Attributing the similarity between individuals to genetic and non-genetic factors is central to genetic analyses. In this paper we use the genomic relationship ( Assigning inter-individual similarities to genetic and non-genetic factors is central to quantitative genetics. Here, the authors look at phenotypic covariance among pairs of individuals for 32 traits across the UK Biobank, from nominally unrelated pairs through to monozygotic twins. It is a key population-dependent parameter in quantitative genetics and determines our ability to predict disease risk in medicine or the response to selection in agriculture. In practice 2. Comparing heritability estimates across different experimental designs can cause confusion because the estimators can have different expectations, even when genetic effects are the only source of trait similarity between individuals. In Fig. The narrow-sense heritability  mating4. Simple models can also be biased by non-additive genetic or common environmental effects, or other confounders which increase the phenotypic covariance among relatives beyond that expected.Most simply, heritability can be estimated by comparing the observed resemblance between relatives to their expectations for a given genetic relationship5, but a disadvantage is that 6. Yang et al.6 used a mixed linear model and restricted maximum likelihood (REML) to estimate 7 and this implies that the slope from the regression of phenotypic correlation on genomic relationship  changes as a function of genomic relatedness within a population, across all pairs of individuals from nominally unrelated pairs through to monozygotic twins. In addition, we compare our heritability estimates with two other experimental designs, namely full-sib identity-by-descent (IBD) regression11 and classic twin pair estimates.In the absence of pedigree information, single nucleotide polymorphisms (SNPs) can be used to estimate genomic relationships between individuals  has the advantage of avoiding confounding between genetic and environmental covariance in relatives by estimating within-family genetic variation . The analysis exploits the fact that although full-sibs share on average 50% of their genome IBD, there is random segregation variation around this average, so that some pairs only share 40% of their genome IBD whereas other pairs share 60% of their genome IBD. A constraint of this type of analysis is that many tens of thousands of full-sib pairs are required for precise estimates due to the relatively small variance in IBD estimates. The second alternative design, a classic twin study, was once the mainstay of genetic analysis in humans and has been widely applied to many traits14. Classic twin analyses contrast phenotypic correlations between monozygotic (Full-sib IBD regression2 and is often violated in human populations. Assortative mating (AM) is a form of non-random mating that occurs when individuals with similar phenotypes tend to mate more often than expected by chance. In humans, it is reported for a number of traits, including height, body mass index (BMI), educational attainment (EA) and a range of psychiatric disorders16. The presence of AM is important for genetic analysis as AM causes causal variants across the genome to be correlated with one another 2; increasing the genetic and phenotypic variance in a population as well as the changing the expected genetic and phenotypic covariance between different types of relative pairs2. Failure to account for AM can bias parameter estimates, lead to confusion about how much variation has been captured by identified variants, how well common disease can be predicted from polygenic risk scores and how much of the phenotypic similarity between relatives is due to environmental similarities.Random mating is an assumption underlying most approaches to estimate heritabilityIn this study we examine the phenotypic covariance between pairs of individuals across the entire spectrum of relatedness, from  unrelated pairs, to distant relatives, full sibs and monozygotic twins. We use data from the UK Biobank and, due to the absence of pedigree information, quantify the genomic relationship (2]. Genomic relationships (17 and hence we account for geographic stratification by fitting birth contemporary group (CG) as a factor based on 378 local authority areas. Traits varied considerably in the variation attributable to technical, demographic and genetic factors, and there was some confounding between these effects. Hence, we assessed the effect of CG after accounting for PCs and all other covariates (see model (4), ‘Methods’). We find, for example, both height and educational attainment (EA) displayed modest stratification (R2 > 0.5%) for both CG and PCs . We investigated the effect of geographic and genetic stratification on phenotypic covariance using 4 models for pre-correction of the phenotype  a steady linear relationship between phenotypic correlation and genomic relationship for unrelated individuals  in Fig. 7 We fitted a weighted linear model in R18 for the unrelated bins  for height, income, lung capacity  and EA. Note that a non-zero intercept could be caused by a range of factors, including common environmental effects or AM4. We chose to investigate the influence of AM on our heritability estimates for close relative pairs and then use full-sib IBD regression to consider the influence of common environmental effects.We find our bin-based weighted HE regression to be a good approximation of the heritability estimated from individual-level HE regression for most traits  and the equilibrium heritability of the trait  and EA . We also find the environmental covariance term to be significantly greater than zero for both height (p = 6.3 × 10−5) and EA (p = 0.03).An individual-level model and REML was used to estimate entclass1pt{minima22 Table . AlthougThe analysis of close relatives detected evidence consistent with the effects of AM for height and EA in the UK Biobank. We, therefore, decided to explore the influence of AM on the interpretation of the full-sib IBD regression results, and also the heritability estimated under another widely used experimental design, namely a classical twin study of monozygotic and dizygotic twin pairs. We show with theory and simulation that the expectation from full-sib IBD regression of 24 for AM (Supplementary Note p > 0.05). We also found that the adjusted twin estimate to be significantly larger than p = 0.01). For EA the standard errors for adjusted estimates were large and confidence intervals spanned much of the parameter space. Unfortunately this prevents meaningful comparisons for this trait , and suggest that We present the phenotypic covariance across the full spectrum of genomic relatedness for 32 quantitative and ordered categorical traits. Our approach is simple and unencumbered by assumptions about the underlying genetic constitution of a trait. We observe that phenotypic correlation increases with genomic relationship from nominally unrelated pairs through to monozygotic twins. The relationship is composed of two linear sections, one in unrelated  but the effects should be minimal unless the confounding effects are directly proportional to p = 0.01; Table 30. In practice, this means monozygotic twins are more similar than expected under an ACE  model including the effects of AM28.We estimate the equilibrium heritability for height from three types of experimental design by adjusting results from our paper and the literature for AM Table . Our est31.Other potential sources of covariance between relatives, such as common environment, non-additive genetic effects and associative (or indirect) genetic effects are not directly considered in our model. Our estimates of 32 are a covariance source that can lead to heritable components in the environment which might be confounded with 32 occur when the phenotype of an individual is dependent on the phenotype of others. This can cause genotype-environment covariance; where the environmental effect of an individual is influenced by the phenotype of a relative, therefore creating a correlation between the individual’s genotype and it’s environment. Traits influenced by associative effects include aggression or competition amongst animals or plants32, and possibly many behavioural traits in humans. Strong evidence has been reported for the presence of associative effects for EA33. Kong et al.33, for example, attributed about 50% of the variance in EA explained by alleles transmitted from parents to offspring to associative effects (i.e. ‘genetic nurture’). A second type of associative effects may also be important for the full-sib IBD regression results. These are sibling effects34, where the phenotype of one sibling influences the second sibling. If present sibling effects have the potential to upwardly bias 31 found that the inflation of genome-wide association effects, compared to within family estimates, could be fully explained by AM for height but not for EA. This suggests that accurate modelling of EA requires accounting for both AM and associative effects.Associative effects35. To explore the impact of additive-by-additive epistatic effects, we use simulation to show that the expected increase in phenotypic covariance with genomic relationship is proportional to p > 0.05/14). However, our study had sufficient power to detect only large additive-by-additive effects  or between (epistasis) locientclass1pt{minimaentclass1pt{minima18 recently used family data from Iceland to obtain heritability estimates for 14 traits, including height (0.55 s.e. 0.04), BMI (0.29 s.e. 0.06) and EA (0.17 s.e. 0.09). These estimates are lower than many pedigree-based estimates28, including those presented here for 18 use their RDR (relatedness disequilibrium regression) method, which is a generalisation of full-sib IBD regression, to estimate within-family genetic variance. Thus the RDR method potentially measures a quantity equivalent to p = 0.02) and EA (p = 0.05). Similarly, the RDR estimate for BMI is lower than our estimate using close relatives (0.50 s.e. 0.03) and other estimates which are free from environmental confounders . Although Young et al.18 conclude that common environmental effects have inflated past estimates, here we highlight that AM is also important for the interpretation of their results. The effects of AM may partially explain the differences between the results from the RDR method and other estimates.Young et al.36) rather than IBS relationships37. IBD relationships are ideal because (true) IBD sharing is independent of the genotyped markers. However, there are challenges associated with the accurate estimation of the proportion IBD in relatives without pedigree information. Hill and White38, for example, highlight that the proportion IBD estimated from the detection of shared segments can underestimate the true value when small segments are missed. The estimation and use of IBD and IBS relationships in close and distant relatives warrants further scrutiny.Our paper makes use of identity-by-state (IBS) relationships to estimate heritability in close relatives. Ideally, these inferences would be made based on the proportion of the genome IBD  and EA  under some assumptions and using the regression of genetic predictors on partner’s phenotype. Similar to Robinson et al., we also find that the inferred correlation between mates for EA using genetic information is higher than Robinson’s reported phenotypic correlation between (likely) partners in the UK Biobank (0.41 s.e. 0.01)21. Further, our meta-analysis