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The use of plant genetic resources (PGR)-wild relatives, landraces, and isolated breeding gene pools-has had substantial impacts on wheat breeding for resistance to biotic and abiotic stresses, while increasing nutritional value, end-use quality, and grain yield. In the Global South, post-Green Revolution genetic yield gains are generally achieved with minimal additional inputs. As a result, production has increased, and millions of hectares of natural ecosystems have been spared. Without PGR-derived disease resistance, fungicide use would have easily doubled, massively increasing selection pressure for fungicide resistance. It is estimated that in wheat, a billion liters of fungicide application have been avoided just since 2000. This review presents examples of successful use of PGR including the relentless battle against wheat rust epidemics/pandemics, defending against diseases that jump species barriers like blast, biofortification giving nutrient-dense varieties and the use of novel genetic variation for improving polygenic traits like climate resilience. Crop breeding genepools urgently need to be diversified to increase yields across a range of environments (>200 Mha globally), under less predictable weather and biotic stress pressure, while increasing input use efficiency. Given that the ~0.8 m PGR in wheat collections worldwide are relatively untapped and massive impacts of the tiny fraction studied, larger scale screenings and introgression promise solutions to emerging challenges, facilitated by advanced phenomic and genomic tools. The first translocations in wheat to modify rhizosphere microbiome interaction (reducing biological nitrification, reducing greenhouse gases, and increasing nitrogen use efficiency) is a landmark proof of concept. Phenomics and next-generation sequencing have already elucidated exotic haplotypes associated with biotic and complex abiotic traits now mainstreamed in breeding. Big data from decades of global yield trials can elucidate the benefits of PGR across environments. This kind of impact cannot be achieved without widescale sharing of germplasm and other breeding technologies through networks and public-private partnerships in a pre-competitive space., (© 2024 The Author(s). Global Change Biology published by John Wiley & Sons Ltd.)

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 β 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 β 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 β coefficients.

Selecting and mating parents in conventional phenotypic and genomic selection are crucial. Plant breeding programs aim to improve the economic value of crops, considering multiple traits simultaneously. When traits are negatively correlated and/or when there are missing records in some traits, selection becomes more complex. To address this problem, we propose a multitrait selection approach using the Multitrait Parental Selection (MPS) R package-an efficient tool for genetic improvement, precision breeding, and conservation genetics. The package employs Bayesian optimization algorithms and three loss functions (Kullback-Leibler, Energy Score, and Multivariate Asymmetric Loss) to identify parental candidates with desirable traits. The software's functionality includes three main functions-EvalMPS, FastMPS, and ApproxMPS-catering to different data availability scenarios. Through the presented application examples, the MPS R package proves effective in multitrait genomic selection, enabling breeders to make informed decisions and achieve strong performance across multiple traits., (© 2024 International Maize and Wheat Organization (CIMMYT). The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Genomic selection, the application of genomic prediction (GP) models to select candidate individuals, has significantly advanced in the past two decades, effectively accelerating genetic gains in plant breeding. This article provides a holistic overview of key factors that have influenced GP in plant breeding during this period. We delved into the pivotal roles of training population size and genetic diversity, and their relationship with the breeding population, in determining GP accuracy. Special emphasis was placed on optimizing training population size. We explored its benefits and the associated diminishing returns beyond an optimum size. This was done while considering the balance between resource allocation and maximizing prediction accuracy through current optimization algorithms. The density and distribution of single-nucleotide polymorphisms, level of linkage disequilibrium, genetic complexity, trait heritability, statistical machine-learning methods, and non-additive effects are the other vital factors. Using wheat, maize, and potato as examples, we summarize the effect of these factors on the accuracy of GP for various traits. The search for high accuracy in GP-theoretically reaching one when using the Pearson's correlation as a metric-is an active research area as yet far from optimal for various traits. We hypothesize that with ultra-high sizes of genotypic and phenotypic datasets, effective training population optimization methods and support from other omics approaches (transcriptomics, metabolomics and proteomics) coupled with deep-learning algorithms could overcome the boundaries of current limitations to achieve the highest possible prediction accuracy, making genomic selection an effective tool in plant breeding., (Copyright © 2024 The Author. Published by Elsevier Inc. All rights reserved.)

Genomic prediction relates a set of markers to variability in observed phenotypes of cultivars and allows for the prediction of phenotypes or breeding values of genotypes on unobserved individuals. Most genomic prediction approaches predict breeding values based solely on additive effects. However, the economic value of wheat lines is not only influenced by their additive component but also encompasses a non-additive part (e.g., additive × additive epistasis interaction). In this study, genomic prediction models were implemented in three target populations of environments (TPE) in South Asia. Four models that incorporate genotype × environment interaction (G × E) and genotype × genotype (GG) were tested: Factor Analytic (FA), FA with genomic relationship matrix (FA + G), FA with epistatic relationship matrix (FA + GG), and FA with both genomic and epistatic relationship matrices (FA + G + GG). Results show that the FA + G and FA + G + GG models displayed the best and a similar performance across all tests, leading us to infer that the FA + G model effectively captures certain epistatic effects. The wheat lines tested in sites in different TPE were predicted with different precisions depending on the cross-validation employed. In general, the best prediction accuracy was obtained when some lines were observed in some sites of particular TPEs and the worse genomic prediction was observed when wheat lines were never observed in any site of one TPE.

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., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

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., (© 2023 The Authors. The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

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., (© 2023 The Authors. The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

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.

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.

