Finally, principal components analysis (PCA) and a hierarchical clustering approach were used to identify IC538070 as a superior genotype with a larger seed size and weight. The identified donors/traits can potentially be used in soybean improvement programsAmong seed attributes, weight is one of the main factors determining the soybean harvest index. Recently, the focus of soybean breeding has shifted to improving seed size and weight for crop optimization in terms of seed and oil yield. With recent technological advancements, there is an increasing application of imaging sensors that provide simple, real-time, non-destructive, and inexpensive image data for rapid image-based prediction of seed traits in plant breeding programs. The present work is related to digital image analysis of seed traits for the prediction of hundred-seed weight (HSW) in soybean. The image-based seed architectural traits (i-traits) measured were area size (AS), perimeter length (PL), length (L), width (W), length-to-width ratio (LWR), intersection of length and width (IS), seed circularity (CS), and distance between IS and CG (DS). The phenotypic investigation revealed significant genetic variability among 164 soybean genotypes for both i-traits and manually measured seed weight. Seven popular machine learning (ML) algorithms, namely Simple Linear Regression (SLR), Multiple Linear Regression (MLR), Random Forest (RF), Support Vector Regression (SVR), LASSO Regression (LR), Ridge Regression (RR), and Elastic Net Regression (EN), were used to create models that can predict the weight of soybean seeds based on the image-based novel features derived from the Red-Green-Blue (RGB)/visual image. Among the models, random forest and multiple linear regression models that use multiple explanatory variables related to seed size traits  were identified as the best models for predicting seed weight with the highest prediction accuracy (coefficient of determination, R Glycine max (L.) Merr.) is an important oilseed and food crop consumed worldwide. The seeds are protein-rich (40%), thereby making them a key crop for global food and nutrition security  of morpho-physiological traits along with genotyping data are considered essential inputs. Current phenotyping strategies in plant breeding have been revolutionized by advances in high-throughput phenotyping platforms that encompass imaging sensors and perform automated image acquisition, processing, and techniques for effective big data analysis, especially for the identification of superior donor genotypes and crop improvement . Image-bchickpea .Phaseolus sp. have used image analysis for varietal characterization. Maize tassels have been phenotyped using a tassel image-based phenotyping system for early yield prediction , are required for the breeding of improved crop varieties with higher productivity. However, most of these phenotyping traits are measured visually through manual counting or low-throughput weighing scales. Traditionally, HSW is phenotyped by counting 100 seeds and measuring the fresh weight of a hundred seeds using a weighing scale. Moreover, recording the HSW of a large set of diverse crop germplasm is laborious, costly, and time-consuming, with the risk of manual errors. Recently, image-based phenotyping methodologies [image-based phenotyping in papaya , high-thediction . HoweverImaging and machine learning (ML) models are gaining popularity and importance for the prediction of genotypes to phenotypes that include yield, days to heading, and thousand-seed weight . Models Seed plays an important role in the life cycle of plants. Breeding new high-yielding soybean cultivars requires genetic variation in seed traits among different soybean cultivars/varieties to select superior genotypes . However, information on seed morphological traits is poorly understood due to difficulties in data collection and visualization. Moreover, a major research gap is found in the identification of novel seed architectural traits (SAT) associated with the seed mass/weight trait and its genetic variation present in the large population of different soybean genotypes. Nothing has been found on the breeding value of these i-traits for their use in crop improvement. We need to decipher the dynamic relationship of these image-based SAT (i-traits) with seed weight through variance and co-variance analysis. To the best of our knowledge, this is the first study to report on image-based SAT data to identify superior donors for improving seed weight traits in soybean. The present study focuses on the development of an image-based methodology to predict the hundred-seed weight of soybean genotypes and discover superior donor genotypes with contrasting seed sizes and/or weight traits. This image-based methodology can potentially be applied to other major field crops to breed better varieties with improved traits to increase productivity.Seed architectural traits were measured from 164 different soybean accessions  was measured using a precision weighing balance  with up to three decimal places.http://www.kazusa.or.jp/phenotyping/smartgrain/index.html) for image processing and analysis (SmartGrain (version 1.2), an open-source image analysis software, was downloaded , and circularity  length of the object). DS is the distance between IS and CG and represents the shape of the seed.The SmartGrain software constructs ellipses on detected grains to identify the total number of grains/seeds and also computes eight different seed architectural traits related to seed size and shape, which include umber of seeds (NS), area size (AS), perimeter length (PL), length (L), width (W), circularity (CS), length-width ratio (LWR), intersection of length and width (IS), center of gravity (CG), and distance between IS and CG (DS) Figure 1th and 25th quartiles) were considered outliers and imputed with the mean of other replications. Outliers and missing values in the data can influence prediction accuracy. Hence, data obtained from an image-based assessment of selected accessions were first subjected to missing value and outlier detection and imputation using the RStudio program (V: 2022.02.3). A multivariate approach was used to detect outliers, where box plots were generated for the continuous variable and observations outside 1.5 times the interquartile range , which used variable averaging and standard deviation as factors to normalize all variables close to zero and in the range from -3 to +3. The z-score feature scaling method was selected as it takes into account both the mean value and the variability in a set of raw scores.The dataset contained variables with different units from pixel to weight in mg, area in cmPsych library , calculation of Tukey’s HSD, broad sense heritability and components of variance , coefficient of variance and its components of variance  using the variability package  in Rstud library  was loadThe multiple independent variables and their relationships with each other greatly influence the prediction accuracy of dependable variables. Hence, trait suitability analysis was performed by estimating the variance inflation factor (VIF) using the library car and the VIF command in Rstudio. The VIF is a measure of the amount of multicollinearity in a set of multiple regression variables. A VIF value greater than 10 was considered to have very high multicollinearity and was removed or reconsidered from further analysis.FactoMineR library  was used, which is an unsupervised method of feature selection that does not use information about the feature value and target value. The PCA also used normalized data, which requires some kind of transformation before analysis. Hence, we used an additional method called the Boruta algorithm, which used wrapper methodology for the accurate identification of superior image features for seed weight prediction. The PCA was performed in RStudio using the  library , and theTo predict soybean weight based on the extracted feature variables, seven regression models were explored in this study: simple linear regression (SLR), multiple linear regression (MLR), random forest (RF), support vector regression (SVR), lasso regression (LR), ridge regression (RR), and elastic net (EN). The caret , mlbench2), root mean square error (RMSE), and mean absolute error (MAE) were used as evaluation metrics to quantify the performance of the regression models and to determine how well the model predicts new data and whether the model is too complicated. The cor function was used to estimate Pearson’s correlation coefficient between the predicted SW value and the actual SW value in the testing dataset. The lm function was used to measure the coefficient of determination (R2) between the predicted and actual SW values in the testing data set. The root mean square error (RMSE) was calculated from the square root of the mean estimated from the difference between actual and predicted SW in the training dataset. The mean absolute error (MAE) was calculated from the mean absolute difference between the predicted and actual SW of the training dataset. The ggplot2 package was used to plot the regression model graphs of the predicted and actual datasets.The predict function was used to forecast the SW value of the testing dataset based on a model developed on the training dataset. The coefficient of determination  estimated from 100 individual seeds of each of the 164 soybean genotypes. We removed NS from further analysis because it was 100 and common to all of the 164 different genotypes. The data preprocessing efforts identified approximately 763 data points that were either missing or found to be outliers, hence statistically imputed to have a complete data matrix array of 1,15,500 data points for further analysis. Finally, the SAT data collected from 100 seeds of each genotype were pooled, and the mean values were analyzed along with the hundred-seed weight. A very low coefficient of variation (<5%) was found for all SAT collected from 100 individual seeds of each genotype (P ≤ 0.001). The presence of genetic variability for seed traits such as seed length, width, and weight has been reported using conventional phenotyping methods. Imaging