of the phenotypic correlation between known partners in the literature (0.42 s.e. 0.01) supports a phenotypic correlation between spouses of around 0.4. Robinson et al.21 suggests that the differences between the inferred and observed correlations could arise if there was indirect assortment on EA, that is direct assortment occurs on a trait genetically correlated with EA (such as intelligence). It may also indicate that equilibrium conditions have not been reached for EA, or that associative effects are influencing estimates of genetic variance. Robinson et al.21 also find evidence of assortment for BMI (0.14 s.e. 0.007) and other metabolic traits which was not replicated in this study, nor in Yengo et al.39. However, the expected inflation in additive genetic variance and heritability for BMI caused by the magnitude of AM reported by Robinson et al.21 is about 7 and 4%, respectively. Standard errors on our estimates of these parameters are of a similar magnitude as these effects and suggest insufficient power to detect the weak assortment for BMI reported by Robinson  unrelated pairs through to monozygotic twins. We observed two approximately linear sections to the distribution, one predicted by The North West Centre for Research Ethics Committee granted ethics approval the UK Biobank study for (11/NW/0382). Participants in the study provided signed electronic consent upon recruitment. This research is approved under the University of Queensland human ethics committee .40. Individuals are aged 40–69 years and are assessed for a range of traits; including physical, socio-economic and cognitive factors, as well as medical history. Most individuals have genotype information for 807,411 or 825,927 markers from the UK BiLEVE or UK Biobank Axiom Arrays41. We identified 417,060 individuals from this cohort that had (1) British or Western European ancestry (see details below), (2) consistent self-reported and genetic sex, (3) one or more recorded phenotypes for 32 quantitative or ordered categorical traits (see details below), (4) self-reported as born in Great Britain with co-ordinates for place of birth, (5) born between 1937 and 1970, (6) aged between 40 and 70 at the time of assessment, and (7) had imputed genotypes41.The UK Biobank is a large prospective cohort study of ~500 K individuals from the United Kingdom41. From these data, we hard-called 1,326,701 bi-allelic HapMap3 SNPs imputed from the HRC reference panel with imputation quality ≥0.3, minor allele count (MAC) > 5 and missingness <0.05 using PLINK (v200aLM)42. We then used a multi-step, iterative process to quality check and identify individuals of British or Western European ancestry using the 2,504 participants in the 1,000 Genomes Project43 with known ancestries as a reference. First, we identified 1,029,456 variants in common with the 1,000 Genomes Project and with minor allele frequency (MAF) > 0.01 in both datasets. Then the UK Biobank participants were projected onto the first two principal components (PC) from the 1000 Genomes Project reference panel using GCTA (v1.9)5. We classified Europeans as those with >0.9 probability as belong to the European supercluster based on the projection. Variants were then filtered for Hardy–Weinberg equilibrium in this tentative European subset (pHWE > 10−5), and the projection and assignments to the European cluster repeated. The resulting classification assigned 456,426 individuals to European ancestry. Next we repeated the above procedure within the European subset of the 1000 Genomes panel to obtain individuals with >0.9 probability of clustering with the GBR (British in England and Scotland) and CEU (Northern and Western European ancestry) ancestry individuals. Using this more stringent criterion, we obtained 449,298 individuals of likely GBR and CEU ancestry.Genotype markers for the UK Biobank sample were quality checked and imputed to the Haplotype Reference Consortium (HRC) and UK10K reference panels by Bycroft et al.5 for European ancestry individuals from a set of 1,123,347 HapMap3 SNPs  originating from the Haplotype Reference Consortium (HRC) imputation panel. From this matrix, we used the --rel-cut-off option in GCTA to identify a subset of 348,502 individuals with a maximum genomic relationship (π) of 0.05 and a further set of 133,387 individuals with a maximum π of 0.02.The genomic relationship matrix (GRM) was constructed using GCTA (v1.9)44 in unrelated individuals with European ancestry (π < 0.05). Genotyped SNPs were those previously used by the UK Biobank to calculate principal components41, with some additional quality control filters . The resulting SNP loading were used to project all individuals onto the PC space. PC projections were conducted specifically in the European ancestry subset to capture genetic stratification related to the UK Biobank data.Principal components were calculated with 137,102 genotyped SNPs using flashPCA (v2.0)Thirty-two quantitative and ordered categorical traits from the UK Biobank were selected from those available that had a high proportion of individuals with records. Phenotypes include anthropometric  and blood traits ; educational attainment, household income, spirometry  and some sex-limited traits . A full listing of traits, UK Biobank field identifiers and the number of records analysed are given in Supplementary Table 45, which is part of the UK Data Servide Census Support. The R-packages sp (v1.4-4) and rgdal (v1.5-18) were used to merge the spatial data from local authority GIS shapefile47 with the birth place coordinates of the UK Biobank participants (see Supplementary Table The Geographic Information Systems (GIS) shapefile containing the boundaries of local authority areas in UK were obtained from the InFuse websiteFour models were fitted to each phenotype. Fixed effects included in all models as factors were sex 2 levels), genotyping batch , year of birth  and age at assessment . Models differed in the degree of geographic or genetic stratification in the model. A list of fixed effects and UK Biobank identifiers can be found in Supplementary Table  levels, Observations more than 5 standard deviations from the mean were excluded from further analysis. Residuals were normalised to have mean zero and unit variance within each sex, and this is the definition of phenotype in this study.10 elements of the genomic relationship matrix represent all the pairwise relationships (π) between the 417,060 individuals with data in our British or Western European ancestry subset of the UK Biobank sample. We excluded pairs known to be direct descendants  due to the different expected covariance under assortative mating2. Covariance bins were constructed based on the distribution of the observed relationships, as a trade-off between accuracy of estimates (tending to increase bin width) and resolution (tending to decrease bin width). For each bin, the average phenotypic covariance for all pairs in a bin was calculated as i and j, and Nk is the number of pairs in bin k. Standard errors were calculated using a blocked Jackknife approach with 100 blocks of individuals.The 8.6 × 1018  of the phenotypic covariance on the average genomic relationship per bin or individual-level cross-product HE regression in GCTA (v1.9)7. We used a maximum relationship threshold of 0.02  of the phenotypic covariance per bin on the average genomic relationship. This weighted HE regression is similar to an analysis based on expected (pedigree) relationships, under the assumption that 7 with two variance components following a similar approach to Zaitlen et al.9 The first component captured the covariance due to close relative pairs by (i) extracting a genomic relationship matrix consisting of a subset of 197,173 individuals with one or more close relatives in the dataset and (ii) modifying the matrix by setting all the small relationships  pedigree matrix. The second component fitted the average covariance for all pairs  by creating a second matrix identical to the modified matrix described above, and then setting any non-zero off-diagonal elements to 1.We estimated the heritability using relatives /log(0.5), and a and b are estimates of If we replace 11 to estimate the genetic variance in the absence of environmental covariance. Simulation verified that heritability obtained from full-sib IBD regression is 41. Pairs were from 17,880 inferred families, with up to 6 members per family. Then, following Hemani et al.22, the proportion of alleles IBD was estimated for each pair using Merlin (v1.1.2)49. Briefly, estimating the proportion of alleles IBD involved pruning the HM3 SNPs into an informative subset of 25,355 autosomal SNPs , estimating IBD probabilities for each variant and combining variants into genome-wide estimates using genetic (recombination) distance. The genetic map was obtained from the 1000 genomes phase 1 website [URL: ftp://ftp.1000genomes.ebi.ac.uk/vol1/ftp/technical/working/20130507_omni_recombination_rates/]. SNPs with duplicate positions were excluded from the analysis and we used allele frequencies calculated from the 348,502 unrelated Europeans subset as input into Merlin. IBD estimates from Merlin showed a strong correlation (0.98) with the KING kinship estimates provided by the UK Biobank .We used full-sib IBD regression22, the full-sib IBD regression was conducted using a mixed linear model with variance components estimated via REML in GCTA (v1.9)5. REML was chosen over a simple full-sib covariance regression as all data and relationships within families are included in the model. We fitted the following model to the data:y* is a vector of residuals from (1) above , 1 is a vector of ones, μ is the mean, a is a vector of additive genetic effects, distributed a ~ N, c is a vector of family effects, distributed c ~ N and e is a vector of residual errors, distributed e ~ N. Covariance matrix A is block diagonal, with 1’s on the diagonal and genome-wide proportion of IBD on off-diagonals for full-sib pairs. C is also a block diagonal matrix with 1’s on the diagonal and 1’s on off-diagonal elements for full-sib pairs. I is an identity matrix. The equivalence between the pair-based full-sib regression and Eq. (Following Hemani et al.22. Full-sib correlations (50 as N is the number of pairs contributing to the estimate.The meta-analysis of full-sib regression results was conducted using the inverse-weighted approach described by Hemani et al.Supplementary FilePeer Review File


