically similar, and subsequently tests the group effects among the different clusters.The power of this approach is comparable to that of collapsing methods when causal variants have the same direction of effect, but its power is significantly higher compared to burden tests when both protective and risk variants are present in the region of interest. Overall, we observe that the Sequence Kernel Association Test (SKAT) is the most powerful approach under the allelic architectures considered.In our overall comparison, we find the analytical framework within which SKAT operates to yield higher power and to control type I error appropriately. The different strategies in place today to search for low-frequency and rare variants affecting complex traits largely fall under 3 categories: genome-wide association studies using dense genotyping platforms , imputation, and next-generation sequencing. Here we focus on the analysis of data generated by next-generation sequencing, although the methods presented here are applicable to data from the other categories. We also discuss ways of extending the methods to allow for genotype uncertainty, which can arise from imputation or low-coverage next-generation sequencing.Large-scale genome-wide association studies have been successful in identifying common variants influencing complex traits. Although these findings have improved our understanding of the genetic basis of many complex traits, for most of the traits they explain only a fraction of heritability. This observation supports the long established idea that low-frequency and rare variants play an important role in common diseases. Thanks to recent advances in sequencing and genotyping technology and to large collaborative efforts that study human sequence variation and the allelic architecture of disease, such as the 1000 Genomes Project  between 1 and 5%) or rare variants (those with MAF <1%) is under-powered, as not enough copies of the minor allele are observed. An alternative approach is to use methods that combine information across multiple low-frequency or rare variant sites within a region, which can be a gene or any other functional genomic region. Currently, there are more than thirty methods developed for rare variant burden analysis, which use different approaches to combine information across multiple variants within the region of interest. One group of tests consists of collapsing methods based on summary statistics  proposed by Mukhopadhyay et al. . This meHere we focus on a continuous phenotype and we explore a hierarchical clustering and kernel-based association test. Specifically, we suggest using the AM kernel to cluster individuals into disjoint clusters and test if the means of the phenotypes within each cluster are the same via ANOVA. We use a simple hierarchical clustering algorithm, where our distance matrix is one minus a standardized AM similarity score matrix. To investigate the performance of the proposed method and its power and type I error, we performed an extensive simulation study with varying sample sizes, different magnitudes of genetic signal and different allelic architectures and compared it to two of the most popularly used rare variant analysis methods. We find that its power is comparable to that of the collapsing test based on the proportion of low-frequency/rare variants when causal variants have the same direction of effect, but its power is almost double than that of the burden test when both protective and risk variants exist. SKAT is, however, the clear winner in both allelic architecture scenarios.ni is the number of low-frequency/rare variants present in the i-th individual with a quantitative phenotype yi, then for the analysis of a quantitative trait this collapsing test is implemented asMorris and Zeggini  introducλ is the increase in the phenotype value for an individual carrying minor alleles at ri low-frequency/rare loci compared to an individual carrying none, β denote regression coefficients for a vector of covariates xi, and εi ∼ N. Association of an accumulation of low-frequency/rare variants with the phenotype can be tested by examining the null hypothesis H0: λ = 0 by using a likelihood ratio test. This method has been implemented in the GRANVIL software (http://www.well.ox.ac.uk/GRANVIL).where yi of sample i is modelled asSKAT  is impleβ is a vector of regression coefficients for genotypes gi =  that individual i carries at p variants within the region, and gij = 0, 1, or 2 is the number of copies of the minor allele. Moreover, α are regression coefficients for a vector of covariates xi, and εi ∼ N.where βj follows an arbitrary distribution centered at zero with variance ωjτ, where τ is a variance component and ωj is a prespecified weight for variant j. To test for association of the variants with the phenotype, SKAT tests H0: τ = 0 by employing a variance component score statistic given bySKAT assumes that each μ‸ is the predicted mean of y under H0. For a study of n individuals, K is an n × n matrix whose  element is given by the weighted kernel functionwhere G is an n × p matrix with  element being the genotype of variant j of individual i.where (ωj) has