We extended cross variance and covariance variance prediction to includedominance effects and predicted the multivariate selection index genetic variance ofcrosses based on haplotypes of proposed parents, marker effects, and recombinationfrequencies. We combined the predicted mean and variance into usefulness criteria forparent and variety development. We present an empirical study of cassava (Manihotesculenta), a staple tropical root crop. We assessed the potential to predictthe multivariate genetic distribution  of 462cassava families in terms of additive and total value using cross-validation. Mostvariance (89%) and covariance (70%) prediction accuracy estimates were greater than zero.The usefulness of crosses was accurately predicted with good correspondence between thepredicted and the actual mean performance of family members breeders selected foradvancement as new parents and candidate varieties. We also used a directional dominancemodel to quantify significant inbreeding depression for most traits. We predicted 47,083possible crosses of 306 parents and contrasted them to those previously tested to show howmate selection can reveal the new potential within the germplasm. We enable breeders toconsider the potential of crosses to produce future parents  and varieties (progeny with top own performance).Diverse crops are both outbred and clonally propagated. Breeders typically use truncationselection of parents and invest significant time, land, and money evaluating the progenyof crosses to find exceptional genotypes. We developed and tested genomic Consider a breeding program implementing some form of genomic selection (GS). Selection to drive improvement in thepopulation’s mean over time to meet the objective of RS centers on allele-substitutioneffects and the breeding value (BV). For the VDP, selecting clones to advance for testingshould be based on the total genetic value (TGV) of an individual which includesnonadditive genetic effects such as dominance.Nonadditive effects can be included in genomic predictions in a number of ways . Predictand variance are available. Theusefulness criterion (UC) or simply “usefulness” of a cross is a prediction of the meanperformance of the selected superior fraction of the progeny: σ is the predicted genetic standarddeviation of the progeny and i is the standardized selection intensity and usefulness for varietydevelopment . Finally, since matings are usuallychosenbased on multiple traits, we extend the prediction to cross variance on SI. We showthat to predict index variance, we must predict the full matrix of trait genetic variancesand covariances  breeding program.Cassava is one of the most important tropical staple foods, especially in Africa(http://faostat.fao.org). Among outbred,clonal crops, GS is relatively mature in cassava breeding , and the species can serve as a model for many others. We leverage a validatedGS pedigree with genome-wide phased haplotypes and a genetic map (https://wolfemd.github.io/PredictOutbredCrossVar/).We present an empirical study of the accuracy for predicting additive and nonadditivegenomic mate selection criteria. We set up a cross-validation scheme that measures theaccuracy of predicting means, variances and usefulnesses of previously untested crossesusing data from a real cassava  or crosses (for MSG) forRS vs VDP.Below, we describe predictions that are applicable as selection criteria, first forgenomic truncation selection TSG) evaluates existing individuals,either for their potential as parents (without regards to specific mates) and/or theirpotential as clonal cultivars. Under a nonepistatic model, the TGVs of individuals in thecurrent population (time t) can be partitioned into a BV (BVg)and a dominance deviation DDg. Genomic recurrent TS  that correspond toallele substitution and dominance deviation effects  and the noncounted (reference-genome) allele, respectively, forone of the two parents (indexed by i). The difference in frequencybetween the parent one (indexed by i) and the parent two (indexed byj) is,p markersindexed by k. Note that ka is the averageeffect and not the allele substitution effect, αestimated by the additive-dominance parameterization presented above. As a result,predicting TGVμ with the formula above may not be appropriate.We adopt a suitable additive-dominance partition, described below, in our primaryanalyses.Here, D, having the effect of squaring all elements.The within-cross additive genetic variance can be predicted deterministically, relying onthe formula for the genetic variance under linkage disequilibrium using Equation 5.16a to predip × p variance-covariance matrix,D, is the expected linkage disequilibrium amongfull-siblings by considering the expected pairwise recombination frequency and eachparent’s haplotype phase. p × pcovariance matrices associated with each parent’s respective p is a vector ofwithin-individual, per-SNP allele frequencies  of the superior progeny from a cross, e therefore distinguish two UCs: vs In the context of the two-part breeding scheme for GS in clonal crops, crosses may beuseful for producing both new parents and new varieties. We, therefore, defineCvariety .Notice  the VDP .Parent selection is often done based on a multi-character selection index (SI). Crossescan be considered for their potential to produce progeny with good merit on one or more SIby first predicting the variances and covariances for each trait on the SI (T1 and T2. Predict (co)variances for all traits on SI. Consider an index with two traits,d and squaring elementsof D. Apply to dominance by substituting Compute the predicted mean and variance on the SI. n × T matrix w are the indexweights. The T × T matrixG is the additive  genetic variance-covariancematrix for traits on the index. The i.e., theBased on these predictions of family means, variances and trait-covariances, we cancompute the mean of selected family members on the index  and subtracting that value from the vector ofdominance effects, to get The scalar a andd do not correspond to allele substitution and dominancedeviation effects directly, but the sum of variance components still equals theAs a result the effects http://www.nextgencassava.org) hasimplemented GS in African and Latin American breeding programs . The pedigree andgermplasm chosen represent parents and offspring from the first three cycles of GSconducted at the International Institute of Tropical Agriculture (IITA). These germplasmand genomic selections have been described in greater detail previously . These traits include both polygenic (DM and logFYLD) and mono/oligenicarchitectures (MCMDS and TCHART). Two of the traits are known to have important dominancevariance (logFYLD and MCMDS), while DM has been shown to be largely additive , fresh root yield innatural-log tons-per-hectare (logFYLD), season-wide mean cassava mosaic disease severity, and total carotenoids by color chart  in thepedigree, including the parents  allowed measurement of the accuracy ofpredicting means, variances, and covariances in previously unobserved crosses, and (2)enabled us to distinguish accuracy predicting BV from TGV. First, define a vector,We conducted five replications of the following procedure: P into k-folds. We chosek = 5 folds or about 42 of 209 parents inP per fold , divide theclones vector C into two mutually exclusive sets:“training” (C and For each of the Estimate marker effects independently by fitting mixed-models (see section below forfurther details) to For each GEBV and GETGV as predicted by theFor each family in BV andTGV. For GEBV/GETGV. For GEBV/GETGV according to the family size (Rpackage::function psych::cor.wt).For sake of comparison, we also include accuracies in the supplement where predictedvalues are correlated to phenotypic (rather than genomic-predicted) BLUPs,e.g., Calculate the accuracy of prediction for each mean .https://github.com/gdlc/BGLR-R), which is itself a direct port of the modelimplemented in the package MTM (We used the multi-trait Bayesian ridge regression (MtBRR) implemented in the developmentversion of the BGLR R package , TMS13, TMS14, and TMS15, whichrepresent the offspring from 2013 (C1), 2014 (C2), and 2015(C3), respectively.We fit an MtBRR to each PMV for each prediction in the cross-validation study and in estimatingpopulation genetic variances. In the Supplementary Appendix, we made a brief comparison ofPMV and VPM and based on these results, used VPM in theexploratory predictions, which are described below. We computed SI means and variancesusing the predicted (and sample) means, variances and covariances of the component traits,and the index weights, given in Supplementary Table S1.We predicted cross means using the posterior mean marker effects. For variancepredictions, GEBV and GETGV based on test-set marker-effects to compute observed usefulness criteria i.e., GEBV of family memberswho were themselves later used as parents. We computed GETGV of family membersadvanced to the penultimate stage of the VDP, the advanced yield trial (AYT). In order tocombine predicted means and variances into usefulness criteria, i.e.,propSel is the proportionselected.We used i.e., N = 306parents). This resulted in 47,083 crosses to predict. We used marker-effects from thefull-model . We predicted means, variances, and covariances for allfour traits and subsequently used these to compute StdSI and BiofortSI means andvariances.We conducted a prediction exercise evaluating the interest of possible future crossescompared to those previously made in terms of additive and total merit,The dataset we analyzed does not include all traits or germplasm relevant to the IITAbreeding program. For that reason, our