Machine learning algorithms translate big data into predictive breeding accuracy.

Statistical machine learning (ML) extracts patterns from extensive genomic, phenotypic, and environmental data. ML algorithms automatically identify relevant features and use cross-validation to ensure robust models and improve prediction reliability in new lines. Furthermore, ML analyses of genotype-by-environment (G×E) interactions can offer insights into the genetic factors that affect performance in specific environments. By leveraging historical breeding data, ML streamlines strategies and automates analyses to reveal genomic patterns. In this review we examine the transformative impact of big data, including multi-trait genomics, phenomics, and environmental covariables, on genomic-enabled prediction in plant breeding. We discuss how big data and ML are revolutionizing the field by enhancing prediction accuracy, deepening our understanding of G×E interactions, and optimizing breeding strategies through the analysis of extensive and diverse datasets.

A graph model for genomic prediction in the context of a linear mixed model framework.

Genomic selection is revolutionizing both plant and animal breeding, with its practical application depending critically on high prediction accuracy. In this study, we aimed to enhance prediction accuracy by exploring the use of graph models within a linear mixed model framework. Our investigation revealed that incorporating the graph constructed with line connections alone resulted in decreased prediction accuracy compared to conventional methods that consider only genotype effects. However, integrating both genotype effects and the graph structure led to slightly improved results over considering genotype effects alone. These findings were validated across 14 datasets commonly used in plant breeding research.

A Penalized Regression Method for Genomic Prediction Reduces Mismatch between Training and Testing Sets.

Genomic selection (GS) is changing plant breeding by significantly reducing the resources needed for phenotyping. However, its accuracy can be compromised by mismatches between training and testing sets, which impact efficiency when the predictive model does not adequately reflect the genetic and environmental conditions of the target population. To address this challenge, this study introduces a straightforward method using binary-Lasso regression to estimate ß coefficients. In this approach, the response variable assigns 1 to testing set inputs and 0 to training set inputs. Subsequently, Lasso, Ridge, and Elastic Net regression models use the inverse of these ß coefficients (in absolute values) as weights during training (WLasso, WRidge, and WElastic Net). This weighting method gives less importance to features that discriminate more between training and testing sets. The effectiveness of this method is evaluated across six datasets, demonstrating consistent improvements in terms of the normalized root mean square error. Importantly, the model's implementation is facilitated using the glmnet library, which supports straightforward integration for weighting ß coefficients.

An extended multiplicative error model of allometry: Incorporating systematic components, non-normal distributions, and piecewise heteroscedasticity.

Allometry refers to the relationship between the size of a trait and that of the whole body of an organism. Pioneering observations by Otto Snell and further elucidation by D'Arcy Thompson set the stage for its integration into Huxley's explanation of constant relative growth that epitomizes through the formula of simple allometry. The traditional method to identify such a model conforms to a regression protocol fitted in the direct scales of data. It involves Huxley's formula-systematic part and a lognormally distributed multiplicative error term. In many instances of allometric examination, the predictive strength of this paradigm is unsuitable. Established approaches to improve fit enhance the complexity of the systematic relationship while keeping the go-along normality-borne error. These extensions followed Huxley's idea that considering a biphasic allometric pattern could be necessary. However, for present data composing 10 410 pairs of measurements of individual eelgrass leaf dry weight and area, a fit relying on a biphasic systematic term and multiplicative lognormal errors barely improved correspondence measure values while maintaining a heavy tails problem. Moreover, the biphasic form and multiplicative-lognormal-mixture errors did not provide complete fit dependability either. However, updating the outline of such an error term to allow heteroscedasticity to occur in a piecewise-like mode finally produced overall fit consistency. Our results demonstrate that when attempting to achieve fit quality improvement in a Huxley's model-based multiplicative error scheme, allowing for a complex allometry form for the systematic part, a non-normal distribution-driven error term and a composite of uneven patterns to describe the heteroscedastic outline could be essential.

Feature engineering of environmental covariates improves plant genomic-enabled prediction.

Introduction: Because Genomic selection (GS) is a predictive methodology, it needs to guarantee high-prediction accuracies for practical implementations. However, since many factors affect the prediction performance of this methodology, its practical implementation still needs to be improved in many breeding programs. For this reason, many strategies have been explored to improve the prediction performance of this methodology. Methods: When environmental covariates are incorporated as inputs in the genomic prediction models, this information only sometimes helps increase prediction performance. For this reason, this investigation explores the use of feature engineering on the environmental covariates to enhance the prediction performance of genomic prediction models. Results and discussion: We found that across data sets, feature engineering helps reduce prediction error regarding only the inclusion of the environmental covariates without feature engineering by 761.625% across predictors. These results are very promising regarding the potential of feature engineering to enhance prediction accuracy. However, since a significant gain in prediction accuracy was observed in only some data sets, further research is required to guarantee a robust feature engineering strategy to incorporate the environmental covariates.

