Rht genes. However, these reduce the yield of straw (itself an important commodity) and introduce other undesirable characteristics. Identification of alternative height-control loci is therefore of key interest. In addition, the improvement of stem mechanical strength provides a further way through which lodging can be reduced.The current approach to reducing the tendency for wheat grown under high fertilizer conditions to collapse (lodge) under the weight of its grain is based on reducing stem height via the introduction of Rht, we assessed variation for plant height and stem strength properties in a training genetic diversity panel of 100 wheat accessions fixed for Rht. Using mRNAseq data derived from RNA purified from leaves, functional genotypes were developed for the panel comprising 42,066 Single Nucleotide Polymorphism (SNP) markers and 94,060 Gene Expression Markers (GEMs). In the first application in wheat of the recently-developed method of Associative Transcriptomics, we identified associations between trait variation and both SNPs and GEMs. Analysis of marker-trait associations revealed candidates for the causative genes underlying the trait variation, implicating xylan acetylation and the COP9 signalosome as contributing to stem strength and auxin in the control of the observed variation for plant height. Predictive capabilities of key markers for stem strength were validated using a test genetic diversity panel of 30 further wheat accessions.To investigate the prospects for genetic alternatives to This work illustrates the power of Associative Transcriptomics for the exploration of complex traits of high agronomic importance in wheat. The careful selection of genotypes included in the analysis, allowed for high resolution mapping of novel trait-controlling loci in this staple crop. The use of Gene Expression markers coupled with the more traditional sequence-based markers, provides the power required to understand the biological context of the marker-trait associations observed. This not only adds to the wealth of knowledge that we strive to accumulate regarding gene function and plant adaptation, but also provides breeders with the information required to make more informed decisions regarding the potential consequences of incorporating the use of particular markers into future breeding programmes.The online version of this article (doi:10.1186/s12864-016-2775-2) contains supplementary material, which is available to authorized users. Lodging is defined as the permanent displacement of a crop from its usually vertical growth habit. This phenomenon may be divided into two main categories: lodging caused by anchorage failure, or root lodging; and lodging caused by stem mechanical failure, also known as brackling or stem lodging. Lodging is a complex trait, influenced by environmental, agronomic and genetic factors and continues to be a widespread problem in wheat grown worldwide. In years where lodging is particularly severe, yield losses as great as 80 % can be expected .Rht-B1 and Rht-D1, which markedly increased the yield potential of wheat following their introduction [Previous efforts to reduce the occurrence of lodging in wheat have centred on reducing the height of plants through incorporation of semi-dwarfing alleles into accessions and the use of plant growth regulators (PGR). The most common semi-dwarfing genes found in modern wheat accessions are the GA-insensitive oduction . Howeveroduction , 4.In recent years we have seen the successful application of GWAS in a number of different plant species –7. This Our aim was to explore the variation available in European wheat breeding material for both height and stem mechanical strength, and in the first application of AT in wheat, to identify molecular markers associated with this variation. This will provide breeders with both insights into the bases of variation for these traits and molecular markers to underpin marker-assisted breeding of wheat accessions with improved lodging resistance.Triticum aestivum ), the transverse of the marked stem end was photographed. All images were later analysed using the digital analysis software Sigma Scan , allowing the following cross-sectional measurements to be determined: whole stem area ; stem hollow area ; the area of stem parenchyma and the thickness of the stem outer cortex. Following these initial measurements, all samples were stored at 55 % relative humidity at 23 °C for a minimum of 2 days in a silica chamber to ensure equilibration of moisture content between samples.Harvesting of material was carried out by hand, cutting the stems as close to the soil as possible using secateurs. Ten plants were harvested for each accession in 2011 and five plants per accession in 2012. Prior to further processing, all plants were dried thoroughly at room temperature. Any plants showing signs of stem tissue damage were excluded from the study. To allow for an in-depth analysis of the relationship between plant morphology, stem structure and stem mechanical strength, the following measurements were determined for each plant harvested: Plant height; main stem  weight and threshed weight; length of the second internode (from plant base) and stem width . A 5 cm section was then removed from the 2nd internode of the main stem using a scalpel. The basal end of this section was marked using a permanent marker pen. To obtain stem cross-sectional measurements  (Eq. (MOR), describing the resistance of the stem material to break under-load (Eq. (MOE) describing the resistance of the stem material to bend elastically   with a three-point bend test setup  Fig. . These mned Fig. . These a I) (Eq. ), were uoad (Eq. ) and theD2 = diameter of whole stem calculated from stem cross-sectional areaD1a = diameter of stem hollow calculated from stem hollow areaWhere:L = the length of the stem sample between the two supportsa= L/2Where:Following the assessment of year by year interactions, traits were assessed for significant genotypic variation and REML-predicted means calculated for use in the subsequent correlation (Genstat 15th edition) and Associative Transcriptomics analyses. These statistical analyses were carried out using Genstat 15th edition .For the mRNA-seq, second true leaves from each of four plant replicates per accession were harvested approximately 14 days after pricking out (21 day after sowing) as close to the midpoint of the light period as possible, pooled and immediately frozen in liquid nitrogen. Samples were extracted using the Omega Biotek EZNA Plant RNA Kit according to manufacturer’s instructions.Transcriptome sequence data was then obtained for each of the 100 wheat accessions included in the training panel. This was achieved using Illumina transcriptome sequencing (mRNA-seq). Illumina sequencing, quality checking and processing were conducted as described previously  except tde novo transcriptome assemblies of Triticum urartu, Aegilops speltoides and Aegilops tauschii  generated using the Trinity assembly package [T. turgidum ssp. dicoccoides, which more closely represents the B genome in hexaploid wheat. This resulted in a reference transcriptome sequence comprising 105,069, 132,363 and 85,296 transcript assemblies for the A, B and D genomes respectively. Based on linkage map information and conserved synteny between wheat and Brachypodium distachyon, these assemblies were arranged into their hypothetical gene order, providing a set of pseudomolecules [The alignment of these reads for SNP detection was facilitated by the development of a reference sequence, as described previously . Briefly package . The B g package  using seBrassica napus, with read mapping and SNP calls made for each accession using Maq and Maq.pl commands, before integrating calls across the panel using the Perl script combiner.pl [The alignment of the diversity panel mRNA-seq reads to this reference sequence enabled the detection of 42,066 SNP markers. SNP-calling was conducted essentially as described previously for biner.pl . Simple In addition, quantification of transcript abundance  provided a measure of expression for each transcript assembly. This provided the information required to explore any relationships between gene expression and the trait of interest in what has been termed a Gene Expression Marker (GEM) analysis .P values (as –log10P) in pseudomolecule order.SNP-based association analysis was performed using 12,456 SNPs . The results were assessed visually by plotting the obtained The filtered SNP dataset was used to construct a kinship matrix using the software TASSEL V3.0 . In addiP values (as –log10P) in pseudomolecule order. The scripts used in this analysis were developed in R (cran.r-project.org).Following the quantification and normalisation of the transcript levels as reads per kb per million aligned reads (RPKM), and the filtering of transcripts with an RPKM of less than 0.4 across accessions, linear regression was performed. This analysis made use of 94,060 GEM markers. By fitting the RPKM values for each unigene as the dependant variable and the trait data as the independent variable, it was possible to assess the relationship between this measure of gene expression and the traits. The results were explored visually by plotting the obtained Leaf material was collected from a test panel of 96 hexaploid wheat accessions grown as part of the WAGTAIL panel ) at KWS, Thriplow in 2013. DNA was extracted according to an adapted method of that described by Pallotta et al. . Genome Following genotyping, a subset of 30 wheat accessions   and Cordiale (for MOE). A wide range of variation was also observed for the various stem structural traits assessed. For example, mean stem hollow area ranged from 1.16 mm2 (for Capelle-Desprez) and 6.51 mm2 (for Starke2). For outer cortex thickness, trait means ranging between 0.24 mm (as seen for Hyperion) and 0.46 mm (as seen for Alba) were recorded. For plant height, despite a lack of segregation at the Rht loci, a trait range of 42.8–98.4 cm was recorded. The tallest accession included within the panel was Steadfast whereas the shortest stem measurements were recorded for Equinox.The diversity panel of 100 wheat accessions was analysed for a range of traits indicative of stem structural and material strength. With