results especially regarding the potential benefitsof new matings are meant as an example. Assessment of the actual best new matings to makein the ongoing breeding program will rely on a broader analysis.workflowr R markdown website .Results along with code generating summaries, figures, and related tables are alsoavailable as part of the Pedigree and Germplasm: There were 3199 individuals in 462 families, derivedfrom 209 parents in our pedigree. Parents were used an average of 31  times as male and/or female parents in the pedigree. The mean family size was 7. The average proportion of homozygosity was 0.84 (range 0.76–0.93)across the 3199 pedigree members . As expected for a population under RS, the homozygosity proportion increased with eachgeneration with C0, C1, C2, and C3 having homozygosity proportion of 0.826, 0.835, 0.838,and 0.839, respectively .Cross-validation Scheme: Across the 5 replications of fivefoldcross-validation, the average number of clones was 1833 (range 1245–2323) for training setsand 1494 (range 1003–2081) for testing sets. The 25 training-testing pairs set up an averageof 167 (range 143–204) crosses to predict (Supplementary Table S2).BLUPs and  SI: The correlation between the two SI  based on i.i.d. (nongenomic) BLUPs ofcomponent traits was 0.43 . The correlation between DM and TCHARTBLUPs was −0.29.Across traits, most accuracy estimates (more than 75%) were lower for prediction offamily-mean TGV than for mean BV (median difference TGV-BV = −0.017). The only exceptionwas for yield (logFYLD), where TGV>BV, median increase of 0.13 (Most (89%) of variance prediction accuracies were greater than zero, with median accuracy0.14 across traits .Most estimates (95%) of UC accuracy were greater than zero, with per-trait accuracieslargely similar to the family-mean predictions. Indeed, the overall correlation betweenmean and UC accuracies was 0.75. As might be expected, given the incorporation ofvariance-predictions and the more limited validation sample size, the UC accuracy was onaverage lower by −0.09 compared to the family-mean accuracy -populations is an important topic, which we mostly leave forfuture study. We make a brief examination of the genetic variance-covariance estimatesassociated with the overall population and component genetic groups. We report allPMV-covariance estimates in Supplementary Table S15 and complete BGLR output in therepository associated with this study. We focus here on genetic variance-covarianceaccounting for LD, as in We found that genome-wide estimates of the effect of homozygosity were consistentlynegative for logFYLD with a mean directional dominance regression coefficient of −2.75log(tons/ha) across genetic groups . Inaddition, DM estimates indicated inbreeding depression effects in several genetic groupsand the majority of cross-validation folds with mean directional dominance regressioncoefficient of −4.82 percent dry matter across genetic groups  and similarly for MCMDS, mean inbreeding effect of 0.32 worsedisease severity across genetic groups .This corresponds to higher homozygosity being associated with lower DM, lower yield, andgreater disease severity  for each of 47,083 possible crosses of 306 parents. We examined thecorrelation structure among these predictions in order to understand the multivariatedecision space they describe (The two SI are (by design) disparate breeding goals. The mean correlation (across var.components) between SIs was low for predictions of the family mean (0.20) and lower forthe UC (0.14), but high for the SD (0.91). The predictions of BV and TGV were stronglycorrelated with 0.95 (0.96) for predicted cross means on the StdSI (BiofortSI), 0.88(0.91) for predicted genetic standard deviation, and 0.93 (0.95) for UC.The predicted cross means and variances had a low, but negative correlation . Across μ vs theσ  and the parent vsUC thevarietyUC . In total, only 202 unique crosses wereselected based on their rank on at least one of the 8 predictions. Of those, 112 wereselected for the StdSI (90 Biofort) and included only 7 (6) self-crosses. No crosses wereselected for both SI. None of the selected crosses have previously been tested in the IITAbreeding program. We plotted the predicted vs theσ  and the Cvariety . We highTMS13F1095P0013).Only 33 parents among 90 “best” crosses were indicated for the BiofortSI with a mediancontribution to 4 crosses. both BV and TGV. Self-crosseswere only selected based on BV. In fact, 22 of 44 parents selected on the StdSI werechosen only for the TGV of their crosses and 4 only for their BVs . As judged by the numberof times a cross was chosen given the four selection criteria, there are 58 unique crossesin the top 50 for the StdSI and 66 for the BiofortSI. This demonstrates a relativelysimple approach for selecting the overall best crosses based on the four predicted mateselection criteria.There were 44 parents represented among the 112 “best” crosses for StdSI with a medianusage in 3 families each  are of direct interest as futureparents and/or cultivars (varieties). We focused on the prediction of the SI-associatedgenetic variance of crosses based on the haplotypes of proposed parents, estimates of markereffects, and estimates of recombination frequencies between marker loci. We combined thepredicted mean and variance of a cross into usefulness criteria for parent (We developed and tested genomic mate selection criteria suitable for multi-trait indexselection in organisms of arbitrary homozygosity level where ther= −0.22). This suggests that, for a given phenotype, breeding programs cannot simply relyon available estimates of family-mean prediction accuracy to determine the adequacy offamily-variance predictions. The UC and family-mean accuracy estimates were reasonablycorrelated (r = 0.75).We worked with 462 real cassava families of heterogeneous size. We made practical use ofthe available data in implementing the parent-wise cross-validation scheme. We found thatprediction accuracy for family means were largely similar to our previously publishedestimates . Variancvs low genetic variances.Previous studies of variance-prediction accuracy evaluated relatively few families, butwith larger size  progeny . If anybias is consistent, then ranking differences between PMV and VPM (or REML) predictions ofcross variance will not occur. Ultimately, if implementing mate selections via theusefulness criteria, choosing the VPM method would mostly have the consequence ofshrinking the predicted values toward the mean.In some circumstances, for computational efficiency, it may be desirable to use the VPMrather than the PMV approach to predict cross variances. Our results show that thecorrelation between VPM and PMV predictions is very high e.g., Other critical considerations for practical implementation include the necessary phasingquality and method. We leveraged a dataset imputed and phased using a validated pedigreee.g., . Promisimany outbred, clonal crops are actually polyploids. For organismswith such genomes, further developments in recombination mapping, phasing, and predictionmodels will be required, but are expected to be possible. In our study, we focused ontrait-associated variance prediction. Considerable development of mate selection criteriahas concerned the avoidance of genetic diversity loss generally, theseare approaches that constrain inbreeding  as a correlated trait, usingan extension of the approach for prediction trait-associated variance.Several extensions and future directions are of interest moving forward from the currentstudy. We have only addressed dominance, but extensions of variance prediction to includeepistasis or even nonlinear kernel types should be straightforward  breeding program. We presented a simple approach forgenomic truncation mate selection that identifies a profile of crosses collectivelyinteresting because of the predicted merit of their progeny in terms ofBy providing predictions of the selection-index-associated means ftp://ftp.cassavabase.org//manuscripts/Chan_et_al_2019. The full repositoryfor this study including all data and output can also be accessed through the CassavabaseFTP server by choosing "Guest" credentials, here: ftp://ftp.cassavabase.org//manuscripts/Wolfe_et_al_2021. Alternatively, allfiles are also available through the Cassavabase FTP server-archive: https://cassavabase.org/ftp/manuscripts/Wolfe_et_al_2021/. The repository,minus large data files, can be found on GitHub, here: https://github.com/wolfemd/PredictOutbredCrossVar/. We used Rmarkdown and theR package workflowr  to document our empirical analysis asa fully reproducible website: https://wolfemd.github.io/PredictOutbredCrossVar/. Finally, we implemented thecore functions for multi-trait prediction of outbred cross variances including additive anddominance effects in an R package predCrossVar, repository on GitHub: https://github.com/wolfemd/predCrossVar}, package reference manual: https://wolfemd.github.io/predCrossVar/, which we used in the aforementionedanalyses. Supplemental Material available at figshare: https://doi.org/10.25386/genetics.14569044.We accessed the pedigree, genetic map and haplotypes from the Cassavabase FTP serverrepository for Chan et al. 2019:


