Arabidopsis thaliana and two breeding datasets from soy and corn. The synthetic phenotypic data allow us to analyze all prediction models and especially the selected markers under controlled and predefined settings. We show that Bayes B and linear regression models with sparsity constraints perform best under different simulation settings with respect to explained variance. Further, we can confirm results from other studies that there is no superiority of more complex neural network-based architectures for phenotype prediction compared to well-established methods. However, on real-world data, for which several prediction models yield comparable results with slight advantages for Elastic Net, this picture is less clear, suggesting that there is a lot of room for future research.Genomic selection is an integral tool for breeders to accurately select plants directly from genotype data leading to faster and more resource-efficient breeding programs. Several prediction methods have been established in the last few years. These range from classical linear mixed models to complex non-linear machine learning approaches, such as Support Vector Regression, and modern deep learning-based architectures. Many of these methods have been extensively evaluated on different crop species with varying outcomes. In this work, our aim is to systematically compare 12 different phenotype prediction models, including basic genomic selection methods to more advanced deep learning-based techniques. More importantly, we assess the performance of these models on simulated phenotype data as well as on real-world data from  Currently, the agricultural industry is under great pressure to deliver new crop varieties quickly for a changing climate and a fewer resource use. Genomic selection (GS) offers breeders the ability to accurately select plants with the potentially highest return on investment for the traits they are interested in, such as yield and drought tolerance, directly from genotype data . By usinArabidopsis thaliana. In their study, the neural networks performed similarly compared to linear regression-based approaches. Arabidopsis thaliana traits, GBLUP still delivered better results. However, with an increasing number of samples, the advantage of GBLUP decreased. In summary, as long as the availability of genomic and phenotypic data in plants is still limited, there is no consistent evidence on advantages using DL-based techniques , the days to flowering , the rosette leaf number , and the flower diameter . After matching of the genotypic and phenotypic data, we filtered the SNP matrix for duplicates, i.e., markers which are identical after encoding, and excluded all SNPs with a minor allele frequency of less than 10%. Thus, between 44k and 67k markers and between 656 and 1,058 samples remained per phenotype  technology. After matching the samples and filtering for duplicates, approximately 8k markers remained.The first dataset of our commercial plant breeding partners contains genotype and phenotype data for 1,411, respective 1,797 unique samples of hybrid corn from the same environment . Phenotype values for yield and percentage water content (PWC) were observed for each hybrid, while the genotypes were determined for the parental lines. The genotype data consists of 8,708 chip-based SNP markers from 870 female and 569 male parental lines. The parents are a mix of doubled haploid homozygous lines and inbred F4/F5 lines that contain some heterozygous loci. Genotypes of the hybrids were constructed The second breeding dataset contains approximately 500 unique parental lines from a soy line breeding program consisting of 810 genetic markers each. The parental lines are after several generations of selfing and are therefore quite homogeneous. All lines were growing in the same environment as well. The markers were selected based on a quantitative trait locus (QTL) analysis and show a high correlation with the traits of interest. Phenotype values for yield, maturation group (MatG), and plant height (Height) were observed for each parent. After matching the samples and filtering for duplicate SNPs, approximately 600 markers remained.Arabidopsis thaliana markers from the LD-pruned genotype matrix described above. We removed all duplicated markers  and markers with no variation. Then, we randomly sampled 10,000 SNPs across all chromosomes with a minor allele frequency greater than 10%. The resulting genotype matrix was used both for the simulation of artificial phenotypes and as input of the different prediction models. For the simulation of artificial phenotypes, we employed the following underlying linear mixed model (LMM). Let n be the number of samples, k the number of fixed effects, and b the number of random effects. Then,Additionally, we simulated artificial phenotypes with different configurations using real homozygous ∈ ℝn denotes the vector of phenotyic values, X∈ ℝ×kn is the design matrix of the fixed effects β ∈ ℝk, and u :=Zγ denotes the random effects , where Z ∈ ℝ ×bn is the design matrix of the random effects and the parameters γ  ∈ ℝ b follow a Gaussian distribution. Further, ϵ ∈ ℝ n is a vector of residuals following a known probability distribution.where y n samples from the genotype matrix and randomly selected 1,000 markers across all chromosomes to simulate the polygenic background . The corresponding parameters γ were drawn from a Gaussian distribution with zero mean and a standard deviation of 0.1. Then, we drew random noise, either from a normal distribution or, for skewed phenotypes, from a gamma distribution. This was parameterized so that the random effect explained a fixed amount h of the phenotypic variance via the following formula:First, we randomly chose xi in a pure additive manner or with additional multiplicative effects, to explain a ratio of about c=0.3 of the total phenotypic variance. For this, we computed the parameters viaTo adjust the skewness, we additionally considered different shape parameters for the gamma distribution. Finally, we added one or several fixed effects h=0.7, h=0.85, h=0.95). For this purpose, we created 12 different configurations, as summarized in A (#100), B (#500), C (#1000), D (#2000), E (MultWeak), F (MultStrong), G (SkewedWeak), H (SkewedStrong), I (Add5), J (Add20), K (Add50), L (Add100).To analyze different scenarios, we simulated various phenotypes for three different heritabilities (Introduction), we included 12 different prediction models in our comparative study. In the following, we first describe classical, statistical prediction models. Afterward, machine learning- and deep learning-based approaches are outlined. Since literature does not show a predominant phenotype prediction model .where y σ2e of the residuals is commonly assigned a scaled-inverse chi-squared distribution and the prior distribution of the marker effects w differs for each Bayesian model (t-distribution (t-distribution (Bayesian linear regression models are based on the same linear mixed model as RR-BLUP (see Equation 4). However, here the variance an model . For insribution . On the ribution , and Bayribution .viaIn addition to RR-BLUP and Bayesian models, we included regularized linear regression models, namely, the Least Absolute Shrinkage and Selection Operator (LASSO)  and Elasw= T∈ ℝ m+1 contains the bias term w0∈ ℝ as well as the model’s coefficients wk∈ ℝ and X*×mn∈ ℝ +1 contains a vector of ones and the genotype matrix X∈ ℝ ×mn. For regularization, both models employ a penalty term Ω(w) weighted by α ∈ ℝ>0. LASSO adds a sparsity constraint, which means that the absolute value of the weights (L1-norm) is used for penalization, i.e., Ω(w) = ∥w∥1. This is often considered as an automatic feature selection, as the weights of unimportant features are pushed toward zero. Elastic Net employs a weighted sum of the L1- and L2-norm , i.e., Ω(w) = λ∥w∥22 + (1-λ)∥w∥1. As a consequence, Elastic Net combines the automatic feature selection effect of LASSO as well as a distribution of the influence among correlated features due to the L2-norm (α controls the strength of the regularization term Ω(w), λ gives the ratio between L1- and L2-regularization in Elastic Net.where  L2-norm . While tvia the so-called kernel-trick, enabling to find solutions for non-linear problems in an implicit higher-dimensional space. The aim is to construct a function that is at most a certain threshold away from the target values of the training data, while at the same time penalizing too complex models. Specifically, a hyperplane with the goal of maximizing the number of samples within a certain decision boundary is fitted. This is achieved by minimizing the termFurther, we included Support Vector Regression (SVR) as a kernel-based approach . SVR allx[i]m∈ ℝ  is the genotype vector of the thi sample, w0∈ ℝ denotes the bias, w m∈ ℝ  denotes the parameters of the SVR model, ϵ ∈ ℝ determines the allowed deviation for any sample from the true targets iy . C ∈ ℝ denotes the strength of the penalization due to deviations from the decision boundary and is usually optimized during hyperparameter tuning. Smaller C values focus more on the minimization of the L2-norm of the model parameters and thus may lead to a smoother and flatter decision function while allowing more prediction errors. By contrast, if C is larger, more emphasis is put on the penalization of model errors, which is more prone to overfitting  , showed Experimental settings). The CNN is composed of an optimized number of blocks, which consists of a convolutional layer, followed by a batch normalization and a dropout layer. After these blocks, max pooling is used for downsampling prior to a flattening layer. The prediction value is determined by a fully connected output layer with a preceding block of another fully connected, a batch normalization and a dropout layer , a Convolutional Neural Network (CNN), and a Local Convolutional Neural Network (LCNN). We designed the architecture of the MLP with different building blocks, consisting of fully connected, batch normalization and dropout layers. The number of these blocks and the number of neurons in each of the fully connected layers were considered as hyperparameters for optimization. After these blocks, a fully connected output layer is added, which delivers the final prediction . For CNNut layer . Importaut layer . Locallyut layer . Prelimiut layer . A rectith percentile of previous trials at the same step. For all prediction methods, we ran 200 trials each. In For hyperparameter search, we applied Bayesian Optimization using the framework Optuna . In contSynthetic data and Real-world data, we encoded the SNP data using an additive genotype encoding, i.e., 0 for the homozygous major allele, 1 for the heterozygous allele, and 2 for the homozygous minor allele . For CNN and LCNN, we used an alternative one-hot encoding. For instance, the nucleotide sequence ACGT is encoded as follows with a one-hot encoding: A → , C → , G → , T → . The one-hot encoding allows to preserve the whole nucleotide information from the input data and might thus be more informative than the commonly used additive encoding. This encoding can be easily handled by a CNN and an LCNN.After the data was prepared as described in https://github.com/grimmlab/easyPheno. Bayesian methods are included using the R package BGLR  to estimate which of the markers are statistically associated with the trait of interest and compared the selected features with the GWAS results. For this