VCU trials can provide unbiased estimates of post-breeding trends given that all data is used. Dropping data of genotypes tested for up to two years may result in biased post-breeding trend estimates.−1 year−1 and a negative non-genetic trend (− 0.11 dt ha−1 year−1) were observed. Bias increased with increasing genotype-by-year variance and disappeared with random selection. We simulated single-trait selection, whereas decisions in VCU trials consider multiple traits, so selection intensity per trait is considerably lower. Hence, our results provide an upper bound for the bias expected in practice.Increasing yield trends are seen on-farm in Germany. The increase is based on genetic trend in registered genotypes and changes in agronomic practices and climate. To estimate both genetic and non-genetic trends, historical wheat data from variety trials evaluating a varieties’ value for cultivation und use (VCU) were analyzed. VCU datasets include information on varieties as well as on genotypes that were submitted by breeders and tested in trials but could not make it to registration. Therefore, the population of registered varieties (post-registration population) is a subset of the population of genotypes tested in VCU trials (post-breeding population). To assess post-registration genetic trend, historical VCU trial datasets are often reduced, e.g. to registered varieties only. This kind of drop-out mechanism is statistically informative which affects variance component estimates and which can affect trend estimates. To investigate the effect of this informative drop-out on trend estimates, a simulation study was conducted mimicking the structure of German winter wheat VCU trials. Zero post-breeding trends were simulated. Results showed unbiased estimates of post-breeding trends when using all data. When restricting data to genotypes tested for at least three years, a positive genetic trend of 0.11 dt haThe online version contains supplementary material available at 10.1007/s00122-023-04266-5. In Germany, on-farm crop yield has increased during the last decades  is a subset of the population of genotypes tested in VCU trials (post-breeding population). In general, the genetic trend can be estimated for both populations. The genetic trend of interest is the genetic trend of varieties that have been registered, as only these varieties can be grown on-farm. We can therefore say that this trend is a post-registration trend. In contrast, trend estimates from VCU trial data that includes all submitted genotypes represent post-breeding trends. This may be of particular interest to breeders. Both trend estimates consider the trend for a target region and thus across the locations within the region.For trend estimation from VCU trial data, a simple and commonly used approach is to restrict the dataset to genotypes which were either registered at the end of a cycle  or which underwent at least three or four years of testing  between 1983 and 2016 (34 years) were used Table . Each trIn general, data were organized in overlapping three-year cycles. Every year a new cycle with a new set of genotypes started. One cycle consists of three trial series, i.e. three years of trials. In each year, three trial series from three subsequent cycles were tested in parallel with one series in the first, one in the second and one in the third year. All genotypes of each cycle were tested in the first year. After the first and second year on average 51% and 26% of all genotypes were culled as the aim is to register only the best genotypes as new varieties. Note that the number of genotypes tested in the first trial series increased from approximately 60 in 1983 to approximately 120 in 2016, but proportions of culled genotypes after the first series remained constant . In contrast, there was an increase in the proportion of genotypes in the third year of testing from 18 to 28% . The selection decision is based on empirical best linear unbiased estimates (BLUEs) of genotype means for several traits. The most important decision criterion is an index combining yield, quality and ratings of resistance . To have a benchmark for selection and to allow comparing genotypes from different series, some well-known check varieties were included in all trials. Each check variety was included in more than one cycle and thus occurs in more than three years  and 618 (21%) out of 2901 candidates were culled after the first year and after the second year of testing, respectively. Furthermore, only about one half of the remaining candidates were registered as varieties later on. The data from candidates included 64,792 mean values from 64,792 genotype-by-year-by-location combinations, whereas the data of checks included 13,010 mean values from 10,003 genotype-by-year-by-location combinations. Only check varieties can occur more than once within a year-by-location combination because they can be present in different series side by side.Within a trial series and cycle, all genotypes were tested in the same set of locations. On average, genotypes within a series were tested in 11.4, 12.6, and 24.1 locations in the first, second and third year, respectively. Within a cycle, only a few locations were repeated across years. On average 1.9, 1.3 and 7.6 locations occurred subsequently in the first two years, in the first and third and in the last two years, respectively. This resulted in a large number of tested genotype-by-location combinations  compared to the number of tested genotype-by-year-by-location combinations . The dataset is sparse in the sense that only 0.65% of the possible genotype-by-year-by-location combinations are available.The complete dataset of historical winter wheat data is denoted as BSA. As VCU trial dataset used for trend analysis are commonly reduced by dropping genotypes tested for up to two years . All effects were simulated as normally distributed with zero expectation and independent and identically distributed effects. VCs estimated from the historical data . Additionally, C datasets were modified afterwards by dropping some observations. Specifically, datasets C-1 and C-2 were created by dropping candidates that were tested only in one or in up to two years. Dropping candidates which were tested for one or up to two years results in an informative missing data pattern  and thus should not affect expectation of parameters estimated from the dataset. Duplicates only occurred for check varieties. As a consequence, the data had a single mean for each genotype-by-year-by-location combination within the dataset. Therefore, model (2) simplifies to model (5) given below. Thus, the model for analysis is identical to the model for simulating the data. After dropping duplicates, data were simulated analogously to dataset C. The simulated dataset was denoted as SM (for single mean). It was reduced to SM-1 and SM-2 by dropping genotypes tested for up to one or up to two years. The datasets SM, SM-1, and SM-2 had 75,795, 55,106 and 41,102 observations, respectively. As the additional drop-out of check varieties’ data was completely at random (MCAR), this step did not change the missing data pattern. Thus, the datasets C and SM had a missing-at-random (MAR) data pattern. The other four datasets  had an informative missing pattern (MNAR). 100 simulation runs were performed for the second simulation.The third simulation was similar to the first one, but replaced the yield-based selection by a random selection. In this case, the missing data pattern is MCAR. This simulation served as a benchmark for the other simulations.In the fourth simulation, the genotype-by-year variance was increased to 55.75. This fourth simulation was added to check if bias in trends can be modified when increasing genotype-by-year variance. All remaining simulation steps including the number of simulation runs are identical to the first simulation. Datasets were denoted as I, I-1 and I-2 (for the increase in genotype-by-year VC).All datasets were analysed using the same model. As model (2) is computationally demanding, it was not used within the simulation. The model was reduced toIn each simulation run and each dataset, the variance components for all effects were estimated. Subsequently, these estimates were averaged across simulation runs. Furthermore, the slopes for genetic and non-genetic trends were estimated. The mean squared error (MSE) between estimated and simulated values of The analysis of the historical VCU trial datasets showed large variances for year, location and year-by-location compared to genetic variances Table . This isGenetic VCs  were slightly smaller for BSA-2 compared to BSA. Additionally, the estimated non-genetic trend was smaller for BSA-2 compared to BSA. If data were reduced to the 48 check varieties only, VC and trend estimates were comparable to the estimates obtained for the complete data.For SM, estimated 95% confidence interval for all VCs covered the simulated value and no bias was detected. In contrast, analysis of C, C-1, C-2, SM-1, and SM-2 showed biased VC estimates compared to the VC simulated Tables , 4. For Means of estimated genetic and non-genetic trends are close to zero with 95% confidence interval covering the value zero for C and SM Tables , 4. In cThe simulations showed that when using a proper mixed model and all available data (model 3 with datasets SM), VC estimates were unbiased. Additionally, non-genetic trend and post-breeding genetic trend can be estimated without bias. This is expected as datasets are then large with an MAR data pattern and the analysis is based on restricted maximum likelihood estimation  differs from the population of genotypes submitted by breeders for registration (post-breeding). Submitted genotypes in the post-breeding population are the result of breeders’ selection. In contrast, registered varieties are based jointly on selection by breeders in their trials and selection exercised by examination offices in VCU trials. The post-registration population is a sub-population selected from the post-breeding population. Therefore, within a cycle both populations differ systematically. Selection performed in VCU trials causes selection gain and therefore results in larger expected means in the post-registration population compared to the corresponding post-breeding population.For the datasets C-1, C-2, SM-1, SM-2, I-1 and I-2, the simulation showed that there are two sources of bias for VC estimates: the differences between model (2) used for data simulation and model (5) used for analysis, as well as the informative drop-out in these reduced datasets.Bias in VC estimates found in C, C-1 or C-2, but not in the corresponding datasets SM, SM-1 or SM-2, were caused by the simplification made in model (5). In Germany, VCU trials are organized in overlapping series. In each year, a new series with new genotypes but usually the same check varieties is started. As these series are tested in the same locations in two or three years, check varieties can occur more than once in a given year-by-location combination. This results in a positive correlation between these mean values. The common approach (model 3) is to ignore this correlation . This increase should decrease the selection gain reached by examination offices in the third year. As the gain decreases in more recent cycles, this should reduce post-registration genetic trend estimate compared to post-breeding genetic trend estimates. In contrast, our simulation showed overestimated genetic trends when using data from candidates with at least two or three years of testing. Therefore, the observed bias in post-breeding trend estimates probably is based on the selection of candidates. Candidates were selected according to their estimated yield in the current year (current and previous years in the second selection step), and thus on the confounded effects of genotype and genotype-by-year. Therefore, candidates with positive genotype-by-year effects are more likely selected for further testing compared to candidates with negative genotype-by-year effects. As this positive effect cannot be reproduced in subsequent years, it is covered by the regression on the year of testing and thus is interpreted as negative non-genetic trend. Furthermore, as the simulated overall trend is zero, the estimated genetic trend must be positive.The simulation results provide an upper bound for the bias for post-breeding genetic and non-genetic trend expected from informative drop-out, as selection in our simulation was based on BLUPs of a single trait only, whereas in actuality selection decisions are more complex. Indeed, the selection of the BSA are based on BLUEs for yield, as well as for a large number of quality and resistance traits. If selection is based on more traits, the selection intensity for yield is much lower than assumed in our simulation. Note that we replaced selection based on BLUE by BLUP-based selection, as BLUPs have smaller mean squared error even in small experiments  shown in our simulation when dropping genotypes tested for up to two years. Note that bias for historical VCU trial data can vary between crops as the ratio of genotype to genotype-by-year variance may differ from the ratio found in winter wheat. For smaller ratio and lower selection intensity the bias is expected to be smaller than the one seen in our simulation. At the same time, reduction of data reduced computational burden, so that there could be reasons to accept the bias of in trend estimates from reduction of VCU trial data. An unbiased estimation of post-registration trends is not possible from VCU trial data. Unbiased post-registration trends require data obtained after registration. In Germany, data of post-registration trials of registered varieties, performed by federal states in Germany (Landessortenversuche), can be used for post-registration trend estimation.The estimated post-breeding genetic trend from the considered winter wheat data across all quality groups was 0.56 dt hag et al.  for the g et al.  reportedl et al.  and Bilgl et al. . For a dl et al. . Rizzo el et al.  reportedSupplementary file1 (DOCX 58 kb)Below is the link to the electronic supplementary material.