the exception of second moment of area, significant variation was present for all traits included in the analysis (P ≤ 0.001) relationships were detected between the absolute strength measures (Fmax and F/V) and the structural traits, however, despite such high statistical significance, in the majority of cases, the amount of variation in stem absolute strength explained by stem structure was found to be modest. Stem parenchyma area (R2 = 0.27 and 0.17 for Fmax and F/V respectively) and outer cortex thickness (R2 = 0.19 and 0.13 for Fmax and F/V respectively) show the closest positive relationships with absolute strength. These traits may therefore be the most promising targets for the improvement of stem structural strength in wheat. In contrast to the modest contributions made by stem geometry, a much closer correlation is seen between the absolute strength measures and stem weight (R2 = 0.42 and 0.47 for Fmax and F/V respectively). These correlations may represent a combined effect of several different stem structural components (each contributing to weight) or may more specifically relate to the density of the materials that make up the plant stem. Plant height also correlates positively with stem absolute strength (R2 = 0.21 and 0.25 for Fmax and F/V respectively).A correlation analysis was performed to analyse the relationships between the absolute strength and the structural and morphological traits to assess which may be good breeding targets Table . Several2 of 0.41, P < 0.001) in comparison to absolute strength traits such as Fmax  , with aOsARF16, Os02g41800; Panel a). The peak found on chromosome 5B coincided with a cluster of SMALL AUXIN UP RNA (SAUR) genes, with high significance GEMs occurring in three of the unigenes with BLAST identity to SAUR genes (Panel b). Although these loci have not been implicated previously in the control of plant height in wheat, the genes identified are excellent candidates for controlling this trait: ARFs are transcription factors that bind specifically to auxin response elements (AuxREs) found in the promoters of early auxin response genes such as the large family of SAUR genes, and mediate their response to auxin [OsSAUR39-55) and an orthologous cluster can also be found on Arabidopsis chromosome 1 (AtSAUR61-68) [OsSAUR39 has been found to negatively regulate auxin synthesis and transport, leading to reduced growth phenotypes when over-expressed [In order to identify loci controlling plant height, AT was conducted using the functional genotypes scored and the plant height trait data obtained. Additional file to auxin . In wheato auxin . On closUR61-68) . In ricexpressed . Our obsAxeA; Os04g01980). AxeA, is thought to have hydrolase activity, specifically acting on ester bonds in the deacetylation of xylans in the plant cell wall [AT for MOR identified three SNP association peaks. On chromosome 2D, two association peaks were found. The first of these . The Tobacco orthologue of this gene, NtSCP1, is known to be important for cell elongation and it has been proposed that this gene may target proteins involved in cell wall remodelling [QUASIMODO 1 (At3g25140). Mutants defective in this gene exhibit a number of defects including reduced homogalacturonan  content in the cell wall and reduced cell adhesion [EIF-2B epsilon subunit (Os02g56740), shows a high association with MOR. In rice, this gene is thought to have a role in the recruitment of mRNAs and the machinery required for translation. A related protein however, EIF-5A, has been found to be involved in a signalling pathway contributing to cell wall integrity and formation [EIF-2B also has a similar, additional function.In addition to the GEM association peak seen on chromosome 2D, several individual GEMs were also found to show significant association with material strength. An example of this can be seen in Fig. odelling , making adhesion . Previouadhesion . As a fiormation . It is tCOP9 SIGNALOSOME SUBUNIT 5B (CSN5B) (Os04g56070). The COP9 signalosome is a multi-protein complex which is known to be involved in protein degradation and has, in plants, been implicated in a number of developmental processes including photomorphogenesis (light-mediated growth), cell cycle progression and gene expression [Aspergillus nidulans exhibits altered expression of genes involved in cell wall remodelling [EIF-2B) gene. Previous studies have shown evidence of interactions between EIF-related genes and the COP9 complex [CSN5B) complex by means of a pathway analogous to that seen in Aspergillus nidilans, contributing to cell wall remodelling.To further analyse the individual GEM associations detected, their respective transcript abundances (measured as RPKM) were mapped as traits against the SNP data of the wheat accessions. Interestingly, for each of the described GEMs, a strong SNP peak was detected on chromosome 2D, the same region previously described for MOR in both the SNP and GEM analyses. An example of this can be seen in Fig. pression . Interesodelling . Further complex . Given tTo test the power of Associative Transcriptomics for the identification of predictive markers, a marker validation study was carried out using a panel of 96 additional wheat accessions and focusing on three SNP associations previously described for MOR. This analysis involved the screening of a completely independent panel of wheat accessions (taken from the WAGTAIL panel) for variation at the three marker loci. These accessions were then phenotyped using the three-point bend test as before and any marker-trait segregation patterns assessed statistically.Although this analysis would ideally focus on segregating variation of the most significant SNP within the association peak, the development of genome-specific marker assays for two of the targeted loci (B_comp6657_c0_seq1:3733 and For D_comp970_c0_seq1:1030) proved problematic (due to mixed traces in sequencing reads). However, genome-specific marker assays were successfully developed for alternative, highly associating SNPs within the corresponding peaks. Additional file P values of ≤0.01 and ≤0.001 for D_comp19374_c0_seq1:702 and B_comp2391_c0_seq1:284 respectively), proving that these markers have robust trait prediction capability. It is also promising to note, that the WAGTAIL accessions showing particularly high mean MOR (between 25.9 and 34.9 N mm−2), are among those carrying increasing alleles at both marker loci  in our training panel has enabled the identification of additional candidate genes that may contribute to controlling height in this species, implicating auxin-related genes as key regulators. Importantly, the loci implicated in plant height control are completely independent to those seen for stem strength and may therefore be used to further maximise lodging resistance in future elite wheat accessions, or to develop taller lodging resistant accessions. Such accessions would also improve the achievable profit margin by increasing the amount of straw that can be harvested for use as animal bedding or biorefining feedstocks.As previously mentioned, the selection of dwarfing alleles is a commonly employed method for lodging control in wheat. The lack of segregation of these loci  as a feedstock for lignocellulosic ethanol production. However, at present, high costs related to the breakdown of lignocellulosic biomass is hindering this fuel source becoming a feasible future alternative. One way through which processibility may be improved, is through altering the composition of the lignocellulosic matrix. In this study, we have shown evidence for the importance of xylan acetylation in contributing to stem material strength in wheat, but xylan acetylation is also known to impede the enzymatic breakdown of lignocellulosic biomass and therefore reduced xylan acetylation is a desirable target for this industry . The resCSN5 locus is very interesting. One of the associating GEMs showing a relationship with the 2D locus, corresponds to an orthologue of EIF-2B. Previous studies have shown evidence of interactions between the COP9 complex and EIF-related genes. This suggests that the utilisation of the GEM data for the assessment of gene-gene interactions through mapping is effective. Several of the GEMs found to interact with the 2D locus are expected to have a role in cell wall remodelling/biosynthesis. Previous work has shown that, in fungi, the COP9 complex has a role in cell wall remodelling, an important aspect of growth [CSN5B) regulates the expression of genes involved in cell wall remodelling, and that this is an important contributor to stem material strength in wheat. To our knowledge, this is the first instance of reporting such a role of the COP9 complex in planta.In addition to the potential role of xylan acetylation, this study has uncovered a possible role of the COP9 signalosome in contributing to stem mechanical strength in wheat. The detection of several interactions between single GEMs and the f growth . It is pThis work illustrates the power of Associative Transcriptomics for the exploration of even the most complex, environmentally sensitive traits. With careful selection of the genotypes included, we have shown that even a relatively small diversity set can, when coupled with high marker density and low linkage disequilibrium, provide the power required for the discovery of novel and agronomically valuable genetic variation. In this study, we successfully identified and validated markers for two loci that provide increased Modulus of Rupture, an important measure of the resistance of the plant material to breakage. We have also shown that this method has the potential to uncover novel targets for breeding of important morphological traits, such as plant height. Furthermore, the coupling of SNP variation with variation at the gene expression level has provided the power required to gain a deeper understanding of the biological context of variation underlying important agronomic traits. This not only adds to the wealth of knowledge that we strive to accumulate regarding gene function and plant adaptation, but also provides breeders with the information required to make more informed decisions regarding the potential consequences of incorporating the use of particular markers into future breeding programmes.


