Novel high-throughput phenotyping (HTP) approaches are needed to advance the understanding of genotype-to-phenotype and accelerate plant breeding. The first generation of HTP has examined simple spectral reflectance traits from images and sensors but is limited in advancing our understanding of crop development and architecture. Lodging is a complex trait that significantly impacts yield and quality in many crops including wheat. Conventional visual assessment methods for lodging are time-consuming, relatively low-throughput, and subjective, limiting phenotyping accuracy and population sizes in breeding and genetics studies. Here, we demonstrate the considerable power of unmanned aerial systems (UAS) or drone-based phenotyping as a high-throughput alternative to visual assessments for the complex phenological trait of lodging, which significantly impacts yield and quality in many crops including wheat. We tested and validated quantitative assessment of lodging on 2,640 wheat breeding plots over the course of 2 years using differential digital elevation models from UAS. High correlations of digital measures of lodging to visual estimates and equivalent broad-sense heritability demonstrate this approach is amenable for reproducible assessment of lodging in large breeding nurseries. Using these high-throughput measures to assess the underlying genetic architecture of lodging in wheat, we applied genome-wide association analysis and identified a key genomic region on chromosome 2A, consistent across digital and visual scores of lodging. However, these associations accounted for a very minor portion of the total phenotypic variance. We therefore investigated whole genome prediction models and found high prediction accuracies across populations and environments. This adequately accounted for the highly polygenic genetic architecture of numerous small effect loci, consistent with the previously described complex genetic architecture of lodging in wheat. Our study provides a proof-of-concept application of UAS-based phenomics that is scalable to tens-of-thousands of plots in breeding and genetic studies as will be needed to uncover the genetic factors and increase the rate of gain for complex traits in crop breeding. A deeper understanding of the biological processes mediated by plant genomes is needed to develop crops with improved stress resilience and yield potential. Connecting genotype to phenotype for quantitative plant traits on a genome level necessitates high-density genetic markers and large population sizes to gain sufficient power and resolution. While the recent advancements in sequencing technologies have provided almost unlimited access to high-density genetic markers, large-scale rapid and accurate phenotyping of complex traits remains a major constraint. High-throughput phenotyping (HTP) tools with improved spatial and temporal resolution can help address this phenotyping bottleneck .Several HTP platforms including greenhouse, ground-based, and aerial systems have been demonstrated for crops , such asLodging, the permanent displacement of the plant stem from vertical position, is an example of a complex trait that is difficult to quantify in the field . ConventImage-derived lodging assessments have been proposed in wheat, maize, and rice . Albeit Here, we demonstrate novel field-based lodging assessment approaches using a commercially available light-weight UAS. By developing multiple time-points of three-dimensional digital elevation models (DEM) from UAS-acquired stereo imaging, we quantified lodging in 2640 wheat breeding plots with high correlation to visual scores and comparable repeatability. Using these precise phenotypic measurements, we identified genomic regions associated with lodging in wheat from a genome-wide association analysis. The limited genetic variation explained by the genome-wide associations led us to test whole-genome prediction models which accounted for a much larger portion of the heritable variation and supported the need for large, precisely measured populations to understand the functional genomics of lodging. Here, we report an original application of UAS for large-scale, high-throughput assessment of complex plant architecture and physiology in breeding and genomic studies with evaluation of lodging in wheat. This highly reproducible approach is scalable to tens-of-thousands of plots or even individual plants of different crops to rapidly quantify plant height, lodging, and could potentially be extended to traits like growth rate.Triticum aestivum L.) breeding lines from CIMMYT’s South Asia Bread Wheat Genomic Prediction Yield Trials were sown in the first week of November  at the Borlaug Institute for South Asia’s Ludhiana (LDH), Punjab, India (30°59′ N and 75°44′ E) location during seasons 2015–2016 and 2016–2017. A total of 590 and 595 unique wheat entries along with the check varieties were planted in alpha-lattice field design during seasons 2016 and 2017, respectively. Entries in each year were divided into 11 trials with each trial containing 53 closely related entries and 7 checks laid out in two complete replicate blocks of 120 plots per trial. Each replicate block was divided into six subblocks of 10 plots each. The experimental unit was an individual six-row plot with dimensions 1.3 m × 3.8 m. Plot-to-plot spacing was 80 cm and 52 cm between ranges and columns, respectively. Sixty best entries from the 2015–2016 season were repeated in the 2016–2017 season as an additional trial. The same experiment was replicated in Faisalabad (FAS) in Pakistan (31°24′ N and 73°02′ E), without the 11th trial. The experimental location in LDH is situated in the north-western wheat growing belt of India. LDH and FAS environments are classified as irrigated mega-environments (ME1) according to CIMMYT’s wheat breeding mega-environment classification system  equipped with a 3-channel Canon S100 digital camera  was used to collect data over the wheat plots. In 2017, the UAS platform was upgraded to a high payload carrying capacity quadcopter DJI Matrice100  carrying a 5-channel multispectral RedEdge camera . A detailed list of UAS and sensor specifications is provided .1 for IRIS+ UAS, and Litchi Android App (VC Technology Ltd.) and CSIRO mission planner application2  for DJI Matrice100. All flights were made at a ground altitude of 25 m in 2016 and 2017. In both years, the image overlap rate between two geospatially adjacent images was set to 80% sequentially and 78% laterally to ensure optimal orthomosaic photo stitching quality. Accordingly, the flight speed, the flight elevation above the ground, and the width between two parallel flight paths were adjusted based on the overlap rate and the camera field of view. Both cameras were automatically triggered with the onboard GPS following a constant interval of distance traveled.Each year the semi-autonomous UAS flights were conducted between 11AM and 2PM. Data acquisition followed the standard operating procedures developed within the Poland Lab at Kansas State University . In eachTo ensure highly accurate digital elevation maps, the UAS images were geo-referenced and geo-rectified using 12 white colored ground control points (GCPs) that were uniformly distributed over the entire 1.5 ha field area. These GCPs were surveyed using a SXBlue III-L differential Global Navigation Satellite System (GNSS) unit  and Precis BX305 Real Time Kinematics GNSS unit  in 2016 and 2017, respectively. To preserve the image pixel intensity, the Canon S100 camera was set to capture raw images, while the MicaSense RedEdge camera was set to capture uncompressed TIFF images.3. After preprocessing, images of both cameras were processed in Agisoft PhotoScan Pro  following the internally established protocols. In the first step of image alignment, the settings were: key-point limit 15000 (MicaSense) and 80000 (Canon) points, reference pre-selection, accuracy high, tie-point limit 0, and adaptive camera model. A sparse point cloud of the entire field area was stitched through the process of image alignment. In the subsequent step, the GCP coordinates were assigned to the individual images where white-colored, square-shaped GCPs were visible on the ground. Typically, at least three images per GCP are required to accurately geo-rectify and geo-reference the orthomosaics. The GCP assignment step was followed by the camera optimization step that adjusted the estimated point coordinates and camera parameters in the model. Based on the optimized camera positions, a dense point cloud model of the entire field was generated by setting the parameters to high quality and moderate depth. Finally, the DEM was built from the dense point cloud model. The detailed processing reports are available on the project data repository  for lens distortion correction and converted to 16-bit TIFF images. Lens distortion corrections were not required for images captured by MicaSense RedEdge camerapository . Each pi2 and λ2 was estimated through an iterative Expectation Maximization algorithm in R package mixtools . Additionally, visual assessment of lodging was carried out post-lodging events in both seasons. Visual scores included the lodging intensity , severity , and a combined lodging index . Additional agronomic and phenological traits were collected at different growth stages during the season. The final grain yield was measured on per plot basis. A detailed trait description as well as the ontology information is provided  three visual scores of lodging namely intensity (LOI), severity (LOS) and lodging index (LI) per plot and additional supporting agronomic measurements per plot; (ii) two digital lodging scores obtained by taking overall summary mean per plot (DLmean) or combined lodging index of normal mixture parameters (DLmix). The variance components for broad-sense line mean heritability or repeatability for each trait and trial were calculated using  package  in R witikl is the phenotypic response variable, μ is the fixed overall mean, Gi is the random genotype effect, Mk(l) is the random effect of sub-blocks nested within a replicate, and eikl is the residual effect. The variance components derived from the model were used to calculate broad-sense heritability on entry-mean basis for each trait:where y2Gσ is the genotypic variance, 2eσ is the residual variance, and r is the number of replicates. Genotypic best linear unbiased estimates (BLUEs) were calculated as follows:where ijkly is the phenotypic response variable, μ is the fixed overall mean, Gi is the random genotype effect, jZ is the random trial effect, k(j)R is the random effect of replicate nested within a trial, kl(j)M is the random effect of sub-blocks within replications nested within a trial, and ijkle is the residual effect. The marker-based genetic correlations between each pair of traits were calculated with sommer cov is the