Ppd-D1, Rht-B1 and Rht-D1 candidate markers. GWAS revealed 51 marker-trait associations (MTAs) on chromosomes 1A, 1B, 2A, 4D and 5B, with Rht-D1 (4D) being the most significant marker. Division of whole panel according to the Rht-D1 genotype resulted in 212 and 294 varieties harboring Rht-D1a and Rht-D1b allele, respectively. The presence of Rht-D1a compared to Rht-D1b (mutant) allele had a large phenotypic influence on AE resulting in its ~17% increase. GWAS performed on the sub-panels detected novel MTAs on chromosomes 2D, 3B and 6A with increased phenotypic variance imparted by individual markers. Our study shows that AE is a highly quantitative trait and wild type Rht-D1a allele greatly improves AE. Moreover, demarcating the quantitative trait loci regions based on intra-chromosomal linkage disequilibrium revealed AE’s candidate genes/genomic regions. Understanding the genetics of AE in elite European wheat and utilizing the linked markers in breeding programs can help to enhance cross-pollination for better exploitation of heterosis.The production and cultivation of hybrid wheat is a possible strategy to close the yield gap in wheat. Efficient hybrid wheat seed production largely depends on high rates of cross-pollination which can be ensured through high anther extrusion (AE) by male parental lines. Here, we report the AE capacity and elucidate its genetics in 514 elite European winter wheat varieties via genome-wide association studies (GWAS). We observed a wide range of variation among genotypes and a high heritability (0.80) for AE. The whole panel was genotyped with the 35k Affymetrix and 90k iSELECT single nucleotide polymorphism (SNP) arrays plus  Harnessing the advantages of heterosis has emerged as an important strategy for improving and stabilizing yield in many crops. Heterosis, a phenomenon where a hybrid offspring exhibits superior performance compared to the parents, has been in the focus of both plant breeders and geneticists . While hThe subject of hybrid wheat breeding has a long history  with a mleistogamy 1) in barley showed that it inhibited the flower opening by reducing the size of the lodicules [Cly1 encoded a transcription factor containing two AP2 domains and a putative microRNA (miR172) targeting site. Cleavage of mRNA directed by miR172 was detectable only in a non-cleistogamous background [Cly1 were detected in wheat in the subtelomeric regions of the long arms of the group 2 chromosomes [TaAP2-A, -B and–D, and had a high transcript abundance in the lodicules. Like the barley genes, the TaAP2 mRNAs were cleaved at their miR172 sites. However, resequencing of the TaAP2 genes showed a high degree of conservation for these genes even across different ploidy levels and no functional variants at the key miRNA172 targeting site were detected [Recent positional cloning of a cleistogamous gene  to perform GWAS of AE by using high marker density platforms and iii) to link the detected QTL to the current physical map of wheat.The aims of this study were i) to study variance of AE in elite European winter wheat varieties also with regard to the dwarfing gene An elite European winter wheat panel consisting of 514 varieties was used in this study . The whoTo estimate the AE, we first estimated the anther retention . AR was scored in six and ten spikes per plot in 2015 and 2016, respectively. The spikes were harvested five to seven days post-anthesis and held at -20°C. After defrosting, AR was scored by counting the anthers retained inside the lateral florets of four spikelets sampled from the central portion of the spikes (two pairs on each side). AE was calculated by subtracting the number of retained anthers from 24, since the total number of anthers housed by eight florets is 24 .yijk denotes the phenotypic record of the i-th genotype in the k-th replication of the j-th environment, μ is the common intercept term, Gi is the effect of the i-th genotype, Ej is the effect of the j-th environment, (G × E)ij is the interaction effect between the i-th genotype and j-th environment, Rj)k of each genotype, we assumed fixed intercept and genotypic effects, whereas all other effects in the aforementioned model remained random. All the above mentioned calculations were performed in R  by usingPpd-D1, and two dwarfing genes Rht-B1 and Rht-D1) [All 514 winter wheat varieties used in this study were genotyped with a 35k Affymetrix and a 90k iSELECT single nucleotide polymorphism (SNP) array , 29 whic Rht-D1) , 34.K = 1 − 10) and using the function snmf which provides least squares estimates of ancestry proportions and estimates an entropy criterion that evaluates the quality of fit of the statistical model to the data by using a cross-validation technique. The number of ancestral populations, which best explain the genotypic data can be chosen by using the entropy criterion. We performed 10 repetitions for each K and the optimal repetition explaining the minimal cross-entropy value was used to visualize clustering among varieties by drawing bar plots [To examine the genetic structure among the genotypes, we performed principal component analysis (PCA) based on SNP genotypes. The first two PCs were drawn two dimensionally to see the pronounced clustering among varieties. We also calculated the variance-covariance kinship among the genotypes following VanRaden (35) to see the genetic relatedness. The aforementioned estimates were performed in Genome Association and Prediction Integrated Tool (GAPIT) . Furtherar plots , 38.y is the vector of the BLUEs of each genotype, β is a vector containing fixed effects of the genetic marker and the intercept, u is a vector of random additive genetic effects of each genotype, X and Z are the corresponding design matrices and e is the vector of residuals. In the model, the genetic (u) and the residual (e) effects were assumed random, independent and normally distributed with null means as K) as the variance-covariance matrix [P<0.001 (−log10(P) ≥ 3.0) for the detection of marker-trait associations (MTAs). To check whether the model we implemented was sufficiently stringent to control the population stratification, family structure or false positives, quantile-quantile (qq) plots were drawn based on observed versus expected P values of all the SNPs at −log10 scale.A regular linear mixed model  was imple matrix  for the e matrix . We set 10(P) and largest effect) from each chromosome on the AE phenotype by taking their both alleles. Boxplots were drawn for varieties containing individual alleles  of MS-SNPs.We studied the influence of the most significant SNPs  with the significant SNPs. The entire chromosome-wise LD-SNPs were BLASTed [Brachypodium distachyon, Sorghum bicolor and rice (Oryza sativa).A detailed description of the LD analysis is given in the  measure  was perf BLASTed  against  BLASTed . This re BLASTed , a resouBrachypodium, Sorghum and rice on corresponding chromosomes. These QTL regions contained several wheat genes (genes that belong to the LD-SNPs and those in between). The transcript IDs of all these genes were taken from wheat sequence [expVIP [ComplexHeatmap [Anchoring the LD-SNPs onto the genome-zipper revealed putative quantitative trait loci (QTL) for AE. With the exception of chromosome 2A and 6A where not all the LD-SNPs were clustered in the same genetic region on genome zipper, all chromosome-wise LD-SNPs were generally clustered together. We extracted these genome zipper regions (QTL spanning ~3–5 cM) containing wheat genes and their syntenic genes of sequence . We used [expVIP  to get txHeatmap .r = 0.68; P<0.001) between the mean AE values of both years (Anther extrusion (AE) was scored in 514 winter wheat varieties for two years (2015 and 2016). We observed a significant positive Pearson’s product moment correlation  based on SNP genotypes to examine the population structure in our panel revealed the absence of distinct sub-populations with first two PCs explaining only 11.36% of the total variation. There seems to be present, however, a substructure dividing the varieties with respect to the wildtype allele Rht-D1a and the mutant allele Rht-D1b of the dwarfing gene Rht-D1 on chromosome 4D  between 1 and 10, with cross-entropy and 10 repetitions. This resulted in the distinction of sub-populations but with slight entropy shift. The bar plots and the cross-entropy plot indicated three weak sub-clusters showing a change of slope in the curve at K = 3. The point that the curve does not reach a minimum value indicates that there might exist a slight sub-structuring in our panel. However, to accurately see the sub-population clustering, bar plots for K = 2–6 were drawn. Nevertheless, we could see no pronounced clustering among varieties  = 5.64) marker (Rht-D1 with AE led us to divide the full set of varieties into two sub-panels with the varieties harboring either the wild type Rht-D1a (212 varieties) or the mutant allele Rht-D1b (294 varieties) and to perform a second round of GWAS on the individual panels. The phenotypic distribution of AE in these sub-panels showed that the Rht-D1a panel had a mean value 15.91 compared to the mean of 11.81 for the Rht-D1b panel  underlying the genetic architecture of AE were identified. The significant MTAs were detected on chromosomes 1A, 1B, 2A, 4D and 5B with ) marker . Of the 1b panel . Moreove1b panel . A seconfull-set . While tto 4.54% . Boxplotto 4.54% . Beside r2 measure  between significant SNP profiles and genome-wide SNPs resulted in the detection of 330 LD-SNPs. The sequences of all the LD-SNPs blasted (BLAST) against wheat genome assembly (IWGSC1+popseq) resulted in 120 unique gene identifiers (gene IDs) on all chromosomes along with their transcript IDs and direction information . With this scheme, we could anchor most of the genes (or LD-SNPs) onto the genome zipper on respective chromosomes. As assumed, the SNPs with high r2 values were co-segregating as they clustered in the same genetic region on respective chromosomes of genome zipper  and wheat [The study of the transcript-profiles of all the genes in the QTL genetic regions of genome zipper revealed that some genes were expressing exclusively or relatively higher in the AE related organs . The stun factor . Interesnd wheat –17.Stable and heritable performance of beneficial traits is required for their appropriate biological understanding and utilization in efficient breeding of crops. However, development and deployment of homogeneous elite wheat varieties has required strict inbreeding in wheat which is a bottleneck in finding suitable pollinators. Breeding for hybrid wheat demands effective pollinators  with stable performance across years. Therefore, defining the pools of male parental varieties with high cross-pollination capacities will serve in efficient hybrid wheat breeding.Anther extrusion (AE) is a major contributing trait for effective cross-pollination to improve hybrid wheat seed production. Our findings suggest that AE is a phenotypically diverse trait and varies widely among the varieties. The phenotypic distribution of AE suggests its strong quantitative nature. High genetic variance coupled with high repeatability and broad sense heritability estimates suggest that the method for AE phenotyping is reliable and the selection of AE is possible with