Early leaf spot (ELS) and late leaf spot (LLS) diseases are the two most destructive groundnut diseases in Ghana resulting in ≤ 70% yield losses which is controlled largely by chemical method. To develop leaf spot resistant varieties, the present study was undertaken to identify single nucleotide polymorphism (SNP) markers and putative candidate genes underlying both ELS and LLS. In this study, six multi-locus models of genome-wide association study were conducted with the best linear unbiased predictor obtained from 294 African groundnut germplasm screened for ELS and LLS as well as image-based indices of leaf spot diseases severity in 2020 and 2021 and 8,772 high-quality SNPs from a 48 K SNP array Axiom platform. Ninety-seven SNPs associated with ELS, LLS and five image-based indices across the chromosomes in the 2 two sub-genomes. From these, twenty-nine unique SNPs were detected by at least two models for one or more traits across 16 chromosomes with explained phenotypic variation ranging from 0.01 - 62.76%, with exception of chromosome (Chr) 08 (Chr08), Chr10, Chr11, and Chr19. Seventeen potential candidate genes were predicted at ± 300 kbp of the stable/prominent SNP positions . The results from this study provide a basis for understanding the genetic architecture of ELS and LLS diseases in African groundnut germplasm, and the associated SNPs and predicted candidate genes would be valuable for breeding leaf spot diseases resistant varieties upon further validation. Arachis hypogaea L. (2n = 4x = 40)] is an allotetraploid originating from South America and is a grain legume that is largely grown in the tropical and subtropical regions of the world .Groundnut [he world . It comphe world . Groundnhe world . It is ahe world . Increashe world . GloballPassalora arachidicola (S. Hori) and late leaf spot (LLS) also caused by the fungus Nothopassalora personata (Berk. & Curt.) are the two most destructive groundnut diseases in Ghana with a potential yield loss of ≤ 70%  caused by the fungus of ≤ 70% . Chemicaof ≤ 70% . Farmersof ≤ 70% . Resistaof ≤ 70% . This maof ≤ 70% . In addiof ≤ 70% .Verticillium dahliae Kleb) in olive (Olea europaea L.) (Puccinia striiformis f. sp tritici) in wheat (Zea mays L.)) -image method (which is the science of making measurements through the use of an RGB camera), together with conventional and marker-assisted selection (MAS) may overcome the flaws of current breeding methods . The apppaea L.) , yellow in wheat , and letays L.)) .via genome-wide association study (GWAS)  . Comparey (GWAS) . By thisy (GWAS) . In addiThe statistical model adopted is one of the setbacks to the power of detection in GWAS . TraditiThe multi-locus models have become the state-of-the-art procedure to identify genetic bases for complex traits due to their power of detection and robustness . TherefoTwo hundred and ninety-four African groundnut collections . The incThe accessions were arranged in lattice design with three replicates. A plot was made up of one row of 2 m long with a spacing of 0.5 m between rows and 0.2 m between plants. One seed was planted per hill. Weeding was carried out whenever necessary to ensure a weed-free trial.® 400EC, Pendimethaline 400g/L, EC) and glyphosate (480g/L SL) at 200 ml/15 liters of water immediately after planting. Weeds were manually controlled regularly by hoeing between the rows and pulling weeds within rows as well as on top of plots using hands to ensure a weed-free experiment. Earthen-up was done 40 days after planting to enhance aeration. A compound fertilizer made of nitrogen(N), phosphorus (P), potassium (K) together with sulphur (S), zinc (Zn) and boron (B), i.e., (N:P:K: 11:22:21+5S+0.7Zn+0.5B) was applied on the sides of the plants two weeks after seedling emergence at a rate of 150 kg/ha. At the same time, the experiment was sprayed against aphis infestation using K-Optimal  at 40 ml in a 15L Knapsack sprayer.Pre-emergence weed control was done by spraying -ti is the number of days between two successive scores  was used to measure the canopy normalized difference vegetation index (NDVI) of the vegetation from each plot. The instrument was aligned horizontally and maintained at a constant height of 50 cm over the plants’ canopy with a walking speed to cover the row within 60 seconds. The GreenSeeker optical sensor uses radiation of 650 ± 10 of red and 770 ± 15 of near-infrared band independently. The sensor uses built-in software to directly calculate the NDVI value using the formula: (NIR-RED)/(NIR+RED) (GreenSeekerNIR+RED) . The NDVThe RGB digital camera  was used to take close-up images of one plot at a time. The camera was set to “auto” to allow the camera to adjust the required sharpness, brightness, and hue depending on the light available, with the zoom of the lens being at 0. A part representing the plot was selected for the image. The camera was maintained at the same height of 80 cm over the row for all pictures and facing the sun to avoid any shadows on the pictures. Pictures were taken at 70, and 90 days after planting. Digital image analysis was carried out in Image J software by converting hue (H), saturation (S), and brightness (B) values into the dark green color index (DGCI).http://github.com/george-haddad/CIMMYT open software; Copyright 2015 Shawn Carlisle Kefauver, University of Barcelona); produced as part of Image J/Fiji  (Green area (GA=H 60-120°), greener area (GGA= H 80-120°), Hue angle, and crop senescence index (CSI=(100*(GA-GGA)/GA)  were extsc/Fiji) . Both GApqr=μ+Gp+Eq+GEpq +Rr(q)+ϵpqr , where ypqr stands for the individual observation of pqrth experiment unit, μ is the total average phenotypic value, Gp is the effect of the pth genotype, E1is the effect of the qth year, GEpq is the interaction effect between the pth genotype and the qth year, Rr(q) is the effect of the rth block within the qth year, and εpqr is the residual error. All factors were considered random.Data collected manually and imaged based across the two years (2020 and 2021) were subjected to analysis of variance (ANOVA) in SAS  with a general linear model procedure (PROC GLM), following statistical model yDescriptive statistics: mean, standard error of the mean, kurtosis, and skewness were calculated in SAS  from the two years data. Pearson correlation coefficients were computed and visualized in R with the corrplot package .2) for each trait was computed following the formula proposed by In addition to the above, broad-sense heritability  was used to retrieve the optimum K (ΔK) (via TASSEL 5.2.31 software (2) fell to half of its highest value. The graph of the LD decay was produced with the help of GraphPad Prism version 5.01  within the pairwise distance of 5 Mb in the genome.Population structure was analyzed re 2.3.3  with there 2.3.3 . After am K (ΔK) . Only thm K (ΔK) . We furtsoftware . A kinshsoftware . LD betwsoftware . The panTo prevent environmental (year) variation in phenotypic data, the best linear unbiased predictor (BLUPs) for each accession for all traits were calculated using R package lme4  with theA. hypogaea V1) (https://phytozome-next.jgi.doe.gov/). The gff3 file was retrieved from the phytozome website (https://phytozome-next.jgi.doe.gov/) and information gene ontology (GO)   availablogy (GO) , proteinogy (GO) , Kyoto Eogy (GO) , and traogy (GO) ) were fu2 of the four image-based traits , vegetative index trait (NDVI), manually scored traits (ELS and LLS), and quantitatively computed traits (AUDPC-ELS and -LLS) among the 294 groundnut accessions based on the two years (2020 and 2021) evaluation in this study are shown in Table. The hue, GA, GGA, CSI (from the image-based phenotyping) and NDVI values ranged (mean ± Standard error of mean) from 38.37-90.20 (68.03 ± 0.56), 0.30-0.92 (0.63 ± 0.01), 0.23-0.81 (0.48 ± 0.01), 9.27-45.90 (26.19 ± 0.45) and 0.36-7.09 (0.68 ± 0.02), respectively , environment (E), and their interaction (GE), while NDVI differed due to E  with quality criteria of minor allele frequency< 0.05 and call rate<0.95. Out of these, 8,152 SNPs were located on one of the linkage groups in the two sub-genomes (A and B), while 619 SNPs were located on scaffolds. The SNPs located on the scaffolds were excluded from the downstream analysis. The longest and shortest chromosome (Chr) spanned 149.79 Mb (Chr15) and 49.33 Mb (Chr08), respectively , replicates within E, G, GE, and error were considered as random effects. With the six multi-locus models, a total of 97 SNPs distributed across the 20 chromosomes with an average of ≈5 SNPs per Chr and range of 1 SNP on Chr15 to 11 SNPs on Chr16 were detected  Table 4.In addition, nine SNPs  were associated with at least one model with PVE ≥ 10%, hence these were considered as major SNPs for downstream analysis for candidate genes prediction Table 4.As typical of quantitative traits, seventy SNPs were trait and model specific with LOD and PVE ranging 3.04 (AX-177637712 on Chr17 with LLS) to 35.90 (AX-147227883 on Chr07 with GGA), and<0.01% (AX-177637712 on Chr17 with LLS) to 21.79% (AX-176797562 on Chr02 with CSI)  of the 17 candidate genes predicted for Cis-acting regulatory elements (CAREs) with PlantCare database , gibberellin (GA), auxin, methyl jasmonate (MeJA), MYB binding site involved in flavonoid biosynthetic genes regulation (MBSI) and so) were detected in at least 1 of the predicted candidate genes highlighting the possibility of their involvement in modulating groundnut response to leaf spot pathogen. The actual roles of the 17 predicted candidate genes warrant further screening and functional validation to unravel the bases of correlation among the studied traits (2 (Leaf spots (ELS and LLS) diseases are the two most destructive groundnut diseases in Ghana resulting in ≤ 70% yield losses which is controlled largely by chemical method . To spee2 Table 1 One of setbacks in phenotyping large germplasm is the laborious nature coupled with human error among others , which hRecent advances in plant phenotyping involve the use of unmanned aerial vehicles (UAVs) to collect several images generating large amounts of data. Several studies have reported that UAVs are faster and more effective for phenotyping large populations for traits such as height and drought tolerance in groundnut breeding , hence pLeaf spot diseases are well known to affect photosynthetic capacity of leaves . Three iThe advancement in high-throughput genotyping, next generation sequencing, bioinformatics tools, statistical models, etc., have served as catalyst to access valuable information from genomic databases and a large number of germplasm, allowing effective harnessing of genetic diversity of a crop . Such diA number of studies by linkage and association mappings have been conducted on leaf spot diseases in groundnut . HoweverOne advantage of GWAS is the power to detect SNPs in a narrow genomic regions of which causal variants could result in variation in traits of economic importance such as leaf spot diseases . HoweverIn all, ninety-seven SNPs were detected by the six multi-locus GWAS models. Out of which twenty-nine SNPs were detected by at least two models for one or more traits across 16 chromosomes with explained phenotypic variation ranging from 0.01 - 62.76%, with exception of Chr08, Chr10, Chr11, and Chr19. Two hundred and fifty-three genes were located within 300 kbp of 14 SNPs, from seventeen potential candidate genes were predicted. Most of the predicted candidate genes were found to SA, ABA, GA, auxin and MeJA responsive and MBSI CAREs implicated in plant response to biotic stresses. The results from this study would be useful for breeding leaf spots resistance cultivars.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.RO-F, ES, MR, DF, DO, and PO-A conducted the experiments. BK, RO-F, DP, and MBa organized and supervised the overall project. BK, YK, and ES performed the data analyses and wrote the manuscript. RO-F, DO and MBu edited the manuscript. All authors contributed to the article and approved the submitted version.This study was made possible by the generous support of the BMGF funded Accelerated Varietal Improvement and Seed Systems for Legumes and Cereals in Africa (AVISA) Project Grant Number OPP1198373 and the American people through the United States Agency for International Development (USAID) Cooperative Agreement No. 7200AA 18CA00003 to the University of Georgia as management entity for U.S. Feed the Future Innovation Lab for Peanut (2018–2023). The funders had no role in experiments, data analyses and publication.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.