Genomic prediction is revolutionizing plant breeding since candidate genotypes can be selected without the need to measure their trait in the field. When a reference population contains both phenotypic and genotypic information, it is trained by a statistical machine learning method that is subsequently used for making predictions of breeding or phenotypic values of candidate genotypes that were only genotyped. Nevertheless, the successful implementation of the genomic selection (GS) methodology depends on many factors. One key factor is the type of statistical machine learning method used since some are unable to capture nonlinear patterns available in the data. While kernel methods are powerful statistical machine learning algorithms that capture complex nonlinear patterns in the data, their successful implementation strongly depends on the careful tuning process of the involved hyperparameters. As such, in this paper we compare three methods of tuning (manual tuning, grid search, and Bayesian optimization) for the Gaussian kernel under a Bayesian best linear unbiased predictor model. We used six real datasets of wheat (Triticum aestivum L.) to compare the three strategies of tuning. We found that if we want to obtain the major benefits of using Gaussian kernels, it is very important to perform a careful tuning process. The best prediction performance was observed when the tuning process was performed with grid search and Bayesian optimization. However, we did not observe relevant differences between the grid search and Bayesian optimization approach. The observed gains in terms of prediction performance were between 2.1% and 27.8% across the six datasets under study.

The success of genomic selection (GS) in breeding schemes relies on its ability to provide accurate predictions of unobserved lines at early stages. Multigeneration data provides opportunities to increase the training data size and thus, the likelihood of extracting useful information from ancestors to improve prediction accuracy. The genomic best linear unbiased predictions (GBLUPs) are performed by borrowing information through kinship relationships between individuals. Multigeneration data usually becomes heterogeneous with complex family relationship patterns that are increasingly entangled with each generation. Under these conditions, historical data may not be optimal for model training as the accuracy could be compromised. The sparse selection index (SSI) is a method for training set (TRN) optimization, in which training individuals provide predictions to some but not all predicted subjects. We added an additional trimming process to the original SSI (trimmed SSI) to remove less important training individuals for prediction. Using a large multigeneration (8 yr) wheat (Triticum aestivum L.) grain yield dataset (n = 68,836), we found increases in accuracy as more years are included in the TRN, with improvements of ∼0.05 in the GBLUP accuracy when using 5 yr of historical data relative to when using only 1 yr. The SSI method showed a small gain over the GBLUP accuracy but with an important reduction on the TRN size. These reduced TRNs were formed with a similar number of subjects from each training generation. Our results suggest that the SSI provides a more stable ranking of genotypes than the GBLUP as the TRN becomes larger., (© 2022 International Maize and Wheat Improvement Center (CIMMYT). The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Genomic selection (GS) is a predictive methodology that is changing plant breeding. Genomic selection trains a statistical machine-learning model using available phenotypic and genotypic data with which predictions are performed for individuals that were only genotyped. For this reason, some statistical machine-learning methods are being implemented in GS, but in order to improve the selection of new genotypes early in the prediction process, the exploration of new statistical machine-learning algorithms must continue. In this paper, we performed a benchmarking study between the Bayesian threshold genomic best linear unbiased predictor model (TGBLUP; popular in GS) and the gradient boosting machine (GBM). This comparison was done using four real wheat (Triticum aestivum L.) data sets with categorical traits measured in terms of two metrics: the proportion of cases correctly classified (PCCC) and the Kappa coefficient in the testing set. Under 10 random partitions with four different sizes of testing proportions (20, 40, 60, and 80%), we compared the two algorithms and found that in three of the four data sets, the GBM outperformed the TGBLUP model in terms of both metrics (PCCC and Kappa coefficient). In the larger data sets (Data Sets 3 and 4), the gain in terms of prediction accuracy of the GBM was considerably significant. For this reason, we encourage more research using the GBM in GS to evaluate its virtues in terms of prediction performance in the context of GS., (© 2022 INTERNATIONAL MAIZE AND WHEAT IMPROVEMENT CENTER (CIMMYT). The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Key Message: Sparse testing using genomic prediction can be efficiently used to increase the number of testing environments while maintaining selection intensity in the early yield testing stage without increasing the breeding budget. Sparse testing using genomic prediction enables expanded use of selection environments in early-stage yield testing without increasing phenotyping cost. We evaluated different sparse testing strategies in the yield testing stage of a CIMMYT spring wheat breeding pipeline characterized by multiple populations each with small family sizes of 1-9 individuals. Our results indicated that a substantial overlap between lines across environments should be used to achieve optimal prediction accuracy. As sparse testing leverages information generated within and across environments, the genetic correlations between environments and genomic relationships of lines across environments were the main drivers of prediction accuracy in multi-environment yield trials. Including information from previous evaluation years did not consistently improve the prediction performance. Genomic best linear unbiased prediction was found to be the best predictor of true breeding value, and therefore, we propose that it should be used as a selection decision metric in the early yield testing stages. We also propose it as a proxy for assessing prediction performance to mirror breeder's advancement decisions in a breeding program so that it can be readily applied for advancement decisions by breeding programs., (© 2022. The Author(s).)

Genomic selection (GS) is a predictive methodology that trains statistical machine-learning models with a reference population that is used to perform genome-enabled predictions of new lines. In plant breeding, it has the potential to increase the speed and reduce the cost of selection. However, to optimize resources, sparse testing methods have been proposed. A common approach is to guarantee a proportion of nonoverlapping and overlapping lines allocated randomly in locations, that is, lines appearing in some locations but not in all. In this study we propose using incomplete block designs (IBD), principally, for the allocation of lines to locations in such a way that not all lines are observed in all locations. We compare this allocation with a random allocation of lines to locations guaranteeing that the lines are allocated to the same number of locations as under the IBD design. We implemented this benchmarking on several crop data sets under the Bayesian genomic best linear unbiased predictor (GBLUP) model, finding that allocation under the principle of IBD outperformed random allocation by between 1.4% and 26.5% across locations, traits, and data sets in terms of mean square error. Although a wide range of performance improvements were observed, our results provide evidence that using IBD for the allocation of lines to locations can help improve predictive performance compared with random allocation. This has the potential to be applied to large-scale plant breeding programs., (© 2022 International Maize and Wheat Improvement Center (CIMMYT). The Plant Genome published by Wiley Periodicals, LLC. on behalf of Crop Science Society of America.)