high accuracy. These estimates are in accordance with recently published reports based on different wheat panels, methods of AE estimations and environments , 18, 19.plus causative gene is greater than expected under independent assortment [High resolution mapping demands a reasonable size of mapping population, a sharp decay in LD, high density of molecular markers (genetic variation) and the extent to which these markers are in linkage disequilibrium (LD) to the causative genes , 46. Thisortment . TherefoRht-D1a. Rht-D1a is the wild type allele for the wheat reduced height (Rht) gene [Rht-D1a allele compared to Rht-D1b (mutant) had a large phenotypic influence on AE resulting in ~17% increase, as the varieties harboring Rht-D1a and Rht-D1b alleles showed an average AE of 15.91 and 11.81, respectively. Similar results were obtained by Boeven, Longin (9). The remaining QTLs generally showed small effects, influencing AE either positively or negatively and imparted a minor phenotypic variance. The comparison of QTL intervals with previously published studies is difficult due to several problems e.g., the use of dissimilar mapping populations and molecular markers. Moreover, the comparison among previously published QTL shows that most of the QTL do not coincide both in linkage and association mapping studies. Based on these results, it seems that AE greatly depends on the mapping population background. A recent study on AE using winter wheat and SNP markers suggested several AE QTL [AX_94426392”. Boeven, Longin (9) reported a QTL on chromosome 1B represented by SNP “wsnp_Ex_c5101_9053178”. Our intra-chromosomal LD analysis shows that both of these SNPs were in LD (r2 = 0.53) with each other, suggesting that they might comprise the same QTL. Similarly Rht-D1 was the most significant marker. The comparison of all other QTL regions suggested no connection.Although it was previously suggested that AE has a low heritability and is mainly controlled by a few, possibly, two genes  our resuht) gene . The preRht genes (Rht-B1 and Rht-D1) influences AE [Rht-D1a as the most significant marker associated with AE. The wild-type Rht-1 genes (Rht-B1a and Rht-D1a) encode DELLA proteins which are sensitive to gibberellin hormones (GAs). Conversely, the mutant alleles (Rht-B1b and Rht-D1b) encode forms of DELLA proteins which are relatively insensitive to GAs [Rht-1b alleles results in reduced height. Coupled with improved inputs of fertilizers, introduction of Rht-D1b allele in wheat has uplifted yield since the onset of the Green Revolution by reducing plant height by about 17% and increasing the assimilate partitioning and consequently harvest index [Rht-D1a and its pronounced positive effect on AE phenotype, it seems that Rht-D1a is a likely candidate gene with a prominent pleiotropic effect on AE. Increased sensitivity to GAs seems to be the reason of high AE in varieties harboring Rht-D1a. However, possibility of other genes or QTL effecting AE in wheat cannot be ruled out because GWAS identified several minor effect loci as well. For example, prevalence of Rht-D1b compared to Rht-B1b is quite high in elite European winter wheat varieties [Rht-B1 was found. These results are in agreement with recent bi-parental and association studies where Rht-D1a alleles were highly associated with increased AE in wheat [Rht-D1b and its homoelocus Rht-B1b to develop the short statured varieties led to improved inbreeding/self-pollination as these alleles confer dwarfism by producing more active forms of GA repressors compared to their counterparts.Recently, it was reported that plant height in wheat which is mainly controlled by ences AE –20, 22. e to GAs , 48. Biost index . In addist index –52. Recest index . Based oarieties  which isin wheat , 19, 22.Rht-D1a will help to i) produce relatively taller male plants and ii) improve pollen shedding by male parents. Taller male plants are required for ease in pollen shed on male part and active reception of pollen on stigma, on female part. Furthermore, pollen shed by taller male parents can travel longer distances.AE is a trait to improve male parents in hybrid wheat breeding and selection of varieties based on versus association mapping studies. This indicates that the association studies are particularly useful for dissection of complex traits to capture maker alleles located close to causal variant from a broader genetic base [GWAS performed on a diverse and extensive set of genotypes takes the advantage of long recombination history and smaller LD decay . Bi-paretic base , 27, 55.r2) between the marker with largest effect and the remaining markers on the same chromosome. Significant markers with large effects on the phenotype mostly act as proxies (by virtue of being in LD) for the causal genetic variant [r2 = 0.20 between adjacent SNPs with a 10% quantile dropping down to 0.001. This indicates that on one hand the marker density across the wheat genome can be increased and on the other hand, the markers with LD >0.20 can be considered as one linkage block or critical QTL region. By adopting this approach, we could demarcate the specific regions on the chromosomes harboring significant MTAs by aligning all significant and LD-SNPs (those in LD to the MS-SNP) on individual chromosomes. The annotated functions and expression profiles of some of the genes in critical QTL regions suggested their involvement in GA production, stamen, anther and floral expansion. For example, genes Traes_1AL_8D078BE99.1, Traes_2AL_AC14A6352.1, Traes_4DS_4C358A987.1, Traes_4DS_7394D3FBE.1 and Traes_5BL_0333145DD.1 expressed either exclusively or at relatively fairly high amount in stamens as compared other organs. The functional annotations of these genes suggest that they mainly belong to protein kinase and synthase families which are known to have roles in various flowering related processes [QTL regions can be demarcated by estimating the intra-chromosomal LD among the SNPs i.e., estimating the LD ( variant . Demarca variant ) can helrocesses . MoreoveRht-D1a is a major QTL to improve AE. Further understanding of pleiotropic effect of Rht-D1 on AE in wheat can help to improve AE for efficient cross-pollination.Hybrid wheat breeding is attractive to both breeders and plant geneticists due to its potential as an alternative to break the yield barriers and understanding the genetic underpinnings of heterosis. Hybrid wheat seed set depends upon the efficient cross-pollination which is hampered by wheat’s strict inbreeding nature. Anther extrusion (AE) in wheat provides the basis for efficient out-crossing. Our results show that AE in elite European winter wheat has wide variation and is genetically stable. Therefore, strong selection response for AE can be expected in breeding programs. Our GWAS results demonstrate the quantitative nature of AE and that S1 Note(PDF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S1 Fig(PDF)Click here for additional data file.S2 FigBar plots show the existence of three to five weak sub-populations. The minimal cross-entropy plot shows slight sub-structuring within the panel.(PDF)Click here for additional data file.S3 Fign denotes the number of varieties present in individual set.(PDF)Click here for additional data file.S4 FigColor key is given in the figure with white marking no expression of genes and purple as highest expression. All genes (transcript IDs) are taken from the QTL genetic regions from genome zipper from corresponding chromosomes. Category refers to the organ categories based on AE-relatedness (blue) and un-relatedness (green).(PDF)Click here for additional data file.


Drosophila. However, the genes contributing to this variability are largely unknown. Here, we conducted a genome-wide association study of ovariole number in a natural population of flies. Using mutations and RNAi-mediated knockdown, we confirmed the effects of 24 candidate genes on ovariole number, including a novel gene, anneboleyn (formerly CG32000), that impacts both ovariole morphology and numbers of offspring produced. We also identified pleiotropic genes between ovariole number traits and sleep and activity behavior. While few polymorphisms overlapped between sleep parameters and ovariole number, 39 candidate genes were nevertheless in common. We verified the effects of seven genes on both ovariole number and sleep: bin3, blot, CG42389, kirre, slim, VAChT, and zfh1. Linkage disequilibrium among the polymorphisms in these common genes was low, suggesting that these polymorphisms may evolve independently.Ovariole number has a direct role in the number of eggs produced by an insect, suggesting that it is a key morphological fitness trait. Many studies have documented the variability of ovariole number and its relationship to other fitness and life-history traits in natural populations of  We measured ovariole number and ovariole asymmetry, and calculated the coefficient of environmental variation (CVE) for these two traits as well. With the exception of ovariole asymmetry CVE, we found high levels of genetic variation among DGRP lines for ovariole number related traits, suggesting that they could be mapped by association analysis. Genome-wide association (GWA) implicated 89 candidate genes for ovariole number, 115 for ovariole number asymmetry, and 769 for ovariole number CVE. Using Minos/P-element insertions and RNAi-mediated knockdown, we confirmed 24 candidate genes for ovariole number. Many of these constructs had quantitative effects, changing as much as 4.6 ovarioles with a single mutation. But we also observed major effects on ovariole number when two candidate genes were perturbed. A Minos insertion in one of the candidate genes, anneboleyn (formerly CG32000), had large, qualitative effects on ovariole morphology. anneboleyn females also produced fewer offspring. Our analysis implicated zfh1 as well, a gene with known effects on ovariole number development , and thus did not examine it as a separate quantitative trait. In addition, for each DGRP line, the coefficient of environmental variation (CVE) for ovariole number and asymmetry was calculated as (σE/μ) × 100, where µ is the mean trait value per replicate, and σE is the within-replicate SD  + ε, where R (replicate), L (line), and V  are random effects, and ε is the error variance. In this model, Y is the phenotype; μ is the overall trait mean; R is the replicate effect; L is the main effect of DGRP line ; L×R accounts for the interaction of each line with the environmentally derived variance across the three experimental replicates; and V(R×L) accounts for environmental variance derived from a fly being reared in a particular culture vial, including potential effects due to differences in rearing density. Broad sense heritability (H2) of ovariole number and asymmetry was calculated as H2 = σ2L/(σ2R + σ2L + σ2R×L + σ2V(R×L) + σ2ε), where σ2L is the variance component among lines, and σ2R, σ2R×L, σ2V(R×L), and σ2ε are all other potential sources of variance in the model.We partitioned the variance in ovariole number and ovariole asymmetry using the ANOVA model ECV and ovariole asymmetry ECV using the ANOVA model Y = µ + L + ε, where Y is the phenotype, μ is the overall CVE mean, L is the random effect of DGRP line, and ε is the error term. Broad sense heritability (H2) of ECV was calculated as H2 = σ2L/(σ2L + σ2ε), where σ2L is the variance component among lines, and σ2ε are the remaining potential sources of variance in the model.We partitioned the variance in ovariole number rP) between each reproductive trait, and between reproductive traits and female values for 14 previously measured sleep phenotypes (rG) between traits were calculated as cov12/√(L12σ × L22σ) .Phenotypic correlations ( × σL22) , where cCVE for each DGRP line with genetic variation segregating in the DGRP using three separate approaches. In each approach, we associated the 3,461,238 sites segregating in the DGRP having a minor allele frequency (MAF) ≥0.01 with ovariole traits. In the first approach, we used the Factored Spectrally Transformed Linear Mixed Model (FaST-LMM) (http://dgrp2.gnets.ncsu.edu) to obtain ovariole phenotypes adjusted for the presence/absence of five common chromosomal inversions and Wolbachia pipientsis infection status, and incorporated these phenotypes into the FaST-LMM model  were calculated as one-half the difference in mean trait value between all DGRP lines carrying the minor allele and those carrying the major allele at that variant position (a/σG) were calculated as variant effect sizes divided by the SD of genetic variation in the trait across the DGRP. Minor allele frequencies were calculated as the quotient of the number of DGRP lines carrying the minor allele at a given locus divided by the total number of DGPR lines with known genotypes at the locus. Effect sizes and allele frequencies were calculated using JMP 13.0.0 (SAS Institute). LD among SNPs was computed using PLINK 1.07 . We chose these collections as they have isogenic control lines, reducing the potential for spurious background effects; 43 candidate genes had stock available . We tested 12 Minos element Mi{ET1} insertion lines  against their isogenic controls, w1118 and w1118; Canton-S B, respectively (Table S1 in File S2). We also tested 32 homozygous UAS-RNAi lines (File S2). Two genes, Mdr49 and bru3, were tested with both Minos element and RNAi constructs. Candidate gene expression was knocked-down in the somatic cells of the ovary using the GAL4 driver lines w{*}; P{w{+mW.hs}=GawB}bab1{PGal4-2}/TM6B, Tb from the Bloomington Stock Center (6803) and TJ-Gal4/ CyO Kr-Gal4, UAS-GFP (gift of B. Oliver) , we individually mated 10 virgin female zfh1 and CG32000 flies to isogenic control males. Parents were cleared from culture vials after 3 d. We counted all live offspring for 5 d, beginning 11 d after initial mating. We compared offspring counts across four conditions: 10 isogenic control males individually mated to 10 isogenic control virgin females, 10 male knockdown/mutant flies individually mated to 10 virgin isogenic control females, 10 isogenic control males individually mated to 10 knockdown/mutant females, and 10 virgin knockdown/mutant males individually mated to 10 knockdown/mutant females. We repeated each assay twice, resulting in measures from 20 female flies per gene/condition. Eighteen vials in the CG32000 assay did not produce live offspring; these failed cultures were more prevalent among vials with CG32000 male parents, suggesting a potential and unanticipated male effect on productivity. We restricted the analysis to offspring-producing vials and used the ANOVA model Y = μ + M + F + M×F + R(M×F) + ε, where Y is the number of offspring, M is the fixed effect of male genotype, F is the fixed effect of female genotype, R is the random effect of experimental replicate, and ε is the error term. In addition, we used a PCR assay to verify the presence of the Minos insertion in CG32000. We used two amplifications, each with one primer placed within the Minos element, and one in CG32000 flanking sequence. Primer pairs were 5′-GAGCCTGCGGATGAAGATC-3′ (CG32000 flanking) and 5′-GGCGCACTTCGGTTTTTCTT-3′ (Minos) and 5′-GTACAATTTACAAAGGATTCGACGTGG-3′ (CG32000 flanking) and 5′-CATTACGCCGCGTTCGAATT-3′ (Minos). The presence of the P-element was verified in both assays .We observed dramatic, qualitative effects on ovary morphology when the candidate genes ECV in all mutant and RNAi knockdown lines (Table S1 in File S2). We used the ANOVA model Y = μ + R + G + R×G + ε and Y = µ + G + ε for ovariole asymmetry and ovariole number CVE, respectively, where R is the fixed effect of experimental replicate, G is the fixed effect of knockdown line genotype, and ε is the error term, to determine whether there are significant differences in ovariole number CVE and asymmetry between mutant or knock-down lines and their isogenic controls. We calculated the FDR for all tests . All DGRP variants with a minor allele frequency ≥0.0238 were tested for association with sleep traits using two models: (1) a GLM model similar to the one described above except that the effect of sex was incorporated as an additional factor; and (2) a FaST-LMM model incorporating population structure. Day average bout length in males was the only phenotype adjusted for Wolbachia infection status, as this was the only phenotype affected. In addition, some sleep characteristics were associated with chromosomal inversions . For sleep tests using UAS-RNAi constructs, we used the Gal4 driver line P{{w+Mc} = Gal4-elav.L}2/CyO (8765) from the Bloomington Stock Center to reduce candidate gene expression in all neurons  as in  was calculated for these traits as well. Sleep measurements were replicated three times, resulting in measurements from 48 flies per sex per line. We analyzed these data for both sexes combined using the ANOVA model Y = μ + S + G + S×G + R(S×G) + ε, where S is the fixed effect of sex, G is the fixed effect of genotype, R(S×G) is the random effect of experimental replicate on the interaction of sex and genotype, and ε is the error term. Sleep and its genetic basis differ between male and female flies .We recorded 5 d of continuous sleep activity from 16 male and 16 female flies per genotype using the File S2 lists ovariole number, ovariole asymmetry, ovariole number CVE, and ovariole asymmetry CVE mean phenotypes for each DGRP line tested; Table S5 in File S2 lists these means adjusted for the effects of Wolbachia infection and chromosome inversion.All data necessary to replicate our analyses are available as supporting files except for raw ovariole trait counts for each fly, which are available upon request. Table S2 in File S2). Quantitative genetic analyses uncovered a highly significant genetic variance component in both traits (P < 0.0001) (File S2), with a broad-sense heritability (H2) of 0.59 estimated for ovariole number, and a H2 of 0.05 estimated for ovariole asymmetry, consistent with previous estimates (rG = 0.72), which suggests that a proportion of the genes affecting each trait are shared between them (Table S4 in File S2). Thus, to the limited extent that ovariole asymmetry is determined by genetics, it may share a common genetic and developmental architecture with ovariole number.The mean values of both ovariole number and right/left ovariole asymmetry varied substantially among DGRP lines, ranging from 12.7 to 29.6, and from 1.2 to 4.6, respectively (ECV) indicates the sensitivity of quantitative traits to the environment . The sensitivity of a trait to the environment can be influenced by both genes and the environment, with the genetic component reflecting the degree of canalization  in ovariole number ECV, but could not detect a genetic component of variance in ovariole asymmetry ECV  (File S2). Thus, genetic factors can influence differences in ovariole number among individual flies of a given genotype, but the degree of asymmetry in ovariole number among individual flies is dominated by environmental or stochastic fluctuations.The coefficient of environmental variation , indicating little overlap in the genes affecting them. Last, we found that ovariole number ECV and the mean value of ovariole asymmetry were highly correlated (rG = 0.70) (Table S4 in File S2). We anticipated this because both traits reflect the organisms’ response to environmental “noise” and thus they may share a common genetic basis. Given the highly significant genotypic contribution to ovariole number, its coefficient of variation and asymmetry we expected to identify genetic variants underlying these traits with some variants in common and others unique to each trait.We calculated the genetic correlation between ovariole number and ovariole number CVE. In each analysis, we considered all variants occurring at a frequency of 1% or greater in the DGRP. The most basic approach was a simple GLM model implemented using SAS. This model does not require the imputation of missing variant allele calls, and did not account for Wolbachia infection status, presence/absence of chromosomal inversions, or population structure, known confounders of association studies in the DGRP . These deviations may reflect population structure, LD, or epistasis. One of our analyses corrected for population structure by incorporating the relationship matrix into the mixed-model analysis  in a small region on chromosome 2R (base-pair position 8583734–5854540), a small region on chromosome 3R (base-pair position 22162040–22178605), and virtually all of the significant polymorphisms on chromosome 4 . Ovariole asymmetry showed little LD , while ovariole CVE had a region of LD on chromosome 3R (base-pair position 12970391–13034018) . These high-LD regions make causal polymorphisms more difficult to distinguish, despite the fact that LD decays within 10–30 bp on average in the DGRP  . However, none of the inversions nor infection status were significantly associated with any of the three ovariole phenotypes (Table S6 in File S2). We hypothesized that variants identified by this study would causally contribute to quantitative variation in ovariole phenotypes, with the caveat that causal polymorphisms would be more difficult to pinpoint in regions of high LD.Quantile–quantile (QQ) plots constructed from the GWA results revealed appreciable deviation of observed from expected P-value of ≤ 1 × 10−5, a threshold applied in many quantitative trait studies in the DGRP (File S2). For ovariole number asymmetry, 175 variants were associated with FDRs ranging from 0.043 to 0.293 (Table S8 in File S2). In addition, 1855 variants were associated with ovariole number ECV, and FDRs ranged from 0.0002 to 0.042 (Table S9 in File S2). We were primarily interested in ovariole number, so we focused on the variants associated with it. However, many of the variants for ovariole number had high FDRs, which indicated less confidence in these variant calls. We addressed this issue with further analysis and testing (see below).We limited our significance threshold to an uncorrected File S1). Consistent with the results of numerous GWA studies (File S1). In contrast, just 12% of identified variants were in gene coding regions. Thus, polymorphisms associated with ovariole number and its related traits tend to fall in noncoding regions, and large-effect variants tend to be rare.Significantly associated SNPs covered the complete allele frequency spectrum, with MAFs ranging from 0.01 to 0.49. Low frequency alleles (MAF <0.05) were associated with each trait, and had larger normalized effect sizes than the more common alleles  and