Recent advances in maize doubled haploid (DH) technology have enabled the development of large numbers of DH lines quickly and efficiently. However, testing all possible hybrid crosses among DH lines is a challenge. Phenotyping haploid progenitors created during the DH process could accelerate the selection of DH lines. Based on phenotypic and genotypic data of a DH population and its corresponding haploids, we compared phenotypes and estimated genetic correlations between the two populations, compared genomic prediction accuracy of multi-trait models against conventional univariate models within the DH population, and evaluated whether incorporating phenotypic data from haploid lines into a multi-trait model could better predict performance of DH lines. We found significant phenotypic differences between DH and haploid lines for nearly all traits; however, their genetic correlations between populations were moderate to strong. Furthermore, a multi-trait model taking into account genetic correlations between traits in the single-environment trial or genetic covariances in multi-environment trials can significantly increase genomic prediction accuracy. However, integrating information of haploid lines did not further improve our prediction. Our findings highlight the superiority of multi-trait models in predicting performance of DH lines in maize breeding, but do not support the routine phenotyping and selection on haploid progenitors of DH lines. The doubled haploid (DH) technology based on in vivo haploid induction has become one of the most important tools in maize breeding during the past two to three decades , and it A typical DH-line-based hybrid breeding scheme includes a first stage of selection among the DH lines per se followed by one or several stages of testcross hybrid selection . AlthougEmpirical studies for predicting field performances of DH lines using genomic prediction have been reported in maize ,7,8,9. TIn this study, we analyzed phenotypic and genotypic data of a DH population derived from a biparental cross, and phenotypic data of haploid lines created from the DH lines. In both populations, a total of 35 traits, including 17 agronomic traits and 18 stalk quality traits, were evaluated in four environments. Our objectives were to (1) characterize phenotypes of the 35 traits in the DH and corresponding haploid populations; (2) estimate phenotypic and genotypic correlations between the DH and haploid lines; (3) compare genomic prediction accuracies of multi-trait models using agronomic traits to predict stalk quality traits in a single-environment trial or across multi-environment trials against conventional univariate models; and (4) evaluate whether including information of haploid lines for predicting DH lines could further improve the prediction accuracy over using DH lines alone.In both the DH and haploid populations , a totalp = 0.012, t-test. The DH population showed larger dispersion for 11 of the 18 stalk quality traits; however, the mean difference was not significant  and crude fat (FI::FAT) measured from the fourth internode above the ground . We furtTo estimate phenotypic and genetic correlations between DH lines and their corresponding haploids, we performed a bivariate analysis for each of the 35 traits in BJ2014 and SJZ2014, which were the two environments with the most complete datasets (see Methods). In BJ2014, phenotypic and genetic correlations of the 35 traits ranged from 0.06 to 0.63 (median = 0.38) and 0.21 to 0.89 (median = 0.71), respectively . In SJZ2We further compared genetic correlations within tissues  in each environment and found generally higher genetic correlations for agronomic traits than for stalk quality traits in SJZ2014 across all tissues . In BJ20p = 0.13) or for stalk quality traits across environments (p = 0.19). However, we observed that agronomic traits generally had higher heritability than stalk quality traits in both environments  of the 35 traits ranged from 0.14 to 0.66 and from 0.20 to 0.61 in the DH and corresponding haploid populations, respectively . In SJZ2ronments .To visualize the genetic composition of DH lines in terms of parental haplotypes, we reconstructed and characterized recombination events on each chromosome of DH lines using the maizeSNP3K chip, which is a subset of the Illumina MaizeSNP50 BeadChip . We foun2)). Estimated prediction accuracies of multi-trait models fit with MegaLMM were significantly higher than both univariates model for 11 (BJ2013), 6 (BJ2014), 7 (SJZ2013), and 15 (SJZ2014) stalk quality traits in the four environments  to multi-trait models that considered all traits at once (fitting with MegaLMM method). For multi-trait genomic prediction, we considered the “trait-assisted” scenario where the key “focal” traits were measured for a subset of DH lines, but some “secondary” traits were measured for all DH lines. We considered stalk quality traits as focal traits and agronomic traits as secondary traits, because all the agronomic traits in our study can be directly measured in the field, while stalk quality traits require complex chemical experiments in the laboratory or calibration of near-infrared spectroscopy (NIRS) models. We applied CV2-style cross-validation  to evaluronments  based on), 6 BJ20, 7  were used in our study. For each model, the uppercase letters before and after the hyphen represent genetic and residual covariance structures, with D = diagonal and UN = unstructured. The diagonal model (D-D) assumes no genetic and residual covariance among locations, and therefore it is equivalent to a single-environment model. In addition, we also fitted the multi-trait model using MegaLMM, which fits a factor-analytic covariance structure for both genetic and residual covariances but uses a novel prior structure for the factor loadings to increase efficiency and power.We compared prediction accuracies of different multi-trait models using the prediction accuracy from GBLUP in the single-environment model (D-D) as a baseline. Here, we estimated prediction accuracy as cor , because the phenotypes of stalk quality traits of the same genotypes were collected from individuals grown in different environments . We founSince each DH line is derived from one haploid plant, Geiger et al.  suggesteFor DH + Hap-based genomic prediction, in each environment, we treated the 18 stalk quality traits of the DH population as focal traits and agronomic traits of DH and all traits of haploid populations as secondary traits, fitted the multi-trait model with MegaLMM, and used the CV2-style cross-validation procedure as described before. We found that no trait showed significant difference in prediction accuracy between DH + Hap-based and DH-based predictions .The availability of phenotypic data of both DH and haploid lines in different environments enabled us to further explore whether DH + Hap-based analysis could improve prediction accuracy of DH lines compared to DH-based analysis in the context of multi-environment trials. In the DH + Hap-based analysis, for predicting each stalk quality trait of DH lines, different environments were treated as different traits and various genetic and residual covariance structures were considered in multi-trait models. Both DH and haploid lines data were used for model training; however, only the DH lines were used for model validation. Since the UN-UN  model was difficult to converge due to increased numbers of parameters compared to fitting DH data alone, we used the factor-analytic method to model genetic covariance structures . We used cor  to estimate prediction accuracy since each experiment unit was phenotyped from different individuals, and the prediction accuracy was calculated across environments. We found that only one stalk quality trait (FI::Lignin) showed significantly improved prediction accuracy in the DH + Hap-based analysis compared to the DH-based analysis .In maize, DH technology can develop pure lines quickly and efficiently from two opposite heterotic pools, resulting in a tremendous number of possible hybrid crosses to be tested in multi-environment field trials . This imposes great challenges in field testing with a limited budget and therefore may counterbalance its potential in accelerating hybrid development. As a solution, plant breeders can select their best candidate DH lines beforehand in order to make only a limited number of promising hybrid crosses and evaluate them intensively in multi-environment field trials. In this study, we compared two possible strategies for selecting the best candidate DH lines, namely, phenotypic selection at the haploid level and genomic prediction of unphenotyped DH lines based on whole-genome molecular markers.Genetic correlations between traits measured in DH and corresponding haploid lines are indicators of achieving selection gain at the DH level from preselection at the haploid level . Geiger In the context of phenotypic selection, the expected selection gain in DH lines from indirect selection of haploid lines can be predicted from the formula )hH > hD . Since tGenomic prediction based on whole-genome molecular markers is another strategy for selecting the best DH line candidates without a need to phenotype all DH lines in the field trials. Agronomic traits can be directly measured in the field and showed high heritability. However, stalk quality traits take more effort to measure and showed lower heritability in our study. In the scenario of a single-environment trial with the DH population, we simulated the case where all DH lines are measured for agronomic traits but only a subset of DH lines are measured for stalk quality traits. We found that when integrating the agronomic traits in multi-trait models to predict unphenotyped stalk quality traits, prediction accuracy was significantly increased in comparison with using stalk quality traits alone with traditional univariate GBLUP or BayesB models. Further, in the genomic prediction of multi-environment trials within the DH population, we found that accounting for genetic covariance among locations  and the internode under the primary ear (EI), and 7 agronomic traits measured from the whole plant (WP). The 9 stalk quality traits included contents of acid detergent fiber (ADF), ash (ASH), cellulose, crude protein (CP), crude fat (FAT), in vitro dry matter digestibility (IVDMD), lignin, neutral detergent fiber (NDF), and water soluble carbohydrate (WSC). The 5 agronomic traits measured from FI and EI included rind penetrometer resistance measured at the middle of the internode (RPR), fresh weight of the internode (FreshWeight), dry weight of the internode (DryWeight), internode diameter, and internode length. The 7 agronomic traits measured from the WP included dry weight, ear height, fresh weight, leaf angle, leaf length, leaf width, and plant height. Details of phenotyping the stalk quality traits and agronomic traits were described by Hu et al.  and MengWithin each environment, for the DH population and haploid population separately, a univariate linear mixed was fitted using the sommer package :yij=μ+GiThe DH population was genotyped with the maizeSNP3K chip (3072SNPs), which is a subset of the Illumina MaizeSNP50 BeadChip . The detWe estimated phenotypic and genotypic correlation between haploid and DH populations for each of the 35 traits in BJ2014 and SJZ2014, respectively. The two environments were selected because both populations have very complete phenotypic data. Numbers of available genotypes ranged from 173–177 and 151–159 across traits in the DH and haploid, respectively. We then used medians to substitute missing values for each trait in both populations and ended up with 187 pairs of genotypes for genetic correlation analysis.D/XH and ZD/ZH are design matrices relating the fixed and random effects to each genotype. Vectors containing the random effects in Equation (1) are assumed to follow a bivariate normal distribution, centered at