covariance of the trait pairs x and y; g(x)var and g(y)var is the variance of traits. The variance and covariance parameters of a pair of traits were estimated by fitting a multivariate model on two traits at a time.where v5 pipeline  of phenotypes, β is a f × 1 vector of fixed effect terms , u is a n × 1 vector of polygenic background effects, and τ is the additive marker allele effect. The respective design matrices: X is a n ×f matrix where f is the number of fixed covariates and n is the number of individuals; Z is a n ×n matrix relating y to u; S is a n ×1 vector of marker scores. The equation 6 was implemented in rrBLUP package in R  were used for Bayes Cπ and RKHS methods.To test for a highly polygenic genetic architecture of lodging in wheat, we generated [RR-BLUP ] and Bay, were u[RR-BLUP . RKHS isR packages BGLR and rrBLUP  predictions across environments on same genetic material ; (2) predictions across years on independent set of lines . In the case of LDH-FAS training-testing combinations, each of the five lodging measures  was used in the training set at LDH to predict the LOI at FAS. The genomic prediction models were implemented in d rrBLUP . We used4. Analysis scripts are available at github.com/singhdj2/digital-lodging.All data associated with the experiments including raw images, orthomosaics, polygons, etc. can be accessed at the public repository2H) of 0.50 to 0.66 for the lodging incidence  breeding efforts, wheat trials were established at Ludhiana (LDH) in NW India and Faisalabad (FAS) in central Pakistan in 2016 and 2017 . Throughncidence .Digital Lodging mean: DLmean) of all differential DEM height points falling under the area of each plot polygon. This measure of lodging was phenotypically and genetically well-correlated to the visual scores of incidence, severity, and lodging index  for the crop before and after the lodging events. A differential DEM was generated by subtracting the post- from pre-lodging DEM giving the overall elevation change between the two time-points . We obsephenor = 0.76–0.91; genor = 0.93–0.97; P < 0.001; Following on the simple mean difference we applied a more informed normal mixture model of the differential DEM pixel distributions. A combined mixture lodging index (DLmix) of digital lodging was derived from the mixture model parameters and compared with the visual scores. The ground-truth validation of the mixture model again showed high phenotypic and genetic correlations to the visual scores (2H), or repeatability, on an entry-mean basis for each of eleven trials in both years , and moderate to high heritability, no significant SNPs were identified for any lodging measure in 2016 . A survey for the 2NS fragment in our material suggested that more than 75% lines carry this translocation fragment, which is known to harbor multiple disease resistance genes in wheat  elite wheat breeding lines. Genome profiling was performed with genotyping-by-sequencing and markers were fitted in a linear mixed model with terms to account for population structure and cryptic relationships (Equation 4). Despite having a relatively large population size   were compared to account for complex genetic architecture of lodging in wheat. As all three models yielded comparable results , only RRability) . Findingability) . In majoability) . In contability) . Furtherr = 0.12, P < 0.01) with early heading  tend to have more lodging while thousand grain weight was negatively associated with lodging  and aerial image acquisition. The flight time depends on the field scale, UAS flying elevation, moving velocity, and the overlapping rate between the successive aerial images. Data processing component includes DEM generation by photogrammetry and plot-level data extraction, and the processing time depend on the data volume and the computer hardware settings. For the implementation standpoint, this work can be replicated with an initial investment of USD 12000, which will cover the cost of sensor hardware (USD 2000), UAS platform (USD 5000), a high-precision GNSS (USD 2000), and the computer software and hardware (USD 3000). A practical implementation of our lodging assessment approach in the field would require a careful monitoring of weather and crop growth conditions. Furthermore, as the operational costs and scale of breeding programs grow in future, the cost-effective and high-throughput tools that can provide multiple layers of data at a fraction of cost would be highly desired. Therefore, a full benefit of our proposed methodology can be realized by integrating it with the routine application of UAS-based trait measurements in research programs. As such, this lodging assessment approach can provide an additional data layer on top of the routine phenotypic measurements  without incurring any extra cost and time effort to the researchers.Unmanned aerial systems-enabled phenotyping allowed us to quantify lodging on 2,640 wheat plots. Using validated digital lodging measurements along with association and genomic prediction analyses, we provide evidence in support of a polygenic genetic architecture of lodging in wheat. Our findings have diverse applications in plant breeding and genetics. First, our highly reproducible UAS based digital lodging methods can be easily scaled and also applied to different crops to rapidly quantify plant height, lodging, and should be extensible to traits like growth rate on large populations. Second, for a complex and quantitatively controlled trait like lodging, whole-genome predictions can account for heritable variation not captured by regular GWAS. Undoubtedly, accurate phenotypic assessment is a critical prerequisite for breeding for lodging resilience, and as shown here, UAS-enabled large-scale quantitative assessment of lodging can be a powerful approach to identify genetic variants for lodging. This comprehensive evaluation of lodging assessment methods lays the foundation for improving our understanding of functional underpinnings of lodging in wheat and other crops. Overall this highlights the future of modern breeding where, in conjunction with powerful genomics and informatics tools, UAS-enabled phenotyping can accelerate the genetic gains in plant breeding to meet the global demand for food, fiber, and fuel.JP and DS conceived and designed the study and wrote the manuscript. DS collected and analyzed UAS and ground-truth data in India. DS and XW performed image analysis. LG contributed alien-fragment data. UK supervised field experiments and collected data in India. MN and MI supervised field experiments and collected ground-truth data in Pakistan. RS provided experimental lines. JP directed the overall project. All authors edited and reviewed the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Accumulating evidence from genome wide association studies (GWAS) suggests an abundance of shared genetic influences among complex human traits and disorders, such as mental disorders. Here we introduce a statistical tool, MiXeR, which quantifies polygenic overlap irrespective of genetic correlation, using GWAS summary statistics. MiXeR results are presented as a Venn diagram of unique and shared polygenic components across traits. At 90% of SNP-heritability explained for each phenotype, MiXeR estimates that 8.3 K variants causally influence schizophrenia and 6.4 K influence bipolar disorder. Among these variants, 6.2 K are shared between the disorders, which have a high genetic correlation. Further, MiXeR uncovers polygenic overlap between schizophrenia and educational attainment. Despite a genetic correlation close to zero, the phenotypes share 8.3 K causal variants, while 2.5 K additional variants influence only educational attainment. By considering the polygenicity, discoverability and heritability of complex phenotypes, MiXeR analysis may improve our understanding of cross-trait genetic architectures. To better understand the phenotypic relationships of complex traits it is also important to understand their genetic overlap. Here, Frei et al. develop MiXeR which uses GWAS summary statistics to evaluate the polygenic overlap between two traits irrespective of their genetic correlation. Understanding the degree to which complex human phenotypes share genetic influences is critical for identifying the etiology of phenotypic relationships, which can inform disease nosology, diagnostic practice, and improve drug development. Most human phenotypes are known to be influenced by multiple genetic variants, many of which are expected to influence more than one phenotypes 3. This has led to cross-trait analyzes, quantifying polygenic overlap, becoming a widespread endeavor in genetic research, made possible by the public availability of most GWAS summary statistics 5.In recent years, genome-wide association studies (GWASs) have successfully detected genetic variants associated with multiple complex human traits or disorders, providing important insights into human biologypolygenic overlap refers to the fraction of genetic variants causally associated with both traits over the total number of causal variants across the two traits considered, while genetic correlation quantifies the correlation coefficient of additive genetic effects for the two traits. The sign of the correlation indicates whether the shared genetic effects predominantly have the same or the opposite effect directions. Available methods can quantify genetic correlation using raw genotypes7 or GWAS summary statistics11. However, these methods report overall positive, negative, or no genetic correlation, but fail to capture mixtures of effect directions across shared genetic variants. This scenario is exemplified by the genetic relationship between schizophrenia and educational attainment. Despite consistent estimates of a non-significant genetic correlation13, many genome-wide significant loci are found to be jointly associated with both phenotypes14. Among 25 shared loci15, 16 had effects in the opposite direction, while 9 had effects in the same direction. Thus, new statistical tools are needed to improve our understanding of the polygenic architecture of complex traits and their intricate relationships.Currently, the prevailing measure to quantify polygenic overlap is genetic correlation. For a pair of traits, 19, which we extend to four bivariate normal distributions as illustrated in Fig. Here, we introduce a statistical tool (MiXeR), which quantifies polygenic overlap irrespective of genetic correlation between traits, using summary statistics from GWAS. To evaluate polygenic overlap between two traits, MiXeR estimates the total number of shared and trait-specific causal variants . MiXeR bypasses the intrinsically difficult problem of detecting the exact location of causal variants, but rather aims at estimating their overall amount. MiXeR builds upon the univariate causal mixture modelWe show in simulations that MiXeR provides accurate estimates of model parameters in the presence of realistic LD structure. Using GWAS summary data, we quantify polygenic overlap of several psychiatric disorders, including schizophrenia and bipolar disorder, with educational attainment and human height, with large implications for understanding how genetic factors overlap between complex human phenotypes.