magnitude given by the Beta density function Beta evaluated at the MAF of variant j and with parameters α1 = 1 and α2 = 25. Other choices for weights are also discussed in Wu et al. [SKAT puts more weight on rare variants and non-zero weight to variants with MAF 1-5%. This is achieved by assuming that u et al. .H0, Q follows a mixture of χ2 distributions  of individuals i ≠ j in the study with sample size n and for each low-frequency/rare variant k in the region of interest spanning p low-frequency/rare variants, the AM kernel assigns a similarity scoreWe then use the ANOVA model to test if the means of the phenotypes within each cluster differ significantly. Specifically, for any pair (g(i)k and g(j)k are the number of minor allele individuals i and j carry at low-frequency/rare variant k. For any pair  of individuals i ≠ j, the AM score across the region of interest is simply the sum of the single-SNV AM scores, i.e.where n × nD matrix with  element being d(ij) = 1 − h(g(i), g(j))/4p. Hierarchical clustering works by initially assigning each individual to their own cluster and then the algorithm proceeds iteratively, at each stage joining the two most similar clusters, continuing until there is just a single cluster. At each stage, distances between clusters are recomputed according to the particular clustering method being used. We use Ward's hierarchical clustering, which minimizes the information loss (defined by Ward in terms of an error sum-of-squares criterion) associated with each grouping. Hierarchical cluster analysis can be readily implemented by using the standard statistics package R, and returns a dendogram, i.e. a tree whose branches represent the different individuals, so that genetically ‘close’ individuals appear in the same or neighbouring branches. A caveat when using hierarchical clustering is that in order to allocate samples to groups, the user needs to ‘cut’ the tree at a prespecified height, or in other words, to prespecify the number of clusters.We perform a hierarchical cluster analysis using the AM score to group individuals according to their genotype similarity, or rather according to their genotype dissimilarity, which is represented by the L, the study samples are allocated to these L distinct clusters according to their position in the dendogram. We then model the phenotype yli of individual i = 1, …, n belonging to cluster l = 1, …, L using a one-way ANOVA model asIf the number of clusters is specified to µ is the general effect of individuals, αl is the cluster-specific treatment effect, and εi is the error component. If individuals' phenotypes between clusters are similar, then α1 = ··· = αL, and therefore H0 for testing disease association is α1 = ··· = αL = 0.where The within-group sum of squares isnl denotes the number of individuals in group l. The between-group sum of squares isand To test association with disease, the ANOVA statistic is given byF-distribution with (L − 1) and (n − L) degrees of freedom.which follows an We vary the number of clusters from 1 to 20, and we repeat the ANOVA modelling step, which is very fast, and report the maximum test statistic. We find that using an upper threshold of 20 for the possible number of clusters is sufficient to capture the genetic diversity of the study samples, by examining the average number of clusters that correspond to the maximum test statistic in our simulation study . To assign significance to the association test, we perform 10,000 permutations of the phenotype to individuals and we repeat the ANOVA step with the number of clusters ranging from 1 to 20, without the need to repeat the hierarchical clustering. The p value of significance of the association test is the proportion of permutations that resulted in a maximum test statistic bigger than or equal to the original maximum test statistic.It is possible to down-weight variants that are not thought to be disease-associated and up-weight variants that are believed to be disease-associated, so that the contribution of the latter to the AM score across the region of interest is higher. We have therefore implemented a version of the model that incorporates weights. In this instance, the AM score across the region of interest is given byωk is the weight of variant k, and the dissimilarity matrix D′ has  element equal towhere ωk = 1 for all k = 1, …, p. Different weighing schemes are possible, and in our simulation study, we used the one proposed by Wu et al. [(ωk) has a magnitude given by the Beta density function Beta evaluated at the MAF of variant k (please see above), so that more weight is assigned to rarer variants.The un-weighted version of the proposed approach can be viewed as the weighted version with weights u et al. , where . KATE is freely available at N individuals by using the HAPGEN2 software [PFKL with coordinates 45,719,934 and 45,747,259 base pairs) with 143 polymorphic SNPs .We conducted an extensive simulation study to examine the type I error and power of the proposed method, and to compare its performance to other popular rare variant methods under different allelic architectures. Haplotype data were simulated under the null model of no