Crop production systems need to expand their outputs sustainably to feed a burgeoning human population. Advances in genome sequencing technologies combined with efficient trait mapping procedures accelerate the availability of beneficial alleles for breeding and research. Enhanced interoperability between different omics and phenotyping platforms, leveraged by evolving machine learning tools, will help provide mechanistic explanations for complex plant traits. Targeted and rapid assembly of beneficial alleles using optimized breeding strategies and precise genome editing techniques could deliver ideal crops for the future. Realizing desired productivity gains in the field is imperative for securing an adequate future food supply for 10 billion people., Competing Interests: Declaration of interests No interests are declared., (Copyright © 2021 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Sparse testing in genome-enabled prediction in plant breeding can be emulated throughout different line allocations where some lines are observed in all environments (overlap) and others are observed in only one environment (nonoverlap). We studied three general cases of the composition of the sparse testing allocation design for genome-enabled prediction of wheat (Triticum aestivum L.) breeding: (a) completely nonoverlapping wheat lines in environments, (b) completely overlapping wheat lines in all environments, and (c) a proportion of nonoverlapping/overlapping wheat lines allocated in the environments. We also studied several cases in which the size of the testing population was systematically decreased. The study used three extensive wheat data sets (W1, W2, and W3). Three different genome-enabled prediction models (M1-M3) were used to study the effect of the sparse testing in terms of the genomic prediction accuracy. Model M1 included only main effects of environments and lines; M2 included main effects of environments, lines, and genomic effects; whereas the remaining model (M3) also incorporated the genomic × environment interaction (GE). The results show that the GE component of the genome-based model M3 captures a larger genetic variability than the main genomic effects term from models M1 and M2. In addition, model M3 provides higher prediction accuracy than models M1 and M2 for the same allocation designs (different combinations of nonoverlapping/overlapping lines in environments and training set sizes). Overlapped sets of 30-50 lines in all the environments provided stable genomic-enabled prediction accuracy. Reducing the size of the testing populations under all allocation designs decreases the prediction accuracy, which recovers when more lines are tested in all environments. Model M3 offers the possibility of maintaining the prediction accuracy throughout both extreme situations of all nonoverlapping lines and all overlapping lines., (© 2021 The Authors. The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Genomic selection in maize (Zea mays L.) has been one factor that has increased the rate of genetic gain when compared with other cereals. However, the technological foundations in maize also exist in other cereal crops that would allow prediction of hybrid performance based on general (GCA) and specific (SCA) combining abilities applied through genomic-enabled prediction models. Further, the incorporation of genotype × environment (G × E) interaction effects present an opportunity to deploy hybrids to targeted environments. To test these concepts, a factorial mating design of elite yet divergent grain sorghum lines generated hybrids for evaluation. Inbred parents were genotyped, and markers were used to assess population structure and develop the genomic relationship matrix (GRM). Grain yield, height, and days to anthesis were collected for hybrids in replicated trials, and best linear unbiased estimates were used to train classical GCA-SCA-based and genomic (GB) models under a hierarchical Bayesian framework. To incorporate population structure, GB was fitted using the GRM of both parents and hybrids. For GB models, G × E interaction effects were included by the Hadamard product between GRM and environments. A leave-one-out cross-validation scheme was used to study the prediction capacity of models. Classical and genomic models effectively predicted hybrid performance and prediction accuracy increased by including genomic data. Genomic models effectively partitioned the variation due to GCA, SCA, and their interaction with the environment. A strategy to implement genomic selection for hybrid sorghum [Sorghum bicolor (L.) Moench] breeding is presented herein., (© 2021 The Authors. The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Implementing genomic-based prediction models in genomic selection requires an understanding of the measures for evaluating prediction accuracy from different models and methods using multi-trait data. In this study, we compared prediction accuracy using six large multi-trait wheat data sets (quality and grain yield). The data were used to predict 1 year (testing) from the previous year (training) to assess prediction accuracy using four different prediction models. The results indicated that the conventional Pearson's correlation between observed and predicted values underestimated the true correlation value, whereas the corrected Pearson's correlation calculated by fitting a bivariate model was higher than the division of the Pearson's correlation by the squared root of the heritability across traits, by 2.53-11.46%. Across the datasets, the corrected Pearson's correlation was higher than the uncorrected by 5.80-14.01%. Overall, we found that for grain yield the prediction performance was highest using a multi-trait compared to a single-trait model. The higher the absolute genetic correlation between traits the greater the benefits of multi-trait models for increasing the genomic-enabled prediction accuracy of traits., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

The International Maize and Wheat Improvement Center develops and annually distributes elite wheat lines to public and private breeders worldwide. Trials have been created in multiple sites over many years to assess the lines' performance for use in breeding and release as varieties, and to provide iterative feedback on refining breeding strategies 1 . The collaborator test sites are experiencing climate change, with new implications for how wheat genotypes are bred and selected 2 . Using a standard quantitative genetic model to analyse four International Maize and Wheat Improvement Center global spring wheat trial datasets, we examine how genotype-environment interactions have changed over recent decades. Notably, crossover interactions-a critical indicator of changes in the ranking of cultivar performance in different environments-have increased over time. Climatic factors explained over 70% of the year-to-year variability in crossover interactions for yield. Yield responses of all lines in trial environments from 1980 to 2018 revealed that climate change has increased the ranking change in breeding targeted to favourable environments by ~15%, while it has maintained or reduced the ranking change in breeding targeted to heat and drought stress by up to 13%. Genetic improvement has generally increased crossover interactions, particularly for wheat targeted to high-yielding environments. However, the latest wheat germplasm developed under heat stress was better adapted and more stable, partly offsetting the increase in ranking changes under the warmer climate., (© 2021. The Author(s), under exclusive licence to Springer Nature Limited.)