Reproductive performance is an important factor, which determines productive life and drives culling decisions in dairy herds. There are strong motives for including reproductive performance in genetic selection programs of dairy cows; however, low heritability estimates reported for reproductive performance measures limit the genetic selection efficiency. More effective genetic selection could be achieved using genomic information. The aim of this study was to identify genomic region(s) associated with the length of the calving interval in Holstein cows. The accuracies of genomic estimated breeding values (GEBVs) with single-step genomic BLUP (ssGBLUP) and the pedigree-based BLUP were compared as well. The results showed that the accuracies of GEBVs using the single-step genomic BLUP were much higher than those estimated using the pedigree-based BLUP. We identified three genomic regions  associated with the length of the calving interval in Holstein dairy cows.ARHGAP29, SEC24D, METTL14, SLC36A2, and SLC36A3 inside the windows associated with the length of the calving interval. The biological process terms including alanine transport, L-alanine transport, proline transport, and glycine transport were identified as the most important terms enriched by the genes inside the identified windows.The aim of the present study was to identify genomic region(s) associated with the length of the calving interval in primiparous (n = 6866) and multiparous (n = 5071) Holstein cows. The single nucleotide polymorphism (SNP) solutions were estimated using a weighted single-step genomic best linear unbiased prediction (WssGBLUP) approach and imputed high-density panel (777 k) genotypes. The effects of markers and the genomic estimated breeding values (GEBV) of the animals were obtained by five iterations of WssGBLUP. The results showed that the accuracies of GEBVs with WssGBLUP improved by +5.4 to +5.7, (primiparous cows) and +9.4 to +9.7 (multiparous cows) percent points over accuracies from the pedigree-based BLUP. The most accurate genomic evaluation was provided at the second iteration of WssGBLUP, which was used to identify associated genomic regions using a windows-based GWAS procedure. The proportion of additive genetic variance explained by windows of 50 consecutive SNPs (with an average of 165 Kb) was calculated and the region(s) that accounted for equal to or more than 0.20% of the total additive genetic variance were used to search for candidate genes. Three windows of 50 consecutive SNPs  were identified to be associated with the length of the calving interval in primi- and multiparous cows, while the window with the highest percentage of explained genetic variance was located on BTA3 position 49.42 to 49.52 Mb. There were five genes including  Milk yield and reproductive performance are two important factors which determine productive life and culling decisions in dairy herds ,2. WhileThe objective of this study was to use the WssGBLUP procedure and imputed high-density panel (777 k) genotypes to identify genomic region(s) associated with calving interval in Holstein dairy cows. The accuracies of genomic estimated breeding values (GEBVs) with the WssGBLUP procedure and the pedigree-based BLUP were compared as well. http://www.gpluse.eu). The data were records of 11,937 lactations on 6866 primiparous and 5071 multiparous Holstein cows calving between 2010 and 2018, distributed among 118 herds in four countries . The calving interval was calculated as the difference between calving dates from successive parities and was restricted to the range of 270 to 700 d. Genotyping was performed using the Illumina Bovine 10 K low-density chip , Bovine SNP50K  or BovineHD SNP panel . Genotypes of animals were imputed to high density (HD) with a reference population consisting of 46 HD males and 749 HD females [Bos taurus autosomes (BTA) were considered. SNP markers with minor allele frequency less than 5% were excluded. Finally, 566,345 out of 730,539 SNPs were available for the association analysis. Ethics approval and consent to participate were not applicable to this study.Data in this study were collected as part of the Genotype plus Environment (GplusE) FP7-Project  [G is the genomic relationship matrix [Z is the matrix of gene content adjusted for allele frequencies ; D is a diagonal matrix of weights for SNP variances; M is the number of SNPs, and pi is the estimated minor allele frequency at ith locus. The genetic analyses for the length of the CI in multiparous cows were carried out using a linear single-trait repeatability animal model, which was the same as the model used for primiparous cows but here, the fixed effect of parity was included into the model. In addition, a third random effect representing the environmental permanent effect associated with animals having repeated records was included into the model. This effect, assumed to be uncorrelated with additive genetic effects, allowed for the partitioning of the environmental variance into permanent and temporary components. The complete model for multiparous cows can be represented as follows:The pedigree consisted of 43,181 individuals . The genetic analyses were carried out through the average information restricted maximum likelihood (AIREML) via AIREMLf90 from the BLUPF90 software package . A lineadata (A) :(3)H−1=Ap matrix .(4)G=ZDk, the effect of lactation number, and pel, is the permanent environmental effect of cow l.Most of the terms in this model were defined as for the linear single-trait animal model except for pPedigree-based (co)variance components and breeding values were estimated considering the same linear animal model used to estimate the (co)variance components mentioned before. In the pedigree-based BLUP the genomic information was excluded, and the direct additive genetic effects were estimated using the pedigree-based relationship matrix. ga) and ungenotyped animals (na). The animal effects of genotyped animals are a function of the SNP effects, Z is a matrix relating genotypes of each locus and u is a vector of the SNP marker effect. The variance of animal effects was assumed as follows:D is a diagonal matrix of weights for variances of markers  and G*) was built with no weight. The analyses were performed using the weighted single-step genome-wide association study (WssGWAS) methodology , consideThe SNP effects were obtained using following equation:VanRaden  as a norD = I in the first step. Step 2. Calculate the G matrix. Step 3. Calculate GEBVs for the entire data set using ssGBLUP. Step 4. Estimate SNP effects from solutions of genomic breeding values in the previous step: (û): th SNP. Step 6. Normalize the vector of variances of SNP effects to get the SNP weights . Step 7. Use SNP weights to construct the D matrix; exit or loop to step 2. The effects of markers were obtained by five iterations from Steps 2 to 7. The accuracies of genomic estimated breeding values (GEBVs) with ssGBLUP and the pedigree-based BLUP were estimated using following formula.PEV is the prediction error variance, and th genomic region was estimated using the following formula.th region that consists of n consecutive SNP , th SNP for all individuals, and th SNP within the ith genomic region. The results were presented by the proportion of additive genetic variance explained by each genomic region of n consecutive SNP. The following iterative process  was usedhttp://www.ensembl.org/index.html) was used for identification of genes. The list of genes inside the genomic region(s) associated with the length of the calving interval, considered as positional candidate genes, was uploaded to Enrichr for gene ontology (GO) enrichment analysis [P value.The chromosome segments associated with the length of the calving interval were selected to explore and determine potential quantitative trait loci (QTL). The database (version UMD3.1) including gene locations, start positions and end sites for all bovine genes  of the length of the CI in primi- and multiparous cows were 395.1 (69.1) and 396.7 (62.9) d, respectively. The median of the length of the CI in primi- and multiparous cows were 375 and 381 d, respectively. The additive and residual variances estimated using the AIREML method for the length of the CI in primiparous cows were 201.3 (SE = 57.60) and 3728.7 (SE = 85.76), respectively. The estimated additive, permanent environmental effect, and residual variances in multiparous cows were 198.3 (67.8), 71.4 (100.4), and 2953.7 (103.15), respectively. The heritability estimates for the length of the CI in primi- and multiparous cows were 0.05 (0.01) and 0.06 (0.01), respectively, which are consistent with findings from other studies on dairy cattle ,31,32,33The single-step genomic BLUP (ssGBLUP) method assumes equal variance for all single nucleotide polymorphisms, which is unlikely in the case for traits whose major genes or QTL are segregating. To overcome the limitation of ssGBLUP, unequal variance or weights for all SNP are applied in an approach called weighted single-step genomic BLUP (WssGBLUP), in which SNP effects are weighted according to their importance for the trait of interest . AccuracAlthough, genome-wide association studies carried out within a variety of cattle breeds identified many single nucleotide polymorphisms (SNPs) associated with the length of the calving interval (CI), the results are inconsistent ,18,49. ZARHGAP29, SEC24D, METTL14, SLC36A2, and SLC36A3 were identified inside the windows associated with CI  associated with the length of the calving interval and the results showed that the identified peaks changed depending on the window size with smaller window sizes being accompanied with large noises. We identified three windows of 50 consecutive SNPs associated with the length of the calving interval. The findings of this study can be used to search for causative mutations, and for breeding through marker-assisted selection to improve the length of the calving interval in Holstein dairy cows.


Haplotype prediction models open many possibilities to improve the accuracy of genomic selection but require more data processing and computing time than single-SNP prediction models. To facilitate haplotype analysis for genomic prediction and estimation using structural and functional genomic information, we developed a computing pipeline to implement haplotype analysis with capabilities for preparation of input data for haplotype analysis, genomic prediction and estimation using GVCHAP, and analysis of GVCHAP results. Data preparation includes utility programs for haplotype imputing; defining haplotype blocks by a fixed number of SNPs, a fixed distance in base pairs per block, or user defined block lengths based on structural or functional genomic information or a mixture of both types of information; and defining haplotype genotypes within each haplotype block. GVCHAP is the main program for genomic prediction and estimation, calculates GREML (genomic restricted maximum likelihood) estimates of variance components and heritabilities, and calculates GBLUP (genomic best linear unbiased prediction) for additive and dominance values of single SNPs as well as additive values of haplotypes with reliability estimates for training and validation populations. A two-step strategy and a method of multi-node processing are implemented to remove the computing bottleneck due to the creation of genomic relationship matrices for large samples. The analysis of GVCHAP results includes calculation of observed prediction accuracies from validation studies and preparation of input files for graphical visualization of heritability estimates of haplotype blocks as well as estimates of SNP effects and heritabilities. The entire pipeline provides an efficient and versatile computing tool for identifying the most accurate haplotype model among many candidate haplotype models utilizing structural and functional genomic information for genomic selection. Current methods using single nucleotide polymorphism (SNP) markers for genomic evaluation mostly use single-SNP prediction models. Haplotype analysis opens many possibilities of using structural and functional genomic information to improve the accuracy of genomic evaluation and gene discovery . CompareGVCHAP implements a multi-allelic haplotype mixed model that treats each haplotype block as a ‘locus’ and each haplotype within the haplotype block as an ‘allele’ . The mixBased on the quantitative genetics models of haplotypes and SNPs , the quaZ = N × n incidence matrix allocating phenotypic observations to each individual = identity matrix for one observation per individual (N = n), N = number of observations, n = number of individuals, αo = m×1 