technology has advantages over conventional phenotyping as it records more trait resolution  per unit of data recording time. The ANOVA results showed statistically significant genotypic variation in selected different soybean genotypes for seed architectural traits and hundred-seed weight  showed a strong and significant positive Pearson correlation coefficient (P<0.001) with SW Figure 2Trait suitability analysis was performed using variance inflation factor (VIF) analysis. It was used to measure the degree of multicollinearity among the independent variables in multiple regression models. In general, multicollinearity does not reduce the predictive power of multiple regression models, but it does reduce the statistical significance of independent variables. A large VIF (>10) of an independent variable indicates a highly collinear relationship among the independent variables  algorithm. Seven features recorded by imaging were subjected to Boruta analysis in all features that recorded values for mean, median, and maximum importance and also remained beyond shadowMax , Pearson’s correlation coefficient (r), statistical significance , root mean square error (RMSE), and mean absolute error (MAE) were estimated between the predicted SW (pSW) and the actual seed weight . In both the training dataset (TrD) and the testing dataset (TsD), the results showed a high positive correlation (>0.80) between aSW and pSW using AS, PL, L, and W with a high statistical significance (p>0.001) (2 = 0.89) in both TrD and TsD (2<0.1). Therefore, it was not found to be suitable for the prediction of SW. Next to AS, PL was identified as the next best predictor, with an accuracy of R2 = 0.82 in TrD and R2 = 0.80 in TsD. Among these two predictor traits, AS was the best choice owing to the lowest RMSE  and MAE  values in both TrD and TsD. Moreover, SW prediction using AS was observed to be more accurate as the RMSE (0.27) and MAE (0.22) values of TsD were significantly lower than TrD . Simple linear regression models were performed with each of the selected independent variables  separately on the dependent variable (SW), and the results are presented in 2 = 0.98) in TrD and the lowest RMSE (0.13) and MAE (0.09). Next to RF, the MLRM model was found to be the best model with a high R2 (0.94), low RMSE (0.23), and MAE (0.18). MLRM was found to be the best predictive model for TsD with R2 (0.94), RMSE (0.20), and MAE (0.15). In TsD, RF was the next best predictor with an accuracy of R2 (0.92), RMSE (0.22), and MAE (0.16). The model equations of Lasso, KNN, and EN recorded relatively low predictive accuracy (R2 < 0.1), high RMSE, and MAE values (>0.15), and were therefore found to be unsuitable for predicting SW. Among the predictor models, RF and MLRM stood out as the best choices owing to the highest prediction accuracy, and correlation with the lowest RMSE and MAE values in both TrD and TsD  on the dependent variable (SW), and the results are presented in  and TsD 5.Morphology is an important and effective attribute and a useful feature to discriminate objects that vary with mass in image-based crop phenotyping . Several2 > 0.95), either because of the smaller sample size or because of the application of powerful machine learning models to predict seed size and weight.Recently, Recently, 2 value, even with a smaller number of seeds. The mass of the seed is determined by its dry matter and moisture content. With the recent advent of RGB and NIR sensors, multi-modal regression algorithms can be developed to predict seed moisture content using the NIR signal and the weight component using the RGB image-derived AS feature. Several smartphone-based Android mobile applications (seed counter and seed counting) are available to estimate various seed architectural traits. This holds promise for the future development of an agronomically user-friendly mobile application that accurately predicts seed weight using SAT. Thus, the enormous labor, time, cost, and space involved in conventional phenotyping can be minimized to hasten the breeding cycle. In this experiment, we demonstrated the image-based methodology to predict the breeder’s best traits of interest (hundred-seed weight) for improving the productivity of soybean genotypes using image-based architectural traits. The contrast donor genotypes were effectively used for bi-parental crossing and mapping of QTLs associated with seed size and weight traits. This methodology can be easily deployed in other major cereal and pulse crops to breed better genotypes with higher productivity.Hundred-seed weight is a very important trait that physiologists and breeders measure to record and maintain the pedigree and yield performance of the genotype. Conventionally, automatic seed counters that work on the principle of vibrator and phototransistor sensors are widely used in the seed industry and by scientific organizations for seed counting. Traditionally, 100 seeds were counted either manually or by machine and then weighed manually using a scale to measure HSW. Recently, a company called Elmor combined a grain counting and weighing machine for the determination of the thousand kernel weight. Through the use of this modern machine, there has been a significant reduction in manual labor efforts. However, the time required for counting and weighing remains a major bottleneck in traditional phenotyping methodologies. It is advantageous to have image-based HSW estimation tools for the automatic measurement of HSW and simultaneous measurement of seed weight using seed architectural traits, such as color traits, of each seed. There is a crucial need to enhance the productivity of soybean plants by breeding for uniform, larger seed sizes per plant. This will result in higher yields and facilitate mechanical harvesting. Moreover, the image-based technology has the added advantage of mapping quantitative trait loci (QTL)’s/genes from seed architectural traits estimated using multiple numbers of seeds harvested from a large number of genotypes. Researchers spend much of their productive time counting and weighing the seeds from a large number of different genotypes. Hence, there is a need for faster, automated image-based phenotyping tools for estimating HSW. Generally, seed weight prediction using imaging techniques uses white light-illuminated platforms, and the major bottleneck associated with causing an error is related to the underestimation of closely located overlapping seeds. Placing seeds in a non-overlapping pattern on the scanning platform took more time in our case. In such cases, tools that automatically place seeds through vacuum tube techniques, predict hundred-seed weight based on a lower number of randomly placed seeds, or use accurate image processing techniques that take care of the overlapping seed count or the sequential imaging of seeds using push broom conveyor systems are the basic engineering needs to be met for the invention of automatic HSW machines. multcomView function in RStudio. The data on seed size and weight diversity clearly showed that the panel used in this study were mostly indigenous germplasm seeds, and, as reported earlier, the exotic lines (Chinese and Korean) soybean seeds were found to possess larger seed size and weight , DS 9712 (8.81g), JS 93-06 (8.61g), PK564 (8.59g), JS9423 (8.52g) and UPSL-332 (8.54g). In contrast, HSW was lowest in BJJF-8 (4.9g), UPSL-365B (5.24g), M-53 (5.29g), L-768 (5.29g), UPSL-736 (5.33g), UPSL-326 (5.233g) and L-780 (5.38g). The superior i-traits (AS) closely associated with SW were found to be highest in soybean genotypes like JS 20-33 (23.65), JS9423 (22.91), DS9712 (22.56), UPSL-332 (22.41), JS 93-06 (22.23) and PK564 (22.17). Genotypes like BJJF-8 (13.67), L-768 (13.92), L-780 (14.15), UPSL-326 (14.15), UPSL-736 (14.24), and M-53 (14.37) were found to have the lowest SA. These genotypes were also identified to follow a similar trend in the case of size and shape-related traits   were performed using the mean and maximum distance between elements of each cluster Table 3 2 value with lower bias and error values was obtained with a multivariate regression model in the testing data set. The donor soybean genotype identified with superior seed size, shape, and weight traits can be utilized for soybean crop improvement programs. The same methodology can be used to breed better crop varieties for higher productivity in other plants.An image processing technique was used to estimate the seed architectural traits and hundred-seed weight of 164 different soybean accessions using a flatbed scanner. The image processing software, SmartGrain, was used to obtain their size, shape, and other seed weight-related features. Precision phenotyping guides breeders in the use of genotyping data for crop improvement. Therefore, breeders require defined information from a large set of accessions or germplasm collections for trait improvement. At present, phenotyping is aided by imaging and machine learning techniques in crop plants, as these can screen more accessions in less time and space for our trait of interest. In the current study, image processing technology was used to extract morphological traits such as surface area, length, width, and perimeter from seeds of soybean accessions to predict the final hundred-seed weight. The strength of the correlation between traits revealed that surface area, perimeter length, seed length, and width were good predictors of hundred-seed weight. Machine learning models were successfully implemented to estimate hundred-seed weight based on superior image-based architectural traits. The highest RThe original contributions presented in the study are included in the article/ND and DR conceived this study. ND and AyR performed the experiment with assistance from DR and AmR. ND and DR implemented the code. DR and AmR worked on data visualization. ND and AyR participated in the analysis with the help of DR and AmR. AyR, AmR, and DR writing—original draft preparation. DR, AmR, SL, RS, and VC writing—review and editing. SL and DR - project administration. VC and RS - supervision. All authors contributed to the article and approved the submitted version.