However, unlike genotypes where the best is usually adjudged through statistical ranking, locations are judged against a benchmark, particularly when phenotyping for disease severity. It was also found that the locations represent one complex mega-environment, justifying the need to test new technologies, including genotypes in all of them before they can be approved for adoption nationally. Again, depending on the phenotypic level considered, genotypic rankings may change, causing environmental groupings to change. For instance, all locations clustered to form one group in 2017 for early and late leaf spot diseases and pod yield when GE was considered, but the groupings changed when G+GE was considered for the same traits in the same year. As a result, assessing genotypic performance at the various levels to arrive at a consensus decision is suggested. Genotypes ICGV-IS 141120 and ICGV-IS 13937 were found to be the best performing.In this study, the differential rankings of 36 groundnut genotypes under varying environmental conditions were studied at various levels of phenotype. Locations that are generally accepted by the crop- and soil-based research community to represent the entire Guinea and Sudan Savanna agro-ecological zones in Ghana were characterized, this time using a crop. The characterization was done based on four farmer-preferred traits  using three models . These models were used to capture specific levels of phenotype, namely, genotype-by-environment interaction (GE), genotype main effect plus GE (G+GE), and environment and genotype main effects plus GE (E+G+GE), respectively. The effect of three major environmental covariables was also determined using factorial regression. Location main effect was found to be highly significant ( Arachis hypogaea L.) is a leguminous oilseed crop grown in the semi-arid and subtropical regions across 40° north and south of the equator  compared with that of the Americas  . This has resulted in the identification of superior genotypes that are better in specific locations  or across locations in a range of crops including groundnuts Padi, . Most st−1; plot−1), number of pods (plot−1), hundred pod weight, and number of seeds (plot−1) in groundnut  categorize the target environment of CSIR-SARI groundnut breeding program into test locations using models that capture various components of the overall phenotype and (ii) determine the effect of GE on trait associations at the various levels of the phenotype.2. Plants were spaced at 0.4 m between rows and 0.1 m within rows.Field experiments were conducted in two seasons (2017–2018) under rain-fed conditions. In the 2017 season, the experiments were conducted at Manga, Damongo, Nyankpala, and Silbele, while in the 2018 season, Tanina was added as an additional location . The loc−1) was applied immediately after planting to suppress weeds followed by one-hand weeding before pegging. Phosphorus in the form of triple super phosphate was applied as a basal fertilizer at the rate of 125 kg ha−1 (100 g plot−1) just after seedling emergence. The plants were further supplemented with calcium by the application of 400 kg ha−1 Omya Calciprill® (38% Ca and 0.6% Mg) between 20 and 25 days after sowing. All other recommended agronomic practices in groundnut production were adhered to. Data were collected on severity of early leaf spot (ELS) and late leaf spot (LLS) diseases as well as pod yield  in 2017. In 2018, data on above ground dry matter  were also recorded in addition to all the datasets recorded in 2017. The ELS and LLS severity were scored on a scale of 1–9, with 1 representing complete resistance and nine representing complete defoliation of plants  – ti = time in days between two sequential disease scores. High AUDPC value represents high disease susceptibility.where YNormality of data was checked using the Shapiro–Wilk test. In situations where the data did not follow the Gaussian distribution, data transformation using the Box–Cox procedure  is the effect of block j nested within replicate i, gk is the effect of genotype k, and εijk is the residual. Significance of the fixed variables and effect estimates was tested and computed using Wald test with car , Error is used; otherwise, Pure Error is used in F-tests.In addition to the traditional model diagnosis, the functions make the in Gauch ]. As a rRelationship among traits at the various levels of phenotype was determined based on Pearson's correlation. The correlation analysis was done and visualized using the agricolae and corrplot  regression. AMMI and FW regression were done using agricolae  for all traits studied in 2017 and 2018 (p < 0.001) different from the other locations. Also, the haulm yield obtained in Nyankpala differed from that of Manga in both years, with Manga being among the lowest in both years. Damongo had the highest  pod yield in 2017, while Silbele had the lowest  across all locations in 2017 and differed from that of 12CS-116, ICGV 86124, ICGV-IS 131091, ICGV-IS 14849, ICGV-IS 13871, and 12CS-098 (p ≥ 0.05). In contrast, genotype ICGV-IS 13937 had the highest pod yield  but did not differ from that of ICGV-IS 07947, ICGV-IS 141120, and ICGV-IS 13842, while genotype ICGV-IS 131065 was the lowest in 2018 (−1), and there was no significant difference between this genotype and ICGV-IS 14849, ICGV-IS 131091, ICGV-IS 131051, or ICGV-IS 13984.The genotype, ICGV-IS 141120, had the highest pod yield  for all the studied traits in 2017 (S) captured by the interactive principal components (PCs) for ELS disease and haulm yield were 71.15 and 95.79%, respectively.The environment and genotype main effects as well as the GE were statistically significant ( in 2017 . However in 2017 . The sigp > 0.05) for ELS, although the AMMI model diagnosis based on Gollob's test suggested AMMI1 as the appropriate model for this trait. On the other hand, AMMI3, 1, and 3 were suggested as appropriate models for haulm yield, LLS, and pod yield, respectively. However, signal–noise estimation showed AMMI0 as the appropriate model for ELS and LLS diseases, with AMMI1 being appropriate for pod and haulm yields  for all traits, with Gollob's test diagnosing AMMI3 for ELS and LLS diseases and AMMI6 and 4 for haulm and pod yields, respectively  for all traits studied in 2017  for ELS diseases but was significant for haulm yield, LLS disease, and pod yield  when the combined data from 2017 and 2018 were considered (p < 0.05) for ELS, haulm yield, LLS, and pod yield, respectively, from the F-test. Hence, based on Gollob's test, GGE4, 6, 3, and 4 were appropriate for these trait analyses, respectively. However, signal–noise estimation diagnosed GGE1 for all the traits, except haulm yield, which GGE2 was diagnosed for. The GGES was 41.28, 75.34, 40.27, and 59.09% with the captured signal being 60.79, 92.68, 73.13, and 99.30% for ELS disease, haulm yield, LLS disease, and pod yield, respectively , with CHINESE being the most susceptible for Silbele and Tanina for ELS disease . On the When 2017 and 2018 data were jointly considered, the most consistent environmental grouping was observed for pod yield, with genotype ICGV-IS 141120 winning in eight of the nine environments .p < 0.001) for all studied traits  main effect was significant (d traits . Howeverp < 0.05) positive correlation at all levels of phenotype  in all years except for E+G+GE in 2018  with farmer-preferred traits. In this work, a high statistical significance of the location main effect for all traits in both years shows the important contribution of the non-genetic component of phenotype to overall crop performance. It also confirms the most common scenario in multi-environmental trials where the location main effect captures the largest of the total variation Gauch, . Althougp-values from Gollob F-test to select a model family of AMMI and GGE can be misleading  , i.e., AMMI2 and GGE2, respectively Gauch, . With thg Gauch, . For ins Piepho,  and sign Piepho,  are by f Piepho, , underesThe use of different models  in this study was not to determine their robustness in revealing patterns in a MET dataset. That has been discussed extensively in the literature already  mean breeders ought not to ignore the environment in which cultivars are to be placed. Therefore, collaborative cultivar development that will see disciplines such as soil scientists and agronomists actively involved in the breeding process is encouraged.This study uses a comprehensive approach in test location characterization and genotype performance to examine four farmer-preferred traits with model diagnosis and at the various levels of phenotype. The study justified the use of the current test locations  to represent the entire Guinea and Sudan Savanna zones in Ghana during METs. GE was driven by the predictable scenario, although latent yearly/seasonal effect exists.Depending on the phenotypic level  at which genotypes performance are assessed, the best-performing genotype may change. Although different statistical models are used to approximate these phenotypic levels in general, comprehensively assessing genotypic performance and arriving at a decision using this approach will likely result in the identification of the most superior cultivar among a set genotypes evaluated. Considering the MET data from the 2 years independently and at the various levels of phenotype, genotypes ICGV-IS 141120 and ICGV-IS 13937 were selected and recommended for on-farm study due to their superior and consistent performance across the traits considered. Genotype CHINESE will continue to be used as a susceptible check for ELS and LLS disease studies, while ICGV-IS 13834 will be the new additional susceptible check to be added.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.RO-F conceived the study. RO-F, DP, JA-D, and FK designed the experiments and came out with an outline. YK, JN, MR, A-RI, and FK implemented the experiments at the different locations. YK conducted the statistical analysis and produced the initial draft. RO-F and DP edited and improved the draft. All authors read and approved the final 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.