Enhancing winter wheat prediction with genomics, phenomics and environmental data.

In the realm of multi-environment prediction, when the goal is to predict a complete environment using the others as a training set, the efficiency of genomic selection (GS) falls short of expectations. Genotype by environment interaction poses a challenge in achieving high prediction accuracies. Consequently, current efforts are focused on enhancing efficiency by integrating various types of inputs, such as phenomics data, environmental information, and other omics data. In this study, we sought to evaluate the impact of incorporating environmental information into the modeling process, in addition to genomic and phenomics information. Our evaluation encompassed five data sets of soft white winter wheat, and the results revealed a significant improvement in prediction accuracy, as measured by the normalized root mean square error (NRMSE), through the integration of environmental information. Notably, there was an average gain in prediction accuracy of 49.19% in terms of NRMSE across the data sets. Moreover, the observed prediction accuracy ranged from 5.68% (data set 3) to 60.36% (data set 4), underscoring the substantial effect of integrating environmental information. By including genomic, phenomic, and environmental data in prediction models, plant breeding programs can improve selection efficiency across locations.

Data Augmentation Enhances Plant-Genomic-Enabled Predictions.

Genomic selection (GS) is revolutionizing plant breeding. However, its practical implementation is still challenging, since there are many factors that affect its accuracy. For this reason, this research explores data augmentation with the goal of improving its accuracy. Deep neural networks with data augmentation (DA) generate synthetic data from the original training set to increase the training set and to improve the prediction performance of any statistical or machine learning algorithm. There is much empirical evidence of their success in many computer vision applications. Due to this, DA was explored in the context of GS using 14 real datasets. We found empirical evidence that DA is a powerful tool to improve the prediction accuracy, since we improved the prediction accuracy of the top lines in the 14 datasets under study. On average, across datasets and traits, the gain in prediction performance of the DA approach regarding the Conventional method in the top 20% of lines in the testing set was 108.4% in terms of the NRMSE and 107.4% in terms of the MAAPE, but a worse performance was observed on the whole testing set. We encourage more empirical evaluations to support our findings.

Deep learning methods improve genomic prediction of wheat breeding.

In the field of plant breeding, various machine learning models have been developed and studied to evaluate the genomic prediction (GP) accuracy of unseen phenotypes. Deep learning has shown promise. However, most studies on deep learning in plant breeding have been limited to small datasets, and only a few have explored its application in moderate-sized datasets. In this study, we aimed to address this limitation by utilizing a moderately large dataset. We examined the performance of a deep learning (DL) model and compared it with the widely used and powerful best linear unbiased prediction (GBLUP) model. The goal was to assess the GP accuracy in the context of a five-fold cross-validation strategy and when predicting complete environments using the DL model. The results revealed the DL model outperformed the GBLUP model in terms of GP accuracy for two out of the five included traits in the five-fold cross-validation strategy, with similar results in the other traits. This indicates the superiority of the DL model in predicting these specific traits. Furthermore, when predicting complete environments using the leave-one-environment-out (LOEO) approach, the DL model demonstrated competitive performance. It is worth noting that the DL model employed in this study extends a previously proposed multi-modal DL model, which had been primarily applied to image data but with small datasets. By utilizing a moderately large dataset, we were able to evaluate the performance and potential of the DL model in a context with more information and challenging scenario in plant breeding.

Bayesian discrete lognormal regression model for genomic prediction.

KEY MESSAGE: Genomic prediction models for quantitative traits assume continuous and normally distributed phenotypes. In this research, we proposed a novel Bayesian discrete lognormal regression model. Genomic selection is a powerful tool in modern breeding programs that uses genomic information to predict the performance of individuals and select those with desirable traits. It has revolutionized animal and plant breeding, as it allows breeders to identify the best candidates without labor-intensive and time-consuming phenotypic evaluations. While several statistical models have been developed, most of them have been for quantitative continuous traits and only a few for count responses. In this paper, we propose a discrete lognormal regression model in the Bayesian context, that with a Gibbs sampler to explore the corresponding posterior distribution and make the predictions. Two datasets of resistance disease is used in the wheat crop and are then evaluated against the traditional Gaussian model and a lognormal model. The results indicate the proposed model is a competitive and natural model for predicting count genomic traits.