purpose, we used permGWAS . For the corn and soy traits, we compared the feature importance of the algorithms with the top 100 GWAS results, since both datasets contain less than 10,000 markers.For the synthetic phenotypes, we compared the importance of the selected features with the simulated effect sizes permGWAS , a permupermGWAS . In conthttps://github.com/grimmlab/phenotype_prediction.In the following section, we first summarize and discuss the results on synthetic data, including analyses of the selected features. Next, we provide an overview of the real-world results and discuss them and compare GWAS results with the selected features of some of the prediction methods. As is observed in Materials and methods, we conducted several experiments on synthetic data to analyze the behavior of phenotype prediction models under predefined settings. A detailed description of the synthetic data generation and all simulation configurations can be found in Synthetic data in Materials and methods.As described in h ∈ {0.7, 0.85, 0.95}. Explained variance estimates v for all prediction methods and simulation settings are summarized in a heatmap  Across all the simulated heritability settings, Bayes B showed the best performance in 29 out of 36 simulations . RR-BLUP was the best-performing method in three cases (once for h=0.85 and twice for h=0.95), XGB on two phenotypes for h=0.7, and LASSO as well as SVR for one trait each, for h=0.7 and h=0.85, respectively. The top performer Bayes B is often closely followed by LASSO, Elastic Net, SVR, and XGB across all three heritabilities. Furthermore, RR-BLUP showed a good overall performance in several cases. Interestingly, none of the three neural network-based approaches wins in any of the 36 simulation settings. Furthermore, when comparing the results of these three prediction models to each other, we cannot determine a clear winner but slight advantages for the MLP with a good performance in general for some traits.We compared the results of 10 phenotype prediction methods on synthetically generated phenotypes for three different heritabilities h, which represents a stronger relationship among samples and less influence of random noise in case of our synthetic data generation model. In the following, we will discuss the results for a heritability of h=0.95 in more detail. Results for h=0.7 and h=0.85 can be found in the Supplementary (A (#100) to D (#2000). The results show in general an improvement of the prediction results with an increasing number of samples across all heritabilities. However, we also observed a drop in performance for the simulation setting C (#1000) with h=0.95 for four out of 10 prediction models. One hypothesis in plant phenotype prediction is that neural network methods have great potential and might outperform other approaches with a higher number of samples being available (A (#100) to D (#2000)), since a deep learning-based method is never best overall  and strong multiplicative (F) effects. These differ regarding the effect size of the multiplicative term of the simulated causal SNPs, which is 0.2 for E and 0.28 for F. In h=0.7 and h=0.85. Across all three heritabilities, the results of the neural network-based methods improved relative to the best-performing approaches for strong multiplicative effects (setting F). This suggests that neural networks might be a valid option in case of highly non-linear phenotypic architectures. For all six scenarios with a skewed distribution of the simulated phenotype (G (SkewedWeak) and H (SkewedStrong)), Bayes B showed the best performance. For the stronger skewed scenario H with h=0.95, the performance of the MLP and CNN drops, while this does not apply for the LCNN.We simulated weak (I (Add5) to L (Add100)) across all three heritabilities, we observe that Bayes B performs best, mainly followed by RR-BLUP, LASSO, Elastic Net, and SVR with a similar performance and outperformed once by the former. If also considering configuration C (#1000) with similar settings but one causal SNP, the advantage of Bayes B tends to decrease with a growing number of causal SNPs. The formulation of Bayes B usually forces unimportant weights toward zero . This effect seems to be more profitable for scenarios with less causal SNPs for which the effect sizes of the causal SNPs also differ more from the background. Consequently, Bayes B can better capture the lower number of causal SNPs with larger effect sizes for scenarios C (#1000) and I (Add5), while this advantage is smaller for scenarios J (Add20), K (Add50), and L(Add100) with more causal markers that have smaller effect sizes. Beyond that, the performance of the MLP and the CNN is rather comparable to the top result for simulation configurations with multiple additive markers. Less causal SNPs can be considered as more noise in the features, which is hard to deal with for the neural network-based approaches if also considering the relatively low number of samples.Considering traits with multiple additive causal SNPs  and B (#500)) and multiple additive markers (K (Add50) and L (Add100)), Elastic Net tends to select the second least features, indicating a strong effect of the L1-regularization part. Without filtering out feature importances smaller than 1% of the largest feature importance, Bayes B selects many features, similar to RR-BLUP, RF, and XGB. However, when considering this filter, the number of important features for Bayes B decreases significantly in many simulation settings (see I (Add5) to L (Add100)) and for scenarios with a stronger multiplicative effect (F (MultStrong)). Furthermore, it cannot be observed for scenario A (#100) with only 100 samples. We see a similar behavior for the other prediction methods, but not as strong as for Bayes B.To evaluate how well the different models are able to capture the determinant markers of synthetic phenotypes, we compared the effect sizes I (Add5) to L (Add100)), stronger multiplicative effects (F (MultStrong)), and a small number of samples (A (#100)), the increase in the TPR is also less pronounced or not existing.Further, we analyzed how many of the actual background SNPs were identified by each prediction model. We can observe that both Bayes B and XGB usually recognized more of them. However, setting the number of detected background SNPs in relation to the number of selected features, which we subsequently call the true positive rate (TPR) and which is given in parentheses in I (Add5) to L (Add100)), the simulated causal SNPs were identified by all prediction models except RR-BLUP in all 24 scenarios (I (Add5) to L (Add100), the number of detected causal SNPs decreased with a growing amount of additive markers. This is expected, as the individual effect sizes also decreased with a higher number of causal markers. Consequently, they were harder to distinguish from background or non-related SNPs. In general, Elastic Net and Bayes B ranked the causal SNPs higher than XGB for these scenarios. Considering all prediction models and heritabilities , so their influence is limited. Probably, this good feature selection is also a reason for the good prediction performance of LASSO, Elastic Net, and Bayes B.h=0.95 in To further analyze the actual values of the feature importances and not only if an SNP was selected at all, we show the min–max normalized feature importances (without filtering) of Bayes B, Elastic Net, and XGB in comparison with the effect sizes for I (Add5) to L (Add100)), the distance between both types is also smaller in the plots. Further, we observe that feature importances of Bayes B and Elastic Net for the causal SNPs tend to be higher in comparison with XGB.As Elastic Net rates less features as important, we see a smaller amount of points in the plots. The causal markers are highlighted by a larger marker size and with a black frame. In all plots, we can see that the causal markers are rated important by every algorithm. However, especially for XGB and in some cases for Elastic Net as well, we observe that background SNPs have often a similar feature importance . As the effect sizes of the causal and background SNPs do not differ that much for scenarios with multiple causal markers . Further, XGB rates several SNPs with a low effect size important (right lower and right middle parts of the plots). Overall, in most scenarios, there are not many points in the lower range of the plots. This suggests that selected background SNPs are rather those with larger effect sizes.In addition, we computed the Pearson correlation coefficient between the effect sizes and feature importances. In almost all cases, Elastic Net shows the highest correlation, closely followed by Bayes B or placed second after Bayes B. As our evaluations show that both Elastic Net and Bayes B perform a good selection of the important features, we assume that the - often slighly - better performance of Bayes B is caused by the selection of more background features, which apparently also contain information regarding the trait of interest.Arabidopsis thaliana and two breeding datasets of corn and soy.Next, we compared the performance of the prediction models for several traits in real-world data, including the model organism Arabidopsis thaliana, we observe that multiple models deliver similar results with differences within the standard deviations. For corn and soy, this observation is not that clear. For three traits, Elastic Net is the top performer, often closely following the prediction models that led to the best results for the other phenotypes. For the traits Diameter in Arabidopsis thaliana as well as for Yield in soy, none of the models performed considerably well. The commonly used model Bayes B that performed best on synthetic data showed a competitive performance for most of the traits. Although LCNNs are supposed to better capture the influence of different marker effects than CNNs and MLPs, the LCNN was outperformed by at least one of the two other deep learning-based approaches for every phenotype except Diameter and corn’s Yield. Comparing the outcome of CNN and LCNN, which both used one-hot-encoded data, to the MLP, we observe that the MLP is superior in five cases. The MLP is furthermore competitive to the top performer for three traits in Arabidopsis thaliana. However, as the additive encoding still leads to a loss of information, this indicates that further encoding strategies should be investigated in the future.In general, no model performed best for all considered traits, as illustrated in the heatmap in If we recap the results on synthetic data, we observe that the best-performing prediction methods on real-world data also performed well. For instance, the top performer on real-world data, Elastic Net, showed its best performance for scenarios with strong multiplicative effects, skewed phenotype distributions, or multiple additive markers. Hence, an explanation for its good performance on real-world data might be that similar genotype–phenotype relationships are present.Arabidopsis thaliana traits, so do the classical ML approaches. Hence, the effect might rather be caused by the genetic architecture or the typical amount of available samples for plant phenotype prediction is still not enough.Similar to the synthetic data, the real-world experiments do not reveal an advantage of neural network-based techniques over the other approaches with an increasing number of samples. Although all three neural networks improve with a growing sample size for the To