Despite being the world's most widely grown crop, research investments in wheat (Triticum aestivum and Triticum durum) fall behind those in other staple crops. Current yield gains will not meet 2050 needs, and climate stresses compound this challenge. However, there is good evidence that heat and drought resilience can be boosted through translating promising ideas into novel breeding technologies using powerful new tools in genetics and remote sensing, for example. Such technologies can also be applied to identify climate resilience traits from among the vast and largely untapped reserve of wheat genetic resources in collections worldwide. This review describes multi-pronged research opportunities at the focus of the Heat and Drought Wheat Improvement Consortium (coordinated by CIMMYT), which together create a pipeline to boost heat and drought resilience, specifically: improving crop design targets using big data approaches; developing phenomic tools for field-based screening and research; applying genomic technologies to elucidate the bases of climate resilience traits; and applying these outputs in developing next-generation breeding methods. The global impact of these outputs will be validated through the International Wheat Improvement Network, a global germplasm development and testing system that contributes key productivity traits to approximately half of the global wheat-growing area., (© The Author(s) 2021. Published by Oxford University Press on behalf of the Society for Experimental Biology.)

Key Message: Genome-wide association revealed that resistance to Striga hermonthica is influenced by multiple genomic regions with moderate effects. It is possible to increase genetic gains from selection for Striga resistance using genomic prediction. Striga hermonthica (Del.) Benth., commonly known as the purple witchweed or giant witchweed, is a serious problem for maize-dependent smallholder farmers in sub-Saharan Africa. Breeding for Striga resistance in maize is complicated due to limited genetic variation, complexity of resistance and challenges with phenotyping. This study was conducted to (i) evaluate a set of diverse tropical maize lines for their responses to Striga under artificial infestation in three environments in Kenya; (ii) detect quantitative trait loci associated with Striga resistance through genome-wide association study (GWAS); and (iii) evaluate the effectiveness of genomic prediction (GP) of Striga-related traits. An association mapping panel of 380 inbred lines was evaluated in three environments under artificial Striga infestation in replicated trials and genotyped with 278,810 single-nucleotide polymorphism (SNP) markers. Genotypic and genotype x environment variations were significant for measured traits associated with Striga resistance. Heritability estimates were moderate (0.42) to high (0.92) for measured traits. GWAS revealed 57 SNPs significantly associated with Striga resistance indicator traits and grain yield (GY) under artificial Striga infestation with low to moderate effect. A set of 32 candidate genes physically near the significant SNPs with roles in plant defense against biotic stresses were identified. GP with different cross-validations revealed that prediction of performance of lines in new environments is better than prediction of performance of new lines for all traits. Predictions across environments revealed high accuracy for all the traits, while inclusion of GWAS-detected SNPs led to slight increase in the accuracy. The item-based collaborative filtering approach that incorporates related traits evaluated in different environments to predict GY and Striga-related traits outperformed GP for Striga resistance indicator traits. The results demonstrated the polygenic nature of resistance to S. hermonthica, and that implementation of GP in Striga resistance breeding could potentially aid in increasing genetic gain for this important trait.

In all breeding programs, the decision about which individuals to select and intermate to form the next selection cycle is crucial. The improvement of genetic stocks requires considering multiple traits simultaneously, given that economic value and net genetic merits depend on many traits; therefore, with the advance of computational and statistical tools and genomic selection (GS), researchers are focusing on multi-trait selection. Selection of the best individuals is difficult, especially in traits that are antagonistically correlated, where improvement in one trait might imply a reduction in other(s). There are approaches that facilitate multi-trait selection, and recently a Bayesian decision theory (BDT) has been proposed. Parental selection using BDT has the potential to be effective in multi-trait selection given that it summarizes all relevant quantitative genetic concepts such as heritability, response to selection and the structure of dependence between traits (correlation). In this study, we applied BDT to provide a treatment for the complexity of multi-trait parental selection using three multivariate loss functions (LF), Kullback-Leibler (KL), Energy Score, and Multivariate Asymmetric Loss (MALF), to select the best-performing parents for the next breeding cycle in two extensive real wheat data sets. Results show that the high ranking lines in genomic estimated breeding value (GEBV) for certain traits did not always have low values for the posterior expected loss (PEL). For both data sets, the KL LF gave similar importance to all traits including grain yield. In contrast, the Energy Score and MALF gave a better performance in three of four traits that were different than grain yield. The BDT approach should help breeders to decide based not only on the GEBV per se of the parent to be selected, but also on the level of uncertainty according to the Bayesian paradigm., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