seven genes  were associated with ovariole number and ovariole number asymmetry, respectively. There were 135 nonsynonymous variants associated with ovariole number ECV. The amino-acid altering variants associated with ovariole number ECV mapped to 86 unique genes. Notably, 16 of them were in CG14117, a gene of unknown function. Although they were a minority of all variants associated with ovariole traits, we would expect many of these nonsynonymous substitutions, insertions and deletions to significantly affect Drosophila female reproductive morphology.Some of the variants were predicted to alter amino acids. Nonsynonymous variants in seven genes .To assess pleiotropy among ovariole traits, we investigated the degree to which ovariole number, asymmetry, and ovariole number ECV were biologically plausible candidates for affecting ovariole development. These included genes with known function in Drosophila sexual differentiation (fru) (Mdr49)   , and oogMinos (P-element insertion lines (UAS-RNAi constructs (File S2). These were genes in which SNPs located within or up to 1000 bp up or downstream of the gene coding sequence were significantly associated with ovariole number in our GWA analyses. Tests of Minos and P-element lines revealed significant effects of nine genes (File S2). Notably, we observed a reduction in ovariole number in all mutant lines except MB00990, which carries a Minos element in kirre. In tests using UAS-RNAi lines, we reduced candidate gene expression in somatic cells of the ovary using the Gal4 driver lines bab1-Gal4 and traffic jam-Gal4 . The transcription factor bric-a-brac 1 (bab1) is expressed during the larval stage by terminal filament precursor, and terminal filament cells of the ovary  is a large Maf transcription factor expressed by somatic gonadal cells throughout ovarian development. It affects terminal filament morphogenesis by regulating the expression of adhesion molecules as the ovary develops . Four RNAi constructs in which gene expression was reduced using the bab1 driver showed phenotypic effects, vs. 15 constructs driven by traffic jam. Notably, different genes impacted ovarioles with the bab1 and tj drivers, though CG31999, Mdr49, RhoGEF64C, and SdhA had significant ovariole differences from the control using both drivers. Thus, the effects of individual genes on ovariole number are mediated by the cellular localization and developmental timing of their expression.Tests of RNAi constructs showed significant phenotypic effects of gene knockdowns for 15 genes . InteresMinos element in CG32000 and RNAi-mediated knockdown of zfh1. Of CG32000 females, 66% had either just one ovary or no visible reproductive tissue; the remaining flies examined had ovaries that were wild type in appearance  and 70%  of flies tested. The remaining bab1 flies had large-scale reproductive abnormalities: either a single, large, mass of tissue in place of ovaries, or free-floating egg chambers without a visible ovary . There was a highly significant effect of zfh1 knockdown on fecundity when we used both the bab1 (P = 0.0014) and traffic jam (P < 0.0001)  , after King Henry VIII of England’s wife Anne Boleyn, who had fertility issues.In addition to these quantitative changes in ovariole number, we observed qualitative disruptions to reproductive morphology in flies carrying a pearance . We alsole ovary . To dete 0.0001)  Gal4 dri < 0.05) . zfh1 haFile S2). Seven genes  also impacted ovariole asymmetry in these tests. These effects suggested a shared genetic architecture underlying ovariole number and the processes that control its variation within an individual, though additional replication would be required to confirm these effects as ovariole asymmetry is dominated by environmental factors. Interestingly, none of the genes impacting ovariole number were also observed to affect ovariole number ECV (Table S13 in File S2). This may be attributed to the difficulty in obtaining accurate estimates of CVE  (Table S14 in File S2). This suggests common variants affecting environmental sensitivity in both phenotypes exist.We computed genetic correlations between ovariole phenotypes and female values for 14 sleep/activity traits measured in the DGRP (File S2). In addition, 42 ovariole asymmetry and 276 ovariole number CVE genes overlapped with sleep traits (Table S15 in File S2). With both sets of traits, we examined the overlap among genes with variants having nominal P-values of 1 × 10−5 or less. However, the number of genes overlapping among any two data sets tends to scale linearly with the number of genes identified . Thus, some overlap between sleep and ovariole number candidate genes existed, but to demonstrate pleiotropy, functional tests of candidate genes for their role in sleep were necessary.Although ovariole number and sleep traits showed little genetic correlation, we noted that 39 genes contained variants significantly associated both with ovariole number and one or more of the 14 measured sleep traits (File S2), while others were common to both males and females (Table S18 in File S2). These tests verified multiple GWAS findings of association between individual genes and specific sleep phenotypes (bin3 mutations on both day and night sleep duration (Tables S17 and S18 in File S2) . These genes may have pleiotropic effects on both sleep and ovariole number; alternatively, the apparent commonality may be due to linkage among candidate polymorphisms  in CG42389 had high r2 values  with ovariole number polymorphism 16608818. Thus, we identified seven genes that exhibited pleiotropic effects on sleep and ovariole number, but the extent of LD among candidate SNPs within these genes was low.We tested 20 of the mutations and gene knockdowns that we assessed for ovariole number for pleiotropic effects on sleep. Some effects on sleep were sex-specific   . We iden species . This suWolbachia infection and chromosomal inversions did identify more candidate genes that were verified in candidate gene tests, as inspection of zfh1)Zn finger homeodomain 1  and dpr13, a fru target crossveinless c (—a component of the EGFR pathway implicated in tissue morphogenesis (EcR). EcR plays an important role in ovary development , in which different polymorphic variants were significantly associated with lifespan, bristle number, startle response, and starvation resistance—though the genetic correlations among these traits were low (Catsup associated with different traits evolved independently of one another (In addition, we examined the GWA results for evidence of pleiotropic genes affecting both sleep and ovariole number traits. While no genetic correlation between ovariole number and sleep existed, and the overlap between polymorphisms common to each was low, there were 344 genes common to both studies. Recent work has argued that the partitioning of genetic variance into components at the phenotype level does not necessarily reflect underlying gene action, which may explain why we were able to find overlapping genes . The GWAwww.g3journal.org/lookup/suppl/doi:10.1534/g3.117.042390/-/DC1.Supplemental material is available online at Click here for additional data file.Click here for additional data file.Click here for additional data file.


Advances in recent genome wide association studies (GWAS) suggest that pleiotropic effects on human complex traits are widespread. A number of classic and recent meta-analysis methods have been used to identify genetic loci with pleiotropic effects, but the overall performance of these methods is not well understood. In this work, we use extensive simulations and case studies of GWAS datasets to investigate the power and type-I error rates of ten meta-analysis methods. We specifically focus on three conditions commonly encountered in the studies of multiple traits: (1) extensive heterogeneity of genetic effects; (2) characterization of trait-specific association; and (3) inflated correlation of GWAS due to overlapping samples. Although the statistical power is highly variable under distinct study conditions, we found the superior power of several methods under diverse heterogeneity. In particular, classic fixed-effects model showed surprisingly good performance when a variant is associated with more than a half of study traits. As the number of traits with null effects increases, ASSET performed the best along with competitive specificity and sensitivity. With opposite directional effects, CPASSOC featured the first-rate power. However, caution is advised when using CPASSOC for studying genetically correlated traits with overlapping samples. We conclude with a discussion of unresolved issues and directions for future research. Pleiotropy refers to a biological phenomenon where a single variant or a gene affects multiple phenotypes. In recenTo identify genetic variants with pleiotropic effects, cross-phenotype genome-wide association studies (GWAS) have employed a range of classic and recently developed meta-analysis methods. Typically, summary statistics of distinct but potentially related traits are combined in a meta-analysis framework to detect specific loci with shared association. Such univariate approaches do not require access to individual-level genotype data, and thus are readily applicable to existing GWAS results. Combining results across studies of different traits can also improve the power of detecting modest cross-phenotype genetic effects, which may not reach genome-wide significance for any single trait.SMC2 and RCCD1, showed association with breast and ovarian cancer but no effect on prostate cancer.[Cross-phenotype GWAS however incur several unique challenges compared to a traditional meta-analysis of a single trait. First, the biological impact of a shared causal variant often varies among different traits,,13 yielde cancer. Some gene cancer.