evaluate the feature importances of Bayes B, Elastic Net, and XGB for the real-world data, we first compared how many markers were found by each model and then checked these against GWAS results.Arabidopsis thaliana, we took the 1,000 most significantly associated markers, i.e., the 1,000 markers with the lowest p-values. Arabidopsis thaliana traits with the number of markers selected by each model  and the corresponding number of top 1,000 GWAS results in parenthesis. Similar to the results on synthetic data, Elastic Net selects less features in comparison with Bayes B and XGB, probably due to the L1-regularization. For the Arabidopsis thaliana traits, we observe that the important SNPs overlap in many cases. For these intersections of all three prediction models, we see the highest ratios of SNPs also being within the top 1,000 GWAS results. Furthermore, Bayes B and Elastic Net agree on the importance of many features, which might be caused by similar underlying assumptions. On average, with a value of 22.5%, Elastic Net shows the highest ratio of selected features also being within the 1,000 considered GWAS results.For Arabidopsis thaliana.For soy and corn, around 600 and 7,000 SNPs were available, respectively. Hence, we only took the top 100 GWAS results for comparison. The results of the feature analysis for soy and corn can be seen in J (Add20) to L (Add100), the difference to the feature importance without filtering is rather small. In general, there seems to be a connection between the GWAS results and feature importances. However, it is not clear to which extent this influences the predictive ability of a model.Additionally, we compared the feature importances after removing those smaller than 1% of the largest one , phenotypes in a commercial breeding program are typically influenced by environmental conditions impeding phenotype prediction. For this reason, the integration of environmental features to phenotype prediction models is highly relevant for future research. Several studies show advantages when integrating such additional information . The following phenotypes have been used: FT10 (https://www.doi.org/10.21958/phenotype:261), DTF1 (https://www.doi.org/10.21958/phenotype:703), RL (https://www.doi.org/10.21958/phenotype:704), and Diameter (https://www.doi.org/10.21958/phenotype:707). All simulated phenotypes, detailed results of the whole hyperparameter optimization, precomputed permutation-based GWAS results, and the code for conducting the simulations and generating all figures can be freely downloaded from our GitHub repository: https://github.com/grimmlab/phenotype_prediction. The fully imputed SNP matrix data for Arabidopsis thaliana data and wrote the simulation scripts to generate synthetic phenotypes, with contributions from FH and DGG. FH and MJ implemented all prediction methods and performed all simulations and comparative and statistical analyses. MJ, FH, and DGG analyzed and interpreted the results. MJ, FH, and DGG wrote the first draft of the manuscript. RD, SJS, and CD contributed to sections of the manuscript. All authors contributed to manuscript revision and read and approved the submitted version.MJ, FH, and DGG contributed to conception and design of the study. PR, CM, and SJS provided the breeding datasets and performed the data preparation for the corn and soy datasets. RD performed the initial breeding data analysis and hybrid simulation. MJ prepared the The project is supported by funds of the Federal Ministry of Education and Research (BMBF), Germany [01∣S21038].www.lrz.de). The authors are grateful for the permissions of data use granted by Computomics’ customers for the corn and soy datasets.This article is funded by the Open Access Publication Fund of Weihenstephan-Triesdorf University of Applied Sciences. The authors gratefully acknowledge the compute resources provided by the Leibniz Supercomputing Centre , Germany [01|S21038]. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Triticum aestivum.L) that causes yield losses and produces mycotoxins which could easily exceed the limits of the EU regulations. Resistance to FHB has a complex genetic architecture and accurate evaluation in breeding programs is key to selecting resistant varieties. The Area Under the Disease Progress Curve (AUDPC) is one of the commonly metric used as a standard methodology to score FHB. Although efficient, AUDPC requires significant costs in phenotyping to cover the entire disease development pattern. Here, we show that there are more efficient alternatives to AUDPC  that reduce the number of field assessments required and allow for fair comparisons between unbalanced evaluations across trials. Furthermore, we found that the evaluation method that captures the maximum variance in FHB severity across plots is the most optimal approach for scoring FHB. In addition, results obtained on experimental data were validated on a simulated experiment where the disease progress curve was modeled as a sigmoid curve with known parameters and assessment protocols were fully controlled. Results show that alternative metrics tested in this study captured key components of quantitative plant resistance. Moreover, the new metrics could be a starting point for more accurate methods for measuring FHB in the field. For example, the optimal interval for FHB evaluation could be predicted using prior knowledge from historical weather data and FHB scores from previous trials. Finally, the evaluation methods presented in this study can reduce the FHB phenotyping burden in plant breeding with minimal losses on signal detection, resulting in a response variable available to use in data-driven analysis such as genome-wide association studies or genomic selection.Fusarium head blight (FHB) is a fungal disease of wheat ( Upon infection, several Fusarium species produce aggressive secondary metabolites, which lead to crop contamination such as, deoxynivalenol, nivalenol, T2 toxin, fumonisin, and mycoestrogen zearalenone, which have negative effects on human diet and on animal growth and fertility Fusarium head blight (FHB), sometimes known as scab, is a global problem causing a great economic burden on the cereal industry due to its significant reductions in grain yield and quality Host resistance to FHB is quantitatively inherited with a complex genetic architecture and is usually split into components of resistance with partial overlapping control Due to its complex genetic control and the fact that phenotyping is a labor and time-intensive process Genomic selection https://www.suscrop.eu/projects-first-call/wheatsustain), where data from multiple partners, locations and years are collected into a common dataset. These datasets are essential to developing robust and powerful models that yield reliable results and allow complex modelling such as genotype-by-environment interaction (GxE) The success of data-driven models such as MAS or GS relies on a good response variable or phenotypic value to properly capture genetic effects and/or complex interactions between genotypes and environments. Research for FHB resistance is often done through cooperative trial networks such as the annual CIMMYT FHB screening nurseries, the US wheat, and barley scab initiative, or the WheatSustain project (via non-linear regression and then collapsed into the parameters that characterize the regressed curve The Area Under the Disease Progress Curve (AUDPC) is commonly used as a quantitative resistance phenotyping strategy because it integrates aspects related to host development and growth AUDPC presents some drawbacks: i) several FHB assessments capturing all stages of disease progress development are required to have a reliable measure of FHB resistance, ii) it yields scores with unusual units (% of severity × time), losing the relationship with both time and FHB severity units and making it difficult for interpretation, and iii) scores obtained from unbalanced number of assessments may be biased due to the inability to capture all stages of the disease development. In fact, thesame phenotypic pattern can yield very different AUDPC scores if assessments are performed just too early or too late during the disease development.via simulation.Here, we compare the use of AUDPC as an informative and integrating method to evaluate FHB resistance in field trials, with alternative scoring metrics by i) developing efficient methodologies/scoring metrics that maximize the information gained in each assessment, avoiding an exhaustive phenotype burden and allowing fair comparison of scores across trials, ii) comparing the predictive ability of statistical models when prior information about developmental traits such as plant height and anthesis date isadded to the model, and iii) quantify the ability of these new alternatives to capture partial diseases components 22.1The WheatSustain winter wheat panel is composed of 230 genotypes (cultivars and breeding lines) covering a wide genetic variability across Europe. We used the breeders’ knowledge and the mean of the coefficient of determination to selectthe training set lines for this experiment Genomic DNA of the 230 varieties was extracted from 1-week-old seedlings, and sent for sequencing using the TraitGenetic 25K single nucleotide polymorphism (SNP) chip. High-quality markers were kept by removing the markers with > 5% heterozygous or missing calls and with a minor allele frequency of< 5%. A total of 22,354 informative markers were retained after filtering. Missing markers were imputed using a multivariate normal (MVN) - expectation maximization (EM) algorithm .Field trials were carried out for two years (2020 and 2021) and three locations, Tulln , Vollebekk , and Feldkirchen . Genotypes were sown in a randomized complete block design with two replications in Tulln and Vollebekk, and non-replicated trials in Feldkirchen. Weather stations collected meteorological conditions for all environments daily from sowing to harvest.Fusarium culmorum or F. graminearum during anthesis/inoculation and FHB disease was evaluated as the percentage of infected spikelets per plot, as an integrated measure for incidence and severity Trials were artificially inoculated with t-th day and l-th location, t-th day and l-th locationand baseT is the fixed threshold to increment GDDs. baseT was set 5°C in this study for all locations. The disease development curves in GDD units for each trial are shown in where 2.2T assessments are combined to approximate the definite integral between x1 and Tx of the function that we would ideally obtain if a set of infinite assessments  were available. Trapezoidal or mid-point rule AUDPC is a particular application of Riemans’s sum where a discrete set of 1, x2, …, xT}be the set of accumulated Growing Degree Days to Anthesis corresponding to the T assessment’s dates and Y={y1, y2, …,yT} the set of T FHB severity evaluations. We define a scoring metric as a function that maps X and Y into a score to be used as the response variable in further analysis.Here, we propose three alternative scoring metrics with the following formulation. Let X={x2.2.1Tx, Ty) and the origin . To integrate more available information, we propose an approach that considers the average time value in which FHB severity reaches the final plateau, instead of just the last assessment. Mathematically:A single-point approach that applies a non-linear transformation, arctan, on the slope computed between a single assessment  is reached, i.e. the first