Heritability Estimation with high Efficiency using LD and association Summary Statistics (HEELS)—that significantly improves the statistical efficiency of summary-statistics-based heritability estimator and attains comparable statistical efficiency as REML . Moreover, we propose representing the empirical LD matrix as the sum of a low-rank matrix and a banded matrix. We show that this way of modeling the LD can not only reduce the storage and memory cost, but also improve the computational efficiency of heritability estimation. We demonstrate the statistical efficiency of HEELS and the advantages of our proposed LD approximation strategies both in simulations and through empirical analyses of the UK Biobank data.Existing SNP-heritability estimators that leverage summary statistics from genome-wide association studies (GWAS) are much less efficient  than the restricted maximum likelihood (REML) estimators which require access to individual-level data. We introduce a new method for local heritability estimation— The authors propose “HEELS”, a new method for precise local heritability estimation. It significantly reduces the variances of summary-statistics-based heritability estimators, offering an REML-like estimator without requiring individual-level data. These methods estimate the so-called SNP-heritability 12.In the last decade, advances in biotechnology have enabled the estimation of genetic variance contributed by genotyped variants without requiring assumptions about the shared environmental effects13. For instance, studies have shown that the variance of the 15. Other methods, such as Generalized Random Effects (GRE) and Randomized HE-regression (RHE-reg) are also less precise than REML based on simulation results11. To address the limitations of existing methods, we introduce Heritability Estimation with high Efficiency using LD and association Summary Statistics (HEELS)—an accurate and statistically efficient estimator of Estimators that use individual-level data are generally more precise , but the applicability of these methods is limited due to data-sharing restrictions. On the other hand, 17. The variant-level statistics required by HEELS includes the marginal association statistics from GWAS and the correlation statistics estimated in-sample . We show both analytically and through extensive simulations that the HEELS estimator attains a comparable level of statistical efficiency or precision as the conventional individual-level-data-based REML estimators, such as GREML1 and BOLT-REML2. The relative efficiency of HEELS is significantly higher than that of the state-of-the-art summary-statistics-based methods, i.e., the estimates from HEELS have much smaller variances.Our work has two main contributions to the literature of 18, but doing so is difficult due to the high dimensionality of LD. Although efforts to release large LD matrices are underway19, better approximation strategies are needed to facilitate efficient sharing of the LD matrix and to improve the computational efficiency of analyses that involve LD. In this work, we show that our proposed “Banded + LR" structure can ameliorate the challenges associated with LD in heritability estimation. We use an optimization approach to solve for the best representation of LD and we evaluate the performance of different low-dimensional approximations in the context of Second, we introduce a low-dimensional representation of the LD as the sum of a banded and a low-rank matrix ("Banded + LR"). This structure is motivated by the fact that releasing the empirical LD is beneficial for many downstream analyses that utilize variant-level statisticsWe applied HEELS to estimate the local SNP-heritability of a wide range of complex traits and diseases in the UK Biobank (UKB). Consistent with our simulation results, the estimates from HEELS are highly concordant with the estimates from REML. We used the more precisely estimated local In summary, we focused on improving the statistical efficiency of the heritability estimator using variant-level summary statistics. We chose LMM as the simplest and most widely understood model to demonstrate the merits of our approach in terms of statistical efficiency gain both conceptually and empirically. We hope our work can encourage future development of methods that produce more precise heritability estimates.17. Because the score equations solved by HEELS are identical to those solved by GREML1, HEELS yields heritability estimates that are as precise as those based on REML-based estimates which typically require individual-level data. We first introduce some notations and define In a nutshell, HEELS uses variant-level statistics, including marginal association statistics and the LD matrix, to estimate SNP-heritability by iteratively solving the REML score equationy be a length-n vector that denotes the phenotypes of n samples. Denote by n individuals based on p markers or SNPs. We standardize X and y such that the variance of the phenotypes is 1 and the variance of each marker-specific genotype vector is 1/p, or diag(X⊤X/n) = 1/p. We use an additive genetic model for the phenotypes as y = Xβ + ϵ, where β is a p × 1 vector assumed to follow ϵ is a length-n vector distributed as y ~ N, where the variance-covariance matrix is Let X and y, and are only provided with the marginal association statistics, S = X⊤y and the LD matrix R = X⊤X.  We show that the REML score equations for S and R only, by applying the Sherman-Woodbury matrix identity to the Anderson’s algorithm for solving the variance components (t) of a heritability estimator as the ratio of the variance of the GREML estimator and the variance of the estimator in comparisonWe first simulated quantitative phenotypes using the LMM model, where the causal effect sizes of all genetic markers follow a normal distribution and contribute to the genetic variance equally. We found that HEELS is unbiased in finite samples and attains high statistical efficiency. In particular, we found a high degree of concordance between the estimates from REML-based estimators (such as GREML and BOLT-REML) which use individual-level data and those from HEELS which only relies on variant-level summary statistics Fig. . When th27. We provide a stylized argument to contrast the statistical efficiency of LDSC and HEELS under the framework of moment-matching methods14 . When the true effect size does not follow a normal distribution, we observe under-coverage for all LMM-based estimators. Nevertheless, the calibration of HEELS is still better than GRE and LDSC, and is most comparable to REML across settings , the impact of LD approximations on heritability estimation remains unclear. We aim to construct a low-dimensional representation of the LD matrix that can help reduce the computational cost of HEELS heritability estimation without incurring much loss of accuracy or efficiency in the R, as the sum of a banded matrix and a low-rank matrix ("Banded + LR"),Rb is a banded matrix with a central bandwidth of b; Rr is a low-rank matrix with rank r; λk and uk  are the k-th eigenvalues and eigenvectors of Rr. We consider six different strategies to decompose or represent the empirical LD using this “Banded + LR" structure  whether the banded and low-rank components are constrained to be positive semi-definite (PSD).It is a well-known challenge in statistical genetics that the LD matrix is expensive to store and compute with. While several low-dimensional representations of the LD have been proposed and used in the literature  is twofold. On one hand, since correlations between two genetic markers are typically induced by physical proximity, the vast majority of the non-zero elements of LD matrix lie on the central band. On the other hand, we want to retain the in-sample correlation structure outside of the central band. We found that oftentimes there are appreciable non-zero off-central-band elements in finite samples, and methods such as HEELS utilizes these values to produce accurate estimates.The “Banded + LR” approximation provides a unified framework for analyzing and evaluating the performance of various LD approximations, because most of the existing LD approximation strategies can be viewed as special cases of Eq. . For insTo solve for the best representation of the LD matrix, we adopt an optimization approach, minimizing entclass1pt{minimaentclass1pt{minimaIn simulations, we found that our proposed “Banded + LR" representations approximated the original full LD well and led to more accurate entclass1pt{minimab = 400 and r = 800), the bias in the heritability estimates is even smaller than that when the full LD is used (relative bias of 0.22% vs 1.12%), while runtime and storage decrease by 68.92% and 74.16% respectively. Overall, we determined that our proposed “Banded + LR" representations can