zero, and with covariance structure Cov = G00, and Cov = 0, where G0 is a 2 × 2 genetic covariance matrix between DH and haploid lines, 0 is a 2 × 2 residual covariance matrix for the DH and haploid populations.We fitted a bivariate linear mixed model with the BGLR package :(1)[yDyHThe genotypic correlation was estimated as follows:For each trait, the phenotypic correlation between the haploid population and the DH population was estimated as the ratio of the phenotypic covariance to the product of the square root of the phenotypic variances for the two populations :(3)rP(DBased on the filtered genotypic data (1316 markers across 187 lines), SNP markers were sorted on each chromosome according to physical positions, marker genotypes were translated to 0 if identical to Chang7-2  and to 1 if identical to Zheng58 , and a small proportion of heterozygous genotypes were set as NA (missing) because these are likely genotyping errors. After the pretreatments, graphical genotypes of each chromosome were plotted with the geom_rect function implemented in ggplot2 , and theThe objective of single-environment prediction is to simulate the case in which the breeding program can afford field trials in only one environment. Since the phenotypes of the DH population were evaluated in four environments, we analyzed each environment separately, leaving out available information from other environments. To this aim, we calculated additive genomic relationships with the A.mat function implemented in the rrBLUP package , and theTo take advantage of available information of all other phenotypes (secondary traits) to predict the phenotype of interest , we fitted a multi-trait model using the MegaLMM package  and usedt-test [The prediction accuracy was estimated as nd Cheng , and use [t-test  was apply = ′, u = ′, and ε = ′. y1, y2, y3, and y4 are the column vectors of phenotypic data in each environment; u1, u2, u3, and u4 are the column vectors of random genetic effects in each environment; ε1, ε2, ε3, and ε4 are the column vectors of random error terms associated with each environment. X and Z are design matrices relating the fixed and random effects to each genotype. Vectors containing the random effects in Equation (4) are assumed to follow a multivariate normal distribution, centered at zero, and with covariance structure Cov = G0K, Cov = IR0, and Cov = 0, where G0 is a 4 × 4 genetic covariance matrix, K is the additive genomic relationship matrix, I is an identity matrix, and R0 is a 4 × 4 residual covariance for the three locations.The DH population was evaluated in four environments for the 35 traits described above. For each of these traits, multi-trait models were fitted, treating phenotypes measured in all environments as different traits. A standard multi-trait linear mixed model was fitted:0 and R0 were assumed to have different covariance structures [G0) and residual (R0) covariance structures, where D = diagonal and UN = unstructured. The diagonal model (D-D) assumes no genetic (G0) and residual (R0) covariance among locations, and therefore it is equivalent to predict each environment separately. All these multi-trait models were implemented using BGLR with parameters of burnIn = 5000 and nIter = 20,000. In addition, we also fitted the multi-trait model using the MegaLMM package [Four different multi-trait linear mixed models  were used in our study, in which Gructures . For eac package .cor, where For all the multi-trait models, we also used the CV2-style cross-validation, which represents a scheme of prediction of lines that have been evaluated in some but not all target environments . To mimiBased on phenotypic data of DH and haploid populations collected in each environment, we explored a scientific question: whether adding the available haploid information could improve prediction accuracy of DH lines compared to using DH lines alone. To answer to this question, we compared prediction accuracies of stalk quality traits of DH lines estimated from agronomic traits of DH lines and all traits of haploid lines (DH + Hap) with those estimated from agronomic traits of DH lines only (DH).We treated phenotypes of agronomic traits of DH lines and all traits of haploid lines as secondary traits and used 80% of stalk quality traits as focal traits in a multi-trait model for model training, and the remaining 20% of stalk quality traits of DH lines were used for cross-validation. The software MegaLMM 0.1.0. was used for model fitting, and prediction accuracy was calculated in the same way as described above in the single-environment prediction in the DH population.Availability of phenotypes of both DH and haploid lines evaluated in multiple environments allowed us to explore whether using information of both DH and haploid lines could improve prediction accuracy of DH lines compared to using DH lines alone.In this analysis, for each trait, multi-trait models were fitted treating phenotypes measured from both DH and haploid lines in all environments as different traits for model training, and only masked phenotypic values of 20% DH lines in each environment for cross-validation. To avoid the issues of nonconvergence for solving mixed-model equations, we used the factor-analytic (FA) method to model genetic covariance structures to reduce the numbers of parameters to be estimated. Four regular multi-trait linear mixed models  and MegaLMM were used for model fitting. The prediction accuracy was calculated in the same way as described above in the multi-environment prediction in the DH population.


Tandem repeat expansions (TREs) are associated with over 60 monogenic disorders and have recently been implicated in complex disorders such as cancer and autism spectrum disorder. The role of TREs in schizophrenia is now emerging. In this study, we have performed a genome-wide investigation of TREs in schizophrenia. Using genome sequence data from 1154 Swedish schizophrenia cases and 934 ancestry-matched population controls, we have detected genome-wide rare (<0.1% population frequency) TREs that have motifs with a length of 2–20 base pairs. We find that the proportion of individuals carrying rare TREs is significantly higher in the schizophrenia group. There is a significantly higher burden of rare TREs in schizophrenia cases than in controls in genic regions, particularly in postsynaptic genes, in genes overlapping brain expression quantitative trait loci, and in brain-expressed genes that are differentially expressed between schizophrenia cases and controls. We demonstrate that TRE-associated genes are more constrained and primarily impact synaptic and neuronal signaling functions. These results have been replicated in an independent Canadian sample that consisted of 252 schizophrenia cases of European ancestry and 222 ancestry-matched controls. Our results support the involvement of rare TREs in schizophrenia etiology. Schizophrenia is a chronic and debilitating mental disorder. Twin, family, and adoption studies consistently support a genetic basis for schizophrenia, with estimates of heritability in the range of 60-65% from pedigree data, and around 81% from twin data . TremendHTT in Huntington’s disease). TREs in the noncoding sequence can occur in 5’ or 3’ untranslated regions (UTRs), introns, promoters, or enhancers. The impact of noncoding TREs depends on the type, length, and locations of the repeats, which may include epigenetic gene silencing, RNA toxicity mediated by protein titration, repeat-associated non-AUG translation, modulation of enhancer activity, and disruptions of boundaries demarcating 3D chromatin domains [Tandem repeats occur in DNA where sequences of one or more nucleotides are repeated directly adjacent to each other. They are a major source of genetic variation in the human genome , 10. The domains , 12–15.CACNA1C, one of the loci being replicated in multiple common variant associations for schizophrenia and bipolar disorder, Song et al. found that an intronic tandem repeat was associated with a higher risk of developing psychiatric disorders and decreased enhancer activity [Due to their repetitiveness and abundance in the human genome, tandem repeats are challenging to study at a genome-wide scale . Recent activity . Most reactivity . Despiteactivity , 23, higIn this study, we carry out a genome-wide investigation in the role of rare TREs in schizophrenia etiology. We first apply a genome-wide TRE detection pipeline  to identWe have complied with all relevant ethical regulations. The study protocol and all procedures on data from human research subjects were approved by the appropriate ethical committees in Sweden and the United States . All participants gave written informed consent.The primary WGS dataset used in this study consists of 1159 Swedish schizophrenia cases and 936 ancestry-matched population control individuals . Full deIndividuals from the schizophrenia case-control cohort were previously sequenced by our group at the National Genomics Infrastructure platform in Sweden . DNA wasWe used ExpansionHunter Denovo (EHdn) , an effiA detailed description of quality control, genome annotations and statistical analyses is provided in PDIA5 chr3:123151603-123152369, F-GCCTTCATAGCAGACATAAGCC, R - TCTGCCAGAGGTTGAGTCAC, HotStar with Q solution, Anneal 63 °C; GABRA1 chr5:161663263- 161663867, F - GCAAGAAAGGGGAGTTACCG, R - CCTAACACCTCATGCTGTACC, GXL, Anneal 60 °C. The sample NA12878 available from Coriell was used as the reference control. A 100 bp ladder was used for size reference (FroggaBio 100 bp).Selected tandem repeats predicted by EHdn were validated with gel electrophoresis size separation of PCR products of the regions of interest. The following coordinates (hg38) were amplified using the reagents, primers. and conditions specified. Takara PrimeSTAR GXL DNA Polymerase (GXL) and Qiagen HotStarTaq DNA Polymerase (HotStar) kits were used. General thermocycling conditions are as follows: GXL - 1 min 98 °C, 37x , 10 min 68 °C. HotStar – 15 min 95 °C, 37x , 10 min 72 °C. Target specific information: We obtained replication association results from an independent dataset from Canada that included 252 unrelated adult cases with schizophrenia of European ancestry and 222 ancestry-matched individuals with no major neuropsychiatric disorders  . This daWe used WGS data from 1159 schizophrenia cases and 936 ancestry-matched population controls from Sweden that were previously generated by our group  Using EHdn  we perfoWe defined a tandem repeat-containing region as a genomic location containing tandem repeats with one or more different motifs overlapping by at least 1 bp. Across all 4592 samples, we identified 21,153 unique tandem repeat motifs in 16,723 distinct regions , which is consistent with a prior report [To assess the possible functional effects of rare TREs, we used burden testing to evaluate whether rare TREs are enriched in different genomic annotations in schizophrenia cases versus controls. Only autosomal TREs were retained for burden analysis. Our power calculation suggested that we had ≥80% power to detect association signals with burden testing when the aggregated minor allele frequency was 0.01 , the genotypic relative risk was ≥4.9, and assuming a type I error level of 1×10r report . FurtherWe first compared the total number of rare TREs in schizophrenia cases versus controls in three ways: genome-wide, in genic regions only, and in intergenic regions only. When a rare TRE overlapped with any gene/transcript by at least 1 bp, it was defined as genic; otherwise, it was intergenic. We observed a significantly increased burden in schizophrenia for rare TREs  and genic rare TREs .de novo tandem repeat mutations were enriched in brain regulatory regions [Previous studies found that, in ASD, rare exonic TREs and rare TREs affecting splicing were enriched, while  regions , 17. MotP = 0.105, Supplementary Table We then compared the total number of rare TREs in schizophrenia cases versus controls within functional annotations experimentally derived from human brain tissue known to affect gene expression  within Our study is underpowered to detect individual loci of rare TREs associated with schizophrenia at genome-wide significance , combined with future improvements in variant detection methods, will likely pinpoint specific tandem repeat loci [With the current sample size, we lack the power to detect individual tandem repeat loci that are associated with schizophrenia risk at genome-wide significance. Prior studies in ASD that had sample size larger than ours but in similar magnitude (~2000 cases) also failed to implicate individual loci of tandem repeats with ASD risk , 17. Muceat loci . SubstanSupplementary Methods and FiguresSupplementary Tables