In a breeding population of tropical rice, GS + de novo GWAS outperformed six other models for a variety of traits and in multiple environments. On the basis of these results, we propose an extended, two-part breeding design that can be used to efficiently integrate novel variation into elite breeding populations, thus expanding genetic diversity and enhancing the potential for sustainable productivity gains.To address the multiple challenges to food security posed by global climate change, population growth and rising incomes, plant breeders are developing new crop varieties that can enhance both agricultural productivity and environmental sustainability. Current breeding practices, however, are unable to keep pace with demand. Genomic selection (GS) is a new technique that helps accelerate the rate of genetic gain in breeding by using whole-genome data to predict the breeding value of offspring. Here, we describe a new GS model that combines RR-BLUP with markers fit as fixed effects selected from the results of a genome-wide-association study (GWAS) on the RR-BLUP training data. We term this model GS +  Oryza sativa) is a model species for crop genomics. In 2002, rice became the first crop species to have its genome sequenced  and 3000 rice genomes have recently been sequenced at ~10X coverage  in rice as well as in a variety of other species. In all cases, markers in critical large effect genes or genomic regions are used to predict the presence or absence of agriculturally valuable traits . AlthougGenomic Selection (GS) offers an alternative to MAS and conventional phenotypic selection. GS has the capacity to use full-genome data to increase breeding efficiency. In GS, a training population is phenotyped for a trait(s) of interest and genotyped using genome-wide markers. A statistical/machine learning model is built from the training population data that take the genotypes of individuals in a breeding population as input and outputs a measure of the value those individuals hold as parents of future breeding – the genome estimated breeding value GEBV; . It can Depending on the crop, trait, and breeding population design, the choice of statistical method used to build the GS model has been shown to have a significant effect on prediction accuracy . Empiricde novo GWAS', or simply ‘GS+GWAS'. There are numerous benefits to this approach. Both GS and GWAS use the same input data sets, a phenotype data set and a genotype data set, thus no additional data are required, only additional analysis. Furthermore, we hypothesize that the significant single-nucleotide polymorphisms (SNPs) identified from de novo GWAS will be more directly relevant to the population undergoing selection than SNPs identified as significant in previously published GWAS on potentially disparate populations, and thus will improve prediction accuracy beyond that which could be obtained using previously published GWAS results. Using de novo GWAS as part of the GS model is also more accessible to breeders, as it does not require an extensive knowledge or literature search on the underlying genetics of a trait of interest.A second open question is how markers to be fit as fixed effects should be identified and/or selected. The previously cited experiments have, for the most part, relied on known functional markers for traits of interest  data from the International Rice Research Institute (IRRI) irrigated rice breeding program, we extract information from our models to evaluate which of currently used environments in IRRI's MET program can be combined for the purposes of model training, and thus define the best combination of environments for trait modeling and prediction in Southeast (SE) Asia.There are several points in a standard pedigree breeding program where an intervention based on GS could significantly shorten the breeding cycle by eliminating a generation of phenotyping or providing the breeder a mechanism for eliminating poor-performing offspring before the next generation of costly field trials  were selected for genotyping from the IRRI irrigated rice breeding program based on the planned inclusion of the lines in the 2011 Multi-Environment Testing Program and presence in the 2011 and 2012 Replicated Yield Trials (RYT) at IRRI (Los Baños).In all, 369 elite breeding lines  the RYT data set, consisting of field data from 2009–2012, two seasons per year (dry season (DS) and wet season (WS)) collected in a single field at IRRI in Los Baños, Philippines, and (2) the MET data set, consisting of field data from 2011 and 2012, two season per year (dry and wet), at a total of eight sites in SE Asia .For the RYT data set, phenotypes collected included plant height, flowering time, maturity date, number of effective tillers or panicles per plant, lodging score, grain yield and rep number .For the MET data set, in addition to the phenotypes collected for the RYT data set, data were collected on field row, field column, phenotypic acceptability score for whole plant, phenotypic acceptability score for panicle and phenotypic acceptability score for grain . The eigGenotyping by sequencing was performed on 369 breeding lines as described in a priori from pedigree records as belonging to the indica or indica-admixed subpopulation groups. To identify outlier individuals belonging to the japonica or japonica-admixed groups, principal components analysis was performed in R  using a 73 147 SNP subset of the 108 005 SNPs used for GS with imputed call rates ⩾0.9 (remaining missing data were then filled using the line means). The results of the principal components analysis were used to identify 31 subpopulation outliers belonging to either the japonica subgroup or containing substantial japonica admixture. These 31 outliers were removed from the data set and were not included in any further analyses (The majority of the 363 lines were characterized https://cran.r-project.org/web/packages/fpc/index.html) with the 73 147 imputed SNPs  using the R fpc package . We also sought to test scenarios using only more recent year data in the training population  and scenarios using more historical year data in the training population  the geographic location of the sites,  and (2) phenotypic data correlation, that is, if sites appeared to be correlated for any of the phenotypes of interest, they were tested in combination . Note thde novo GWAS, GS + historical GWAS, RR-BLUP, Bayesian LASSO (BL), Reproducing Kernel Hilbert Spaces (RKHS) and random forest (RF), and one non-GS method: multiple linear regression (MLR). The four non GS+GWAS GS statistical methods were chosen based on their demonstrated success in accurately predicting GEBVs in variety of crops and because they represent the different types of statistical methodologies used to build GS models, that is, linear parametric methods , non-linear semi-parametric methods (RKHS), non-linear, non-parametric methods (RF), as well as maximum-likelihood methods , Bayesian methods (BL) and machine learning methods . For an overview of the methods, see Seven statistical methods were used for each RYT experiment, including six GS methods: GS + P-values determined for each marker by F-test. Note that this is statistical equivalent of a crude GWAS. Linear models were then tested using 1 through the first 100 most significant markers, and the model with the best fit was returned. The returned model was then used to calculate the accuracy for the given fold. For the marker subset experiments where the number of markers in the subset (p) was <100, models were tested using 1 through p markers. Note that our MLR methodology was modified slightly from MLR using a subset of markers derived from single marker regressions (MLR) served as our non-GS marker-based prediction control. For each fold, single marker regression was run for all markers and For the RYT experiments, three CV accuracies were calculated. CV1 accuracies that are also the accuracies reported for the MET data and the CV experiments using marker subsets, were calculated by including the validation year/season in the training population, excluding individuals in the validation fold, for example, for experiment 1, CV1, the training population consisted of data on all training population individuals from years 2009 to 2011 all seasons, as well as the 2012 , function mixed.solve, with the least square means for the complete population used as input. The narrow-sense heritabilities were calculated as the additive genetic variance divided by the total phenotypic variance.Narrow sense heritabilities  were caly is the vector of observations, X is an incidence matrix for fixed effects containing only a vector of 1s for the intercept, β is a vector of fixed effect estimates containing the intercept, Z is an incidence matrix for random effects relating individuals to observations and u is a vector of random individual effects with u ~ N, where G is a genomic relationship matrix calculated using all markers  or from previously published GWAS data .The markers fit as fixed effects were selected from GWAS output, either from a GWAS calculated using the genotype and phenotype data on the individuals in the training population  five times, once for each validation fold . The inpP-value (low to high) and perform multiple-test correction using False Discovery Rate (FDR), then bin the SNPs on each chromosome into 500 Kb bins and output the lowest P-value SNP in each bin. This step was performed to group SNPs into GWAS peaks—as this was a breeding population with extensive linkage disequilibrium (LD) (Sort the GWAS output by ium (LD) , peaks wium (LD) .P-value SNP. If only one or two SNPs pass the FDR threshold, save only the SNPs that pass the threshold. Save also the single most significant SNP for flowering time.For each fold, load respective GEMMA fold output(s) and save up to the three most significant SNPs (FDR=0.1) for the trait of interest. If no SNPs pass FDR, save only the lowest P-values of the selected fixed effect SNPs=average corrected P-value for model.Test the markers saved from 3. in all combinations and select the markers that, by themselves, constitute the best linear fit using only the training data, that is, select the combination of markers that results in the maximal correlation between the phenotype training data and a prediction resulting from a linear model of the selected marker genotypes. Calculate the average of the FDR corrected Proceed with model solving and validation phenotype prediction using markers selected in 4.For selection of fixed effects using For the RYT data set, both the 2012 DS and 2012 WS phenotype data were used as the input for GEMMA for each CV experiment. For the MET data set, the 2012 DS RYT data, 2012 WS RYT data, and the 2012 MET phenotype data for the respective validation year, site and season of a given CV experiment were tested as the input to GEMMA for each CV experiment.P-value SNP for flowering time (the 'fourth' marker added to the yield and plant height top three markers) and found that the differences between these models were generally small, although in most cases including the flowering time SNP as a fixed effect improved model accuracy. Given that flowering time alone can shift performance of other agronomic traits, it is always worth controlling for its effect in breeding populations that encounter significant differences in flowering time, as is typical in many rice breeding programs. As SNP selection was performed for each fold, the RR-BLUP+fixed effects models differed slightly in terms of the markers fit as fixed effects by fold.Note that we tested models both with and without the lowest de novo GWAS method presented here will also most likely be unsuitable. For a detailed analysis of the GWAS results by themselves, including candidate gene analysis, see The above methodology was appropriate in our case because we had already analyzed the GWAS results on the training population data. For a group that wished to replicate our methodology on a new population, we recommend first running GWAS on their training population data to broadly visualize the trait genetic architecture. If a trait has no significant GWAS peaks or peaks that are very near the significance threshold after applying multiple-test correction, the above methodology is not recommended. This GS+GWAS method is intended for traits with one or more medium–large effect QTL segregating in the population. In other words, if random forest is NOT at all predictive for a given trait in a given population, the GS + de novo GWAS models, except the input to step two of the above algorithm (the GWAS results) was derived from the literature, in our case, from the results of For the GS + historical GWAS models, the same procedure was used as for the GS + t-test  to determine the effect of statistical method, validation population, and composition of the training population on prediction accuracy. The MET CV results . Heat maps were generated using Python3 Matplotlib.pcolormesh (http://matplotlib.org)  or chosen at random were selected from the 58,318 genotyping-by-sequencing SNPs with call rates ⩾75% and minor allele frequency ⩾0.05 as described in the de novo GWAS models, the RYT 2012 DS data were used for the phenotype input for flowering time, and the RYT 2012 WS data were used for the phenotype input for plant height and grain yield, as these produced the best GS + GWAS models using the full genotyped data set  and statistical method on accuracy (α=0.05). Accuracy was calculated for each of the 10 SNP subsets. A mean accuracy and s.e. for each subset size were also calculated by averaging the CV results of the 10 subsets for each subset size. ANOVA and Pairwise Student's de novo GWAS), (b) markers as fixed effects extracted from the literature  and (c) adding data from multiple environments to the training population. Two data sets consisting of 108 005 SNPs on ~363 elite irrigated rice breeding lines were used, a RYT data set consisting of 4 years of data (2009–2012), two seasons per year (dry and wet), taken at a single site at IRRI in Los Baños, Philippines, and a multi-environment trial (MET) data set, collected over two years  at four locations in 2011 and eight locations in 2012 , Bayesian LASSO, and multiple linear selection  were included as fixed effects  was also the most accurate overall, outperforming RF, the next best performing model for some trait x season combinations  