A marker weighting approach for enhancing within-family accuracy in genomic prediction.

Genomic selection is revolutionizing plant breeding. However, its practical implementation is still very challenging, since predicted values do not necessarily have high correspondence to the observed phenotypic values. When the goal is to predict within-family, it is not always possible to obtain reasonable accuracies, which is of paramount importance to improve the selection process. For this reason, in this research, we propose the Adversaria-Boruta (AB) method, which combines the virtues of the adversarial validation (AV) method and the Boruta feature selection method. The AB method operates primarily by minimizing the disparity between training and testing distributions. This is accomplished by reducing the weight assigned to markers that display the most significant differences between the training and testing sets. Therefore, the AB method built a weighted genomic relationship matrix that is implemented with the genomic best linear unbiased predictor (GBLUP) model. The proposed AB method is compared using 12 real data sets with the GBLUP model that uses a nonweighted genomic relationship matrix. Our results show that the proposed AB method outperforms the GBLUP by 8.6, 19.7, and 9.8% in terms of Pearson's correlation, mean square error, and normalized root mean square error, respectively. Our results support that the proposed AB method is a useful tool to improve the prediction accuracy of a complete family, however, we encourage other investigators to evaluate the AB method to increase the empirical evidence of its potential.

Multivariate Genomic Hybrid Prediction with Kernels and Parental Information.

Genomic selection (GS) plays a pivotal role in hybrid prediction. It can enhance the selection of parental lines, accurately predict hybrid performance, and harness hybrid vigor. Likewise, it can optimize breeding strategies by reducing field trial requirements, expediting hybrid development, facilitating targeted trait improvement, and enhancing adaptability to diverse environments. Leveraging genomic information empowers breeders to make informed decisions and significantly improve the efficiency and success rate of hybrid breeding programs. In order to improve the genomic ability performance, we explored the incorporation of parental phenotypic information as covariates under a multi-trait framework. Approach 1, referred to as Pmean, directly utilized parental phenotypic information without any preprocessing. While approach 2, denoted as BV, replaced the direct use of phenotypic values of both parents with their respective breeding values. While an improvement in prediction performance was observed in both approaches, with a minimum 4.24% reduction in the normalized root mean square error (NRMSE), the direct incorporation of parental phenotypic information in the Pmean approach slightly outperformed the BV approach. We also compared these two approaches using linear and nonlinear kernels, but no relevant gain was observed. Finally, our results increase empirical evidence confirming that the integration of parental phenotypic information helps increase the prediction performance of hybrids.

A novel method for genomic-enabled prediction of cultivars in new environments.

Introduction: Genomic selection (GS) has gained global importance due to its potential to accelerate genetic progress and improve the efficiency of breeding programs. Objectives of the research: In this research we proposed a method to improve the prediction accuracy of tested lines in new (untested) environments. Method-1: The new method trained the model with a modified response variable (a difference of response variables) that decreases the lack of a non-stationary distribution between the training and testing and improved the prediction accuracy. Comparing new and conventional method: We compared the prediction accuracy of the conventional genomic best linear unbiased prediction (GBLUP) model (M1) including (or not) genotype × environment interaction (GE) (M1_GE; M1_NO_GE) versus the proposed method (M2) on several data sets. Results and discussion: The gain in prediction accuracy of M2, versus M1_GE, M1_NO_GE in terms of Pearson´s correlation was of at least 4.3%, while in terms of percentage of top-yielding lines captured when was selected the 10% (Best10) and 20% (Best20) of lines was at least of 19.5%, while in terms of Normalized Root Mean Squared Error (NRMSE) was of at least of 42.29%.

Do feature selection methods for selecting environmental covariables enhance genomic prediction accuracy?

Genomic selection (GS) is transforming plant and animal breeding, but its practical implementation for complex traits and multi-environmental trials remains challenging. To address this issue, this study investigates the integration of environmental information with genotypic information in GS. The study proposes the use of two feature selection methods (Pearson's correlation and Boruta) for the integration of environmental information. Results indicate that the simple incorporation of environmental covariates may increase or decrease prediction accuracy depending on the case. However, optimal incorporation of environmental covariates using feature selection significantly improves prediction accuracy in four out of six datasets between 14.25% and 218.71% under a leave one environment out cross validation scenario in terms of Normalized Root Mean Squared Error, but not relevant gain was observed in terms of Pearson´s correlation. In two datasets where environmental covariates are unrelated to the response variable, feature selection is unable to enhance prediction accuracy. Therefore, the study provides empirical evidence supporting the use of feature selection to improve the prediction power of GS.