improve the computational efficiency of HEELS across hyperparameter settings without incurring large loss of accuracy and efficiency.Relative to using the full LD matrix ("Exact_LD"), approximating the LD using a “Banded + LR" structure markedly improves the computational efficiency of HEELS, reducing the runtime by 29.40%, 73.02% and 73.26% for “Seq_Band_LR", “PSD_Band_LR" and “Joint_Band_LR", respectively Table . The stob and r  and leads to the smallest accuracy and efficiency loss, though it tends to produce slightly upwardly biased In comparing the performance of the three “Banded + LR" strategies, we found that they have varying degrees of sensitivity with respect to changes in the hyperparameter values mentclasspt{minimab and r using cross-validation (“CV”). We refer to this procedure as “pseudo-validation”, as it does not require actual held-out samples but only relies on simulated summary statistics (Methods). We validated the effectiveness of this procedure, by verifying that the optimal hyperparameter values obtained from this algorithm indeed yield accurate 36, and adopted several computational techniques to speed up the approximation and the tuning procedure , which is the gold standard or the most efficient estimator but requires individual-level data .We applied HEELS to estimate the local SNP-heritability of 30 anthropometric, medical and behavioral traits in the UK Biobank (Methods), using the LD blocks estimated by Berisa and Pickrellh2 estimates that are concordant with those which are based on the full LD , WHR (r2 = 0.919), educational attainment (r2 = 0.991) and neuroticism (r2 = 0.990). In contrast, the correlations are much lower for less polygenic traits, such as HDL (r2 = 0.295), LDL (r2 = 0.537) and autoimmune diseases (r2 = 0.757)  with the severity of COVID-19, as the PLR of patients can indicate the degree of cytokine storm56 and one meta-analysis57. One plausible explanation for the pleiotropic effects of this region is that it hosts the Hedgehog (Hh)-interacting protein (HHIP) gene, which is associated with multiple pulmonery traits, such as FEV1/FVC ratio, chronic obstructive pulmonary disease (COPD) and lung cancer61. As a regulator of the Hh signaling pathway, HHIP is vital for embryonic lung development and is also involved in mature airway epithelial repair62. We hypothesize that the observed pleiotropic effects at this locus may be attributable to the HHIP gene and its broad influence on lung functionality64.Another region of particular interest is Chr4:143–146 Mb, which is highly enriched for all three of the lung function traits in our analysis 68. Future research is needed to develop heritability estimators that are more efficient than REML under a sparse genetic architecture. Another direction is to adopt a more flexible heritability model, where SNP-specific contributions to the genetic variance varies depending on the allele frequency and the level of LD. This alternative scheme was put forward by authors of the LDAK9 model and have been examined carefully in their subsequent works. In simulations, we observed that indeed, HEELS can be biased under mis-specified models, and that the amount of bias varies with the strength of MAF/LD dependency , facilitate privacy-preserving benchmarking efforts73, and alleviate problems related to mismatched ancestry when using external reference panels for meta-analyses74.Second, we emphasize that HEELS depends on the in-sample LD. This requirement is related to the fact that we define heritability in the LMM conditional on the genotypes local heritabilities. Applying HEELS to a larger set of markers  can be difficult for two main reasons. First, the computational cost of running HEELS scales with the number of markers (rather than the sample size), so the estimation will require additional computational resources when applied to larger regions on the genome. Second, we determined in simulations that aggregating local heritability estimates can lead to biased global heritability estimates, a phenomenon that has been observed previously10, and may be attributable to LD leakage, i.e., non-zero correlations between SNPs on different blocks34. It is of future research interest to develop scalable algorithms to optimally approximate the LD for larger regions on the genome using our proposed Banded + LR representations. This advance will make HEELS applicable to estimate the total genetic variance of hundreds of thousands of markers.Lastly, we note that the HEELS estimator is best suited for studying and contrasting y be a length-n vector that denotes the phenotypes of n samples. Denote by n individuals based on p markers or SNPs. We standardize X and y such that the variance of the phenotype is 1 and the variance of each marker-specific genotype vector is 1/p, or diag(X⊤X/n) = 1/p. Let S and R denote the the marginal association statistics and the in-sample LD matrix, i.e., S = X⊤y and R = X⊤X.  Our goal is to develop a heritability estimator using the two statistics , which attains comparable statistical efficiency as the REML estimator based on individual-level data . We start by considering the likelihood function, assuming individual-level data can be accessed.Let y = Xβ + ϵ, where β is a p × 1 vector assumed to follow ϵ is a length-n vector distributed as y ~ N, where We use the standard genetic association model with additive effects, 22, known as the mixed model equations (MME), which maximize the joint density of the outcomes and the random effects,21 We exploit the “dual" form of this algorithm, which gives rise to the HEELS estimator. For simplicity, we have assumed that all of the observable environmental factors have been projected out, but the covariates (i.e. fixed effects) can be easily incorporated back into the model by adopting the restricted maximum likelihood approach using the projection matrix76.Henderson developed a set of equationsS = X⊤y and the empirical LD matrix R = X⊤X to solve for the variance component estimates that maximize the likelihood in Eq. . In practice, when only the Z-statistics are available, we scale the estimates of y⊤y/n by 1. We conducted extensive simulations to validate that the HEELS estimator remains unbiased when such an approximation is applied, although the efficiency of the estimator can be slightly affected. We note that the HEELS procedure can be viewed as equivalent to an EM algorithm , or via joint optimization which solves for the diagonal and the low-rank matrices simultaneously. In the latter case, we allow elements of the diagonal matrix to be either identical ("Spike_PSD") or different ("Spike_PSD_hetero").Below we briefly explain the differences between the low-dimensional representation strategies listed in Table The “Seq_Band_LR" strategy first bands the LD matrix and then performs low-rank decomposition on the residual off-banded matrix. It does not make any PSD assumption on the constituents of its solution. The main advantage of this strategy is that it most accurately represents the banded structure of the LD matrix, i.e., the banded component matches exactly the central band of the original LD matrix. A drawback of this approach is its lack of flexibility in approximating the off-central-band structure.In contrast, the “Joint_Band_LR" strategy jointly approximates the banded and low-rank components using PSD matrices. It provides greater flexibility of approximation for all elements indiscriminately, as the elements of the banded matrix and the low-rank matrix are jointly optimized to minimize the Frobenius norm of the error matrix. A benefit of “Joint_Band_LR" over “Seq_Band_LR" is that due to its explicit minimization of the approximation error, its solution is, by definition, closer to the original LD matrix. A potential shortcoming of the “Joint_Band_LR" strategy, however, is that by imposing a PSD assumption on both the banded and the low-rank components of the LD representation, we constrain the solution to a PSD matrix and it is more computationally intensive to solve.To strike a balance between accurately representing the central band of the LD matrix and ensuring the computational efficiency of our algorithm, we developed a hybrid strategy, “PSD_Band_LR", which first approximates the banded component of the LD matrix using a PSD matrix followed by a low-rank decomposition of the residual matrix. On one hand, it differs from “Seq_Band_LR" in that the banded component of the approximation is guaranteed to be PSD. On the other hand, “PSD_Band_LR" differs from “Joint_Band _LR" in that it sequentially solves for the banded and the low-rank constituents of the representation, as opposed to simultaneously. As a result, “PSD_Band_LR" preserves the original structure of the LD matrix better than “Joint_Band_LR" does, leading to a more accurate representation of the