Triticum aestivum L.) from deep planting, has a poorly understood genetic architecture, is a vital factor affecting stand establishment and grain yield, and is historically correlated with coleoptile length. This study aimed to dissect the genetic architecture of seedling emergence while accounting for correlated traits using one multi-trait genome-wide association study (MT-GWAS) model and three single-trait GWAS (ST-GWAS) models. The ST-GWAS models included one single-locus model [mixed-linear model (MLM)] and two multi-locus models [fixed and random model circulating probability unification (FarmCPU) and Bayesian information and linkage-disequilibrium iteratively nested keyway (BLINK)]. We conducted GWAS using two populations. The first population consisted of 473 varieties from a diverse association mapping panel phenotyped from 2015 to 2019. The second population consisted of 279 breeding lines phenotyped in 2015 in Lind, WA, with 40,368 markers. We also compared the inclusion of coleoptile length and markers associated with reduced height as covariates in our ST-GWAS models. ST-GWAS found 107 significant markers across 19 chromosomes, while MT-GWAS found 82 significant markers across 14 chromosomes. The FarmCPU and BLINK models, including covariates, were able to identify many small effect markers while identifying large effect markers on chromosome 5A. By using multi-locus model breeding, programs can uncover the complex nature of traits to help identify candidate genes and the underlying architecture of a trait, such as seedling emergence.Unknown genetic architecture makes it difficult to characterize the genetic basis of traits and associated molecular markers because of the complexity of small effect quantitative trait loci (QTLs), environmental effects, and difficulty in phenotyping. Seedling emergence of wheat ( Complex traits are controlled by many quantitative trait loci (QTLs) and are influenced by environmental conditions . Challenp-value inflation for each marker and reduces false positives  has enabled the discovery of QTLs in a collection of diverse populations or diversity panels rather than using a mapping population . GWAS caositives .p-values due to population structure . Some of the first GWAS models, such as general linear models and mixed-linear models (MLMs), were single-locus, single-trait GWAS (ST-GWAS) models created to implement the covariates along with kinship matrices . Howevertructure . MLMs wetructure . CMLMs wtructure . These mtructure . Comparetructure . These mtructure . FarmCPUtructure . Additiotructure . Correlatructure . MT-GWAStructure . Howevertructure .In Washington state, seedling emergence of deep-sown winter wheat is a complex trait affected by many factors and is dependent on the environment to display variation . SeedlinRht-B1b and Rht-D1b are mutant alleles that cause the semi-dwarfing stature of wheat  at the Washington State University Dryland Research Center in Lind, WA . The plots were planted using a custom-built deep-furrow planting system to a depth of between 10 and 15 cm, depending on moisture variation among years. The plots were planted 1.5 m wide and 6.1 m long with 31 cm row spacing at a density of 120 seed per square meter. Emergence notes were taken on two populations within the breeding program. The diverse association mapping panel (DP) represents a diverse panel of inbred breeding lines (BLs) from Pacific Northwest breeding programs not selected exclusively in deep-furrow trials. In contrast, the second population is composed of FLind, WA . The BLsLind, WA . In 2016Seedling emergence was visually assessed and recorded as a percentage of the total plot that emerged 6 weeks after planting for each trial. Adjusted means from the emergence data collected in the unreplicated trials were adjusted using residuals calculated for the unreplicated lines in individual environments and across environments using the modified augmented complete block design (ACBD) model . The adjijY is the phenotypic value for the trait of interest of the i-th block and j-th check ; μ is the mean effect; iBlock is the fixed effect of the i-th block; jCheck is the fixed effect of the j-th replicated check cultivar; and ijε are residual errors with a random normal distribution of where ijY is the phenotypic value for the trait of interest of the i-th block and j-th check in the k-th environment ; μ is the mean effect; iBlock is the fixed effect of the i-th block; jCheck is the fixed effect of the j-th replicated check cultivar; kEnv is the fixed effect of the k-th environment; and ijkε are residual errors with a random normal distribution of where Best linear unbiased predictors (BLUPs) for heritability were calculated for each trial and across trials using a mixed linear model for the full augmented randomized complete block design in a single environment and is as follows:ijY is the phenotypic value for the trait of interest of the l-th genotype nested in the j-th check in the i-th block ; μ is the mean effect; iBlock is the random effect of the i-th block with the distribution Checkj is the fixed effect of the j-th replicated check cultivar; Genk(j) is the genotype k in the j-th check with the distribution ijε are residual errors with a random normal distribution of where ijklY is the phenotypic value for the trait of interest of the l-th genotype nested in the j-th Check of the i-th block and k-th environment ; μ is the mean effect; iBlock is the random effect of the i-th block with the distribution jCheck is the fixed effect of the jth replicated check cultivar; Genl(j) is the random effect of the genotype l in the j-th check with the distribution kEnv is the random effect of the k-th environment with the distribution ijklε are residual errors with a random normal distribution of where BLUP are the genotype variance and mean-variance, respectively, of a difference between two BLUPs for the genotypic effect BLUPs ; Genl(j) is the random effect of the l-th genotype with kEnv is the random effect of the k-th environment with Repm(k) is the random effect of the replication m in the k-th environment; and ijklε are residual errors with a random normal of distribution of where Adjusted means for coleoptile length were calculated across trials using a linear model as follows:lmY is the phenotypic value for the trait of interest of the k-th environment of the m-th replication ; kEnv is the fixed effect of the k-th environment; Repm(k) is the fixed effect of the replication m in the k-th environment; and ijkε are residual errors with a random normal distribution of where Phenotypic correlations were conducted between seedling emergence in the DP across years along with coleoptile length. Due to the unreplicated nature of the seedling emergence phenotypes, genetic correlations between seedling emergence in the DP and coleoptile length was calculated using the R package “sommer” with the multivariate Newton-Raphson algorithm used for multiple random effects and covariance structures using the multivariate model in AY and BY are vectors  of trait-adjusted means for emergence using models 1 and 2, and adjusted means for coleoptile length using model 7, respectively. βi is a vector  of fixed effects of PCs, iu is a vector  of random effects for individuals with iε is a vector  of residuals with X and Z are incidence matrices for fixed effects  and random genetic effects , respectively, for each trait. The distribution of the multivariate response and phenotypic variance-covariance V following the models in where K is the additive genetic relationship matrix  calculated by k-th genotype and was implemented using the “a.mat” function in R for the k-th random effect ; and I is an identity matrix  for the residual term. The terms i, respectively, and σukAB and σABε are the genetic and residual covariance between traits A and B. Genetic correlations (rG) between seedling emergence and coleoptile length were then calculated using the function “cov2cor” in the R package sommer  assays in the WSU Winter Wheat Breeding Laboratory using allele-specific SNP markers for semi-dwarf causing mutant alleles Rht-B1b and Rht-D1b previously reported in Rht-B1b (1), Rht-D1b (2), Rht-B1b heterozygous (3), Rht-D1b heterozygous (4), Rht-D1b with a heterozygous Rht-B1b (5), Rht-B1b with a heterozygous Rht-D1b (6), and both Rht-B1b and Rht-D1b heterozygous (7).All winter wheat lines in the DP were genotyped with Kompetitive Allele Specific PCR , the ST-GWAS models were implemented using the Genome Association and Prediction Integrated Tool GAPIT; . Both thAdditionally, MTMM was implemented using the “sommer” package for MT-GWAS to identify pleiotropic interactions between seedling emergence and coleoptile length within the DP using the multivariate models 8 and 9. The MT-GWAS model was then implemented in the package “sommer” to obtain marker effects using the inverse of the phenotypic variance matrix (V) and is a generalized linear model of the form:b is the marker effect (1 × 2), y is the multivariate response variable (1 × 2), V- is the inverse of the phenotypic variance matrix V (2 × 2), Z is the incidence matrix for the random effect to perform the GWAS, and Mi is the i-th column of the marker matrix. Furthermore, we implemented three additional F-tests for joint analysis using the scripts proposed in where Significant associations were based on a Benjamini–Hochberg false discovery rate (FDR) threshold . The pheHeritability for seedling emergence was moderately high in the BLs and a few years in the DP, whereas the heritability decreased in combined years. The highest heritability in a single trial was 0.88 in the DP in 2018, and the BLs had a heritability of 0.77 . The tri3:5 trial in 2015 was significantly correlated to DP 2017. The genetic correlations between the DP seedling emergence to coleoptile length showed moderate to large correlations in and across years  or Rht-D1b (0.347), with Rht-B1b conveying higher mean seedling emergence than Rht-D1b , 2B (1), and 5A (3). The MLM identified 16 markers across years, with all but one on chromosome 5A, and with the other marker located on chromosome 5B. For these markers in the DP, only S5A_522153944 was identified by all three models.Because of the lack of identified loci for seedling emergence, the identified markers were compared for significance across years, populations, and correlated traits to insure consistency. No markers were significantly associated for both seedling emergence and coleoptile length in either ST-GWAS or MT-GWAS. Using ST-GWAS models within the DP, 23 out of 107 unique markers were found significant in more than 1 year. BLINK only identified one marker, R2 LD values above 0.8. The two largest effect consistent markers in the DP, S5A_522153944, and S5A_522153953, were found on chromosome 5A and improved seedling emergence by 30%. These two markers had a maximum R2 of 10% in the DP. Other consistent markers identified across years in the DP were located on chromosomes 2A (2), 2B (3), 5A (15), 5B (1), and 7A (1). Overall, the consistent markers across years accounted for 30% of the combined 2015–2019 DP variation. The GWAS on the BL population displayed more consistent results than in the DP, and only identified consistent markers on chromosome 5A. There were four significant consistent markers identified in the BLs  for simple traits, the MLMs have been shown to have difficulties with low power and false positives for complex traits . MLMs evR2 values, indicating the ability of multi-locus models to identify small-effect markers for complex traits.Fixed and random model circulating probability unification and multi-locus models provide the best trade-off between power and false positives . Multi-lp-values we observed