Arachis hypogaea L.) is a multi-purpose legume serving millions of farmers and their value chain actors globally. Use of old poor-performing cultivars contributes to low yields (< 1 t/ha) of groundnut in sub-Saharan Africa including Tanzania. The objectives of this study were to determine the extent of genetic variation among diverse groundnut collections using phenotypic traits and simple sequence repeat (SSR) markers to select distinct and complementary genotypes for breeding. One hundred and nineteen genotypes were evaluated under field conditions for agronomic traits and susceptibility to rust and leaf spot diseases. The study was conducted in two locations across two seasons. In addition, the 119 accessions were profiled with 13 selected SSR markers. Genotype and genotype by environment interaction effects were significant (p < 0.05) for days to flowering (DTF), late leaf spot score at 85 and 100 days after planting, pod yield (PDY), kernel yield (KY), hundred seed weight (HSW) and shelling percentage (SP). Principal components analysis revealed that plant stand, KY, SP, NPP (number of pods per plant), late leaf spot and rust disease scores accounted for the largest proportion of the total variation (71.9%) among the tested genotypes. Genotypes ICGV-SM 08587 and ICGV-SM 16579 had the most stable yields across the test environments. Moderate genetic variation was recorded with mean polymorphic information content of 0.34 and gene diversity of 0.63 using the SSR markers. The majority (74%) of genotypes showed high membership coefficients to their respective sub-populations, while 26% were admixtures after structure analysis. Much of the variation (69%) was found within populations due to genotypic differences. The present study identified genotypes ICGV-SM 06737, ICGV-SM 16575, ICG 12725 and ICGV-SM 16608 to be used for development of mapping population, which will be useful for groundnut improvement. This study provided a baseline information on characterization and selection of a large sample of groundnut genotypes in Tanzania for effective breeding and systematic conservation.Groundnut (The online version of this article (10.1007/s10722-020-01007-1) contains supplementary material, which is available to authorized users. Arachis hypogaea L., AABB, 2n = 4x = 40) is an allotetraploid and a predominantly self-pollinating legume crop cultivated in most parts of the world. About 26.54 million hectares of groundnut is cultivated globally with an annual production of approximately 43.92 million tons of shelled grain , elite inbred lines and commercial cultivars -Naliendele station, forms part of important groundnut genetic resources in Tanzania.Several studies that documented genetic variation in groundnut focused on using morphological traits , restriction fragment length polymorphism (RFLP), random amplified polymorphic DNA (RAPD), single nucleotide polymorphisms (SNP) and microsatellites or simple sequence repeat (SSR) markers have been used in genetic variation studies on groundnut  namely Naliendele Agricultural Research Centre and Chambezi Experimental Station. The genotypes were screened for resistance to rust disease and late leaf spot during the 2018 and 2019 seasons. TARI-Naliendele  is situated at an altitude of 135 m above sea level (masl). The mean monthly temperatures for TARI-Naliendele ranges between 24.3 °C in July and 27 °C in December while the mean annual rainfall is between 820 and 1245 mm with a unimodal rain distribution. A dry spell of one to two weeks often occurs at the end of January or at the beginning of February. The soils at TARI-Naliendele described as sandy loam with pH of 4.5. Chambezi Experimental Station  is located at an altitude of 12 masl. The monthly temperatures at Chambezi vary between 24 °C in September and 30 °C in February. The site is characterized by a bi-modal rainfall pattern, commencing from October to December and April to June with expected dry spells from January to March. The annual rainfall ranges between 600 and 1000 mm, which is marked by high variation in amount and distribution. The soils at Chambezi were also sandy loam with a pH of 5.0.2. The recommended practices for fertilizer application and weeding in Tanzania were followed  was estimated as the product of pod yield per plot and shelling percentage and was converted to t ha−1 accordingly, using the plot size after adjusting for moisture content.Data on yield and yield components were recorded during plant growth and at harvest maturity. The initial plant stand (IPS) was determined by counting the number of plants in each plot after germination. Days to 75% flowering (DTF) were recorded by counting the number of days from sowing to the time when 75% of the plot stand had reached flowering. Plant height  was measured from ten randomly sampled plants in each plot from the soil surface to the tip of main stem. The number of pods per plant (NPP) was recorded as the average number of pods from ten randomly sampled plants. Final plant stand (FPS) was recorded as the number of plants in each plot before harvesting. Pod yield (PDY) was measured by weighing the dried pods from each plot and was recorded in grams per plot. Shelling percentage (SP) for each genotype was calculated from a random sample of pods weighing 200 g, as the proportion of shelled seed weight to the total weight of the unshelled pods. Additionally, 100 seed weight  for each genotype was recorded as an average weight of two samples of 100 randomly selected kernels per plot. Kernel yield  to 9 (most affected)  procedure was followed during DNA extraction  to test the effects of genotypes and locations and their interaction using the restricted maximum likelihood model (REML) procedure for alpha lattice designs in GenStat 18on Payne . The meaon Payne . Multivaon Payne . The genon Payne  analysisThe major allele frequency, the number of effective alleles, heterozygosity and gene diversity were calculated using the simple allele frequency estimator while polymorphic information content values were estimated using the equation below , where pi is the frequency of ith allele.PIC = 1–Σ (piK) values  was conducted using PowerMarker software version 3.25 (Liu and Muse p < 0.05) impact on IPS, FPS, DTF, PH, NPP, PYD, KY, HSW and SP (Table p < 0.05) different due to the interaction effect between genotype and location. All the traits were significantly (p < 0.05) affected by the genotype x season interaction except number of pods per plant and rust score at 100 days after planting. Rust score at 85 days after planting did not show significant (p > 0.05) difference across seasons and locations. There was wide genotypic variation for most assessed traits (p < 0.001) due to genotype main effect for all traits except NPP and SP.The ANOVA revealed that the 3-way interaction involving genotype, location and season had significant (−1), ICGV-SM 16613 (926.8 kgha−1) and ICGV-SM 08587 (893.7 kgha−1) with moderate rust disease scores except for ICGV-SM 08587, which showed resistant to rust disease at hundred days after planting (Table −1 and kernel yield were 291 kgha−1. The highest average rust (35.17%) and late leaf spot (31.96%) scores were observed 100 days after planting compared to 85 days after planting. Pendo 98, which was used as a susceptible check showed moderate infection to both diseases (Supplementary Table 1) and it attained an average pod yield of 692.5kgha−1 The five bottom performing accessions in terms of pod yield were Narinut 15 (252.5 kgha−1), ICGV-SM 16574 (310.6 kgha−1), ICGV 95342 (318.1 kgha−1), ICGV-SM 08584 (338.4 kgha−1) and ICGV-SM 06711 (338.7 kgha−1). These accessions yielded below average pod yield. Narinut 15 and ICGV-SM 08584 showed resistance reaction to groundnut rust and late leaf spot.The top 10 accessions with high pod yield and the five bottom performing genotypes are summarized in Table ng Table . The meaThe two axes in the GGE biplot accounted for 100% of the variation in the tested germplasm collections. Genotype ICGV-SM 16560, which represented with number 7 was found on the vertex of the polygon in the sector belonging to Chambezi site while ICGV-SM 16579, which represented with number 26 was the vertex genotype for TARI-Naliendele  and NPP  (Table p < 0.01), %LLSI85 , %LLSI100  and %RI100  exhbited negative associations with KY. At Chambezi, KY was significantly correlated with FPS (r =  − 0.392), PH (r = 0.556), NPP (r = 0.637), %LLSI85 (r = − 0.153), %LLSI100 (r = 0.192), %RI100 (r = 0.358) and PDY (r = 0.639) at p < 0.01 (Table The Pearson correlation coefficients (r) among the traits were calculated and presented in Table The multi-variate relationship among traits was elaborated by the principal component analysis to show the contribution of each trait to the overall variation. Traits with high loadings on a given principal component (PC) are important as they account for more variation explained by that PC. The first four principal components accounted for 71.9% of the total variation Table . The higIn total, the 13 SSR markers used in this study amplified 38 alleles Table . The numThe Evanno method estimated the best ‘K’ value to be 2 and, thus, the genotypes could be divided into two subpopulations Fig. . The popST). The results showed that sub population 2 with an FST of 0.47 was more differentiated than subpopulation 1, which had an FST of 0.01  variation for yield and yield components showing that the germplasm could potentially provide vital genetic resources for groundnut improvement in Tanzania. The variation exhibited by phenotypic traits signify differences in genetic composition of the individuals  analysis highlighted that late leaf spot, kernel yield, plant height, shelling percent and pod yield were mostly associated with PC1, showing that these traits accounted for much of the variation among the genotypes and could be used as the basis for selection. Accessions with higher performance in these traits could be selected for groundnut improvement. Rust scores were associated with PC4 as there was no wide range of variation for rust reaction among the accessions. This showed that most genotypes were more inclined towards susceptibility rather than resistance. Similarly, , which is significantly higher than 0.11 and 0.59 obtained by Ren et al.  of 0.47 within subpopulation 2 indicates a higher genetic diversity within this subpopulation from which parental lines could be selected to produce variable populations for selection. The high FST was similar to 0.47 reported by Below is the link to the electronic supplementary material.