–20 Distie cancer. A seriesThe aim of this study is to evaluate the performance of seven recently developed meta-analysis methods in various contexts of cross-phenotype GWAS: (1) One-sided Association analysis based on SubSETs (ASSET1), (2) TwoWe examined the performance of ten published meta-analysis methods: (1) FEMA; (2) ASSET1; (3) ASSET2; (4) BE; (5) CPASSOC; (6) REMA; (7) HE-REMA; (8) Fisher; (9) WICS; (10) CPMA. We summarized the major characteristics of ten meta-analysis methods in K study traits , assuming causal SNPs in Hardy-Weinberg equilibrium with the population minor allele frequency (MAF) f (f = 0.1). We refer to the number of traits with non-null effects as Ta (2 ≤ Ta ≤ K). To examine a list of scenarios with various heterogeneous effects, we tested three types of effect size distributions: (1) normal distribution, (2) bimodal normal distribution, and (3) uniform distribution. For the normal distribution, the effect size βi was selected from N (ln(μ), (kln(μ))2) where μ = 1.1 and k = 0.5 . When a trait was not associated with an SNP, the effect size βi was drawn from N )2) where k = 0.25. For traits with opposite directional effects, we assigned a negative sign once the effect size βi is randomly selected for the trait. For the scenario of bimodal normal distribution, the effect size βi of each trait was generated from one of two independent normal distributions, N (0.5ln(μ), (kln(μ))2) and N (1.5ln(μ), (kln(μ))2), with equal probabilities. Under the uniform distribution, we chose the effect size β in the range of 0 to 2ln(μ). We assumed an equal number of subjects for K traits, setting N cases and N controls . Given a randomly selected effect size and N, the MAF of a variant in cases was calculated assuming the control MAF f, and the 1-degree-of-freedom chi-square test was conducted for assessing association with each trait. This procedure was repeated 10,000 times for K traits under each setting. We repeated the same procedure assuming the odds ratios (ORs) μ of 1.2.We generated 10,000 sets of association summary statistics for p-value was significant at a designated α level (α = 0.05). The type I error rate was estimated as the proportion of the simulation runs showing significant p-value when the null hypothesis was true at α = 0.05, 0.01, and 0.001.The empirical power of each method was calculated as the proportion of the simulation runs using non-null effects where the meta-analysis m-value for each trait instead of binary classification of traits. We thus calculated the sensitivity and the specificity of the BE method using the m-value thresholds as suggested in the original publication[m-value of 0.9 for non-null effects and the maximum of 0.1 for null effects. This prediction mode was referred to as BEm.0.9/0.1. This classification however left many traits indeterminate. For comparison with other methods, we thus used the m value of 0.5 to divide all traits into either non-null (m>0.5) or null (m≤0.5) effects. We referred to this classification mode as BEm.0.5/0.5.For the methods ASSET1, ASSET2, CPASSOC, and BE we calculated the sensitivity and the specificity of each method under the same simulation settings we described in the previous section. The ASSET and CPASSOC output the predicted list of associated traits. We calculated the average proportion of detected associated traits  and the average proportion of discarded null traits  using the predicted lists. The BE method outputs the posterior probability blication: the minhttps://www.med.unc.edu/pgc). The study subjects included a total of 27,888 controls and 33,332 cases with either autism spectrum disorder (ASD), attention deficit hyperactivity disorder (ADHD), bipolar disorder (BIP), major depressive disorder (MDD), or schizophrenia (SCZ). All subjects were of European ancestry and no overlapping subject existed across the five studies. Summary statistics for each disorder included about 1.2 million SNPs obtained from imputation using HapMap III data. In our evaluation, we included 1,105,533 SNPs with imputation quality score R2 ≥ 0.6 and minor allele frequency ≥ 1% in all five studies. The original cross disorder study identified four genome-wide significant loci with pleiotropic effects using the inverse-variance-weighted fixed-effects meta-analysis method.[In addition to simulation, we empirically examined the performance of ASSET, CPASSOC, and BE using the genome wide association summary statistics of five neuropsychiatric disorders. The GWAShttp://biobank.ctsu.ox.ac.uk/) and elsewhere.[Pmeta ≤ 5 x 10−8) were compared among FEMA, ASSET, CPASSOC, and WISC.To examine how each method deals with sample overlaps, we used the GWAS data of individuals with doctor-diagnosed asthma or allergic diseases obtained from the UK Biobank (data-field 6152)). Among 152,249 participants with genotype data, a total of 112,551 of European ancestry with high-quality genotyping and complete phenotype/covariate data were used in this study. After excluding subjects with both allergic diseases and asthma, the study sample included 19,508 subjects with allergic diseases , 7,908 subjects with asthma, and 76,768 controls without the two conditions. Detailed genotyping and QC procedures of UK Biobank were described previously (lsewhere. After stlsewhere. After mePmeta ≤ 5 x 10−8). Note that in all settings, simulated GWAS samples A and B have no heritability due to a random assignment of phenotypes.We also examined the type I error rates occurring from overlapping samples for the four methods FEMA, ASSET, CPASSOC, and WISC. Using 120,000 samples from the UK Biobank data, we generated two artificial GWAS samples, each with randomly selected 30,000 cases. The remaining 60,000 subjects were splitted into the two GWAS samples as controls by varying the percentage of their overlapping  as described in the previous section. Meta-analyses of the three pairs of GWAS samples were performed using FEMA, ASSET, CPASSOC, and WISC. We repeated this procedure 1,000 times, and counted the proportion of meta-analysis results where genome-wide significant loci were identified  different distribution models for effect sizes, (2) a subset of traits with null effects, and (3) existence of opposite directional effects. The simulation results showed that the ASSET1 method, which conducts an exhaustive search of all subset-based fixed-effects models, performs the best when less than a half of traits carry effects. As the number of associated traits increased, ASSET1 however lost its edge, revealing the substantial burden of multiple testing corrections arising from its exhaustive search. In contrast, FEMA, BE, and HE-REMA showed much improved power when a variant is associated with more than a half of traits . It is nK = 5, 8, 10), and significance levels . We also examined the estimated type I error rates of the ten meta-analysis methods. m.0.5/0.5 method exhibited the best sensitivity, followed by ASSET1/2, CPASSOC, and the conservative m-value threshold model BEm.0.9/0.1. All methods tended to show improved sensitivity as more traits show non-null effects, but CPASSOC disposed of an opposite trend. When some effects occur in the opposite direction, ASSET2 showed superior sensitivity to other methods in all conditions. ASSET1 featured the best specificity while the other methods showed comparable performance in multiple settings. The BEm.0.9/0.1 approach assigned a considerable number of traits to an ambiguous group , resulting in a substantial loss of its prediction accuracy.We next evaluated the performance of four meta-analysis methods that prioritize a subset of study traits with which a genetic variant is most likely to be associated: ASSET1, ASSET2, CPASSOC, and BE. Pmeta ≤ 5 x 10−8; LD-clumping—clump-p1 5e-8—clump-p2 1e-5—clump-r2 0.2—clump-kb 500; We also investigated the prediction performance of the three meta-analysis methods ASSET1, BE, and CPASSOC using actual GWAS summary statistics of five neuropsychiatric disorders. In termsCACNA1C on 12p13.33, and the MHC region on 6p21.33 feature a substantially increased level of pleiotropic association.After the publication of the original meta-analysis study, larger dg = 0.55; P = 9.07x10-13).[When studying related traits or disease phenotypes, it is not uncommon to encounter the use of overlapping subjects across different GWAS datasets. Among the ten methods studied here, ASSET, CPASSOC, and WICS are best suited for this situation. We empirically investigated the power of the three methods using GWAS summary statistics of two traits, allergy and asthma, that share genuine genetic correlation (r7x10-13). While thUsing simulations, we also examined how the four methods—ASSET1, ASSET2, CPASSOC, and WICS—control falsely induced correlations when two arbitrary traits with no genetic correlation share study samples. Cross-phenotype GWAS have opened a wide field of genomics research in pleiotropy, but little attention has been put into the evaluation and comparison of analytic methods used in the field. In this study, we aimed to fill this gap by evaluating the performance and the properties of ten meta-analysis methods for GWAS, especially in the context of cross-phenotype studies.Extensive simulation indicates that the selection of proper analytic methods has important effects on the statistical power and inference of the study findings in cross-phenotype GWAS. Unlike a traditional meta-analysis of a single trait, heterogeneity of genetic effect is inevitable in cross-phenotype GWAS and thus calls into question the use of the fixed-effects model, the most commonly used meta-analysis method in GWAS. In practice, we found that despite the assumption of constant effect sizes, fixed-effects-based methods consistently outperformed the other methods under the presence of diverse heterogeneity. The superior power of the fixed-effects method has previously shown for GWAS meta-analysis of a single trait, which exCharacterizing trait-specific association is another important issue in cross-phenotype GWAS because most meta-analysis methods do not nominate specific traits that drive the pleiotropic signal. Manual examination of forest plots is thus often necessary in order to clarify trait-specific association. Three fixed-effects-based methods—ASSET, BE, and CPASSOC—address this limitation by prioritizing the list of most likely associated traits via a model selection procedure. In contrast to the similar level of specificity, sensitivity of the methods varied substantially depending on the direction and the distribution of non-null effects, signifying the need for further method development.We also investigated how meta-analysis methods deal with artificially inflated correlation among study traits due to overlapping subjects. When individual-level genotype data are available, overlapping subjects are typically split across different studies, making each GWAS independent from each other. Here we looked into an alternative approach that statistically adjusts artificially inflated correlation within the meta-analysis framework. Given the exact numbers of overlapping samples, we confirmed that ASSET and WICS can properly accommodate artificially induced correlation. If such information is not available, CPASSOC is the only usable method, but our study shows that when traits with genuine correlation are meta-analyzed, CPASSOC’s empirical adjustment strategy may not adequately control increasing false positive findings. Caution is thus warranted for the use of CPASSOC in the cross-phenotype studies of potentially overlapping samples.all variants share the same genetic correlation across all traits , which is violated in most circumstances of cross-phenotype studies. In addition, misleading results can arise when using inadequately fitted meta-analysis models, thus it is recommended to perform the goodness-of-fit test before conducting meta-analysis [While we found the superior performance and utility of three fixed-effects-based methods, ASSET, BE, and CPASSOC Click here for additional data file.S2 Fig(PDF)Click here for additional data file.S3 Fig(PDF)Click here for additional data file.S4 Fig(PDF)Click here for additional data file.S5 Fig(PDF)Click here for additional data file.S6 Fig(PDF)Click here for additional data file.S7 Fig(PDF)Click here for additional data file.S8 Fig(PDF)Click here for additional data file.S9 Fig(PDF)Click here for additional data file.S10 Fig(PDF)Click here for additional data file.S11 Fig(PDF)Click here for additional data file.S12 Fig(PDF)Click here for additional data file.S13 Fig(PDF)Click here for additional data file.S14 Fig(PDF)Click here for additional data file.S15 Fig(PDF)Click here for additional data file.S1 Note(PDF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.


