Heterosis is widely used in agriculture. However, its molecular mechanisms are still unclear in plants. Here, we develop, sequence, and record the phenotypes of 418 hybrids from crosses between two testers and 265 rice varieties from a mini-core collection.Phenotypic analysis shows that heterosis is dependent on genetic backgrounds and environments. By genome-wide association study of 418 hybrids and their parents, we find that nonadditive QTLs are the main genetic contributors to heterosis. We show that nonadditive QTLs are more sensitive to the genetic background and environment than additive ones. Further simulations and experimental analysis support a novel mechanism, homo-insufficiency under insufficient background (HoIIB), underlying heterosis. We propose heterosis in most cases is not due to heterozygote advantage but homozygote disadvantage under the insufficient genetic background.The HoIIB model elucidates that genetic background insufficiency is the intrinsic mechanism of background dependence, and also the core mechanism of nonadditive effects and heterosis. This model can explain most known hypotheses and phenomena about heterosis, and thus provides a novel theory for hybrid rice breeding in future.The online version contains supplementary material available at 10.1186/s13059-022-02822-8. Hybrid breeding is a revolutionary technology in agricultural production and for food security. Due to their dramatic increased yield by tens of percent and even double compared to inbreds , hybridsArabidopsis, maize, and rice, and many genes appear to be dominant, overdominant, or parent-specific in expression [PMA1 and MSB2 in yeast [PCSK9 in human heart diseases [Dw3 in sorghum, and GS3 and Ghd7 in rice [SFT gene affecting fruit yield of tomato [FNS gene impacting flower color in Mimulus lewisii [Although heterosis has been utilized extensively in agriculture, its mechanistic understanding is still fragmentary and challenging . Regardipression –16. At tin yeast , PCSK9 idiseases , Dw3 in  in rice , 20. Thef tomato , the SHEf tomato , and the lewisii . The sec lewisii , 25, or  lewisii –28, repr lewisii . However2 population from an indica-indica rice hybrid indicated that the contributions of the dominant factors varied by traits and single-locus dominance has relatively small contributions in all traits [2 individuals from 17 crosses demonstrated that the heterosis mainly attributes to accumulation of numerous rare superior alleles with positive dominance [2” derived from Zhenshan97 and Minghui63 [1 population derived from Peiai64S and 9311 [Rice is one of the crops that successfully utilize heterosis in breeding. Numerous studies have been carried out to investigate genetic and molecular mechanisms of heterosis in rice; however, there is still no consensus on such mechanisms –32. Earll traits . Recent ominance . Althouginghui63 , and theand 9311 . Furtherjaponica variety Nipponbare and indica variety 9311) and 265 rice varieties from a mini-core collection [1, thus resulting in the insufficient function of two homo-alleles in parents, but the relatively or completely sufficient function of one allele in F1, that renders the target locus nonadditive in effect, as contributing to heterosis. So heterosis in most cases is not the heterozygote advantage but the homozygote disadvantage (insufficiency in function and performance) under the insufficient genetic background. The model can explain the most known hypotheses and phenomena about heterosis, thus providing a novel theory for future hybrid rice breeding.To get insight into rice heterosis, we generate and record the phenotypes of 418 hybrids from crosses between two testers , after excluding SNPs with minor allele frequency (MAF) less than 5% and missing rate larger than 50%. According the neighbor-joining tree of 267 parental lines based on the above SNPs and the posterior validation errors in different number of run K in admixture, all the 267 lines could be classified into japonica and indica subspecies  and indica×9311 (I×9311), and two kinds of inter-subspecific combinations, i.e., japonica×9311 (J×9311) and indica×Nipponbare (I×Nip).We identified 4,625,141 SNPs in the parent panel (We phenotyped the 418 hybrids and their 267 parents in 2013 at Changsha (CS)  and Sanya (SY)  of China. Six yield-related traits were investigated, including spikelet number per panicle (SPP) and its two component traits (both primary and secondary branch numbers per panicle (PBP and SBP)), 1000-grain weight (KGW), panicle number per plant (PNP), and grain weight per plant (GWP) , (2) eight sets from F1 (four types of combinations in two environments), and (3) eight sets of calculated middle-parent heterosis value (Hmp) (four types of combinations in two environments) . The Manhattan plot of the results of association analysis is shown in Additional file We carried out genome-wide association studies (GWAS), using 120 sets of genetic and phenotypic data. The phenotypic data consists of three types of datum panels evaluated for six yield traits  under two environments (Changsha and Sanya). The three types of datum panels include 20 sets of data for each of the traits, i.e., (1) four sets from parents (both 1 datum panel (F1_QTL), and 636 and 818 QTLs from the Hmp datum panel (Hmp_QTL)  and Hmp_QTLs (6.6% on average), regarding the traits related to grain number  and grain size (KGW). As for PNP, the situation is combination-dependent. The three panels of QTLs related to grain weight per plant (GWP) were rather environment-specific , 828 and 895 QTLs from the F1_QTL, and Hmp_QTL), we found that the genetic architecture affecting hybrids synchronizes more with that impacting heterosis (24.09±21%), compared to that affecting inbred parent (12.28±10%), but there were some exceptions for some combinations, environments, and traits  in different types of panels by GWAS. Therefore, in order to estimate the relative degree of additive and nonadditive effect of each QTL and throw light on the understanding of the genetic basis underlying heterosis, we estimated the additive effect (a) and dominance effect (d) of each QTL on six yield traits using the parental, F1 and Hmp datum panels . A QTL is referred as overdominance preferred if the absolute ratio of dominant effect to additive effects  is no less than 1.5, and dominance preferred if 0.5≤|d/a|<1.5 , and additive preferred if |d/a|<0.5 . We called those QTLs being dominance preferred or overdominance preferred as nonadditive QTLs.As expected according to the quantitative genetic theory, we can detect the QTLs showing significant additive effect in the parental datum panel, nonadditive effect in the Hmp datum panel, and both additive and nonadditive effects in the F1_QTLs and Hmp_QTLs showed apparently more nonadditive effects than P_QTLs , with only a small portion of QTL represented additive effect . Conversely, the majority of P_QTLs demonstrated additive (44.16%) and dominant (37.08%) effects, and only a small proportion (18.74%) showed overdominance. Consistent with the observation that SPP-related trait  did not exhibit obvious heterosis in Sanya  than that in indica hybrids (from 80.4% in Changsha to 62.8% in Sanya) , both FTo compare the response of different genetic components to the environment and their genetic background, comparative analysis from the levels of environmental and genetic background were conducted. First, we examined the environmental stability among the QTLs of additive, dominant, and overdominant ones, the result showed that a larger proportion of additive QTLs showed environment-stable than nonadditive QTLs, regarding most types of combinations for all traits except for PNP. Meanwhile, a higher proportion of dominant QTLs showed environment-stable than overdominant QTLs for most of the combinations and traits , we estimated the phenotypic coefficient of variation of the same genotype under different genetic backgrounds of individuals in the tested population, the result showed that homozygous genotypes of QTLs with nonadditive effects exhibited higher variability, as compared to those with additive effects . Expression patterns can be classified as additive preferred (A) (13%), dominant preferred (D) (39%), and overdominant preferred (OD) (48%) in at least one of three tissues , thus it is challenging to investigate the molecular mechanism of heterosis at the phenotypic level. Transcription is such an intermediate step for a gene to perform its functions in development of complex phenotypes. Therefore, it is informative to explore gene expression patterns between parents and their FArabidopsis thaliana combinations and observed the same phenomenon  dominance. For the negative regulation, the performance is similar, but the receptor expresses as negative  dominance, when the insufficient ligand background can only suppress partial function of two homo-alleles in parents, instead relatively full function of one allele in the F1 .For the positive regulation, when the activator as the background is insufficient  for the functional allele of the receptor, the receptor will express as positive  dominance. In contrast, when the background is sufficient (larger X/K), the receptor will express as additive effect Fig. a. AppareScenario 2: Two alleles of one polymorphic site under two independent backgrounds, that is, two alleles of one polymorphic site of the receptor, can be bound by two respective and independent ligands as the backgrounds of the receptor  dominant allele with a larger function and that from the other allele with a smaller function. When both backgrounds of two alleles are sufficient (higher X/K), the receptor in both parents and F1 can express the full function as two alleles and one allele, respectively, as a result the receptor expresses as additive . As different from Scenario 1, we can also observe positive overdominance under Scenario 2, when the receptor in FK) to the ligand and show different maximum functions (μ). Thus, we considered two situations: (1) One allele has higher affinity and shows a larger maximum function, and the other has lower affinity and shows a smaller maximum function (abbreviated as HALF/LASF) , the overdominance can only be found when both alleles are functional, which result from the cumulation or complementation between the  dominance of the allele with a larger function and the effect of the other allele with a smaller function  Fig. e. As ind2 lines from the crosses between randomly selected RILs derived from Minghui 63 and Zhenshan 97 [Arabidopsis hybrid Col×C24, the results showed that overdominance was more frequently observed when both parental alleles were functional than that when only one parental allele was functional  dominant effects exhibited higher variability [It is intriguing that in the observed experiments we have found extensive evidence that can represent the three features of the HoIIB model mentioned above. First, we observed the homo-insufficiency of the allele with a large function and the cumulation or complementation from the allele with a smaller function at various levels including transcription, QTL, and traits. Using transcriptome profile from the 1, 2, and 3 mm young