column vector of SNP additive effects, m = number of SNPs, Wα = n × m model matrix of αo, δo = m×1 column vector for dominance effects of SNP genotypes, Wδ = n × m model matrix of δo, αh = nhα×1 column vector of haplotype additive effects, nhα = number of haplotype additive effects, Whα = n ×nhα model matrix of αh, b = c×1 column vector of fixed effects such as herd-year-season in dairy cattle, c = number of fixed effects, X = N×c model matrix of b, a = Wααo = SNP genomic additive values, d = Wδδo = SNP genomic dominance values, ah = Whααoh = haplotype genomic additive values. The haplotype coding represented by Whαis: ij and α1k do not share allele k), ij and α1k share allele k, i≠j), and ij and α1k share allele k, i = j), where aij = additive value of haplotype genotype with the ith and jth haplotypes, and α1k = additive effect or the average effect of gene substitution as the difference between the allelic (haplotype) effects of the first and the kth haplotypes (Wα and Wδ are the same as defined by the single-SNP quantitative genetics model (y) = Xb, andwhere plotypes . SNP codcs model . The firwhere Based on Eqs. 1, 2, the mixed model with genomic relationship matrices is a reparameterized and an equivalent model of Eqs. 1, 2, i.e.,Ag = SNP genomic additive relationship matrix, Dg = SNP genomic dominance relationship matrix, Agh = haplotype genomic additive relationship matrix, a = Tαα = Wααo = SNP genomic additive values, d = Tδδ = Wδδo = SNP genomic dominance values, ah = Thααh = Whααoh = haplotype genomic additive values, V = phenotypic variance-covariance matrix, andwhere α, kδ and kαh defined by Eqs. 8–10 is an average of the diagonal elements of Each of kand the genomic relationship matrices in Eqs. 4–6 can be expressed as:j = ii = 1 + f and aij = 2fij, where aij = additive relationship between the ith and jth individuals, fij = coancestry coefficient between the ith and jth individuals, and f = inbreeding coefficient; but underestimates genetic variance components and heritability compared to the Hayes-Goddard method when inbreeding is present. The Hayes-Goddard method does not preserve the properties of pedigree additive relationships. Although these two methods for calculating genomic relationship matrices have different interpretations and generally have differences in estimates of variance components and heritabilities, these methods and the quantitative genetics model of Eqs. 1, 2 without using genomic relationships yield identical GBLUP and reliability  and gene based blocking. The parameter file contains controls for running GVCHAP, including the prediction model, the use of EM-REML and AI-REML, and information about the input and output files. Two utility programs (count-snps.py and count-haps.py) fill in the number of SNPs and the number of haplotype blocks for each SNP genotype file and each haplotype genotype file.The GVCHAP analysis produces GBLUP (genomic best linear unbiased prediction) and GREML (genomic restricted maximum likelihood estimation) for SNP effects and values as well as haplotype additive values with options to improve computing speed .The prediction model can include SNP additive and dominance values, and haplotype additive values. For these values, GVCHAP offers seven models that include the full model of Eq. 3 and six variations of Eq. 3:y = Xb + Z(a + d + ah) + e;Model 1: SNP additive, dominance and haplotype additive values, y = Xb + Z(a + ah) + e;Model 2: SNP and haplotype additive values, y = Xb + Z(d + ah) + e;Model 3: SNP dominance values and haplotype additive values, y = Xb + Zah + e;Model 4: haplotype additive values only, y = Xb + Z(a + d) + e;Model 5: SNP additive and dominance values, y = Xb + Za + e;Model 6: SNP additive values only, y = Xb + Zd + e.Model 7: SNP dominance values only, Models 1–4 contain haplotype additive values, and Models 5–7 are SNP models. The comparison between Models 1–4 and Models 5–7 for prediction accuracy provides an estimate whether haplotypes improve the prediction accuracy. For example, haplotypes improved the prediction accuracy if any of the haplotype models (Models 1–4) was more accurate than the three SNP models (Models 5–7) in validation studies. Similarly, validation studies can identify the most accurate model among the seven prediction models. Each of the seven models is configured by the starting values of the variance components in the parameter file through four parameters, var_snp_a, var_snp_d, var_snp_e, and var_hap_a for starting values of SNP additive variance, SNP dominance variance, residual variance, and haplotype additive variance respectively. These seven models and the main results of GBLUP and GREML for each model are summarized in GVCHAP calculates GREML estimates of variance components and hertiabilities for each of the genetic effects in the prediction model using a combination of EM-REML and AI-REML for iterative solutions adopted from GVCBLUP . The proGREML estimates may provide helpful information for choosing among the seven prediction models in Converged GREML estimates of variance components are used for calculating GBLUP and reliability for each type of genetic values and the sum of SNP and haplotype values. In the output file for GBLUP and reliability, an individual is flagged with ‘T’ if the individual is in the training population with phenotypic observations, or ‘V’ if the individual has missing phenotypic value or is in the validation population with phenotypic value set as missing value. For the example of Model 1 with SNP additive and dominance values as well as haplotype additive values, GBLUP and reliability for each and the sum of these values are calculated. After sorting the output file by training (T) and validation (V) populations, the GBLUP estimates are:a, d, ah, or g = a + d + ah. In the absence of validation studies, reliability or the expected prediction accuracy is the measure of prediction accuracy for a type of genetic value, e.g., SNP additive or dominance value, or haplotype additive value, or the sum of all these genetic values. The reliability formula for where ‘∧’ indicates estimated value, subscript ‘1’ indicates training population, and subscript ‘0’ indicates validation population or individuals with missing phenotypic observations. Each of the above GBLUP estimates is accompanied by its reliability. The square root of a reliability estimate is the correlation between GBLUP and the unobservable true genetic value being predicted by the GBLUP, and is the expected accuracy for predicting the unobservable true genetic valu’e, P = V−1−V−1X(X′V−1X)−X′V−1; th diagonal elements of Ag, Dg and agh respectively; and subscripts ii of the numerator indicates the ith diagonal element of the numerator matrix. The reliability formula for any of Models 2–7 can be readily derived from Eq. 21, e.g., the reliability of Model 2 is obtained from Eq. 21 by deleting all terms involving ‘δ.’where For a validation study, this computing pipeline has a utility program (get-correlations.R) calculating the observed accuracy for predicting the phenotypic values using a type of genetic values  or a sum of several types of genetic values  for each validation. This observed accuracy is calculated as the correlation between the predicted genetic values and the phenotypic values in the validation population  that were omitted when calculating GBLUP. The expected accuracy for predicting phenotypic values is the product between the expected accuracy for predicting genetic values and the square root of heritability . For genth validation population, 0gij = expected prediction accuracy for predicting the genotypic values of the jth individual in the ith validation population calculated as the square root of reliability from the GVCHAP output file for GBLUP and reliability based on Eq. 21,R0gi = expected prediction accuracy for predicting the genotypic values of the ith validation population, n0i = number of individuals in the validation population, R0g = expected prediction accuracy for predicting the genotypic values of k validation populations, R0p = expected prediction accuracy for predicting the phenotypic values of k validation populations, and h2 = heritability. The get-correlations. R program calculates Eqs. 22–25, but Eq. 26 needs to be calculated by the user using results in the GBLUP and GREML output files.where GVCHAP calculates and saves SNP effects and heritability estimates, and saves haplotype heritability estimates in separate files for graphical visualization using SNPEVG2  to identGVCHAP calculates and saves fixed effects in a separate file and outputs the estimates of the fixed effects for all individuals. Two types of fixed effects can be included in the prediction model, classification variable for a fixed factor with a small number of levels such as male or female, and covariable for a fixed factor with many levels such as age. Selected SNPs can be fitted as fixed effects through declarations in the parameter file for column positions of those SNPs in the phenotype file, typically as covariables to minimize the use of degrees of freedom such that the residual degree of freedom is still sufficiently large.Three potential applications involve the use of fixed effects. These include estimation of SNP contributions to prediction accuracy and genomic heritability , genomicwhere The computing time of GVCHAP for calculating SNP additive and dominance genomic relationship matrices, haplotype additive relationship matrix, and each GREML iteration was evaluated using five samples and the Mesabi supercomputer at the University of Minnesota . The resTo remove repeated calculations to create genomic relationship matrices in validation studies and multivariate analysis, we designed a two-step strategy that saves genomic relationship matrices from the first run as binary files and loads the saved genomic relationship matrices for the remaining runs. For the example of a 10-fold validation, genomic relationship matrices are calculated only for the first of the 10 validation runs, and the remaining 9 validation runs load the stored genomic relationship matrices calculated and saved by the first run. This strategy virtually eliminates computing time for creating genomic relationship matrices when running GVCHAP. Our experience showed loading the saved genomic relationship matrices was nearly instantaneous and required only negligible computing times. With this strategy, days of computing time could be saved even for the smallest sample with 7549 individuals and 328,512 SNPs in our test runs . For a sThe long computing time required by GVCHAP to create a haplotype additive genomic relationship matrix using a single node  was due α, kδ, and khα are defined by Eqs. 8–10. Different where kstrategy  and can strategy .