central band. Finally, compared to “Seq_Band_LR", “PSD_Band_LR" produces LD approximations that allow for more stable HEELS estimation .b and the rank of the low rank component r. We considered two measures to evaluate its performance: (1) the LD approximation accuracy, measured by the ratio of the Frobenius-norms between the approximation matrix and the target matrix, We introduce a unified framework for contrasting the different LD approximation approaches in the context of heritability estimation. For a given LD representation—characterized by its structure ("Strategy") and the values of its hyper-parameters: the band size b and r, the performance of the HEELS estimator can be greatly influenced by the assumed structure of the approximation strategy and the hyperparameter values. For example, for each of the “Banded + LR" strategies, we identified an approximate range of an underlying transition point (bmin) that marks the minimum optimal value of b, i.e., widening the bandwidth up to this value can substantially reduce the bias in b beyond this threshold value has a diminishing “de-biasing" effect on For low-dimensional representations with smaller b and r are sufficiently large, but can produce estimates with large bias if b and r are not appropriately chosen; approximating the LD matrix by simultaneously solving for the banded and low-rank components ("Joint_Band_LR") leads to less-biased estimates even when b and r are sub-optimal, although solving for the approximation is more computationally expensive than “Seq_Band_LR"; the hybrid strategy which approximates the banded component using a PSD matrix first and finds the low-rank decomposition of the residual ("PSD_Band_LR") is least sensitive to changes in hyperparameter values and produces heritability estimates that are most stable across LD approximation settings.Comparing across the three “Banded + LR" strategies, we we found that banding the full LD first and then approximating the residual using a low-rank matrix ("Seq_Band_LR") yields the most unbiased heritability estimates when b, r), we used a more principled way to evaluate the performance of low-dimensional LD representations. We propose using a data-adaptive procedure to identify the best low-dimensional representation of the LD matrix, using simulated phenotypic data and cross-validation , where we solve Rresid is the residual off-banded component to be decomposed or approximated, and Rresid via SVD81. The simulation results indicate that using the optimization approach leads to better approximation of the LD and less variable An important aspect of our LD approximation algorithm is hyperparameter tuning. While heuristics or prior knowledge about the structure of the LD may be used to determine the optimal values of  <0.01. For experiments that involve subsets of the UKB individuals, we recalculated MAF and re-applied the filters above to the subsample. The environmental effects are drawn independently from the genetic effects for each individual. This ensures that population structure or cryptic relatedness among individuals have minimal impact on our estimates in the simulations.n), the ratio of n to the number of markers (p) and the degree of polygenicity . Given the raw genotype matrix G, we first standardized the genotype matrix: for each SNP j and individual i, we generated Gij ∈ {0, 1, 2} and fj is the in-sample MAF of SNP j. For a given degree of polygenicity, we randomly sampled pcausal markers. Denote the set of causal markers by C. We drew standardized effect sizes from the distribution, i-th individual using yi = ∑j∈CXijβj + ϵi, where X = , we computed the marginal association statistics using OLS: We simulated phenotypes with different genetic architectures using real genotypes from the UK Biobank, varying sample size . We estimated the local SNP-heritability of 30 phenotypes from different trait domains, including anthropometric traits , hematological traits , lipid or metabolic traits , lung function traits , behavioral traits  and immunologically relevant traits .We applied HEELS to analyze the local heritability of various traits using the variant-level statistics from association studies of unrelated white British individuals in the UK Biobank, using common variants with MAF >1% on the UK Biobank Axiom array  and the GRE estimates , after verifying that the estimates from the two methods indeed coincide when the number of eigenvectors used in TSVD equals to the rank of the genotype matrix. We used the 1,703 approximately independent loci estimated by Berisa and Pickrell37 to define the regions as units of analysis (1.6 Mb on average or 300-400 markers per block using the genotype array data), since these non-overlapping LD blocks been been widely used in previous studies40 and have been demonstrated to capture the true correlation structures among genotypes reasonably well83.We used PLINK to exclude SNPs with MAF <1%, genotype missingness >1%, genotyping rates <90%, and Hardy-Weinberg disequilibrium https://yanglab.westlake.edu.cn/software/gcta/#Download); LD Score regression (https://github.com/bulik/ldsc); GRE (https://github.com/bogdanlab/h2-GRE); HESS (https://github.com/huwenboshi/hess); BOLT-REML v2.3.4 . We also used Python (3.6.3) to perform statistical analyses and used R (3.6.3) for data visualization.The following software packages were used in simulation studies and real data analyses: GCTA (Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


Chronic kidney disease (CKD) is a complex disorder that causes a gradual loss of kidney function, affecting approximately 9.1% of the world’s population. Here, we use a soft-clustering algorithm to deconstruct its genetic heterogeneity. First, we selected 322 CKD-associated independent genetic variants from published genome-wide association studies (GWAS) and added association results for 229 traits from the GWAS catalog. We then applied nonnegative matrix factorization (NMF) to discover overlapping clusters of related traits and variants. We computed cluster-specific polygenic scores and validated each cluster with a phenome-wide association study (PheWAS) on the BioMe biobank . NMF identified nine clusters that reflect different aspects of CKD, with the top-weighted traits signifying areas such as kidney function, type 2 diabetes (T2D), and body weight. For most clusters, the top-weighted traits were confirmed in the PheWAS analysis. Results were found to be more significant in the cross-ancestry analysis, although significant ancestry-specific associations were also identified. While all alleles were associated with a decreased kidney function, associations with CKD-related diseases  were found only for a smaller subset of variants and differed across genetic ancestry groups. Our findings leverage genetics to gain insights into the underlying biology of CKD and investigate population-specific associations. CKD affects approximately 9.1% of the global population, with a higher prevalence in high-income countries. The leading risk factors for developing CKD are diabetes (40% of cases) and hypertension (29% of cases), followed by heart disease, family history of CKD, and obesity. Other factors, such as exposure to HIV and contaminants, are additionally important in low-income countries, 5. The genetic ancestry also plays a crucial role, with increased risk rates of kidney failure in Black/African Americans and Hispanics/Latinos compared to individuals of European ancestry. If left untreated, CKD increases the mortality risk for individuals with cardiovascular disease (CVD) and can result in the complete loss of kidney function. Therefore, early detection is critical for improving quality of life and life expectancy. During the early stages of CKD, cost-effective treatment options are available and can be tailored to the cause of the disease.Chronic kidney disease (CKD) is a primarily asymptomatic disease characterized by a gradual loss of kidney function over a period extending from several months to years. The main biomarkers for CKD detection include the urinary albumin/creatinine ratio (ACR) and the estimated glomerular filtration rate (eGFR) . While ACR facilitated diagnosing albuminuria – an indicator of kidney damage characterized by an elevated excretion of urinary albumin – the eGFR estimates the filter volume of the glomerulus per unit of time using different biomarkers such as serum creatinine. An abnormal kidney activity is indicated by high ACR values, reduced eGFR, or both.CKD is defined by a reduced functionality of the kidneys, which limits its filtering capability over a period of at least three months–13. The association between genetic variants and various phenotypes has been studied, and the results are often shared in publicly available databases, like the GWAS Catalog. The association of one genetic