the tropical japonica subpopulation, and (3) the all, or combined subpopulations . Consistent with previous results, we found that ~5000 SNPs were as effective for prediction as the full marker set of 108 005 SNPs  over two seasons/year (dry and wet) taken at IRRI headquarters in Los Baños and at four additional sites in SE Asia during 2011, and at eight additional sites in 2012. Because of typhoons and pests in 2011, data were available for only two of four sites in the DS and one of four sites in the WS, while in 2012, data were available on only a subset of lines due to breeding program progression . The unbde novo GWAS and RR-BLUP models for all traits, as well as GS + historical GWAS and RF models for flowering time and plant height. For the GS + de novo GWAS models we used as GWAS inputs the results of GWAS run on the validation site and year , as well as the RYT 2012 DS and 2012 WS GWAS results used previously.The composition of the training population was varied in terms of sites, seasons, and years, as is typical for MET data . We testValidation site, validation season, the combination of sites in the training population, and the statistical method all contributed significantly to prediction accuracy in the MET data set . The comHistorically, these eight sites have been treated as representative of the key rice growing regions in the Philippines/SE Asia, or as a single target population of environments for breeding purposes. Our results here indicate that splitting these sites into the 'northern' and 'southern' groups, with Agusan included in both groups, improves prediction accuracies up to 10-fold. Results were especially significant for prediction of grain yield .These results reflect the correlation of phenotypes within the northern and southern groupings; de novo GWAS was clearly the best statistical method across experiments. For the best overall experiments for grain yield , and Agusan was well correlated with the other southern sites . IsabelaConducting multi-location field trials is a challenging and massive logistical operation that, in the public sector, is also under-resourced. GS, on one hand, appears to be more sensitive to low-quality data and/or a poorly defined target population of environments (TPE) than phenotypic selection  an easier and more stream-lined procedure than delving into the literature to ensure that the GWAS markers tagged previously reported genes of large effect.In this study, we aimed to develop a generically useful approach to identifying SNPs to include in GS prediction models as fixed effects that would take advantage of the matrix of genotypic and phenotypic data already generated for the GS study, and would not require independent, de novo GWAS, and in the majority of cases, the GS + historical GWAS models were significantly worse than the GS + de novo GWAS models  ⩾2.0. Finally, it is worth noting that as with any GWAS-based methodology, controlling for subpopulation structure in the population is essential, otherwise, associations may be spurious and lead to decreased prediction accuracies.While the GS + de novo GWAS approach will be successful for rice breeding within the boundaries described above. The approach should allow breeders to extract information from the training population and, simultaneously, to learn which regions of the genome are significantly associated with traits of interest in their material. The breeder can then use that information to improve the accuracy of their GS models. Consequently, breeding programs can operate with significant autonomy, unencumbered by the need to identify genes or QTL underlying traits of interest, as was the case for MAS and many previously tested GS plus fixed effect models. Furthermore, the accuracy of our GS + de novo GWAS models can be iteratively improved, as information from subsequent training populations is continuously fed back into the model to improve model fit and accuracy.Our results indicate that the GS + How, then, does the GWAS and GS information generated by a breeding program intersect with published information about genes, QTLs, expression networks, physiological pathways, developmental phenotypes, etc. As breeding programs increasingly invest in the sequencing, genotyping and large scale phenotyping of populations and germplasm resources in environments that are relevant to the development of new, commercial crop varieties, they will build important bridges that enable data and information to flow between the world of basic biological research and that of applied or translational science, leading to the development of collaborations and research networks that will help bring these two worlds closer together. Scientists interested in population biology, molecular genetics and gene discovery will help discover and characterize genes and alleles associated with phenotypes of interest to the plant breeder, providing useful tools and insights about natural variation that can be help breeders, agronomists, gene bank managers, physiologists and ecologists to better manage natural variation and to generate sustainable systems capable of producing the food, feed, fiber and fuel needed for a growing world population.VpE) and Genotype x Environment (GxE) interactions (VpGE). Previous GS experiments in wheat and barley have found that multi-environment GS models can lead to improved accuracies by borrowing information from correlated environments . To determine which lines from these populations to use as parents in future crossing and population development, training populations representing these new populations would be genotyped and phenotyped as the basis for GWAS to identify new and highly effective allele combinations that were predictive of top-performing offspring . The significant GWAS-SNPs would then be used as fixed variables in GS models  to facilitate the efficient selection of lines from the new populations that carried favorable exotic alleles in the genetic background of elite lines with high GEBVs.In summary, here we demonstrate that by incorporating information from GWAS and correlated sites into GS models, prediction accuracies can increase to the point that genotyping and performing GS is more cost-effective than planting and phenotyping additional yield trials (http://dx.doi.org/10.5061/dryad.7369p. MET phenotype data will be uploaded to rice diversity.org on article publication and are also available from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.vv28j.The genotype data and RYT phenotype data are available from the Dryad Digital Repository:


To avoid inflated type I error and reduced power in genetic association studies, it is necessary to adjust properly for population stratification and known/unknown subject relatedness. It would be interesting to compare the performance of a principal component-based approach with a linear mixed model. Furthermore, with the availability of genome-wide sequencing data, the question of whether it is preferable to use common variants or rare variants for such an adjustment remains largely unknown. In this paper, we use the Genetic Analysis Workshop 18 data to empirically investigate these issues. We consider both a quantitative trait and a binary trait. In genetic association studies, population stratification and known or cryptic relatedness are always issues. If not suitably accounted for, these may cause inflated type I errors and reduced power. A popular approach to adjusting for population stratification is to construct principal components (PCs) from some similarity matrix for the samples and to include the PCs as covariates in a regression model . This isIn this paper, we compare the PC-based approach with LMM to determine which approach can better control the inflation of type I error arising from correlated samples. The association testing is carried out for a quantitative trait and a binary trait in the Genetic Analysis Workshop 18 (GAW18) family-based sequencing data. For a complete comparison, we construct and consider PCs from different similarity matrices: the sample covariance matrix and the IBS matrix. Finally, we discuss the best choice of variants for constructing the similarity matrix, which has been the subject of several recent studies -8.m largest eigenvalues j λand the corresponding eigenvectors j vfor j = 1, ..., m and denote Y = β0 + mγ X+ Zζ + gβ + δ , where δ ~ N . For a binary trait we adopt a logistic model: Logit(E(Y )) = β0 + mγ X+ Zζ + gβ.In the PC-based approach, for a given similarity matrix, we obtain its n subjects. In the 2 models above, Y = β0 + Zζ + gβ + u + δ, where Y , Z, and g are defined as above, u is the random effect for other polygenic effects and δ is the residual error. It is assumed that δ ~ N and K is the IBS matrix. We use EMMAX [In an LMM, se EMMAX  for paraFor hypothesis testing, PCA.V and PCA.IBS adopted the Wald test and EMMAX adopted the F-test.r2 <5%, and filtering out those with missing call >0.05, there were 63,157 CVs left. We randomly selected 10,837 CVs from those to construct the similarity matrix. The IBS matrix was obtained by EMMAX, and the covariance matrix was obtained by the R function cov with "use = pairwise.complete.obs" to utilize the maximum number of variants.We used the GAW18 sequencing data containing 959 individuals and 8,348,674 single nucleotide variants (SNVs) across all 11 chromosomes, among which 2,791,923 SNVs were CVs and 3,977,003 were RVs. After pruning by PLINK [SBP1, and the hypertension diagnosis at time point 1, HTN1. The former is a quantitative trait and the latter is a binary trait. There are 855 samples available. Gender, smoking, and age are the covariates.We used the measurements of systolic blood pressure (SBP) at time point 1, p values should have followed a uniform distribution. This also meant that the proportion of the tests with p value <0.05 should be close to 0.05 and the inflation factor λ close to 1; λ is the inflation factor of p values estimated by the function gcontrol2 in R package gap. It is calculated as the ratio of the medians of the observed and expected statistics, respectively.We carried out single single-nucleotide polymorphism (SNP) analysis on a set of 6228 CVs randomly selected from all the pruned CVs. Based on the findings of previous GWAS that most of the SNPs were not significantly associated with hypertension, we could assume these 6228 CVs were null SNPs. Because some subjects were from the same families and thus correlated, we expected to observe an inflated type I error if we treated the samples as independent. If the PC-based method or LMM was effective in adjustment, the SBP1 the observed p values deviate from the theoretical uniform distribution (λ = 1.14). For HTN1, the observed p values seem to follow the uniform distribution (λ = 0.94). This observation might indicate a mild heritability in the GAW18 data set.Figure p values of SBP1 with adjustment. We can see the p values are almost uniformly distributed. The proportion of the p values <0.05, estimating the type I error rates, is around 0.05 and of λ's around 1. Figure p values obtained from the 2 PC-based models and EMMAX. There are also differences in the estimated SNP effects, βˆs. However, both the p values and βˆs from the 3 methods are highly correlated.Table H N1. Table p values follow a uniform distribution after adjustment. Figure p values or βˆs from the 3 methods are weaker than those for SBP1. This contrast is partly a result of the logistic link in the PC-based models differing from the identity link in the LMM.We also apply the methods to the binary trait Lastly, we examine which type of variants, CVs or RVs, are more capable of capturing the underlying sample structure. For this purpose, we use PLINK to randomly select 11,103 variants from 1,104,098 pruned RVs to construct the covariance matrix or IBS matrix.λs in testing 6228 CVs for both SBP1 and HTN1. EMMAX is a little conservative for HTN1. Interestingly, we can see a greater distinction between PCA.V and PCA.IBS here than in the previous results, where the similarity matrices were based on CVs. The PCA.IBS is better than the PCA.V at controlling the inflation.Table p values smaller than 0.05. However, we fail to obtain reasonable p values with 200 PCs included. This might be because the model could not be fitted, given the small sample size.Originally, the weaker performance of PCA.V based on RVs was thought to be a result of insufficient inclusion of PCs. Following the suggestion of Patterson et al , we use >1, with the top 25 PCs explaining 19.06% of the total variance; for the IBS matrix, there are only 32 eigenvalues >1, and the top 25 PCs explain 11.91% of the total variance. For the covariance matrix calculated with RVs, there are 433 eigenvalues >1 with the top 25 PCs explaining 7.73% of the total variance; for the IBS matrix, there is only 1 eigenvalue >1, with the top 25 PCs explaining 27.02% of the total variance. In short, when using CVs for constructing the similarity matrix, the top 25 PCs of either type can approximate the correlation structure equally well. Although the top 25 PCs of the IBS matrix can still preserve a large proportion of the variation, when using RVs for the similarity matrix, the counterpart of the covariance matrix does a poorer job of approximation.Alternatively, we turn to the scree plots Figure  to explaIn this paper, we address 3 questions: (a) how the PC-based approach and LMM perform in controlling type I error for correlated samples; (b) whether the IBS or covariance matrix should be used to generate PCs; and (c) whether CVs or RVs should be used to construct the similarity matrix. Based on the association testing of 6228 almost uncorrelated CVs from the GAW18 data, we find that PC-based models were capable of taking into account the sample correlations and worked as well as the LMM. This result is different from the claim made in Price et al [HTN1, even without any adjustment. Although our studies show a positive answer, more studies might be needed to confirm the effectiveness of a PC-based model for testing the binary trait.One limitation in our study was that in GAW18 data, there is no serious inflation in type I error for testing The authors declare that they have no competing interests.Wei Pan proposed the analysis plan, and Yiwei Zhang provided all statistical analysis and drfted the manuscript. All authors read and approved the final manuscript.