Vaccinium spp.) is an important autopolyploid crop with significant benefits for human health. Apart from its genetic complexity, the feasibility of genomic prediction has been proven for blueberry, enabling a reduction in the breeding cycle time and increasing genetic gain. However, as for other polyploid crops, sequencing costs still hinder the implementation of genome-based breeding methods for blueberry. This motivated us to evaluate the effect of training population sizes and composition, as well as the impact of marker density and sequencing depth on phenotype prediction for the species. For this, data from a large real breeding population of 1804 individuals were used. Genotypic data from 86,930 markers and three traits with different genetic architecture  were evaluated. Herein, we suggested that marker density, sequencing depth, and training population size can be substantially reduced with no significant impact on model accuracy. Our results can help guide decisions toward resource allocation  in order to maximize prediction accuracy. These findings have the potential to allow for a faster and more accurate release of varieties with a substantial reduction of resources for the application of genomic prediction in blueberry. We anticipate that the benefits and pipeline described in our study can be applied to optimize genomic prediction for other diploid and polyploid species.Blueberry ( Genomic prediction, originally proposed for animal breeding , which is extremely important in the polyploid context. Polyploidy is a common event in plants, as about 70% of all angiosperms and 95% of all pteridophytes underwent polyploidization during their evolution (Soltis and Soltis Vaccinium spp.), sequencing depths of 50X–80X have been recommended to achieve confidence in the allele dosage estimation process , and (iii) total yield . Fruit weight and fruit firmness measurements were obtained from five randomly sampled fully mature berries. To measure weight, an analytical scale was used . Firmness values were obtained with the FirmTech II firmness tester . Yield was evaluated using a 1 (low) to 5 (high) rating scale based on visual assessment.The blueberry genotypes included in this study comprise a representative population of the University of Florida Blueberry Breeding Program  were obtained for all genotypes using a single trait analysis. The linear model considered genotype and year as fixed effects  minimum mapping quality score of 20; (ii) minimum SNP phred quality score of 10; (iii) biallelic markers; (iv) maximum genotype and marker missing data of 0.2; and (v) minor population allele frequency of 0.05. In addition, markers were kept when presenting average sequencing depth per site across all individuals of 60X. To avoid the use of imputation methods, it was required that all data points presented a minimum sequencing depth of 2X. A total of 87,628 SNPs were obtained after filtering, and only SNPs on the scaffolds associated with blueberry chromosomes Table  were kepContinuous genotypes were used for all tests following this formula: #a/(#A + #a), where (#a) and (#A) refer to the sequencing depth for the alternative and the reference allele, respectively, as described by de Bem Oliveira et al. .To evaluate the effect of marker density on phenotype prediction, we obtained nine scenarios of marker filters: 500, 1000 (1k), 2000 (2k), 3000 (3k), 5000 (5k), 10,000 (10k), 20,000 (20k), 40,000 (40k), and 60,000 (60k) markers. Results obtained with these filters were compared with results obtained for the complete set of markers 86,930 (86k). An equal number of markers was sampled from each chromosome. Samplings were independently performed five times for each scenario. In order to avoid eventual bias associated with marker position, a cumulative approach was applied, e.g., the first set of 1k markers was also included into the first set of 2k markers, which was included into the 3k set and so on. Principal component analyses were performed using the R package adegenet v. 1.3-1 (Jombart and Ahmed nij) for the locus i of the genotype j was obtained assuming nij ~ Poisson(sequencing depth), as described by Gorjanc et al. . To obtain the realized sequencing depth for each of the new scenarios, we assumed a Poisson distribution with the mean corresponding to each sequencing depth scenario. Therefore, for each scenario, the total number of sequence reads  on phenotype prediction by applying seven filters, assuming values between 50 and 5000 probes . For sampling, a fixed distance between probes was set, and chromosome information was considered Table . To assuTo define how to best create the training population, two approaches were considered: (i) random sampling and (ii) sampling considering family information. As with the number of markers, a cumulative approach was adopted for sampling. For the random scenario, samplings comprising 120, 240, 480, 960, and 1560 individuals were used to create the training populations.For the scenario considering family information, filters were applied considering a cumulative increase in the number of individuals sampled per family. Only data from families with ten individuals or more were used in these analyses, for a total of 103 families or 1706 genotypes. Training populations tested contained 1, 3, 6, 9, 12, and 15 individuals per family.In order to understand the interaction between training population size/composition and sequencing depth, all analyses were performed considering four of the sequencing depth scenarios previously described . These scenarios were chosen considering results obtained for the sequencing depth analysis in this study.y is a vector of adjusted phenotypic values, X is the incidence matrix linking observation in the vector y to their respective genotype effects in the vector g. Normality was assumed for the additive and residual effects, where G, was estimated using the ratio option in the AGHmatrix R package   were performed, using functions implemented in the R package agricolae . Five random samples were obtained for training and testing populations , and testing populations were kept constant for all factors analyzed. Predictive ability for all scenarios was obtained by computing the Pearson correlation between predicted and adjusted phenotypes (LSMeans). Mean squared errors were obtained as the average squared difference between the predicted and adjusted phenotypes. In order to verify significance between the factors tested in each analysis, post hoc tests assuming Tukey correction  obtained in the relationship matrices analyses had also reached a plateau around 10k SNPs Fig. . The PC1The probe analysis confirmed these results. In the scenario containing 50 probes, predictive ability values were as low as 0.33, 0.32, and 0.18; they reached a plateau around 0.44, 0.47, and 0.33, respectively, for fruit firmness, fruit weight, and yield when the number of probes varied between 2k and 5k. In addition, an increase of only 0.03 for predictive ability was observed when using all the 9.3k probes Fig. .It is interesting to notice that the mean number of markers captured per probe was 18 Fig. , and thaModel performance was significantly improved with the increase of training population sizes, independent from the population composition , the sample size (N), and the proportion of the heritability explained by the markers used , and Mendelian sampling (within family effect). The use of pedigree and genomic information can be used to estimate population structure. Yet, the increase in the number of individuals for a given family can help to estimate the Mendelian sampling effect , can generate up to 3 000 Gb of sequencing data when running a full flow cell. Therefore, to obtain a depth of 12X a total of 417 samples could be multiplexed per run, while to obtain a depth of 60X only 83 samples could be multiplexed per run .For an example of the effect that changing sequencing depth could have in the allocation of resources, consider this scenario: blueberry possesses a genome of 0.6 Gb, therefore 7.2 Gb of sequencing data would be necessary to theoretically cover the genome of one sample considering a depth of 12X, while 36 Gb of data per sample would be necessary to obtain a depth of 60X. Next generation sequencing platforms available on the market, such as IlluminaBy investigating multiple combinations of genotype and phenotype scenarios, here we provide guidelines for optimizing genomic prediction implementation for blueberry breeding. We show that accurate predictions can be obtained with moderate marker density  and low-to-mid sequencing depth (6X–12X). Moreover, we showed that total costs for genomic prediction implementation can be significantly reduced, making use of a smaller training population size for building the prediction models , and that the use of family information to compose the training set can improve the results obtained. Altogether, our findings have important cost implications for a practical implementation of genomic prediction. The effect of this parameter reduction should be validated in future studies. While this study focused on the genomic prediction implementation for a specific breeding scheme in blueberry, the pipeline explained here can be used to improve and guide resource allocation decisions for other crops, especially polyploids.Supplemental FiguresSupplemental Table


Population stratification continues to bias the results of genome-wide association studies (GWAS). When these results are used to construct polygenic scores, even subtle biases can cumulatively lead to large errors. To study the effect of residual stratification, we simulated GWAS under realistic models of demographic history. We show that when population structure is recent, it cannot be corrected using principal components of common variants because they are uninformative about recent history. Consequently, polygenic scores are biased in that they recapitulate environmental structure. Principal components calculated from rare variants or identity-by-descent segments can correct this stratification for some types of environmental effects. While family-based studies are immune to stratification, the hybrid approach of ascertaining variants in GWAS but reestimating effect sizes in siblings reduces but does not eliminate stratification. We show that the effect of population stratification depends not only on allele frequencies and environmental structure but also on demographic history. Population structure refers to patterns of genetic variation that arise due to non-random mating. If these patterns are correlated with environmental factors, they can lead to spurious associations and biased effect size estimates in genome-wide association studies (GWAS). Approaches such as genomic control (GC) , principTo address these questions, we investigated the effect of population structure on GWAS in a simulated population with a similar degree of structure to the UK Biobank. We considered the fact that different demographic histories can give rise to the same overall degree of population structure  to describe population structure. Since rare variants are not well-represented on SNP arrays, the GRM is usually constructed from common variants. This will lead to insufficient correction if common variants do not adequately capture recent population structure. To test this, we simulated a GWAS  of a non-heritable phenotype  based on common variants will inadequately capture and correct population structure with a recent origin. This might partly explain why polygenic scores derived from studies such as the UK Biobank  and FINNa priori unknown. An empirical solution to this problem is to carry out a set of preliminary GWAS, each with different sets of PCs and use the summary statistics with the smallest inflation (This still leaves the question of exactly which frequency of variants (or length of IBD segments) to use. The structure in most studies exists on multiple time scales, even