panicles of 9311, PA64S, and their hybrids (LYP9), we investigated expression levels in the two parents for those genes with additive, positive dominant, and positive overdominant effects, respectively. The homo-insufficient expression was substantially observed in the higher parent for genes with dominant and overdominant transcription, compared to those with additive transcription , we found that SSU1 showed a strong co-expression with its transcription factor FZF1 in strain BY4743 of Saccharomyces cerevisiae  and homozygous (ssu1/ssu1) knockout strain of SSU1 in BY4743 , indicating the effective mutation. Apparently, the SSU1/ssu1 genotype showed obvious nonadditive expression (d/a = 1.899) in the system comprising genotypes SSU1/SSU1, SSU1/ssu1 and ssu1/ssu1 under normal FZF1 background  of genotypes SSU1/SSU1, SSU1/ssu1 and ssu1/ssu1, and the transcription level of FZF1 (representing the background sufficiency). We really observed dramatically decreased dominance degree of SSU1 along with the increasing of background, i.e., expression level of FZF1, and SSU1 even nearly transited into additive expression when the expression of FZF1 upregulated more than 10 folds  of the target gene and the transcription factor as its background, and carried out the experiment in the simple diploid organism, yeast. We screened the reported transcription factors and its target genes in yeast according to the following criteria: 1) the promoter region being bound by a transcription factor has been clearly validated; 2) there is strong and simple regulatory relationship between the transcription factor and its target gene. After investigating the co-expression of six pairs of genes  dominant loci to reach their maximum function, but also the one that causes the instability of the target genes. Therefore, identification of (over-) dominant loci will provide us with a start point or hint to discover the key limiting factors along the genome, or gene regulatory network that impacts such important traits as yield, and thus guide the improvement of hybrids.1 hybrids compared to 9311. Regarding different subspecific combinations, negative overdominant QTLs were identified more frequently in indica combinations for traits related to SPP and PNP but in japonica ones for KGW; however, negative dominant and positive nonadditive QTLs tended to be detected in japonica combinations for all traits. Regarding different environments, the colocalized nonadditive QTLs tended to be detected in Sanya compared to Changsha , compared to that showing additive expression, suggested the greater impact of the insufficient genetic background exerted by the TF to the expression of its target gene. Indeed, besides TF vs its target as demonstrated in yeast experiment, the principle of HoIIB can also be extended to the actions between other biological molecules, such as kinase vs its target, small RNA vs its target, signaling molecule vs its target, and so on.dl null mutations possess larger Kcat, female flies heterozygous for dl null allele will express as dominant [.Of course, according to our HoIIB model, the additive effect also can transit to dominance or overdominance, when the background changes from sufficiency to insufficiency. In fact, sufficiency and insufficiency are relative and dynamic. The transition from insufficiency to sufficiency for one factor may cause new insufficiency for its counterpart factor. This may explain the challenge to the dominance and epistasis hypotheses, that is, why does heterosis not decrease along with the pyramiding of superior alleles [The HoIIB can not only give a unique explanation to dominance and overdominance, but also can interpret most known mechanisms, models, and phenomena about heterosis. The nonlinearity of the enzyme catalytic system was frequently described to explain heterosis . But as dominant ..Of cour alleles .The balance between genes involved in a biological complex system is another important hypothesis about heterosis. This hypothesis suggests that an imbalance in the concentration of the subcomponents of a protein–protein complex / pathway / network can be deleterious. The typical example of gene balance indicated that mutation of the subunit in a complex (or the factor in an interacting pair) can result in imbalance and thus is harmful, which might indicate the impact of gene imbalance on dominance . ObviousThere are plenty of other examples that indicate the dependency of heterosis on genetic background and can be explained by the HoIIB. First, in the comparisons of functional categories of enzymes, binding proteins, and transcription regulators, the proportion of haplosufficient genes  is the highest among genes that encode proteins with enzymatic functions , which iHd3a basically meets the above mentioned three criteria. Firstly, the expression level of Hd3a shows significantly negative correlation with SPP, and its expression level highly depends on its background regulator Ehd1  and Sanya (short day) and 1439 hybrids in Hangzhou (long day) and Sanya (short day) [Hd3a appears nonadditive phenomenon under long-day environment, where its background factor Ehd1 is seriously insufficient  the regulation relationship between the target gene and its upstream gene had been clarified in literature; (2) the upstream gene is strongly affected by environment condition, and we thus do not have to take a long time to manipulate the background gene like the experiment conducted in yeast; (3) the genetic effect of the alleles had been verified and the gene expression level and phenotypic performance is linear correlated. We checked the heading date genes identified in SPP-related QTLs and found that  the reguon level , 60. So,ort day) . The resThe HoIIB model may affect future utilization of heterosis in several aspects. First, our HoIIB model indicated that in most cases heterosis is not the consequence of heterozygote advantage, but the homozygote disadvantage under insufficient background. This implies that current utilization of heterosis is not the best way to take advantage of maximum function of target genes . TherefoSecond, although the above discussion may illude us to think that hybrid breeding is not necessary, our point is that utilization of heterosis will still be an important breeding strategy for a long time and even forever. Firstly, from the perspective of favorable alleles accumulation, even though all insufficient factors can be improved to their maximum functions, followed by integration into an inbred line in theory, it is impossible to be realized in a short time  and special combining ability (SCA), and provides guidance in breeding by genome selection. It was well known that additive effects contribute mainly to GCA, and nonadditive effects, including dominance and epistasis, to SCA . Our HoITo address the century-old mystery of heterosis, we assembled a large-scale of hybrid phenome, genome, and transcriptomic data to explore the mechanism. From these assembled data, we observed an important but common phenomenon that nonadditive factors are more background or environment dependent than that of additive ones. Further dynamic simulation combined with experimental results demonstrated a core molecular mechanism underlying heterosis, i.e., homo-insufficiency under insufficient background (HoIIB). The HoIIB elucidates that: heterosis in most cases is not the heterozygote advantage but the homozygote disadvantage under the insufficient genetic background; the limiting factor(s) generally exist along with the nonadditive factor(s), and the repeatedly identified additive ones must be the systematic limiting factors, which should be focused in future genetic improvement. HoIIB model can explain most known hypotheses and phenomena about heterosis, thus providing a novel informative guidance and perspective for the future hybrid breeding.1 population. The F1 population was constructed by the crossing between two testers (temperate japonica variety Nipponbare and indica variety 9311) as female parent and the varieties in MCC as male parent. It took us five seasons to generate 455 combinations and to exclude the false crossing, we documented the false hybrids by comparing the phenotypic differences between hybrids and the corresponding female parent and further surveying the phenotypic segregation in the F2 population of each combination. Finally, we used 418 combinations with at least 100 F1 seeds for each combination in this study  of cultivated rice  as the pThe parental varieties were resequenced as part of the 3000 rice genome project . Genomicjaponica Nipponbare reference genome (IRGSP-1.0) using the BWA software with default parameters except for “aln –m 10000 –o l –e 10 –t 4”. The alignment results were then merged and indexed as BAM files [The 83-bp paired-end reads of 267 rice varieties were mapped to the temperate AM files . SNP calAM files . To miniindica and japonica subspecies were generated respectively.SNP and InDel calling for each sample were conducted independently using the UnifiedGenotyper package in GATK with a minimum phred-scaled confidence threshold of 50, and a minimum phred-scaled confidence threshold for emitting variants at 10. The SNP and InDel calling at the population level was performed using the UnifiedGenotyper package in the GATK pipeline with 50 for the minimum phred-scaled confidence threshold for variant calling and 30 for the minimum phred-scaled confidence threshold for variant emitting. Genotypes of the 267 rice varieties were called at the SNP sites. For the genotype datasets of all the accessions, SNPs with more than 50 % missing data and SNPs with MAF < 2% were excluded and 4,625,141 high-quality SNPs were generated. For the genotype datasets in each subspecies, SNPs with MAF < 2% were excluded and finally 3,562,187 and 1,649,161 high-quality SNPs for 1 genotypes for each combination were inferred by the genotypes of their parents.The Fjaponica and indica subspecies   and Sanya (SY)  of China. One combined plot including the F1 and the corresponding parents for each combination was planted with randomized complete block of two replicates in each environment. Each combined plot included five rows consisting of two testers (Nipponbare and 9311), F1 and MCC parent in sequence. The row and plant distances were 29.5 and 16.7 cm respectively, with 10 plants in each row, being wider than the general field production so as to decreasing the interface among plants as much as possible.We planted the 418 FThe yield-related traits were measured in two environments for each combination as follows. Five healthy plants in the middle of each row were used to measure six yield traits. The panicle number per plant (PNP) and grain weight per plant (GWP) was the average of all five plants. And we selected the main panicles of five plants to count the spikelet number per panicle (SPP), the secondary branch number per panicle (SBP), and primary branch number per panicle (PBP). The 1000-grain weight (KGW) was rescaled by the grain weight of 300 grains selected from five main panicles.F1 − (P1 + P2)/2, i.e., the deviation of F1 from middle-parent performance, where F1, P1, and P2 represent the phenotypic values