π12; correlation of effect sizes within the shared polygenic component, ρ12, and genetic correlation, rg) in the presence of a realistic LD structure  and high polygenicity  plots . It characterizes MAF-dependent architecture in terms of a single parameter S, ranging from S = 0  to S = −1 . We simulated three intermediate values, S = −0.25, S = −0.5, and S = −0.75, which cover the range of BayesS estimates observed for real GWAS data. The results , univariate polygenicity (π12) are underestimated by up to 25%; correlation of effect sizes (ρ12) is overestimated by 25%; however, the genome-wide genetic correlation (rg) appears to have no bias.Another assumption in the MiXeR model is that effect sizes are independent of allele frequencies. To asses this assumption, we ran simulations with effect sizes drawn from the BayesSN = 11,015,833 variants, but only a fraction  of the variants enter LD structure estimation and fit procedure. The results , which at genome-wide level is observed as genetic correlation of rg = 0.16 (0.01) according to MiXeR, or rg = 0.14 (0.01) according to LDSR.Furthermore, MiXeR reveals important differences among traits with low genetic correlation, represented as Venn diagrams of shared and unique polygenic components Fig. , 13a–g. MiXeR estimates of the unique polygenic components provide insights into trait-specific genetic architectures. For example, schizophrenia has 2.1 K causal variants not shared with bipolar disorder, less than 0.1 K variants not shared with educational attainment, but as many as 7.5 K variants not shared with height. Also, for the other phenotypes, the number of trait-specific causal variants varies across different pairs of traits Fig. .zj1, zj2), the predicted density βj1, βj2) that underlie model predictions. Figure 34 to compare the observed and predicted distributions of z-scores, and show that MiXeR-based prediction provides accurate estimates of the data Q–Q plots , likely because they did not specifically model the polygenic overlap. For example, Ruderfer et al.40 performed a combined GWAS of schizophrenia and bipolar disorder, and a differential GWAS of schizophrenia cases versus bipolar disorder cases. Our results indicate a higher polygenicity of schizophrenia than bipolar disorder, which is in line with the recent study by Bansal et al.14, who highlighted two schizophrenia subtypes. Our results also indicate that both schizophrenia and bipolar disorder have a small fraction of causal variants conferring disorder-specific risk , in agreement with the cross-trait LD score regression estimate of 0.188 (0.023)  Table .18, or 484 K Affymetrix SNPs in ref. 19). When expressed as a total number, our estimates of polygenicity are consistent with previously reported results19  is conceptually simpler and more flexible, resulting in unbiased estimates of model parameters across a wide range of simulation scenarios  or 484 K Affymetrix SNPs (ref. 19). Finally, our model individually processes all SNPs, without grouping them into bins (ref. 16).MiXeR has some notable advantages compared with the existing methods that implement causal mixture. First, our mathematical model for the likelihood term 45 suggests that certain phenotypes, including height, require at least two causal components of small and large effects. We note that the MiXeR model still provides a good fit for SNPs not reaching the GWAS significance threshold , which underestimate the true value by up to 25% in the case of extreme MAF-dependent architecture with S = −0.75  to compare causal mixture model versus the infinitesimal model, as shown in Supplementary Table π1 and The MiXeR method requires large GWAS studies. Our recommendation is to apply MiXeR to studies with at least entclass1pt{minima18, and to explicitly account for MAF-dependent architectures46. Further extensions may account for differential enrichment for true associations across genomic annotations20. Another limitation to address is that the MiXeR model assumes similar LD structure among studies, and is not currently applicable for analysis across different ethnicities. We also aim to extend the MiXeR modeling framework to be used to improve power for discovery of shared and trait-specific SNPs by estimating the posterior effect size of SNPs associated with one trait given the test statistics in another trait, as well as for improving predictive power of polygenic risk scores.In our future work, we plan to incorporate an additional Gaussian component to model small and large effectsIn conclusion, MiXeR represents a useful addition to the toolbox for cross-trait GWAS analysis. By considering the intricate polygenic architectures of complex phenotypes, MiXeR allows for measures of polygenic overlap beyond genetic correlation. We expect this to lead to new insights into the pleiotropic nature of human genetic etiology.yk is a quantitative phenotype or disease liability of k-th individual, gjk is 0, 1, 2-coded number of reference alleles for j-th variant, and βj is the additive genetic effect of allele substitution. We say that a genetic variant is causal for a trait if it has a non-zero effect on that trait (βj ≠ 0).Consider a simple additive model of genetic effects, ignoring gene-environment interactions, epistasis and dominance effects. Under these assumptions, the contribution of the genotype to the phenotype is modeled as a sum of individual contributions from genetic variants: 16, π1) of variants have an effect on the trait, while the effect of the remaining variants is zero. For the mathematical convenience, we chose a Gaussian distribution for the non-null arm of the causal mixture. A drawback with the gaussian prior is that a large fraction of causal variants will have effect sizes close to zero. We would prefer to count a variant as causal only if it has a sufficiently large effect size, using for example a bi-modal prior distribution with probability mass separated from zero, but for such prior, it was not feasible to accurately model the effects of the LD structure.MiXeR builds upon the univariate causal mixture modelβj1, βj2 of variant j on the two traits as a mixture of four bivariate Gaussian components ; π12 is a weighting of the component affecting both traits; and π0 is a fraction of variants that are non-causal for both traits, π0 + π1 + π2 + π12 = 1; ρ12 is the correlation coefficient of the effect sizes in the shared component. All parameters are assumed to be the same for all genetic variants.In a joint analysis of two traits, we expect some variants to affect both traits; some variants to affect one trait but not the other; and most variants to have no effect on either trait. We assumed that for a given trait, all causal variants follow the same distribution of effect sizes, regardless of what effect a variant has on the other trait. Within the shared component, we model correlation of effect sizes, to account for genetically correlated traits. Based on these assumptions, MiXeR models additive genetic effects βj1, βj2), which are distorted by limited sample size , cryptic relatedness within a GWAS sample, as well as LD between variants. To disentangle these effects, we derive the likelihood term for observed GWAS signed test statistics , incorporating effects of the LD structure ; heterozygosity Hj = 2pj(1 − pj), where pj is the minor allele frequency of the j-th variant; the number of subjects genotyped per variant (Nj1 and Nj2); and variance distortion parameters ρ0. Specifically (see Supplementary Note The effects mentclass2pt{minimThe nine parameters of the model (π12 = 1 (so that π0 = π1 = π2 = 0) reduces our model to an infinitesimal assumption that underlies cross-trait LD score regression8. Under this constraint, our model predicts that GWAS-signed test statistics follow a bivariate Gaussian distribution with zero mean and variance–covariance matrixForcing zj1, zj2) ∼ N, where E(zj1zj2) being proportional to the LD score of j-th SNP, and parameters ρ0, σ01, σ02 playing the role of LD score regression intercepts47. The only distinction here is that we choose to model effect sizes that are independent of allele frequency, leading to the incorporation of Hi into our model; this factor is absent from the LD score regression model due to the assumption there of effect sizes that are inversely proportional to Hi. Thus, MiXeR is a direct extension of cross-trait LD score regression, which relaxes the infinitesimal assumption.i.e.,  distribution of a given GWAS SNP as a mixture of K = 20,000 bivariate normal distributions, all having equal weight in the mixture. For each k = 1, …, K, we randomly draw the location of causal variants , and calculate the variance–covariance matrix r2 correlations between the assumed causal variants and the GWAS SNP. ThenThe “full model” for GWAS z-scores approximates ; 48; and E [Zj1Zj2], 50. Of interest is that the “fast model” involves the forth power of allelic correlation where ⊕ denotes convolution of probabilistic distribution functions , 51 (phase 3 data), obtained from the LD score regression website52. In total, 14 individuals were excluded due to relatedness53. For simulations, LD scores were estimated from the actual genotypes that we use to produce synthetic GWAS summary statistics. LD r2 coefficients were calculated using PLINK54 with LD r2 cutoff of 0.05 and fixed window size of 50,000 SNPs, corresponding on average to a window of 16 centimorgans. We deliberately chose a larger LD window compared with the LDSR-recommended window of 1 centimorgan, because the later appears to truncate a noticeable part of LD structure. At the same time, we did not observe an effect of using an unbiased estimate55 of r2, thus fall back to the standard Pearson correlation coefficient. We employ small integer compression56 for efficient storage of the LD matrix.To estimate the LD structure, we use 489 individuals from the 1000 Genome projectWe fit the model by direct optimization of weighted log likelihoodwj chosen by random pruning (64 iterations at LD r2 0.1). Optimization is done by the Nelder–Mead Simplex Method57 as implemented in MATLAB’s fminsearch. First, we fit univariate parameters separately for each trait, i.e., π12 = 1 to estimate rg and ρ0. Then, we proceed with the “full model” optimization of the parameters specific to the bivariate model , constraining all other parameters to their univariate estimates, and also constraining rg and ρ0 to the estimates from the infinitesimal model. The additional analysis  on each