in relatively homogeneous populations . In suchnflation . By lettnflation .PCA- or LMM-based corrections are only effective when environmental effects are smoothly distributed with respect to ancestry or when they can be expressed as a linear function of the GRM. Sharply distributed effects  may not be fully corrected with any method, regardless of the demographic history of the population. Such confounders are an important concern for rare variant studies. Because local effects lead to inflation in the tails of the test statistic distribution, single rare variant associations should always be treated with caution. Fortunately, burden tests are more robust to local effects than single rare variant tests, although, the degree to which burden statistics will be sensitive to local effects depends on the number of variants and the recombination distance between them—short genes with fewer variants will be more sensitive to local effects.Even imperfect correction for population structure is probably sufficient to limit the number of genome-wide false positive associations in GWAS. But when information is aggregated across a large number of marginally associated variants, even small overestimates in effect sizes can lead to substantial bias in polygenic scores. Essentially some of the predictive power of polygenic scores will derive from predicting environmental structure rather than genetic effects. Comparison of polygenic scores derived from standard GWAS and sibling-based studies suggests that this effect can be substantial , and it Our study focused on population structure arising from ancient admixtures and geographic structure because these are relatively well-understood and easy to model. However, our results generalize to any type of population structure, for example due to social stratification or assortative mating. What we refer to as local environmental effects also includes socially structured factors such as cultural practices. Ultimately, no single approach can completely correct for population stratification and replication in within-family studies and populations of different ancestry will provide greater confidence. To facilitate the evaluation of any residual population stratification in summary statistics, we recommend that studies report the following: (i) Summary statistics for all methods of correction attempted (e.g. PCA or LMMs where the GRM is constructed from variants in different frequency bins); (ii) Summary statistics for association with any available demographic variables such as birthplace e.g. ; (iii) Smsprime (We used msprime  to simulm) chosen to match the degree of structure observed in Britain. To select an appropriate value for m, we simulated a 10 Mb genome (10 chromosomes of 1 Mb each) with mutation and recombination rates of 1× 10−8 per-base per-generation, for 9,000 individuals (250 per-deme) for a range of migration rates under each demographic model   and λlo the UKB . Because the UKB , we matcWhere ectively .m1 and m2, where m1 represents the migration rate between the source populations mixing 100 generations before present (2.5kya) and m2 represents the migration rate between adjacent demes in the grid  to match the mean We parameterized the ‘complex’ model with two migration rates, the grid . We sele Britain ; Table 1data.gov.uk and assigned each individual of ‘White British’ ancestry in the UKB to a region based on their birthplace. We calculated the proportion of individuals sampled from each region and used these as weights in our simulations to mimic the sampling distribution in the UKB. To generate a migration matrix between regions, we generated an adjacency matrix for the NUTS2 districts using the ‘simple features’ (sf) R package  map for 35 regions in England and Wales (version 2015) from  package , where aTo study the effect of stratification on test statistic inflation, we simulated non-heritable phenotypes r height  and σl2 We simulated 18,000 individuals (500 from each deme) under each demographic model and split the sample into two equally sized sets, a training set on which GWAS and PCA were carried out, and a test set for polygenic score predictions. Common-PCA and rare-PCA were carried out using PLINK  on a setWe performed GWAS using –glm in PLINK 2.0 with 100 PCs as covariates . As indiWe fitted LMMs using GCTA-LOCO  where thWe calculated genomic inflation  genetic values .Thank you for submitting your article "Demographic history impacts stratification in polygenic scores" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.eLife". Please let us know if you would like to pursue this option. As the editors have judged that your manuscript is of interest, but as described below that additional analyses are required before it is published, we would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). First, because many researchers have temporarily lost access to the labs, we will give authors as much time as they need to submit revised manuscripts. We are also offering, if you choose, to post the manuscript to bioRxiv  along with this decision letter and a formal designation that the manuscript is "in revision at Summary:This paper provides a strong and clear advance on the issue of population stratification in human genome-wide association studies and the downstream biases that arise from it. The authors reaffirm that while such biases can be subtle regarding individual SNP effects, polygenic scores nonetheless accumulate large errors genome-wide. Through simulations of various realistic demographic models, they show that no single approach they tested completely corrects for population structure, indicating that complex demographic considerations are required to elucidate the role of stratification on polygenic scores. Principal components calculated from rare variants appear to better capture recent population structure than common variants, such that a multivariate approach with multiple sets of PCs may be superior.Essential revisions:1) Demographic parameters: There is immense interest in clinical applications of PRS, but as this and previous work has shown, FST between discovery and target cohorts is only the first indicator of issues in translation. In the Discussion, the authors should consider proposing more comprehensive frameworks for assessing stratification beyond FST. For example, is there a standard approach that the field could use to quantify stratification in GWAS summary statistics (e.g. in comparison to a reference panel)? Since FST itself is insufficient, what demographic parameters or metrics in the discovery and target cohorts could be reported to facilitate translation?2) Effects of imputation: The results reported here indicate that GWAS summary statistics contain less population stratification when PCs are calculated using rare variants. This solution seems great in theory. In practice, concerns with this approach in GWAS studies may arise because of varying imputation accuracy as a function of ancestry and allele frequency, with especially low imputation accuracy among rarer variants and in underrepresented ancestries. It would be very helpful to use the simulation framework and data here to determine the extent to imputation errors impact PRS accuracy in the UK Biobank when including PCs from more accurately imputed common versus less accurately imputed rare variants.(3a) One proposal in the Discussion is that considering two sets of PCs in a standard linear regression or linear mixed model may reduce residual stratification. How collinear are PCs computed from common and rare variants, e.g. in Figures 1, 2, 4, 6, Figure 1—figure supplement 2, Figure 2—figure supplement 1, Figure 4—figure supplements 1 and 2, Figure 5—figure supplement 1 and Figure 3—figure supplement 1, particularly as a function of number of SNPs used in their calculation? Further analysis would be helpful to guide whether and the extent to which there is a tradeoff between stratification and power differences from collinearity and # degrees of freedom. .(3b) Is it actually important that the PCs be obtained by independent eigendecomposition/SVD on variants from different frequency bins? Alternatively, would it be sufficient to just make sure to include variants of different frequency classes in the genotype matrix, and then get a single set of PCs from the combined set? E.g. if you combine the common and rare variants into a single genotype matrix and then include the top 200 PCs from that matrix, does this approach perform equally as well as the one where you independently get the top 100 PCs each from common and rare? Some care would need to be taken to make sure this comparison was done fairly, as you'd want to make sure that the common and the rare variants explained an equal amount of variance in the top 200 PCs, mimicking the situation where you've provided an equal number of rare and common PCs. Given that PCA is a linear procedure, the answer to this question seems like it would depend on whether the decision to split the genotype matrix by frequency bin before doing the PCA(s) represents some important non-linearity in your model of population structure. If this is indeed the case, it seems like breaking out of the linear constraint of PCA would be a more general path forward, and that would seem worth noting. If the combined approach can indeed match the approach of performing PCA separately, then it suggests that it's just a matter of making sure certain patterns are represented in some way in the underlying genotype matrix, and that, also, would seem worth noting.4) Previous work, e.g. by Kerminen et al., 2019, has shown reduced overprediction across geographical regions when using mixed models. As this manuscript further considers PCs and LMMs as a function of allele frequency, more guidance regarding which PCs and GRM(s) should be included based on rare and/or common variants to minimize stratification would be helpful.5) Fine-mapping: How much does fine-mapping have the potential to help? E.g. if we use state-of-the-art fine-mapping methods like SuSiE that produce posterior probabilities, can we diminish PRS stratification from lead SNP effects, and to what extent (maybe dependent on demographic history and sample size)?6) Siblings: We agree with the authors' statement that ascertaining SNPs in the usual way and re-estimating effect estimates in siblings is not immune to stratification . In addition to stratification, there is also most likely also a tradeoff in accuracy. With these different strategies and tradeoffs in mind, in addition to correlation between polygenic scores and latitude, it would also be helpful to know how correlation between polygenic scores and phenotype vary with different SNP selection and effect size estimation strategies .7) To help round out the manuscript, we would like the authors to add one or more examples based on their simulation results to illustrate how strategies they propose for dealing with uncorrected, residual population structure would actually work. Essential revisions:1) Demographic parameters: There is immense interest in clinical applications of PRS, but as this and previous work has shown, FST between discovery and target cohorts is only the first indicator of issues in translation. In the Discussion, the authors should consider proposing more comprehensive frameworks for assessing stratification beyond FST. For example, is there a standard approach that the field could use to quantify stratification in GWAS summary statistics (e.g. in comparison to a reference panel)? Since FST itself is insufficient, what demographic parameters or metrics in the discovery and target cohorts could be reported to facilitate translation?ST or even a multivariate measure like PCA can’t capture the complexity of population structure particularly since, as we show, this structure changes over time . Therefore, we suggest that rather than trying to summarize population structure and demography, studies instead try to