of each trait in F1, P1, and P2 respectively. Degree of middle-parent heterosis (dHmp) for each trait was measured as: (F1 − (P1 + P2)/2)/(P1 + P2)/2). In addition, we denoted the positive overdominant heterosis (POD) when the F1 shows the phenotypic value over the higher parent, range between the two parents (RBP) when the F1 shows the phenotypic value between two parents and negative overdominant heterosis (NOD) when the F1 shows the phenotypic value below the lower parent  for each trait of each combination was measured as: japonica and indica subspecies and four types of hybrid combination  were used. The following linear model was fitted to the transformed data:For each variety, there are two environments and each environment has two replicate of phenotype data. Two parent population including Yij is the ijth phenotypic observation for the ith rice variety under jth environment, k represents two replications, μ is the overall mean, Gi and Ej is the genotypic and environmental effect. Gi × Ej the genotypic and environmental interaction effect, εijk is the random residual effects.Here japonica and indica respectively, the F1 trait value of four kinds of combinations  respectively, and the middle-parent heterosis value (Hmp) of four kinds of combinations  respectively. For the CMLM analysis, we used the equation [GWAS was conducted in GAPIT using the compressed mixed linear model (CMLM) . The pheequation , 68:\docy represents phenotype, X represents genotype matrix, P is the matrix of principal components, and K is the kinship matrix. α and β represent fixed effects of genotype and population structure, and μ and e represent random effects of kinship and residuals. The first five principal components were used to estimate the population structure. The matrix of genetic similarity based on simple SNP matching coefficients was used to model the variance-covariance matrix of the random effect.Here, P thresholds [p value from permutation (p_per) for each SNP and we set the highest −log(p_per) as the FDR of that SNP. The SNP was denoted as significant association when the −log(p_GWAS) is larger than the highest −log(p_per), where p_GWAS is the association p value for each SNP for original phenotypic data.To avoid the over correction of the Bonferroni method, 1000 permutation tests were used to estimate the significant resholds . For eac1 will show the genotypes A and H (the heterozygous genotype). For the investigated trait, we set PA as the mean phenotype of parents with genotype A, PB as that of parents with genotype B, FA as that of F1 with genotype A, and FH as that of F1 with genotype H. The additive effect of each SNP was half of the absolute difference between the two homozygotes, i.e., a = |PA – (PA + PB)/2|. The traditional estimation for dominance effect was expressed as d = FH − (FA + FB)/2, here we rescaled the dominance effects identified as d = FH − (FA − PA) − (PA + PB)/2, in which FA − PA means the background heterozygous effects.Firstly, we estimated the additive and dominance effects for each significant SNP locus. We defined the tester’s genotype (Nipponbare or 9311) of each SNP as A, and the non-tester’s genotype as B. When some varieties in the MCC parental panel show as A and the others show as B, their Fr2 ≥ 0.8). For each block, a tagSNP was selected from the largest group of strongly linked significant SNPs in that block [Secondly, in order to delimit QTLs, we firstly calculate LD blocks for all significant SNPs  using GAB algorithm in Haploview 5.0  is no less than 1.5, and  dominance preferred if 0.5≤|d/a|<1.5, and additive preferred if |d/a|<0.5. The dominant and overdominant QTLs can further be classified as positive ones when their d > 0 or negative ones when their d < 0.Finally, considering that the degree of dominance in real data is usually continuous, it is difficult to make a rigid distinction between additive, dominant, and overdominant, we used a gradient division method to obtain an approximate description of additive, dominant, and overdominant genetic components. Specifically, we defined a QTL is referred to as overdominance preferred if the absolute ratio of dominant effect to additive effect  in each genotype, then taken the average of the phenotypic variation coefficient of these different genotypes  as the phenotypic variation coefficient of the QTL. For each genetic type , the average phenotypic variation coefficient of all QTLs in this genetic type is calculated as the phenotypic variation coefficient of QTL of this genetic type. According to the above calculations, the phenotypic variation coefficient of additive, dominant, and overdominant were obtained for each trait, and the cumulative value of all the investigated traits was used as the final result. The statistical significance between the ratio that the cumulative phenotypic coefficient of variation in dominant and overdominant QTLs was larger than that of in additive QTLs and the expected ratio (16:16) was obtained by chi-square test.p =0.01. In detail, if LYP9 is significantly higher than the higher parent, the gene was classified as positive overdominance (POD); if LYP9 is significantly lower than the lower parent, the gene was classified as negative overdominance (NOD); if LYP9 is significantly higher than the middle-parent, but shows no significance from the higher parent, the gene was classified as positive dominance (PD); if LYP9 is significantly lower than the middle-parent, but shows no significance from the lower parent, the gene was classified as negative dominance (ND); if LYP9 is significantly higher than the middle-parent and significantly lower than the higher parent, the gene was classified as positive partial dominance (PPD); if LYP9 is significantly lower than the middle-parent and significantly higher than the lower parent, the gene was classified as negative partial dominance (NPD); if LYP9 is not significantly different from the middle-parent, significantly lower than the higher parent and significantly higher than the lower parent, the gene was classified as middle-parent (MP) or additive expression (A).The transcriptome was from the 1, 2, 3, and 4 mm young panicles respectively in combination of hybrid LYP9 and its parents (9311 and PA64S) in Changsha. The raw RNA-seq data of 9311, PA64S, and LYP9 were download from Genome Sequence Archive of Beijing Institute of Genomics, Chinese Academy of Sciences (gsa.big.ac.cn) under accession no PRJCA000131 . All theThe raw RNA-seq data of Col×C24 Col-0×Per-1, Col-0×Aa-0, Col-0×Ak-1, Col ×C24, and their parents were downloaded according to the information provided by the original literature , 14. Subhttp://plantregmap.gao-lab.org/), and the determination coefficient between genes with additive, dominant, and overdominant expression patterns and their upstream transcriptions factors were calculated separately.Rice or Arabidopsis genes were divided into additive, dominant, and overdominant expression modes according to the methods described in the above introduction. The upstream transcription factors of each gene were retrieved from the annotated database  and Pfa6a-His3Mx6 (His) were performed using primers (HRR-SSU1-F and HRR-SSU1-R) to obtain recombinant components. The recombinant component was verified by sequencing and then transformed into strain BY4743. After verification of positive clones by electrophoresis and sequencing, the heterozygous mutant strains (SSU1/ssu1) contain single-strand DNA substitution (Leu or His) and diploid mutant strains (ssu1/ssu1) that contain both Leu and His substitution were successfully constructed , two types of heterozyzous mutant strain , and diploid mutant strain (referred as ssu1/ssu1). The methods related to yeast cultures, transformations, and growth assay mainly referred to Gietz et al. [RNA was extracted from BY4743 strain, and the coding sequence of Saccharomyces cerevisiae 18S RNA was used as reference genes to normalize the data.Total RNA isolated from fresh yeast cultures and reversed transcribed using a protocol as previously described. RT-qPCR analysis was performed using gene-specific primers listed in Additional file SSU1/SSU1), heterozygous mutant (referred as SSU1/ssu1), and diploid mutant (referred as ssu1/ssu1) which transferred the empty vector PAG416GAL as control. FZF1 overexpression (FZF1-OE) strains were divided into 0–10, 10–20, and >20 groups according to the upregulation ratio between FZF1 expression levels in FZF1-OE and empty event, referred as OE (0–10), OE (10–20), and OE (>20) , OE (5–10), and OE (>10) /2Dominance effect = d/a = Dominance effect /Additive effectDegree of dominance We used four kinds of strains including WT , and the measurements were taken every 2 h for 2 days after 20s pre-shaking. Growth parameters were calculated from each treatment by directly fitting OD measurements versus time to the reparametrized Gompertz equation proposed by Zwietering et al. [Yeast cultures were incubated at 30°C. Liquid SD-Ura medium was used to keep the pAG416GAL plasmid during overnight growth. Three culture conditions were set in liquid medium, including normal SD-Ura medium, 2mM Kg et al. :\documeny = ln(ODt/OD0), OD0 is the initial OD, and ODt is the OD at time t; A = ln(ODt/OD0) is the asymptotic maximum, μmax is the maximum specific growth rate (h−1), and λ is the lag phase period (h). Phenotypic data were fitted to the reparametrized Gompertz model by non-linear least-squares fitting using the Gauss-Newton algorithm as implemented in the nls function in the R statistical software, v.4.0.where The formula of additive, dominance, and degree of dominance for maximum growth rate of yeast are the same as described in expression analysis.http://www-deletion.stanford.edu/YDPM/YDPM_index.html) for nonlethal gene deletion strains grown in YPD, YPG, YPDGE, YPE, and YPL media. Here, we consider only nonlethal mutations for which homozygous and heterozygous growth rate data are available on the media. For each media, we used the average performance of the top 10% as normal wildtype (WT), homozygous deletion of the strain as homozygous type (Hom), and the deleted gene in heterozygous strain recorded as Het. The additive effect, dominance effect and the degree of dominance was calculated as:Additive effect = |WT − Hom|/2Dominance effect = Het − (WT+Hom)/2d/a = Dominance effect/additive effectDegree of dominance Steinmetz et al. measured growth rates of strains with precise deletions of each gene in the yeast genome using a parallel molecular bar-coding strategy . We usedd/a| >0.5 as nonadditive performance, only the genes identified as |d/a| >0.5 in 4 or more than 4 kinds of media were used to further GO enrichment analysis.Here we defined the genes with |GO analysis was performed using methods available at the agriGO website .http://rle.cbi.pku.edu.cn/) [The protein sequences of genes encoding rate-limiting enzyme (RLE) in human, mouse, and yeast were obtained from the database of RLEdb (edu.cn/) . The canT-test  QTLs and additive QTLs were compared with a two-tailed paired Additional file 1. Figures S1-S54.Additional file 2. Table S1-S13.Additional file 3. Supplementary methods [ methods –87.Additional file 4. Review history.


Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with complex human traits, but only a fraction of variants identified in discovery studies achieve significance in replication studies. Replication in genome-wide association studies has been well-studied in the context of Winner’s Curse, which is the inflation of effect size estimates for significant variants due to statistical chance. However, Winner’s Curse is often not sufficient to explain lack of replication. Another reason why studies fail to replicate is that there are fundamental differences between the discovery and replication studies. A confounding factor can create the appearance of a significant finding while actually being an artifact that will not replicate in future studies. We propose a statistical framework that utilizes genome-wide association studies and replication studies to jointly model Winner’s Curse and study-specific heterogeneity due to confounding factors. We apply this framework to 100 genome-wide association studies from the Human Genome-Wide Association Studies Catalog and observe that there is a large range in the level of estimated confounding. We demonstrate how this framework can be used to distinguish when studies fail to replicate due to statistical noise and when they fail due to confounding. Replication is a gold standard in scientific discovery. Consensus emerges when a result has been replicated repeatedly by multiple researchers. Recently, a vigorous discussion has emerged of how often replication of an initial study fails across all fields of science, including genomics (Genome-wide association studies (GWAS) are an ideal model to study replication because there are a large number of GWAS data sets with replication studies publicly available. GWAS replication studies are typically conducted in an independent cohort using only the variants that were significant in the initial (“discovery”) study. In the National Human Genome Research Institute Catalog of Published GWAS, thousands of genetic variants have been associated with complex human traits but not all associated variants achieve significance in replication studies , which is the inflation of effect size estimates for significant variants in a study due to statistical chance. This phenomenon occurs because the reported findings are a small fraction of many possible findings. In the case of GWAS, the significant associations are discovered after examining millions of variants and pass a stringent genome-wide significance threshold. This can result in inflated effect size estimates of significant variants in a study, especially when studies have low power  will represent only the effect of the confounders. Genomic control scales all of the association statistics using GCλ. Recently, it has been observed that due to polygenicity and linkage disequilibrium (LD) structure in the genome, the majority of variants (including the one corresponding to the median statistic) either affect the trait or are correlated with variants that affect the trait. This breaks the genomic control assumption. While LD-score regression has been shown to distinguish polygenicity and confounding  is determined by estimating the maximum likelihood parameters of jy is the normalized phenotype for individual j, kjx is the standardized genotype of variant k in individual j, kβ is the effect size of the variant k, je is the error, and N is the number of individuals.In GWAS, an association study is performed between each genetic variant and the phenotype using a linear model. The effect size of each variant  are k^=XkTyN . The reskS will follow the standard normal distribution, which can be used to compute the significance of association. In the standard GWAS framework, we assume that the standardized effect size is caused by a true genetic effect Under the null hypothesis, N1 be the sample size of the discovery study and N2 be the sample size of the replication study. Given Let λ is the same across multiple studies on the same trait. We define the prior distribution of λ as λ and integrate over all possible values to λ to obtain the posterior distributions of We assume that We correct for WC by computing the conditional distribution of the replication statistic  and a confounding component Suppose in addition to study-specific environmental effects, there are also study-specific confounders. We model these confounders in the discovery study and replication study as Similar to the case without confounding, the posterior distributions of tributed  and 12.Therefore, the joint distribution is Similar to the WC only model, we can find the expected statistic in a replication study correcting for WC by computing the conditional distribution of the replication statistic ( (sk(1)) .(14)(skhttps://docs.scipy.org/doc/scipy/reference/optimize.minimize-neldermead.html).The variance in the true genetic effect , and let z be the corresponding z-score from a unit normal distribution. We use the joint distribution of the z-scores to compute the probability of a variant not being significant in the discovery study . Since the negative log likelihood function is convex, run time for parameter estimation is negligible.An implementation of our framework is publicly available |sk(1))  and 8.z be the z-score threshold corresponding to t. For a genetic variant k with association statistic r) as the average probability of replication for variants significant in the discovery study (Let ry study .(16)r=1We used the marginal distribution of the discovery summary statistics  to compugp asWe computed the variance explained by genetics We computed the variance explained by confounding in the discovery study For all simulations, we fixed the sample size of the discovery study  using complete data and (2) using incomplete data. When using complete data, we used the z-scores for all 1 million variants simulated to estimate the variance components. When using incomplete data, we used z-scores for only the variants that were significant in the discovery study.k asIn order to compare our WC model to previous methods, we generated a second set of simulations. These simulations were identical to the previous set of simulations, except that we fixed the variance in the study-specific confounders to be zero. Thus, we simulated the z-scores for each SNP Methods section.The main goal of this framework is to account for WC and study-specific confounding in discovery and replication GWAS of the same phenotype. We compare this model to a naive model that only accounts for WC. We introduce these 2 models without accounting for difference in sample size for clarity, but we relax this constraint in the In GWAS, WC is the phenomenon where the association statistics for variants meeting a genome-wide threshold tend to be overestimated. WC can be observed in k from the discovery and replication studies as normally distributed random variables  and study-specific confounding effects (skMethods). The naive model that only accounts for WC estimated that 56% of variants would replicate, whereas our model that also accounts for confounding estimated that 18% of variants would replicate, which is closer to the observed replication. This difference in the estimated replication under each model is due to the study-specific confounding effects estimated in the second model, which both decreases the expected value of the statistics in the replication study and increases the variance of the statistics in the replication study. After correcting for WC and confounding, most variants are within the 95% confidence intervals for the model. Thus, in this study, modeling study-specific confounders is necessary to explain the observed patterns of replication.We correct for both WC and confounding by computing the conditional distribution of the replication statistic given the discovery statistic . By takiWe apply this framework to simulated data and 100 human GWAS in the GWAS catalog. For all data sets, we compute the expected replication rate under the 2 models in order to compare how well each model fits the data, relative to each other.To demonstrate that our approach accurately models the effects of WC and confounding to explain replication rates, we generated simulated data, where the variance in the genetic (Methods). For each combination of parameter values, we repeated this 1,000 times to generate a total of 64,000 simulations. We then used a Bonferonni corrected significance threshold of 5e−8 to identify variants that were significant in the discovery study. The number of significant variants in the discovery study for each simulation ranges from 263 to 11,362 variants . However, it is substantially closer to the observed replication rate than our WC only model, which estimated that 973 variants would replicate.We compared our estimated replication rates under the WC model with those previously reported in The primary difference between our estimated replication under the naive WC model and the estimated replication using ZhongPrentice is that our framework model’s WC by accounting for uncertainty in the true effect sizes of the variants. ZhongPrentice treats the true effect size as fixed and attempts to estimate the true effect size by removing the bias due to WC, which is modeled as a function of the true effect and the significance threshold for the discovery study. In this framework, variants with true effect sizes close to the significance threshold of the discovery study have high bias due to WC, regardless of whether the estimated effect size was inflated or not.gσ to be one of 4 values, and we fixed In practice, the true effect size is not known, so it is difficult to compare these WC corrections in real data. To compare these 2 models of WC, we simulated GWAS z-scores for discovery and replication cohorts, where the true effect size was known and the study-specific confounding was set to zero. For each simulation, we fixed variants . We compgσ increases, the difference between the observed and expected replication rates decreases on average for both models  and low confounding (4%). This study validated their findings using a linear model with a linear mixed model. This analysis provided support that the inflated statistics were due to the polygenic nature of the trait, rather than residual ancestry differences . However, it has also been observed that studies can have confounding and poor replication despite high genetic correlation (One application of this framework would be to identify which studies to include in a meta-analysis or mega-analysis. In GWAS, meta-analysis has discovered many associations that were not identified by each individual study (Our method uses summary statistics to quickly determine why studies fail to replicate and quantify confounding between studies. As more association studies are performed, the outstanding challenge is to integrate these data sets. We expect that this method will be useful for better understanding why studies fail to replicate and for determining whether to combine data from data from independent cohorts.jkac261_Supplementary_Figure_S1Click here for additional data file.jkac261_Supplementary_Figure_S2Click here for additional data file.jkac261_Supplementary_Figure_S3Click here for additional data file.jkac261_Supplementary_Figure_S4Click here for additional data file.jkac261_Supplementary_Figure_S5Click here for additional data file.jkac261_Supplementary_Figure_S6Click here for additional data file.jkac261_Supplementary_Figure_S7Click here for additional data file.jkac261_Supplementary_Figure_S8Click here for additional data file.jkac261_Supplementary_Figure_S9Click here for additional data file.jkac261_Supplementary_Figure_S10Click here for additional data file.jkac261_Supplementary_Figure_S11Click here for additional data file.jkac261_Supplemental_MaterialClick here for additional data file.jkac261_Supplementary_Table_S1Click here for additional data file.jkac261_Supplementary_Table_S2Click here for additional data file.jkac261_Supplementary_Table_S3Click here for additional data file.