variant with multiple traits can be considered to identify secondary traits associated with a phenotype. This understanding can help elucidate potentially shared disease mechanisms, assuming that genetic variants affecting a shared pathway also have a similar impact on the associated traits.Over the past few decades, many large-scale genomic studies, such as genome-wide association studies (GWAS), have successfully identified more than 500 independent genetic variants associated with reduced kidney function. Non-negative matrix factorization (NMF) is a family of algorithms within multivariate analysis that addresses the dimensionality challenge by extracting meaningful features from a given data set, 17.Soft-clustering methods provide a means to reduce the genetic complexity of a heterogeneous disease while also accounting for shared disease mechanisms. In contrast to hard-clustering approaches like K-means or hierarchical clustering, soft-clustering enables the factorization of high-dimensional data by identifying overlapping clustersIn this study, we aimed to deconstruct the heterogeneity of CKD by identifying its genetic subtypes. First, we collect all published variant-trait associations for variants associated with reduced kidney function and apply soft-clustering using NMF. We used the algorithm’s weights to calculate cluster-specific polygenic scores (cPGS) within the BioMe biobank. Finally, we use a phenome-wide association study (cPGS-PheWAS) to validate and interpret the clusters. By deconstructing the complexity of CKD, this methodology contributes new insights into the disease pathways of CDK and enhances our understanding of population-specific differences for CDK.The most frequent CKD-associated secondary traits retrieved from the GWAS Catalog are related to kidney function , hemoglobin levels , T2D, body weight , and pulse pressure (systolic and diastolic blood pressure measurements), among others . CKD-associated traits and their associated CKD variants were factorized into nine partly overlapping clusters by conducting NMF. To ensure the results were robust, we repeated the clustering with bNMF and got comparable results (Tab.S1). The top seven traits per cluster are summarised in Me cohorts . Except for the ‘Increased body mass’ and the ‘Reduced blood volume’ clusters, we replicated at least 3 of the clusters’ top 5 traits (Each cluster was examined by conducting a cPGS-PheWAS with 988 quantitative traits and 832 binary traits on the four Bio5 traits . The levMe cohort. Me cohort (ALL) and the individual continental populations EUR , AMR , and AFR . A normal distribution was observed for the cluster ‘Increased urate’ . Although polygenic scores are expected to have a normal distribution, the other eight clusters present either a skewed tail  or several peaks in their cPGS distributions . As illustrated in We extracted the cluster weights of the W matrix and used them to calculate cluster-specific polygenic scores (cPGS) for participants of the BioMe participant might have high polygenic scores in multiple clusters. Therefore, to understand the cluster overlap in terms of relative risk, we checked how many individuals belonged to the top decile of 1 or more clusters. 58%  of the whole BioMe cohort (ALL) were at high risk in at least 1 cluster. Of these, 60.2% were in the top decile for only 1 cluster, while 37% were at risk for 2–3 clusters .As the cPGS are calculated separately per cluster, each BioCKD is typically defined as a progressive loss of kidney function over time. Although numerous genetic variants have been identified as associated with CKD, their relationship to disease pathways remains largely unclear. The work described here is the most comprehensive assessment of how variants associated with CKD can be grouped according to different CKD-related factors. Specifically, we included variant-trait associations of 322 CKD SNPs and 229 related metabolic traits from publicly available GWAS datasets. By analyzing these associations with NMF, a factorization approach that allows for minimal overlap between groups, we identified 9 clusters of CKD variants and associated traits., 20. A second cluster, which we summarised as ‘Increased inflammation,’ was strongly clustered around rising serum C-reactive protein (CRP) concentrations. CRP is a common inflammatory biomarker in chronic diseases like CKD, diabetes, and cardiovascular diseases–23. In line with that, patients with CKD commonly experience chronic inflammatory states. These states tend to worsen as the disease progresses toward end-stage renal disease and are reflected, or even modulated, by increasing CRP levels–28.CKD is commonly recognized as a heterogeneous condition with various underlying causes and risk factors, which are unlikely to represent a single disease process. This complexity is also reflected by the associated traits retrieved from published GWAS, which are related to kidney function, hemoglobin levels, T2D, body weight, and pulse pressure, among others. Attempting to deconvolute CKD’s genetic heterogeneity and differentially grouping these traits, the nine clusters we identified represented different aspects of CKD. For example, the ‘Increased urate’ cluster, whose clustering weights represent abnormal levels of urinary metabolites like urate, blood/serum urea nitrogen, blood proteins, and Cystatin C, is related to decreasing kidney function. In normal conditions, such blood metabolites are excreted by the kidneys, but in CKD they accumulate and exert a detrimental biological activity. We could observe similar associations in clusters ‘Increased inflammation,’ ‘Reduced lipids,’ and ‘Reduced inflammation.’ Notably, we found multiple significant associations for cluster ‘Increased inflammation’ with reduced risk of dementias. Glycerophospholipids play an essential role in neural membranes, 31, and their levels are directly correlated with serum triglycerides and inversely correlated with total cholesterol and eGFR.We then studied the genotype-phenotype correlation to demonstrate the utility of the clusters. We could replicate most of the top-weighted features on quantitative traits , while the validation on binary traits  was less robust and required additional clinical interpretation. For the clusters of ‘Increased urate’ and ‘Increased inflammation,’ the top traits were confirmed by the PheWAS. CKD is also associated with dyslipidemia comprising high levels of triglycerides and LDL-cholesterol, and low levels of HDL-cholesterol and apolipoprotein A1. Despite this lack of genetic diversity, we could still validate our results in BioMe, a biobank enriched for populations with non-European ancestries. We were most powered when jointly analyzing across ancestries (ALL), while signals replicated in different ancestral groups with some group-specific differences. This result suggests that, although most CKD risk factors converge across ancestral groups, ancestry-specific studies are essential. Another two limitations are the filtering rules used to select traits and variants for the algorithm’s input matrix and the possible existence of non-additive interactions between risk factors that we did not consider in this study. Lastly, one of the input CKD studies, the PAGE study, was also conducted using BioMe data. However, this should not impact the results since we are not looking at CKD case/control scenarios but at CKD subtypes.A limitation of this study is the need for more genetic diversity in the GWAS Catalog, which mainly consists of studies performed on the European population. This European bias is well described in the literature and has important implications for disease risk prediction across global populations.Understanding the biological pathways that lead to CKD is essential to improve clinical management. For example, some clusters group similar traits but with opposite effect directions , while others suggest potentially protective effects . This behavior might indicate that CKD can affect the same metabolic pathways differently, confirming the genetic complexity of the disease. Additionally, the clusters have a limited degree of overlap and, as each represents a specific set of variants, participants might be high risk  for more than one cluster. This additive disease model, similar to the mutational signatures in cancer, suggests a possible interplay of genetic susceptibility to multiple disease-causing mechanismsIn summary, by clustering genetic variants associated with CKD, we identified clusters with distinct trait associations, likely representing mechanistic pathways involved in CKD. We confirmed the validity of these clusters phenotypically. Further clinical investigations could explore whether individuals with a common disrupted pathway also share similar complications, a comparable rate of disease