Cultivated bread wheat (Triticum aestivum L.) is an allohexaploid species resulting from the natural hybridization and chromosome doubling of allotetraploid durum wheat (T. turgidum) and a diploid goatgrass Aegilops tauschii Coss (Ae. tauschii). Synthetic hexaploid wheat (SHW) was developed through the interspecific hybridization of Ae. tauschii and T. turgidum, and then crossed to T. aestivum to produce synthetic hexaploid wheat derivatives (SHWDs). Owing to this founding variability, one may infer that the genetic variances of native wild populations vs improved wheat may vary due to their differential origin and evolutionary history. In this study, we partitioned the additive variance of SHW and SHWD with respect to their breed origin by fitting a hierarchical Bayesian model with heterogeneous covariance structure for breeding values to estimate variance components for each breed category, and segregation variance. Two data sets were used to test the proposed hierarchical Bayesian model, one from a multi-year multi-location field trial of SHWD and the other comprising the two species of SHW. For the SHWD, the Bayesian estimates of additive variances of grain yield from each breed category were similar for T. turgidum and Ae. tauschii, but smaller for T. aestivum. Segregation variances between Ae. tauschii-T. aestivum and T. turgidum-T. aestivum populations explained a sizable proportion of the phenotypic variance. Bayesian additive variance components and the Best Linear Unbiased Predictors (BLUPs) estimated by two well-known software programs were similar for multi-breed origin and for the sum of the breeding values by origin for both data sets. Our results support the suitability of models with heterogeneous additive genetic variances to predict breeding values in wheat crosses with variable ploidy levels., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

Genomic selection (GS) is revolutionizing plant breeding since the selection process is done with the help of statistical machine learning methods. A model is trained with a reference population and then it is used for predicting the candidate individuals available in the testing set. However, given that breeding phenotypic values are very noisy, new models must be able to integrate not only genotypic and environmental data but also high-resolution images that have been collected by breeders with advanced image technology. For this reason, this paper explores the use of generalized Poisson regression (GPR) for genome-enabled prediction of count phenotypes using genomic and hyperspectral images. The GPR model allows integrating input information of many sources like environments, genomic data, high resolution data, and interaction terms between these three sources. We found that the best prediction performance was obtained when the three sources of information were taken into account in the predictor, and those measures of high-resolution images close to the harvest day provided the best prediction performance., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

Key Message: Historical data from breeding programs can be efficiently used to improve genomic selection accuracy, especially when the training set is optimized to subset individuals most informative of the target testing set. The current strategy for large-scale implementation of genomic selection (GS) at the International Maize and Wheat Improvement Center (CIMMYT) global maize breeding program has been to train models using information from full-sibs in a "test-half-predict-half approach." Although effective, this approach has limitations, as it requires large full-sib populations and limits the ability to shorten variety testing and breeding cycle times. The primary objective of this study was to identify optimal experimental and training set designs to maximize prediction accuracy of GS in CIMMYT's maize breeding programs. Training set (TS) design strategies were evaluated to determine the most efficient use of phenotypic data collected on relatives for genomic prediction (GP) using datasets containing 849 (DS1) and 1389 (DS2) DH-lines evaluated as testcrosses in 2017 and 2018, respectively. Our results show there is merit in the use of multiple bi-parental populations as TS when selected using algorithms to maximize relatedness between the training and prediction sets. In a breeding program where relevant past breeding information is not readily available, the phenotyping expenditure can be spread across connected bi-parental populations by phenotyping only a small number of lines from each population. This significantly improves prediction accuracy compared to within-population prediction, especially when the TS for within full-sib prediction is small. Finally, we demonstrate that prediction accuracy in either sparse testing or "test-half-predict-half" can further be improved by optimizing which lines are planted for phenotyping and which lines are to be only genotyped for advancement based on GP.

Wheat quality improvement is an important objective in all wheat breeding programs. However, due to the cost, time and quantity of seed required, wheat quality is typically analyzed only in the last stages of the breeding cycle on a limited number of samples. The use of genomic prediction could greatly help to select for wheat quality more efficiently by reducing the cost and time required for this analysis. Here were evaluated the prediction performances of 13 wheat quality traits under two multi-trait models (Bayesian multi-trait multi-environment [BMTME] and multi-trait ridge regression [MTR]) using five data sets of wheat lines evaluated in the field during two consecutive years. Lines in the second year (testing) were predicted using the quality information obtained in the first year (training). For most quality traits were found moderate to high prediction accuracies, suggesting that the use of genomic selection could be feasible. The best predictions were obtained with the BMTME model in all traits and the worst with the MTR model. The best predictions with the BMTME model under the mean arctangent absolute percentage error (MAAPE) were for test weight across the five data sets, whereas the worst predictions were for the alveograph trait ALVPL. In contrast, under Pearson's correlation, the best predictions depended on the data set. The results obtained suggest that the BMTME model should be preferred for multi-trait prediction analyses. This model allows to obtain not only the correlation among traits, but also the correlation among environments, helping to increase the prediction accuracy., (© 2020 The Authors. The Plant Genome published by Wiley Periodicals, Inc. on behalf of Crop Science Society of America.)

Key Message: Comparative assessment identified naïve interaction model, and naïve and informed interaction GS models suitable for achieving higher prediction accuracy in groundnut keeping in mind the high genotype × environment interaction for complex traits. Genomic selection (GS) can be an efficient and cost-effective breeding approach which captures both small- and large-effect genetic factors and therefore promises to achieve higher genetic gains for complex traits such as yield and oil content in groundnut. A training population was constituted with 340 elite lines followed by genotyping with 58 K 'Axiom_Arachis' SNP array and phenotyping for key agronomic traits at three locations in India. Four GS models were tested using three different random cross-validation schemes (CV0, CV1 and CV2). These models are: (1) model 1 (M1 = E + L) which includes the main effects of environment (E) and line (L); (2) model 2 (M2 = E + L + G) which includes the main effects of markers (G) in addition to E and L; (3) model 3 (M3 = E + L + G + GE), a naïve interaction model; and (4) model 4 (E + L + G + LE + GE), a naïve and informed interaction model. Prediction accuracy estimated for four models indicated clear advantage of the inclusion of marker information which was reflected in better prediction accuracy achieved with models M2, M3 and M4 as compared to M1 model. High prediction accuracies (> 0.600) were observed for days to 50% flowering, days to maturity, hundred seed weight, oleic acid, rust@90 days, rust@105 days and late leaf spot@90 days, while medium prediction accuracies (0.400-0.600) were obtained for pods/plant, shelling  %, and total yield/plant. Assessment of comparative prediction accuracy for different GS models to perform selection for untested genotypes, and unobserved and unevaluated environments provided greater insights on potential application of GS breeding in groundnut.