time that the maximum disease reached was recorded.where 2.2.2We define GDD50 as the accumulated growing degree days in which a plot reaches 50% of the total FHB severity. This concept has been described as the latent period in disease progression in the literature , and hasL and R are the indexes of the closest points  to the target disease level (50%), so  and  are the best points to linearly interpolate GDD50.where 2.2.3This score is measured as the percentage of FHB severity with the highest variability among plots in the FHB assessment. Mathematically this is expressed as:N×T matrix with FHBit being the disease value for i-th plot and t-th assessment, and FHB.t is the mean disease value in the t-th assessment. Thus, fhb_max is the highest variability assessment index. This metric is easy to measure but requires the phenotypic information of all lines before computing it.where FHB is a 2.3A stochastic simulation was conducted to obtain a reliable dataset that mimic the same conditions as BOKU’s real database, i.e a set of 6 observations of the disease progress curve for 230 genotypes through 2 years and 2 replicates by year.Following the phenotypic records from field experiments, we assumed that the disease progress curves follow a sigmoid or logistic behaviour based on two parameters:y is the FHB incidence/severity recorded for a given x value of accumulated GDDs. Parameter a determines the position of the curve on x-axis and coincides with both the inflection point and the required accumulated GDDs to reach a FHB incidence/severity equal to 50%. Parameter b determines the shape of the sigmoid curve and coincides with the reciprocal value of the rate parameter, also known as intrinsic rate of increaseapparent infection ratewhere a) and a gamma distribution (parameter b) as realistic density distributions derived from real data. Populations of a and b parameters were used to calculate the definite integral values .Real marker information was used to genotype the training population: the simulated genome consisted of 22,354 markers for each trait and marker effects are assumed to randomly follow a normal distribution. True breeding values were calculated by summing effects across all markers and then, scaled to follow a normal distribution  where chosen to partially disconnect genotypic information and true breeding values and approximate four different heritability values . Assessments were performed from days 10 to 30 after anthesis with a period of 4 days between them. Anthesis dates were stochastically computed according to field data.We also simulated 11 scenarios with different assessment protocols Table 2 2.4Predictive ability of scoring metrics was tested by applying Genomic Best Linear Unbiased Predictors (GBLUP) model y is the response variable, i.e. scores. X and Z are known design matrices for fixed  and random effects (genotypes or lines). β is the vector of regression coefficients of fixed effects (least squares). Vector u contains the random genetic additive effects or GEBVs. Random term and residual variances are denoted as where ormation . Since tTo test the performance of predictions based on scoring metrics, we formulated three prediction scenarios using a 5-fold cross-validation scheme. All scenarios involve an independent analysis for each of the four scoring metrics. Scenarios 1 and 2 were applied to field data and only scenario 3 was applied to simulated data.Scenario 1. Whole field data were analyzed simultaneously in a two-step strategy. In the first step, genetic effects (BLUEs) were estimated once by removing environmental effects: y is the vector with observed phenotype, X1 and X2 are design matrices for fixed effects, ĝ is the vector with estimates for genetic effects (BLUEs). Z is the design matrix of random effects and û is the vector with predictions of random effects . Both random terms û and ϵ are assumed to be uncorrelated with where In the second step, data was split into train and test according to the cross-validation scheme. BLUEs from training data were used as response variable in four GBLUP models involving different combinations of phenological traits as fixed effects: No covariates (None), Anthesis date (AD), Plant height (PH) and both (AD + PH). The obtained BLUPs (GEBVs). Accuracy values were obtained by correlating predicted GEBVs from unseen lines with BLUEs. This step was replicated 25 times.ĝ is the vector with BLUEs from first step, μ is the intercept, X is the design matrix for fixed effects, g*is the vector with predictions of random effects (GEBVs), which are assumed to be correlated with additive genomic relationship matrix K as covariance structure. where Scenario 2. Field data was split by trial and analyzed independently using a single step strategy and the same combinations of phenological traits as fixed effects. Accuracy values were obtained by correlating predicted GEBVs from unseen lines with phenotypic records. This analysis was replicated 10 times for each of the 6 trial subsets.y is the vector with observed phenotype, X1 and X2 are design matrices for fixed effects, g* is the vector with predictions of random effects (GEBVs), which are assumed to be correlated with additive genomic relationship matrix K as covariance structure. where Scenario 3. A single step GBLUP model was used to predict GEBVs in each of the 44 simulated predictive tasks:y is the vector with observed phenotype, X is the design matrix for fixed effects, g* is the vector with predictions of random effects (GEBVs), which are assumed to be correlated with additive genomic relationship matrix K as covariance structure. where a and b and the integral value computed from them. Each predictive task was replicated 30 times. Average accuracy values were calculated and summarized in different ways:GEBVs were not only correlated with the observed scored values as shown in previous scenarios: correlations were extended to genetic effects for parameters a and Parameter b) and compute the percentage of tasks in which each scoring metric was the best (higher Pearson’s correlation between GEBVs and the respective parameter).For each of the 44 predictive tasks, we determined the best performers predicting the four categories  was calculated as the percentage of gain in AUC compared with AUDPC.For each of the 11 scenarios of assessment protocols, we computed the Area Under the Curve (AUC) of the interaction plots resulted by plotting heritability (x-axis) against accuracy (y-axis). The relative performance of alternative scoring metrics  showed greater performance for all years and locations.σ2 obtained relatively good accuracy and angle was clearly the worst in both years. In trials where the number of FHB assessments were lower, alternative metrics showed better performance with angle and Max σ2 being the most predictable metrics in Feldkirchen 2020 (average accuracy of 0.58) and all alternatives outperforming AUDPC in Feldkirchen 2021 (average accuracy of 0.42). Angle was also the best transformation in Vollebekk 2020 with average accuracy of 0.58 and only GDD50 metric was worse than average in Vollebekk 2021.In Tulln trials, AUDPC yielded the largest accuracy values, with an average of 0.63 and 0.61 in 2020 and 2021, respectively. GDD50 and Max 3.3all (6), mids and limits (3), pair 3-6 (2), and last (1). As a general trend, accuracy values increase with higher heritability values. When GEBVs are correlated with phenotype/observed score, best curves and AUC values are obtained by Max σ2 and AUDPC: 0.41, 0.40 and 0.41 for scenarios all, mids and pair 3-6, respectively. Highest AUCs are also obtained in these three scenarios when correlating with integral but in that case GDD50 was also a top performer. Although best integral predictions were obtained without restrictions on available data, minimum accuracy losses (<1%) were found when using just the restricted information of assesment protocols mids and pair 3-6.Most representative scenarios for each number of assessment are shown in limits and last were, respectively, -4.8% and -9.1% when predicting phenotype and -5% and -13.3% when predicting integral. Angle has a relative good performance predicting phenotype but has the worst performance predicting integral. AUDPC has a considerable drop in overall accuracy predicting phenotype when only the last point is available (-36.8% of AUC gain respect to accuracy obtained with 6 points).Drop accuracy gains for σ2 was the best performer predicting phenotype in 46% of predictive tasks. Angle and AUDPC were the best in 27% and 25%, respectively and GDD50 was the best just in 2%. When predicting integral, AUDPC and GDD50 were the best performers, with 45% and 30% respectively. GDD50 was the best performer in almost half (46%) of the predictive tasks for sigmoid parameter a. Angle was the best performer in 84% of tasks predicting sigmoid parameter b and AUDPC was the best in the remaining 16%.σ2 outperformed AUDPC predicting phenotype in 7 out of 11 assessment protocols, including when all the information is available. Results showed similar AUC gain patterns for integral and parameter a. Alternative methods, and especially Angle, perform better predicting parameter b except in those protocols that capture just the early stages of disease development (first and xtitfirsts). GDD50 was better predicting the integral and parameter a in four assessment protocols  but was penalized in those where only the first stages of disease development werecaptured. All alternative scoring metrics outperform AUDPC predicting phenotype when just the fourth or last assessment is available. Data from 4Besides the common issue of accurately characterizing the disease pattern, the research of FHB resistance has the temporal component factor issue, i.e. since disease patterns changes over time, multiple evaluations of plants/plots are required to properlyquantify disease resistance. This imposes an important drawback in plant breeding programs because i) breeders cannot always measure the disease progression across the crop developmental phases, and ii) increase phenotyping cost and time. Here, we proposed alternative metrics to AUDPC with the aim to i) cope with multi-trial, unbalanced data with different experimental conditions, and ii) yield scores that are fair, comparable, and easy to interpret so they can lead to the elaboration of guidelines for less time-and-labor-consuming but equally informative phenotyping.4.1via cross-validation. Although AUDPC was expected to reach the best accuracy values in trials with higher number of assessments, the non-optimal results of Feldkirchen 2021  of unseen lines GDD50 was adapted from the well-known parameter “latency period” The area under the curve of a sigmoid is asymmetric with respect to the x-axis, which is much greater on the right side or, in other words, after the inflection point (GDD50). Therefore, given a fixed interval to measure AUDPC (0-30 DAYS), the higher theinflection point, the more important part of the area moves outside the measurement window .Angle scoring metric was conceived as a straightforward approach which minimum requirements, i.e. just one informative datapoint but with the ability to keep the characteristic non-linearity of the disease progress curve by applying arctan function. Its drawbacks are the inability of integrating more information when it is available and the uninformative nature of its units (degrees or radians) when brought to the field. Here, angle emerged as the most