–6 for heritability tolerance and 10–8 for variance component tolerance. Since heritability estimates are rarely reported with more than three decimal points, the 10–6 tolerance for heritability could significantly reduce the number of EM-REML iterations. With two types of tolerance levels, iteration stops when any of the two tolerance levels is reached.With the removal of the computing bottleneck for processing haplotype genotypes by the two-step strategy and MNP method, the computing bottleneck becomes iterative solutions for GREML. The computing time per iteration increased from less than 1.5 min for 15,098 individuals to 22–29 min for 37,745 individuals . The curThe number of individuals is the limiting factor within each iteration because of matrix inversions and the need to store genomic relationship matrices for GREML. As the number of individuals increases, the sizes of the genomic relationship matrices and hence the required memory to store those matrices increase, and the computing time may increase rapidly. The choice of statistical model has a major impact on the memory requirement. Model 1 with haplotype additive effects and SNP additive and dominance effects requires the most memory, whereas Model 4 with haplotype additive effects requires the least memory among all models with haplotype effects. Therefore, Model 4 is the computationally competitive choice among Models 1–4 if Models 1–3 do not have substantially better prediction accuracy than Model 4. As shown in The GVCHAP program provides a capability for GBLUP and GREML to identify optimal prediction models using haplotypes based on structural and functional genomic information for genomic selection. The utility programs for data preparation and summary analysis of GVCHAP results eliminate most of the tedious and time-consuming data work. The entire pipeline provides an efficient and versatile computing tool to investigate candidate haplotype models utilizing structural and functional genomic information for genomic selection.http://animalgene.umn.edu.The GVCHAP computing pipeline is available at All datasets generated for this study are included in the article/YD conceived the study. DP was the author of the current version of GVCHAP and the utility programs. CW was the author of the initial version of GVCHAP. ZL was the author of the MNP program. CB and CT provided extensive evaluation that improved GVCHAP and the utility programs. ZL and DP evaluated computing time required by GVCHAP. DP, ZL, and YD prepared the user manual and prepared the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Effect Direction MEta-analysis (EDME) to quantify pleiotropy using GWAS of 34 Cholesky-decorrelated traits in 44,000+ cattle with sequence variants. The effect-direction agreement between independent bull and cow datasets was used to quantify the false discovery rate by effect direction (FDRed) and the number of affected traits for prioritised variants. Variants with multi-trait p < 1e–6 affected 1∼22 traits with an average of 10 traits. EDME assigns pleiotropic variants to each trait which informs the biology behind complex traits. New pleiotropic loci are identified, including signals from the cattle FTO locus mirroring its bystander effects on human obesity. When validated in the 1000-Bull Genome database, the prioritized pleiotropic variants consistently predicted expected phenotypic differences between dairy and beef cattle. EDME provides robust approaches to control GWAS FDR and quantify pleiotropy.In genome-wide association studies (GWAS), variants showing consistent effect directions across populations are considered as true discoveries. We model this information in an  Xiang et al. developed an Effect Direction Meta-analysis (EDME) approach to identify true pleiotropy. They used Cholesky-transformation to decorrelate the traits and identified many pleiotropic variants that consistently predicted phenotypic differences in cattle. From this, a p value can be calculated for the null hypothesis that the variant has no association with the trait. Using the p values and the number of significant variants, it is common to calculate a false-discovery rate (FDR)1. However, this conventional FDR depends on the calibration of the p value which in turn depends on the data conforming to the statistical model assumed in calculating the p value.Genome-wide association studies (GWAS) find mutations associated with complex traits. A GWAS produces estimates of the effect of each variant on a trait measured by a regression coefficient Effect Direction MEta-analysis (EDME) for effect direction meta-analysis. EDME is easily extended to calculate the FDR by effect directions (FDRed) for a multi-trait GWAS. This will allow us to know the number of traits that a significant variant is associated with and precisely which traits these are.The important implication of FDR is that true discoveries would be confirmed in a powerful, independent experiment. In this paper we directly use the ability to confirm a finding in an independent study to estimate the FDR by using the proportion of sequence variants which have an effect in the same direction in two independent datasets. We call this FDRed for ‘effect direction’ based on a statistical model we call 3, meta-analysis of public GWAS summary statistics significantly improved our understanding of pleiotropy8. Naturally, traits that are genetically correlated must share part of their causal variants, however, if traits are uncorrelated, can we still detect widespread pleiotropy?Due to the recent availability of many GWAS results with large sample sizes in humans9. After GWAS, we focus on using the information of the consistency of variant effect directions to identify pleiotropic variants associated with uncorrelated traits, instead of distinguishing different types of pleiotropy10. We aim to use: (1) the consistency of variant effects in different populations to evaluate the FDRed independent of their p values; (2) the information on the consistency of variant effects for multiple traits across different populations to quantify pleiotropy at both the variant and trait levels. We propose an EDME of GWAS of 34 complex traits of over 44,000 dairy bulls and cows with over 17.6 million sequence variants. A validation analysis with the 1000-bull genome database confirms the informativeness of pleiotropic variants prioritised by the EDME model.Our study starts with multi-trait GWAS of individual data where the traits are decorrelated by a Cholesky transformation9 to be applied to the 34 traits. The Cholesky transformation decorrelates the 34 traits by ordering the traits from 1 to 34 and correcting each trait for all the traits before it in the list. We use this method because the traits vary in their completeness, i.e., some traits have more records than others. By ordering the traits from the trait with most complete data to the trait with least complete data, we can make use of all the data because the Cholesky transformation of the Kth trait in the list only needs data on the K − 1 traits and individuals with trait K to have data on all K − 1 traits. Thus the Cholesky transformation produces uncorrelated traits and makes maximal use of incomplete data 11. On average at p < 1e−6, 1900 (±813) variants were significant per trait in bulls and 2018 (±795) in cows. The FDR calculated by conventional methods  at p = 1e−6 was 0.22 (±0.045) for bulls and 0.1(±0.021) for cows across 34 CT traits.On average across 34 CT traits, the heritability was 0.42  in bulls and 0.164 (±0.029) in cows  variants that truly decrease the trait value, the ‘true positive’ (T+) variants that truly increase the trait value and the ‘true zero’ (T0) variants with no reliable effects on the trait  was the observed number of variants with inconsistent effect directions (‘+−’ and ‘−+’) and n(B) was the observed number of variants with consistent effect directions (‘++’ and ‘−−’) in GWAS of two different populations. Tr denoted the combined number of T− and T+. Then, the FDR and TDR by effect directions  were calculated as Eqs. We assume that true positives were always observed in the ++ class and true negatives in the −− class and that true zero effect variants have one-fourth probability of being in any of the four classes. This then allowed the calculationsn(A)), the FDRed and conventional FDR averaged across 34 CT traits were compared within a range of p value thresholds imposed in both sexes  at p = 1e−6, to 14(±12) at p = 1e−100  significant variants for both sexes, the single-trait FDRed was 0.032(±0.015) while the conventional FDR was 0.98(±0.015). At the p = 1e−9 level, amongst 408(±213) significant variants for both sexes, the single-trait FDRed dropped to 0 and the conventional FDR was 1.6e−05(±3.4e−06)  Fig. . When imt values of both sexes . For a group of variants, Π values allowed the use of the same logic calculating the single-trait FDRed  was the total number of variants selected.The single-trait EDME was extended to multiple traits (see Methods) to calculate FDRed and quantify pleiotropy. For each variant, the dot product of the vector of signed mentclass2pt{minimTrue Effect (TE) for each variant , As well as this multi-trait estimate of FDR, it is also possible, for each sequence variant, to count the number of traits with the same direction of effect in population 1 (bulls) and population 2 (cows). Allowing for the fact that half the traits were expected to be in the same direction by chance, the EDME logic can estimate the number of traits showing a iant Eq. . While tn(variant), Eq. trait, suggesting pleiotropic variants that affect each trait (illustrated in the following results).The estimated number of TE averaged across a group of variants p value threshold in both sexes  and it dropped to 0 at the p = 1e−6 level where the estimated number of TE per variant was 9.63. That is, the average number of traits affected by a single-nucleotide polymorphisms (SNP) in this group is 9.63. Additional analysis with functional data13 indicated that both single-trait and multi-trait FDRed can help find informative variants at lenient p value thresholds where conventional FDR was large  < 1e−6 from the weighted meta-analysis combining GWAS results of bulls and cows , and their Π values, which indicate the effect direction agreement for multi-trait analysis, were correlated with their conventional FDR based on pwm  (Supplementary Data ZNF613 (Chr18:58.1M) which was close to the CTU1 region (Chr18:57.5M). Variants from the CTU1 region had observed TE on 20 CT traits. Both GC and CTU1 loci were reported as lead dairy cattle pleiotropic loci in the 2017 pleiotropy study9. Other commonly known major loci for dairy cattle (see refs. 16) were also captured, including DGAT1 (Chr14:1.8M) that had TE on up to 17 CT traits, MGST1 (Chr5:93.9M) that had TE on ∼13 CT traits, CSN1S1 (Chr6:87.1M) that had TE on ∼12 CT traits, GHR (Chr20:32M) that had TE on ∼15 CT traits and ENSBTAG00000048091 (beta-lactoglobulin-2-like), a potentially duplicated gene of the adjacent PAEP  that had TE on ∼11 CT traits.The most pleiotropic variants accounting for 0.00003% of the genome with observed TE on 22 CT traits were close to the egion Chr:88.8M (SPC (Chr29:45.6M), coding for the enzyme pyruvate carboxylase which is needed for gluconeogenesis and lipogenesis, had TE on ∼18 CT traits. A pleiotropic locus with TE on ∼12 CT traits was SLC22A6 (Chr29:41.9M) which had reported roles in regulating water metabolism in mammals17. In addition, variants from the X chromosome (chromosome 30) with pleiotropic effects were also identified. Tagged genes included CD40LG (Chr30:20.2M) and ARHGEF6 (Chr30:20.3M), although these variants only affected 2–3 CT traits . Each set of variantstrait was tested for whether the variantstrait had specific associations with the trait that they were assigned to. For each trait, the single-trait FDRed was calculated using the trait-related variantstrait. Such single-trait FDRed (average < 0.1) was much smaller than the single-trait FDRed calculated using those general pleiotropic variants associated with any one of the 34 traits   in the variantstrait related to dairy cattle CT stature (trait 19)  and they had significant sharing of pleiotropic variantstrait amongst themselves, CT milk production traits did not have significant sharing of pleiotropic variantstrait with every