Key Message: Genomic selection with a multiple-year training population dataset could accelerate early-stage testcross testing by skipping the first-stage yield testing, which significantly saves the time and cost of early-stage testcross testing. With the development of doubled haploid (DH) technology, the main task for a maize breeder is to estimate the breeding values of thousands of DH lines annually. In early-stage testcross testing, genomic selection (GS) offers the opportunity of replacing expensive multiple-environment phenotyping and phenotypic selection with lower-cost genotyping and genomic estimated breeding value (GEBV)-based selection. In the present study, a total of 1528 maize DH lines, phenotyped in multiple-environment trials in three consecutive years and genotyped with a low-cost per-sample genotyping platform of rAmpSeq, were used to explore how to implement GS to accelerate early-stage testcross testing. Results showed that the average prediction accuracy estimated from the cross-validation schemes was above 0.60 across all the scenarios. The average prediction accuracies estimated from the independent validation schemes ranged from 0.23 to 0.32 across all the scenarios, when the one-year datasets were used as training population (TRN) to predict the other year data as testing population (TST). The average prediction accuracies increased to a range from 0.31 to 0.42 across all the scenarios, when the two-years datasets were used as TRN. The prediction accuracies increased to a range from 0.50 to 0.56, when the TRN consisted of two-years of breeding data and 50% of third year's data converted from TST to TRN. This information showed that GS with a multiple-year TRN set offers the opportunity to accelerate early-stage testcross testing by skipping the first-stage yield testing, which significantly saves the time and cost of early-stage testcross testing.

"Sparse testing" refers to reduced multi-environment breeding trials in which not all genotypes of interest are grown in each environment. Using genomic-enabled prediction and a model embracing genotype × environment interaction (GE), the non-observed genotype-in-environment combinations can be predicted. Consequently, the overall costs can be reduced and the testing capacities can be increased. The accuracy of predicting the unobserved data depends on different factors including (1) how many genotypes overlap between environments, (2) in how many environments each genotype is grown, and (3) which prediction method is used. In this research, we studied the predictive ability obtained when using a fixed number of plots and different sparse testing designs. The considered designs included the extreme cases of (1) no overlap of genotypes between environments, and (2) complete overlap of the genotypes between environments. In the latter case, the prediction set fully consists of genotypes that have not been tested at all. Moreover, we gradually go from one extreme to the other considering (3) intermediates between the two previous cases with varying numbers of different or non-overlapping (NO)/overlapping (O) genotypes. The empirical study is built upon two different maize hybrid data sets consisting of different genotypes crossed to two different testers (T1 and T2) and each data set was analyzed separately. For each set, phenotypic records on yield from three different environments are available. Three different prediction models were implemented, two main effects models ( M1 and M2 ), and a model ( M3) including GE. The results showed that the genome-based model including GE ( M3 ) captured more phenotypic variation than the models that did not include this component. Also, M3 provided higher prediction accuracy than models M1 and M2 for the different allocation scenarios. Reducing the size of the calibration sets decreased the prediction accuracy under all allocation designs with M3 being the less affected model; however, using the genome-enabled models ( i.e. , M2 and M3 ) the predictive ability is recovered when more genotypes are tested across environments. Our results indicate that a substantial part of the testing resources can be saved when using genome-based models including GE for optimizing sparse testing designs., (Copyright © 2020 Jarquin et al.)

A combined multistage linear genomic selection index (CMLGSI) is a linear combination of phenotypic and genomic estimated breeding values useful for predicting the individual net genetic merit, which in turn is a linear combination of the true unobservable breeding values of the traits weighted by their respective economic values. The CMLGSI is a cost-saving strategy for improving multiple traits because the breeder does not need to measure all traits at each stage. The optimum (OCMLGSI) and decorrelated (DCMLGSI) indices are the main CMLGSIs. Whereas the OCMLGSI takes into consideration the index correlation values among stages, the DCMLGSI imposes the restriction that the index correlation values among stages be zero. Using real and simulated datasets, we compared the efficiency of both indices in a two-stage context. The criteria we applied to compare the efficiency of both indices were that the total selection response of each index must be lower than or equal to the single-stage combined linear genomic selection index (CLGSI) response and that the correlation of each index with the net genetic merit should be maximum. Using four different total proportions for the real dataset, the estimated total OCMLGSI and DCMLGSI responses explained 97.5% and 90%, respectively, of the estimated single-stage CLGSI selection response. In addition, at stage two, the estimated correlations of the OCMLGSI and the DCMLGSI with the net genetic merit were 0.84 and 0.63, respectively. We found similar results for the simulated datasets. Thus, we recommend using the OCMLGSI when performing multistage selection., (Copyright © 2020 Cerón-Rojas and Crossa.)