N = 3819). We tested additional cohorts including the York Cohort, the Specific Language Impairment Consortium (SLIC) cohort and the Raine Cohort, and stratified them for a definition of dyslexia whenever possible. We did not observe any associations between rs133885 in myosin-18B and mathematical abilities among individuals with dyslexia or in the general population. Our results suggest that the myosin-18B variant is unlikely to be a main factor contributing to mathematical abilities.Twin studies indicate that dyscalculia  is caused partly by a genetic component, which is yet to be understood at the molecular level. Recently, a coding variant (rs133885) in the myosin-18B gene was shown to be associated with mathematical abilities with a specific effect among children with dyslexia. This association represents one of the most significant genetic associations reported to date for mathematical abilities and the only one reaching genome-wide statistical significance. We conducted a replication study in different cohorts to assess the effect of rs133885 maths-related measures. The study was conducted primarily using the Avon Longitudinal Study of Parents and Children (ALSPAC), ( Dyscalculia is a condition where mathematical ability is severely impaired and is recognized as a clinical syndrome in the World Health Organisation (WHO) International Classification of Diseases  and Diagnostic and Statistical Manual of Mental Disorders (DSM-5). Individuals with dyscalculia have profound difficulties in acquiring basic mathematical skills, in the absence of a general cognitive impairment and despite access to adequate educational opportunities  or specific language impairment (SLI), dyscalculia has a clear neurobiological and genetic basis  for mathematical abilities did not report any significant associations (Baron-Cohen MYO18B) gene is the only marker that has been found to be associated with mathematical ability at statistically significant level, as reported in a separate study . The association and relatively large effect size appear to be specific in dyslexia cohorts. The same variant showed a weaker, but still statistically significant, association in a general population cohort from the UK (Twin Early Development study or TEDS)  and the same trend was observed in a combined general population sample . rs133885 is a missense variant and was therefore indicated to be directly causative. Neuroimaging of 79 healthy adults showed that carriers of the rs133885 risk genotype, associated with low mathematical performance, displayed a reduced depth of the right intraparietal sulcus. Numerical processing has long been understood to be localized to the parietal lobes , the York Cohort , the Specific Language Impairment Consortium (SLIC)  and the Raine cohort (N = 667), for a total of N = 5144 individuals. These cohorts were stratified for a dyslexia definition where possible and relevant. We found no evidence of association and our data suggest rs133885 is not a major and common factor contributing to maths skills.We conducted the first replication analysis of the genetic association between rs133885 and mathematical ability in several cohorts: the Avon Longitudinal Study of Parents and Children (ALSPAC)  measures. DNA is available for approximately 11 000 ALSPAC children. Informed written consent was obtained from the parents after receiving a complete description of the study at the time of enrolment into the ALSPAC project, with the option for them or their children to withdraw at any time. Ethical approval for the present study was obtained from the ALSPAC Law and Ethics Committee and the Local Research Ethics Committees  the arithmetic subtest of the Wechsler Intelligence Scale for Children (WISC) Wechsler , which c the aritet al.N = 467 individuals met criteria for dyslexia, while N = 4149 were assigned to the unaffected subgroup. The remaining individuals had incomplete reading data, and were excluded from subgroup analysis (N = 844).We included ALSPAC participants with white European ethnicity to avoid confounding effects of population stratification, and with a performance IQ > 85 to avoid the possibility that low reading and maths performance were related to a general cognitive impairment, similarly to our previous analysis in the same cohort  as well as in a subgroup of families with a history of dyslexia and/or having a child with language impairment . The individual phenotypes selected for association analysis were: (1) numerosity judgement (NJ) derived from two tests, dot counting and number transcoding , (2) mathematical calculation (MC)  and the University of York Department of Psychology Ethics Committee.et al.The SLIC cohort is a family-based cohort collected to study language impairment. This cohort has been described previously in detail  had (1) no known intellectual or neurosensory disability, (2) a nonverbal IQ score ≥ 4th percentile on the Raven's Colored Progressive Matrices, corresponding to approximately > −1.75 SD the population average of the 50th centile, and (3) biological parents who were both of white European origin. The phenotype used was the numeracy outcome variable, which is similar to the mathematical achievement (MA) score used in ALSPAC, and is derived from The Western Australian Literacy and Numeracy Assessment (WALNA)  Study was started as a randomized controlled trial to evaluate the effects of repeated ultrasound in pregnant women in Perth, Western Australia. In total, 2900 pregnant women were recruited between 1989 and 1991 prior to 18 weeks gestation at the King Edward Memorial Hospital   and an effect size of 0.26% in a general population sample (N = 1080). We assumed the variant was directly functional, as suggested in the original study, and we modelled the calculation for a singleton cohort, an allele frequency of 0.45 based on our general population cohort (ALSPAC) with α = 0.05 (http://hapmap.ncbi.nlm.nih.gov/index.html.en). The analysis predicted that sample sizes of 157 and 3015 were required to achieve > 80% power to detect an effect size of 4.87% and 0.26% respectively. The ALSPAC subgroups (TableN = 3819), as well as in the unaffected group (N = 3027), following stratification for dyslexia, with an effect size of 0.26%. The dyslexia subgroup (N = 329) had more than 80% power to detect an effect size of 4.87%, which however is a very large effect on the basis of what we would expect for complex traits. The smallest effect size our general population sample (N = 3819) was predicted to detect was 0.21% (>80% power) and 0.275% (>90% power). The smallest effect sizes the dyslexia subgroup (N = 329) could detect was 2.4% (>80% power) and 3.2% (>90% power).Ludwig and colleagues reported different effect sizes in the subgroups they analysed on the basis of a dyslexia definition. We assumed an effect size of 4.87% which was reported in the combined sample of individuals with dyslexia , the unaffected general population  or in the dyslexia subgroup . The statistics above refer to results obtained under an additive model which yielded relatively smaller P-values compared to a genotypic model.We conducted an association analysis selecting available phenotypes that would best match those used in the original report Table. The ana036 Table. We ran N = 109 families, N = 291 individuals) and a subgroup of families selected for the proband having language difficulties or a family history of dyslexia, as a single group to avoid analyzing very small sample sets . We tested a wider range of maths-related phenotypes . Under the same assumptions reported in N = 109 unrelated singletons, the minimum effect size that could be detected in this small cohort (>80% power) is 7%.To further investigate this association we then extended the analysis to additional cohorts for which both mathematical and reading measures were available. The York cohort has been characterized with a large number of cognitive tests including mathematical measures. The cohort has been primarily collected to study the development of language and reading development in young children with a family history of dyslexia and/or exhibiting a language deficit. We analysed both the entire cohort  was found for rs133885 and the available maths measures , 21% had reading or spelling ability greater than 1.5 SD below than that expected for their age. Of the children alone, 22.8% had reading or spelling abilities more than 1.5SD below that expected for their age. No association . Under the assumptions shown in The Raine cohort is an epidemiological longitudinal cohort representing the general population. The cohort was filtered for ethnicity and to remove individuals presenting sensory or neurological problems that would have impacted their maths scores for specific reasons. We did not filter the cohort for a dyslexia definition, because that would have led to a sample size too small to be analysed. We ran association analysis in 667 individuals for a MA score Table and deteet al.N = 3819 individuals), the York cohort  and the SLIC  and Raine cohorts . Consistently with the original study, we conducted our analysis stratifying the samples for a dyslexia definition, when possible. We could not detect any association between rs133885 and maths abilities.We have conducted the first independent replication study for the previously reported associations between rs133885 in the myosin-18B gene and mathematical abilities identified through a GWAS  which were approximately 3 times the size of TEDS (N = 1080). Therefore, our analysis does not support the role of this variant in contributing significantly to maths abilities. It is possible that the lack of replication can be attributed to an over estimation of the effect size in the discovery sample according to the well-established phenomenon known as ‘winner's curse’  with dyslexia. This unusually large effect size and strength of association compared with what is generally observed for other complex traits is driven by the discovery sample (N = 200) where the reported effect size was of 15.78%. This is an extremely large effect size especially for a common marker (rs133885 MAF = 45%) and was most likely an overestimation of any potential genuine associations. The associations observed in the replication samples showed consistent trends of associations but with weaker strengths and effect sizes, only marginally contributing to the global association. Given the small sample size, it is possible the association in the discovery sample was a false positive, driving the signal of the combined dataset.Power calculations predicted that sample sizes of 157 and 3015 were required to replicate the original finding in a dyslexia and general population cohort, respectively. The sample size in the