Heritability estimation provides important information about the relative contribution of genetic and environmental factors to phenotypic variation, and provides an upper bound for the utility of genetic risk prediction models. Recent technological and statistical advances have enabled the estimation of additive heritability attributable to common genetic variants (SNP heritability) across a broad phenotypic spectrum. Here, we present a computationally and memory efficient heritability estimation method that can handle large sample sizes, and report the SNP heritability for 551 complex traits derived from the interim data release  of the large-scale, population-based UK Biobank, comprising both quantitative phenotypes and disease codes. We demonstrate that common genetic variation contributes to a broad array of quantitative traits and human diseases in the UK population, and identify phenotypes whose heritability is moderated by age , sex  and socioeconomic status (education). Our study represents the first comprehensive phenome-wide heritability analysis in the UK Biobank, and underscores the importance of considering population characteristics in interpreting heritability. Heritability of a trait refers to the proportion of phenotypic variation that is due to genetic variation among individuals. It provides important information about the genetic basis of complex traits and indicates whether a phenotype is an appropriate target for more specific statistical and molecular genetic analyses. Recent studies have leveraged the increasingly ubiquitous genome-wide data and documented the heritability attributable to common genetic variation captured by genotyping microarrays for a wide range of human traits. However, heritability is not a fixed property of a phenotype and can vary with population-specific differences in the genetic background and environmental variation. Here, using a computationally and memory efficient heritability estimation method, we report the heritability for a large number of traits derived from the large-scale, population-based UK Biobank, and, for the first time, demonstrate the moderating effect of three major demographic variables  on heritability estimates derived from genome-wide common genetic variation. Our study represents the first comprehensive heritability analysis across the phenotypic spectrum in the UK Biobank. H2), or the fraction due to additive genetic variation  /N, κ = tr[K2]/N, and vK = N(κ − τ2). SNP heritability is then estimated as To obtain unbiased estimates of approach ,71, whicapproach –16 and papproach , and matapproach ,18. SpecK are small, such that K ≈ I and y is Gaussian distributed and thus may be suboptimal for binary traits. However, Visscher and colleagues have empirically shown that this sampling variance approximation is accurate for both continuous and binary traits when the sample size is large [To estimate the sampling variance of r et al.  and maketerature . We noteis large   of K into the memory to compute the SNP heritability estimate, and does not need to explicitly compute P0 or any other N × N matrices. See https://github.com/chiayenchen/mmhe.We note that for large sample size c = P(1 − P)/φ(t)2, P is the population prevalence, t = Φ−1(1 − P) is the liability threshold, Φ is the cumulative distribution function of the standard normal distribution, and φ is the density function of the standard normal distribution [For binary traits, the above calculation gives a heritability estimate on the observed scale, which is dependent on prevalence of the trait in the population. We transformed this heritability estimate to the underlying liability scale under the assumption of a classical liability threshold model ,73, whicribution . Since tR2>0.02 and excluded SNPs in the major histocompatibility complex (MHC) region (chr6:25-35Mb) and chromosome 8 inversion (chr8:7-13Mb). Top PCs were then computed using flashPCA [In all heritability analyses, we included genotyping array, UK Biobank assessment center, age at recruitment and top 10 principal components (PCs) of the genotype data as covariates. Other covariates such as sex and handedness  were adjusted where appropriate. See flashPCA  on the pz-score of their difference: p-value can then be computed as p = 2 ∙ Φ(−|z|), where Φ is the cumulative distribution function of the standard normal distribution.To examine how heritability estimates are modified by sex, we estimated heritability for each non-sex-specific trait in males and females separately. For binary traits, sample prevalence was calculated in each sex. To test if heritability estimates are significantly different by sex, we assumed that the two SNP heritability estimates to be contrasted, k-th age range, α is an intercept, γ is the slope and ϵk is the residual of the regression, and testing whether γ is significantly different from zero. We weighted heritability estimates by the inverse of their standard errors when fitting the regression model, and thus put more emphasis on estimates with better precision. We only analyzed physical and cognitive measures, and did not consider disease codes and medical history in age stratification analyses because age at recruitment does not reflect disease onset.To examine whether SNP heritability estimates vary with age, we used a sliding window approach and estimated heritability for every age range of 10 years  by stratifying the samples. For binary traits, sample prevalence was calculated in each age range separately. We assessed whether heritability estimates exhibited a linear trend with age by fitting a regression model, Similarly, we used a sliding window approach to estimate the SNP heritability for each trait from the bottom 1/3 quantile to the top 1/3 quantile of the Townsend deprivation index at recruitment, a measure of material deprivation within the population of a given area. For binary traits, sample prevalence was calculated in each SES bin separately. For traits that do not reflect the status of participants at the time of recruitment , we have implicitly made an assumption that the SES of participants had not changed dramatically throughout their lives.p-values using the effective number of independent traits we analyzed. Specifically, for each stratification analysis , we calculated the Pearson correlation coefficient for each pair of the traits using their overlapping samples. The correlation between traits that had no sample overlap, e.g., male- and female-specific factors, was set to zero. We then conducted a principal component analysis (PCA) to the constructed phenotypic correlation matrix, and estimated the effective numbers of independent traits that explained 99% of the total phenotypic variation in sex, age and SES stratification analyses to be 400, 31 and 440, respectively. Finally, we multiplied uncorrected p-values by the corresponding effective number of independent traits to obtain corrected p-values.To account for multiple testing in our stratification analyses, we corrected the S1 Text(DOCX)Click here for additional data file.S1 TableSNP Heritability estimates stratified by sex and socioeconomic status (SES) measured by the Townsend deprivation index are also presented.(XLSX)Click here for additional data file.S2 TableSNP Heritability estimates stratified by sex and socioeconomic status (SES) measured by the Townsend deprivation index are also presented.(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S1 Fig(A) A breakdown of the 79 self-reported non-cancer illness codes into different functional domains; (B) A breakdown of the 194 ICD-10 codes into different functional domains.(TIFF)Click here for additional data file.S2 Fig(TIFF)Click here for additional data file.S3 Fig(TIFF)Click here for additional data file.S4 Fig(TIFF)Click here for additional data file.


The widely used genetic pleiotropic analyses of multiple phenotypes are often designed for examining the relationship between common variants and a few phenotypes. They are not suited for both high dimensional phenotypes and high dimensional genotype (next-generation sequencing) data.To overcome limitations of the traditional genetic pleiotropic analysis of multiple phenotypes, we develop sparse structural equation models (SEMs) as a general framework for a new paradigm of genetic analysis of multiple phenotypes. To incorporate both common and rare variants into the analysis, we extend the traditional multivariate SEMs to sparse functional SEMs. To deal with high dimensional phenotype and genotype data, we employ functional data analysis and the alternative direction methods of multiplier (ADMM) techniques to reduce data dimension and improve computational efficiency.Using large scale simulations we showed that the proposed methods have higher power to detect true causal genetic pleiotropic structure than other existing methods. Simulations also demonstrate that the gene-based pleiotropic analysis has higher power than the single variant-based pleiotropic analysis. The proposed method is applied to exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) with 11 phenotypes, which identifies a network with 137 genes connected to 11 phenotypes and 341 edges. Among them, 114 genes showed pleiotropic genetic effects and 45 genes were reported to be associated with phenotypes in the analysis or other cardiovascular disease (CVD) related phenotypes in the literature.Our proposed sparse functional SEMs can incorporate both common and rare variants into the analysis and the ADMM algorithm can efficiently solve the penalized SEMs. Using this model we can jointly infer genetic architecture and casual phenotype network structure, and decompose the genetic effect into direct, indirect and total effect. Using large scale simulations we showed that the proposed methods have higher power to detect true causal genetic pleiotropic structure than other existing methods.The online version of this article (doi:10.1186/s12864-016-3169-1) contains supplementary material, which is available to authorized users. In the past several years, a large number of statistical methods for association analysis of both qualitative and quantitative traits with next-generation sequencing data were developed –14. Mostp values of univariate analysis, and dimension reduction methods , where yi = T is a vector of collecting n observation of the endogenous variable i. Covariates, genetic variants as exogenous or predetermined variables are denoted by X =  where xi = T. Similar to independent variables in the regression, the exogenous variables are outside the models and are not influenced by the variables in the model. Similarly, random errors are denoted by E = , where we assume E[ei] = 0 and E[eieiT] = σi2In for i = 1, …, M. Recall that the relationships between the phenotypes and genotypes are traditionally described by the regressions where the phenotypes are taken as dependent variables and genotypes are taken as independent variables are predictors. In the regression models, the dependence relationships among dependent variables or phenotypes cannot be explicitly expressed. Therefore, the regression models cannot be used to determine which phenotypes cause the variations of which phenotypes. To overcome this limitation, we introduce linear structural equations. The linear structural equations for modeling relationships among phenotypes and genotypes can be written as , Γi = T, B = , Bi = T.where We assume that the random errors in the structural equations are independent and uncorrelated with exogenous variables. We apply the sparsity penalty to each equation to ensure that the sparse SEMs are identifiable.The ordinary least squares estimator is biased and inconsistent for the parameters of structural equations. To ensure the consistent estimates of the parameters in the SEMs, we use a generalized least square method that can be interpreted as a two-stage least square estimate method to estimate the parameters in the SEMs .yi is the vector of observations of the variable i, let Yi−  be the observation matrix Y after removing yi from it and γi−  be the parameter vector Γi after removing the parameter γii. The ith equation:Recalling that can be rewritten aswhere XT on both sides of eq.  technologies will generate unprecedentedly massive and highly-dimensional genomic variation data. Despite their promise, next generation sequencing platforms also have three specific features: high error rates, enrichment of rare variants and large proportion of missing values. Available causal analysis platforms for genetic studies which are mainly designed for common variants provide useful tools for single marker-based pleiotropic genetic analysis, but have limitations in analyzing thousands of sequences collected for very large population-based studies of humans. To address the critical barrier in causal genetic analysis