genetic association for 2software , so thatN individuals, where N = 1,000, 2,000, 3,000. Causal variants were randomly selected such that their individual MAF did not exceed 0.02 and their total MAF did not exceed 0.05, as implemented in Asimit et al. [yi was assigned to each individual i according to a linear modelHaplotypes were randomly paired to form t et al. . A contis is the number of causal variants, gi1c,…,gisc are the genotypes of the causal variants for individual i, and εi follows a standard normal distribution. Each causal variant k = 1, …, s had an effect βk on the phenotype. To examine the type I error, all regression coefficients βk were set to 0, which translated to the null disease model of no association. We simulated scenarios where all causal variants were deleterious, and other scenarios where half of the causal variants were deleterious and the rest were protective. For the deleterious variants, βk was set to 1.2, 2 and 3, whereas for the protective variants, βk = −1.2, −2, −3. We also considered a scenario where the effect size was not fixed, but it varied with the MAF of the causal variant. Following Wu et al. [βk as |βk| = 0.4|log10MAFk| to allow rarer causal variants to have larger effects. As the individual MAF cannot exceed 0.02, the smallest individual effect is |βk| = 0.68. where u et al. , we set βk > 0), the power of each test is calculated as the proportion of replicates for which the test yielded a p value of less than a 5% significance threshold. For data simulated under the null disease model of no association, we calculate the false-positive rate of each test as the proportion of replicates for which the test yielded a p value of less than 5%.Using this procedure we generated 1,000 replicates under each simulation scenario. We subsequently used the simulated data with KATE, GRANVIL and SKAT. For each simulation scenario where the data have been simulated with a genetic signal (regression coefficients PFKL in chromosome 21). This gene is representative of chromosome 21 in terms of size and number of variants with MAF <5 or <1%, and we therefore believe that our conclusions are robust to the choice of gene. However, all three methods can be implemented genome-wide, which would give a more complete picture of their relative power.These results are based on a single gene region , but becomes computational intensive as the number of samples increases . We used 10,000 permutations to assign significance in the simulation study presented here, although an adaptive number of permutations is also possible and could reduce KATE's running time. In this adaptive design, the default number of permutations can be 1,000 and increased to 10,000 only if the p value is less than a pre-specified threshold, as implemented by Asimit et al. [In terms of computational speed, both GRANVIL and SKAT are very fast, as they do not require permutation testing. In contrast, KATE relies on permutation to assign significance. KATE is reasonably fast for a small number of samples , which is a technique that combines analysis of variance and regression analysis. In this situation, the permutation procedure needs to be adapted, so that at each permutation and for each pair of individuals we exchange not only their phenotypes but also their covariate values.In our overall comparison, we find the analytical framework within which SKAT operates to yield higher power and to control type I error appropriately.


The genomic estimated breeding values (GEBV) of the young individuals in the XIV QTL-MAS workshop dataset were predicted by three methods: best linear unbiased prediction with a trait-specific marker-derived relationship matrix (TABLUP), ridge regression best linear unbiased prediction (RRBLUP), and BayesB.The TABLUP method is identical to the conventional BLUP except that the numeric relationship matrix is replaced with a trait-specific marker-derived relationship matrix (TA). The TA matrix was constructed based on both marker genotypes and their estimated effects on the trait of interest. The marker effects were estimated in a reference population consisting of 2 326 individuals using RRBLUP and BayesB. The GEBV of individuals in the reference population as well as 900 young individuals were estimated using the three methods. Subsets of markers were selected to perform low-density marker genomic selection for TABLUP method.The correlations between GEBVs from different methods are over 0.95 in most scenarios. The correlations between BayesB using all markers and TABLUP using 200 or more selected markers to construct the TA matrix are higher than 0.98 in the candidate population. The accuracy of TABLUP is higher than 0.67 with 100 or more selected markers, which is nearly equal to the accuracy of BayesB with all markers.TABLUP method performed nearly equally to BayesB method with the common dataset. It also provides an alternative method to predict GEBV with low-density markers. TABLUP is therefore a promising method for genomic selection deserving further exploration. With the availability of whole genome high-density single nucleotide polymorphism (SNP) chips in many livestock and plant species, methods