in the joint analyses. We observed such large inflation of p-values that we had to use the more stringent Bonferroni cut-off as the threshold. The MT-GWAS model we used implemented a single-locus model and, therefore, suffered limitations in identifying small effect loci similar to the MLM. However, the COM model did identify consistent markers across years on chromosome 7A, whereas the ST-GWAS model only identified a single-year combination. The identification of a significant marker in the COM model not seen in the ST-GWAS, combined with the lack of significant interaction effect loci, confirms the positive genetic correlation seen in the majority of years between seedling emergence and coleoptile length. However, due to the lack of evidence of pleiotropic loci in our other methods, the genetic correlation may be due to the correlation of shared loci such as the Rht alleles.There was little to no increase in identifying pleiotropic loci using MT-GWAS compared to ST-GWAS models. This may be due to the lack of similar significant markers or pleiotropic loci between seedling emergence and coleoptile length, along with the inflated The lack of increase in ability to identify pleiotropic loci using the MT-GWAS models may also be due to the lack of phenotypic correlation between seedling emergence and coleoptile length . Even thRht alleles and coleoptile length. These correlated traits were used because of previous studies reporting large associations between the traits , breeding programs can uncover the complex nature of traits to help identify candidate genes and the underlying architecture of a trait to make more efficient breeding decisions and selection methods.This study displayed the ability of GWAS to dissect the genetic architecture of a complex trait such as deep-sown seedling emergence. Both the ST-GWAS and MT-GWAS models identified a few large effects and many small effect markers for seedling emergence. Additionally, neither the ST-GWAS nor the MT-GWAS models identified large pleiotropic effect markers between seedling emergence and coleoptile length. The ST-GWAS and MT-GWAS models did not identify the same significant markers for seedling emergence or coleoptile length, and the MT-GWAS models did not identify any interaction effect markers. However, by using multi-locus models in conjunction with covariates for correlated traits, we were able to identify more small effect loci over single-locus models to dissect a complex trait in both the DP and BL populations. Additionally, the DP displayed the necessity for combining years for consistent identification of significant markers for a trait dependent on the environment for phenotypic variation. Furthermore, the MT-GWAS models displayed a lower ability to identify small effect loci over ST-GWAS models for single-trait analysis and inflated https://github.com/lfmerrick21/GWAS-Complex-Traits.The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: LM conceptualized the idea, analyzed the data, and drafted the manuscript. AB genotyped the KASP markers, and reviewed and edited the manuscript. ZZ reviewed and edited the manuscript. AC supervised the study, conducted field trials, edited the manuscript, and obtained the funding for the project. All authors contributed to the article and approved the submitted version.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.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Our study presents the largest whole-genome investigation of leadership phenotypes to date. We identified genome-wide significant loci for leadership phenotypes, which are overlapped with top hits for bipolar disorder, schizophrenia, and intelligence. Our study demonstrated the polygenetic nature of leadership, the positive genetic correlations between leadership traits and a broad range of well-being indicators, and the unique association of leadership with well-being after accounting for genetic influences related to other socioeconomic status measures. Our findings offer insights into the biological underpinnings of leadership. miR-2113/POUSF2 and LINC01239) and schizophrenia loci (ZSWIM6). We found positive genetic correlations between leadership position and several positive well-being and health indicators, including high levels of subjective well-being, and low levels of anxiety and depression (|gr| > 0.2). Intriguingly, we observed positive genetic correlations between leadership position and some negative well-being indicators, including high levels of bipolar disorder and alcohol intake frequency. We also observed positive genetic correlations between leadership position and shortened longevity, cardiovascular diseases, and body mass index after partialing out the genetic variance attributed to either educational attainment or income. The positive genetic correlation between leadership and bipolar disorder seems potentially more pronounced for those holding senior leadership positions (gr: 0.10 to 0.24), partially due to shared genetic variants with educational attainment. Our findings provide insights into the polygenic nature of leadership and shared genetic underpinnings between the leadership position and one’s health and well-being. We caution against simplistic interpretations of our findings as advocating genetic determinism.Twin studies document leadership role occupancy  as a heritable trait. However, previous studies have been underpowered in identifying specific genes associated with this trait, which has limited our understanding of the genetic correlations between leadership and one’s well-being. We conducted a genome-wide association study (GWAS) on individuals’ leadership phenotypes that were derived from supervisory/managerial positions and demands among 248,640 individuals of European ancestry from the UK Biobank data. Among the nine genome-wide significant loci, the identified top regions are pinpointed to previously reported GWAS loci for bipolar disorder ( Leadership has been demonstrated to have profound influences on the performance and well-being of individuals, groups, organizations, and the world. One school of thought in leadership research—inspired by the Great Man theory —focuses The management literature has a long history of examining the phenotypic relationship between leadership and job incumbents’ well-being –12. An iThe main goal of this research is twofold. First, we conducted a genome-wide association study (GWAS) of two leadership variables—leadership position and managing demands—with the UK Biobank (UKB) data and replicated top variants in three independent samples. Due to the multifaceted nature of the leadership construct, we adopted the approach in leadership research from the management and behavioral genetics and focused on the two leadership phenotypes with a focus on holding a leadership position and performing critical managing functions , 20. LeaManagement research has defined leadership as a process of influencing individuals in a group or an organization to move toward a common goal . Given tSI Appendix, Fig. S1 and SI Appendix, Table S1.For GWAS analyses, we treated leadership position as a binary variable (leaders versus nonleaders) obtained from the UK SOC 2000 system. For the managing-demands variable, we linked the UK SOC 2000 job codes in the UKB data to the occupation codes from the O*NET database to construct a score indicating the levels of the managing demands by averaging ratings of nine items from the O*NET , 25 . Among all the participants, 48.11% were males and the average age was 54.3 y, ranging from 39 to 71. A subset of 219,474 participants with available data on the managing demands phenotype was included in the discovery stage. The average managing demands score was 3.13, ranging from 0.95 to 5.12. Leadership position was moderately correlated with managing demands for the whole sample (Pearson correlation r: 0.63) or by sex . In general, those who held leadership positions, compared to their nonleader counterparts, had higher education qualifications (37.94% versus 34. 16% with college or university degree), higher household income , lower Townsend deprivation index (−1.98 versus −1.51), more likely owned accommodation lived in (94.6% versus 91.6%), had more vehicles in the household (66.43% versus 54.98% with two or more cars), and relied more on the car for commuting to the workplace .In the analyses with the UKB data, we included 248,640 participants of European ancestry with 17.29% being leaders  and 82.71% as nonleaders , the Add Health Wave IV dataset , and the Wisconsin Longitudinal Study dataset . The mean age (years) of participants was 60.4 in the UKB follow-up dataset , 28.4 in the Add Health dataset , and 68.6 in the WLS cohort .We also performed replication analyses in three independent datasets: the UKB follow-up dataset . For managing demands, there was moderate inflation of the test statistics (λGC ranging from 1.10 to 1.20). However, the estimated linkage disequilibrium score (LDSC) regression intercept (ranging from 1.02 to 1.05) suggests that the inflation was largely due to the presence of polygenic inheritance  with minor allele frequency (MAF) >1% in 248,640 White participants from UKB data. The sex-stratified GWAS were also performed. The quantile–quantile (Q–Q) plots showed little evidence of inflation in test statistics for leadership position  for the whole sample in the UKB discovery phase for the single-trait analysis , despite the much smaller sample size . All top single-nucleotide polymorphisms (SNPs) except one retained genome-wide significance in the meta-analysis combining all datasets, with the effect sizes and directions largely concordant . For sex-specific analyses, we identified three loci, among which one signal for managing demands at gene NPAS2 on chromosome 2 in females remained significant across the discovery and replication samples. The nine independent SNPs showing genome-wide significance across all the datasets were reported in Initially, we identified nine potential signals . Three loci, miR2113/POU3F2, LINC01029, and NPAS2, exhibited significant pleiotropic associations for leadership position after Bonferroni correction . By incorporating information from the managing demands, we noted that Z-score statistics were boosted for testing the association between variants and leadership-position phenotype. With the increased statistical power, MTAG-leadership results were employed in the heritability and genetic correlation analyses, along with the GWAS results from the single-trait analyses.We also conducted multitrait analyses on leadership position and managing demands using the multitrait analysis of GWAS (MTAG) method  with leamiR2113 and POU3F2, which contains dozens of putative fetal brain–specific enhancers. Intriguingly, the lead SNP rs1487441-A allele associated with increased managing demands (and a higher level of leadership position as well) in our study was previously reported to be associated with an increased risk for bipolar disorder (P = 2.58 × 10−8)   . GWAS re × 10−8) , 29, sug neurons . Consistdisorder . The top × 10−9) .KLF5 gene on chromosome 13q22.1. The KLF5 gene encodes a member of the Kruppel-like factor subfamily of zinc-finger proteins, which is enriched in the motifs of transcription factors for schizophrenia   . Zswim6  × 10−9) , an impoZNF618 and RGS3 on chromosome 9q32. The ZNF618 gene encodes zinc-finger protein 618, and rgs3 is a GTPase-activating protein that inhibits G protein–mediated signal transduction. The rs7035099-C allele associated with leadership position was also associated with, although not reaching genome-wide significance, an increased level of risk tolerance (P = 4.91 × 10−4) (P = 9.55 × 10−4)   and extrNPAS2 gene on chromosome 2q11.2 (p. Ser471Leu). The