The methodology developed herein used correlations of 500-SNP effects in a 100-SNPs sliding window in each chromosome to identify local genomic regions that either drive or antagonize the genetic correlations between traits. We used Fisher’s Z-statistics through a permutation method to confirm which regions of the genome harboured significant correlations. About 30% of the total genomic regions were identified as driving and antagonizing genetic correlations between male and female fertility traits in the two populations. These regions confirmed the polygenic nature of the traits being studied and pointed to genes of interest. For BB, the most important chromosome in terms of local regions is often located on bovine chromosome (BTA) 14. However, the important regions are spread across few different BTA’s in TC. Quantitative trait loci (QTLs) and functional enrichment analysis revealed many significant windows co-localized with known QTLs related to milk production and fertility traits, especially puberty. In general, the enriched reproductive QTLs driving the genetic correlations between male and female fertility are the same for both cattle populations, while the antagonizing regions were population specific. Moreover, most of the antagonizing regions were mapped to chromosome X. These results suggest regions of chromosome X for further investigation into the trade-offs between male and female fertility. We compared the CS with two other recently proposed methods that map local genomic correlations. Some genomic regions were significant across methods. Yet, many significant regions identified with the CS were overlooked by other methods.Although the genetic correlations between complex traits have been estimated for more than a century, only recently we have started to map and understand the precise localization of the genomic region(s) that underpin these correlations. Reproductive traits are often genetically correlated. Yet, we don’t fully understand the complexities, synergism, or trade-offs between male and female fertility. In this study, we used reproductive traits in two cattle populations  to develop a novel framework termed correlation scan (CS). This framework was used to identify local regions associated with the genetic correlations between male and female fertility traits. Animals were genotyped with bovine high-density single nucleotide polymorphisms (SNPs) chip assay. The data used consisted of ~1000 individual records measured through frequent ovarian scanning for age at first The online version contains supplementary material available at 10.1186/s12864-022-08898-7. In animal genetics, insight into the nature of the genetic relationships between quantitative traits are important because they improve our understanding of complex traits and diseases , 2. ThesOver the past 100 years, different methods have been employed to estimate the genetic correlation between traits –17. TradFurthermore, local genomic correlation can either drive a global correlation estimate or antagonize it. In theory, various genomic regions will contribute to the global correlation between complex traits. Further, some regions will be driving  the global genetic correlation while others might antagonize it (antagonizing regions). For instance, if the global genetic correlation between two traits is 0.70, some local regions will yield a significant and positive correlation, say 0.90, while other regions may antagonize the overall estimate, and in that region the correlation could be − 0.50. Also, some local genomic regions may be neutral, say 0.02 and not significant for the correlation between the studied traits. Identifying driver and antagonizing regions are of particular interest if they are for two important traits which are unfavourably correlated, for example milk yield and fertility in dairy cattle. Identification of such regions could lead to more targeted genomic selection and rapid genetic gains for both traits. Current genomic tools have created a great opportunity to advance our knowledge of genetic correlations between complex traits, by investigating the regions in the genome that drive or antagonize these correlations.corpus luteum  and serum levels of insulin growth hormone . These phenotypes are from animals raised in a research station with precise measurement taken by regular ovarian scan  and lab AGECL, , 28). Th. Thcorpu  estimates for each pairwise trait in two beef cattle populations were identified. The total number of windows generated for all trait pairs in BB was 5413 and the number in TC was 6731. The r estimates for all windows were plotted against their genomic position  . Compared to the genotype data (~ 600 K SNPs for each breed), about 164 k and 194 K SNPs remained after LD pruning for BB and TC breed, respectively. In summary, we observed no substantial differences between the pattern of the r estimates, we applied Fisher’s Z-statistics following a permutation test of 10,000 iterations (see Methods). Significant level was set at Bonferroni-corrected P-value < 0.05. Windows with r estimates that passed this threshold were considered significant and those that failed were termed “neutral” windows. Table To identify windows with significant r estimates for each local region (window) and their corresponding P-values for SUPERGNOVA and LAVA. Of note, the r estimated in SUPERGNOVA depends on local heritability estimates, and in many cases, these estimates are unstable and often negative. SUPERGNOVA ignores negative heritability estimates, leaving the correlation estimates as ‘NA’. Furthermore, some of the estimates are also out of bound, i.e., estimates with r > 1 or r < − 1. LAVA, on the other hand, tends to avoid unstable local correlation estimates by filtering out non-associated loci with low local heritability. Despite this, some estimates are often out of bounds and are either capped at +/− 1  or excluded from the analyses . In addition, the r estimate in LAVA depends on variance of the phenotypes. If the variance of local region is negative, the window will be excluded from the analysis.To demonstrate the performance of CS, we compared the results from CS with SUPERNOVA and LAVA across all the trait pairs investigated. Additional file r range  for all traits pairwise (Table r > 1).For SUPERGNOVA, about 5%, on average, of the total number of windows analysed were within the se Table . Approxir estimate either capped at +/− 1 or out of bound.For LAVA, out of the total number of windows , about 30 and 60% of the total windows were analysed for all trait pairs in BB and TC, respectively  from CS with SUPERGNOVA and LAVA in the two population for all trait pairs studied . In addition, the lists of windows with their chromosome position and genomic coordinates for all driver, and antagonizing regions are presented in Additional file r estimate for the driver windows was − 0.96 (bovine chromosome (BTA)14: 23.04 - 25.29 Mb) in BB and − 0.91 (BTAX: 39.76 - 42.86 Mb) in TC. For the antagonizing windows, the largest r estimate was 0.87 (BTAX: 40.87 - 43.88 Mb) in BB and 0.62 (BTAX: 66.62 - 69.622 Mb) in TC.For the correlation between AGECL and IGF1b  and − 0.55 (TC), see Additional file r estimate for the driver windows was 0.97 (BTA14: 22.68 - 24.96 Mb) in BB and 0.87 (BTA5: 46.13- 47.89 Mb) in TC, while the estimate for the antagonizing was − 0.62 (BTA1: 49.01 - 51.67 Mb) in BB and − 0.90 (BTAX: 65.64 - 68.39 Mb) in TC. All r estimates are plotted in Fig. For the correlation between IGF1c and IGF1b  and 0.93 (TC), see Table Defining driver and antagonizing regions separately for each pair of traits, allowed us to identify the genes and QTLs within these regions for each of the two beef cattle populations. The percentage of the overlapping genes Fig.  and QTLsThe percentage of overlapping genes for each pair of traits in the two populations were as follows: for AGECL vs IGF1b driver regions, 32% of genes annotated in BB were present in TC and 27% of genes annotated in TC were found in BB, whereas, for the antagonizing regions 18% of genes annotated in BB were present in TC and 13% of genes annotated in TC were found in BB. For IGF1c vs IGF1b, the two populations shared 48% of total number of genes annotated for the driver regions and about 10% were shared for the antagonizing regions.The percentage of overlapping QTLs for each pair of traits in BB and TC population were as follows: for AGECL vs IGF1b driver regions, 38% of the QTLs annotated in BB were present in TC and 20% of the QTLs annotated in TC were present in BB, whereas, for the antagonizing regions, 14% of the QTLs annotated in BB were present in TC and 18% of the QTLs annotated in TC were present in BB. For IGF1c vs IGF1b, 51% of the genes annotated in BB were present in TC, and 47% of the genes annotated in TC were present in BB, whereas, for the antagonizing regions, 14% of the genes annotated in BB were present in TC and 11% of the genes annotated in TC were present in BB population.To infer biological function and mine the existing literature, we examined the classes of QTL  present in the significant genomic regions identified above using GALLO . The larP-value< 0.05) for the driver and antagonizing regions for all pairwise traits in each population are presented in Additional file We performed a chromosome-wide QTL enrichment analysis to further test the significance of the QTLs identified for all the driver and antagonizing regions in each cattle population, for each trait pair using GALLO . EnricheFor the driver regions, the number of QTLs enriched over a wide range of chromosomes for AGECL vs IGF1b were 254 and 157 in BB and TC beef cattle population, respectively. The number was 213 (BB) and 198 (TC) for IGF1c vs IGF1b. For AGECL vs IGF1b, the most enriched chromosome (no of enriched QTLs in parenthesis) was BTA14 (33) and BTA14 (19) in BB and TC, respectively. For IGF1c vs IGF1b, the most enriched chromosome was on BTA5 (43) in BB and BTA14 (46) in TC.For the antagonizing regions, the number of QTLs enriched across the bovine chromosomes for AGECL vs IGF1b were 102 and 171 in BB and TC beef cattle population, respectively. The number was 136 (BB) and 154 (TC) for IGF1c vs IGF1b. For AGECL vs IGF1b, the most enriched chromosome in BB were both BTA2 (12) and BTA17 (12) in BB, whereas in TC, the most enriched chromosome was BTA26 (29). For IGF1c vs IGF1b, on the other hand, the most enriched chromosome was BTA6 (26) and BTA26 (29) in BB and TC, respectively.To identify the common results and shared biology between the driver and the antagonizing regions, we also investigated the overlaps of the QTL types associated with the studied trait  in the two populations. The relationship between the top 10 enriched reproductive QTLs in BB and TC are presented in Additional file http://www.ingenuity.com), we identified the canonical metabolic pathways enriched at Benjamini–Hochberg corrected P-values  of p < 0.01. The graphical presentation of the canonical metabolic pathways predicted by IPA to be enriched and the proportion of driver and antagonizing genes in each pathway for all pairwise traits investigated in each population are illustrated in Additional file r estimates are not the same as gene expression values, and IPA was originally designed to mine gene expression data. In summary, several biological pathways known to be involved in reproduction  were significantly enriched for all pairwise traits investigated across the two breeds. Rho GDP Dissociation Inhibitor (RHOGDI) pathway was the only significant signaling pathway found to be inhibited