summarize the empirical effects of population structure by investigating the behaviour of different association tests. Some suggestions (which we now discuss in the Discussion) are:It’s certainly true that a single number like Fa) Report summary statistics for association with demographic variables such as birthplace and ethnicity. A nice example of this was presented in Haworth et al., 2019, where they reported the genomic inflation in GWAS on birthplace in the UK Biobank.b) Report summary statistics using PCA/LMMs where the GRM is constructed from variants of different frequencies (see more detailed response to point 4 below).c) Report genomic inflation (for multiple quantiles) stratified by frequency of the variant.d) Genomic inflation in summary statistics may be too subtle to be observed with standard methods (e.g. LD score regression) if stratification impacts the test statistic distribution non-uniformly . In such cases, the distribution of polygenic scores with respect to genetic principal components or geography  could be an indicator of residual stratification in the summary statistics, though difficult to distinguish from true population differences in genetic value.Ultimately, it is hard to completely rule out stratification. But, by reporting a more detailed set of association metrics, it will be possible to get a better sense of how much stratification is plausible in any particular analysis.2) Effects of imputation: The results reported here indicate that GWAS summary statistics contain less population stratification when PCs are calculated using rare variants. This solution seems great in theory. In practice, concerns with this approach in GWAS studies may arise because of varying imputation accuracy as a function of ancestry and allele frequency, with especially low imputation accuracy among rarer variants and in underrepresented ancestries. It would be very helpful to use the simulation framework and data here to determine the extent to imputation errors impact PRS accuracy in the UK Biobank when including PCs from more accurately imputed common versus less accurately imputed rare variants.To investigate how imputation accuracy of rare variants impacts rare-PCA, we used Beagle to impute rare variants (MAF < 0.001) using phased genotypes of common variants (MAF > 0.1) in a set of 9,000 individuals. We used the phased sequences of an independent set of 9,000 individuals as reference. Even though the imputation accuracy of rare variants is indeed lower than that of common variants , imputed rare variants capture population structure just as effectively as the un-imputed variants . However, our reference panel was simulated under the same demographic history as the imputation set, which may not be realistic, especially for populations where appropriate reference panels are not available. In general, whether or not you can use imputed rare variants depends on how well you can impute them–an empirical question which is very dataset-dependent. We also suggest alternatives  that may be more robust when appropriate reference panels or large sequencing data are not available. We now summarize this point in the Discussion and in .(3a) One proposal in the Discussion is that considering two sets of PCs in a standard linear regression or linear mixed model may reduce residual stratification. How collinear are PCs computed from common and rare variants, e.g. in Figures 1, 2, 4, 6, Figure 1—figure supplement 2, Figure 2—figure supplement 1, Figure 4—figure supplements 1 and 2, Figure 5—figure supplement 1 and Figure 3—figure supplement 1, particularly as a function of number of SNPs used in their calculation? Further analysis would be helpful to guide whether and the extent to which there is a tradeoff between stratification and power differences from collinearity and # degrees of freedom. .2  between common and rare-PCs is quite high ( ~ 0.5) because common and rare variants capture the same structure, which is constant in time. On the other hand, in the recent structure models, common-PCs explain only a small fraction ( ~ 0.03) of the variance in the first rare-PC. The complex structure model is intermediate. This is essentially the same intuition that we get from looking at the principal component plots: In the recent structure model rare and common-PCs are distinct, in the perpetual structure model they are similar, and reality is intermediate. Finally we feel that the number of PCs is generally not large enough (compared to the sample size) for the loss of degrees of freedom to be a concern.The collinearity between common and rare-PCs will depend on demographic history. We now discuss this in the main text in the Results section. In Figure 1—figure supplement 1, we show the proportion of variance in each rare-PC explained by the first 50 common-PCs (and vice versa) under the three demographic models. Under the perpetual structure model, the r(3b) Is it actually important that the PCs be obtained by independent eigendecomposition/SVD on variants from different frequency bins? Alternatively, would it be sufficient to just make sure to include variants of different frequency classes in the genotype matrix, and then get a single set of PCs from the combined set? E.g. if you combine the common and rare variants into a single genotype matrix and then include the top 200 PCs from that matrix, does this approach perform equally as well as the one where you independently get the top 100 PCs each from common and rare? Some care would need to be taken to make sure this comparison was done fairly, as you'd want to make sure that the common and the rare variants explained an equal amount of variance in the top 200 PCs, mimicking the situation where you've provided an equal number of rare and common PCs. Given that PCA is a linear procedure, the answer to this question seems like it would depend on whether the decision to split the genotype matrix by frequency bin before doing the PCA(s) represents some important non-linearity in your model of population structure. If this is indeed the case, it seems like breaking out of the linear constraint of PCA would be a more general path forward, and that would seem worth noting. If the combined approach can indeed match the approach of performing PCA separately, then it suggests that it's just a matter of making sure certain patterns are represented in some way in the underlying genotype matrix, and that, also, would seem worth noting.a priori unknown is another reason to allow more flexibility in the model fit.We now discuss this point in –the third paragraph of the Discussion. Typically, the genotypes are scaled by the inverse variance (4) Previous work, e.g. by Kerminen et al., 2019, has shown reduced overprediction across geographical regions when using mixed models. As this manuscript further considers PCs and LMMs as a function of allele frequency, more guidance regarding which PCs and GRM(s) should be included based on rare and/or common variants to minimize stratification would be helpful.a priori. One approach that we like is to carry out multiple GWAS, each with PCs (or a combination of PCs) computed from variants in different frequency bins and use the summary statistics with the smallest inflation  the demographic history of the sample, which can be inferred from genetic and historical data, but also on (ii) the distribution of confounding environmental effects, which we do not know n Figure  – thus eIn our simulations, when the population structure could be represented in the GRM, both PCs and LMMs performed similarly. This is also consistent with Kerminen et al., 2019, where the reduction in overprediction was only marginally better with LMMs. The original intent behind LMMs was to correct for background genetic effects (e.g. in controlled laboratory crosses) with the implicit assumption of an infinitesimal genetic architecture. Recent methods such as Bolt-LMM are flexible to the infinitesimal assumption but still model the confounding environment as a simple linear function of the GRM. PCA-based approaches are more flexible in that they allow environmental effects (of which there may be many) to be modeled by multiple parameters (the same as the number of PCs used in the model). Thus, our view is that PCA-based corrections are preferable to LMMs when the distribution of environmental effects are unknown — almost always the case. However, further work is required to study the efficacy of each approach under different demographic histories and environmental effects.5) Fine-mapping: How much does fine-mapping have the potential to help? E.g. if we use state-of-the-art fine-mapping methods like SuSiE that produce posterior probabilities, can we diminish PRS stratification from lead SNP effects, and to what extent (maybe dependent on demographic history and sample size)?If the causal variants were known precisely then, as we show, there is little effect of stratification. So this question is really an empirical one about how well fine mapping approaches can identify causal variants. As suggested, we ran SuSiE on our simulated GWAS and used the effect sizes of variants with the highest posterior probability to calculate polygenic scores. However, this approach improves prediction accuracy and reduces bias only very slightly compared to the approach where we used the most significant hits. We describe this analysis in the subsection “Polygenic scores capture residual environmental stratification” and in Figure 4—figure supplement 3. Why this is the case is a question on the efficacy of statistical fine-mapping, which we think needs further investigation.6) Siblings: We agree with the authors' statement that ascertaining SNPs in the usual way and re-estimating effect estimates in siblings is not immune to stratification . In addition to stratification, there is also most likely also a tradeoff in accuracy. With these different strategies and tradeoffs in mind, in addition to correlation between polygenic scores and latitude, it would also be helpful to know how correlation between polygenic scores and phenotype vary with different SNP selection and effect size estimation strategies .The prediction accuracy is indeed greater for the hybrid approach (standard discovery + sibling re-estimation) relative to either the standard GWAS or sib-based GWAS . Further investigation shows that this is not an effect of re-estimation in siblings but because re-estimation, in general, produces more unbiased effect size estimates. In fact, the increase in prediction accuracy with re-estimation is even greater than the increase in accuracy with a larger sample size . This suggests that perhaps one easy way to reduce the bias-accuracy tradeoff is to split GWAS into discovery and re-estimation sets. We thank the reviewer for suggesting this analysis and we have incorporated the results in Figure 6 and Figure 6—figure supplement 2, and into the subsection “Polygenic scores based on effect sizes re-estimated in siblings are not immune to stratification”.7) To help round out the manuscript, we would like the authors to add one or more examples based on their simulation results to illustrate how strategies they propose for dealing with uncorrected, residual population structure would actually work.We have now made suggestions in –the Discussion alongside edits suggested in point 4. Briefly, we recommend that researchers first explore the population structure in their data, which for most studies will exist on multiple timescales, by carrying out PCA on variants in different frequency bins or IBD segments of varying lengths. Then, carry out a set of preliminary GWAS, each with different sets of PCs and use the summary statistics with the smallest inflation. To reduce computational burden, these GWAS can first be carried out on a subset of variants uniformly sampled from the genome to find the optimal combination of PCs (e.g. based on genomic inflation) before carrying out a full GWAS on all variants .