of them, and report the standard deviations. In cases when joint hessian was not positive definite, we estimate marginal errors of fitted parameters.We estimate standard errors of all parameters from the observed Fisher’s information, based on the “fast model”. It is known from the likelihood optimization theory that the observed Fisher’s information may not be suitable for a parameter near its boundary, which is applicable to the mixture weights k − 2F and F is the log-likelihood from Eqs. , and We apply standard formulas and estimate AIC = 2rom Eqs. , k is thi, j in a subset J the squared allelic correlation T iterations of random pruning the log-likelihood function can be calculated as follows:The log-likelihood cost function and the Q–Q plots apply a weighting scheme to SNPs to 0avoid overcounting evidence from large LD blocks. As an alternative to weighting by inverse LD score, we chose to infer the weights by random pruning. This technique is a stochastic procedure which averages log-likelihood function across repeatedly selected subsets of variants, such that for each pair of variants wj = |{t:j ∈ Jt}|/T, |S| denotes cardinality of set S. Random pruning with stringent threshold r2 = 0.1 justify independent modeling of the residuals in Eq.  density as defined by Eq. (pdfj(z) across 1% of randomly sampled SNPs, and numerically integrate the resulting probability density function to convert it into a cumulated distribution function. Error bars on data Q–Q plots represent the 95% binomial confidence interval q is the probability of observing a p-value as extreme as, or more extreme then the chosen p-value, and ntotal is the effective number of SNPs after controlling for LD structure, which in our case was calculated as a sum of random pruning weights across all SNPs.Univariate Q–Q plots and stratified Q–Q plots for the model were constructed from d by Eq. , given fS(N) of narrow-sense heritability captured by genome-wide significant SNPs at a given sample size N. The S(N) is defined as follows:Causal mixture model can project the future of GWAS discoveries, by estimating proportion zt = 5.45 gives z-score corresponding to the standard genome-wide significance threshold 5 ∙ 10−8, and C ≡ P ⋅ E denotes a posterior effect size E of the non-centrality parameter δ2 for a GWAS SNP j, given certain z-score, multiplied by a prior probability of observing that z-score. Probability density function P is given by Eq.  can be calculated from the Bayesian rule. Thus, C and where 60, with MAF above 0.05, ambiguous SNPs excluded, imputation INFO above 0.9, MHC and other long-range LD regions excluded. Calculation of the LD structure, LD scores ηj are based on 9,997,231 SNPs from 1000 Genomes Phase 3 data, downloaded from LD score regression website. In simulations we generate GWAS and estimate LD structure on a subset of 11,015,833 SNPs from 1000 Genomes Phase 3, with MAF above 0.002, call rate above 90%, excluding duplicated RS numbers; the fit procedure was constrained to ~ 130 K GWAS SNPs, keeping only HapMap3 SNPs, and pruning SNPs at LD r2 threshold of 0.1.To enable a direct comparison of our model with LD score regression, we use the same set of SNPs in our log-likelihood optimization, which consists of approx. 1.1 million variants, subset of 1000 Genomes and HapMap3Neff = 4/(1/Ncase + 1/Ncont) to account for imbalanced numbers of cases and controls, both in MiXeR and in LD score regression. In addition, we ran LDSR using MiXeR MAF model , and show the results alongside with original LDSR estimates /var(y) to a predefined level.For each simulation run, we use PLINK to obtain GWAS summary statistics, including Wald’s test z-score and βj1, βj2) from the four-component mixture model (Eq. (π12). We chose the total polygenicity in both traits to be 3 × 10−3 or 3 × 10−4 and include an additional scenario of uneven polygenicity . For each combination h2, we set polygenic overlap to be a fraction of total polygenicity f from six equally spaced values (0.0 to 1.0 with a step of 0.2). Correlation of effect sizes ρ12 set to 0.0 or 0.5. Heritability was set to 0.1, 0.4, or 0.7, which let us keep GWAS sample size constant  because the distribution of GWAS z-scores depends on N and h2 only through their product, h2 × N . Finally, for each combination of heritability, polygenicity, polygenic overlap, and correlation of effect sizes, we repeat simulations ten times.For the simulations shown in Fig. For the simulations with differential enrichment, we simulate three levels of polygenicity , three levels of heritability , and for each combination, generate 20 pairs of genetically independent traits (except for having shared pattern of enrichment). To simulate the enrichment, we keep a constant variance of effect sizes across all SNPs, but modulate the probability of having causal variant proportionally to LDSR regression coefficient. We use --per-allele flags in LD score estimation to run simulations with the MiXeR MAF model.For simulations with MAF-dependent architectures, we simulate effect sizes as follows:S = 0 corresponds to the MiXeR MAF model, S = −1 corresponds to the LDSR MAF model. The same model is implemented in BayesS software19, thus we choose parameter S from −0.25, −0.50, and −0.75, which corresponds to the range of BayesS estimates observed on real GWAS data.Parameter Supplementary InformationPeer Review File


DLEC1, which is associated with chronic obstructive pulmonary disease.Family-based designs have been shown to be powerful in detecting the significant rare variants associated with human diseases. However, very few significant results have been found owing to relatively small sample sizes and the fact that statistical analyses often suffer from high false-negative error rates. These limitations can be avoided by combining results from multiple studies via meta-analysis. However, statistical methods for meta-analysis with rare variants are limited for family-based samples. In this report, we propose a tool for the meta-analysis of family-based rare variant associations, metaFARVAT. metaFARVAT is based on a quasi-likelihood score for each variant. These scores are combined to generate burden test, variable-threshold test, sequence kernel association test (SKAT), and optimal SKAT statistics. The proposed method tests homogeneous and heterogeneous effects of variants among different studies and can be applied to both quantitative and dichotomous phenotypes. Simulation results demonstrated the robustness and efficiency of the proposed method in different scenarios. By applying metaFARVAT to data from a family-based study and a case-control study, we identified a few promising candidate genes, including  In recent decades, genome-wide association studies (GWAS) have identified tens of thousands of common variants associated with various complex diseases. However, in spite of their success in discovering disease susceptibility loci (DSL), the DSL identified by GWAS only partially explain disease heritability, and rare variants have been implicated as one contributor to this missing heritability  than unrelated subjects. For instance, the probability of sibling pairs sharing rare alleles can be calculated  using whole-exome sequencing (WES) data from family-based samples from the Boston Early-Onset COPD Study (EOCOPD) and case-control samples from the COPDGene study.K studies available and that each study is of either a population-based, case-control, or family-based design. It is assumed that kN subjects are available in study k. We assume that there are M rare variants in a gene, and the minor allele count of variant m for subject i in study k is coded by imkx. Traits can be either quantitative or dichotomous, and iky indicates a phenotype of subject i in study k. Their vectors are denoted by:We assume that there are m is missing or monomorphic in study k, we assume that 0, and its variance and covariance with m is missing for all studies, then it should be removed from the analysis.In some cases, rare variants may be observed only in a subset of studies. If variant Φk. If we let i and subject i' for study k, and ikd be the inbreeding coefficient for subject i, Φk is defined by:Parental genotypes are transmitted to offspring under Mendelian transmission, and thus our test statistics consider the genetic correlation between family members. The genetic variance-covariance matrix among family members can be specified by a kinship coefficient matrix, Φk  can be estimated with large-scale genotyping data and should alternatively replace a priori specified weight for each study. We assume that the statistics for study k are weighted by vk, and their K × K dimensional diagonal matrix is denoted by WB. Second, rare variants have different gene annotations, genomic coordinates, and functional characterization, and various annotation tools have been proposed to choose important features based on their biological properties. We denote the weight for rare variant m by mw, and we let WW be their M × M dimensional diagonal matrix.Last, meta-analysis of rare variant association analyses with multiple studies requires two different types of weights. First, when multiple studies are combined, each study has different features, such as sample size and disease diagnosis, and such differences can be handled with an ik for subject i at study k to improve the efficiency of the proposed score test  with covariates or the prevalence were shown to be the most efficient  −1ZtH−1. For a dichotomous phenotype, use of the generalized linear mixed model might be considered an appropriate approach, but we estimated T in the same way for quantitative phenotypes when individuals were randomly selected because of its superior statistical power  between cases and controls.The homogeneous model assumes that the effect sizes of each variant are expected to be similar among different studies, and thus the proposed scores for each study can be collapsed across studies as follows:vk to be one. However, the proposed statistics are sometimes unavailable, and the appropriate choice can vary according to the available information. For instance, if standardized test statistics and sample sizes are available, then the inverse function to the square root of the sample size can be utilized.Here, we set Rare variant association analysis can be categorized into burden and variance-component tests  be an M-dimensional column vector whose 1st,…, mth elements are 1 and the others are 0. If we let:Last, rare variant association analysis utilizes rare variants, but the definition of a rare variant is not clear. VT approaches are very useful in such scenarios. We assume that rare variants are sorted in ascending order of overall MAF. We let then the covariance between Therefore, we let:t(m) and let t(|max|) = max{ |t(1)|,…, |t(M)|}, the p-value for the VT method can be calculated by:If we denote