High-throughput phenotyping (HTP) technologies can produce data on thousands of phenotypes per unit being monitored. These data can be used to breed for economically and environmentally relevant traits (e.g., drought tolerance); however, incorporating high-dimensional phenotypes in genetic analyses and in breeding schemes poses important statistical and computational challenges. To address this problem, we developed regularized selection indices; the methodology integrates techniques commonly used in high-dimensional phenotypic regressions (including penalization and rank-reduction approaches) into the selection index (SI) framework. Using extensive data from CIMMYT's (International Maize and Wheat Improvement Center) wheat breeding program we show that regularized SIs derived from hyper-spectral data offer consistently higher accuracy for grain yield than those achieved by standard SIs, and by vegetation indices commonly used to predict agronomic traits. Regularized SIs offer an effective approach to leverage HTP data that is routinely generated in agriculture; the methodology can also be used to conduct genetic studies using high-dimensional phenotypes that are often collected in humans and model organisms including body images and whole-genome gene expression profiles.

In this paper we propose a Bayesian multi-output regressor stacking (BMORS) model that is a generalization of the multi-trait regressor stacking method. The proposed BMORS model consists of two stages: in the first stage, a univariate genomic best linear unbiased prediction (GBLUP including genotype × environment interaction GE) model is implemented for each of the L traits under study; then the predictions of all traits are included as covariates in the second stage, by implementing a Ridge regression model. The main objectives of this research were to study alternative models to the existing multi-trait multi-environment (BMTME) model with respect to (1) genomic-enabled prediction accuracy, and (2) potential advantages in terms of computing resources and implementation. We compared the predictions of the BMORS model to those of the univariate GBLUP model using 7 maize and wheat datasets. We found that the proposed BMORS produced similar predictions to the univariate GBLUP model and to the BMTME model in terms of prediction accuracy; however, the best predictions were obtained under the BMTME model. In terms of computing resources, we found that the BMORS is at least 9 times faster than the BMTME method. Based on our empirical findings, the proposed BMORS model is an alternative for predicting multi-trait and multi-environment data, which are very common in genomic-enabled prediction in plant and animal breeding programs., (Copyright © 2019 Montesinos-Lopez et al.)

Kernel methods are flexible and easy to interpret and have been successfully used in genomic-enabled prediction of various plant species. Kernel methods used in genomic prediction comprise the linear genomic best linear unbiased predictor (GBLUP or GB) kernel, and the Gaussian kernel (GK). In general, these kernels have been used with two statistical models: single-environment and genomic × environment (GE) models. Recently near infrared spectroscopy (NIR) has been used as an inexpensive and non-destructive high-throughput phenotyping method for predicting unobserved line performance in plant breeding trials. In this study, we used a non-linear arc-cosine kernel (AK) that emulates deep learning artificial neural networks. We compared AK prediction accuracy with the prediction accuracy of GB and GK kernel methods in four genomic data sets, one of which also includes pedigree and NIR information. Results show that for all four data sets, AK and GK kernels achieved higher prediction accuracy than the linear GB kernel for the single-environment and GE multi-environment models. In addition, AK achieved similar or slightly higher prediction accuracy than the GK kernel. For all data sets, the GE model achieved higher prediction accuracy than the single-environment model. For the data set that includes pedigree, markers and NIR, results show that the NIR wavelength alone achieved lower prediction accuracy than the genomic information alone; however, the pedigree plus NIR information achieved only slightly lower prediction accuracy than the marker plus the NIR high-throughput data., (Copyright © 2019 Cuevas et al.)

Genomic selection (GS) models have been validated for many quantitative traits in wheat (Triticum aestivum L.) breeding. However, those models are mostly constrained within the same growing cycle and the extension of GS to the case of across cycles has been a challenge, mainly due to the low predictive accuracy resulting from two factors: reduced genetic relationships between different families and augmented environmental variances between cycles. Using the data collected from diverse field conditions at the International Wheat and Maize Improvement Center, we evaluated GS for grain yield in three elite yield trials across three wheat growing cycles. The objective of this project was to employ the secondary traits, canopy temperature, and green normalized difference vegetation index, which are closely associated with grain yield from high-throughput phenotyping platforms, to improve prediction accuracy for grain yield. The ability to predict grain yield was evaluated reciprocally across three cycles with or without secondary traits. Our results indicate that prediction accuracy increased by an average of 146% for grain yield across cycles with secondary traits. In addition, our results suggest that secondary traits phenotyped during wheat heading and early grain filling stages were optimal for enhancing the prediction accuracy for grain yield.

Hyperspectral reflectance phenotyping and genomic selection are two emerging technologies that have the potential to increase plant breeding efficiency by improving prediction accuracy for grain yield. Hyperspectral cameras quantify canopy reflectance across a wide range of wavelengths that are associated with numerous biophysical and biochemical processes in plants. Genomic selection models utilize genome-wide marker or pedigree information to predict the genetic values of breeding lines. In this study, we propose a multi-kernel GBLUP approach to genomic selection that uses genomic marker-, pedigree-, and hyperspectral reflectance-derived relationship matrices to model the genetic main effects and genotype × environment ( G  ×  E ) interactions across environments within a bread wheat ( Triticum aestivum L.) breeding program. We utilized an airplane equipped with a hyperspectral camera to phenotype five differentially managed treatments of the yield trials conducted by the Bread Wheat Improvement Program of the International Maize and Wheat Improvement Center (CIMMYT) at Ciudad Obregón, México over four breeding cycles. We observed that single-kernel models using hyperspectral reflectance-derived relationship matrices performed similarly or superior to marker- and pedigree-based genomic selection models when predicting within and across environments. Multi-kernel models combining marker/pedigree information with hyperspectral reflectance phentoypes had the highest prediction accuracies; however, improvements in accuracy over marker- and pedigree-based models were marginal when correcting for days to heading. Our results demonstrate the potential of using hyperspectral imaging to predict grain yield within a multi-environment context and also support further studies on the integration of hyperspectral reflectance phenotyping into breeding programs., (Copyright © 2019 Krause et al.)