with NGS data, we extend the multivariate SEMs to functional SEMs where exogenous genotype profiles across a genomic region are represented as a function of the genomic position. To effectively reduce the dimension of the data, we use genetic variant profiles which will recognize information contained in the physical location of the SNP as a major data form. The densely distributed genetic variants across the genomes in large samples can be viewed as realizations of a Poisson process. The densely typed genetic variants in a genomic region for each individual are so close that these genetic variant profiles can be treated as observed data taken from curves. The genetic variant profiles are called functional.Large simulations have shown that combining information across multiple variants in a genomic region of analysis will greatly enhance power to detect association of rare variants . To joint be a genomic position. Define a genotype profile xi(t) of the i-th individual asLet Q and q are two alleles of the marker at the genomic position t, PQ(t) and Pq(t) are the frequencies of the alleles Q and q, respectively. Suppose that we are interested in k genomic regions or genes , denoted as Tj, j = 1, 2, …, k. We consider the following functional structural equation models:where βij(t) are genetic effect functions.where xnj(t), n = 1, …, N, j = 1, 2, …, k in each genomic region in terms of orthogonal principal component functions:Functional principal components (FPCs) are efficient summary statistics. The FPCs simultaneously employs genetic information of the individual variants and correlation information (linkage disequilibrium) among all variants. The FPCs view the genetic variation across the genomic region as a function of its genomic location and uses intrinsic functional dependence structure of the data and all available genetic information of the variants in the genomic region. The neighboring genetic variants are linked. The genotypes at one SNP are dependent on the genotypes at nearby SNPs. The FPCs account for the space-ordering of the genetic variation data. Expanding the genotype functions in terms of a few orthogonal FPCs will substantially reduce the dimensions of the genetic variation data while preserving the intrinsic correlation structure and the space-ordering of the data. Specifically, For each genomic region or gene, we use functional principal component analysis to calculate principal component function . We expaφjl(t), j = 1, …, k, l = 1, …, Lj are the l-th principal component function in the j-th genomic region or gene and ηijl are the functional principal component scores of the i-th individual.where η be a matrix collection of all functional principal component scores, the parameter matrix B can be defined as that in Y and Γ can be defined as that in the previous section. The structural functional equations can be reduced in terms of functional principal component scores  would take on the value y when variable X is set to x by external intervention. Direct effect is defined as sensitivity of Y to changes in X while all other variables in the model are held fixed. Indirect effect is to measure the portion of the effect which can be explained by mediation alone, while inhibiting the capacity of Y to respond to X . The total effect is defined asGiven a directed graph model calculus , 42. SupXj is called a parent of X in G if there is a directed edge Xj → X. Let pax denote the set of all parents of X in G. In the linear SEMs, we assume that E is linear in X and pax:Note Then,k directed paths from X to Y and pi are the product of the path coefficients along the i-th path. The total effect of X on Y is then defined as ∑i = 1kpi. As shown in Additional file X on Y is ag + bdh + acdh. By its definition, direct effect measures the sensitivity of Y to changes in X while all other variables in the model are held fixed. In other words, all links from X to Y other than the direct link will be blocked. As a consequences, the direct effect is equal to the path coefficient from X to Y. In the linear SEMs, the indirect effect of X on Y mediated by M is equal to the sum of the products associated with directed paths from X to Y through M [X to Y. The indirect effect of X on Y which is mediated by B and D is equal to bdh.When a directed graph is given, it is easy to calculate total effect . Assume hrough M . In AddiX on Y is the regression coefficient β of the following linear regression:In the SEMs for genotype-phenotype networks, since all SNPs only form undirected graph and there are no directed links between SNPs although we can observe linkage (or correlation) between SNPs; SNPs in the genotype-phenotype networks do not have parents. The total effect of SNP Y on X. This indicates that the traditional simple regression for association studies captures the total effect of a genetic variant on a phenotype.which is a simple regression of YME. Since genetic variants, and other risk factors and phenotypes will affect the mediating phenotypes, the mediating phenotypes in the graphics may have parents. Their parents are denoted by S. Total effect of the mediation phenotype on the target phenotype is calculated byIf we include environments and risk factors such as smoking and obesity in the model and want to evaluate the effects of the environments and risk factors on the phenotype, these variables play mediating roles and will also be taken as phenotypes. We denote these mediating phenotypes by β is the total effect of the mediation phenotype YME on the target phenotype Y. In this case, a simple regression of Y on YME can no longer be used to measure the total effect of the mediation phenotype YME on the target phenotype Y. To observe this, we simulated 1000 individuals with the SEM as shown in Additional file N. The total effect of the mediation phenotype YME on the target phenotype Y is 3.5. We obtain the simple regression:where It is clear that the coefficient of the simple regression is 5.85. This value is far away from the total effect 3.5. However, using eq.  we obtaiYME on the target phenotype Y.where the regression coefficient 3.54 measured the total effect of the mediation phenotype j-th gene and the i-th phenotype in the genotype-phenotype network, we formally investigate the problem of testing the coefficient of the path directed from the j- th gene to the i-th phenotype:Testing connection between the againstβji(t) is expanded in terms of the principal component functions:If the coefficient function of path or genetic effect function 0 in Eq. (then testing the null hypothesis H0 in Eq.  is equivbjig can be estimated by solving problems (i -th equation is given by [The path coefficients problems  and 9)..bjig cagiven by 15\documewhereΛi be the submatrix that corresponds to bji in the matrix j-th gene to the i-th phenotype asLet H0 : bji = 0, Tg is asymptotically distributed as a central χG).Under the null hypothesis of no association l-th parameter of the i-th equation, the statistic is given byFor testing a single parameter or single variant’s path coefficient in the SEMs, the l-th diagonal element of the matrix H0 : Δil = 0, Tc is asymptotically distributed as a central χ(1)2 distribution.where Testing for the path coefficients within the network results in multiple testing problems. Both false discovery rate approach and Bonferroni correction can be used to adjust for multiple testing , 44.We evaluated the performance of the sparse SEM approach for genetic analysis of multiple quantitative traits in simulation studies of a genotype-phenotype network where SNP-based simulations and gene-based simulations were considered. The simulations were carried out for common variants, rare variants and half common and half rare variants. The genotype data were selected from the NHLBI’s Exome Sequencing Project (ESP) with 3248 individuals of European origin, which were then used to generate a population of 1,000,000 individuals.Γij in the SEMs for modeling phenotype sub-network were generated from a uniformly distributed random variable over the interval  or  if an edge from node j to node i was presented in the phenotype sub-network; otherwise Γij =0. Similarly, the parameters Bij in the SEMs for modeling the direction from the genotype (SNP) node j to the phenotype node i were generated from a uniformly distributed random variable over the interval  or  if an edge from node j to node i was presented in the genotype-phenotype network, otherwise Bij = 0. The indicator variables for coding genotypes of the SNP were as previously described. Using the randomly generated network structure and parameters in the structural equations, we produced the phenotypes by the model: Y = − XBΓ− 1 + εΓ− 1, where ε ~ N, and X is a matrix of indicator variables for coding genotypes. For the randomly generated phenotype network, the expected number of degrees per node is three. Simulations were repeated 100 times. Five-fold cross validation was used to determine the penalty parameter λ that was then employed to infer the network while running power simulations. Two measures: the power of detection (PD) and the false discovery rate (FDR) were used to evaluate the performance of the algorithms for identification of the network structures. Specifically, let Nt be the total number of edges among 1000 replicates of the network and Ntrue be the total number of true edges detected among simulated network and NFalse be the false edges detected among We first study the SNP-based simulations. The genotype-phenotype network consisted of two parts. The first part was the phenotype network that was modeled by a DAG. The second part was the connections between the genotypes and phenotypes in which the genotypes were directed to the phenotypes. We randomly generated a genotype-phenotype network structure  with coordinate ascent algorithms . The SMLWe first compare the power and FDR of the S2SEM and SML under the assumption that each QTL had only connection with one phenotype, and no pleiotropic effects were present. We considered two scenarios: 10 phenotypes and 10 SNPs, 30 phenotypes and 30 SNPs. Results were shown in Additional file Now we compare the power and FDR of the S2SEM and SML under the assumption of the presence of pleiotropic genetic effects. We considered three scenarios: ten phenotypes and SNPs, 30 phenotypes and SNPs, and 100 phenotypes and SNPs. The simulation results were shown in Fig. Next we compare the computational time of the S2SEM and SML methods. Table When we study the general genotype-phenotype networks, construction of large genotype-phenotype requires heavy computations. The SML methods are not suitable for the general genotype-phenotype network inference due to its large computational time and have not be applied to general genotype-phenotype network estimation. Next we compared the S2SEM with the QTLnet algorithm  which caFigure We observed three features. The first, the power of S2SEM in all three cases was higher than QTLnet method. Second, the power of the two methods to detect the structure of the networks with the common variants was the highest, followed by the half common and half rare variants. The power of two methods to detect the structure of the network with the rare variants was the lowest. Third, in general, the power increased when the sample sizes increased. To fully evaluate the performance of the two methods, we also presented the FDR for detection of the structure of the networks as a function of sample sizes in Fig. Finally, the simulation results for the third scenario: 100 phenotypes and 1000 SNPs were shown in Fig. Figures To evaluate its performance, we applied the sparse functional SEMs with a gene as a unit of analysis to a sample of 1011 European-Americans (EA) with complete exome sequencing  and 11 phenotypes: high density lipoprotein cholesterol (HDL), low density lipoprotein cholesterol (LDL), triglyceride (Trig) and total cholesterol (TotChol), fast glucose, systolic blood pressure (SBP), diastolic blood pressure, body mass index (BMI), fastinsulin, Fibrinogen, and platelet count (PLATELET) (no missing phenotype data). Inverse rank normal transformation of the phenotypes was used in the analysis.P-values for testing path coefficients < 0.05 from the analysis at the first stage. To dissect pleiotropic genetic structure, at the second stage, we select 142 genes that were connected with more than one phenotype for further analysis. The sparse functional SEMs were applied to the selected 142 genes and 11 phenotypes to infer genotype-phenotype networks. To improve the accuracy of estimation, a stability selection procedure was used to infer the structure of the network. In other words, we randomly resampled data and estimated the genotype-phenotype networks 100 times. We only selected arrows when their P-values for testing the path-coefficients were