Partial least squares enhance multi-trait genomic prediction of potato cultivars in new environments.

It is of paramount importance in plant breeding to have methods dealing with large numbers of predictor variables and few sample observations, as well as efficient methods for dealing with high correlation in predictors and measured traits. This paper explores in terms of prediction performance the partial least squares (PLS) method under single-trait (ST) and multi-trait (MT) prediction of potato traits. The first prediction was for tested lines in tested environments under a five-fold cross-validation (5FCV) strategy and the second prediction was for tested lines in untested environments (herein denoted as leave one environment out cross validation, LOEO). There was a good performance in terms of predictions (with accuracy mostly > 0.5 for Pearson's correlation) the accuracy of 5FCV was better than LOEO. Hence, we have empirical evidence that the ST and MT PLS framework is a very valuable tool for prediction in the context of potato breeding data.

Statistical Machine-Learning Methods for Genomic Prediction Using the SKM Library.

Genomic selection (GS) is revolutionizing plant breeding. However, because it is a predictive methodology, a basic understanding of statistical machine-learning methods is necessary for its successful implementation. This methodology uses a reference population that contains both the phenotypic and genotypic information of genotypes to train a statistical machine-learning method. After optimization, this method is used to make predictions of candidate lines for which only genotypic information is available. However, due to a lack of time and appropriate training, it is difficult for breeders and scientists of related fields to learn all the fundamentals of prediction algorithms. With smart or highly automated software, it is possible for these professionals to appropriately implement any state-of-the-art statistical machine-learning method for its collected data without the need for an exhaustive understanding of statistical machine-learning methods and programing. For this reason, we introduce state-of-the-art statistical machine-learning methods using the Sparse Kernel Methods (SKM) R library, with complete guidelines on how to implement seven statistical machine-learning methods that are available in this library for genomic prediction (random forest, Bayesian models, support vector machine, gradient boosted machine, generalized linear models, partial least squares, feed-forward artificial neural networks). This guide includes details of the functions required to implement each of the methods, as well as others for easily implementing different tuning strategies, cross-validation strategies, and metrics to evaluate the prediction performance and different summary functions that compute it. A toy dataset illustrates how to implement statistical machine-learning methods and facilitate their use by professionals who do not possess a strong background in machine learning and programing.

Efficacy of plant breeding using genomic information.

Genomic selection (GS) proposed by Meuwissen et al. more than 20 years ago, is revolutionizing plant and animal breeding. Although GS has been widely accepted and applied to plant and animal breeding, there are many factors affecting its efficacy. We studied 14 real datasets to respond to the practical question of whether the accuracy of genomic prediction increases when considering genomic as compared with not using genomic. We found across traits, environments, datasets, and metrics, that the average gain in prediction accuracy when genomic information is considered was 26.31%, while only in terms of Pearson's correlation the gain was of 46.1%, while only in terms of normalized root mean squared error the gain was of 6.6%. If the quality of the makers and relatedness of the individuals increase, major gains in prediction accuracy can be obtained, but if these two factors decrease, a lower increase is possible. Finally, our findings reinforce genomic is vital for improving the prediction accuracy and, therefore, the realized genetic gain in genomic assisted plant breeding programs.

Two simple methods to improve the accuracy of the genomic selection methodology.

BACKGROUND: Genomic selection (GS) is revolutionizing plant and animal breeding. However, still its practical implementation is challenging since it is affected by many factors that when they are not under control make this methodology not effective. Also, due to the fact that it is formulated as a regression problem in general has low sensitivity to select the best candidate individuals since a top percentage is selected according to a ranking of predicted breeding values. RESULTS: For this reason, in this paper we propose two methods to improve the prediction accuracy of this methodology. One of the methods consist in reformulating the GS (nowadays formulated as a regression problem) methodology as a binary classification problem. The other consists only in a postprocessing step that adjust the threshold used for classification of the lines predicted in its original scale (continues scale) to guarantee similar sensitivity and specificity. The postprocessing method is applied for the resulting predictions after obtaining the predictions using the conventional regression model. Both methods assume that we defined with anticipation a threshold, to divide the training data as top lines and not top lines, and this threshold can be decided in terms of a quantile (for example 80%, 90%, etc.) or as the average (or maximum) of the performance of the checks. In the reformulation method it is required to label as one those lines in the training set that are equal or larger than the specified threshold and as zero otherwise. Then we train a binary classification model with the conventional inputs, but using the binary response variable in place of the continuous response variable. The training of the binary classification should be done to guarantee a more similar sensitivity and specificity, to guarantee a reasonable probability of classification of the top lines. CONCLUSIONS: We evaluated the proposed models in seven data sets and we found that the two proposed methods outperformed by large margin the conventional regression model (by 402.9% in terms of sensitivity, by 110.04% in terms of F1 score and by 70.96% in terms of Kappa coefficient, with the postprocessing methods). However, between the two proposed methods the postprocessing method was better than the reformulation as binary classification model. The simple postprocessing method to improve the accuracy of the conventional genomic regression models avoid the need to reformulate the conventional regression models as binary classification models with similar or better performance, that significantly improve the selection of the top best candidate lines. In general both proposed methods are simple and can easily be adopted for use in practical breeding programs, with the guarantee that will improve significantly the selection of the top best candidates lines.