NPAS2 gene codes neuronal PAS domain protein 2. It plays a key role in the acquisition of memory; such epistatic clock genes are potentially involved in the etiology of autistic disorder  for the leadership-position trait was estimated to be in the range between 3 and 9%  from GWAS summary statistics using the LDSC method for the whole sample and sex-specific samples . The estimates, ranging from 5 to 10% , were similar to those using the BOLT-restricted maximum likelihood (BOLT-REML) method . Overall, for leadership position and managing demands, the SNP-h2 estimates ranged from 3 to 8% and 4 to 10%, respectively. For MTAG-leadership, the SNP-h2 was estimated to range from 4 to 9%. Across sexes, there were substantial genetic correlations for MTAG-leadership, leadership position, and managing demands . A partially shared genetic architecture was observed between leadership position and managing demands (gr = 0.57) as well as in males and females.Overall, common SNP heritability  in the UKB and Add Health datasets . We speculate that those holding senior leadership positions may have a higher heritability. As the sample size for the senior leader in each cohort was small, we performed a meta-analysis to combine GWAS summary statistics for senior leadership across the three datasets . The SNP-h2 for the whole sample was estimated at 7% , slightly higher than that for leadership position ; the 95% CIs were overlapped. Meanwhile, there was partially shared genetic architecture between the senior leadership position and leadership position .In sensitivity analyses, we estimated SNP-h2 estimates for leadership traits were lower than those estimated from the twin studies (around 30%) , such as risk tolerance and extraversion, and slightly larger than agreeableness and subjective well-being but less than physical traits, metabolites such as high-density lipoprotein (HDL), low-density lipoprotein (LDL), body mass index (BMI), and intelligence.The SNP-und 30%) , 6, 7, pP values  and with the Lassosum approach . Using PGSs generated at the threshold of 0.05 , we categorized PGSs into five quantiles in the logistic regression to model leadership position, accounting for age, sex, and genotyping arrays. The top PGS quantiles (top 20th), as compared to the lowest 20th quantiles, were associated with an increased likelihood to hold a leadership position  as well as a senior leadership position . PGSs accounted for a small amount of variance of leadership position, with an incremental R2 at 0.04%, on top of age and sex.To test whether the aggregate estimates of genetic effects are associated with leadership position, we constructed polygenic scores (PGSs) based on the MTAG-leadership GWAS summary statistics in the independent UKB follow-up dataset. The PGSs were significantly associated with the leadership position at varying threshold SI Appendix, Table S14). The significance level was set at a false discovery rate (FDR) <0.05 to account for multiple testing , neuroticism , intelligence , and height . Leadership position was genetically correlated with extraversion at nominal significance . For MTAG-leadership, integrating information from the managing demands phenotype, the genetic correlation with intelligence substantially increased compared to analyses with leadership position variable alone . The genetic correlation remained significant for other variables: risk tolerance , neuroticism , height , and extraversion . The genetic correlation for leadership position was higher with income than educational attainment ; substantially stronger correlations were observed for MTAG-leadership in a similar pattern .We found that the leadership position variable had significant genetic correlations with risk tolerance , overall health rating , HDL , physical exercise , and negative correlations with depression symptoms , anxiety , attention deficit hyperactivity disorder (ADHD) , number of noncancer illness , LDL, and triglycerides (TG) . Moreover, we also observed that leadership was positively and genetically correlated to bipolar disorder  and alcohol intake frequency , both being indicators of low levels of health and well-being. In general, the genetic correlation estimates with the variable leadership position alone were similar to, and sometimes lower than, those with MTAG-leadership. However, leadership position was significantly correlated with BMI  and cardiovascular disease (CAD) , while these two indices were not significant correlated with MTAG-leadership .In the UKB data, we found positive genetic correlations of leadership position and MTAG-leadership with positive physical and mental health and well-being variables at large. For MTAG-leadership, there were positive genetic correlations with subjective well-being , the findings also reveal unique genetic correlations between some well-being variables with leadership position. Notably, the significant positive genetic correlation remained at a similar magnitude for subjective well-being after accounting for genetic influences related to educational attainment; the positive genetic correlations became negative for overall health rating and physical exercise, while the negative genetic correlations became positive for ADHD and number of noncancer illnesses after partialing out genetic influence related to income. The change of genetic correlations was mostly evident after partialing out the genetic variance of income, perhaps in part because the genetic variants associated with high income tend to be more strongly associated with well-being variables than the genetic variants for leadership position. Intriguingly, the negative genetic correlations between leadership position (or null for MTAG-leadership) and some well-being variables  were strengthened and became significant after accounting for both educational attainment and income. The positive genetic correlations between leadership position and shortened longevity, CAD and BMI, were in contrast to the directions of genetic correlations observed for both educational attainment and income  and 1.7-fold of MTAG-leadership . The 95% CIs were wide for senior leadership likely due to the small sample size, whereas the trend suggested that the shared genetic factors predisposing to bipolar disorder could be potentially more pronounced for senior leaders. A strengthened positive genetic correlation was observed between senior leadership and physical exercise . Such a pattern, however, was not observed for alcohol intake frequency .The genetic correlations between leadership position and an increased risk of bipolar disorder and alcohol intake frequency, as well as physical exercise, were further assessed for those holding senior leadership positions. Senior leaders had a larger genetic risk for bipolar disorder  and changed to the opposite direction with physical exercise after accounting for genetic influences related to income . For analyses with those holding senior leadership positions, the genetic correlation with bipolar disorder attenuated after partialing out genetic variance related to educational attainment , whereas it remained at a similar magnitude, but marginally significant, after partialing out income . The results suggest that bipolar disorder could link to common biological mechanisms underlying educational attainment and leadership but not income.After partialing out the genetic variance related to other SES variables, the genetic correlations were substantially weakened and became nonsignificant with alcohol intake frequency. For MTAG-leadership, the genetic correlation was marginally significant with bipolar disorder after partialing out genetic influences related to income , as well as the low levels of physical exercise, emerged. Our study demonstrated the polygenetic nature of leadership, the shared genetic basis between leadership traits and a broad range of well-being indicators, and the unique associations with well-being after accounting for genetic influences related to other SES measures.miR-2113/POUSF2 and the rs4977839-A allele at LINC01239/ELAVL2 associated with leadership position and a high level of managing demands were also found to be associated with an increased risk for bipolar disorder , findings on significant influences of specific genetic variants should not be explained as suggesting genetic determinism. As research on social influences, significant genetic influences suggest only that such influences are probabilistic, not deterministic. Environmental influences play important roles in mediating or moderating genetic influences. A more complete understanding of human behaviors should take various forms of interplay between nature and nurture into consideration.SI Appendix, Fig. S1).UKB data are from a population-based cohort study in the United Kingdom, which involves above 500,000 participants aged 40 y or older during their recruitment between 2006 and 2010 , 63. Parn = 22,875), the Add Health Wave IV cohort , and the WLS cohort . The details of replication cohorts were presented in SI Appendix, Supplementary Notes.Replication samples included participants from the UKB follow-up cohort . Leadership position refers to whether one person holds a supervisory position . Managing demands were measured with nine items on typical managerial and supervisory tasks  primary job?” Response options ranged from 1 = “I supervise or supervised other employees,” 2 = “I supervise other employees, some of whom supervise others,” and 3 = “I do or did not supervise anyone.” We constructed the variable of the leadership position by assigning 1 to participants who selected the first and second options and 0 to those who chose the third option. In the sensitivity analyses, we selected those who chose 2 as those who hold senior leadership positions. After linking the occupational codes reported by participants to the O*NET database to extract leadership managing demands, we included 4,696 individuals in GWAS for managing demands.n = 5,899). Thus, the leadership position variable represents levels of managerial authority, influence, and responsibility. In addition, the US Census 1970 and 1990 job codes from WLS data were linked through crosswalks to the US O*NET-SOC version 2010 to extract the phenotype of managing demands from the US O*NET database. The WLS replication sample included 5,120 participants for managing demands.For the WLS cohort, participants were asked three questions about their leadership position. The three items at each wave were “Do you have authority to hire and fire others at current/last job?” , “Can you influence or set the rate of pay received by others at current/last job?” , and “Do you supervise the work of others, that is, what they produce and how much at current/last job?” . Given that participants were randomly selected to answer these questions at each wave, we used the average leadership position score across three items reported at their respective last wave . The phenotypical and genetic correlations between this item and managing demands were 0.74 and 0.97 in the UKB data. A separate GWAS analysis on this item generated similar results to those of managing demands. As this item was largely overlapping with managing demands, we thus dropped it from further analyses.We used imputation genotypes released by UKB , which includes the full set of genotypes imputed on the Haplotype Reference Consortium (HRC) data, UK10K, and 1000 Genomes phase-3 reference panels. The QC and imputation were done by UKB and have been described elsewhere . A EuropSI Appendix, Supplementary Notes.For the Add Health cohort, the genotypes were imputed on the HRC, with QCs detailed in ref. https://alkesgroup.broadinstitute.org/BOLT-LMM/downloads)  . The