The American Simmental Association has an ongoing project assessing carcass composition and quality. Typically, when animals for mating are selected on maternal traits, there is a concomitant reduction in carcass value as many maternal traits are antagonistic to carcass traits. Analysis of the current data showed the correlation between hot carcass weight and calving ease direct to be lower than previously reported. This shows that multi-trait selection reduced the problem that arose when selecting for carcass traits or maternal traits individually.USDA quality and yield grade are primary driving forces for carcass value in the United States. Carcass improvements can be achieved by making selection decisions based on the results of genetic evaluations in the form of expected progeny differences (EPD), real-time ultrasound imaging, and physical evaluation of candidate breeding animals. In an effort to advance their ability to accurately predict the breeding value of potential sires for carcass traits, the American Simmental Association launched the Carcass Merit Program as a means to collect progeny sire group carcass information. All records were extracted from the American Simmental Association database. Progeny data were organized by sire family and progeny performance phenotypes were constructed. Sire genotypes were filtered, and a multi-locus mixed linear model was used to perform an association analysis on the genotype data, while correcting for cryptic relatedness and pedigree structure. Three chromosomes were found to have genome-wide significance and this conservative approach identified putative QTL in those regions. Three hundred ninety-three novel regions were identified across all traits, as well as 290 novel positional candidate genes. Correlations between carcass characteristics and maternal traits were less unfavorable than those previously reported. With the first matings at the Sheek Ranch in Cabool, Missouri, in the spring of 1997, the American Simmental Association (ASA) launched a program that has influenced all producers and users of Simmental genetics. Simply known as the Carcass Merit Project (CMP), the enrolled sires of the Simmental and Simbrah breeds have been randomly mated to 35,000 commercial females to collect difficult-to-get progeny carcass information by sire group. Ten thousand carcass records have been collected and carcasses average 74% USDA Choice quality grade and a 2.8 USDA carcass yield grade, with tenderness data having been completed. In terms of calving ease (CE), 4400 British heifers have been mated and the resulting calves have an average birth weight (BW) of 78.6 lbs. For feed conversion, 1318 sire-identified SimAngus™  progeny steers have been used, resulting in an average dry matter feed conversion 6.3:1 and an average daily gain of 1.64 kg/day. Data have been collected from 41 different herds across 18 states, with steers fed and harvested in nearly every cattle feeding region in the United States. These data include all of the crossbred offspring as well as Simmental offspring. To clarify, the commercial dams included in analysis were 3.48% Angus, 0.03% Gelbvieh, 0.23% Red Angus, 70.23% Simmental, and 26.03% with no breed information available. The calves were 3.07% Angus, 0.03% Gelbvieh, 0.21% Red Angus, and 96.7% Simmental.These data allowed the ASA to improve the accuracy of expected progeny differences (EPD) used for the selection of economically relevant traits. It improved confidence levels of traits, from calving assistance all the way to predicting end-point product value. In the last 25 years, a shift has occurred in the US beef industry from a commodity-based market to one that is based on quality or product yield ,2. This Data were gathered by the ASA CMP. All steer performance records containing calf BW, calving ease direct (CED) scores , calvingn = 1–150 progeny per family) were calculated. Sires with either SNP50K or comparable imputed 50 K data from higher or lower density SNP chips were used in the overall analysis. Genotype data quality control was done through SNP filtering [Progeny data were organized into 150 sire families. Performance averages for all traits  relationship matrix was created to correct association analysis for genomic relationships amongst samples. This was done by utilizing the Identity by Descent (IBD) estimation tool within Golden Helix. The complete algorithm used by Golden Helix SVS is spelled out in Purcell et al. .Principal component analysis (PCA) was used to account for cryptic relatedness and the first three eigenvectors represented greater than 50% of the stratification in the SNP data. Identity by Descent calculated relatedness between individuals and the first ten PCA-generated eigenvectors were used as covariates in the association analysis to account for pedigree structure and cryptic relatedness. A multi-locus mixed linear model (MLMM)  in Goldep-value) was 5 × 10−8 [p-value) of 5 × 10−5 threshold, and these additional regions were also used to identify additional potential candidate genes for further research.Benjamini–Hochberg multiple comparison corrections were used to minimize false-positive associations . A genomp < 0.001), the proportion of genetic variation explained by the marker was reported. This was determined by partitioning the variance for the model. This was re-estimated in each step of the MLMM, as described by Segura et al. [Genomic regions within 100,000 base pair (bp) of each significant marker were identified and highlighted. The same process was done for all of the identified markers for each chromosome, which created some overlap of highlighted areas. Previously reported significant markers were then cross-referenced with the highlighted areas. For significant markers  method to perform a bivariate restricted maximum likelihood (REML) analysis in SVS software . The following parameters were set for the analysis: residual covariance was not excluded, a gender correction was not applied as we used datasets of all dams for maternal data and all steer performance data, samples with missing phenotypes were dropped and we did not account for gene by environmental effects as we did not have that sufficient data to include it, and an IBD genomic relationship matrix was used for relatedness. These correlations were calculated using 1,681 animals that had either genotype and progeny data or genotype and individual data and 37,468 filtered markers.The dataset consisted of samples from 3849 individuals. Samples were grouped by sire and 2745 individuals had known sires, producing 395 sire families. Sire families ranged in size from one to 150 progeny  with reported data for carcass traits. Progeny performance averages were constructed. The resulting 395 progeny performance averages were used in our association analysis which provided a smaller than ideal dataset for this purpose. As our primary objectives were to examine genetic correlations in this population and identify genomic regions of interest for further research, we proceeded, but we acknowledge the limitations of this dataset for identifying QTL and causative mutations with the smaller sample size represented.Genome-wide analysis found only one region for each: KPH ). Previously reported QTL for carcass traits that overlap regions identified in this study are included in Although the sire family structure of the data limited the resolution of our association analyses, areas of the chromosomes with vertical clusters of markers were of interest as they suggested putative QTL in those regions. Within a 100,000 bp window of each putative QTL region, positional candidate genes were identified using Genome Build Bos taurus ARS-UCD1.2. Putative QTL regions were compared to known QTL using AnimalQTLdb  on chromosome 2 for HCW in Aberdeen Angus-sired steers. For MARB, retinoic acid receptor-related orphan receptor C (RORC) was identified on chromosome 3 by Barendse et al. [IFNAR1) in Angus–Brahman cross cattle and, on chromosome 5, Ujan et al. [MYF5) in Chinese Bos taurus. These results are similar to the results of our analysis and lend confidence to the regions and candidate genes we identified.In terms of positional candidate genes, Gill et al.  identifie et al.  in Austre et al.  in Anguse et al.  identifin et al.  identifiThe correlation between HCW and CED (−0.20) was less than the correlation previously reported −0.31) by MacNeil et al. 1 by MacN found a Three chromosomes harboring QTL for various carcass traits were identified. Across all traits, 393 novel regions and 290 novel positional candidate genes were identified for the multi-locus model. Additionally, the detrimental genetic correlations between carcass characteristics and maternal traits are less than what has been previously reported, indicating that multi-trait- or index-based selection has been effective in reducing the strength of negative genetic relationships between traits. Further research is needed into the identified potential candidate genes and the role they may play in improving the value of beef carcasses. Additionally, this research supports the hypothesis that balanced selection on both maternal and carcass quality traits can improve productive efficiency.