other CT trait. Although traits like CT body condition score (BCS) had the least amount of pleiotropic variantstrait, CT BCS had significant sharing of pleiotropic variantstrait with a wide range of other CT traits.Among the 900,820 combinations of trait by variant, we counted the number of variants that affected each pair of CT traits Fig. . Many patrait sharing index, i.e., the number of pleiotropic variantstrait overlapping divided by the number in the union for each trait pair, averaged across the other 33 traits was calculated. As shown in Fig. trait sharing index was used to rank CT traits from ‘influential’ (sharing pleiotropic variantstrait with many traits) to ‘independent’ (sharing pleiotropic variantstrait with few traits). The first trait protein yield was ranked as the most influential trait, followed by other CT milk production traits. The CT type trait Bone (trait 21), the original trait of which indicated the flatness of legbone of the cattle but is negatively correlated with fatness, ranked the fifth for its influence. The last CT trait BCS ranked relatively high for its influence, given its small number of pleiotropic variantstrait. The CT temperament (trait 8) and the overall type  were ranked as relatively independent amongst traits analysed  using variants as instrumental variables implemented in GSMR20 were conducted for 50 raw trait pairs that had the least amount of variant sharing after Cholesky transformation . Raw somatic cell count (SCC) also had some putative causal effects on raw mammary related traits  of these variants were detailed in Supplementary Data IGFBP7 (Chr6:74.5 M)23, DNMT3B (Chr13:62.6M)24, SLC24A4 (Chr21:57.6M)25, SLC37A126 and FTO (Chr18:22.1M)27 which were reported as single-trait or production trait QTL previously. However, there were also many loci not previously reported in cattle, such as intergenic variants tagging MCF2 (ChrX:23M), CTNNA2 (Chr11:54.9M), NSF (Chr19:46M) and KRT14 (Chr19: 42.4M).To the best of our knowledge, we defined the novel pleiotropic variants as those which were outside the ±2 Mb region of the 1181 pleiotropic SNPs with FTO gene had pleiotropic effects on raw fat percentage, milk yield and many raw linear assessment traits, including likeability (Like), rear teat placement (TeatPR) and teat length (TeatL)  already indicated the existence of multiple QTL in this region .Two examples of the less reported pleiotropic loci in cattle are given in Fig. tL) Fig. . Variantion Fig. . To furtits Fig. . This ob31, including KRT9, KRT14, KRT15, KRT16, KRT19, KRT35, and KRT36. Again, cluster analysis indicated the existence of several QTL in this region. The joint analysis showed that selected top variants had a correlated pattern of effects on milk production traits. These same variants had a less correlated pattern of effects on raw traits of SCC, temperament and many raw linear type traits of the mammary gland  93,513 variants prioritised by pwm < 1e−6 alone and (3) a random set of 93,513 variants. Overall, both the EDME with pwm and pwm alone prioritised pleiotropic variants predicted that dairy cattle were genetically better than the beef cattle for dairy traits and the difference in predictions between beef and dairy was generally lowest in the Random set  prediction of the largest advantage in gEBV of dairy over beef cattle  to estimate the FDR and the number of true discoveries. This method does not depend on the exact calculation of p values which depends on a statistical model that may not describe the data exactly.In this paper, we focus on finding pleiotropic variants and identifying the traits that each variant affects using EDME. Our approach differing from other published studies in three respects. Firstly, we use individual animal data rather than GWAS summaries. This is partly out of necessity because few summary data are available for cattle and most non-human species, but also, because some information is lost in summaries, it is better to start with individual data when this is available. Secondly, we use uncorrelated traits by applying a Cholesky transformation to the 34 raw traits. The choice of Cholesky transformation maximises the amount of data used by ordering the traits from the trait with the most complete data to the trait with the least complete data. Each CT trait is the raw trait corrected for all traits before it in this order. Transformed traits are always difficult to interpret but some interpretation of the CT traits is still possible. For instance, survival corrected for milk production traits focusses on reasons for death or culling other than milk production. However, when the number of traits considered increases, CT traits ordered late in the list would have reduced interpretability, but this does not affect the estimation of the multi-trait 11, therefore, the power for detecting lead variants across 34 traits was different between these two populations, as shown in heritability estimates  and dissect pleiotropy. The two types of analysis serve different purposes and data availability in two species.EDME quantifies the number of traits associated with variants in general and with particular variants based on the agreement of variant effect-directions for multiple traits across two populations. This unique analysis provides additional quantities for pleiotropy which fills a gap in our previous methods where only the multi-trait p < 1e−6 in both sexes we estimate that the average number of traits affected per variant (TE) was 9.6 and this supports the conclusion that pleiotropic effects on uncorrelated traits are widespread. This conclusion is also reached by Jordan et al.7 using a different analysis in humans. Widespread pleiotropy was also found by analyses of GWAS of correlated traits in humans8. However, EDME showed that variants varied widely in the number of traits affected from 1 to 22. In general, variants with a large effect on one trait tended to have small effects on many traits  to inform trait biology which is supported by published data18 . Only those bulls’ phenotypes which were based on records from more than 15 progeny were included. Phenotype data of up to 11,923 bulls included 6569 CRV bulls  with phenotypes derived from their Interbull MACE breeding values (https://interbull.org/ib/interbullactivities) degressed on the Australian scale and converted to the scale of the daughter trait deviation. The remaining 5354 bulls and all 32,347 cows were from DataGene. All these animals included Holstein , Jersey (2059 ♂ / 6174 ♀), cross breed (0 ♂ / 2850 ♀) and Australian Red dairy breeds (125 ♂ / 424 ♀).No live animals were used in this study. Phenotype data was based on trait deviations for cows and daughter trait deviations for bulls . Cn was a K (number of traits)×1 vector of Cholesky scores for animal n; L was the K × K lower triangular matrix of the Cholesky factor which satisfied LLt = COV, the K × K covariance matrix of raw scores after standardisation as z-scores, gn was a K × 1 vector of traits for animal n. Cholesky transformation decorrelated all traits at once. However, as a result, the Kth Cholesky-transformed trait can be interpreted as the Kth original trait corrected for the preceding K − 1 traits and each Cholesky-transformed trait had a variance of close to 1 (Supplementary Data 9) and this would result in sample size for all traits being determined by the trait with the smallest number of records, i.e., 1439 bulls and 4086 cows. Another condition required to be met for the current Cholesky transformation was that the same descending order of the selected traits matches between the bull and the cow data sets. This allowed that CT traits were the same in bulls and cows such that the GWAS of one trait in two sexes were comparable.Phenotype decorrelation was conducted using Cholesky transformation, with the formula of mentclass2pt{minim37y = vector of phenotypes for bulls or cows, breed = three breeds for bulls, Holstein, Jersey and Australian Red and four breeds for cows ; bx = regression coefficient b on variant genotypes x; a = polygenic random effects ∼N where G = genomic relatedness matrix based on all variants. The above GWAS model was also applied to estimate the total genomic variance for heritability calculations for all traits, but without including the “bx” term in the model.The 34 decorrelated traits were analysed one trait at a time independently in each sex with linear mixed models using GCTAχ2 statistic for the ith variant was calculated based on its signed t values generated from each single-trait GWAS: 1). ti was a K (number of traits = 34) × 1 vector of the signed t values of varianti effects, i.e., b/se, for the K traits; ti′ was a transpose of vector ti(1 × K); and V−1 was an inverse of the K × K correlation matrix where the correlation was calculated over the all estimated variant effects  of all trait pairs. The χ2 value of each variant was examined for significance based on a χ2 distribution with k degrees of freedom to test against the null hypothesis that the variant had no significant effects on any one of the Kth traits. The conventional FDR of χ2 tests were calculated following1.The multi-trait t values of bull GWAS and cow GWAS results was performed using the formula12). Where tw was the weighted t value for bulls and cows accounting for the phenotypic error differences between bulls and cows11, calculated as the quotient of the weighted variant effects Bw and the weighted effect error sew; bbull and sebull were the variant effects and errors obtained from single-trait GWAS in bulls and bcow and secow were the variant effects and errors from cow GWAS. Once the tw of each trait was obtained, the multi-trait meta-analysis was performed using Eq. 9, where over 630,003 SNPs from the high-density SNP chip panel were used for GWAS with 25 traits in bulls and cows.To fully utilise the GWAS summary data obtained in bulls and cows separately, a weighted multi-trait meta-analysis of the signed p values adjusted (divided) by their functional-and-evolutionary trait heritability (FAETH) score13. Then, variants ranked within the top 10% within each sex were selected for LD pruning, using Plink 1.938 with r2 > 0.95 within 5 Mb windows. For pruned variants, in each 5 Mb window, with the overlapping size of 2.5 Mb, we calculated t values (beta/s.e. from GWAS described above) of 34 CT traits for varianti and variantj; r) measured as the correlation between the genotypes of varianti and variantj. These ρ values were clustered using graph based Random Walks determining densely connected subgraphs (clusters)39 implemented in igraph40. On average there were 12 variants per cluster in bulls and cows. The clustering of the variants aimed at finding groups of variants tagging the same QTL. Normally, variants with strong LD were considered as tagging the same QTL. However, variants tagging one QTL should also show similar effect patterns across multiple traits . Therefore, by adding the correlation of effect t value, i.e., ρij to better group variants tagging the same QTL than using rcor or rLD alone. After clustering, up to 50 clusters were retrieved within each window. To verify if identified clusters can represent local QTL, the top 100 variants from clusters based on their FAETH adjusted multi-trait p value were selected. These 100 top variants were used to conduct a conditional analysis of GWAS37 of 34 traits in each sex. A meta-analysis of the conditional GWAS results used Eq. The use of sequence variants led to a large number of variants in high LD. Consequently, a single QTL might be tagged by