asshttps://zzz.bwh.harvard.edu/plink/download.shtml). The LD structure was estimated from the European panels in the 1000 Genomes Project of phase 3 as the reference population. The index lead SNP was identified (P < 5 × 10−8), independent from other variants at each locus (r2 < 0.01). A locus was defined by an index SNP with the region flanking 500 kb on both sides. The coordinates and variant identifiers were reported on the National Center for Biotechnology Information B37 (hg19) genome build. The functional annotation and gene mapping were performed using ANNOVAR (version 2018Apr16), including types of intronic, exonic, intergenic, 5′-UTR, 3′-UTR, etc. (http://locuszoom.org/), and the 1000 Genomes data of the European population was used to estimate LD information.Independent significant variants and their surrounding genomic loci were identified using LD clumping in PLINK version 1.07 . For the binary trait of leadership position, the coefficients obtained from the linear mixed model in the UKB discovery samples were on the standardized scale. Therefore, we transformed these coefficients to make them comparable with the observations in all the samples. We rescaled the beta coefficients with the following formula: βs = β/k*(1−β), where k is the prevalence of leaders in the UKB; the ORs were calculated accordingly using the scaled beta coefficient βs.Genome-wide significant SNPs were evaluated in the UKB follow-up dataset, the Add Health dataset, and the WLS cohort. The detailed information for association analyses in the replication datasets is presented in To combine the GWAS summary statistics for the two leadership variables, we applied the MTAG approach . MTAG ishttps://github.com/bulik/ldsc) with GWAS summary statistics to estimate common SNP-h2 for three phenotypes: leadership position, managing demands, and MTAG-leadership for the whole sample and subsamples by sex in the UKB discovery data . In the sensitivity analyses, we calculated SNP-h2 estimation of senior leadership phenotype using GWAS data in the UKB discovery sample with LDSC and BOLT-LMM approaches. We did not estimate SNP-h2 by sex due to the small sample size. To increase effective sample size, we also estimated heritability for senior leadership using meta-analysis results combining the results with the Add Health sample .We used the software LDSC version 1.0.1 . For MTAG-leadership, we used the same percentage as for the leadership position. For the senior leadership position testing statistics from the meta-analysis across UKB and the Add Health cohorts, the prevalence is the weighted average percentage in UKB and the Add Health dataset (2.30% for senior leadership position).For the binary trait of leadership position, the estimated heritability should be transformed to the liability scale using the transformation derived by Lee et al. . As the We first computed the genetic correlation between leadership position and managing demands, for the overall sample and subsamples by sex, using the GWAS summary statistics from the UKB discovery sample. We adopted the bivariate LDSC method by regressing the product of testing statistics (z-statistics) from each phenotype against the LD scores .SI Appendix, Table S14. We used summary statistics from the previously published large-scale GWAS or GWAS results from UKB data, for instance, subjective well-being SI Appendll-being , etc. Thll-being . Note thWe used two sets of summary statistics for leadership traits: 1) single-trait GWAS on the leadership position and 2) MTAG-leadership by combining the association statistics for the leadership position and managing demands using the MTAG method. We excluded variants (INFO < 0.8 and MAF < 0.01) and merged SNPs to the HapMap3 European panel; the MHC region on chromosome 6 was removed. Bivariate LDSC regression was applied for genetic correlations between each pair of leadership and other traits . As we eTo estimate the genetic correlations after partialing out the genetic variance of other socioeconomic variables , we used the Genomic SEM . For eachttps://www.prsice.info/quick_start/), a method shown to have decent prediction accuracy involving LD pruning followed by P-value thresholding . Independent lead variants associated with the phenotype were identified by the “clumping and thresholding” approach, removing those within 250 kb and in linkage disequilibrium r2 ≥ 0.1 with the lead variant in the region. An individual’s PGS is a weighted sum of the genotypes across all independent variants. The weighting factor is the estimated additive effect size, beta coefficient, at each variant from the MTAG-leadership summary statistics. Prediction accuracy was based on an ordinary least squares regression of the leadership position on the PGS and a set of standard covariates, including age, sex, and the top genetic PCs. The McFadden pseudo-R2 for PGS was calculated as the incremental variance for leadership variables . To evaluate the genetic effect on a leadership position for subjects in the highest quantiles of PGS, we performed the logistic regression for the leadership position variable, regressing on five quantiles of PGS, sex, age, and genetic array. Top genetic PCs were not included in the final model, as none of them was significant (P > 0.05). In sensitivity analyses, we applied Lassosum (https://github.com/tshmak/lassosum) to create PGS, with tuning parameters for the penalized regression across all the variants optimized in the testing samples (A PGS estimates the cumulative effects of thousands of genetic variants identified from GWAS, including many with small effects. Using the GWAS results from MTAG-leadership, we generated PGSs in the UKB follow-up sample. The PGSs were constructed in PRSice (sholding . Variant samples .Supplementary File


Polygenic scores have become a central tool in human genetics research. LDpred is a popular method for deriving polygenic scores based on summary statistics and a matrix of correlation between genetic variants. However, LDpred has limitations that may reduce its predictive performance.Here, we present LDpred2, a new version of LDpred that addresses these issues. We also provide two new options in LDpred2: a ‘sparse’ option that can learn effects that are exactly 0, and an ‘auto’ option that directly learns the two LDpred parameters from data. We benchmark predictive performance of LDpred2 against the previous version on simulated and real data, demonstrating substantial improvements in robustness and predictive accuracy compared to LDpred1. We then show that LDpred2 also outperforms other polygenic score methods recently developed, with a mean AUC over the 8 real traits analyzed here of 65.1%, compared to 63.8% for lassosum, 62.9% for PRS-CS and 61.5% for SBayesR. Note that LDpred2 provides more accurate polygenic scores when run genome-wide, instead of per chromosome.LDpred2 is implemented in R package bigsnpr.Bioinformatics online. In recent years, the use of polygenic scores (PGS) has become widespread. A PGS aggregates (risk) effects across many genetic variants into a single predictive score. These scores have proven useful for studying the genetic architecture and relationships between diseases and traits . PGS arep of variants that are causal, is a Gibbs sampler and is particularly sensitive to model misspecification when applied to summary statistics with large sample sizes. It is also unstable in long-range LD regions such as the human leukocyte antigen (HLA) region of chromosome 6. This issue has led to the removal of such regions from analyses (LDpred is a popular method for deriving polygenic scores based on summary statistics and a Linkage Disequilibrium (LD) matrix only . Howeveranalyses .p and the SNP heritability h2, and therefore does not require validation data to tune hyper-parameters. We show that LDpred2 provides higher predictive performance than LDpred1 (LDpred v1.0.0), especially when there are causal variants in long-range LD regions, when the proportion of causal variants is small, and when GWAS sample size is large. We also show that the new sparse option performs equally well as the non-sparse version, enabling LDpred2 to provide sparse effects without losing any predictive accuracy. Moreover, LDpred2-auto, which does not require any validation set, performs almost as well as the main LDpred2 model that tunes hyper-parameters from a grid in a validation set, provided some quality control is performed on the summary statistics.Here, we present LDpred2, a new version of LDpred that addresses these issues while markedly improving its computational efficiency, allowing exploring a larger grid of parameters in the same computational time as LDpred1. We provide this faster and more robust implementation of LDpred in R package bigsnpr . We alsoR). We use 300 000 other individuals for running logistic GWAS to create summary statistics. We use the remaining 52 320 individuals as test set for evaluating models.We use the UK Biobank imputed data for both real data analyses and simulations . We resti-th individual as jw are weights generated from a Gaussian distribution i for variant j, iϵ follows a Gaussian distribution i’ys are scaled such that the variance of the genetic liability is exactly h2 and the variance of the total liability is exactly 1. Such simulation of phenotypes based on real genotypes is implemented in function snp_simuPheno of R package bigsnpr. We also vary the sample size to compute GWAS summary statistics in the scenario with 3000 causal variants; in addition to a GWAS sample size of 300 000, we also use 10 000, 20 000, 50 000 and 120 000. We design two other simulation scenarios with 300 or 3000 causal variants randomly chosen in the HLA region . In these two scenarios, we use We simulate binary phenotypes with a heritability of e of 15% . We varyAll simulation scenarios are summarized in We use the same data as in the simulation analyses. We use the same 10 000 individuals as validation set, and use the remaining 352 320 individuals as test set. We use external published GWAS summary statistics listed in P-values) between 0.1 and the most significant P-value, equally spaced on a log scale. For lassosum  and refer to this method as lassosum-auto. For PRS-CS , Stacked C+T (SCT), lassosum(-auto), PRS-CS(-auto) and SBayesR (We use the Area Under the ROC Curve (AUC) to compare methods. We sample 10 000 bootstrap replicates of the individuals in the test set and compute the AUC for each of these. We then report the mean of these 10 000 values, along with their quantile at 2.5% and at 97.5% to act as the 95% confidence interval (CI) for the AUC. This is implemented in function AUCBoot of R package bigstatsr.R. Let us denote by S the diagonal matrix with standard deviations of the m variants, G the genotype matrix of n individuals and m variants and y the phenotype vector for n individuals.In this section, we explain how we can obtain joint effects from summary statistics  and a correlation matrix When solving a joint model with all variants and an intercept Using the Woodburry formula, we get When fitting each variant separately in GWAS, the marginal effects (assuming no covariate) simplify to G is We further note that the correlation matrix of Then we get R is usually not available but is computed from another dataset. Also note that In practice, the correlation matrix j, let us denote by j residualized from K covariates, e.g. centering them. Then, For the marginal effect S, therefore we can assume that jn for different variants. Note that LDpred1 and other similar methods scale the output dividing by the standard deviation of genotypes. This is correct when The first approximation is possible because For summary statistics of binary traits derived from a logistic