Our method provides a comprehensiveframework to benchmark and leverage the combined power of PRS for maximal performance in adesired target population.Polygenic risk scores (PRS) are an emerging tool to predict the clinicalphenotypes and outcomes of individuals. Validation and transferability of existing PRSacross independent datasets and diverse ancestries are limited, which hinders thepractical utility and exacerbates health disparities. We propose PRSmix, a framework thatevaluates and leverages the PRS corpus of a target trait to improve prediction accuracy,and PRSmix+, which incorporates genetically correlated traits to better capture the humangenetic architecture. We applied PRSmix to 47 and 32 diseases/traits in European and SouthAsian ancestries, respectively. PRSmix demonstrated a mean prediction accuracy improvementof 1.20-fold (95% CI: ; P-value = 9.17 × 10 PRS are generated when risk alleles for distinctphenotypes are weighted by their effect size estimates and summed2. Risk alleles included in PRS have traditionally beenidentified from genome-wide association studies (GWAS) results conducted on a trainingdataset, which are weighted and aggregated to derive a PRS to predict distinct phenotypes.The association between PRS and the phenotype of interest is subsequently evaluated in atest dataset that is non-overlapping with the training dataset3.Thousands of polygenic risk scores (PRS) have been developed to predict anindividual’s genetic propensity to diverse phenotypes4, LDpred6, PRS-CS7, etc.) to obtain the highest prediction accuracy in the studied dataset.PRS metadata enables researchers to replicate PRS in independent cohorts and aggregate SNPeffects to refine PRS and enhance the accuracy and generalizability in broaderpopulations8. However, optimizing PRSperformance requires methodological approaches to adjust GWAS estimate effect sizes thattake into account correlated SNPs  and refine PRS for thetarget population12. Furthermore, numerousscores are often present for single traits with varied validation metrics in non-overlappingcohorts. There is a lack of standardized approaches combining PRS from this growing corpusto enhance prediction accuracy and generalizability while minimizing bias, for a targetcohort13.Most PRS have been developed in specific cohorts that may vary in terms ofpopulation demographics, admixture, environment, and SNP availability. Limited validation ofmany PRS outside of the training datasets and poor transferability of PRS to otherpopulations may limit their clinical utility. However, pooling of data from individual PRSgenerated and validated in diverse cohorts has the potential to improve the predictiveability of PRS across diverse populations. The Polygenic Score Catalog  is apublicly available repository that archives SNP effect sizes for PRS estimation. The SNPeffect sizes were developed from various methods (e.g. P+TAll of Us ResearchProgram (AoU) and the Genes & Health cohort, and 2) present and evaluate new methods forcombining previously calculated PRS to maximize performance beyond all best performingpublished PRS. To better capture the genetic architecture of the outcome traits, we proposedPRSmix, a framework to combine PRS from the same trait with the outcome trait. Previousstudies highlighted the effect of pleiotropic information on a trait’s geneticarchitecture15. Therefore, we proposed PRSmix+ to additionally combinePRS from other genetically correlated traits to further improve the PRS for a giventrait.To address these issues, we sought to: 1) validate previously developed PRS in twogeographically and ancestrally distinct cohorts, the 16.To assess the prediction improvement, we performed PRSmix and PRSmix+ for 47 traitsin European ancestry and 32 traits in South Asian ancestry. We evaluated 1) the relativeimprovement of the proposed framework over the best-performing pre-existing PRS for eachtrait, 2) the efficient training sample sizes required to improve the PRS, 3) the predictiveimprovement in 6 groups including anthropometrics, blood counts, cancer, cardiometabolic,biochemistry and other conditions as the prediction accuracies varied in each group, and 4)the clinical utility and pleiotropic effect of the newly built PRS for coronary arterydisease. Overall, we show that PRSmix and PRSmix+ significantly improved predictionaccuracy. An R package for preprocessing and harmonizing the SNP effects from the PGSCatalog as well as assessing and combining the scores was developed to facilitate thecombining of pre-existing PRS scores for both ancestry-specific and cross-ancestry contextsusing the totality of published PRS. The development of this framework has the potential toimprove precision health by improving the generalizability in the application ofPRSA single PRS may only reflect genetic effects captured in the discovery datasetof a single study that may be only a part of the total genetic effects underlying thetrait of interest. Therefore, we harmonized and combined multiple sets of PRS to establisha new set of scores, which gather information across studies and traits. Our approachleveraged multiple well-powered PRSs to improve prediction accuracy and is detailed in17 as the resource of SNP effects to estimate singlePRSs. To avoid overfitting, we used All of Us and Genes & Healthcohorts  and the null model of only covariates.For binary traits, the prediction accuracy was converted to liability R2 withdisease prevalence approximated as the prevalence in the corresponding cohort.Our combination frameworks leveraged the PGS Catalogorts see  due to n18 to construct linear combinations of the PRS. Weproposed two combination frameworks: 1) PRSmix combines the scores developed from the sameoutcome trait, and 2) PRSmix+ combines all the high-power scores across other traits.Trait-specific combinations, PRSmix, can leverage the PRSs developed from differentstudies and methods to more fully capture the genetic effects underlying the traits. Ithas also been shown that complex traits are determined by genes with pleiotropiceffects15. Therefore, weadditionally proposed a cross-trait combination, PRSmix+, to make use of pleiotropiceffects and further improve prediction accuracy.To combine the scores, we employed Elastic NetFirst, we evaluated the improvement for each method, defined as the fold-ratio ofthe method compared to the prediction accuracy of the best single PRS. For a faircomparison with the proposed framework, we selected the best single PRS from the trainingset and evaluated its performance in the testing set. First, we performed simulations toassess the improvement with various heritabilities and training sample sizes. We estimatedthe slope of improvement of prediction accuracy by increasing training sample sizes forvarious heritabilities.All of Us program, in which 47 traits were tested in U.S. residents ofEuropean ancestry, and (2) the Genes & Health (G&H) cohort, in which 32 traitswere tested in British South Asian ancestry  theancestry . In eachancestry  and 3. C2 between PRSmix and PRSmix+ against thebest-performing single simulated PRS.To compare the performance of PRSmix and PRSmix+ against the best single PRS andevaluate the sample sizes needed for training the mixing weights, we performed simulationswith real genotypes of European ancestry in the UK Biobank given the large sample sizesavailable . Brieflytraining = 200 samples for the high heritable trait (h2= 0.4) to Ntraining = 5000 samples for the low heritable trait(h2=0.05)   and 2b. tability .All of Us research program who had undergone whole genome sequencing,and Genes & Health participants of South Asian ancestry. We randomly split theindependent cohorts into training (80%) and testing sets (20%). The training set was usedto train the weights of each PRS, referred as mixing weights, that indicate how much eachPRS explain the phenotypic variance in the training set, and the PRS accuracies wereevaluated in the testing set  and 1.19-fold  compared to the best PRS from PGS Catalogfor European ancestry and South Asian ancestry, respectively.To determine if a trait-specific combination, namely PRSmix, would improve theaccuracy of PRS prediction, we used data from European ancestry participants in theting set . We curan 2%see . Traits In European ancestry, we observed the greatest improvement of PRSmix against thebest single PRS for rheumatoid arthritis of 3.36-fold. Furthermore, in South Asianancestry, we observed that PRSmix of coronary artery disease had the best improvement of2.32-fold compared to the best-performance single PRS. Details of the prediction accuracyare shown in 2 for continuous traits and liability R2 for binarytraits (see −6) and 1.42-fold  higher compared to the bestPGS Catalog for European ancestry and South Asian ancestry, respectively. PRSmix+significantly improved the prediction accuracy compared to PRSmix, in both European andSouth Asian ancestry with 1.46-fold  and 1.19-fold, respectively (We next assessed the contribution of pleiotropic effects from cross-trait PRSsto determine if these would further improve the combination framework (PRSmix+), byincluding high-power PRSs from within 2600 PRSs in the PGS Catalog. To evaluate the powerof PRS and improve computational efficiency, we employed the theoretic power and varianceof partial Raits see . We obseaits see  and Soutaits see . We obseectively .Consistent with our simulation results, a smaller improvement was observed fortraits with a higher baseline prediction accuracy from PGS Catalog , noting −9). We note that PRSmix and PRSmix+ improveprediction accuracy for all traits  for CAD. PRSmix+ equipped with both LDpred2-auto and PGS Catalogscores also outperformed the Elastic Net combination of LDpred2 scores best observed with1.6-fold  fordepression. Interestingly, height, a highly polygenic trait21, demonstrated has the similarly best performance undera trait-specific combination  and PRSmix+ equipped with both LDpred2-auto and PGS Catalog scores  for T2D and2.87-fold  for CAD . PRSmix+g scores . Employig scores . On the g scores .24. The single best CAD PRSs(PRSCAD) s from the PGS Catalog in the training set were from Koyama S. etal25. and Tamlander M. etal.26 in European and South Asianancestries, respectively  and with Tamlander M. et al. for South Asian ancestry was 0.006 , which is the leading cause of disability andpremature death among adultsectively . In the  × 10−4) .