less than 0.05 and they were present in the estimated network more than 80 times, i.e., the probability for each arrow to be selected was more than 0.8. We identified a genotype-phenotype network with 137 genes directly connected to 11 phenotypes and 341 edges. One hundred fourteen genes out of 137 genes showed pleiotropic genetic effects. The results were presented in Fig. p-values according to network in Fig. P-values < 10− 7 and stability ~1. This showed that the inference about phenotype sub-network is highly reliable. We also observed that large proportion of the edges in the phenotype network had two directions. This demonstrated that the SEMs had limitations for inferring causal networks.The analysis consisted of two stages. At the first stage, the sparse functional SEMs were applied to each of the 259 KEGG pathways and 11 phenotypes to infer genotype-phenotype networks. The remaining 12,737 genes which were not mapped to KEGG pathways were divided into 100 groups according to the order of chromosomes. Again, the sparse functional SEMs were applied to each group of genes and 11 phenotypes. We identified 1789 genes with PIK3R5 directly affected seven phenotypes, HS1BP3 directly affected five phenotypes, 11 genes directly affected four phenotypes, and 33 genes directly affected three phenotypes and remaining 102 genes directly affected two phenotypes. To assess the roles of path analysis in detecting genetic pleiotropic effects, we presented Table P-values of three genes that affecting more than four phenotypes for path coefficients, the marginal effects of single and multiple traits (simple regression and multiple regression), and the minimum of P-values derived from principal component analysis (PCA) based regression. Table P-values for path coefficient were less than that for the marginal effect of corresponding single trait. Estimation of the marginal genetic effect of single trait only explores information of the target trait and genetic variants. However, estimation of the path coefficient uses information of all the relevant traits and genetic variants. This implies that path analysis has higher power to detect genetic risk variants than the traditional marginal analysis. From Table P-value for path coefficient was less or close to that for marginal effects of multiple relevant traits or their PCA analysis. Additional file We observed that SEMs provide a powerful tool to distinguish four types of effects: direct, indirect, total and marginal (estimated by a simple regression) effects. Additional file P-values for testing path coefficients were smaller than that for testing the marginal effects  and 25 tests in which the P-values for testing marginal effects were smaller than that for testing the path coefficients. This showed that using SEMs for path analysis will discover additional QTLs that may be missed by marginal association analysis. In theory, the total effect of the causal X on outcome Y is equal to the summation of the product of the path coefficients along all possible paths between X and Y [X in the linear regression of Y on X and its parent set. Let Z = Parentx. The total effect βYX. Z can be expressed by [Additional file  X and Y . In the essed by 19\documeZ = φ is empty. Therefore, for the SNP or gene X, we have βYX. Z = βYX. For example, the estimator of the direct effect of gene MET on the phenotype SBP was −0.0596. MET also had path MET → DBP → SBP. The indirect effect of MET on SBP was 0.0621 × 0.605 = 0.0376. Thus, the total effect of MET on SBP was −0.022. The marginal effect βYX of MET on SBP estimated by SRG was −0.0212. The total effect of MET on SBP estimated from Fig. MET on SBP. This example showed that if the causal relationships among the variables were completely captured by a DAG, the total effect and marginal effect were almost equal. Therefore, in the genotype-phenotype estimation process, we can use the relationship between the total and marginal effects to check whether the causal relationship modeled by a DAG is complete.Since causal relations between SNPs do not exist, any SNP does not have its parent, i.e., the set P-values of 22 SNPs in seven genes for testing the path coefficients. We observed that single SNP made only a mild contribution to the direct effect, the multiple SNPs made significant contributions to the phenotype variation. This showed that the gene-based genotype-phenotype inference had higher power than the single SNP-based genotype-phenotype inference.Multiple SNPs within a gene jointly have significant genetic effects, but individually each SNP make mild contributions to the phenotype variation. Table Since the most existing methods for genotype-phenotype network estimation only take a single SNP as a variable  and cannot take a gene as a unite of analysis, next we illustrate the application of S2SEMs for inference of genotype-phenotype network using SNPs and compared their results with that of QTL-driven phenotype network method (QTLnet) . The numP-values for the coefficients of all the paths connecting SNPs within a gene and a phenotype was less than 0.05. At the second stage, we used Bonferroni correction to adjust P-values for multiple tests. In Fig. P-values for path coefficients connecting gene and phenotype was less than 0.05. Figures The gene-based genotype-phenotype network with 55 nodes (11 phenotypes and 44 genes) and 110 edges estimated using the selected 45 genes and the FSEM method was shown in Fig. P-values for the coefficients of all the paths that connect SNPs within a gene and a phenotype without Bonferroni correction. Figure P-values (<0.05) for the path coefficients of the edges connecting the SNPs in the gene to the phenotypes were summarized in Additional file LBP connected to the phenotypes TRIGS and TOTCHOL, and DOCK1 connected to the phenotype HDL, the SNP-based and gene-based S2SEM method, respectively, discovered 31 and six genes connected to phenotypes. These results showed that all proposed SEM methods including FSEM, gene-based and SNP-based S2SEM methods outperform the QTLnet method.Next we study the SNP-based genotype-phenotype network estimation using the S2SEM method. In other words, we connected genes to the phenotypes using the minimum of lues <0.0 for the ADAMTS19 effected SBP and DBP, rs116623954 in the gene CNIH3 affected FASTINSULIN and FIBRINOGEN, rs13223756 in the gene MET affected SBP and DBP). Second, multiple SNPs in the same gene affected the same phenotype. Three SNPs: rs754555, rs754554 and rs754553 in the gene DFNA5 jointly affected BMI, two SNPs: rs11017658 and rs61758438 in the gene DOCK1 jointly affected SBP. Third, the pleiotropic effects of the gene were due to different SNPs. The SNPs: rs564665 and rs141647150 in the gene DAB1 affected phenotypes DBP and FASTGLUCOSE, respectively; the SNPs: rs376043577 and rs3731878 in the gene IHH affected BMI and PLATELET COUNT, respectively; SNPs rs2232585 and rs2232605 in the gene LBP affected FIBRINOGEN and PLATELET COUNT, respectively. SNPs rs2305610, rs372123385 and rs17027957 in the gene OSBPL10 affected BMI, DBP and FIBRINOGEN, respectively; three SNPs: rs144082896, rs140962261 and rs11547635 in the gene SYN3 affected TRIGS, SBP and FASTINSULIN, respectively. You can find more examples from Additional file Similar to the gene-based FSEM method, we observed several remarkable features from these results obtained by the S2SEM method. First, we observed three SNPs that showed pleiotropic genetic effects  our sparse two-stage SEMs (S2SEM) outperformed QTLnet method. Since the gene-based version of QTLnet method has not been developed we only compared the power and false discovery rates of the variant-based SEMs and gene-based functional SEMs. We found that for all spectrums of allele frequencies  the gene-based functional SEMs substantially outperformed the variant-based multivariate SEMs.P-values for testing path coefficients were smaller than that for testing the marginal effects. This demonstrated that only using marginal association analysis we might miss identification of many significant QTLs.The fourth issue is how to distinguish four types of effects: direct, indirect, total and marginal effects. The current paradigm for genetic association analysis of multiple phenotypes is genetic marginal analysis in which the effects of the genetic variants on the phenotypes are estimated by regressing phenotypes on the genetic variants. This paradigm is unable to unravel the structure of the genotype-phenotype network and to estimate direct, indirect and total effects of the genetic variants on the phenotypes. The direct, indirect and total genetic effects provide valuable information for dissecting genetic structure of complex traits. We developed sparse SEMs and FSEMs as a causal inference tool to estimate direct, indirect and total genetic effects in addition to estimating marginal genetic effects. We observed that the most effects were indirect effects due to mediation. In traditional QTL analysis, we often identify QTL by testing association of the marginal effect with the single trait. The FSEMs and SEMs provide complimentary information about path coefficients. Interestingly, we found that many The fifth issue is how to solve the large genotype-phenotype networks with up to hundreds of nodes or genes. A key to the large network inference is computation efficiency of the algorithms. Two strategies were employed to solve this problem. The first strategy was to reduce the dimension of data using functional data analysis. We first expand the genotype profiles in a genomic region (gene) in terms of orthonormal eigenfunctions. Genetic information across all variants in the genomic region including all single variant variation and their linkage disequilibrium is compressed into functional principal component scores. We use genetic information compressed into functional principal component scores to infer genotype-phenotype networks. The second strategy is to use ADMM algorithms to optimally solve the sparse SEM problem. The widely used algorithms for sparse SEMs are coordinate descent algorithms borrowed from the lasso originally designed for the sparse linear regression. The ADMM algorithms are parallel and efficient. Their convergence rates are fast. The ADMM algorithms allow inferring networks with hundreds or even thousands of nodes.Major limitation of the SEMs for joint inference of genetic architecture and causal phenotype networks is the presence of two directions associated with one edge in the estimated network, which leads to a cyclic graph. To remove the cycles from the graph we need to strictly enforce the global constraint that the graph structure has to be acyclic. Such problems are often casted into a combinatorial optimization problem. We rank graph structures via a scoring metric that measure how well the DAG models fit the data. Combinatorial optimization algorithms are then used to search the optimal DAG with the best score .Although their application to genome-wide genotype-phenotype network construction is difficult due to computational limitations, the SEMs are suitable to the phenome-wide association studies where starting phenomics, defined as the unbiased study of a large number of phenotypes in a population. We study the complex networks between multiple expressed phenotypes and genetic variants. Since the number of genetic variants in the phenome-wide association is quite limited and hence the size of the genotype-phenotype network is limited, the required computational time of construction of genotype-phenotype networks using SEMs is in the range the current computer system can reach. Advances in biosensors and sequencing technologies generate large amounts of phenotype and genetic data. SEMs and causal inference may emerge as a new paradigm of genetic studies of complex traits. The main purpose of this paper is to stimulate discussions about what are the optimal strategies to facilitate the development of a new generation of genetic analysis. We hope that our results will greatly increase the confidence in joint inference of genetic architecture and causal phenotype networks.We have developed sparse SEMs and sparse FSEMs as a statistical framework for joint analysis of genetic architecture and causal phenotype network, which may emerge as a new generation of genetic analysis of multiple phenotypes. Our proposed sparse functional SEMs can incorporate both common and rare variants into the analysis and the ADMM algorithm can efficiently solve the penalized SEMs. Using this model we can jointly infer genetic architecture and casual phenotype network structure, and decompose the genetic effect into direct, indirect and total effect. Using large scale simulations we showed that the proposed methods have higher power to detect true causal genetic pleiotropic structure than other existing methods.