the realization of Here, where E = βmk, the null hypothesis can be expressed by β11 = … = βMK = 0, and we consider the following score vector and its variance matrix:As in the homogeneous model, we propose burden and variance component tests for the heterogeneous model. The heterogeneous model assumes that the effects of specific variants are heterogeneous among studies. If we let ekk is a K × K dimensional matrix whose  element is 1 and the others are 0. Then, the burden test can be expressed as:where We let:and we let Then, Therefore, the variance component test is defined by:p-value for pIf we denote the p-value is also obtained by the numerical algorithm for the FARVAT statistic , and for non-founders, the average of maternal and paternal polygenic effects was combined with values independently sampled from N. Random error was independently sampled from N. Therefore, the heritability of the simulated trait is 0.5. The genetic effect at variant m in study k was the product of βmk and the number of disease susceptibility alleles. To evaluate the type-1 error estimates, βmk was assumed to be 0. To evaluate the statistical power estimates, if we let ah2 be the proportion of variance explained by rare variants, βmk values were iteratively sampled with a two-step approach. U. Then, if we let:Quantitative phenotypes were defined by summing the phenotypic mean, genetic effect, polygenic effect, main genetic effect, and random error, and we assumed there was no environmental effect shared between family members. The phenotypic mean was denoted by α = 0.3. The polygenic effect for each founder was independently generated from mk values were sampled from the uniform distribution U. This procedure was repeated until kv converged. We assumed that ah2 = 0.01. βmk was generated from heterogeneous or homogeneous scenarios. For homogeneous scenarios, we assumed that the effects of each rare variant were in the same direction in all studies. For heterogeneous scenarios, the signs (±) of βmk values sampled from U were chosen randomly.β1) of ≤40%, physician-diagnosed COPD, and without severe alpha-1 antitrypsin deficiency. All first-degree relatives, older second-degree relatives, and additional affected family members were enrolled. There were 49 pedigrees with at least two affected family members selected for WES. COPDGene was a multi-center study of smokers with and without COPD and included African-Americans and non-Hispanic whites  <0.7), as well as 195 controls with normal spirometry (frequency-matched to COPD cases on pack-years of cigarette smoking), were chosen for WES.We considered previously reported WES data from Boston Early-Onset COPD Study (EOCOPD) families and COPDGene case-control subjects for meta-analysis  <10. Finally, 88,737 rare variants in 13,935 genes were analyzed in the EOCOPD data set, and 24,846 rare variants in 10,550 genes were tested in the COPDGene data set. For both EOCOPD and COPDGene data, GRMs were estimated for variants with MAFs >5% and were incorporated as variance-covariance matrices of genotypes to adjust for population substructure. Effects of covariates for binary phenotypes were adjusted by using the BLUP as an offset. First, we fitted the linear mixed model with adjustments for age, sex, and pack-years of smoking as covariates, and then BLUP was set as the offset for the proposed methods. A description of the two datasets is provided in Sequencing for both cohorts was performed at the University of Washington , using Nimblegen V2 capture , and the Illumina platform . Participants selected from the COPDGene cohort were sequenced via the NHLBI Exome Sequencing Program, and EOCOPD subjects were sequenced as part of the Center for Mendelian Genomics. Quality control (QC) filtering for both data sets was performed by the method of Qiao et al.  and filtHom) and heterogeneous metaFARVAT (metaFARVATHet) at the 0.1, 0.01, 10−3, and 10−4 significance levels with dichotomous phenotypes. Estimates of type-1 error rates were virtually equal to nominal significance levels. However, VT type metaFARVATHom showed inflation, especially when there were three studies, and if the number of rare variants is small, it is not recommended. Quantile-quantile (QQ) plots in Hom and metaFARVATHet are statistically valid.To evaluate statistical validity, type-1 error estimates for both dichotomous and quantitative phenotypes were calculated at various significance levels using 20,000 replicates of 200 unbalanced families. For each replicate, we performed three different meta-analyses, including 3, 6, and 9 studies. −6 significance level, showing the changes in power under different scenarios. Empirical power estimates were calculated with 2,000 replicates for seven different statistics: burden, SKAT, SKAT-O, and VT type statistics for metaFARVATHom and burden, SKAT, and SKAT-O type statistics for metaFARVATHet. Results are provided in p-values across studies: the minimum p-value method and Fisher's method. If we let kp be the p-value from the kth study , the minimum p-value and Fisher's method can be obtained by:Secondly, empirical power estimates for dichotomous phenotypes were calculated at the 2.5 × 10p-value approach usually performed the least efficiently, especially when there were equal numbers of protective and deleterious rare variants in the targeted gene. Moreover, the power of the minimum p-value approach was not much improved by including more studies in the meta-analysis. The Fisher approach always performed better than the minimum p-value approach but was less powerful than the metaFARVAT method, regardless of the scenario. Statistical power estimates depend on the scenarios, and both tables show that the best power estimates are usually found from metaFARVATHom and metaFARVATHet under homogeneous and heterogeneous scenarios, respectively. Statistical power estimates also depend on the proportion of rare variants with deleterious or protective effects on the phenotypes, which is often unknown. For example, when all rare causal variants had deleterious effects on the phenotype, burden, and VT type metaFARVAT outperformed all other approaches, but if there were variants with deleterious and protective effects, SKAT-type metaFARVAT was the most efficient. SKAT-O metaFARVAT was not always the most powerful, but its empirical power estimates were usually very close to those of the most efficient approach.According to our results, the minimum Hom under homogeneous scenarios. The SKAT-O type statistic in seqMeta did not perform well when there were as many protective variants as deleterious variants in the gene. metaFARVATHet outperformed other methods when the effects of each rare variant differed among studies and when there were variants with deleterious and protective effects within a gene.The proposed methods can be applied to quantitative phenotypes, and results for quantitative phenotypes are provided in Hom and metaFARVATHet. For both statistics, v1 and v2 were set to 1. The QQ plots in Het and metaFARVATHom preserved the nominal significance level. However, VT type metaFARVAT exhibited some inflation, and its results are therefore not included in −6 and is indicated by a solid blue line. DLEC1 achieved genome-wide significance under both methods, and ZNF441 was implicated with potentially significant results  by metaFARVATHom SKAT-O.To identify rare variants associated with COPD, we separately conducted rare variant analyses with EOCOPD and COPDGene data. Manhattan and QQ plots are provided in Family-based association methods are robust against population substructure, and because of genetic homogeneity among family members, they are often utilized for rare variant association analyses. Multiple approaches have been proposed, and Tang and Lin  providedDLEC1 was found to be genome-wide significant. DLEC1 is a protein-coding gene encoding a cilia and flagella-associated protein. This gene has been implicated in several cancers but has not been previously associated with COPD. However, cilia-associated genes have been previously implicated in COPD (Tilley et al., In this study, we proposed a new meta-analysis method for family-based rare variant association analyses with dichotomous phenotypes, which can test both homogeneous and heterogeneous effects of variants in different studies. metaFARVAT can also be applied to quantitative phenotypes, and is able to combine all study designs, including family-based, case-control, and population-based designs. Furthermore, the proposed method was applied to a meta-analysis of EOCOPD and COPDGene data, and Despite the robustness and efficiency of the proposed method, there are still some limitations of the developed method. First, VT methods sort rare variants according to their MAFs and search the optimal threshold for rare variants. This approach is useful when it is not clear how to define rare variants. However, we found that type-1 error can be inflated if the number of rare variants is too small, and it is computationally intensive if there are a large number of variants to investigate. This problem can be solved by using a permutation method, and further investigation of this approach is necessary. Secondly, sufficiently large samples are necessary to guarantee that SKAT-O follows the assumed asymptotic distribution of the SKAT-O approach under the null hypothesis. Therefore, the SKAT-O type metaFARVAT also has this limitation when it is applied to a dichotomous phenotype with a small sample size. Thirdly, the proposed method cannot be applied to X- or Y-linked genes because the distributions of variants in X and Y chromosomes are different in males and females. Such an improvement will be considered in our future work. Lastly, in the simulation studies, we considered a limited number of rare variants and excluded noise variants. However, in practice, it is not known which rare variants are causal and which represent noise. Extensive simulations are thus necessary in our future work.Despite the importance of rare variant analyses with family-based samples, this field of study has suffered over the last decades from a lack of statistical methods. In this study, we proposed new methods for family-based samples, enabling such statistical analyses.http://healthstat.snu.ac.kr/software/metaFARVAT/.The R package for metaFARVAT can be downloaded from LW and SW conceived and designed the experiments, performed the experiments, analyzed and interpreted the data, and drafted the manuscript. SL maintains the software homepage. DQ, MC, ES, and CL edited the manuscript. All authors read and approved the final version of the manuscript.In the past 3 years, ES received honoraria from Novartis for Continuing Medical Education Seminars and grant and travel support from GlaxoSmithKline. MC has received grant support from GSK. The remaining 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.