across breeds in all pairwise traits investigated using IPA comparison analysis.Leveraging our methodology’s directionality of gene effects with Ingenuity Pathway Analysis  to gain further insight into the biology of studied traits and their relationships. Although the methodology was applied to beef cattle traits, using high-density SNP chip genotypes, the general framework can be applied to any species, any trait, and it can easily accommodate sequence-level data.Complex phenotypes, like fertility, consist of multiple genetically correlated traits rather than independent traits . The corSignificant regions emerging from CS were compared with those identified by SUPERGNOVA and LAVA. The CS identified more significant regions affecting the correlations between traits than existing methods, such as SUPERGNOVA and LAVA. This is because the CS does not use local heritability estimates, as found in SUPERGNOVA, or estimate negative local variance, as found in LAVA. The absence of these limitations resulted in more significant regions emerging from the CS approach for the same dataset. Despite differences between our method and SUPERGNOVA or LAVA, six significant local genetic correlations were shared between the three methods, all in the BB population. These regions were all located on chromosome 14. Chromosome 14 regions have been extensively documented as affecting many economically important traits cattle, including fertility traits –41. Chror ranged from 0.46 to 0.77), but it differed from LAVA (r ranged from − 0.16 to 0.15). In a typical scenario, correlation statistics stabilize with a sample size of 250 data points  is the start point of each window, K is the window length and ji = j + K-1. The window is then shifted 100 SNP effects away from the start of the previous window and a new r is computed for each shift yielding a new estimate for each chromosome. The resulting r estimates for all the chromosomes combined were denoted as W1….Wn. The graphical illustration of this framework is presented in Fig. Where j ∈ [0, r estimates, while the antagonizings were windows with significant positive r estimates. For the positively correlated relationship between IGF1c and IGF1b, the driver windows were windows with significant and positive r estimates and the antagonizings were windows with significant and negative r estimates.Depending on the global correlation observed between the traits considered, the driver and antagonizing windows can be deduced. In this study, AGECL and IGF1b were negatively correlated. Hence, the driver windows were windows with significant and negative To showcase that the SNP effects from the back-solve approach are not biased by LD, we pruned the genotypes data of each breed based on pairwise LD to obtain a pruned subset of SNPs that are in approximate linkage equilibrium (LE) using PLINK v.19 . The LD r estimate were obtain using Fisher’s Z method [1…p10000) for each trait. Subsequently, we estimated correlations for 100-sliding windows of 500-SNP effects for each iteration in each window between the two traits as described above. We then estimated the mean of the permutation distribution of the r estimates across all the iterations to obtain a single value (rp) for each window. Next, the significance between the real estimate r and rp for each window was determined by Fisher’s Z-statistic: for r and rpp i.e., Zr-rp:Significant window for each Z method . FirstlyP-values for each window, we estimated the cumulative distribution function for Zr-rp while accounting for a two-tail test. The significance level was then set at Bonferroni-corrected P-value < 0.05. As a result, significant windows were selected for the drivers and antagonizings genomic regions for each trait pair. Windows that were not significant were tagged “neutral windows” i.e., windows with no effect on the trait pairs. Finally, the r estimates of the significant windows for the driver and antagonizing regions were ranked from top to bottom in percentage (%). The rank values were used solely for the purpose of subsequent downstream analyses, i.e., pathway analyses. The ranking was done separately for the driver and antagonizing windows for each pairwise trait investigated in each population.Where n is the sample size of the SNP effects for each window, in our case i.e., 500. To retrieve the corresponding To showcase the performance of CS, we compared the results from CS for each trait pair in the two populations with the results SUPERGNOVA and LAVA. Both SUPERGNOVA and LAVA are tools used to estimate local genetic correlation between complex traits in human using GWAS summary statistics.1 and Y2 with sample size n1 and n2, respectively. The standardized trait values of Y1 and Y2 follows the linear model below: Xi and Zi are standardised genotype matrices and βi and γi are the vector of joint genetic effects in region i. ϵ and δ are the error terms.For illustration, consider two traits Yp) between the two traits in region i is then estimated by minimizing the distance between the empirical covariance of Z scores [i are estimated from an external reference panel  [https://www.animalgenome.org/cgi-bin/QTLdb/index [r estimates and the rank values specific for their window.The significant windows along with their corresponding chromosome coordinates, e=GALLO) . The .gtdb/index , 98), wedb/index . The twoThe number and percentage of genes and QTLs annotated within a population (BB or TC) and the overlaps across populations (BB and TC) were investigated. Furthermore, we examined the QTLs representativeness and diversity to explain better the genomic content of the significant windows for the driver and antagonizing regions. Hence, the visualization of the percentage of cattle QTL classes from the cattle QTL database  were plotted using a pie chart by GALLO (27).P-value for the QTL enrichment status of each annotated QTLs within the significant windows was estimated. These estimated P-values were corrected for multiple testing using a false discovery rate (FDR) of 5%. In addition, we used chord plots to reveal the relationships between the two breeds for the enriched reproductive QTLs based on the driver and antagonizing genomic regions.To further test the significance of the QTLs, a within population QTL enrichment analysis was conducted using a chromosome-based approach. The QTL enrichment analysis, using all the QTL information annotated within the significant windows for the driver and antagonizing regions, was performed using the qtl_enrich function from GALLO , 100. Brr estimates and rank values for the significant driver and antagonizing windows for each pairwise trait in BB and TC populations were subjected to enrichment analysis using the commercial QIAGEN’s Ingenuity Pathway Analysis . The IPA allows identifying overrepresented biological mechanism, metabolic pathways, and diseases and biological functions that are highly relevant to the traits of interest using the directionality of the submitted gene list [r estimates. Thus, we leveraged on the directionality of each gene by allowing the driver genes to be upregulated and antagonizing genes to be downregulated.The annotated genes along with their corresponding ene list , 102. Frr estimates and rank values were uploaded into IPA. The r estimates were used as the “Expr Log Ratio” and the rank values (see identification of significant windows in methods) were used as P-values. The IPA software recognizes gene with positive signs (+) for “Expr Log Ratio” as upregulated genes and negative sign (−) as downregulated genes. We aim to allow the driver gene lists to have positive values for “Expr Log Ratio” and the antagonizing gene lists to be negative. Where this is not achievable based on the original r estimates , we reversed the sign for the driver and antagonizing genes to meet this objective.Summarily, a merged dataset containing gene identifiers that were significant for both the driver and antagonizing windows for each pairwise trait in each population and their corresponding Of note, IPA can only analyse a maximum of 8000 gene list. In most cases, the merged gene list for each trait pair in each population is often > 8000. Hence, we used the rank values as the cut-off to select the top ~ 80% genes from the driver and antagonizing gene list for the pathway analyses whenever the gene list is more than 8000. Using a proportion of the gene list to infer biological pathways might result in the loss of some important biological information relevant to the trait of interest. We analysed the driver and antagonizing gene list separately for each pairwise trait in each population to ensure no important information was lost because of the cut-offs. Further, we compare the result of the separate analyses with the merged gene list from the ~80% cut-off.http://www.ensembl.org/biomart/martview/) [P-values  of p < 0.01.The pathway analysis was conducted using the “Core Analysis” function implemented within IPA. In this analysis, associations were calculated using direct and indirect relationships among the gene lists. At first, the gene lists were mapped to human gene data. Genes without an associated gene symbol or gene annotation were subjected to an annotation by homology using BioMart application available in the Ensembl database (rtview/) , 104. Wihttps://github.com/optimist0372/Correlation-Scan). Analysis script and the exact package version (v0.05) used to generate the main results can be downloaded from https://github.com/optimist0372/Correlation-Scan.CS was implemented as a Perl package, which is publicly available at the GitHub repository .Additional file 2. The genome plot of the LD pruned sliding window correlation estimates for the trait pairs in Brahman (BB) and Tropical Composite (TC) .Additional file 3. The correlation estimates from SUPERGNOVA and LAVA portioned using 500 SNPs windows with sliding windows of 100 SNPs for all trait pairs in Brahman and Tropical Composite population. (Table S3-S10).Additional file 4. The number of significant driver and antagonizing windows for each trait pair in Brahman and Tropical Composite population (Table S11).Additional file 5. The number of windows, chromosome number, chromosome coordinates, correlation estimates and rank value for the drivers and antagonizing regions (Bonferroni corrected p < 0.05) in Brahman (BB) and Tropical Composite population for the studied trait (Table S12-19).Additional file 6. The global genomic correlation estimates, heritabilities (standard error in parenthesis), number of animals and number of SNP from previous study in Brahman and Tropical Composite population (Table S20).Additional file 7. The percentage of QTL type and trait related to reproduction QTLs for the QTL annotation results obtained for the drivers and anatgonizing regions of the two trait pairs in Brahman (BB) and Tropical Composite (TC) population .Additional file 8. The enriched QTLs of the driver and antagonizing regions for all trait pairs in Brahman and Tropical Composite cattle. The enriched QTLs are rank based on the adj.pval (Table S21-28).Additional file 9. The chord plot showing the relationship between the top 10 enriched reproductive QTLs between Brahman (BB) and Tropical Composite (TC) for the driver (top) and the antagonizing (bottom) regions of the studied traits .Additional file 10. Canonical pathways significantly enriched  for all trait pairs in Brahman and Tropical Composite population .Additional file 11. The final dataset used for Ingenuity Pathway Analysis (IPA) for all trait pairs in Brahman and Tropical Composite cattle (Table S29-32).