many sequence variants. To give an indication of the differentiation of pleiotropic QTL from sequence variants, a sliding-window (5 Mb) variant clustering was conducted. All calculations regarding this clustering were done separately in each sex. Firstly, variants were ranked by their multi-trait Meta-analysis of the conditional GWAS results showed that pleiotropic effects dramatically dropped, but only for those variants from the clusters with which the top 100 variants were selected  variants with ‘true negative’ effects on the trait, i.e., T− variants that truly decrease the trait value, (2) variants with ‘true positive’ effects on the trait, i.e., T+ variants that truly increase the trait value and (3) variants with ‘true zero’ effects on the trait, i.e., the T0 variants that had no effects on the trait. In practice, a GWAS conducted for the same trait in two different populations would have four categories of variant effect directions: (1) the ‘−−’ where the effect was consistently negative for the trait in two populations, e.g., bulls and cows in this study; (2) the ‘++’ where the effect was consistently positive for the trait in bulls and cows; (3) the ‘+−’ where the effect was positive for the trait in bulls but negative in cows; and (4) the ‘−+’ where the effect was negative for the trait in bulls but positive in cows.The R code of EDME can be downloaded from T0 variants which should have no TE, they were expected to be randomly distributed across the four observed categories  of variants. This meant that each one of the four categories of the ‘++’, ‘−−’, ‘+−’ and ‘−+’ variants contain an equal amount of the T0 variants . Therefore, the total number of ‘+−’ and ‘−+’ variants observed was equal to one-half of the total number of T0 variants expected. This then allowed the deduction of model Eq. T0. Once the number of T0 was known, the total number of T− and T+ variants can be determined by equating the expectation with the observed number of ‘++’ and ‘−−’ variants (n(B)) as described in the first and the third quadrant of the right panel of Fig. 2aT0 and Tr were determined, the false discovery rate by effect direction (FDRed) and true discovery rate by effect direction (TDRed) can be calculated based on the total number of variants entered the analysis in the two populations (n(A) + n(B)) as described in Eqs. If there were t values of bulls and cows with the same length of K, where K is the total number of traits. The idea was that the effect direction across multiple traits, i.e., the sign of the Π value, was not driven by the small trait effects which were more likely to arise from noise. Instead, the sign of the Π value was driven by relatively large trait effects which were likely to be robust. Then, the number of variants with negative Π values were used to calculate the multi-trait FDRed in Eq. For equation ti1⋅ti2T , the Π vn(B) that was equivalent to T0) and Tr). As K = 1), the multi-trait Eq. MTR was the multi-trait version of TDRed for Eq. For one variant analysed in K traits across the two populations, the single-trait Eq. R in Eq. , where \entclass1pt{miniman(variant) multiplied by the number of K traits, each one of the total X number  of variants would have K number  of t values. Then, for a total X number of variants by K number of traits, a X × K length  vector of t values can be obtained. If t value  in the X × K vector would be prioritised by Eq. For Eq. X × K TC of trait by variant was achieved, two additional pieces of information can be estimated. One was the count of the traits assigned to each variant in the X × K vector and this was the observed TE for each variant. The other was the count of the variants with positive Π assigned to each trait in the X × K vector and this was the identification of the pleiotropic variants related to each trait, variantstrait. See the online tutorial for using EDME to quantify pleiotropy and to do other related analyses at https://ruidongxiang.com/effect-direction-meta-analysis-edme-of-gwas/.Once a prioritised set of trait in overlaps between 34 CT trait sets were counted. The significance of overlaps were compared with the expected number using the hypergeometric test (p) using the variant-overlap matrices generated by GeneOverlap41 in R. This analysis required four types of counts: the size of overlap between set A  and set B , the size of set A, the size of set B and the size of background . The number of variants in the overlap and in the union of pleiotropic variantstrait between traits was obtained. The number of overlapping dividing the number of the union was used to calculate the sharing index for each trait pair. For each trait, its sharing indices with the other 33 traits (excluding self-pair) were averaged and the averaged sharing index was then used to rank each trait.The number of pleiotropic variantst values  for those 93,513 variants prioritised by p value and multi-trait EDME were used as variant input for GSMR. Settings of MR followed the default options of GSMR, including the threshold of HEIDI outlier test being p < 0.01. Both forward and reverse analysis were conducted. GSMR generated MR p values were corrected for multi-testing by the Bonferroni method. A putative causal relationship was defined as the forward MR was significant and the reverse MR was not significant at Bonferroni corrected p < 0.05 level.This analysis was conducted using GSMRtrait identified by the multi-trait analysis, their single-trait GWAS from bulls and cows were mapped and were analysed for single-trait FDRed using Eq. 18 and their enrichment in each set of variantstrait was tested using the hypergeometric test. The p value of enrichment was adjusted for multi-testing.For each set of variants37 function. The model for the joint analysis was the same as Eq. t value was re-calculated based on the beta (‘bJ’) and se (‘seJ’) generated from the joint analysis for each trait using Eq. t values were presented in Fig. The joint analysis was conducted using GCTA-COJO35) contained the whole genome sequence of cattle independent of the Australian data with no phenotype but with breed information. To perform a validation test without phenotype in the validation population, we used the genotypes of selected variants and 37 raw traits  prioritised by EDME and p value, (2) prioritised by p value alone and (3) a random set of variants with the matching variant number. These 3 sets of genomic prediction equations were generated for each of the 37 original traits  in both the bull and cow data sets. The summary statistics of these 37 raw traits were given in Supplementary Data N = 2334).The genomic best linear unbiased prediction (gBLUP) implemented in MTG2N = 567), Jersey (N = 66), Brown Swiss (N = 148), Finnish Ayrshire (N = 25), Normandy (N = 44), Norwegian Red (N = 24), Swedish Red (N = 16). The 1000-bull beef cattle included Angus (N = 272), Beef Booster (N = 29), Belgian Blue (N = 16), Blonde d’Aquitaine (N = 26), Braunvieh Beef (N = 4), Charolais (N = 128), Hereford (N = 75), Limousin (N = 82), Maine Anjou (N = 5) and Simmental (N = 225). The mean of gEBV of the 1000-bull dairy and beef cattle were compared using a t test. For the t test of each trait between dairy and beef cattle, a t value was calculated as the mean difference (with reference level set to beef cattle) divided by the standard error and this t value was presented in Fig. The dairy cattle in the 1000-bull genome included Holstein N = 56, Jersey Further information on research design is available in the Peer Review FileReporting SummarySupplementary Data 1-12Description of Additional Supplementary FilesSupplementary Information


R2 = 0.032; liability R2 = 0.017; P < 10−52), Latino , and European individuals , further highlighting the advantages of incorporating data from diverse human populations.Schizophrenia is a common, chronic and debilitating neuropsychiatric syndrome affecting tens of millions of individuals worldwide. While rare genetic variants play a role in the etiology of schizophrenia, most of the currently explained liability is within common variation, suggesting that variation predating the human diaspora out of Africa harbors a large fraction of the common variant attributable heritability. However, common variant association studies in schizophrenia have concentrated mainly on cohorts of European descent. We describe genome-wide association studies of 6152 cases and 3918 controls of admixed African ancestry, and of 1234 cases and 3090 controls of Latino ancestry, representing the largest such study in these populations to date. Combining results from the samples with African ancestry with summary statistics from the Psychiatric Genomics Consortium (PGC) study of schizophrenia yielded seven newly genome-wide significant loci, and we identified an additional eight loci by incorporating the results from samples with Latino ancestry. Leveraging population differences in patterns of linkage disequilibrium, we achieve improved fine-mapping resolution at 22 previously reported and 4 newly significant loci. Polygenic risk score profiling revealed improved prediction based on trans-ancestry meta-analysis results for admixed African (Nagelkerke’s  Schizophrenia is a common ~0.6–1%), chronic and debilitating neuropsychiatric syndrome for which most of the variability in liability is attributable to genetic factors (~80%) %, chroni–11, mostThe past decade has seen the successes of psychiatric GWAS abound, including the first definitive demonstration of polygenic influences on schizophrenia risk and its shared basis with bipolar disorder , and eveThe largest genome-wide association studies (GWAS) have disproportionately focused on cohorts of European descent , 18, 19.N = 2259 African-American individuals) [To our knowledge, the largest schizophrenia cohort of African ancestry that has been genotyped is the Molecular Genetics of Schizophrenia (MGS-AA) study  , 24, 25.viduals) . It is bviduals) –28, owinviduals) , 30.We have undertaken the largest GWAS of admixed African individuals to date, with a combined sample size of 6152 schizophrenia and schizoaffective disorder cases and 3918 screened controls from the Genomic Psychiatry Cohort (GPC). With available sample sizes now on a par with earlier European GWAS that yielded the first replicated, genome-wide significant associations with single nucleotide polymorphisms (SNP), we consider evidence of novel genetic associations and assess trans-ancestry replication support for 128 independent associations  identified in the landmark study of the Psychiatric Genomics Consortium Schizophrenia Working Group (PGC-SCZ2). We consider the implications of the pronounced underrepresentation of African and Latino populations in psychiatric GWAS and highlight the potential for improved fine-mapping resolution at identified risk loci by incorporating data from diverse populations.The GPC is a large cosmopolitan sample of repository and newly ascertained schizophrenia and bipolar disorder cases and screened controls, with considerable representation of individuals with African, European, and Latino ancestries. In the present analysis, we considered as cases all individuals with a diagnosis of schizophrenia or schizoaffective disorder. Details of ascertainment and diagnosis are given in the Supplemental Material.N = 33,422 participants was performed on Illumina Infinium arrays in a total of 11 “batches”   and defaNeff = 4/(1/Ncases + 1/Ncontrols). We preferentially assigned samples to batches with smaller ratios of Neff∶N when this was ameliorative of case−control imbalance, and