progression, or a different treatment response. In the future, classifying patients with CKD using their genotype may improve care by offering a more personalized and genetically informed clinical plan., 36, 37 (LDlinkR (R version 4.2.1) to retrieve all proxy SNPs in linkage disequilibrium (r2 > = 0.6) with the lead variants, across all available 1000G human populations, 39 and used the GWAS Catalog database to link the proxy SNPs to 805 associated traits  . We excluded gender-specific GWAS and GWAS performed on less than 100 individuals. Additionally, as we are interested in secondary features associated with CKD, we excluded GWAS of traits directly related to eGFR or CKD . We kept trait-variant associations with a significance threshold of less than 1×10−6 using a Bonferroni correction for all 2,401 associations in our data set. To reduce sparsity in the data, we excluded traits associated with less than five variants; this threshold was empirically defined by comparing the clustering results of traits associated with up to 15 CKD variants. We standardized effect sizes across all GWAS by dividing the regression coefficient beta (B) by the standard error, using the GWAS summary statistic results. Traits and variants were then arranged as a matrix with the standardized effect sizes (β) as values. Tab.S5 contains, for each input CKD variant, the list of CKD-associated secondary traits extracted from the GWAS Catalog and the corresponding exclusion criteria for those excluded during the filtering steps.We identified and aligned the alleles of 508 independent genetic variants associated either with decreased kidney function (defined as low eGFR levels for at least three months) or with CKD (using ICD-9/10 codes) from the most recent GWAS and GWAS meta-analyses, 36, 37 . We then  into a matrix of traits  and one of variants , so that HxW ≈ X . The facPLINK and the variant cluster weights to calculate cluster-specific polygenic scores (cPGS) of the BioMe biobank participants. cPGS were standardized within each cluster. The normality of each cPGS distribution was tested with the Anderson-Darling method. Differences between ancestry-specific distributions were tested with the Mann-Whitney test.The results of clustering provide cluster-specific weights for each variant and trait. We used Me biobank participants  using PLINK, excluding relatives above 2nd-degree  and variants with minor allele frequency below 0.05, 46. We trained a random forest classifier to infer the genetic ancestry of BioMe participants using the 1000 Genomes labels as reference. The labeled ancestries are Admixed American , African , European , South Asian , and East Asian . For sub-population-specific analyses, we removed participants with mixed ancestry (defined as having a random forest probability ≤ 0.5) and outliers by only including the quantiles 0.25–0.90 .We validated our results using the genetic and linked electronic health records (EHR) data of 31,701 Bioicipants . As a fiMe data set by performing a phenome-wide association study (cPGS-PheWAS). We fitted linear regression models to analyze 988 quantitative traits  and logistic regression models for 832 binary traits with cPGS as independent variables, adjusting for sex, age, and the first ten genetic principal components (stats R package). Binary traits included Phecodes mapped to ICD-9 and ICD-10 codes (a Phecode is considered if at least two relevant diagnostic codes were present in a patient’s EHR)  and curated phenotypes. Controls were identified as the reference category. Traits were only considered if present or measured in at least 100 biobank participants. The model parameters were standardized using the effectsize R package (refit method) . Standardized coefficient estimates (linear regression) and odd ratios (logistic regression) were reported with the corresponding 95% confidence intervals. The Bonferroni method was used to adjust for multiple testing, and the alpha threshold was defined as 2.7e-05 (0.05/(988 + 832)). We then compared the PheWAS results with the traits in the top decile of NMF’s trait weights.For each cluster, the cPGS were associated with the phenotypes available in the Bio


Anaplasma marginale, Babesia bigemina, Babesia bovis, and Ehrlichia ruminantium), as well as for relevant traits such as body weight and body condition score (BCS), in 1,694 cattle from four African countries . Heritability estimates within countries were mostly not significant, ranging from 0.05 to 0.84 across traits and countries, with standard errors between 0.07 and 0.91. However, the weighted mean of heritability estimates was moderate and significant for body weight and BCS , with significant heritabilities also observed for the presence of A. marginale (0.16) and E. ruminantium (0.19). In a meta-analysis of genome-wide association studies (GWAS) for these traits, two peaks were identified as reaching the suggestive significance threshold : one on chromosome 24 for BCS and one on chromosome 8 for the E. ruminantium infection status. These findings indicate that there is likely to be a genetic basis that contributes to pathogen presence/absence for tick-borne haemoparasite species, which could potentially be exploited to improve cattle resistance in Africa to the economically important diseases caused by these pathogens.The control of tick-borne haemoparasites in cattle largely relies on the use of acaricide drugs against the tick vectors, with some vaccination also being used against selected pathogens. These interventions can be difficult in Africa, where accessibility and cost of vaccines can be issues, and the increasing resistance of tick vectors to the widely used acaricides is a complication to disease control. A potential complementary control strategy could be the exploitation of any natural host genetic resistance to the pathogens. However, there are currently very few estimates of the extent of host resistance to tick-borne haemoparasites, and a significant contributing factor to this knowledge gap is likely to be the difficulty of collecting appropriate samples and data in the smallholder systems that predominate livestock production in low- and middle-income countries, particularly at scale. In this study, we have estimated the heritability for the presence/absence of several important haemoparasite species (including  In Africa, livestock forms a critical part of the livelihoods of most rural households, with approximately 162 million low-income livestock keepers . In mostTheileria parva , bovine anaplasmosis , bovine theileriosis, caused by Theileria annulata, East Coast fever, caused by Theileria parva, and ehrlichiosis or heartwater of cattle (Ehrlichia ruminantium)  . Both banantium) .Bos taurus indicus) with taurine (Bos taurus taurus) cattle  cattle , one rea) cattle , and thi) cattle .Trypanosoma genus, where the tolerance of some African taurine breeds has been long recognised and characterised, and loci underpinning this trait have been identified (Theileria parva pathogen has been known for some time. T. parva infection is responsible for East Coast fever (ECF), a TBD that causes significant mortality in infected, susceptible cattle in East and Southern Africa. T. parva challenges than exotic breeds and EASZ from non-endemic areas. Likewise, a notable recent study by T. parva infection and identified a locus associated with tolerance to ECF. The identification of this locus by T. parva. However, in general, only a few studies have reported naturally occurring loci with large effects that confer resistance to disease in livestock  have already reported quantitative trait loci for resistance to ticks (see https://www.illumina.com/ documents/products/datasheets/datasheet_bovine HD.pdf) and the Axiom Genome-Wide BOS1  arrays are the best at capturing the diversity across African breeds/populations, even if compared with Bos t. indicus-specific arrays .The population consisted of 1,694 one- to two-year-old cattle across four African countries , which is a subset of the 1,740 cattle used in Body weight was estimated using a Rondo tape according to the manufacturer’s recommendations . It is based on the measurement of thoracic girth, which is reported to be highly correlated with body weight in cattle . Body co® FTA® cards, air-dried, labelled appropriately, and packed in foil pouches with a silica gel, prior to DNA isolation. DNA was isolated from 2 × 5 mm diameter blood-soaked FTA card punches using the MagMAX DNA Multi-Sample Ultra Kit according to the manufacturer’s recommendations. DNA isolation was performed using the KingFisher 96-flex instrument, processing 92 samples per run and including extraction controls for each run. Eluted DNA was collected in a final volume of 75 µL and used for downstream processing. Testing was performed to assess the absence/presence  of