regression, instead of equation (2), we have ms valid . Howeverms valid . Let us val<0.05 .LDpred assumes the following model for effect sizes, p is the proportion of causal variants, M the number of variants and h2 the (SNP) heritability. h2 using constrained LD score regression (intercept fixed to 1) and recommend testing a grid of hyper-parameter values for p .where jβ, we use a Gibbs sampler as in j is computed as j-th column without the j-th row of the correlation matrix, j-th element. Then, the probability that variant j is causal is computed as To estimate effect sizes Computing jβ is sampled according to Then, Therefore, the posterior mean of 1: 2: for  do ▹ Gibbs iterations3: for each variant j do ▹ All variants4: 5: Compute 6: Compute jβ according to (7)7: Sample jω according to (8)8: Compute end for9: if  then10: 11: end if12: end for13: 14: 15: Return LDpred2 comes with two extensions of the LDpred model.p and h2 within the model, as opposed to testing several values of p and estimating h2 using constrained LD score regression . We also provide a sparse option for LDpred2-auto by running LDpred2-grid with one set of parameters only: with the sparsity enabled and using the estimates of p and h2 from LDpred2-auto.The second extension, which can be enabled using a third hyper-parameter in LDpred2-grid, aims at providing sparse effect size estimates, i.e. some resulting effects are exactly 0. When the sparse solution is sought and when p from a sequence of 21 values from h2 within et al. (2015); and whether sparsity is enabled or not. In total, this grid is of size h2 and a sequence of 30 values from p. Running many Gibbs chains aims at checking whether models did not diverge (and hopefully converged). As a criterion for non-divergence, we compute the standard deviations of the resulting predictors from the 30 models, keep only those within three median absolute deviations from their median, and average the remaining vectors of effects as final effect sizes for the ‘auto’ version.When running LDpred2-grid, we test a grid of hyper-parameters with There is a window size parameter that needs to be set in LDpred; for a given variant, correlations with other variants outside of this window are assumed to be 0. The recommended value for this window (in number of variants) has been to use the total number of variants divided by 3000, which corresponds to a window radius of around 2 Mb . Using aIn this paper, we investigate if it would be beneficial to run LDpred2 per chromosome, instead of genome-wide. It may be beneficial for some phenotypes to assume that their genetic architecture is different for different chromosomes. For example, chromosome 6 clearly encompasses a larger proportion of the heritability of autoimmune diseases compared to other chromosomes . AssuminWe provide an LD reference for European ancestry to be used by researchers who cannot compute their own. We use the 362 320 UKBB individuals as used here, with some further quality control based on allele frequencies. Indeed, some large allele frequency mismatches have been reported recently in the UKBB when comparing to other datasets, which are apparently due to mismappings . Note thp<10−5 . We alsop , h2 (the SNP heritability), and possibly the sparsity option (as a third hyper-parameter) are tuned using a validation set; (iii) LDpred2-auto, which automatically estimates p and h2 from data and therefore is free of hyper-parameters to tune. Note that the sparse option in LDpred2-grid slightly modifies the Gibbs sampler in LDpred2 to be able to fit effects that are exactly 0. For users who do not particularly care about sparsity, they can still tune this parameter in LDpred2-grid to explore a larger parameter space. For this paper, in order to show the effect of this sparse option on predictive performance, we deliberately separate the LDpred2-grid method in two ‘different’ methods that we call LDpred2-grid-nosp  and LDpred2-grid-sp  in the results. As a recall, LDpred v1 has two options: LDpred1-inf, and LDpred1-grid where only p is tuned while h2 is estimated from constrained LD score regression .Here, we present LDpred2, a new version of LDpred  or genome-wide (‘gwide’). Finally, we compare LDpred2 to several other methods: Clumping and Thresholding (C + T), Stacked C + T (SCT), lassosum, PRS-CS and SBayesR . For example, in simulations with 300 causal variants, a mean AUC of 73.6% is obtained with LDpred1 while a value of 81.7% is obtained with LDpred2. In these scenarios, all non-infinitesimal models of LDpred2 perform equally well. As expected, LDpred1 performs poorly in HLA scenarios, i.e. when causal variants are located in a long-range LD region. In contrast, all LDpred2 models perform well in these two HLA scenarios, but LDpred2-auto performs slightly worse. There are two possible explanations for this: first, these two scenarios are very extreme scenarios where causal effects may have large effects in strong LD; second, because there is no contribution from the other chromosomes in these scenarios, any prediction added to the score from other chromosomes would be noise that could reduce the performance of the overall score. In the ‘both_40’ simulation scenario, where effects in HLA are generated with a smaller heritability (20%) and where there are also other effects all over the genome contributing another 20% of heritability, predictive performance of LDpred2-auto are on par with the other LDpred2 models.Most results show that it is beneficial to run LDpred2 genome-wide instead of per chromosome. et al., 2020) and likely contributed to discrepancies in reported predictive accuracy of LDpred (p = 1). We hypothesize that LDpred1 does not use a LD window size that is large enough to account for long-range LD such as in the HLA region. In LDpred2, we use a window size of 3 cM, which enables LDpred2 to work well even when causal variants are located in long-range LD regions. We argue against removing these regions as sometimes suggested in the literature  since these regions, especially the HLA region, contain many variants associated with many traits, and are therefore often useful for prediction. As sample size grows, the Gibbs sampler used in LDpred relies more on the LD being calculated and adjusted for appropriately, providing an intuitive explanation for why LDpred1 performs much worse than LDpred2 when GWAS sample size is large. Other modifications, such as a better handling of numerical errors when working with exponentials (Equation 6), or a larger hyper-parameter search space, may also contribute to the improved robustness in LDpred2.The previous version of LDpred has been widely used and has the potential to provide polygenic models with good predictive performance . Yet, itp (21 instead of 7 by default in LDpred1) and for h2 (3 instead of 1). When testing the grid of hyper-parameters of p and h2, we also allow for testing an option to enable sparse models in LDpred2 (see below). Overall, we test a grid of 126 different values in LDpred2 instead of 7 in LDpred1. We also use a larger window size for computing correlations between variants (see above), yet LDpred2 is still as fast as LDpred1. The efficiency of LDpred2 is achieved through an efficient parallel implementation in C++. Efficient parallelization over the grid of hyper-parameters is possible because we use an on-disk sparse matrix format accessed using memory mapping. This new data format is available in R package bigsparser, which has been developed for this paper. It takes between 12 and 36 h to run all the LDpred2 models over 1.1 million HapMap3 variants at once (genome-wide) using 30 cores; LDpred1 takes a similar time . It takes a little more than two hours to pre-compute the LD matrix for 10 000 individuals and 1.1 million HapMap3 variants (using 16 cores). This pre-computation is fast compared to running the Gibbs sampler in LDpred2 and needs to be performed only once for all traits. It can also be further parallelized on different compute nodes for different chromosomes; then it takes only 11 min for the largest chromosome.In LDpred2, we also expand the grid of hyper-parameters examined with now more values for p and h2, which therefore does not require any validation set to tune hyper-parameters from. LDpred2-auto is an attractive option in many applications, especially since we also provide an LD reference that can be used directly (Section ‘Software and code availability’). LDpred2-auto almost always performs equally well as LDpred2-grid in simulations as well as in real data applications.LDpred2 also extends the original LDpred model in two ways. First, we provide a sparse option in LDpred2-grid which provides models that truly encourage sparsity, in contrast to LDpred1 which outputs very small non-zero effect sizes . In pracp (∼0.001) is off compared to the best performing p in LDpred2-grid . One possible explanation for this discrepancy is that the summary statistics we use for CAD come from a meta-analysis of 48 small studies, with some of them from non-European ancestries. Moreover, the summary statistics we use for Asthma come from a meta-analysis of 66 small multiancestry studies. This could break some of the assumptions used in LDpred2-auto and explain why LDpred2-auto underperforms for CAD and Asthma compared to LDpred2-grid. For example, for these two phenotypes, the summary statistics are off compared to the expected identity line in the QC screening procedure presented here . Future work is needed to study how to make best use of these multiancestry meta-analyses from many small studies in the context of genetic prediction. Future work is also needed to assess how relevant the estimation of parameters from LDpred2-auto is, and whether its estimates and its predictive performance could be improved by e.g. incorporating functional annotations.However, LDpred2-auto requires that some quality control is performed on summary statistics . This quality control aims at ensuring that effects are transferable from the external GWAS summary statistics to the data where PGS are computed. Note that this quality control is also beneficial for other methods such as lassosum (data not shown). Even when this quality control is performed, LDpred2-auto can slightly underperform in some situations, e.g. for CAD and Asthma here . When loWe have shown that LDpred2 provides a better, faster and more robust implementation of the LDpred model. When compared to recently derived methods that showed higher predictive performance than LDpred1, LDpred2 provides the highest predictive performance for all the real traits tested here. For now, we recommend using the same HapMap3 variants used in PRS-CS and used here when running LDpred2. Indeed, HapMap3 variants have passed a number of quality controls, are generally well imputed and offer a good coverage of the whole genome. However, investigating alternatives in variant selection for LDpred2 and other PGS methods is a direction of future research for us. Would it be beneficial e.g. to use a set enriched for statistically significant variants?https://github.com/privefl/bigsnpr). A tutorial on the steps to run LDpred2 using some small example data is available at https://privefl.github.io/bigsnpr/articles/LDpred2.html. The European LD reference we provide here is available at https://doi.org/10.6084/m9.figshare.13034123. We note that this is LD summary data and not individual-level data.The newest version of R package bigsnpr can be installed from GitHub (see https://github.com/privefl/paper-ldpred2/tree/master/code. We have extensively used R packages bigstatsr and bigsnpr (All code used for this paper is available at  bigsnpr  for easy bigsnpr  for shapbtaa1029_Supplementary_DataClick here for additional data file.