ALSPAC cohort exceeded these numbers. One difference in our analysis stems from the different phenotypes used for quantitative association analysis  and Raine (N = 667) cohorts are larger than the York cohort but less well-characterized with mathematical measures making direct comparisons more challenging because of inconsistency across available phenotypes. The high variability of measures described here also highlights a particular challenge for genetic investigations of cognitive traits. Our analysis demonstrates how difficult it is to make direct comparisons across different studies collected and assessed under variable criteria. Establishing universal or more directly comparable strategies, which will make it possible to match different studies and ideally to combine samples, would be an important advance for the field of cognitive and neurodevelopmental trait genetics.In addition to the ALSPAC samples we investigated other cohorts, smaller in size and therefore underpowered to detect small effects, but which allowed further exploration of any possible trend of association. The York cohort is smaller in size but has been characterized extensively for numerical skills and is enriched for children presenting language and reading difficulties. In particular, the maths phenotypes of the York cohort are in line with those used by Ludwig et al. (Ludwig The field of complex trait genetics, as other research areas, is becoming increasingly aware of publication bias towards positive findings Munafo  and the MYO18B variant is not contributing to mathematical skills in general.In this study, we were unable to replicate the association between rs133885 in the myosin-18B gene and mathematical abilities. Although we could not reconstruct the exact study design, we based our analysis on a large sample and extended our investigations to several independent cohorts. We conclude that the


The combined application of multiple methods increases sensitivity, but does so at the expense of a higher false positive rate. MiST, SKAT-O, and KBAC have the highest individual mean power across simulated datasets, but we observe wide architecture-dependent variability in the individual loci detected by each test, suggesting that inferences about disease architecture from analysis of sequencing studies can differ depending on which methods are used. Our results imply that tens of thousands of individuals, extensive functional annotation, or highly targeted hypothesis testing will be required to confidently detect or exclude rare variant signals at complex disease loci.Genome and exome sequencing in large cohorts enables characterization of the role of rare variation in complex diseases. Success in this endeavor, however, requires investigators to test a diverse array of genetic hypotheses which differ in the number, frequency and effect sizes of underlying causal variants. In this study, we evaluated the power of gene-based association methods to interrogate such hypotheses, and examined the implications for study design. We developed a flexible simulation approach, using 1000 Genomes data, to (a) generate sequence variation at human genes in up to 10K case-control samples, and (b) quantify the statistical power of a panel of widely used gene-based association tests under a variety of allelic architectures, locus effect sizes, and significance thresholds. For loci explaining ~1% of phenotypic variance underlying a common dichotomous trait, we find that all methods have low absolute power to achieve exome-wide significance (~5-20% power at α=2.5×10 Re-sequencing technologies allow for a more complete interrogation of the role of human variation in complex disease. The inadequate power of single variant methods to assess the role of less common variation has led to the development of numerous statistical methods for testing aggregate groups of variants for association with disease. Such endeavors pose substantial analytical challenges, however, due to the diverse array of genetic hypotheses that need to be considered. In this work, we systematically quantify and compare the performance of a panel of commonly used gene-based association methods under a range of allelic architectures, significance thresholds, locus effect sizes, sample sizes, and filters for neutral variation. We find that MiST, SKAT-O, and KBAC have the highest mean power across simulated datasets. Across all methods, however, the power to detect even loci of relatively large effect is very low at exome-wide significance thresholds for sample sizes comparable with those of ongoing sequencing studies; as such, the absence of signal in studies of a few thousand individuals does not exclude a role for rare variation in complex traits. Finally, we directly compare the results reported by different gene-based methods in order to identify their comparative advantages and disadvantages under distinct locus architectures. Our findings have implications for meaningful interpretation of both positive and negative findings in ongoing and future sequencing studies. To assess whether multiple variants in the same gene contribute to disease, a much larger array of potential genetic models must be considered. If the causal alleles are rare (defined here as MAF<1%), then power to detect each variant’s effect individually is limited. For example, power to detect a variant with MAF = 0.5% and relative risk (RR) = 3 in 3K case-control samples (1.5K cases and 1.5K controls) at α = 5×108 is ~5% –4.NOD2 for Crohn’s disease [PCSK9 for coronary heart disease [LPL for hypertriglyceridemia [MTNR1B for type 2 diabetes [Re-sequencing experiments have identified a handful of rare variants which modulate risk for common, complex diseases. Examples include variants in ociation), PCSK9 fociation), LPL forn method), and MTNLPL or MTNR1B exist undiscovered across the genome, what is the power of different gene-based methods to detect them? What effect sizes are studies of a given sample size well-powered to detect? To what extent does power depend on the underlying architecture of causal allelic variation, and how should researchers navigate through the ensemble of available gene-based tests? To interpret the results of gene-based association methods in sequencing studies, it is critical to quantify the power of each method to detect signals under a range of hypothesized locus architectures.As large-scale (e.g. genome-wide or exome-wide) studies are now being conducted in hundreds and thousands of individuals, several questions emerge. If loci similar to Although the introduction of each novel gene-based association test has typically been accompanied by evaluation of the test’s performance alongside alternatives, each such analysis has compared different subsets of tests, made different assumptions about locus architecture and study design, and employed different simulation approaches. Comparative studies on the relative power of different methods –11, whilIn this study, we systematically explore the power of eleven currently available and widely-used gene-based association methods to detect rare variant signals drawn from a range of principled genetic architectures of disease, in sample sizes consistent with those of ongoing re-sequencing studies. We assess the impact of locus architecture, effect size, and functional variant filters on the power of each method at stringent levels of significance. By evaluating all tests together at loci simulated under a range of continuous frequency-effect size distributions, we characterize each method’s success and failure modes, and describe genetic hypotheses for which particular methods may be better powered than others.We first developed a simulation approach to evaluate the power of each gene-based method. We assumed two key requirements for simulations to be informative: 1) simulated genetic variation must approximate the site frequency spectrum (SFS) and haplotype structure of empirical data, and 2) the distribution of relative risks by frequency class should correspond to hypotheses about the genetic architecture of disease that are compatible with observation.To achieve these objectives, we employed the program HAPGEN2  to simulWe modeled the complex disease type 2 diabetes , and introduced phenotypic effects  by sampling up to 35 exonic causal variants per locus  datasets where no variants were assigned any causal effects , we found that power is very low (<20%) across all architectures and tests considered. At a less stringent threshold of α = 10-4, which might be used to nominate loci for follow-up , power of the best performing tests across AR1-AR5 remained low (10–50%). This was true irrespective of the allele frequency threshold used for variant inclusion; results for a MAF threshold of 0.5% and 5% are shown in In the context of an exome-wide sequencing study, where an appropriate threshold may be α = 2.5×10We noted that at a nominal level of significance (α = 0.05), many methods had high power (~75%-95%) to detect loci at which deleterious variants (AR1-AR5) explain ~1% of phenotypic variance Figs  and S7. ), we found that MiST, SKAT-O, and KBAC consistently achieve highest power, while UNIQ is least-powered. However, we did observe differential behavior of these tests depending on the significance threshold: MiST and SKAT-O retained greater power than unidirectional alternatives at stringent thresholds (α<10-5), while at less conservative thresholds (α>10-3), KBAC was more sensitive  effects Fig , and 2Eive Figs  and S7.-4 in 3K individuals) to AR2 (23%) to AR1 (36%). Power was higher still under architectures where variants with MAF<1% (i.e. those variants tested) contributed all of the locus’ effect (AR4 and AR5): here, the power of MiST was ~50% at α = 10-4. Power also depends on the direction of causal effects at a locus: under AR6 (where both risk and protective effects are present), the variance-component tests (SKAT and C-ALPHA) and combined tests (MiST and SKAT-O) were least affected (by design) [-4, while that of unidirectional tests was reduced to <5% . This is evidenced by the gain in power under models with a greater contribution of rare variants: the power of MiST, for example, increased from AR3 (10% at α = 10 design) –24 and o<5% Figs  and S7. <5% Figs .decreased as the contribution of rare variants increased: power at a genome-wide threshold of α = 5×10-8 for single variants was ~20%, ~10%, and ~7% under AR3, AR2, and AR1, respectively  exceeded that of the best gene-based test (<5% at α = 2.5×10-6 under AR3), though each method detected unique loci. These results confirm that single variant and gene-based association methods should be jointly employed for maximal power across divergent locus architectures.As expected, the comparative advantage of gene-based tests was most evident under architectures where there is strong purifying selection against causal alleles , as compared to ~23% when VE = 1% , indicating that exome-wide sequencing studies of this size are substantially under-powered to interrogate genes for weaker effects  by genetic variants is 0.5%, 1%  increasing sample size, or b) excluding neutral variation at a locus.