Most transcriptome-wide association studies (TWASs) so far focus on European ancestry and lack diversity. To overcome this limitation, we aggregated genome-wide association study (GWAS) summary statistics, whole-genome sequences and expression quantitative trait locus (eQTL) data from diverse ancestries. We developed a new approach, TESLA , to integrate an eQTL dataset with a multi-ancestry GWAS. By exploiting shared phenotypic effects between ancestries and accommodating potential effect heterogeneities, TESLA improves power over other TWAS methods. When applied to tobacco use phenotypes, TESLA identified 273 new genes, up to 55% more compared with alternative TWAS methods. These hits and subsequent fine mapping using TESLA point to target genes with biological relevance. In silico drug-repurposing analyses highlight several drugs with known efficacy, including dextromethorphan and galantamine, and new drugs such as muscle relaxants that may be repurposed for treating nicotine addiction. A multi-ancestry transcriptome-wide association study using an optimal linear combination of association statistics provides insights into tobacco use biology and suggests opportunities for drug repurposing. Although some of these associations point to genes and pathways of known biological importance, including the nicotinic receptor and dopaminergic signaling pathway genes1, the underlying mechanisms for most of the identified loci are unknown. On top of this, the genetic architecture of tobacco use outside of European populations remains understudied. In the present study, we combined GWAS datasets totaling 1.3 million individuals: 1.2 million from the GWAS and Sequencing Consortium of Alcohol and Nicotine use (GSCAN) and 150,000 diverse ancestries from the Trans-Omics Precision Medicine (TOPMed)2 to further empower gene discovery and elucidate the genetic architecture of smoking behavior.Cigarette smoking is a major heritable risk factor for human diseases. The availability of large datasets has enabled a breakthrough in the genetics of smoking addiction, with >400 loci discovered to date3, TIGAR4, PrediXcan5 and UTMOST6) use eQTLs to predict gene expression levels in silico, which the method then uses to identify genes associated with the phenotype of interest. Various TWAS methods have been widely applied to different complex traits to understand the functional consequences of regulatory variations9.Dissecting the mechanisms of GWAS hits for tobacco use is crucial to understand the etiology of nicotine addiction and related disease outcomes. TWAS approaches . MATCH-TWAS may be difficult or even impossible to implement in practice because eQTL data may not be broadly available for disease-relevant tissues in non-European ancestries. In addition, because most causal variants have been observed to be consistent across ancestries13, MATCH-TWAS can suffer from substantial power loss by using only the GWAS data from the matched ancestry, due simply to smaller sample size. Another possible strategy is to ignore ancestral differences and perform TWAS using GWAS fixed effect (FE) or random effect (RE) meta-analysis results combining different ancestries (FE-TWAS and RE-TWAS). FE-TWAS and RE-TWAS do not fully leverage ancestral differences in phenotypic effect sizes and linkage equilibrium (LD) patterns, which also leads to suboptimal power.TWAS in its original form requires GWAS and eQTL data to be from matched ancestries. Direct integration of eQTLs with GWAS data from nonmatched ancestries  was shown to have suboptimal powerGiven the lack of sizable eQTL datasets from disease-relevant tissues in a matched ancestry, it is important to develop methods to optimally integrate an existing eQTL dataset from a given ancestry (European or any ancestry) in a multi-ancestry meta-analysis. To achieve this goal, we developed a new method, TESLA, which exploits shared phenotypic effects across ancestries and accommodates between-ancestry genetic effects, and consistently improves power over existing methods. We identify many more gene-level associations than alternative methods, such as MATCH-TWAS and FE-TWAS. We also performed fine mapping, enrichment and drug-repurposing analyses for TWAS hits to learn new biology and gain clinical insights related to tobacco use phenotypes.5. Specifically, it first builds gene expression prediction models using eQTL datasets that measure both gene expression levels and genotypes and obtains weights on eQTL SNPs (wj). The eQTL weights are then used to calculate a weighted sum of phenotypic effect estimates (which we denote as bj for the effect of variant j) for gene-level association tests. When adapting TWAS to integrate European eQTL data with non-European GWAS data, power loss was observed empirically10, but the theoretical reason behind the power loss was not well established.For all presentations, we call the genetic effects on GWAS phenotypes ‘phenotypic effects’ and the effect of gene expression the ‘eQTL effect’. TWAS was originally developed to integrate eQTL and GWAS datasets derived from matched ancestrieswj is the eQTL effect of SNP j from the gene expression prediction model and c is the effect of genetically regulated gene expressions on the phenotypes. The phenotypic effect of variant j satisfies In the present study, we propose a proportionality condition under which trans-ancestry TWAS attains its optimal power. Specifically, the proportionality condition states that TWAS has optimal power if the phenotypic effects and eQTL weights from the gene expression prediction model are proportional to each other. This condition is satisfied when the eQTL SNPs influence phenotypes via their regulatory effects, that is, First, TESLA models phenotypic effects across ancestries using meta-regression, which takes phenotypic effect estimates, standard deviations and genome-wide allele frequency principal components  as input. We estimate ancestry using genetic PC analysis on per-study allele frequencies, although other methods may also be used. When no PC is included, the model is equivalent to a fixed-effects meta-analysis; when one or more PCs are included, the meta-regression coefficients quantify the extent of SNP effect heterogeneity as a function of ancestry. For example, in the present study, the first PC separates cohorts of individuals with recent African–American ancestries . We show that TESLA consistently outperforms or performs competitively compared with other methods across all scenarios  and 2. IP values are two sided, unless stated otherwise. Tissue-specific TESLA results were also combined using the Cauchy combination test14 to obtain a P value of a multi-tissue TWAS for each gene. A schematic description of the TESLA analysis flow is shown in Fig. We applied TESLA to summary-level association statistics derived from 61 cohorts in GSCAN and TOPMed studies of 4 smoking traits including smoking initiation , cigarettes per day , smoking cessation  and age of smoking initiation  , which was 6.9%, 504% and 12.5% more than FE-TWAS, RE-TWAS and EURO-TWAS, respectively  away from known GWAS sentinel variants   than GTEx . As the sample size of non-European ancestry GWASs is relatively small , the number of gene × trait associations identified using African–American eQTL data is small, but a significant portion is replicated in the TWAS using European eQTLs  Human Brain Repository, which contains a higher representation of non-European ancestry , neurotransmitter catabolic process (GO:0042135), negative regulation of synaptic transmission, GABAergic (GO:0032229), Lewy body (GO:0097413) and dopaminergic synapse (GO:0098691) , dopaminergic synapse (GO:0098691) for SmkInit (P = 1.2 × 10−9) and behavioral response to nicotine (GO:0035095) for CigDay (P = 2.3 × 10−14). This finding is consistent with increasing evidence showing that cerebellum functions extend beyond motor control and involve rewarding and addictive behaviors22.We used gene ontology (GO) enrichment analysis to find pathways, tissues and cell types relevant to tobacco use (Supplementary Table 91) Fig. . Importa23 , whereas there are more diverse GO items in substantia nigra, an important brain tissue for reward. The top GO terms enriched with TESLA hits include: ‘positive regulation of fatty acid transport’ (weight = 31.3%), ‘epithelial cell morphogenesis’ (weight = 31.1%), ‘negative regulation of feeding behavior’ (weight = 15.5%) and ‘sensory of touch’ (weight = 6.7%) , as well as glutamatergic neuroblasts , as relevant cell types for CigDay in the cerebellum  data from neurons in the mouse central nervous system to prioritize specific cell types related to tobacco use phenotypes27 and examined whether these drug target pathways were enriched with TESLA hits in 13 brain tissues from GTEx. We identified 102 putative drugs pathways under stringent Bonferroni’s threshold for testing 1,642 drugs (7.9 × 10−7) , caudate basal ganglia  and cerebellum . The drug target pathway for ganaxolone33, a drug used for seizure disorders, is enriched with CigDay loci in hippocampus  and substantia nigra .Second, TESLA enrichment pointed to drugs with putative smoking cessation effects, which are being evaluated in clinical trials. For example, the target pathway of dextromethorphan34.Enrichment analysis also identified potential drugs for treating smoking addiction, which are supported by preliminary clinical evidence. For example, galantamine, a Food and Drug Administration-approved medication for the treatment of cognitive deficits associated with Alzheimer’s disease, increases synaptic acetylcholine levels by inhibiting acetylcholinesterase, an enzyme that breaks down acetylcholine. Galantamine also directly stimulates α7- and α4β2-nicotinic acetylcholine receptors (nAChRs) via its positive allosteric modulator actionsIn addition to individual drugs, we also evaluated the potential of drug classes that can be repurposed for smoking cessation. To do so, we grouped all the identified drugs into 15 categories based on their indications see . The topIn the present study, we conducted a multi-ancestry TWAS using GWASs and whole-genome sequence data from 1.3 million individuals. Our TWAS results highlighted shared mechanisms