predictable metric when just one point was provided (σ2). This metric was computed a posteriori, i.e. many different assessments may be performed to calculate Max σ2, although just one would be finally used. When field design implies just one assessment, Max σ2 is equivalent to just consider the disease percentage and drop the time information. Our results indicated thatMax σ2 yielded optimally across and within trials indicating that metrics that capture variance are very informative. Moreover, simulation results indicate that, for higher heritability, there is a positive correlation between predictive accuracyand coefficient of variance (CV), as shown in With the aim to determine the role of capturing variance on predictability, we calculate the assessment with the maximum variance of the FHB evaluation Max σ2. This mσ2 was the most predictable metric and GDD50 the least predictable one. In addition, alternative metrics were more predictable than AUDPC in assessment protocols that simulate Vollebekk conditions  are enough informative to obtain both a predictable phenotype and a good approach of the integral Figure 34.4Patterns of disease development over time are usually well-fitted to nonlinear models a) which can be targeted by computing GDD50 and the apparent disease rate (rate parameter or parameter b), which was successfully captured by our Angle approach. Due to this findings, we suggest further analysis to properly understand the basis of these relations and to transfer this knowledge to field trials and real selection processes.In our approach, we applied this knowledge to the problem of characterizing disease curves where datapoints were not enough to use standard nonlinear fitting procedures. Simulation experiment allowed us to understand the role of each scoring metric on thecapture and prediction of the partial disease components reflected in the sigmoid function such as the latency period (inflection point or parameter 5σ2) to efficiently capture and integrate field information. Our findings demonstrated that if the field assessments capture critical growth stages of disease development such as the inflection point and/or the end of the disease growth, then a reduction in the number of assessments did not imply a significant predictive accuracy loss. Field assessments protocols that try to capture maximum variance are a great approach to characterize quantitative resistance. GDD50 is a feasible alternative to measure FHB resistance as soon as disease sampling covers 50% of the disease infection. Thus, historical data analysis could be performed to predict the most optimal time to measure FHB in the field experiment, due tothe predictive role of GDD measures. In addition, alternative metrics such as GDD50 and Angle are good approaches to compute sigmoid parameters, which can be translated into quantitative resistance components without the usual requirements of data availability in non-linear fitting procedures. We propose the following guideline for phenotyping FHB resistance:In this study, we tested the ability of scoring metrics , characterizing FHB resistance as the percentage of infected spikelets per plot when variance is high is a great approach for the prediction of unseen genotypes.◼ If the number of assessments is restricted but a targeted strategy is possible, capturing inflection point is essential to characterize disease progress curve. Following our field data, the optimal measurements should be carried out between 20 and 30 days after anthesis/inoculation.The original contributions presented in the study are included in the article/G-AJ performed statistical analyses, wrote large part of the article and prepared the figures. I-SJ conceived the study, and wrote a large part of the article. LM, BH, I-SJ, and HL conceived the project and obtained fundings. I-SJ and G-AJ drafted the manuscript. LM, ML, MS, HL and BH, collected and performed initial quality check of the field data. All authors discussed the results and reviewed the manuscript. All authors contributed to the article and approved the submitted version.The WheatSustain project was carried out under the ERA-NET Cofund SusCrop (Horizon 2020 Grant No 771134), being part of the Joint Programming Initiative on Agriculture, Food Security and Climate Change (FACCE-JPI). I-SJ was supported by the Beatriz GalindoProgram (BEAGAL18/00115) from the Ministerio de Educación y Formación Profesional of Spain and the Severo Ochoa Program for Centres of Excellence in R&D from the Agencia Estatal de Investigación of Spain, grant SEV-2016-0672 (2017-2021) to the CBGP. G-AJ is working under a UPM predoctoral grant as part of the programme “Programa Propio I+D+i” financed by the Universidad Politécnica de Madrid. ML, MS, and BH were supported by the Austrian Federal Ministry of Agriculture, Regions and Tourism (grantnumber DaFNE-101402). LM was supported by the Research Council of Norway (NFR grant 299615), and and HL by Deutsches Bundesministerium für Bildung und Forschung (031B0810).Author HJ was employed by Secobra Saatzucht GmbH.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.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Intermediate wheatgrass (IWG) is a perennial forage grass that is currently being domesticated as a grain crop. It is a primarily wind-pollinated outcrossing species and expresses severe inbreeding depression when self-pollinated. Characterization of pollen dispersal, mating parameters, and change in genetic diversity due to pollen movement is currently lacking in IWG. In this study, we examined pollen dispersal in an IWG selection nursery by evaluating 846 progeny from 15 mother plants and traced their parentage to 374 fathers. A set of 2,500 genomic loci was used to characterize the population. We assigned paternity to 769 (91%) progeny and the average number of fathers per mother plant was 37, from an average of 56 progeny examined per mother. An extensive number (80%) of pollination events occurred within 10 m of the mother plants. Pollination success was not correlated with trait attributes of the paternal genotypes. Mating system analysis confirmed that IWG is highly outcrossing and inbreeding was virtually absent. Neither genetic diversity nor the genome-estimated trait values of progeny were significantly affected by pollinator distance. The distance of pollinator in an IWG breeding nursery therefore was not found to be a major contributor in maintaining genetic diversity. These findings reveal the pollen dispersal model in IWG for the first time and its effect on genetic diversity, which will be valuable in designing future IWG breeding populations. Information generated and discussed in this study could be applied in understanding gene flow and genetic diversity of other open-pollinated species. The reproductive success of plants in a nursery can have profound influence on the genetic makeup of succeeding generations as well as on their trait and behavioral expression. A better understanding of pollen movement is therefore important in outcrossing plant populations, especially so in breeding populations, as high genetic diversity is desired for population maintenance and variety development.ST, for example) while spatially expansive gene flow can limit local adaptation  Barkworth and D. R. Dewey subsp. intermedium, 2n = 6x = 42] is a cool-season perennial grass species that is native to the Mediterranean and Eastern European regions (Intermediate wheatgrass (IWG) [ regions . It is p regions . The cro regions . The Uni regions . The IWG regions . The IWG regions . Crain eThis study was conducted with the primary goal of understanding the extent of pollen dispersal in IWG. Specifically, we: (i) studied the parameters and patterns of mating in IWG, (ii) traced the parentage of progeny used to create the next breeding population, (iii) studied patterns of genetic diversity in both parents and progeny, and (iv) evaluated the effect of pollen dispersal in progeny diversity and trait distribution. For this purpose, we characterized several aspects of population properties as functions of pollen dispersal, such as number and distance of paternal genotypes contributing to the progeny, genetic diversity among the progeny, and genomic-predicted trait distribution in the progeny.1 genets obtained from 12 bi-parental crosses among eight UMN_C3 genets were transplanted in the same field. The eight UMN_C3 genets were selected because of their relatively large grain size observed in 2017. The site of population establishment is located within the University of Minnesota’s Agricultural Research Station in St. Paul, MN, USA . Each seedling was planted approximately 0.91 m (3 ft) apart with border IWG plants surrounding the nursery (The intermediate wheatgrass (IWG) population used in this study is the breeding germplasm from the fourth recurrent selection cycle at the University of Minnesota and is referred to as UMN_C4. This population was developed by inter-crossing 73 cycle 3 UMN_C3;  genets s nursery . The ninSeed sampling for this study was done by selecting fifteen mother plants  during 2019 in the nursery that were positioned away from the plot borders. Upon maturity, 10 seed-bearing inflorescences were harvested per plant, dried at 36°C for 72 h, and threshed using a Wintersteiger LD 350 . From the threshed grain, half-sib progeny were selected for genotyping at random without any preference for seed size, color, or its hulled state. The number of sampled half-sibs per mother plant ranged from 44 to 72 with an average of 56 and a total of 846.Thinopyrum intermedium v2.1 reference genome (bwa 0.7.5a (Seeds sampled from the 15 mother genets (families) were germinated and maintained in a greenhouse during September–December in 2019. From each seedling 10–12 cm, leaf tissue was collected and dried on silica for 5 d. Leaf tissue from UMN_C4 genets were collected in July 2018. DNA was extracted using the BioSprint 96 DNA Plant Kit  and sequenced using the genotyping by sequencing method  on Illume genome  using bwa 0.7.5a . SAMtoola 0.7.5a  were usea 0.7.5a  in Tassea 0.7.5a . Imputato, He, respectively), polymorphism information content (PIC), and number of loci assumed to be following Hardy–Weinberg equilibrium; all of these parameters were estimated in Cervus 3.0.7 , observed and expected heterozygosity (Hus 3.0.7 . We noteST) using Weir and Cockerham’s method (snpStats 1.40.0. Because of a large number (~85 million) of data points for each of the families, the estimates of genetic diversity have been averaged over the genome per mother genet (family). Population structure was analyzed from a subset of 2,500 SNPs (detail below) using two methods: (1) principal component (PC) analysis with the function prcomp in R 4.0.2  R 4.0.2  with numWe used Cervus 3.0.7 to carry out paternity analysis on 846 half-sib progeny collected from 15 mother plants. Initially, all 21,256 genomic markers were used which led to the program halting with a “floating-point overflow error.” The number of markers was then reduced to a randomly selected set of 2,500 in a similar approach to a recently published study in IWG . For patks.test in R 4.0.2 , single-locus outcrossing rate (ts), bi-parental inbreeding (tm-ts), and correlated paternity (rp). Parameter estimations were done with the Newton–Raphson procedure  a pairwise genetic relationship among the progeny estimated using the function UP 4.6.1 , (ii) Nee StAMPP , (iii) StAMPP H; , and  of the half-sib progeny are not