anaplasmosis, babesiosis, theileriosis, and ehrlichiosis. The inhibitor tolerant and highly processive SsoAdvanced Universal Probes Supermix DNA polymerase master mix (Bio-Rad) was used in all PCR assay development and final detection assays. Published assay primers and probes (Blood samples (approximately 125 μL) were collected from the middle ear vein using a sterile lancet and capillary tube. Samples were then applied onto Whatmand probes  were evar2  >0.85 and a MAF >0.05 were considered for the within-population GWAS .Animals were genotyped using the Illumina HD genotyping array. The SNP genotype data were subjected to quality control (QC) measures, as previously described in Descriptive statistics were calculated for body weight and BCS for each country, whereas prevalence was calculated for the haemoparasites and defined as the percentage of animals that were positive by qPCR at any time during the period considered in this study.G) was calculated using VanRaden’s method 2 (2m) across the four African countries. In addition, Q statistics . Variance components for all traits were estimated within the country using ASReml 4 , fittingmethod 2 , with almethod 2  in R wasatistics  were useu, and errors, ϵ, follow multivariate normal (MVN) distributions given by u ∼ MVN  and ϵ ∼ MVN , where VG and VE are the genetic variances associated with G and environmental variance, respectively. GEMMA provides a regression coefficient for each SNP, and their statistical significance was assessed using a Wald test. A Bonferroni correction was used to account for multiple testing and identify the p-values for genome-wide (p < 0.05) and suggestive  significance thresholds. The within-country analyses were followed by a meta-analysis using a weighted Z-score model as implemented in the METAL software  across countries. The same data were also used to carry out GWAS to identify potential loci underlying genetic variation in the traits of interest, with a meta-analysis across countries being conducted.To estimate the heritability of the presence of tick-borne haemoparasites, body weight, and body condition score in African cattle, we analysed four independent datasets from Burkina Faso, Ghana, Nigeria, and Tanzania, for a total of 1,694 cattle. Heritability estimates were then used to calculate the weighted mean of heritability estimates  are presented per country in Theileria is not presented as it was not detected in any sample. The highest prevalence was observed for A. marginale across all countries (ranging between 43% and 97%), with Ghana presenting the highest prevalence. In general, prevalence was lower in Burkina Faso than in other countries for all parasites considered. This might have an impact on the estimation of the heritabilities and analyses of GWAS, as there is insufficient information to generate reliable results. Similarly, the analyses for A. marginale in Ghana may be affected by the very high prevalence.2) estimates for body weight and BCS as well as the haemoparasite traits for each country. For most traits, the standard errors of the heritability estimates were large, making the estimated h2 not significant. While these estimates are not significant and there is little consistency across countries, there is evidence of genetic variation. These results are probably a reflection of the challenges of collecting consistent phenotypes in the settings concerned, as well as the limitations associated with issues such as small herd sizes.2m) and Q statistics for each trait. The h2m was moderate and significant (p < 0.05) for both body weight and BCS , with significant Q statistics for BCS. When looking at the haemoparasite traits, although the h2m estimates are low, ranging between 0.10 for B. bigemina and 0.19 for E. ruminantium, the estimates for A. marginale and E. ruminantium are both significant, suggesting a genetic component to the presence of these parasites in African cattle.p < 1.91 × 10−7 and p < 1.89 × 10−7, respectively). The first peak  was observed for the body condition score on chromosome 24 (GAREM1 gene (p = 4.5 × 10−8) was identified for the E. ruminantium infection status on chromosome 8 (Tudor domain-containing protein 7 (TDRD7) gene has previously been associated with immune responses.Within-country GWAS analyses did not generally show any regions associated with the traits of interest, reflecting the low sample numbers. To overcome this limitation, we performed meta-analyses across countries for the two quantitative and four haemoparasite phenotypes. When the prevalence of a phenotype was ≥0.05 or ≤0.95 within a country, the corresponding results were excluded from these meta-analyses. Across these six phenotypes, two peaks reached suggestive significance  for traits of economic importance. Moreover, traditionally, the implementation of a breeding programme required an accurate pedigree. In smallholder properties in tropical and subtropical environments, there is often no pedigree recording and no phenotype data recording, rendering conventional breeding practices impossible to implement. Current molecular tools allow for investigating the genetics of complex traits without requiring pedigree information, making selection based on the genome a possibility. One of the key shortcomings of using these technologies in low- and middle-income countries is the cost associated with them. Genotyping arrays are currently the most commonly used tool in GWAS. However, the current commercial genotyping arrays are often biased toward variants common to European breeds, and we have recently shown that they poorly tag variants segregating in indicine breeds, with implications for performing GWAS in African breeds . Further. We could not include Theileria parva in the analysis as we did not detect any infections in our sample set. This was expected for Ghana, Burkina Faso, and Nigeria but was surprising for Tanzania, where both the tick vector and Theileria parva are endemic  with genotypes imputed from HD to the whole-genome level, both independently and via meta-analysis. We have shown evidence of genetic variation for most traits, with the weighted mean of heritability estimates being moderate for body weight and BCS and low for haemoparasites, and we have identified two peaks reaching the suggestive significance threshold  in the meta-analysis endemic . The exp endemic ), the as2m) were moderate and significant . This estimate of the heritability of body weight is consistent with that previously estimated within European cattle, where values generally fall between 0.4 and 0.7  were also previously reported by A. marginale.Estimates for haemoparasites were lower, ranging between 0.10 and 0.19. Low heritability estimates for the infection levels of GAREM1 gene. In a study on body mass in humans and mice, GAREM1 is required for normal growth and for maintaining average body size in these species. This gene is consequently a potentially interesting candidate for follow-up work further exploring its potential link to BCS in African cattle.Previous studies have identified a region on chromosome 5 associated with BCS in tropical cattle , but thea priori unbalanced distribution of allele frequencies, which is likely to inflate the rate of false-positive associations between the traits and the markers, making true associations harder to detect. However, our meta-analysis showed evidence of a peak on chromosome 8 for the E. ruminantium infection status. This region overlaps several genes, though TDRD7 is potentially the strongest candidate for being linked to the infection status. Given that E. ruminantium is an intracellular bacterium, this gene could be relevant as it is an important factor involved in cellular responses to viral infection  and A. marginale . However, none of these regions were significant in our analyses.Considerable work has been carried out to address the genetic control of resistance to ticks [see nfection . A previE. ruminantium, which should be further explored. These data suggest that future larger-scale studies to explore the genetic basis of resistance/tolerance to tick-borne pathogens have merit, as improving the resolution by increasing animal numbers has the potential to identify genetic traits that may contribute in the future to reducing the disease burdens on smallholder farmers in Africa.In conclusion, in this study, we aimed at estimating heritabilities and identifying loci underlying genetic variations for important haemoparasites, as well as body weight and body condition score, in African cattle. Despite the relatively modest heritability estimates in the within-country analysis, our meta-analysis results have indicated the possibility of improving these traits. Moreover, our meta-analyses have identified two regions associated with body condition score and presence/absence of