To examine potential interactions between education, a recognized social determinant of health, and genetic variants contributing to blood pressure, we used linear regression models to investigate two-way interactions for systolic and diastolic blood pressure (DBP). We identified a two-way interaction between rs6687976 and education affecting DBP (p = 0.052). Individuals homozygous for the minor allele and having less than a high school education had higher DBP compared with (1) individuals homozygous for the minor allele and high school education or greater and (2) individuals not homozygous for the minor allele and less than a high school education. To our knowledge, this is the first EHR -based study to suggest a gene-environment interaction for blood pressure in African Americans, supporting the hypothesis that genetic contributions to hypertension may be modulated by social factors.African Americans experience the highest burden of hypertension in the United States compared with other groups. Genetic contributions to this complex condition are now emerging in this as well as other populations through large-scale genome-wide association studies (GWAS) and meta-analyses. Despite these recent discovery efforts, relatively few large-scale studies of blood pressure have considered the joint influence of genetics and social determinants of health despite extensive evidence supporting their impact on hypertension. To identify these expected interactions, we accessed a subset of the Vanderbilt University Medical Center (VUMC) biorepository linked to de-identified electronic health records (EHRs) of adult African Americans genotyped using the Illumina Metabochip ( African Americans have a higher prevalence of hypertension, or chronically high blood pressure, compared with other racial/ethnic groups . DespiteCurrent GWAS findings explain only a proportion of the expected contribution from additive genetic effects. Previous twin and family studies estimate these traits have moderate to high heritability (30–70%) , suggestARHGAP22 rs4593967 (SBP) and IQCK rs950928 (DBP), neither of which has been previously associated with blood pressure. We also identified a novel SNP-education interaction affecting DBP, suggesting social determinants of health may modify genetic effects contributing to complex human traits.Here, we examine the modifying effects of education, a measure of socioeconomic status (SES) and recognized social determinant of health, on SBP and DBP traits among African Americans drawn from a clinical setting. Previous epidemiologic studies suggest that in addition to alcohol consumption and smoking, social environment and specifically SES has a strong influence on blood pressure and hypertension . FurtherThe study population is derived from BioVU, a DNA biobank of the Vanderbilt University Medical Center (VUMC) linked to de-identified EHRs. DNA samples are extracted from discarded blood samples drawn for routine clinical care . These sn = 15,863)  . We extr 15,863) . Educati 15,863) . EducatiThe median value of all blood pressure measurements within an individual’s EHR prior to a recording of blood pressure-altering medications in the patient’s medication list were used in analyses. Medications included in the keyword list of anti-hypertensives were angiotensin converting enzyme inhibitors, angiotensin II receptor blocker, beta blockers, non-dihydropyridine calcium channel blockers, hydralazine, Minoxidil, central alpha antagonists, direct renin antagonists, aldosterone antagonists, alpha antagonists, and diuretics including thiazides, K-sparing, and loop diuretics. Any blood pressure measurement found after any mention of these types of medications were excluded from analyses.n = 11,301). All genotyping quality control was performed using PLINK 1.9  was calculated using 1000 Genomes Phase 3 data and an expectation-maximization algorithm adapted from Haploview .The decision was made to focus on a set of SNPs which had a 2 (p < 0.05) from the larger study sample missing education data in the EHR but varied by only 3 mmHg : ARHGAP22 rs4593967 and IQCK rs950928, respectively.To test for possible interactive effects between education and genetic variants associated with SBP and DBP, we examined three models: (1) initial single SNP tests of association without education as a covariate, (2) single SNP tests of association with education as a covariate, and (3) single SNP tests of association with SNP × education interaction terms. In the first model, single SNP tests of association were performed for SBP and DBP using linear regression adjusting for age, age squared, sex, BMI, smoking status, and percent global African ancestry. For both SBP  and DBP p < 4.32 × 10-7), and two other SNPs (rs10921895 and rs3804485) were associated at a suggestive significance threshold (p < 7.24 × 10-6). For DBP, rs950928 and rs8056711 passed Bonferroni correction. However, these SNPs have the same effect size and are in perfect linkage disequilibrium (r2 = 1.0), so they likely represent the same association.The second set of models included education in addition to other relevant covariates . The addp < 1.4 × 10-5, as described above. No interaction terms met a strict Bonferroni correction  with rs4593967 in African-descent populations from the 1000 Genomes Project. ARHGAP22 encodes the rho GTPase activating protein 22 and is widely expressed with highest expression levels in the brain. Variants within ARHGAP22 have been associated with diabetic retinopathy, conduct disorder, daytime sleep, and self-employment  compared with European-descent populations (∼0.15). IQCK rs950928 is in perfect or strong linkage disequilibrium with rs8056711 and rs59009734 in African-descent populations, neither of which has been previously associated with human disease or traits. IQCK, which overlaps with several genes including KNOP1, encodes for IQ motif containing K and serves as an EF hand protein binding site. Like ARHGAP22, IQCK is highly expressed in the brain. A search within the Genotype-Tissue Expression , there was sufficient power (80%) to detect significant associations with moderate effect size of 1.0 and a minor allele frequency of 0.20. For less common variants (MAF = 0.10), the study was powered to detect alleles with an effect size of 1.5 or greater. For variants with a MAF of 0.05, an effect size of 2.0 was needed in order to detect the variant’s effect. This study was not powered to detect any of the variants reported in the recent one million-person GWAS of blood pressure, as the variant with the largest effect size in that study was less than 1.0, with a median effect size of 0.219 mmHg . As the addition of local ancestry to the model did not alter the association, we expect that this observation is a result of true modifying effects of SES rather than ancestry. Individuals with two minor alleles and less than a high school education had higher blood pressure compared to those with two minor alleles and a high school education or those with less than a high school education and fewer minor alleles  could suggest an example of a possible biological impact of the adversity experienced due to lower educational achievement. Only individuals homozygous for the minor allele who had less than a high school education experienced an increase in DBP. This association needs to be replicated; however, it suggests a potential pathway for the biological imbedding of stress experiences  affecting blood pressure and risk for hypertension. Further studies are needed to support this hypothesis. We anticipate that this research will encourage other investigators to continue to study the genetics of health outcomes associated with racial health disparities and to incorporate social determinants of health within these studies.BH conducted the analyses and wrote manuscript. EF-E helped to extract the phenotype data from the electronic health record. MA and DC contributed to guidance on project, and manuscript writing and editing.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. The handling Editor declared a past co-authorship with one of the authors DC.


We estimated genetic parameters and conducted genomic prediction for five types of sperm morphology abnormalities in a large Duroc boar population. Results reflect that the studied traits showed moderate to low heritability and moderate to high repeatability. Both genomic best linear unbiased prediction (GBLUP) and single-step GBLUP (ssGBLUP) showed comparative predictive abilities, and ssGBLUP outperformed GBLUP under many circumstances. To our knowledge, this is the first time that the genetic parameters and genomic predictive ability of sperm morphology abnormalities were reported in such a large Duroc boar population.Artificial insemination (AI) has been used globally as a routine technology in the swine production industry. However, genetic parameters and genomic prediction accuracy of semen traits have seldom been reported. In this study, we estimated genetic parameters and conducted genomic prediction for five types of sperm morphology abnormalities in a large Duroc boar population. The estimated heritability of the studied traits ranged from 0.029 to 0.295. In the random cross-validation scenario, the predictive ability ranged from 0.212 to 0.417 for genomic best linear unbiased prediction (GBLUP) and from 0.249 to 0.565 for single-step GBLUP (ssGBLUP). In the forward prediction scenario, the predictive ability ranged from 0.069 to 0.389 for GBLUP and from 0.085 to 0.483 for ssGBLUP. In conclusion, the studied sperm morphology abnormalities showed moderate to low heritability. Both GBLUP and ssGBLUP showed comparative predictive abilities of breeding values, and ssGBLUP outperformed GBLUP under many circumstances in respect to predictive ability. To our knowledge, this is the first time that the genetic parameters and genomic predictive ability of these traits were reported in such a large Duroc boar population. H (a blend of both pedigree- and genetic-marker-derived relationship matrices) as a relatedness matrix. The ssGBLUP approach has been used in the genetic evaluation of pigs [Genomic prediction (GP) , also te of pigs ,9, dairy of pigs ,11, dair of pigs , and bee of pigs . PreviouArtificial insemination (AI) has been used globally as a routine technology in the swine production industry. The advantages of elite boars can be disseminated in larger populations rapidly through the implementation of AI. Production of high-quality semen  is essential to guarantee good AI results. Duroc boars have been used as a terminal sire breed in most commercial pig production systems. However, due to small single-boar populations and difficulties in obtaining large-scale measurements of these traits, the genetic parameters and genomic prediction accuracy of economically important semen traits have seldom been reported. Previously, it has been reported that the heritability of boar semen traits is moderate to low ,15, suggIn this study, we estimated genetic parameters and conducted genomic prediction for five types of sperm morphology abnormalities in a large Duroc boar population. Random cross-validation and forward prediction scenarios were designed to assess the predictive ability or EBV reliability of GBLUP and ssGBLUP. Furthermore, the predictive performance of ssGBLUP was compared to GBLUP.This study was carried out in accordance with the principles of the Basel Declaration and recommendations of the Institutional Animal Care and Use Committee of Foshan University. The protocol was approved by the Institutional Animal Care and Use Committee of Foshan University.The Duroc boar population used in this study was kept in the AI station of Guangxi Yangxiang Co., Ltd., Guigang, China, which is one of the largest boar AI stations in the world. The dataset consisted of 5284 pigs, which can be traced back to 12 generations in the pedigree. Fresh semen of 2693 boars collected from 2015 to 2018 was evaluated using the UltiMateTM CASA system . After ejaculation, 10 µL of fresh semen was diluted 10–30 times (based on