−16) compared to PRSmix  and the best PRS from the PGS Catalog . In South Asianancestry, the integrated score with PRSmix+ showed significant continuous netreclassification of 27%  compared to PRSmix  and the best PGS Catalog . Our results also demonstrated an improvement in net reclassification for modelswithout clinical risk factors  and 0.008  in European and South Asianancestries, respectively. PRSmix obtained an incremental AUC of 0.016  and 0.006  in European and South Asianancestries, respectively. The best PGS Catalog had the smallest incremental AUC of 0.012 and 0.003  in European andSouth Asian ancestries, respectively.We assessed the incremental area under the curve (AUC) between the full model ofPRS and covariates and the null model with only covariates . PRSmix+−16), 1.60  and 1.74 , respectively. The top decile of PRSmix+ compared tothe remaining population demonstrated an increased risk of OR = 2.53 . The top decile for the best PGSCatalog versus the remainder was OR = 1.67 . For South Asian ancestry, an increased risk with OR per 1-SD ofthe best PGS Catalog, PRSmix and PRSmix+ was 1.24 , 1.39 , 1.40  and 1.50 , respectively. In South Asian ancestry, PRSmix+demonstrated an OR of 2.34 , and with the best PGS Catalog, OR was 1.73  for the top decile versus theremaining population.We also compared the risks for individuals in the top decile versus theremaining population . For EurMoreover, we observed that there is a plateau of improvement for PRSmix from thetraining size of 5000 in both European and South Asian ancestries , which aAllof Us between PRSCAD with 1815 phecodes to compare the pleiotropy ofPRS and assess the relationship between CAD PRS and disease phenotypes given the inherentuse of pleiotropy in development (−25) and 1.07  for circulatory system and endocrine/metabolic system  in elopment . As expec system . The Phec system .All of Us and Genes & Health cohortsshowcasing a framework to develop the most optimal PRS for a given trait in a targetpopulation leveraging all existing PRS. Across 47 traits in All of Us cohort and 32 traitsin the Genes & Health cohort with either continuous traits or binary traits withprevalence > 2%, we demonstrated substantial improvement in average predictionR2 by using a linear combination with Elastic Net. The empiric observations areconcordant with simulations. To our knowledge, there has been a number of emerging studiesto combine PRS, but there is a limited number of frameworks that comprehensively evaluate,harmonize, and leverage the combination of these scores27. Our studies permit several conclusions for the development,implementation, and transferability of PRS.In this paper, we propose a trait-specific framework (PRSmix), and cross-traitframework (PRSmix+) to leverage the combined power of existing scores. We performed andevaluated our method using the 28.By leveraging the PGS Catalog, our work carefully harmonizes the risk alleles to estimatePRS across all scores and provides newly estimated per-allele SNP effects  to assist the interpretability of the models.First, externally derived and validated PRS are generally not the most optimal PRSfor a given cohort. Consistent with other risk predictors, recalibration within the ultimatetarget population improves performance10. We assessed the expected sample sizes to estimate the mixing weights viasimulations and real data. Our results demonstrated that while low heritability traitsbenefit the most, they require a greater training sample size.Second, previous studies selected an arbitrary training sample size to estimatethe mixing weights, which may lead to a poor power of the combination frameworks andinaccurate estimate of sampling variance30.Third, we leveraged all PRS, including those not trained on the primary trait, tosystematically optimize PRS for a target cohort. We showed that PRSmix improved theprediction by combining the scores matching the outcome trait. In addition, we showed thatPRSmix+ was able to leverage the power of cross-traits, which highlighted the contributionof pleiotropic effects to enhance PRS performance. We leverage prior work demonstrating theeffects of pleiotropy on complex traits19 using a limited number of correlated traits. wMT-SBLUP requiredGWAS’s sample sizes, heritability, and genetic correlation between all traits.LDpred2-auto required GWAS summary statistics and initialized heritability and proportion ofcausal SNPs. Krapohl et al.20 and Abrahamet al.8 proposed to use Elastic Net tocombine the scores developed from summary statistics, and correlated traits were selectedwith prior knowledge. However, these strategies consider scores developed from a particularmethods using predefined summary statistics. Our framework utilizes all PRSs available inthe PGS Catalog which were optimized for their target traits. Additional summary statisticsand PRS scores could be added to further enhance the models. We let our Elastic Net modelpenalize the component PRSs without the need for prior knowledge. Elastic Net can selectPRSs to include and efficiently handle multi-collinearity33.Furthermore, PRSmix and PRSmix+ only required a set of SNPs effect to estimate the PRSs andestimated the prediction accuracy to the target trait to select the best scores for thecombination. Additionally, compared to the preselected traits for stroke by Abraham etal.8 we also observed that our methodcould identify more related risk factors to include compared to previous work conducted onstroke  in the target cohort might limit the validation and transferabilityof PRS37. Although these factors wereconsidered by using a subset of the target cohorts as training data, it is necessary to havePRS developed on similar baseline characteristics. Lastly, with the expanding of allbiobanks, there might be no perfect distinction between the samples deriving PRS and thetesting cohort, future studies may consider the potential intersection samples to train thelinear combination.Our work has several limitations. First, the majority of scores from PGS Catalogwere developed in European ancestry populations. Further non-European SNP effects willlikely improve the single PRS power, which may in turn, also improve the prediction accuracyof our proposed methods. Second, the Elastic Net makes a strong assumption that the outcometrait depends on a linear association with the PRS and covariates. However, a recent studydemonstrated there is no statistical significance difference between linear and non-linearcombinations for neuropsychiatric diseaseIn conclusion, our framework demonstrates that leveraging different PRS eithertrait-specific or cross-trait can substantially improve model stability and predictionaccuracy beyond all existing PRS for a target population. Importantly, we provide softwareto achieve this goal in independent cohorts.All of Us Research Program is a longitudinal cohortcontinuously enrolling (starting May 2017) U.S. adults ages 18 years and older fromacross the United States, with an emphasis on promoting inclusion of diverse populationstraditionally underrepresented in biomedical research, including gender and sexualminorities, racial and ethnic minorities, and participants with low levels of income andeducational attainment.38 Participantsin the program can opt-in to providing self-reported data, linking electronic healthrecord data, and providing physical measurement and biospecimen data.39 Details about the All ofUs study goals and protocols, including survey instrumentdevelopment,40 participantrecruitment, data collection, and data linkage and curation were previously described indetail.41The All of Us ResearcherWorkbench platform, which is a cloud-based analytic platform that was built on the Terraplatform.42 Researchers gainaccess to the platform after they complete a 3-step process including registration,completion of ethics training, and attesting to a data use agreementattestation.43All of Us uses a tiered approach based on what genomic data isaccessible through the Controlled Tier, and includes both whole genome sequencing (WGS),genotyping array variant data in multiple formats, as well as variant annotations,access to computed ancestry, and quality reports.44 This study includes data on the 98,600 participants with (WGS) datain the All of Us v6 Curated Data Repository release. Participant datain this data release was collected between May 6, 2018 and April 1, 2021. This projectis registered in the All of Us program under the workspace name“Polygenic risk score across diverse ancestries and biobanks.”Data can be accessed through the secure 45.Genes & Health is a community-based genetics study enrolling British SouthAsian, with an emphasis on British Bangladeshi (two-thirds) and British Pakistani(remaining) people, with a goal of recruiting at least 100,000 participants. Currently,over 52,000 participants have enrolled since 2015. All participants have consented forlifelong electronic health record access and genetic analysis. The study was approved bythe London South East National Research Ethics Service Committee of the Health ResearchAuthority. 97.4% of participants in Genes & Health are in the lowest two quintilesof the Index of Multiple Deprivation in the United Kingdom. The cohort is broadlyrepresentative of the background population with regard to age, but slightlyover-sampled with females and those with medical problems since two-thirds of peoplewere recruited in healthcare settings such as General Practitioner surgeries17, which is a publiclyaccessible resource cataloging published PRS, including the metadata. The metadataprovides information describing the computational algorithms used to generate the score,and performance metrics to evaluate a PRS17. At the time of this study, over 2,600 PRS were cataloged in the PGSCatalog  designed to predict 538 distinct traits.Polygenic risk scores were obtained from the Polygenic Score (PGS)CatalogAll of Us v6 Data Release as detailed in Clinical phenotypes were curated using a combination of electronic health recorddata, direct physical measurements, and/or self-reported personal medical history data,from the glmnet” R package46 (version 4.1) to combine the estimated PRS. First, we randomly splitthe independent cohorts into 80% of training and 20% testing. The PRS in the training setwas standardized with mean 0 and variance 1. Before conducting linear combination, wefirst evaluated the performance of each individual PRS by their power and P-value (seebelow). An Elastic Net algorithm was used with 5-fold cross-validation and defaultparameters to estimate the mixing weights of each PRS. The mixing weights were thendivided by the corresponding original standard deviation of the PRS in the trainingset.We proposed PRSmix to combine PRS of outcome traits and PRSmix+ to combinehigh-power PRS (defined in the following subsection) from all traits obtained from PGSCatalog. The linear combination was conducted by using an Elastic Net algorithm from the“i in the training set, respectively. i. To derive the per-allele effect sizesfrom the combination framework, we multiplied the SNP effects with the correspondingadjusted mixing weights: Where j and j in PRSi. We setj is not in PRSi. The adjusted effect sizes were then utilizedto calculate the final PRS.Where The mixing weights for PGS Catalog scores for PRSmix and PRSmix+ in Europeanancestry are provided in 47: ϕ is the Chi-squared distribution function,α is the significance level, and λ isthe non-centrality parameter which can be estimated as R2 is the sample size and estimatedprediction accuracy in the testing set, respectively. R2 canbe estimated as partial R2 or liabilityR2 for continuous traits and binary traits, respectively.Briefly, partial R2 compared the difference in goodness-of-fitbetween a full model with PRS and covariates including age, sex, and first 10 PCs, and anull model with only covariates. Additionally, for binary traits, liabilityR2 was estimated with the disease prevalence approximated asthe prevalence in the samples. The theoretical variance and standard error ofR2 can be estimated as follow50:We selected high-power PRS to conduct the combination by assessing the power andvariance of prediction accuracy. The power of PRS can be estimated based on the power ofthe two-tailed test of association as follow−5(0.05/2600) for the combination with Elastic Net.Therefore, we can analytically estimate the confidence interval of predictionaccuracy for each of the score. We selected high-power scores defined as power >0.95 with P-value <= 0.05 or P-value <= 1.9 × 102 across different traits with its95% confidence interval and evaluated the significance difference from 1 using atwo-tailed paired t-test.To compare the improvement, for instance