-4, under AR2) in 10K samples and was largely retained (~50%) even at α = 2.5×10-6  may benefit least from increases in sample size  even in 10K samples, unless the RR of that variant was over 3. Moreover, as sample sizes increase, the threshold required to assess significance for gene-based methods will remain the same (as the number of independent tests performed will not change), while that for single variant association tests will need to become more stringent as more novel variants are discovered. Hence, we expect the joint application of single variant and gene-based methods to remain beneficial even as sample sizes increase.As the number of observations of rare alleles increases with sample size, the performance of single variant association tests will certainly improve, but our analysis suggests that gene-based tests will still uniquely identify loci at which the aggregate signal is driven by variants too rare to be individually detected. When the top single variant in our simulated datasets had MAF < = 0.4%, the locus was rarely detected by single variant association in a sample of 3K individuals Fig , and 3F.-4 exceeded 50% when only disease-causing variants were included (increasing from ~22% prior to variant filtering). These tests may therefore be most powerful for testing targeted hypotheses at loci where rich functional annotation enables exclusion of a subset of neutral variants. Conversely, variance-component tests  as well as combined methods  are characterized by a relative immunity to neutral variation. This latter group of methods, then, are attractive options for jointly testing large numbers of less strictly filtered variants .Our study also confirmed that gene-based tests are highly sensitive to the fraction of neutral variation at a locus Figs  and S13,2 = 0.99) exhibit very high correlation, as expected (2 = 0.92), while others were much less related or even uncorrelated . While in this latter case low correlation was driven by the lower mean power of UNIQ relative to SKAT-O, it is worth noting that there did exist a set of true causal loci (where many case-private singletons segregate) at which UNIQ reported p<10-4, but SKAT-O reported p>0.01 : SKAT-O detected a set of causal loci entirely undetected by SKAT, but was more conservative on the whole, reporting p-values up to an order of magnitude higher than those reported by SKAT at the majority of loci tested. These correlations were also architecture-dependent: under AR2 (where there are only deleterious effects), for example, SKAT-O exhibited high concordance with KBAC (R2 = 0.86), while under AR6 , SKAT-O was most concordant with C-ALPHA and SKAT (R2 = 0.93). MiST shared this behavior, reflecting the ‘unified’ design of these tests as combinations of a unidirectional burden test and a bidirectional variance-based method [Other methods, such as SKAT and SKAT-O, showed asymmetric concordance  and the other gene-based methods. We focused here on loci where VE = 1%, simulated under AR2. For each comparison, we characterized the properties of loci at which KBAC (but not the other method) reports p<0.01, and vice-versa. In the comparison between KBAC and C-ALPHA  more readily detected loci at which signal is driven by either many rare variants private to cases, or by a single relatively frequent case-unique (or control-unique) variant . To test this, we employed a stepwise forward selection approach, starting with each of the three best-performing gene-based methods across architectures  and using the degree of difference (in orders of magnitude) between additional methods’ reported p-values as the inclusion criterion see , S1 Text-4), we found that particular combinations of tests  could jointly achieve ~31% sensitivity at α = 10-4 . However, this gain came at the cost of a higher false positive rate (FPR): after adjusting the p-value significance threshold to correct for the increase in FPR, we found negligible gains in power compared to the application of a single test . Even in 10K case-control samples, power remains modest (~60% at α = 2.5×10-6). Based on estimates of variance explained by known rare and common variant signals , it seems probable that for any given complex trait, at best a handful of loci will have effects on this scale. The full potential of exome sequencing to provide biological insights into disease, then, will depend largely on the detection of loci of smaller aggregate effects, and will require far larger sample sizes than these.In sample sizes comparable to those of many contemporary sequencing studies , we find that while gene-based association methods augment the power of single variant tests by preferentially detecting loci at which rare variants drive the causal architecture, their absolute power is low. All gene-based methods evaluated in this study have limited power, even to detect loci explaining as much as 1% of the variance in phenotypic liability underlying a common trait such as type 2 diabetes (mean power across architectures is ~5–20% at α = 2.5×10-4), MiST and SKAT-O have the highest power across architectures simulated here, especially when rare variants have bidirectional effects on disease. Thus, for investigators looking to discover signals across thousands of loci , these tests are likely to maximize sensitivity.The low mean power to detect disease-associated loci prompted the question of whether some methods are better powered than others to discover novel signals under specific hypothesized locus architectures. We find that at more stringent significance thresholds (α<10Weighted sum methods (and KBAC in particular), on the other hand, are consistently best-powered to detect rare variants of deleterious effect at less stringent levels of significance, and also show the greatest gains in power when neutral variation can be filtered out. These attributes may be useful in various scenarios: to test a small number of biological hypotheses , to prioritize signals for further follow-up from a discovery scan, or to place bounds  on the total number of genes harboring rare variants of a given effect size that are likely to exist.In addition to MiST, SKAT-O and KBAC, we find that other methods may have individual strengths under particular scenarios ; these methods may be optimal for testing such specific genetic hypotheses. Finally, in larger sample sizes , our simulations demonstrate that the increasing number of neutral  rare variants may limit gains in the power of some methods (e.g. FRQWGT). Here, MiST is best-powered at stringent significance thresholds. Taken together, these results suggest that the interpretation of novel signal discovery (or the lack thereof) in sequencing studies may vary based on the specific gene-based methods that are used.http://mccarthy.well.ox.ac.uk/publications/2014/moutsianas_simulations/) allow the investigation of this question for any complex trait by generating simulated data using a custom, user-specified RR-by-allele frequency heat-map and disease prevalence.This study has a number of limitations. It is based on simulated data . It doeIn summary, we find that specific gene-based association methods are best deployed in the setting of particular experimental study designs, and when testing for particular genetic models of disease. Such an approach will likely enable meaningful interpretation of both positive and negative findings in ongoing sequencing studies, and is bound to remain important even as sample sizes increase and new statistical methods for aggregate testing of rare variants are developed.Simulated datasets were generated using HAPGEN2 . HAPGEN2et al [An excess of rare variation was introduced to the data using an empirically selected value of θ = 0.08 for the mutation parameter in HAPGEN2, so as to match the singleton count observed in empirical re-sequencing data in a sample of this size. We used the SFS reported by Nelson et al , which wForward population genetic simulations of global complex disease architecture  were conducted across a range of disease models varying in mutational target size and coupling to purifying selection . By varyPick an exonic variant at randomIntroduce an effect by sampling from the frequency-RR distribution of the respective architectureIf the cumulative variance explained  by variants at the locus is below of the specified threshold, go to step (i) and repeatIf the variance is above the specified threshold, remove one of the introduced effects (at random) and go to step (i)If the number of introduced variants is over 35, quit and restart, else:Accept the sampling and simulate data using the variants and effect sizes chosen, using HAPGEN2.If the cumulative variance explained is close enough to the specified threshold , thenVariant effects were selected from the frequency-effect size distributions described above. We simulated these effects at randomly selected exonic variants across each gene. We used variant frequencies measured in the augmented reference panel of 12,514 individuals. In unidirectional architectures, all rare variants were assumed to increase risk of disease (RR>1). In bidirectional architectures, protective effects were sampled in the same way, but the relative risks were inverted. Variant effects were sampled until the cumulative variance explained (VE) on the liability scale by each locus reached the desired threshold . The following procedure was followed for introducing variation at each locus:The upper bound of 35 on the total number of causal variants introduced per locus was imposed due to instability in HAPGEN2 behavior above this threshold; this limit was rarely reached in 3K samples, but it did restrict architectures simulated in 10K samples  Figs.The calculation of variance explained at each locus was conducted using the method described by So et al., which is available online as an R script . This cahttp://cran.r-project.org/web/packages/MiST/index.html) [The latest releases of the PLINK/SEQ (v0.09)  and EPACex.html) . All exoi.e. not previously detected by the tests already included. Novel signals were defined as loci for which the p-value reported by the candidate test for inclusion was lower by a specified multiplicative “margin” (factor) than the lowest p-value reported by tests already included in the composite test. Three margins were used ; a margin of 100, for example, implies that for signals to be considered novel, they p-value of the candidate test needs to be two orders of magnitude lower than the lowest of the ones already included in the composite test.The subsets of tests chosen for inclusion into composite tests were selected using a stepwise forward selection approach. Starting with a single test , the next test to be included at each step was the one which reported the greatest number of novel signals, http://mccarthy.well.ox.ac.uk/publications/2014/moutsianas_simulations/. The website also contains the software used for the script generation , which S1 Text(PDF)Click here for additional data file.S1 Fig2) as a function of the distance between each pair of variants. The pairwise r is shown for the empirical 1000 Genomes reference panel used in this study (red lines) and variants in the simulated panel which was expanded using HAPGEN2 Click here for additional data file.S2 FigAll simulations discussed in this manuscript were conducted (in HAPGEN2) to match the empirical site frequency spectrum reported across 202 genes in Nelson et al . This comparator dataset was chosen because of its large sample size . To confirm that the site frequency spectrum across these 202 genes  is representative of the distribution across all genes, we compared the SFS at these genes to that observed for all other genes in REFSEQ across the genome (‘All other genes’) in a dataset of 2,657 European individuals who were whole-exome sequenced by the Go-T2D Consortium. These data confirm that the Nelson et al genes are not outliers on the basis of observed minor allele counts.