evaluated in the field. Rather, an election , is implelection  and wereGenotyping of the UMN_C4 population and 846 progeny from the selected 15 mother genets resulted in 21,256 high-quality SNP markers that met our filtering criteria of minimum minor allele frequency of 3% and maximum missing proportion of 10%. For this study, we used a randomly selected set of 2,500 genome-wide SNP markers. The mean marker distribution was 119 per chromosome with a minimum of 53 (Chromosome 21) and maximum of 222 (Chromosome 20). Minor allele frequency for these markers ranged 0.04–0.25 with an average of 0.10.E) for the second parent , which was 0.93 for each of the maternal families. The proportion of markers that deviated from Hardy–Weinberg equilibrium were low with 102 (4.1%) markers on average per family and ranged from 92 to 124 markers (3.7–5.0%).Measures of population diversity estimated from the 2,500 SNP markers are summarized in ST) values were relatively high with an average of 0.24 and ranged from 0.19–0.28. While all families grouped together, principal component (PC) analysis indicated weak population stratification with the first two axes explaining only 3.9% of the overall genetic diversity  grouped progeny derived from a mother plant within same clusters (Genetic relationships among the sampled progeny and their mother plants as well as the whole nursery are shown in iversity . A STRUCclusters . On averm) of 1.041 and single-locus outcrossing rate (ts) of 0.997 (p), a measure of diversity of the pollen cloud received by the maternal plant, was estimated to be 0.180 and was significantly different from zero (p = 2.42E-07).High outcrossing rates were observed in the 15 IWG families with high multi-locus outcrossing rate (tof 0.997 . The ratResults of paternity assignment from CERVUS of the 846 progeny (mean of 56 per mother plant) are also summarized in n = 60, 11% of all fathers) were located in the West–Northwest direction whereas the North–Northeast direction had the least fathers . The direction of paternal plants and their distances from the maternal plants were negatively correlated and non-significantly different from zero: Pearson’s correlation coefficient r = −0.10, p = 0.16. During the week of anthesis (07/01/19–07/07/19), air movement in the East–Southwest direction was minimal (2.3 kph or 1.4 mph) yet frequent ; and the furthest father (C418S0072) in the nursery was located 27.28 m away from the mother genet C418S0295 . Mating D = 0.67112, p < 2.2E-16) between pollination distance and progeny count suggested that the effect of pollen distances on progeny frequency was non-random.The majority of the half-sib plants (60%) that fathered an offspring were located within 1.8 m of the mother plant with 40% located next (0.91 m) to the mother plant . The furpollen)2 = ½ M, where M is the average of squared distance between putative father and mother plants. In our study, this distance (σpollen) was observed to be 4.96 m. This distance was similar to our apparent mean pollination distance of 6.9 m (median = 5.6 m). Neither strong nor significant correlations were observed between trait attributes of the father genets and their success in pollination (number of progeny per father): Pearson’s correlation coefficient (r) of 0.08 for plant height, 0.08 for days to heading, and 0.06 for spring growth vigor. Likewise, poor correlations were observed between paternal traits and pollination distance: −0.10 for plant height, 0.08 for days to heading, −0.11 for spring growth vigor.We also estimated the axial standard deviation distance for pollen dispersal using the method of D, a measure of diversity per locus, was significantly (p < 0.05) different between bins 6–9 m (0.0131) and 12–15 m (0.0138) but not among the remaining bins. Shannon’s diversity index (H), which measures the overall community diversity, was similar among the bins except for the last bin that had a value close to zero. Rarefaction index, a measure of community richness, was also similar among the bins except the last bin where the value was two. A similar trend was observed for diversity estimates of the progeny fathered by the half-sib fathers as no significant differences were observed among the distance bins (Genetic distance among the progeny were not significantly different among the pollination distance bins . Nei’s Dnce bins . These ence bins .p < 0.05) from progeny in the 0–3 m bin (n = 8) in this bin.The relationship between pollination distance and trait data of the progeny was investigated by using genome-predicted trait values from a genomic selection model. Predicted trait values from a genomic selection model were used because the progeny are not evaluated in the field prior to their selection for advancement in our breeding scheme. For grain yield per spike, progeny in the furthest distance bins (21–24 and 24–27 m) were significantly different (–3 m bin . For theLolium perenne L.) with a range of 0.17–0.32 (Brachypodium sylvaticum) with value of 0.19  of 0.24 in our population which has been shown to range 0.01–0.47 in different perennial ryegrass populations  was greater than the theoretical maximum value of 1, which suggests a near-obligate outcrossing nature of the species, in accordance with the known mating behavior of IWG. Multi-locus outcrossing rate greater than 1, that is, an upward bias of tm, could result from a computational drawback where large number of DNA markers increase tm . Most fathers of the progeny were located within a short range from the mother plants, although pollen flow was recorded from longer distances as well. We observed a very high outcrossing rate with inbreeding virtually absent (< 1%). The multi-locus outcrossing rate  indicates more diversity with an increasing value of H and was nearly identical for all groups except the most distant bin that had no meaningful diversity. The rarefaction index, which is a method used to compare communities when sample sizes are different, indicated that the offspring sampled from different distance bins are quite similar to each other despite the progeny count favoring the short distance. This was true for progeny fathered by the entire nursery as well as the progeny fathered by half-sib genets adjacent to the mother plants  except for the immediate 1–2 plants . We therS and Z . While tS and Z  and is cS and Z . In coll1) of other perennial species has been found to vary depending upon the trait type and diversity of the parent population  for the aforementioned traits, which can potentially reduce genetic diversity of the progeny. As the locations of these selected mother plants can be randomly distributed in the field, we were curious to know if distances among mother and father plants had any effect on progeny diversity and trait performance. The effect of pollination distances on genetic diversity and trait performance in the progeny population  can be found at: PB conceptualized the study, collected or generated the data, performed the data analyses, and wrote the manuscript. YB contributed to the methodology and statistical analyses, helped refine result interpretation, and assisted in writing the manuscript. JA and PB acquired the funding, provided feedback on the study, and assisted in writing the manuscript. All authors contributed to the article and approved the submitted version.Funding for this study was provided by the Forever Green Initiative at the University of Minnesota through the Minnesota Department of Agriculture, General Mills Inc., and PepsiCo. The funders were not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Vitis vinifera L.) genotypes, while statistical evaluation of those has certain limitations, especially when we have no information about the traits that are discriminative to a certain sample set. High numbers of investigated characters could cause redundancy, while reducing those numbers may result in data loss. Grapevine is one of the most important horticultural crops, with many cultivars in production. The characterization of the genotypes is of undeniably high importance. In this study, we analyzed a dataset of scientific and historical importance with 125 morphological traits of 97 grapevine cultivars described by Németh in 1966. However, the traits are not independent in a set of a large number of categorical traits with too few cultivars. Therefore, the number of traits was first reduced using a simple and effective algorithm to eliminate traits with redundant information content using the asymmetric measure of association Goodman and Kruskal’s λ. We reduced the number of traits from 125 to 59 without any information loss. For the classification, we applied a random forest (RF) method. In this way, 93% of the cultivars were correctly classified using only four traits of the data set. To our knowledge, only a few studies applied a trait elimination algorithm similar to ours in ampelography that can be used for other biological data sets of similar structure. The classification results give a morphological explanation to several cultivars from the Carpathian Basin, a territory where all three Vitis vinifera L. geographical groups, occidentalis, orientalis and pontica, are represented. We found that the information-loss-avoiding data reduction method we applied in our study solved the redundancy-caused interdependencies and provided a suitable dataset for classifying grapevine genotypes. For example, this method may successfully be applied in digital image analysis-based traditional morphometric investigations in ampelography.There are hundreds of morphologic and morphometric traits available to classify and identify grapevine ( Vitis vinifera L.) is one of the most widespread horticultural crops. The domestication of this liana-like plant dates back to 6000 B.C. in the Trans-Caucasus [Grapevine : occidentalis, orientalis and pontica, according to their putative origin based on the morphological similarities of the members within each of the groups [convarietas, sub-convarietas, provarietas and sub-provarietas. Convarietas occidentalis consists of Western-European cultivars such as Pinot noir, Chardonnay, Gamay, etc. Convarietas orientalis includes the Eastern  cultivars such as Chasselas, while the group pontica consists of cultivars with their origin of Georgia, Hungary, Greece, etc. such as Furmint, Gohér, and Ezerjó.Detailed taxonomic classification of the cultivated plant dates back to Linnaeus, de Candolle, and Alefeld. The later author introduced the term ‘variety group,’ which became  variety . In the . Negrul  classifie groups . Accordie groups ,8,9 gaveCertain morphological traits such as linear, angular parameters, and weight are described as continuous variables, while a number of lobes or seeds in the berry are introduced as ordinal variables. Part of the ampelographic characteristics is discrete/nominal variables such as the leaf or berry shape. A special type of variable is the dichotomic variable, which would have two values: most frequently, the presence or absence of an organ or feature. Numerical representation of morphological data is frequently applied in ampelography to provide international standards while blurring the intra-cultivar variability. Ravaz  already Discriminant analysis (DA) is a widely applied statistical method to investigate grape species, cultivars, or clones where continuous variables are the input. For example, Preiner et al.  showed tWith the spread of remote sensing in precision viticulture (PV), machine learning (ML) methods are frequently applied in big data management and evaluation processes in the classification of cultivars based on hyperspectral image analysis , in yielconvarietas classification most successfully. Our objective was dual: (1) finding a trait selection method for data with a great number of dependent traits of ordinal and nominal types without information loss that can be step-wisely controlled by the user; (2) finding out how the selected traits can predict the three convarietas  into which the cultivars were classified by Németh, according to their geographical origin.In this study, 125 morphological traits of 97 cultivars reported by Németh [Previous research aiming at geographical origin and morphological trait-based classification is scarce in ampelography, while the information-loss-avoiding trait selection method can be used not only for this special data set but also in similar investigations.We tested the hypothesis that (1) classification result is more easily interpretable by the original traits and (2) for this, redundancy reduction is possible to carry out without variable transformation and loss of information contained by the original data.We evaluated the distribution of the categories of each trait. Among the 125 investigated traits, 52.8% (66 out of the 125) had three categories, and 21.6% had two categories. The traits with 4, 5, 6, and 7 categories were present in 11.2%, 9.6%, 0.8%, and 1.6%, respectively. The most diverse trait was the ‘density of the leaf blade’s hairs on the lower side’ with its nine categories. For example, the trait ‘young shoot’s (2–4 cm) color’ has five categories, but the trait ‘density of the young shoot’s (2–4 cm) hairs’ has only three. The numbers of categories are shown in section ‘Materials and Methods’, in We found several relations between and among the morphological traits. Relations between or among certain determined trait—predictor trait(s) ; λ = 1) are listed in pontica, 0.91 in the occidentalis and 0.86 in the orientalis group). Note that 0.86 represents the highest hit rate in the orientalis group with three predictor traits.As a second step to select the most important few traits out of the 59 remaining ones that can effectively discriminate between the three convarietas due to Németh, the RF method was carried out. The estimated proportion of the correctly classified cultivars reached 0.93 with three and four predictor traits and 0.94 with five predictor traits. Without variable selection, just 0.84 of the cultivars would be classified correctly. The best three-predictor-combination trait set is ‘density of the hairs on the lower side of the leaf,’ ‘width of the pith of cane internode,’ and ‘compactness of the unripe bunch,’ with 0.93 overall hit rate  were not examined because of the low numbers of cultivars in the samples.In this study, we set out from a numerical phenotypic dataset of about 97 grapevine cultivars characterized by Németh [The 125 morphological traits showed many interdependencies, typical in data analysis with many traits and relatively few cases. Data with related variables contain redundant information.Therefore, we started reducing the rate of redundancy contained by the traits. Dimension reduction (DR) methods like principal component analysis (PCA) or discriminant analysis (DA) are often successfully used for dimension (and interdependency) reduction preceding genotype classification according to morphology, moreover, morphometric traits , howeverVariable selection (VS) methods keep a subset of the original traits, and they are based on association or mutual information rate . Note thIn what follows, we describe a variable selection method(1)that preserves all information contained by the original data set while traits are omitted if one or more other traits completely predict them;(2)that can be step-wisely controlled by the users and(3)which can also manage asymmetric association .Vitis species and cultivars. Thus, in the case of Vitis vinifera L., e.g., the tendril’s branching is constant with two branches, in contrast to some other Vitis species with tertiary branches.We found two traits—tendril’s branching and leaf petiole’s cross section—which were constant in the whole data set, so they could not have been applied for discrimination between the groups; we omitted them. Having constant traits was not surprising since ampelographic descriptions should be suitable for all There were a lot of weaker or stronger dependencies between the 123 traits, suggesting that the number of traits could be reduced without any information loss.For computational feasibility, we chose the strategy to omit step-by-step those traits which were completely predictable by some others. First, those were predictable by a single trait, then those were predictable by two, and so on, up to four predictors.To ascertain complete predictability, we used Goodman-Kruskal’s λ , which iFirst, we detected the situations when one trait determined another λ = 1, . We founSince Goodman-Kruskal’s If a trait was completely determined by others, it was eliminated from the data set. By doing this, we reduced the number of traits step by step. We found several trait pairs, the combination of which perfectly determined another trait of the data set. Since we cannot give the whole list because of their rather large number, we give an example in In Inspecting all the twin cases (a trait determined by two other ones), we realized that we could eliminate a determined trait only if we do not need that one for predicting another trait. Finally, we could leave out the following five traits (determined by two other ones) without any information loss .We continued this process and omitted 19 further traits that were perfectly determined by a triplet of the remaining traits .In the next round, we managed to leave out the following 36 traits as they were perfectly determined by four other traits .The process can be continued until the number of traits is sufficiently low for an effective application of a classification method. We stopped the reduction process after having eliminated 66 traits.Note that although some of the relations we found might appear just in this particular dataset, the reduction was necessary to make the follow-up procedures  more effective and reliable. However, in the case of another data set, the algorithm we used to eliminate the traits with redundant information can be applied the same way.With the remaining 59 traits, we performed a random forest method.For the classification, we applied the random forest (RF) method, using the packages rpart , nnet 3, randomFRandom forest is a generalization of CART (Classification And Regression Trees ). CART iThe random forest method is a machine learning algorithm for classification and regression , i.e., fThe RF trees are random since, in each step of the algorithm, a random sample from the whole training dataset is taken with replacement. The dataset that is not used in a step (approximately 1/3) is called out-of-bag (OOB). A great advantage of RF is that it is not sensitive to outliers and missing data . SummariIn our case, since the orientalis group has only seven cultivars (out of the 97 ones), the simple random partitioning into training and test sets would be inappropriate because it might often happen that the orientalis group would lie even fully within one part . For example, for a split of a training set of 80 cultivars with a test set of 17 ones, the probability of having all orientalis cultivars into the same set is 25%, and for a split of 70 + 27 cultivars, it is still as high as 9%. If the orientalis group is fully in the test set, with no cultivar in the training set, the fitted model will be unable to explain this group correctly. On the other hand, if it is fully in the training set, then the result of cross-validation reflects solely on the classification of the other two groups. Therefore, to provide that each group is represented proportionally in both the training and test set, we decided to make the random partitioning separately by stratified sampling . We workA cross-validation run was carried out with 2000 replications. This means that the hit rates are estimated from 14,000, 10,000, and 2000 output values for the pontica, occidentalis, and orientalis groups, respectively, resulting in acceptable precision .Conjecturing that the classification power  may already be fairly acceptable with merely three predictor traits, all combinations of three traits were tried. After that, the best three trait combinations (those with a hit rate greater than 0.8) were completed with each trait set to get four predictor trait models. Finally, the best four- and five-trait combinations of models were selected and are reported here.Vitis vinifera L. is not a single species but cultivars belonging to five different species. Hegi [Vitis vinifera L. has two subspecies as subsp. sylvestris (Gmel.) and subsp. sativa (DC.). The classification of grapevine cultivars according to their geographic origin dates back to Odart [proles: orientalis, occidentalis, and pontica and classified the cultivars into these. This later theory was continued by Németh [convarietas.The origin of the grapevine and classification of the large numbers of cultivars are the focus of many studies. According to Andrasovszky , Vitis ves. Hegi  assumes to Odart , Andrasoto Odart , Marton to Odart , and Negto Odart . The laty Németh , who desFinding discriminative morphological traits and classifying cultivars according to their geographical origin has not only agro-historical importance but, according to Negrul, it would improve the success of breeding  found aCorrelation among the traits has high importance in molecular linkage maps and QTL analysis. A former study showed that certain phenological and morphological traits significantly correlate positively and negatively. Mapping of the population of F1 progenies obtained from the cross between Italia and Big Perlon revealed a positive correlation between veraison length and mean seed number and between mean berry weight and seed weight. While the correlation between mean seed number and dry matter was negative . Note thAs demonstrated in several studies, traits are usually interrelated, meaning they are not independent. It can cause redundancy and difficulties in statistical analysis . The othComparisons of the natural classification of different authors sometimes show contradictions. Lőrincz et al.  introducVitis sylvestris C.C. Gmel Hegi.) leaf samples showed high intra- and interspecific diversity. In their study, Chitwood et al. [Recent morphometric evaluations according to elliptic Fourier description outline analysis and landmark-based generalized Procrustes analysis of large numbers of grapevine and wild grape (d et al.  grouped Vitis vinifera L. geographical groups, —Negrul’s proles or Vitis vinifera L. convarietas—occidentalis, orientalis and pontica are represented. Within these geographical groups, further classifications are possible, as done by Negrul [The variable selection method we applied can be useful in general in biological classification. In the case of grapevine, the study of other datasets would be promising, especially those where genetic and morphological data are both available. The introduced result of this special dataset is particular; however, the dataset is rich in cultivars from the Carpathian Basin, especially from Hungary, a territory where all the three y Negrul  and Némey Negrul ; howeverOur study showed that variable selection from categorical ampelographic data based on Goodman-Kruskal’s