between PRSmix and the best PGSCatalog, we estimate the mean fold-ratio of Rh2 equal to 0.05, 0.1, 0.2, and 0.5. We randomly selectedM=1000 causal SNPs among 1.1 million HapMap3 variants with INFO > 0.6, MAF >0.01 and P-value Hardy-Weinberg equilibrium > 10−7. We removedindividuals with PC1 and PC2 > 3 standard deviation from the mean. We randomlyremove one in a pair of related individuals with closer than 2nd degree. The geneticcomponents were simulated as PRSs where PRS1, PRS2, and PRS3 are considered trait-specificscores with genetic correlations are 0.8 and 0.4 for cross-trait scores. PRS4, PRS5 andPRS6 are simulated as pleiotropic effects on the outcome traits with genetic correlationequal to 0.4. The SNP effects for PRSs are simulated by a multivariate normal distributionMVN where Σ is the covariance matrixbetween PRSs. The main diagonal contains the heritability of the traits ash2/M and the covariance between PRSs aresimulated as rg *h2/M whererg is the genetic correlation betweenPRSs (0.8 for trait-specific scores and 0.4 for cross-trait scores). The PRSs of theoutcome are estimated by the weighted combination of PRS where the weights follow U.7 phenotypes were simulated as We used UK Biobank European ancestry to conduct simulations for trait-specificand cross-trait combinations. Overall, we simulated 7 traits with heritability2 of the combined PRS to the R2 ofbest single PRS to assess the improvement of the combination strategy. To evaluate theimprovement across different heritabilities, we estimated the slope of improvement perlog10(N) increase of training sample sizes on the fold-ratio of predictiveimprovement.We split the simulated cohort into 3 data sets for: 1) GWAS 2) training set:training the mixing weights with a linear combination and 3) testing set: testing thecombined PRS. We incorporated PRS1, PRS2 and PRS3 to assess the trait-specific PRSmixframework. We combined all 6 single PRS to evaluate the cross-trait PRSmix+ framework. Wecompared the fold-ratio of the R39. We curated Europeanancestry by predicted genetic ancestry with a probability > 90% provided by AoUyielding 48,112 individuals in the AoU. For variant quality control beyond AoU centralefforts, we further filtered SNPs to include MAF > 0.001 which retained 12,416,130SNPs. We performed a similar quality control for imputed genotype data for South Asianancestry in the Genes & Health cohort with additional criteria of INFO score >0.6 and genotype missing rate < 5%. Individuals with a missing rate > 5%were removed. Eventually, 44,396 individuals and 8,935,207 SNPs remained in Genes &Health.The AoU data version 5 contains more than 700 million variants from whole genomesequencingWe applied PRSmix and PRSmix+ for coronary artery disease as a clinicalapplication. The phenotypic algorithm includes at least one ICD or CPT code below: ICD9410x, 411x, 412x; ICD10 I22x, I23x, I24.1, I25.2 CPT 92920–92979 (PCI),33533–33536, 33517–33523, 33510–33516 (CABG) or self-reportedpersonal history of MI or CAD. CAD in Genes and Health cohort was defined with at leastone ICD10 I22x, I23x, I24.1, I25 or operation codes K401, K402, K403, K404, K411, K451,K452, K453, K454, K455, K491, K492, K499, K502, K751, K752, K753, K754, K758, K759 orSNOMED codes 1755008, 22298006, 54329005, 57054005, 65547006, 70211005, 70422006,73795002, 233838001, 304914007, 401303003, 401314000.The category-free NRI was used to evaluate the clinical utility. NRI wascalculated by adding the PRS to the baseline logistic model including age, sex, the first10 principal components, and clinical risk factors. The clinical risk factors includetotal cholesterol, HDL-C, BMI, type 2 diabetes, and current smoking status or modelincludes only age, sex, and 10 principal components. NRI was calculated as the sum of NRIfor cases and NRI for controls: 2 tocompare the PRS performance, we also used the incremental area under the curve (AUC) tocompare the PRS. The incremental AUC was estimated as the difference between the AUC ofmodels with the integrative score versus the model with only clinical variables.51 since this methodcan infer heritability and the proportion of causal variants. LDpred2-auto was conductedwith 800 burn-in iterations and 500 iterations. The proportion of causal variants wasinitialized between 10−4 and 0.9. Furthermore, LDpred2-auto does notrequire a validation set, the SNP effect sizes were averaged between scores. We used1,138,726 HapMap3 variants that overlapped with SNPs from whole-genome sequencing datain the All of Us cohort. The LD reference panel developed from European ancestry wasprovided by the LDpred2-tutorial.LDpred2 is a Bayesian method that computes the adjusted SNP effect sizes fromGWAS summary statistics. LDpred2 utilizes the SNP effect sizes as prior and incorporatesLD between markers to infer the posterior effect sizes. In our work, we implementedLDpred2-auto19 calculates themixing weights of PRS using sample sizes from GWAS summary statistics, SNP-heritabilityand genetic correlation. We compared wMT-SBLUP with our method using 5 traits that wereoriginally assessed with wMT-SBLUP including CAD, T2D, depression, height, and BMI. Wecurated 26 publicly available GWAS summary statistics  to theoutcome trait and conducted Elastic Net using the glmnet Rpackage46.Elastic Net for linear combination: we also implemented linear combination byElastic Net with the LDpred2-auto-derived PRSs for contributing traits since thisstrategy was proposed by several works52. The phecodes werebased on ICD-9 and ICD-10 to classify individuals. PheWAS was conducted on Europeanancestry only in AoU. For each phecodes as the outcome, we conducted an associationanalysis using logistic regression on PRS and adjusted for age, sex, and first 10 PCs. Thesignificance threshold for PheWAS was estimated as 2.75 × 10−5(0.05/1815) after Bonferroni correction.We obtained the list of 1815 phecodes from the PheWAS website (last accessedDecember 2022)https://www.pgscatalog.org/. Our new scores are deposited in the PGSCatalog. The All of Us and Genes & Health individual-level data is a controlled accessdataset and may be granted at https://www.researchallofus.org/ and https://www.genesandhealth.org/, respectively.The PGS Catalog is freely available at https://github.com/buutrg/PRSmix.The weights from the PRSmix and PRSmix+ scores in this manuscript have beenreturned to the PGS Catalog. The R package to implement PRSmix and PRSmix+ in independentdatasets is at Analyses were performed on the AoU Researcher Workbench in Jupyter Notebook 14using R version 4.0.0 programming language. Results are reported in compliance with theAoU Data and Statistics Dissemination Policy.Supplement 1Supplement 2


Estimation of heritability and genetic covariance is crucial for quantifying and understanding complex trait genetic architecture and is employed in almost all recent genome-wide association studies (GWAS). However, many existing approaches for heritability estimation and almost all methods for estimating genetic correlation ignore the presence of indirect genetic effects, i.e., genotype-phenotype associations confounded by the parental genome and family environment, and may thus lead to incorrect interpretation especially for human sociobehavioral phenotypes. In this work, we introduce a statistical framework to decompose heritability and genetic covariance into multiple components representing direct and indirect effect paths. Applied to five traits in UK Biobank, we found substantial involvement of indirect genetic components in shared genetic architecture across traits. These results demonstrate the effectiveness of our approach and highlight the importance of accounting for indirect effects in variance component analysis of complex traits. Complex human traits are influenced by both genetic and environmental factors. Recent evidence suggests that genetic effects on human traits can sometimes be mediated by the environment. One example is that parental genomes could influence parental behavior and family environment, which, in turn, shape the phenotypes of their children. Since parent and offspring genotypes are correlated, these environmentally mediated effects will be captured by conventional genome-wide association studies and may potentially bias our interpretation of genotype-phenotype associations. In this work, we propose a principled statistical framework named PARSEC to partition the genetic components of single traits and the shared genetic components between traits into direct and indirect effect paths. It marks an important methodological innovation by resolving a limitation in almost all existing genetic correlation estimation approaches and may have broad and impactful applications in future GWAS analysis for complex traits that are affected by parental genetics and family environment. Genetic correlation is an effective metric for quantifying the shared genetic architecture of multiple complex traits ,2 and haAs genetic correlation analysis becomes standard in GWAS, challenges arise in interpreting the pervasive correlations observed across many phenotypes. We now know that parents’ genomes can influence parental behaviors and family environment which, in turn, shape the phenotypes of their children. Additionally, because parent and offspring genotypes are correlated, typical GWAS can be severely confounded by parental genotypes, and effect estimates obtained in GWAS are mixtures of direct genetic effects  and indirect genetic effects  ,16. TherIn the past few years, an extensive literature has investigated the decomposition of phenotypic variance based on gene-environment relations. Methods like M-GCTA ,31, TrioIn this paper, we introduce a statistical framework named PARSEC  to estimate the variance and covariance components of direct/indirect genetic effects on trait pairs using data from a limited number of families. This framework enables us to partition both heritability and genetic covariance into direct and indirect pathways, and gain knowledge of how genetics and environment jointly contribute to complex traits as well as the correlation between trait pairs. We employ the method of moments to obtain accurate estimates of variance and covariance parameters from family-based data and use a Jackknife approach to obtain confidence intervals. We apply our framework to five complex traits in UK Biobank (UKB)  and part1 and Y2, standardized own- genotypes X, and standardized parental genotypes Xp+Xm:Our approach is built on a pair of linear models for a pair of standardized traits Y1 and ϵ2 are assumed to have mean 0 and variance-covariance matrix Σ. αk and βk  are random effect vectors denoting direct (of own- genotypes) and indirect effects  on two traits. They share the variance-covariance structure below with M being the number of SNPs and IM being the identity matrix.Error terms ϵα and ρβ are two key parameters we focus on, although other cross terms are also estimated and may be of interest in practice. These two parameters quantify the covariance of direct effects and covariance of indirect effects on two traits, respectively. We apply the method of moments to produce parameter estimates and employ a Jackknife approach to quantify the standard error of parameter estimates. More statistical details are described in the Methods section.Here, ρS1 Table. Results related to covariance of direct effects and covariance of indirect effects are shown in Fig 1. Results for the estimates of all 14 parameters are shown in  We observed unbiased estimates and well-controlled confidence interval coverage rates for all parameters across various settings.We first performed simulations to demonstrate that our method produces unbiased estimates with well-calibrated confidence intervals. We randomly selected 2000 families from UKB with data on full sibling pairs and imputed parental genotypes to perform simulations. The imputation is based on expectation of the average of parental genotypes