Genome-wide association studies (GWAS) in samples of European ancestry have identified thousands of genetic variants associated with complex traits in humans. However, it remains largely unclear whether these associations can be used in non-European populations. Here, we seek to quantify the proportion of genetic variation for a complex trait shared between continental populations. We estimated the between-population correlation of genetic effects at all SNPs ( Genome-wide association studies (GWASs) have discovered > 70,000 genetic variants associated with human complex traits and diseases4. However, most GWASs have been heavily biased toward samples of European (EUR) ancestry (~ 79% of the GWAS participants are of EUR descent)5. Progress has been made in recent years in uncovering the genetic architecture of traits and diseases in a broader range of populations11. Given the population genetic differentiation among worldwide populations15, the extent to which the associations discovered in EUR populations can be used in non-EUR such as Africans (AFR) and Asians remains unclear. Genetic correlation  or LD, and whether the between-population 28, the genetic risk prediction of complex diseases29 in the future in non-EUR populations and the detection of signatures of natural selection that has resulted in genetic differentiation among worldwide populations. In this study, we focus on estimating the correlation of genetic effects at all SNPs (denoted by 30 (treating the phenotypes in the two populations as different traits) for two model complex traits, i.e., height and body mass index (BMI). We investigate the influence of the between-population differences in allele frequencies or LD on the between-population genetic heterogeneity. To do this, we first used genome-wide SNP genotype data to estimate 30 or a summary level data-based method31. We then examined whether the between-population genetic overlap is enriched (or depleted) at the SNPs with stronger between-population differentiation in allele frequency or LD.Previous trans-ethnic genetic studies have shown that the estimates of 32. We imputed the AFR data to the 1000 Genomes Project (1000G) reference panel (Methods). After quality control (QC), 1,018,256 HapMap3 SNPs with MAF > 0.01 in both the two data sets were retained for analysis (Methods). We first used the bivariate GREML approach30 to estimate .14 that the estimate of . . The .5 based on GWAS summary data from the UKB and BBJ.We used GWAS data on 49,839 individuals of EUR ancestry from the UK Biobank (UKB) and 17,426 individuals of AFR ancestry from multiple publicly available datasets including the UKB . We used the trait-associated SNPs identified in previous GWAS meta-analyses conducted by the GIANT consortium36  of the GIANT summary data (Methods)37. To avoid potential bias in estimating We have quantified above the between-population mentclass2pt{minim effects . We used38) was 0.90 . We stratified the SNPs into two LDCV groups with no difference in MAF or LD score between the groups in each individual population using the approach described above  for height and BMI between EUR and AFR  prediction given the limited accuracy of genetic prediction using EUR-based GWAS results in non-EUR populations. As discussed in recent studies29, a number of genetic and non-genetic factors affect the accuracy of using predictors constructed in EUR populations in non-EUR populations, such as the differences in genetic architecture, allele frequency and LD structure between EUR and non-EUR populations, and the differences in environmental exposures and definitions of clinical phenotypes. By modelling the relative accuracy , Wang et al. quantified how much proportion of the loss of RA using EUR-based PRS in AFR can be explained by the differences in allele frequency and LD47. They found the quantities varied between traits, e.g., ~ 65% for height and ~ 84% for T2D, reflecting differences in genetic architecture between traits 47. One of the limitations of our study is that African Americans have substantial proportions of European ancestry, and our data do not cover the full diversity of the European and non-European populations. We focus only on the individuals that show similar ancestries with the individuals of European and African ancestries, respectively, in the 1000G . The EUR data used in bivariate GREML analysis were two random sets  from UKB-EUR. We found that compared to the original In summary, our study confirmed a large estimate of genetic correlation at common SNPs between worldwide populations for height48. QC of the UKB SNP genotypes had been conducted by the UKB QC team32 and the EUR-UKB data had been imputed to the HRC and UK10K reference panel. For the EUR-UKB imputed data , we filtered out SNPs with missing genotype rate > 0.05, MAF < 0.01, imputation INFO score < 0.03 or P-value for HWE test < 10–6. We cleaned the WHI and CARe (AFR-WC) genotype data following the protocol provided by the dbGaP data submitters. We further removed SNPs with SNP call rate < 0.95, MAF < 0.01 or Hardy–Weinberg Equilibrium (HWE) test P < 0.001, and removed individuals with sample call rate < 0.9. We imputed the AFR-UKB and AFR-WC data to the 1000G using IMPUTE249, and applied the same filtering thresholds as above to the imputed data. We then combined the cleaned AFR-UKB and AFR-WC as one AFR data set. Since the AFR samples are ancestrally more heterogeneous than the EUR-UKB sample, we removed the AFR individuals whose PC1 or PC2 were more than 6 s.d. away from the mean of the AFR in 1000G in AFR-WC and AFR-UKB separately (the PC-based QC of the EUR-UKB sample was described in a previous study50). Only the SNPs in common with those in HapMap3 SNPs . These unrelated AFR individuals were a subset of the AFR samples after PC-based QC. The first 20 principal components (PCs) were derived from the GRM in each population. Phenotypes in each population were adjusted for covariates  in each gender group of each cohort and inverse-normal transformed after removing outliers that were 5 s.d. from the mean for height and 7 s.d. from the mean for BMI (because the phenotype distribution tends to be right skewed for BMI). We choose these two traits because they are two of the most commonly studied quantitative traits and we only have access to the individual-level data of only these two traits in WHI-AFR.GWAS data of 456,422 individuals of European ancestry were from the UKB (EUR-UKB). GWAS data of 24,077 individuals of African ancestry were from the UKB . We also performed the bivariate GREML analyses based on GRMs (and PCs thereof) for which the SNP genotypes were standardized using the allele frequencies computed from the combined sample of EUR and AFR. The bivariate GREML analyses were also performed to estimate 52. The GWAS summary data for UKB-EUR (n =  ~ 450 k) have been published in a previous study52 and are publicly available (see URLs).To estimate 51. We first split the SNPs into 125 bins according to their MAF in EUR and 125 bins based on the frequencies of the same alleles in AFR . We next split each frequency bin into 4 LD bins according to LD scores of the SNPs34 in EUR and 4 bins based on LD scores in AFR. We thereby obtained 250,000 (125*125*4*4) bins in total. We then equally divided the SNPs in each bin (39.To compare the difference in FST-stratified SNP sets described above). We computed the P-value for the difference using a We tested the difference in The sampling covariance of the estimates of 36. We used the rb method developed by Qi et al.31 to estimate the correlation of SNP effects between populations at the top associated SNPs accounting for sampling errors in the estimated SNP effects. To avoid bias due to ‘winner’s curse’, we re-estimated the SNP effects in our samples  using fastGWA52. Since fastGWA controls for relatedness52, we used all the samples passed QC (including close relatives) for the GWAS analysis (37 (threshold P-value = 31.We obtained the trait-associated SNPs for height and BMI from the GIANT meta-analyseshttp://cnsgenomics.com/software/gctaGCTA: https://www.cog-genomics.org/plink2PLINK: https://github.com/brielin/PopcornPopcorn: https://www.broadinstitute.org/collaboration/giant/index.php/GIANT_consortium_data_filesGWAS summary data for height and BMI in GIANT: GWAS summary data for BMI in Biobank Japan in NBDC Human Database:https://humandbs.biosciencedbc.jp/en/http://www.ukbiobank.ac.uk/UKB consortium: http://fastgwa.info/ukbimp/phenotypesUKB-EUR GWAS summary data: http://www.affymetrix.com/support/technical/byproduct.affx?product=Axiom_GW_HuOriginAffymetrix Human Origins array: http://dalexander.github.io/admixture/publications.htmlADMIXTURE: Supplementary Information


Multivariate testing tools that integrate multiple genome-wide association studies (GWAS) have become important as the number of phenotypes gathered from study cohorts and biobanks has increased. While these tools have been shown to boost statistical power considerably over univariate tests, an important remaining challenge is to interpret which traits are driving the multivariate association and which traits are just passengers with minor contributions to the genotype-phenotypes association statistic.P-value statistics of multivariate association models. We validate MetaPhat with Global Lipids Genetics Consortium GWAS results, and we apply MetaPhat to univariate GWAS results for 21 heritable and correlated polyunsaturated lipid species from 2,045 Finnish samples, detecting seven independent loci associated with a cluster of lipid species. In most cases, we are able to decompose these multivariate associations to only three to five central traits out of all 21 traits included in the analyses. We release MetaPhat as an open source tool written in Python with built-in support for multi-processing, quality control, clumping and intuitive visualizations using the R software.We introduce MetaPhat, a novel bioinformatics tool to conduct GWAS of multiple correlated traits using univariate GWAS results and to decompose multivariate associations into sets of central traits based on intuitive trace plots that visualize Bayesian Information Criterion (BIC) and https://sourceforge.net/projects/meta-pheno-association-tracer.MetaPhat efficiently decomposes associations between