updated batch-wise values of Ncases, Ncontrols and Neff after each assignment.We used the KING software package  to identPrincipal components analysis (PCA) was performed with GCTA v1.2.4) , using a.2.4 , usWithin each broadly defined ancestry group, we tested for association between imputed genotype dosages and a diagnosis of schizophrenia (or SAD) by logistic regression using PLINK , 37, andhttps://www.med.unc.edu/pgc/results-and-downloads) and have been widely utilized in dozens of follow-up studies, and thus represent a meaningful benchmark for genetic analysis. We apply the same filters for SNP association results as described in the original study  and interpret the PGC-SCZ2 results as being broadly representative of findings based on European populations.In our primary trans-ancestry meta-analyses, we combine genome-wide summary statistics for African and Latino ancestry GWAS with the PGC-SCZ2 study results. The discovery phase of PGC-SCZ2 included 34,241 cases and 45,604 controls from 46 European and 3 East-Asian case-control studies, and 1235 parent affected offspring trios from 3 family-based samples of European ancestry [r2 < 0.1 within a 500 kilobase (kb) window) using the 1KGP Phase 3 European (EUR) data, and preferentially retaining the most significant SNP in the PGC-SCZ2 analysis . For varying P value thresholds applied to the PGC-SCZ2 results, we used a binomial sign test to determine if the proportion of same-direction effects in the admixed African or Latino analyses was greater than expected by chance . Reciprocal analyses comparing the observed directions of effects in PGC-SCZ2 to the African and Latino ancestry results were also performed, with LD-clumping based on the corresponding 1KGP reference population.Linkage disequilibrium (LD) based “clumping” was used to obtain approximately independent sets of SNPs (r2 < 0.1 within a 500 kb window); for analyses of African, Latino, and European cohorts, we utilized reference data for AFR, AMR, and EUR populations, respectively. For SNPs significant at varying P value thresholds (PT) in the training dataset, individual-level scores were constructed by summing the number of copies of a given allele by its corresponding effect estimate . We evaluated the significance of case−control differences using logistic regression and covarying ancestry-based principal components (PCs) and a study indicator variable. Predictive values of these scores are reported both in terms of Nagelkerke’s pseudo-R2 (fmsb package in R) [r2) to 0.5 and 0.8.We performed polygenic risk score profiling based on the PGC-SCZ2 summary statistics (the “training” dataset), testing these scores for association with case−control status in African, Latino, and European cohorts from the GPC (the “target” datasets). For each pair of training and target datasets, results for overlapping SNPs (or indels) meeting quality control requirements  were subjected to LD-based clumping in the appropriate reference population from the 1KGP (ge in R)  as well ge in R) . We examBecause genetic prediction is generally worse when comparing training and testing datasets of divergent ancestry, with greater attenuation of predictive value for more divergent populations , 28, 41,P value <10−6 in the publicly available PGC-SCZ2 summary statistics. For each index SNP, we considered SNPs correlated at r2 ≥ 0.6 within a 3 megabase window which had P < 10−4 in the PGC-SCZ2 discovery analysis. We constructed credible SNP sets by combining their posterior probabilities until the sum exceeded 99%, following the approach of Huang et al. [P value among these SNPs; we followed-up regions attaining greater significance in the combined PGC-SCZ2/GPC-AA analysis and for which the credible set in the combined analysis represented a shorter genomic interval than the corresponding interval in the PGC-SCZ2 analysis. We considered a region to be “fine-mapped” if the genomic interval for the reduced credible set was smaller than the corresponding interval for SNPs with LD r2 ≥ 0.6 to the index SNP (based on 1KGP EUR reference data).We attempted to fine-map 276 autosomal and X-chromosome regions around statistically independent SNPs with association g et al. . Crediblλ) and its value scaled to a sample size of 1000 cases and 1000 controls (λ1000) from genome-wide distributions of test statistics; these values were 1.04 and 1.008 for the admixed African GWAS, and 1.055 and 1.031 for the Latino GWAS, indicating that our results are not likely to be confounded by population substructure.Manhattan and quantile−quantile (QQ) plots for GWAS of admixed African and Latino ancestry individuals are presented in the Supplemental Material . In the Latino ancestry GWAS, we identified a novel genome-wide significant association with SNPs in GALNT13 on chromosome 2q23.3  .Our primary GWAS in admixed African individuals did not yield any SNP findings that reached the accepted threshold for genome-wide significance  accounting for a larger fraction of the genome. This is explainable by the greater degree of statistical enrichment of the PGC-SCZ2 results and corresponding larger number of independent significant findings. The larger number of statistically independent tests genome-wide in the African ancestry GWAS was a reflection of the lower background LD in the African ancestry reference data from the 1KGP. We observed similar results when restricting analyses to individuals with at least 75% African ancestry genome-wide , we observed the best overall prediction at a P value threshold (PT) of 0.05; these scores explained ~3.5% of the variance in schizophrenia liability among Europeans (P = 4.03 × 10−110), ~1.7% among Latino individuals (P = 9.02 × 10−52), and ~0.5% among admixed African individuals (P = 8.25 × 10−19)  Fig. . Consistr2 < 0.1) with PT ≤ 0.5 in the discovery analysis . Scores trained on African ancestry GWAS results also significantly predicted case−control status across populations; scores based on a PT ≤ 0.5 and pairwise r2 < 0.8 explained ~0.2% of the variability in liability in Europeans (P = 2.35 × 10−7) and ~0.1% among Latino individuals (P = 0.000184)  were of greatest predictive value among Latinos  and Europeans ; with scores based on PT ≤ 0.05 and pairwise r2 < 0.1 showing nominally significant association with case-control status among African ancestry individuals .Polygenic scores based on African ancestry GWAS results were significantly associated with schizophrenia among admixed African individuals, attaining the best overall predictive value when constructed from approximately independent common variants ; while scores based on PT ≤ 0.05 accounted for ~2.1% and ~3.7% of the variability in liability among Latino (P = 1.10 × 10−59) and European individuals (P = 1.73 × 10−114), respectively.We next considered polygenic scores constructed from trans-ancestry meta-analysis of PGC-SCZ2 summary statistics and our African and Latino GWAS, which revealed increased significance and improved predictive value in all three ancestries. Among African ancestry individuals, meta-analytic scores based on PT, joint models incorporating both PGC-SCZ2 and ancestry-specific scores yielded significant improvements in goodness-of-fit .We also considered whether these schizophrenia polygenic risk scores also indexed risk of bipolar disorder in independent cases from the GPC. We observed a similar pattern of findings as those reported above, albeit with systematic attenuation of signal in terms of explained variance and statistical significance, which is expected .The degree of improved fine-mapping resolution varied between loci, and in two instances was reduced to a single SNP , polygenic scores based on a larger European cohort showed attenuated effects in the MGS-AA sample , reflectGALNT13 at 2q23.3. This locus encodes polypeptide N-acetylgalactosaminyltransferase 13, which has been shown to be specifically expressed in neurons and may be responsible for synthesizing Tn antigen; the 3′ UTR region contains two microRNA target sequences. The associated allele at the leading SNP at this locus (rs776877) has an odds ratio of ~1.4, which is larger than expected given that the majority of associated variants in PGC-SCZ2 have an odds ratio less than 1.2. This may be attributable to the phenomenon described as “winner’s curse” [Q = 33.1605; P = 6.30 × 10–8; I2 = 93.97%). It is also worth noting that a prior study of psychosis in Mexican and Central American families yielded some evidence of linkage to 2q33 [GALNT13 as a schizophrenia risk locus will require detailed follow-up and replication in an independent Latino cohort.While GWAS of schizophrenia in admixed African ancestry individuals did not yield any genome-wide significant findings, our analysis of Latino cases and controls revealed a novel genome-wide association with SNPs in s curse” . This SN to 2q33 . HoweverP < 10−6 in the PGC-SCZ2 discovery phase but did not attain genome-wide significance in a combined analysis with 1513 cases and 66,236 controls from deCODE genetics. It is noteworthy that the effective sample size (Neff) of the deCODE replication sample—the total sample size adjusted for imbalanced numbers of cases and controls—is smaller than the effective sample size of the African ancestry cohort (Neff = 5 917 vs. Neff = 9 574). That we observed fewer genome-wide significant associations overall is consistent with expectation that gains in statistical power from increasing sample size will be largest when adding ancestry-matched subjects. With greater “genetic distance”  between the discovery and replication samples, we would expect greater attenuation in terms of realized gains in statistical power relative to increase in sample size. For example, consider that meta-analysis with Latino results (Neff = 3 527) yielded 101 loci, including 12 newly replicated loci.Meta-analysis of African ancestry results with PGC-SCZ2 summary statistics yielded 94 associated loci, of which 11 were not among the 108 previously reported, and 7 were newly genome-wide significant. These additional loci were significant at Comparing the 18 newly significant loci reported here  to identify a likely causal variant at an associated locus , 48, andWe do not specifically model admixture within individuals or adjust for local ancestry in tests of common variant association, instead adjusting for global ancestry proportions within broadly defined ancestry groups. Importantly, our resultant test-statistic distributions do not suggest significant confounding by population substructure. It is likely that much larger samples of African and Latino ancestry are needed to capture the extensive genetic diversity present in these populations , 52.We do not give specific consideration to enrichment of observed associations in particular biological pathways or other functional annotations (e.g. tissue-specific eQTLs), or evidence of cross-ancestry and cross-trait genetic correlations. This is in part owing to our concern that many current and trending methods utilize reference LD information, and the suitability of these data to admixed populations is an unresolved, empirical question.We have conducted the largest GWAS of schizophrenia among admixed African individuals to date and demonstrate the potential of more diverse studies to refine the catalog of schizophrenia risk loci and enhance the generalizability of aggregate genetic findings. Addressing disparities in representation of African and Latino ancestries in psychiatric genetics research presents both scientific opportunities and imperatives , necessiSupplemental Materials