Although previous studies have shown that gut microbiota may be involved in the occurrence of deep venous thrombosis (DVT), the specific link between the two remains unclear. The present study aimed to explore this question from a genetic perspective.N = 9,059). GWAS summary data of the gut microbiota were obtained from the Flemish Gut Flora Project  and two German cohorts . All the participants were of European ancestry. Linkage disequilibrium score (LDSC) regression has great potential for analyzing the heritability of disease or character traits. LDSC regression was used to analyze the genetic correlation between DVT and the gut microbiota based on the GWAS summary data obtained from previous studies. Mendelian randomization (MR) was used to analyze the genetic causal relationship between DVT and the gut microbiota. We used the random effects inverse variance weighted, MR Egger, weighted median, simple mode, and weighted mode to perform MR analysis. We performed a sensitivity analysis of the MR analysis results by examining heterogeneity and horizontal pleiotropy.Genome-wide association study (GWAS) summary data of DVT were obtained from the UK Biobank (P = 0.022), Dialister , Streptococcus , and Lactobacillales  had suggestive genetic correlation with DVT. In addition, the MR analysis showed that Streptococcaceae had a positive genetic causal relationship with DVT . There was no heterogeneity or horizontal pleiotropy in the MR analysis (P > 0.05).Linkage disequilibrium score analysis showed that Streptococcaceae  had suggestive genetic correlations with DVT, and Streptococcaceae had a positive causal relationship with DVT. Our findings provide a new research direction for the further study of and prevention of DVT. Deep venous thrombosis (DVT) is a venous thromboembolic (VTE) disease that includes superficial thrombophlebitis and pulmonary embolism (PE). DVT most often occurs in the deep veins of the lower extremities, but it can also occur in the deep visceral veins of the upper extremities and vena cava . DVT is Venous thrombosis  is a common and serious disorder associated with both genetic and acquired risk factors. Genetic risk factors can be subdivided into strong, moderate, and weak. Strong risk factors include deficiencies in antithrombin, protein C, and protein S. Moderately strong are Factor V Leiden, prothrombin 20210A, non-O blood group, and fibrinogen 10034T. There are many weak genetic risk factors, including fibrinogen, factor XIII, and factor XI variants . DVT is Gut microbiota is a bacterial community that colonizes the human gut and is interdependent with the human body throughout life. In recent years, the gut microbiota has been found to be related to immune, metabolic, and neurological characteristics; drug metabolism; and cancer . EnvironDeep venous thrombosis and PE are common causes of morbidity and mortality in VTE . StudiesLinkage disequilibrium score (LDSC) regression has been applied to existing genome-wide association study (GWAS) summary data to assess the heritability of diseases and traits, which can correct for polygenic inheritance effects and confounding factors in GWASs. Mendelian randomization (MR) is a new strategy for investigating causation between different traits based on Mendel’s laws of inheritance . In MR sThe GWAS summary data for DVT were obtained from the UK Biobank (UK Biobank fields: 20002). In short, the UK Biobank participants were of European ancestry. The UK Biobank contains the ancestry genetic association maps for 118 non-binary traits and 660 binary traits for a total of 452,264 participants . In total, 9,059 DVT cases and 443,205 controls were included in our study. The Affymetrix UK BiLEVE Axiom and Affymetrix UK Biobank Axiom arrays were used for genotyping. We excluded individuals who were identified by the UK Biobank as outliers based on either the genotyping missingness rate or heterogeneity, whose sex inferred from the genotypes did not match their self-reported sex, and who were not of European ancestry. Finally, we removed individuals with missingness >5% across variants that passed our quality control procedure and those that had a missing phenotype for 40 or more traits. An estimated 90 million genetic variants were identified in the Haplotype Reference Consortium, 1000 Genomes, and UK10K projects. After quality control, 62,394 genotype variants and 9,113,133 variable estimates were obtained. In previous studies, all participants signed an informed consent form and obtained approval from the ethics committee. Detailed information on genotyping, estimation and quality control can be found in a previous study .N = 2,223) and two German cohorts . Previous studies have provided additional information on the age, sex, height, body mass index, and waist-to-hip ratio distribution of the FGFP cohort , where p is the minor allele frequency, the expected χ2 statistic of variant j is:The basic principle of the LDSC approach is to directly estimate heritability and genetic correlation from GWAS summary data using the deviation of the observed χfounders . Under aN is the sample size, M is the number of SNPs, such that h2/M is the average heritability explained per SNP, a measure of the contribution of confounding biases, such as cryptic relatedness and population stratification, andwhere j, which measures the amount of genetic variation tagged with j  the genetic IVs should have a strong link to the exposure; (2) the genetic IVs are not associated with confounders linked to the chosen exposure and outcome; and (3) genetic IVs influence the outcome only through exposure and not pathways .P < 1 × 10–5)  was carried out to eliminate the LD between the included IVs (P < 1 × 10––5). Fourth, the PhenoScanner database2 was used to assess whether the selected SNPs were associated with confounders  . Second,uded IVs . Third, founders . We consfounders . Fifth, P-value > 0.05 was considered to indicate no heterogeneity , MR Egger, weighted median, simple mode, and weighted mode to perform the MR analysis. Random effects IVW was the main method used, and the weighted median, simple mode, and weighted mode were used as supplementary methods. The MR analysis results were dominated by the random effects IVW. We used Cochran’s Q statistic for MR-IVW analyses and Rucker’s Q statistic for MR Egger analyses to detect heterogeneity, and ogeneity . We usedeiotropy . Becauseeiotropy . The diseiotropy .P-value in the range of 0.00068–0.05 as a suggestive association. Among the 74 gut microbiota, four taxa had suggestive genetic correlations with DVT: Streptococcaceae , Dialister , Streptococcus , and Lactobacillales   .After a series of quality controls and removing a smoking-related SNP (rs2952251), we finally obtained 16 SNPs as IVs for the MR analysis of Streptococcaceae and DVT, including three palindromic SNPs . We obtained 12 SNPs as IVs for MR analysis of Dialister and DVT, including one palindromic SNP (rs517089). We obtained 17 SNPs as IVs for the MR analysis of Streptococcus and DVT, including two palindromic SNPs (rs395407 and rs6563952). After removing a smoking-related SNP (rs2952251), we obtained 18 SNPs as IVs for the MR analysis of Lactobacillales and DVT, including four palindromic SNPs . None of the SNPs were proxied.P = 0.043, OR = 1.003) had a positive genetic causal relationship with DVT. The weighted median results also showed that Streptococcaceae  had a positive genetic causal relationship with DVT. The MR Egger, simple mode, and weighted mode analyses showed that Streptococcaceae had no genetic causal relationship with DVT (P > 0.05). In addition, random effects IVW, MR Egger, weighted median, simple mode, and weighted mode showed that Dialister, Streptococcus, and Lactobacillales had no genetic causal relationship with DVT (P > 0.05) (The random effects IVW results showed that Streptococcaceae ( > 0.05) , 3.P > 0.05). The results of the MR Egger test of horizontal pleiotropy showed that our MR analysis results had no horizontal pleiotropy (P > 0.05). The MR-PRESSO global test results also showed that our MR analysis results showed no horizontal pleiotropy (P > 0.05). The MR-PRESSO distortion test results appeared to have no outliers  is a precursor of TMAO production in the liver and is abundant in animal products such as eggs, liver, beef, and pork. The dietary supplement choline is a nutrient that contains TMA. In mice, dietary supplementation with TMAO or choline increased plasma TMAO levels, ADP-induced platelet aggregation and shortened the rate of clot formation in vivo. Unrecognized mechanistic links between specific dietary nutrients, gut microbes, platelet function, and thrombotic risk provide new potential therapeutic targets and nutritional interventions for the prevention of cardiovascular events and DVT  can differentially modulate gut microbiota based on their nature. Antidiarrheal TCMs of different natures showed distinct effects on the gut microbiota. Hot-natured TCMs have no influence on the gut microbiota, warm-natured TCMs have a moderate influence, cool-natured TCMs have a strong influence, and cold-natured TCMs substantially change the structure of the gut microbial community . Dietary and DVT . TMAO le and DVT . We specOur study analyzed genotype data from GWAS summary datasets with a large sample size. LDSC has a strong genetic estimation ability, and MR has a strong genetic causal inference ability, so the results of our study are reliable. However, this study has certain limitations. First, all subjects in this study were of European descent, and the results of this study should be interpreted with caution when extended to individuals of different ethnicities. Second, the SNP set related to the gut microbiota comes from previously published GWAS research, and the GWAS data on the gut microbiota available on different platforms are very limited; therefore, we could only analyze limited gut microbiota at certain taxonomic levels. As some gut microbiota may have been overlooked, more GWASs of the gut microbiota are needed to illustrate the interaction between gut microbiota and host genetics. Third, as the data are from different populations, the results may be affected by some confounding factors, and further research on data from the same population may be needed in the future.Based on the GWAS summary data from a large population, we analyzed the genetic correlation between DVT and the gut microbiota and found that Streptococcaceae, Dialister, Streptococcus, and Lactobacillales have suggestive genetic correlations with DVT. There was a positive genetic causal relationship between Streptococcaceae and DVT. Our results provide a new direction for further research on DVT. We will continue to study the specific relationship between these gut microbes and DVT and explore their potential value in the pathogenesis and prevention of DVT.https://broad-ukb-sumstats-us-east-1.s3.amazonaws.com/round2/additive-tsvs/20002_1094.gwas.imputed_v3.both_sexes.tsv.bgz and here: https://doi.org/10.5523/bris.22bqn399f9i432q56gt3wfhzlc.Publicly available datasets were analyzed in this study. This data can be found here: PX and MY designed the study. MY, PL, and FZ analyzed the data and interpreted the results. KX and RF provide the software support. MY wrote and edited the manuscript. PX provided the foundation support. All authors read and approved the final manuscript.