multivariate phenotypes and genetic variants into smaller sets of central traits and improves the interpretation and specificity of genome-phenome associations. MetaPhat is freely available under the MIT license at:  Genome-wide association studies (GWAS) of common diseases and complex traits in large population cohorts have linked thousands of genetic variants to individual phenotypes. In emerging biobank studies as well as in some disease specific collections have focused on, for example, Type 2 diabetes (T2D)  or coron1.identify and annotate significant variants via multivariate GWAS from univariate summary statistics using metaCCA;2.perform decomposition by systematically tracing the traits of highest and lowest statistical importance to identify subsets of central traits at each associated variant;3.plot the traces of trait decompositions and cluster the variants based on the ranking of the importance of traits.P < 5e-8, the established genome-wide threshold in the field . By default, two lead variants were defined as independent if their distance is higher than 1 million base pairs. At step four, we carried out the decompositions of multivariate association by starting from model with all K traits and removing one trait at a time until only one trait remains. We proceeded via two different strategies that we named the highest trace and the lowest trace. More specifically, starting from the model with all K traits, we tested all unique combinations of (K-1) traits to find the subset with the highest CCA statistic  that we assigned to the highest trace and the subset with the lowest CCA statistic  that we assigned to the lowest trace. We continued both traces iteratively until only a single trait remained by always choosing the subset with the highest CCA statistic on the highest trace and the subset with the lowest CCA statistic on the lowest trace. Intuitively, at each step, the trait dropped on the highest trace was the trait that was best replaceable by the other traits in the model with respect to the genetic association considered. Analogously, at each step, the trait dropped on the lowest trace was the trait that was most irreplaceable by the other traits in the model with respect to the genetic association considered. Altogether, we evaluated K2 subsets out of all possible 2K subsets while building these two traces. Base pair distances, GWAS P-value thresholds, and other program parameters could be updated using command-line arguments.MetaPhat requires as input a set of related GWAS summary statistics from correlated traits. The program implements efficient multi-trait genome-wide association testing, identification of significant associations, and systematic tracing of trait subsets to identify the central traits that consist of a statistically optimal set of traits together with a set of driver traits. A workflow is shown in he field ] were idWe used the two traces to identify central traits that are primarily responsible for the association with the variant as explained next.P-values and Bayesian Information Criterion , and r1 to derive BIC from the maximized likelihood of the linear model written as a function of R2 = r12.where x and (mean-centered) traits y = T.Consider a linear model between a (mean-centered) variant where we do not include the intercept parameter as its maximum likelihood estimate (MLE) is zero after mean-centering. The log-likelihood function isand MLEs areThus, the log-likelihood at maximum isthat  is,Hence, the logarithm of the likelihood ratio between the MLE and the null model can be written asHence, we have that, for an additive constant c. Since c does not depend on the model dimension, we can ignore it in the BIC calculation, when we are only interested in the differences in BIC between models.which is possible to compute directly from the metaCCA output for models with at least two traits up to an additive constant R2 can be computed directly from the univariate GWAS summary statistics asFinally, for a single-trait model, which can be plugged in the BIC formula above to yield BIC for the single-trait model.https://sourceforge.net/projects/meta-pheno-association-tracer.MetaPhat is written in Python (compatible for 2.7 and 3+) and requires R (3.4+) for plotting. The command-line based program has been tested on multiple operating systems and cloud images. Library requirements and command options are further described in P-value and BIC statistics. For each variant, trace plots using P-values and BIC are generated, showing the highest trace, the lowest trace and the inverted lowest trace. In addition, the univariate P-values and directions of effects for each trait are also plotted. The estimated phenotype correlation matrix, clustered heatmaps of trait importance for the chosen variants and a similarity between variants using trait rankings on the lowest trace are produced. Optionally, intermediate statistics during the decomposition can be plotted to get a more detailed view of the decomposition process.MetaPhat outputs tabular text files and several plots. A summary result file contains, for each chosen variant, the driver traits and the optimal subset with their Our lipidomics data set consisted of the univariate GWAS results of 21 correlated lipid species with polyunsaturated fatty acids that were reported to exhibit high heritability  and showP-value threshold of 5e-8 within a window of 1 Mb. P-value, and central traits. MetaPhat has strongly reduced the multivariate association for all seven variants into smaller and more specific groups of central traits.Using the lipidomics data sets with GWAS summary statistics from the 21 polyunsaturated lipids, MetaPhat found seven independent lead variants after clumping the 415 variants exceeding the standard GWAS APOE gene and is known for its effect on LDL, as reported, for example, in the GLGC analysis  and further determined that the association was driven by CE14 and PCO23 . The BIC-optimal subset for this variant extended the drivers by one additional trait and included CE14, PC36, and PCO23, which form the central traits. The trace plots for rs7412 are shown in P-values for defining driver traits) and We considered in more detail rs7412, which is a missense variant in the analysis . With thBUD13 and rs261290 near ALDH1A2 both have only one driver trait (PI9 for BUD13 and PE7 for ALDH1A2) and three or five central traits , TC, HDL, and LDL in GLGC data and rs66505542 itself with several cell phenotypes  in the GWAS catalog, while rs261290 has been reported to be associated with HDL , TC, and TG in GLGC data (mapped to LIPC gene) and with HDL in the GWAS catalog.Variants rs66505542 near l traits . EarlierFADS1/2 since its 18 central traits show its wide effects across the lipidomics traits studied here. Previously reported FADS1/2 associations are with all lipid traits  in GLGC data and with metabolite measurements and gallstones in the GWAS catalog.A very different picture emerges for rs174567 near Trait importance map that clusters each variant based on the lowest trace is shown in DOK7) where we found TC and TG as central traits compared to previously reported univariate associations with TC, TG, and LDL. As TC and LDL are highly correlated, it is understandable that the smaller dimension of the set TC, TG, may in some analyses be preferred over the set that also includes LDL. In We processed the Global Lipids Genetics Consortium (GLGC) GWAS study for four plasma lipids  . AdditioK-1 non-empty subsets that have quickly become infeasible to systematically assess, while MetaPhat only considers about K2 models. For example, in our example with K = 21 traits, the gain in performance is about 4,700-fold compared to the complete subset testing. To further increase performance and usability, we have implemented flexibility for multi-thread processing to enable high performance and memory efficiency. On a moderate Google cloud image , the complete MetaPhat workflow for our lipidomics analysis, containing 21 lipids and 8.5 million SNPs, was completed in less than 2.5 h (143 min). Using 10 processors and 9 gigabytes of memory, the GLGC job with the four basic lipids and 2.4 million imputed SNPs completed in 24 min. MetaPhat also allows decomposition and plotting of custom SNPs. For example, the custom analysis of the 13 GLGC variants associated with three or more traits, shown in MetaPhat considerably cuts down the computational demands of comprehensive subset testing. With K traits, there are 2It is expected that a particular genetic variant may affect only a subset of related biomarkers that are risk factors of complex disorders, such as T2D or coronary heart disease. We implemented MetaPhat to systematically decompose and visualize statistically significant multivariate genome-phenome associations into a smaller group of central traits, based only on univariate GWAS summary statistics. We are not aware of comparable software to MetaPhat that would automatically carry out multivariate GWAS and identify central traits for the associations from summary statistics. ASSET  aims to APOE association (rs7412) benefited from multivariate testing (driven by CE14 and PCO23 traits), as the univariate P-value was insignificant (P > 1e-4) across all 21 GWAS traits . This variant is known to have a strong effect on LDL, and In our results from an analysis of 21 lipidomics traits, we demonstrated that the shown in , but mulMBOAT7 has been previously reported to be associated with human blood metabolites , as carried out only a single multivariate GWAS to pick the lead variants. This cutoff can be adjusted according to the preferences of the users. MetaPhat also optionally allows the running of metaCCA+ (Our software implements flexible parameters for custom multi-thread chunking to enable high performance, genome-wide, multi-trait meta-analysis while integrating metaCCA for multivariate testing followed by systematic decomposition of traits. Thus, a limitation of MetaPhat is that it relies on metaCCA, but other multivariate GWAS algorithms could also be used provided that these methods can work with univariate GWAS results as inputs and produce suitable metrics that can be used to derive the model comparison statistics. With regard to false positives, we used the standard GWAS cutoff (metaCCA+  