(PDF)Click here for additional data file.S3 FigA) AR1 assumes strong coupling to purifying selection; that is, variants under selection (more likely rare) have larger effects on disease. (B) AR2 assumes moderate coupling to selection, and (C) AR3 assumes no coupling to selection (thus effect sizes are more uniform across the frequency spectrum). Figures on the right are zoomed-in versions of those on the left (only showing variants with MAF up to 1%).The below frequency-RR distributions were learned from population genetic forward simulations of global genetic architecture . ((PDF)Click here for additional data file.S4 FigA) and (B) variant counts are shown for the simulated architecture AR2 (moderate selection). In (A) is shown a histogram of simulated loci, binned by the number of causal variants sampled per locus in order for the locus to explain 1% of phenotypic variance. In (B) is shown a histogram of simulated loci, binned now by the total number of exonic variants with MAF<1%, e.g. the total number of variants included in gene-based association testing. In (C), distributions of variant counts  are shown as box plots, under all six simulated architectures . In (tectures .(PDF)Click here for additional data file.S5 Fig(A) alpha = 0.05 and (B) alpha = 1e-04. Some tests, such as SKAT, appear to be relatively conservative (as has been previously described).All gene-based tests were relatively well-calibrated and had expected type I error rates at both (PDF)Click here for additional data file.S6 FigA) were simulated under architecture AR2 ; results in (B) were simulated under AR6 . FPR-corrected power is calculated using an empirically-derived threshold at which the observed false positive rate is 1e-04; this threshold varies for each gene-based method based on how conservative each method is . Results in ((PDF)Click here for additional data file.S7 FigA), architectures were simulated with causal variants spanning the full frequency spectrum , and all causal alleles increase risk of disease. Gene-based association testing was performed only on variants with MAF < 1%. In (B), only variants with MAF<1% are causal . In (C), variants across the full site frequency spectrum are causal, but causal alleles are mixed in direction of effect; some increase risk of disease, while others reduce risk of disease.Causal variants at each simulated gene explain 1% of phenotypic variance. In ((PDF)Click here for additional data file.S8 FigCausal variants at each simulated gene explain 1% of phenotypic variance (contributed by variants across the full frequency spectrum). In Figs (PDF)Click here for additional data file.S9 Fig2). Across all the gene-based tests evaluated here, the mean p-values are lower  when the extent of LD between causal variants at the locus is low.Each boxplot below shows the range of p-values reported by each gene-based method for loci binned by the average pairwise linkage disequilibrium Click here for additional data file.S10 FigA,C,E). The significance threshold used for the gene-based test is 2.5e-06; the threshold for single variant association (Fisher’s exact) is 5e-08. Blue boxplot shows range of power for single variant association across genes simulated; pink shows power of the gene-based test; green shows the fraction of loci detected only by the gene-based test (and not single variant association); yellow shows the combined sensitivity of both gene-based and single variant association. Next to each boxplot  are scatterplots showing the distinct sets of loci detected by single variant association (loci above the upper dotted red line at 5e-08) and by gene-based association (highlighted in orange). Loci are plotted based on the minor allele frequency (x-axis) and association p-value (y-axis) of the most associated single variant across the locus. Similar plots for AR1, AR2, and AR3 are shown in Power is measured across one hundred simulations of phenotypic effects at each of 24 human gene loci in N = 3K samples. Under each architecture , the power of one of the best-performing gene-based tests (SKAT-O) at alpha = 2.5e-06 is compared to single variant association ((PDF)Click here for additional data file.S11 FigA) VE = 0.5%, per locus, N = 3K samples, (B) VE = 2%, N = 3K samples, (C) VE = 1%, 10K samples. In Power is shown here under AR2 (moderate coupling to selection) for varying locus effect sizes and sample sizes. ((PDF)Click here for additional data file.S12 FigA) The number of total segregating variants (red) and the number of variants simulated to have causal effects (blue) per locus. (B) The distribution of number of causal variants per locus in 10K samples with and without the variant cap. We only simulated loci with fewer than 35 causal variants (pink distribution).We simulated loci at which the site frequency spectrum  matched empirical datasets (see main manuscript (PDF)Click here for additional data file.S13 FigAll results shown in this figure are for loci that explain 1% of phenotypic variance; gene-based tests run in 3K samples (1.5 cases / 1.5K controls) or in 10K samples (5K cases / 5K controls); loci simulated under AR2 (moderate selection).A–B) Each point represents a simulated locus . The x-axis shows the ratio of number of causal variants (variants to which phenotypic effects are assigned) relative to total number of variants tested across the locus . The y-axis shows p-values reported by the gene-based association method SKAT-O. All loci simulated in both 3K and 10K samples are shown as grey points in both panels (A) and (B). Red points are loci simulated in 3K samples; blue points are loci simulated in 10K samples. Blue points (loci simulated in 10K samples) are left shifted relative to red points (loci simulated in 3K samples) because the fraction of neutral variation increases with sample size in these simulations. Blue points are also shifted up, as p-values in 10K samples are more significant than those in 3K samples. In both sample sizes, SKAT-O p-values are more significant as the ratio of causal to total number of variants increases.(C–D) Mean p-values reported by two gene-based association methods (SKAT-O and FRQWGT) as a function of the proportion of causal variation at a locus, in 3K (C) and 10K (D) samples. In 3K samples, both methods show similar performance, but in 10K samples SKAT-O significantly outperforms FRQWGT method, regardless of the proportion of causal variation. While the lower mean power of FRQWGT in 10K samples may be partially attributable to the larger number of neutral variants in this sample size (D) suggests that FRQWGT may also be less-powered for other reasons . This underscores the need to select well-powered gene-based methods for association testing in large sample sizes. Power of the gene-based method MiST at alpha = 1e-04 in 3K and 10K samples, as a function of the ratio of causal to total number of variants per locus. Regardless of this ratio, power of MiST is substantially higher in 10K samples (blue) as compared to 3K samples. Power in both sample sizes increases as the proportion of causal variation increases, but power in 3K samples is more sensitive to this property than is power in 10K samples. In 10K samples, power remains ~60–70%, regardless of the proportion of causal variation. This further suggests that the causal variant cap in HAPGEN2, while restrictive, does not dramatically affect characterization of gene-based test power in 10K samples.((PDF)Click here for additional data file.S14 Fig2 correlation coefficients between p-values reported by each gene-based association method. Correlation coefficients are shown under all simulated architectures: (A) AR1, (B) AR2, (C) AR3, (D) AR4, (E) AR5, and (F) AR6.All results shown here are for loci which explain 1% of phenotypic variance; gene-based tests run in 3K samples (1.5 cases / 1.5K controls). Values represent R(PDF)Click here for additional data file.S1 Table24 genes on chr10 were selected from the center of the distribution of human gene coding length . Below a(XLSX)Click here for additional data file.S2 TableThe below range of locus architectures were modeled at simulated loci; variant effect sizes were sampled from joint frequency-effect size distributions learned from forward population genetic simulations . The architectures were chosen to reflect a range of different rare variant contributions and effect sizes. Briefly, the ‘selection parameter’ controls the degree to which the effect of a variant on evolutionary fitness is coupled to its effect on disease. When tau = 1, variants that are deleterious for fitness (and thus rarer in the population) have the largest effects on disease. When tau = 0, all causal variants have comparable additive effects on disease regardless of their effects on fitness, and thus common causal variants contribute a greater proportion of total heritability . At each(PDF)Click here for additional data file.S3 TableTest combinations were picked using step-wise forward selection starting from each of the three best-performing gene-based association methods across architectures . First column lists the architecture see . The fou(PDF)Click here for additional data file.