Optimizing Sparse Testing for Genomic Prediction of Plant Breeding Crops.

While sparse testing methods have been proposed by researchers to improve the efficiency of genomic selection (GS) in breeding programs, there are several factors that can hinder this. In this research, we evaluated four methods (M1-M4) for sparse testing allocation of lines to environments under multi-environmental trails for genomic prediction of unobserved lines. The sparse testing methods described in this study are applied in a two-stage analysis to build the genomic training and testing sets in a strategy that allows each location or environment to evaluate only a subset of all genotypes rather than all of them. To ensure a valid implementation, the sparse testing methods presented here require BLUEs (or BLUPs) of the lines to be computed at the first stage using an appropriate experimental design and statistical analyses in each location (or environment). The evaluation of the four cultivar allocation methods to environments of the second stage was done with four data sets (two large and two small) under a multi-trait and uni-trait framework. We found that the multi-trait model produced better genomic prediction (GP) accuracy than the uni-trait model and that methods M3 and M4 were slightly better than methods M1 and M2 for the allocation of lines to environments. Some of the most important findings, however, were that even under a scenario where we used a training-testing relation of 15-85%, the prediction accuracy of the four methods barely decreased. This indicates that genomic sparse testing methods for data sets under these scenarios can save considerable operational and financial resources with only a small loss in precision, which can be shown in our cost-benefit analysis.

Multimodal deep learning methods enhance genomic prediction of wheat breeding.

While several statistical machine learning methods have been developed and studied for assessing the genomic prediction (GP) accuracy of unobserved phenotypes in plant breeding research, few methods have linked genomics and phenomics (imaging). Deep learning (DL) neural networks have been developed to increase the GP accuracy of unobserved phenotypes while simultaneously accounting for the complexity of genotype-environment interaction (GE); however, unlike conventional GP models, DL has not been investigated for when genomics is linked with phenomics. In this study we used 2 wheat data sets (DS1 and DS2) to compare a novel DL method with conventional GP models. Models fitted for DS1 were GBLUP, gradient boosting machine (GBM), support vector regression (SVR) and the DL method. Results indicated that for 1 year, DL provided better GP accuracy than results obtained by the other models. However, GP accuracy obtained for other years indicated that the GBLUP model was slightly superior to the DL. DS2 is comprised only of genomic data from wheat lines tested for 3 years, 2 environments (drought and irrigated) and 2-4 traits. DS2 results showed that when predicting the irrigated environment with the drought environment, DL had higher accuracy than the GBLUP model in all analyzed traits and years. When predicting drought environment with information on the irrigated environment, the DL model and GBLUP model had similar accuracy. The DL method used in this study is novel and presents a strong degree of generalization as several modules can potentially be incorporated and concatenated to produce an output for a multi-input data structure.

Sparse multi-trait genomic prediction under balanced incomplete block design.

Sparse testing is essential to increase the efficiency of the genomic selection methodology, as the same efficiency (in this case prediction power) can be obtained while using less genotypes evaluated in the fields. For this reason, it is important to evaluate the existing methods for performing the allocation of lines to environments. With this goal, four methods (M1-M4) to allocate lines to environments were evaluated under the context of a multi-trait genomic prediction problem: M1 denotes the allocation of a fraction (subset) of lines in all locations, M2 denotes the allocation of a fraction of lines with some shared lines in locations but not arranged based on the balanced incomplete block design (BIBD) principle, M3 denotes the random allocation of a subset of lines to locations, and M4 denotes the allocation of a subset of lines to locations using the BIBD principle. The evaluation was done using seven real multi-environment data sets common in plant breeding programs. We found that the best method was M4 and the worst was M1, while no important differences were found between M3 and M4. We concluded that M4 and M3 are efficient in the context of sparse testing for multi-trait prediction.