using two or more sibling genotypes . We explWe applied our model to 12,571 families in UKB with full sibling data available and parental genotypes imputed (Methods). A focal trait we studied in this paper is educational attainment due to its known substantial component in the indirect genetic effect path . In our Fig 2A).First, we examined parameter estimates for the variance of direct genetic effects, variance of indirect genetic effects, and covariance between direct and indirect effects on the same trait. These parameters are the partitioned terms of trait heritability; therefore, we can reconstruct total heritability estimates by linearly combining these three terms. For comparison, we also calculated LDSC heritability estimates using GWAS performed on the same data. We observed a high correlation . The BMI indirect effect was close to zero and not significant. Similarly, we found a significant direct genetic component (p = 4.8×10−3) and a weaker indirect component for height. Notably, the direct and indirect genetic components for height showed a significant positive covariance (p = 7.7×10−3). The direct and indirect genetic components for EA were similar in size but only the indirect component reached statistical significance. Consistent with multiple previous studies [Results of these three parameters are shown in  studies ,36, we dFig 3B and S2 Table). Error term covariances are significant for all 5 traits in our analysis. Branigan et al. [Some other parameters in PARSEC also have important implications. For example, we obtained the estimated covariance between siblings’ error terms for each trait which quantifies the degree to which siblings’ phenotypic correlation is explained by their shared environment .PARSEC also partitions the total genetic covariance between two traits into direct and indirect effect paths. Similar to the analysis for total heritability, we reconstructed the total genetic covariance estimates based on partitioned parameters (Methods) and compared them to LDSC estimates. We found a high correlation between these estimates  and ρβ  are shown in Fig 4A and 4B . We found a significant direct effect covariance (ρα = 0.044) between BMI and worse overall health , height and income (ρβ = 0.032), and EA and overall health (ρβ = -0.018). EA and income have substantial and statistically significant covariances in both direct and indirect genetic components (ρα = 0.044 and ρβ = 0.032). Across all trait pairs, direct effects explain an average of 79.6% of total genetic covariance, suggesting substantial contribution of indirect effect components and their correlation with direct effects.Estimation results for Fig 4C and 4D). We identified a number of significant correlations. For example, we found highly significant correlations between the indirect effect of BMI and the direct effect of both EA  effects on birth weight, then correlated them with other complex traits . They coIn these examples, people were able to partition the direct/indirect effects of one trait, and then quantify how they correlate with the combined effects of a second trait. In this paper, we introduced PARSEC, a new statistical framework to decompose heritability and genetic covariance of complex traits by direct and indirect effect paths. Our approach provides a more refined partition of the shared genetic components, allowing both traits’ direct/indirect effects to be investigated which provides a more complete picture of the complex genetic sharing underlying multiple phenotypes. Through simulations and application to five traits using full siblings and their imputed parental genotypes in UKB, we demonstrated that our model produces unbiased estimates with well-controlled confidence interval coverage.Partitioned variance and covariance components can be combined to recover traditional heritability and genetic covariance estimates. But stratified heritability and genetic covariance estimates provided important new insights into the genetic basis of complex traits. First, our analysis confirmed that traits like EA have a substantial indirect genetic component. One interpretation is that a substantial proportion of trait heritability is mediated through parents and the family environment they create although other mechanisms remain possible . For somOur study also has several limitations. First, parental genotypes used in our analysis were not directly measured but imputed based on siblings’ genotypes. The imputation accuracy depends on several factors including the degree of assortative mating in the population and number of siblings in each family. These may affect the accuracy of parameter estimates in PARSEC. But based on analysis that was conducted by SNIPar, the estimates for multiple regression were proved to remain unbiased and consistent. On the other hand, while our approach can be applied to measured genotypes and phenotypes in parent-offspring trios, available data in existing population cohorts often have smaller sample sizes which may lead to reduced statistical power. Second, we focused on genetic covariance instead of genetic correlation in our cross-trait analysis. Although it is also possible to calculate genetic correlations by combining stratified genetic covariance and heritability estimates, these correlation estimates tend to be numerically unstable at the sample size in our analysis. Third, our analyses were limited to quantitative traits. In our current analysis, multiple traits  were converted into continuous values from categorical input. For applications involving binary or categorical outcomes, future work is needed to expand the statistical model. Fourth, our analysis does not distinguish maternal and paternal indirect effects due to constraints in the data , although we note that our model can be easily extended to estimate maternal and paternal effects separately if genotype data are available for both parents. We also assumed absence of sibling effects and indirect genetic effects from other distant family members. This assumption is partly supported by evidence in the literature , but theTaken together, our method is a first step to explore the covariance structure of direct and indirect effects for complex human traits. It marks an important methodological innovation and may have broad and impactful applications in future GWAS analysis for traits that are affected by parental genetics and family environment.Y1 and Y2 denote two complex traits, X denotes own genotypes, and Xp and Xm denote paternal and maternal genotypes. Since we used sibling pairs data as input (that will be described later in this section), we assume the total number of sibling pairs is N. Then Y1 and Y2 are vectors with length 2N, and X, Xp and Xm are 2N-by-M matrices, where M is the total number of SNPs. We assume both genotypes and phenotypes  to be standardized. α1 and α2 are random effect terms that quantify the direct genetic effects on Y1 and Y2, i.e., how someone’s own genotypes affect their own phenotype. Following conventions in the linear mixed model literature on modeling heritability [We assume a pair of linear genetic models as follows:tability , we alsoβ1 and β2 are random effect terms for quantifying indirect genetic effects on two traits, i.e., how the parents’ genotypes affect someone’s phenotype. These random effects also follow normal distributions.Here, αk and βk) can be correlated. Direct effects on two different traits , or indirect effects on two traits , can both be correlated. Fairly generally, we assume α1, α2, β1, and β2 to have a joint distribution:Importantly, direct and indirect effects on the same trait  and offspring phenotypes on two traits . While this is true, the number of trios available even in large population biobanks such as UKB is limited. Therefore, we made two important adjustments. One is that in our analyses, we leveraged the relatively large number of full sibling pairs available in UKB and recent statistical genetic advances in parental genotype imputation [Xp+Xm. These become the input data in our analysis. This also leads to the second adjustment we made which has also been shown above–we do not distinguish paternal and maternal indirect effects and instead focus on their average. This is similar to what was done in the indirect effect GWAS literature when sample size was small [Based on the model formulation, naturally one would assume that the data required to fit this model would be genotypes of parent-offspring trios  are both normally distributed random variables. But we allow 1) correlation of errors on two traits for the same individual, which is a common assumption in the genetic correlation estimation literature [One implication of having sibling pairs instead of independent samples or trios in the analysis is that we also need to consider the shared environmental effects between siblings. Error terms on two traits  where S4 Table. Notice that the variances of error terms are not included in the parameter list. We replace them by one minus the rest of the variance terms since the phenotypic variance is standardized to be one. The cross-product matrix of phenotypes is the estimate of cov(Y) based on real data, i.e., F is the Frobenius norm. To minimize this function, we use the gradient descent method. That is, we let Θ = B, where A is a matrix and B is a vector. Then we could obtain parameter estimates by solving this linear equation.For simplicity, we denote the whole set of 14 parameters as Θs. To account for multiple testing in real data applications, we calculated false discovery rate (FDR) based on all estimates for all pairs of traits.While the variance of each parameter estimate can be derived under this statistical framework, they can be numerically unstable (and even turn negative) when sample size is limited. Therefore, we applied a resampling-based block Jackknife approach  to quantZ denotes the covariate data matrix and γ denotes their fixed effects. To account for fixed effects, we can multiply a matrix Q that satisfies QZ = 0 to both sides of the equation. Matrix Q could be obtained by deriving the orthogonal vector spaces of the singular value decomposition of matrix Z. After multiplying matrix Q on both sides, the equation becomes the following without a fixed effect term.Our model can also incorporate fixed effect covariates . For simThen, the estimation procedure for all parameters is the same as before.h2 and genetic covariance ρgc can be recovered from the decomposed variance component parameters as follows:Following the model described above, total heritability Fig 2).By plugging in empirical estimates on the right-hand side of these equations, we could obtain estimates for total heritability and genetic covariance . We used KING  to inferFor phenotypes, participants were selected as overlapping samples of five phenotypes: height, BMI, EA, income, and overall health. We obtained height and BMI phenotypes from UKB data fields 12144 and 21001. Following previous work , we usedS1 Table. All settings were repeated 200 times. In each repeat, we simulated phenotypes by generating indirect effects, direct effects, and error terms based on the proposed penetrance model using the true parameters. Then, we produced parameter estimates using our statistical framework, and obtained variance estimates using block Jackknife.We utilized imputed genotypes in UKB as input. SNPs with missing rate greater than 5% and minor allele frequency less than 5% were removed from the dataset. 2000 full sibling pairs were randomly selected in UKB. We simulated phenotypes using real genotypes and preset parameters. A total of four settings  were explored. The parameter values for each setting are listed in S1 FigPanels A and B show results for simulation settings 1 and 2, respectively. Red dots denote pre-determined true parameter values in simulations.(TIF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(PDF)Click here for additional data file.