the sensory concentration) with a special diluent and 1 µL of the diluted semen was used for evaluation. Among the phenotyped boars, 29,526 observations of morphology abnormality traits for 1304 boars were available and used in this study .PD: Proximal droplet—a droplet of cytoplasm attached to the base of the head where the midpiece emerges.DD: Distal droplet—a cytoplasmic droplet attached further down the midpiece/tail from the base of the head. If the droplet is located at more than 4 µm from the base of the head, the droplet is defined as distal. It may indicate an immature sperm and is considered a defect.BT: Bent tail—the bending rate of the tail exceeds 20°/µm.CT: Coiled tail—the tail bends 180° or more over its length.DMR: Distal midpiece reflex—the tail is wrapped around a distal cytoplasmic droplet, typically at the end of the midpiece (close to 4 µm from the end base of the sperm head), and the tail returns to the sperm head, usually becoming visible at the top of the head.The definitions of the five types of sperm morphology abnormalities are described in the CASA system as below:p-value of ≥10−5. After quality control, 1623 individuals with 36,254 SNPs remained for further analysis. Among the genotyped boars, 1231 had phenotypic data. DNA was extracted from a total of 1733 pigs (fresh semen of boars and ear tissues of sows) using genome extraction kits  and genotyped using the GGP 50k SNP array , which contains 50,703 SNPs in total. Genotypic data were filtered using Plink software [Missing genotypes were simply treated as heterozygotes since the SNPs of unknown physical position were not removed from the dataset, which made LD-based imputation difficult. Considering the low proportion of missing genotypes (0.14%) and the number of markers of unknown physical position (7144), the strategy used in this study may be preferable compared with removing position-unknown SNPs and imputing the missing genotypes.y is a vector of phenotypic records; X, Z, and W are incidence matrices associated with b, a, and p, respectively; b is a fixed-effect vector (combining the year and season of ejaculation); a~N  is a vector of the individual additive genetic values; K is the relatedness matrix ; σa2 is the additive genetic variance; p~N is a vector of random permanent environmental effects for each individual; I is the identity matrix; σp2 is the variance of permanent environmental effects; covariates Age and Intv are the age of the boar in months at the time of ejaculation and collection interval (days), respectively; e~N is a vector of residuals; and σe2 is the residual variance. The relationship matrices used in different methods are defined as follows:In this study, the single-trait repeatability model used was as follows:BLUP: The conventional BLUP [A was used as covariance.nal BLUP  model waGBLUP: In the standard GBLUP [KG = ZZ’/∑mi = 12pi(1 − pi) = , where Z is a MAF-adjusted genotype matrix , ip is the MAF of the ith SNP, and m is the total number of SNPs.rd GBLUP , the relssGBLUP: The inverse of the relatedness matrix H, using both pedigree and genetic markers [A is the pedigree-based additive genetic relationship matrix, A22 is a submatrix of A for the genotyped individuals, and Gw = 0.9G + 0.1A22, the weights were the same as our recent paper [ markers ,6, can bnt paper .https://www.vsni.co.uk/). We additionally estimated the genetic correlations among the traits using a multitrait model, where the model is similar to Model (1) except that the response variable was replaced with an n × t matrix .The variance components were estimated from the full dataset via the same model as Equation (1) using average information restricted maximum likelihood (AI-REML) . The varThe breeding value estimations described in this section were performed using the BLUPF90 software family .DRPs: In order to assess predictive ability, DRPs with the removal of the parental average (PA) for all individuals in the pedigree  were calculated as described by Garrick et al. [k et al. . A BLUP k et al. ,22.Cross-validation: We designed a 5-fold cross-validation to assess the predictive ability of GBLUP and ssGBLUP. In order to ensure comparability between GBLUP and ssGBLUP, only genotyped individuals were included in the test sets. The genotyped individuals were randomly divided into five groups, and each group was treated as a test set once. For GBLUP, the remaining four groups of genotyped individuals were used as training sets. For ssGBLUP, all individuals in the pedigree except those in the test set were used as a training set. The predictive ability was calculated as the Pearson’s correlation between the DRP and the predicted genetic values in the test set. The cross-validation  was repeated 20 times.Forward prediction: In real pig breeding programs, historical records are used to predict genetic values of newly born individuals. Therefore, a forward prediction was designed to assess the predictive ability of different models to mimic the real pig breeding situation. In this scenario, boars from the first to ninth generations were treated as a training set and used to fit the prediction model. Boars from the 10th and 11th generations were treated as a test set and used to validate the model. The estimated variance components, heritability, and repeatability are shown in In the random cross-validation scenario, ssGBLUP outperformed GBLUP for all traits in respect to predictive ability . The corIn the forward prediction scenario, ssGBLUP outperformed GBLUP in four out of five traits, with the exception of the bent tail, for which the predictive ability of ssGBLUP was similar to that of GBLUP . The corIn the pork industry, production of high-quality semen depends on different factors including appropriate nutrition, a comfortable environment, good air quality, sufficient movement, and so forth . HoweverWe estimated the genetic parameters of five types of sperm morphology abnormalities in a large Duroc boar population. The results showed that the traits were all heritable, though moderate to low heritability was observed . The hery = u + g + e), may lead to loss of information. The results of this study showed that the predictive ability of ssGBLUP was acceptable and reliable in both the random cross-validation and forward prediction scenarios and was comparable to the predictive ability obtained in a previous study on piglets born alive [The accuracy of the genetic evaluation of sperm morphology abnormalities was further investigated by integrating pedigree, genetic markers, and phenotypic records simultaneously. The ssGBLUP was implemented for the genetic evaluation of the studied sperm morphology abnormalities, with comparison to GBLUP. DRP was calculated and used to evaluate the predictive ability, but it was not used as a response variable in the prediction model. The raw phenotypic records were used as the response variables and the full model was used as the prediction model, which was based on the consideration that using DRP as the response variable, followed by a simple prediction model . However, an alternative parameter setting, such as a grid search [A simple method was used to blend the pedigree-derived relationship matrix and the marker-derived relationship matrix to construct the d search , could bd search  should ad search  and thusd search  and daird search ,30 with d search  or tightd search . In addiIn conclusion, the sperm morphology abnormality traits included in this study have low to moderate heritability. Both GBLUP and ssGBLUP showed comparative predictive abilities, and ssGBLUP outperformed GBLUP under many circumstances. To our knowledge, this is the first time that the genetic parameters and genomic predictive ability of these semen traits were reported in such a large Duroc boar population.


Genome-wide association studies (GWAS) are widely used to identify regions of the genome that harbor genetic determinants of quantitative traits. However, the multiple-testing burden from scanning tens of millions of whole-genome sequence variants reduces the power to identify associated variants, especially if sample size is limited. In addition, factors such as inaccuracy of imputation, complex linkage disequilibrium structures, and multiple closely-located causal variants may result in an identified causative mutation not being the most significant single nucleotide polymorphism in a particular genomic region. Therefore, the use of information from different sources, particularly variant annotations, was proposed to enhance the fine-mapping of causal variants. Here, we tested whether applying significance thresholds based on variant annotation categories increases the power of GWAS compared with a flat Bonferroni multiple-testing correction.Whole-genome sequence variants in dairy cattle were categorized according to type and predicted impact. Then, GWAS between markers and 17 quantitative traits were analyzed for enrichment for association of each annotation category. By using annotation categories that were determined with the variants effect predictor software and datasets indicating regions of open chromatin, “low impact” variants were found to be highly enriched. Moreover, when the variants annotated as “modifier” and not located at open chromatin regions were further classified into different types of potential regulatory elements, the high impact variants, moderate impact variants, variants located in the 3′ and 5′ untranslated regions, and variants located in potential non-coding RNA regions exhibited relatively more enrichment. In contrast, a similar study on human GWAS data reported that enrichment of association signals was highest with high impact variants. We observed an increase in power when these variant category-based significance thresholds were applied for GWAS results on stature in Nordic Holstein cattle, as more candidate genes from previous large GWAS meta-analysis for cattle stature were confirmed.Use of variant category-based genome-wide significance thresholds can marginally increase the power to detect the candidate genes in cattle. With the continued improvements in annotation of the bovine genome, we anticipate that the growing usefulness of variant category-based significance thresholds will be demonstrated.The online version of this article (10.1186/s12711-019-0463-9) contains supplementary material, which is available to authorized users. Cattle is one of the most important domestic animals in human history. Both breeding programs and genetic studies in cattle depend largely on the availability of a reliable cattle reference genome  and refeTo address this problem, additional information from independent sources are needed. For example, gene expression data have facilitated the identification of candidate genes from GWAS data , and expDue to many reasons, such as LD, inaccuracy of imputation, random sampling errors, etc., the lead single nucleotide polymorphism (SNP) may not be the causative one . Using a2 > 0.2) with the lead SNPs, as potential causal variants to estimate the enrichment of each of the annotated variants’ categories. We make the hypothesis that the category-based significance threshold will increase the power of a GWAS study. We tested this hypothesis by performing an association study on stature in cattle and comparing the results with those of a previously reported large meta-analysis in cattle stature and genes reported for human height.In this study, we implemented a previously proposed, category-based Bonferroni adjustment based on the enrichment  of variant annotations observed for association signals  that werSince, no animal experiments were performed in this study, approval from an ethics committee was not required.http://www.nordicebv.info/). For details on the genetic evaluations performed for these 17 traits/indices in Nordic countries, see http://www.nordicebv.info/production. The phenotypic values used in the association analysis included de-regressed proofs that were derived for animals based on the effective daughter contributions of sires and maternal grandsires .