shown toFinally, we remind the reader that MetaPhat decompositions are sequential, dropping one trait at a time, and hence are not guaranteed to produce the globally optimal subset. Additionally, for highly correlated traits, such as LDL and total cholesterol, the choice of which one is dropped first may not be completely robust to small changes in data.The ability of MetaPhat to identify and visualize central traits will also be valuable in supporting efforts and pipelines  comparinAll datasets generated for this study are included in the article/MP, SR, and JL conceived the project. MP developed the theory. JL implemented and tested the method. RT assisted with the testing. JL and MP draft the manuscript. All authors provided critical feedbacks and important contributions to the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Diospyros spp.), separated sexuality, the presence of separate male and female individuals (dioecy), is controlled by the Y chromosome-encoded small-RNA gene, OGI. On the other hand, sexuality in hexaploid Oriental persimmon (Diospyros kaki) is more plastic, with OGI-bearing genetically male individuals, able to produce both male and female flowers (monoecy). This is thought to be linked to the partial inactivation of OGI by a retrotransposon insertion, resulting in DNA methylation of the OGI promoter region. To identify the genetic factors regulating branch sexual conversion, genome-wide correlation/association analyses were conducted using ddRAD-Seq data from an F1 segregating population, and using both quantitative and diploidized genotypes, respectively. We found that allelic ratio at the Y-chromosomal region, including OGI, was correlated with male conversion based on quantitative genotypes, suggesting that OGI can be activated in cis in a dosage-dependent manner. Genome-wide association analysis based on diploidized genotypes, normalized for the effect of OGI allele dosage, detected three fundamental loci associated with male conversion. These loci underlie candidate genes, which could potentially act epigenetically for the activation of OGI expression.Sexuality is one of the fundamental mechanisms that work towards maintaining genetic diversity within a species. In diploid persimmons ( In contrast to animals, hermaphroditism is thought to be ancestral and most common in flowering plants. A minority of species have subsequently, and independently, evolved separated sexuality, with separate male and female individuals (dioecy).Diospyros spp.), the Y chromosome-encoded small-RNA gene OGI is responsible for expression of maleness, through the repression of its autosomal counterpart, a gene called MeGI.Diospyros kaki) has evolved a more plastic sex determination system from the dioecious system, possibly through epigenetic regulation of OGI and MeGI.,OGI), exhibit monoecy, where both male and female flowers are produced by the same tree, although they often produce only female flowers.OGI by the presence of a highly methylated retrotransposon insertion, named Kali, within the OGI promoter region, and on the variable DNA methylation of the MeGI sequence  an 2.1.1 population produced from a cross between ‘Yamatogosho’ (6 A + XXXXXX) × ‘Taishu’ (6 A + XXXXYY), named the YTF1 population, was developed in 2009, and exhibited variation in the frequency of male production since the first flowering in 2013–14. Flower sexuality from a total of 5,016 non-male  parental branches was assessed for 5 years, from 2014 to 2018. A male conversion branch was defined as a non-male parental branch producing male flowers on at least one branch https://github.com/lh3/bwa)OGI allele were used . To test if a locus affected male conversion in a dosage-dependent manner, Pearson product moment correlation analysis was conducted between the ratio of alternative alleles at each locus and the phenotype values of each individual. The coefficient values were standardized using z-transformation, to estimate P-values. Significant association loci were detected with the threshold of −log > 5.60, representing a Bonferroni-corrected significance threshold of 0.1.Allele composition (or quantitative genotype) at each SNP locus was estimated from the frequency of alternative alleles in mapped reads. Genome-wide correlation analysis was conducted using a total 40,111 of the 95,639 SNPs, in which duplex–pentaplex genotypes were predicted in at least 23/83 YTFP-value) > 5.98, representing a Bonferroni-corrected significant threshold of 0.1. Linkage disequilibrium (LD) surrounding the loci highly associated with the sex expression (P < 10E−6) was evaluated using squared Pearson’s correlation coefficient (r2) with the −r2 command in the software PLINK version 1.07.Diploidized genotype at each locus was defined with the threshold of 5% (and 95%) of alternative alleles in the mapped reads to call heterozygosity. Genome-wide association analysis was conducted using the R package rrBLUP, with a linear mixed model (LMM).OGI was estimated with quantitative PCR using LightCycler 480 , according to a previous reportOGI and the control locus, L5R, quantitative PCR analyses were conducted using THUNDERBIRD SYBR qPCR Mix . For six individuals of the YTF1 population, due to the lack of DNA, allele dosage on Chr. 15, the peak of 17,052,751-bp on the sex-chromosome was used as a proxy for OGI allele dosage (around 18.12-MB on Chr. 15).23Allele dosage of OGI allele dosage, which substantially affect male production ability, ‘partial correlation’ analysis was conducted, based on quantitative genotypes. The partial correlation, considering the effect of OGI allele dosage, assumes the following equation:byr is the correlation coefficient between the quantitative genotype at the locus and the phenotype; ayr is the correlation coefficient between OGI allele dosage and the phenotype; and abr is the coefficient between OGI allele dosage and the quantitative genotype at the locus. The partial correlation coefficient values were standardized with z-transformation to estimate P-values.To assess the effect of loci on the male conversion traits independently of the effect of y is a vector of the phenotype; oβ is a fixed effect for OGI allele dosage (O) and Z is an incident matrix relating y to g. The variable g models the genetic background of each line as a random effect with Var[g] = Kσ2g, where σ2g is the genetic variance. K is an additive kinship matrix calculated from the genotype data. S is a vector of genotype of each polymorphic site. The variable τ models the additive SNP effect. ε is a matrix of the residual effects with Var[ε] = Iσ2e, where I is an identity matrix and σ2e is the residual variance. To solve the mixed model, we used functions in the R package rrBLUP.K was calculated using the ‘A.mat’ function. The variance components σ2g and σ2e were estimated using the ‘mixed.solve’ function. P-values for the SNP markers were calculated using the ‘GWAS’ function, which we slightly modified to use quantitative values of OGI allele dosage as a fixed effect.For the diploidized additive model with diploidized genotypes, we assumed the following LMM:1 population, 53 of 83 individuals only produced female flowers despite carrying at least one copy of the OGI gene (N = 30) showed a wide range of male conversion rate, i.e. conversion from non-male  parental branches producing male flowers within the 5 years assessment . Although some SNP loci exhibited significant transmission distortion (P < 1E-11), other loci within the same haploblocks did not exhibit this distortion .e traits . AlthougOGI allele numbers, as determined by quantitative PCR, were highly correlated with the numbers of alleles in the nearest peak produced using the additive model . Multiple regression tests with the loci quantitatively associated with male conversion abilities indicated that, amongst these loci, OGI exhibited the strongest effect , the peaks on the sex chromosome, both with quantitative and diploidized genotypes, was significantly reduced  in the highest peak on Chr. 5 , whereas the other two loci might act for OGI activation independently.Both the additive and diploidized additive models showed consistent associations between Chr. 5 and male conversion rate . For Chrn Chr. 5 . On the ion rate . These sr2 > 0.15; OGI, which is normally silenced via SINE insertion on the promoter and the resultant DNA methylations.OGI activation loss-of-function of genes regulating DNA/histone methylation to silence transcription would be good candidates. Histone remodelling genes such as Chromatin remodelling 4,Arabidopsis,OGI activation/repression.Significant LD was maintained over ∼2–5 Mb of the peaks on Chr. 5, 8, and 9  partial correlation , and (ii) rrBLUP with the covariate of OGI dosage (in GWAS using diploidized genotypes), improved our ability to detect candidate loci. On the other hand, issues involving haplotype phasing still remain to be solved, since polyploids have more than two haplotypes per reference region, which are generally difficult to define, not only for conventional binary genotypes but also for quantitative genotypes. For instance, in our hexaploidy samples, the presence of many (>2) homologous haploblocks caused LD inconsistent with the order of the SNPs markers, despite of the F1 segregation line in which LD decay completely depends on recombinations (Ipomoea batatas) with 90 chromosomes (2n = 6x = 90), 96 linkage groups (LGs) were generated, using only double-simplex SNPs showing a Mendelian segregation ratio in an F2 progeny.Genome-wide analyses in polyploid genomes are often challenging in terms of (i) genotype calling, and (ii) haplotype phasing.inations , as obseOGI have a higher probability of male conversion. If we hypothesize that male conversion is associated with OGI activation, we can propose the following two hypothesis for cis-regulation of OGI to maintain OGI silencing  epigenetic cis-factors of OGI, such as DNA/histone methylation, are modified independently, and thus, more copies of OGI alleles result in higher probability of OGI expression release. On the other hand, in both the additive and the diploidized additive models, all the loci on Chr. 5, 8, and 9 significantly affects male conversion rate  mulion rate . This sug of OGI . Such a dsaa012_Supplementary_DataClick here for additional data file.