using the genomic information to detect the underling architecture of complex traits have become popular. In breeding programmes, the method to predict genomic estimated breeding values (GEBV) with whole-genome markers was termed genomic selection, as proposed by Meuwissen et al. . The genThe aim of this study is to validate the TABLUP method and compare it with the ridge regression BLUP (RRBLUP) and the BayesB method using the simulated common dataset provided in the XIV QTL-MAS workshop. We tried to assess the performance of different methods and explain the results either with or without knowing the simulated true breeding values (TBV).The common dataset consists of 3 226 individuals from five consecutive generations (F0 - F4). Each of the 2 326 individuals in generation F0 to F3 has phenotypic records on two traits: a quantitative trait Q and a binary trait B. In this study, we only deal with trait Q. Individuals with phenotypic records (F0 - F3) and without phenotypic records (F4) were treated as reference and candidate population, respectively. A genome consisting of 10 031 biallelic SNPs on 5 chromosomes with 100 million bps length each were simulated without any missing data and genotyping error. All SNPs were included in our analyses.Both RRBLUP and BayesB were used to estimate SNP effects in the reference population. The statistical model for marker effect estimation can be written as:b is a vector of fixed effects ; ig is the random effect of marker i; m is the total number of markers; e is a vector of residual errors; and X and Zi are design matrices corresponding to b and ig. We assumed that residuals e are independent and follow a normal distribution, ig were also assumed to be normally distributed, π for BayesB.where y is the vector of phenotypic values or estimated breeding values; π, was estimated from a pre-analysis of the simulated data. The Markov chain was run for 10 000 cycles with 100 cycles of Metropolis-Hastings sampling in each Gibbs sampling, and the first 2 000 cycles were discarded as burn-in. All the samples of marker effects after burn-in were averaged to obtain the marker effect.In RRBLUP, the variance of marker effect was assumed to be identical for all markers and was calculated as The GEBVs of all genotyped individuals were estimated using three methods: TABLUP, RRBLUP and BayesB. For RRBLUP and BayesB, the GEBV of a genotyped individual was calculated as the sum of all marker effects according to its marker genotypes as proposed by Meuwissen et al. .For TABLUP, the GEBVs were estimated based on the following model:y is the vector of phenotypes of individuals in the reference population and u is the vector of breeding values of all genotyped individuals (F0 - F4) with the variance-covariance matrix equal to TA is a trait specific relationship matrix, and the where ls F0 - F with theThe TA matrix was constructed by using genotypes of all markers and their estimated effects obtained from either RRBLUP or BayesB , as proposed in our previous study . As an aThe pedigree and phenotype data of generations F0 - F3 were used to estimate the variance components. The estimated variances are 56.6 for additive genetic effect and 47.7 for residual effect. Therefore, the estimated heritability of trait Q is 0.54.Figure Table Different subsets of markers were selected based on their size of estimated effects to construct the TA matrix. Figure The correlations between TAB and BayesB are always the highest for all numbers of markers. Generally, the correlations increase with the increase of number of markers, but become almost constant when the numbers of markers are over 1 000. Even though only 500 markers  were selected, the correlations of GEBVs between TABLUP and BayesB or RRBLUP are 0.92. In particular, the correlation between TAB and BayesB is close to 1.0 when the numbers of markers are over 500. This implies that TABLUP with only a proportion of selected markers might be recommendable for genomic selection in candidate populations because of the remarkably reduced cost for genotyping, even though there might be a little loss of accuracy.The availability of true breeding values (TBVs) allowed a more efficient assess of methods. Table TheTABLUP method performed comparably to the currently widely used BayesB and RRBLUP methods. It provides the possibility to use low-density markers for estimating GEBV with a relatively high accuracy. It is therefore a promising method for genomic selection and deserves further exploration.QTL: quantitative trait locus; MAS: marker assisted selection; SNP: single nucleotide polymorphism; GEBV(s): genomic estimated breeding value(s); TBV(s): true breeding value(s); RRBLUP: ridge regression best linear unbiased prediction; TABLUP: best linear unbiased prediction with trait specific relationship matrix; TAB: TABLUP with weights from BayesB; TAP: TABLUP with weights from RRBLUP.The authors declare that they have no competing interests.ZZ, DXD and LJF carried out the data analyses and contributed the manuscript. QZ and DJK coordinated the analyses and contributed to the manuscript. All authors have read and contributed to the final text of the manuscript.