SEP) leads to a loss of more than 50% of the grain number potential. In this study, we quantified 75 plant growth‐associated traits at seven stages during the SEP and mapped 15 696 single nucleotide polymorphism (SNP) markers in 210 accessions of wheat (Triticum aestivum). Our genomewide association study identified trait‐associated SNPs that are shared among various stages of the SEP, as well as SNPs that are shared between plant growth traits and grain yield in the field. The genomic selection analysis shows variation among the prediction abilities of various traits and stages. Furthermore, we found that the allelic variants of Ppd‐D1 (chromosome 2D) and Rht‐D1 (chromosome 4D) loci affect some plant growth traits (e.g. leaf area and spike length). These results have identified a narrow time window within the SEP in which plant growth traits can be manipulated to alter grain yield. This suggests that there may be multiple ways to regulate plant growth during the SEP, to ultimately influence grain number in wheat.One of the primary objectives of wheat breeding was to increase grain yield. Floral abortion during the stem elongation phase ( We further showed an overlap in the single nucleotide polymorphism (SNP)‐associated traits between plant growth traits and grain yield, suggesting a genetic association between these traits. In addition, we identified SNPs that may be applied to genetically manipulate plant growth. The results from our genomic prediction analysis indicated the ability to predict plant growth traits.Ppd‐D1 (chromosome 2D) and Rht‐D1 (chromosome 4D) loci on plant growth traits.The results presented in this study will be useful for designing strategies to increase floret fertility by selecting plant growth traits with yield‐relevant effects during the SEP. Our results are divided into four parts: (i) trends in the plant growth traits among the seven SEP stages; (ii) identification of SNP–trait‐associated markers that are shared between different stages, shared between different traits at the same stage, and shared between plant growth and grain number traits; (iii) genomic selection analysis results; and (iv) effects of allelic variants of According to the floral development and abortion process, we divided the SEP into seven stages: TS, WA, GA, YA, TP, HD and AN Table . We moniAs shown in Figures The measured traits displayed variable trends among the seven developmental stages suggesting that the different traits peaked during different SEP stages Figure . MoreoveBy dividing the SEP into seven stages according to the floral development and abortion process, we identified SNP–trait associations for plant growth traits at various stages for the first time. We also revealed differences in the SNP–trait associations among the seven stages.10(P)>4.0) among the seven stages (Table Spike growth (leaf length of the main shoot) can be used as an example: we identified shared SNP markers  The strong variation in spike length at the early stages leads to a decrease in the number of associated SNP markers; (ii) most of the detected SNP–trait associations at the late developmental stages  are related to the determination of spike length, but the most important effects on spike elongation may occur at different stages.Information on the SNP–trait associations for all the plant growth traits across the seven stages is provided in Data et al., As this experiment was conducted in glasshouse, we selected 30 genotypes from the 210 wheat accessions to measure the traits in field and glasshouse simultaneously to display the connections of data between field and glasshouse  and Rht‐D1 (chromosome 4D) loci on plant growth traits. As an example of how these allelic variants of Ppd‐D1 and Rht‐D1 loci can influence plant growth traits, we assessed their influence on leaf area and spike length of the main shoot. As shown in Table Ppd and the tall allele of Rht were significantly associated with higher leaf area. The effect of Rht alleles on leaf size may be attributed to their influence on stem and leaf growth.Ppd sensitive allele was associated with significantly longer spikes at five of the seven stages   Table . This maes Table . The effPlant growth during the SEP is important for the determination of grain number, and most of the grain number potential is lost during this phase. Therefore, this study was designed to uncover more detailed information on the seven SEP stages so that plant growth traits may be intricately manipulated to increase grain yield in wheat. Furthermore, highly plastic plant growth during the SEP provides the potential for the improvement of floret fertility in wheat. In this study, we identified SNP–trait associations that were shared among various SEP stages, and SNP–trait associations that were shared between plant growth traits and grain yield in field. The results of this study suggest that there may be several ways to increase floret fertility by manipulating specific stages during the SEP. However, it does not mean that the potential improvement of floret fertility will be easily achieved.et al., et al., et al., The general strategy for decreasing floral abortion and increasing floret fertility in wheat is to improve assimilate partitioning to the growing spikes during the SEP. Lengthening the duration of the SEP has been widely investigated as an alternative approach to increase the number of fertile florets at AN  that strongly reduced tillering  in wheat leads to a reduction in grain yield because tillers compete for assimilates with the main shoot but are aborted before reaching physiological maturity and do not contribute to the final grain yield (Borras‐Gelonch Reduced height (Rht) genes has been the most successful method for adjusting the ratio between spike and stem DWs. The Green Revolution refers to the vast increases in grain yield achieved after the 1960s, which resulted from the introduction of dwarf mutations   Data . It implTaken together, the results of our genomic selection analysis may be used in the future to manipulate plant growth traits in wheat breeding. In summary, this study provides phenotypic and genotypic information related to wheat plant growth during the seven stages of the SEP. This information may aid in the implementation of wheat breeding strategies based on the manipulation of plant growth traits during the SEP.Rht‐D1) (chromosome 4D) and photoperiod (Ppd‐D1) (chromosome 2D) loci. Seeds were sown into 96‐well trays and germinated in a glasshouse  for 14 days. At the two‐ to three‐leaf stage, seedlings were transferred to 4 °C to vernalize for 63 days. Vernalized seedlings were transferred to a hardening stage  for 7 days to gradually acclimatize. Finally, plants were transplanted into 0.5‐L pots  in the glasshouse . Supplemental light  was supplied, and plants were irrigated when required.A total of 210 European hexaploid winter wheat cultivars were selected based on allelic variants of reduced height  was found. Then, we dissected the developing spikes/spikelets every 2 days from the terminal spikelet  until anthesis  stage. When the appropriate stages were identified, three plants from each cultivar were randomly selected and their tiller number and tiller dry weight (DW) were measured. The leaf number, node number, plant height, spike length, spikelet number, leaf area, spike DW, leaf DW and main DW of plants in different developmental stages were measured from the main shoot. Tiller and leaf numbers indicate the numbers of ‘active’ green leaves and tillers.et al., et al., The measurements of the maximum number of floret primordia, grain number, floret primordium loss, grain survival within individual spikelets and grain size traits  are described elsewhere  and the dwarfing gene Rht‐D1 (chromosome 4D) in the wheat populations used in this study. Markers for Ppd‐D1 (chromosome 2D) and Rht‐D1 (chromosome 4D) were used for genotyping as described previously , a genotyping array including approximately 90 000 gene‐associated SNPs, was used to characterize genetic variation in allohexaploid and allotetraploid wheat populations. A total of 46 977 SNPs from the wheat 90k array were genetically mapped using a combination of eight mapping populations  of hypothetical ancestral populations. Then, we performed a principal component analysis (PCA) on the wheat population of 210 cultivars. The first 10 principal components were used for subsequent analysis analyses according to the ADMIXTURE results. The PCA results did not reveal any apparent population structure among the varieties  > 4) for all investigated traits, which is above or close to the threshold of most traits. A genomewide pairwise linkage disequilibrium (LD) analysis was performed for the SNP markers using GENSTAT 17. LD was estimated with squared allele frequency correlations (r2) between loci pairs. To investigate the average LD decay in each chromosome, the pattern and distribution of intrachromosomal LD were visualized with LD plots generated by GENSTAT. To determine the critical r2 with a genetic distance between loci, the smoothed second‐degree LOESS curve was fitted using GENSTAT.Only SNPs with minor allele frequencies ≥0.05 were used to carry out the GWAS. GWA mapping was conducted based on 15 696 mapped SNP markers (7934 SNP markers from the 90k Infinium chip and 7762 from the 35k Affymetrix chip) from the wheat population. We used the false discovery rate (FDR) to assess the threshold for all the traits. The genomewide significance threshold of the GWAS was determined to be et al., Y are the adjusted entry means, 1n is a vector of ones, n is the number of genotypes, μ refers to the overall mean, and ga is the additive effect. In the model, μ is a fixed effect and the rest are random effects that have normal distributions, ga∼N and e∼N, where Ga is the relationship matrices, and σa2 and σe2 are the variance of additive effects and the residuals. Details on how to calculate these relationship matrices are described by Zhao et al. (Based on the adjusted entry means, we applied a RR‐BLUP (ridge regression best linear unbiased prediction; VanRaden, o et al. . The preT.S. conceived the project. T.S. and Z.G. designed the experiments. Z.G. conducted phenotyping measurements in the glasshouse trials. G.L and Z.G. managed the main data analysis, including GWAS and genomic selection analysis, figure design and generation, and Y.Z. and J.C.R. supervised the data analysis in R. M.S.R. and M.W.G. developed and mapped the SNP markers. Z.G., T.S. and G.L. wrote the manuscript, and Y.Z., J.C.R, M.S.R. and M.W.G. were involved in reviewing the manuscript.Figure S1 Genetic population structure determined by principal component analysis with SNP markers.Click here for additional data file.Figure S2 The ranges for all the developmental traits at the seven stages during the stem elongation phase.Click here for additional data file.Data S1 The associated SNP markers of plant growth traits and grain yield in field.Click here for additional data file.Data S2 The allelic variants of Rht‐D1 and Ppd‐D1 on plant growth traits.Click here for additional data file.