with other substance use behaviors  and psychiatric phenotypes . Leveraging shared disease pathways, we identified drugs that may be repurposed for smoking cessation treatment, including dextromethorphan and galantamine, which are already being assessed in clinical trials. Given the tremendous public health burden that continues to be incurred by smoking, repurposing drugs for smoking cessation is extremely valuable, because it offers a potentially quicker and more cost-effective route to treatment than the development of new therapeutic targets.35.Our work also made important methodological contributions. TESLA showed robust performance over other methods across different genetic architectures, which makes it a desirable choice in practice, because the true phenotypic effects across ancestries are unknown. TESLA improves power because it jointly analyzes samples from multiple ancestries, maximizes sample sizes and accommodates between-ancestry heterogeneities. The magnitude of increased power depends on the genetic architecture of the traits across ancestries. TELSA has the largest advantage when causal variants are shared between ancestries but have heterogeneous effects. Its performance is comparable to other well-performing methods when the effects are unique to European ancestry or homogeneous across ancestry groups. Importantly, the power improvement of TESLA over alternative methods tends to increase as a larger fraction of non-European samples is included. This ensures that TESLA will be even more useful because genetic studies are expanding to non-European populations, as part of the biomedical research community’s vision for precision health using genomics36 39, another possibility is to extend VC-TWAS in the same way as het-meta-SKAT39, which assumes that genetic effects are heterogeneous. These extensions may not be optimal, because they do not properly consider genetic effect heterogeneities across ancestries. It would be an important future research area to develop optimal strategies to integrate VC-TWAS into trans-ancestry genetic studies.TESLA is optimal when the phenotypic effects are mediated by the eQTL effects. When there are residual genetic effects of eQTL SNPs that influence phenotypes , methods such as variance component (VC)-TWASAlthough TESLA optimizes the power for TWASs using existing eQTL datasets, it does not take away the need to generate eQTL datasets from non-European populations. The ancestry of the eQTL dataset strongly influences the interpretation of TESLA results. When a European eQTL dataset is used, TESLA identifies target genes specific to European ancestry. Therefore, if a genetic variant has heterogeneous effects, meta-regression will put the most weight over cohorts of European ancestry and less weight on cohorts from non-European ancestry. Similarly, when an eQTL dataset of African ancestry is used , TESLA identifies target genes in African ancestries and cohorts with individuals of African ancestries would contribute the most to meta-analysis. As additional non-European eQTL datasets are generated, TESLA will become even more useful to understand the impact of noncoding variants in non-European populations.40. TESLA will further improve power over existing methods as more non-European GWASs and eQTL datasets are generated.In summary, our study represents an attempt to extend GWASs and TWASs of tobacco use to non-European ancestries. The gene discoveries deepen our understanding of the etiology of tobacco use phenotypes and implicate translational applications. The methodology is broadly useful for next-generation trans-ancestry genetic studies of complex diseases and address critical challenges for multi-ancestry TWASsIn this section, we describe the smoking phenotype definition, the summary association statistics from the GSCAN and TOPMed consortium, as well as the TESLA method. The enrichment and drug-repurposing analyses are described in 44.Smoking initiation (SmkInit): a binary trait that compares ever smokers with never smokers. Ever smokers were defined as individuals who have smoked >99 cigarettes in their lifetime, which is consistent with the definition by the Center for Disease ControlCigarettes per day (CigDay): a quantitative trait that measures the average number of cigarettes smoked per day by an ever smoker.Smoking cessation (SmkCes): a binary trait that compares former against current smokers.Age of smoking initiation (AgeInit): a continuous outcome that measures the age when one starts regular smoking.We analyzed the following four smoking behavior-related traits because of their broad availability in existing epidemiological and medical studies, as well as their biological relevance to addiction behaviors:1.More detailed definitions for the four phenotypes can be found in 45, a model-based method that relies on the strength of consistency of association signals across studies.Our study used GWAS summary association statistics from 61 participating studies as input  are used, so that the standard deviation sjk is inversely proportional to 46.We use 36) of the cohort allele frequencies as input, which serve as proxies for the cohort ancestry :wj are the weights obtained from a gene expression prediction model. The variance for the statistic w is the vector of eQTL weights trained from gene expression prediction models, that is, J being the total number of variants used in the prediction model. Vz is the covariance matrix between z-score statistics, which can be approximated based on reference panels.TWASs (and similar methods) were proposed to integrate eQTL effects with GWASs, to identify transcripts/genes that are associated with phenotypes. The TWAS statistic is often written in the form of a linear combination of It is well understood that the choice of the weights can affect the power for the statistic In TWAS methods, the eQTL effects are used as weights to combine phenotypic effect estimates of GWASs from the same ancestry. If the phenotypic effects are mediated by the eQTL effects, that is, 47.In contrast to TWASs using European GWASs and eQTL datasets, measured phenotypic effects can differ between ancestries in multi-ancestry genetic studies due to possibly different causal variants, allele frequencies or LD patterns. As a result, the proportionality condition may be violated when the GWAS and eQTL data come from different ancestries. Nor will the proportionality condition hold when FE or RE meta-analysis results from a multi-ancestry study are used with European eQTL dataset for TWASs. Suboptimal power is expected. Alternatively, if a TWAS is performed using European GWAS results and European eQTL dataset, and if the phenotypic effects and eQTL effects are homogeneous in the European population, the proportionality condition is expected to hold. Yet this strategy leaves out non-European GWAS data in the study and can still lead to suboptimal power when causal variants are shared between ancestriesLeveraging ancestral diversity while accounting for between-ancestry heterogeneities can improve the accuracy of the phenotypic effects in the matched ancestry of the eQTL data. For GWAS cohorts from different ancestries than the eQTL dataset, TESLA projects their phenotypic effects in the direction of eQTL weights, which are then meta-analyzed with other studies to get more accurate phenotypic effect estimates. TESLA uses these improved phenotypic effects to perform TWASs for optimal power.F, where each row represents a study and each column represents a variant site. We then perform singular value decomposition for F, that is, lth PCs for study k as k as We model the phenotypic effect estimates of eQTL SNPs of a given gene as a fixed effect of the ancestry captured by the allele frequency PCs. To calculate the PCs of allele frequencies, we code the allele frequency matrix using variant sites shared across all studies as L) and consider a series of models We vary the number of PCs used (that is, L = 0, 1, 2 or 3. When no PCs are included in the model, it is equivalent to the FE meta-analysis, which is suitable for modeling variants that have homogeneous effects across studies. When one or more PCs are included in the model, it can capture phenotypic effect heterogeneity between studies.In our simulations and data analyses, we considered M[L], the phenotypic effect follows a normal distribution:Under model ML][ can be fitted using the weighted least square method36. The solution satisfies:Model L PC coordinates of the eQTL dataset are denoted Based on meta-regression coefficients, we can estimate phenotypic effects in the ancestry of the eQTL dataset so that the eQTL weights and phenotypic effect estimates satisfy the proportionality condition. The first j1 and j2, that is, k. Given that each cohort may come from different ancestries, we use ancestry-specific reference panels to estimate LD and approximate the correlations between We denote the vector of estimated effects as Based on the phenotypic effect estimate We further calculated the standardized statistic as Four different TWAS statistics are calculated that correspond to the models with 0–3 PCs. The model with 0 PC is equivalent to FE-TWAS. When the same eQTL weights are used in each study, FE-TWAS is also equivalent to conducting TWAS in each participating study and then combining results using inverse-variance, weighted meta-analysis .P-value approach to find the overall P value for the statistic. Specifically, we denote the P values for the four statistics as P-value statistic We use a minimal P values from correlated test statistics, from which we chose to use the Cauchy combination14 due to its excellent power and the ease of calculation. In our analysis, we assigned equal weight to each tissue in the Cauchy combination test.In addition to the single-tissue TESLA statistic, we also calculated a cross-tissue TWAS statistic. Numerous methods exist to combine Further information on research design is available in the Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41588-022-01282-x.Supplementary InformationSupplementary Figs. 1–9, Tables 1–9 and legends for Supplementary Tables 10–15.Reporting SummarySupplementary Table 1Supplementary Tables 5 and 10–15.