Psoriasis is a common inflammatory skin disease with a known genetic component. Our previously published psoriasis genome-wide association study identified dozens of novel susceptibility loci in Han Chinese. However, these markers explained only a small fraction of the estimated heritable component of psoriasis. To better understand the unknown yet likely polygenic architecture in psoriasis, we applied a linear mixed model to quantify the variation in the liability to psoriasis explained by common genetic markers  in a Han Chinese population.-9) of the variation in the liability to psoriasis is captured by common genotyped and imputed variants. We discuss these results in the context of the strong association between HLA variants and psoriasis. We also show that the variance explained by each chromosome is linearly correlated to its length , and quantify the impact of a polygenic effect on the prediction and diagnosis of psoriasis.We explored the polygenic genetic architecture of psoriasis using genome-wide association data from 2,271 Han Chinese individuals. We estimated that 34.9% (s.e. = 6.0%, P = 9 × 10Our results suggest that psoriasis has a substantial polygenic component, which not only has implications for the development of genetic diagnostics and prognostics for psoriasis, but also suggests that more individual variants contributing to psoriasis may be detected if sample sizes in future association studies are increased. However, the SNPs identified in these studies collectively explain only a small fraction of the heritable components of these traits as estimated from twin studies, leading the research community to question where the remaining heritable component of these traits resides – a phenomenon and quest commonly referred to as the search for sources of ‘missing heritability’[Genome-wide association studies (GWAS) have achieved a good deal of success in establishing thousands of individual SNPs (single nucleotide polymorphisms) associated with various common diseases and complex traits .The samples were genotyped on the Illumina Human610 Quad BeadChip human array as described previously. SamplesA genetic similarity matrix was constructed based on published methods. SubjectIn total, 494,641 genotyped and 5,610,687 imputed autosomal SNPs passed quality control thresholds (see Methods). We refer to the genotyped data as set G and genotyped and imputed data as set G + I (Table 2SNP) was explained by all autosomal SNPs . This value rose slightly to 34.9%  in the G + I dataset (Table -9) of phenotypic variance was explained by HLA markers   after omitting chromosome 6 due to its exceptional contribution : frequent (MAF > 0.05) or infrequent (0.01 < MAF < 0.05). Markers with infrequent variants in the G and G + I datasets explained 1.1%  and 3.0%  of the variation in liability to psoriasis, respectively. Markers with frequent variants captured greater than 30% of the phenotypic variation in this population in both datasets . Using the genroc calculator[http://gump.qimr.edu.au/genroc/) and assuming the prevalence of psoriasis among Han Chinese is 0.47%[Given our estimates of hentified,22. Theslculator  will be required to detect additional markers with increasingly small effects (odds ratios < 1.1)[Although there has been continued debate as to whether the heritability of common diseases is mostly accounted for by common variants with small effects or rare variants with larger effects, there have been few definitive studies to settle this debate. Our study demonstrates that common SNPs are likely to explain a large portion of the heritability in psoriasis among Han Chinese. Given that the reported loci in our previous GWAS explain a modest fraction of the heritability estimated from twin studies and our estimate of hs < 1.1),23,24.. However, this may be due to the under-representation of SNPs with low minor allele frequency on the genotyping array and imputation strategies we used. In addition, it is expected that weaker additive genetic effects are not well tagged by SNPs with low frequency due to weak linkage disequilibrium with rare causal variants. Our estimate of h2SNP was less than half of established heritability of psoriasis in the Han Chinese population[To further illustrate the important role of the collective effect of common variants each with small effect on psoriasis, we implemented a partitioning analysis based on minor allele frequency in our datasets. We find that only a small fraction of phenotypic variation can be attributed to SNPs with low frequent variantspulation. This diWe find that more than 13.0% of the liability to psoriasis can be explained by markers in the HLA region alone, which is consistent with overwhelming evidence from GWAS studies implicating variants in this region. It is notable that chromosome 6 explained a large proportion of phenotypic variation. Although this may be a result of the high linkage disequilibrium between variants in the HLA region, this nevertheless highlights the important role of the HLA locus in the susceptibility of psoriasis. In addition, although several specific susceptibility genes and variants in the HLA region have been revealed, future We have performed a polygenic analysis of psoriasis in Han Chinese samples. We estimated the contribution of common variants to psoriasis phenotypic variation. Our study suggests that substantial polygenic component has been hidden in psoriasis, which not only has implications for the development of genetic diagnostics and prognostics for psoriasis, but also suggests that more individual variants contributing to psoriasis may be detected if sample sizes in future association studies are increased.The authors declare that they have no competing interests.XJZ and NJS designed this study, analysis and interpretation of results and helped to revise the manuscript. XYY conducted the analysis as well as wrote the manuscript. NEW conducted the imputation analysis and participated in the revising the manuscript. SY, HC, YC collected the samples. FSZ, XBZ and XDZ conducted the genotyping experiments and genotype calling. All authors read and approved the final manuscript.