Genomic selection is revolutionizing plant breeding. However, still lacking are better statistical models for ordinal phenotypes to improve the accuracy of the selection of candidate genotypes. For this reason, in this paper we explore the genomic based prediction performance of two popular machine learning methods: the Multi Layer Perceptron (MLP) and support vector machine (SVM) methods vs. the Bayesian threshold genomic best linear unbiased prediction (TGBLUP) model. We used the percentage of cases correctly classified (PCCC) as a metric to measure the prediction performance, and seven real data sets to evaluate the prediction accuracy, and found that the best predictions (in four out of the seven data sets) in terms of PCCC occurred under the TGLBUP model, while the worst occurred under the SVM method. Also, in general we found no statistical differences between using 1, 2 and 3 layers under the MLP models, which means that many times the conventional neuronal network model with only one layer is enough. However, although even that the TGBLUP model was better, we found that the predictions of MLP and SVM were very competitive with the advantage that the SVM was the most efficient in terms of the computational time required., (Copyright © 2019 Montesinos-López et al.)

Genomic selection and high-throughput phenotyping (HTP) are promising tools to accelerate breeding gains for high-yielding and climate-resilient wheat varieties. Hence, our objective was to evaluate them for predicting grain yield (GY) in drought-stressed (DS) and late-sown heat-stressed (HS) environments of the International maize and wheat improvement center's elite yield trial nurseries. We observed that the average genomic prediction accuracies using fivefold cross-validations were 0.50 and 0.51 in the DS and HS environments, respectively. However, when a different nursery/year was used to predict another nursery/year, the average genomic prediction accuracies in the DS and HS environments decreased to 0.18 and 0.23, respectively. While genomic predictions clearly outperformed pedigree-based predictions across nurseries, they were similar to pedigree-based predictions within nurseries due to small family sizes. In populations with some full-sibs in the training population, the genomic and pedigree-based prediction accuracies were on average 0.27 and 0.35 higher than the accuracies in populations with only one progeny per cross, indicating the importance of genetic relatedness between the training and validation populations for good predictions. We also evaluated the item-based collaborative filtering approach for multivariate prediction of GY using the green normalized difference vegetation index from HTP. This approach proved to be the best strategy for across-nursery predictions, with average accuracies of 0.56 and 0.62 in the DS and HS environments, respectively. We conclude that GY is a challenging trait for across-year predictions, but GS and HTP can be integrated in increasing the size of populations screened and evaluating unphenotyped large nurseries for stress-resilience within years.

Key Message: Our study indicates that copy variants may play an essential role in the phenotypic variation of complex traits in maize hybrids. Moreover, predicting hybrid phenotypes by combining additive-dominance effects with copy variants has the potential to be a viable predictive model. Non-additive effects resulting from the actions of multiple loci may influence trait variation in single-cross hybrids. In addition, complementation of allelic variation could be a valuable contributor to hybrid genetic variation, especially when crossing inbred lines with higher contents of copy gains. With this in mind, we aimed (1) to study the association between copy number variation (CNV) and hybrid phenotype, and (2) to compare the predictive ability (PA) of additive and additive-dominance genomic best linear unbiased prediction model when combined with the effects of CNV in two datasets of maize hybrids (USP and HELIX). In the USP dataset, we observed a significant negative phenotypic correlation of low magnitude between copy number loss and plant height, revealing a tendency that more copy losses lead to lower plants. In the same set, when CNV was combined with the additive plus dominance effects, the PA significantly increased only for plant height under low nitrogen. In this case, CNV effects explicitly capture relatedness between individuals and add extra information to the model. In the HELIX dataset, we observed a pronounced difference in PA between additive (0.50) and additive-dominance (0.71) models for predicting grain yield, suggesting a significant contribution of dominance. We conclude that copy variants may play an essential role in the phenotypic variation of complex traits in maize hybrids, although the inclusion of CNVs into datasets does not return significant gains concerning PA.

Genomic selection (GS) has been promising for increasing genetic gains in several species. Therefore, we evaluated the potential integration of GS for grain yield (GY) in bread wheat ( L.) in CIMMYT's elite yield trial nurseries. We observed that the genomic prediction accuracies within nurseries (0.44 and 0.35) were substantially higher than across-nursery accuracies (0.15 and 0.05) for GY evaluated in the bed and flat planting systems, respectively. The accuracies from using only a subset of 251 genotyping-by-sequencing markers were comparable to the accuracies using all 2038 markers. We also used the item-based collaborative filtering approach for incorporating other related traits in predicting GY and observed that it outperformed genomic predictions across nurseries, but was less predictive when trait correlations with GY were low. Furthermore, we compared GS and phenotypic selections (PS) and observed that at a selection intensity of 0.5, GS could select a maximum of 70.9 and 61.5% of the top lines and discard 71.5 and 60.5% of the poor lines selected or discarded by PS within and across nurseries, respectively. Comparisons of GS and pedigree-based predictions revealed that the advantage of GS over the pedigree was moderate in populations without full-sibs. However, GS was less advantageous for within-family selections in elite families with few full-sibs and minimal Mendelian sampling variance. Overall, our results demonstrate the importance of applying GS for GY at the appropriate stage of the breeding cycle, and we speculate that gains can be maximized if it is implemented in early-generation within-family selections., (Copyright © 2018 Crop Science Society of America.)

Key Message: We were able to obtain good prediction accuracy in genomic selection with ~ 2000 GBS-derived SNPs. SNPs in genic regions did not improve prediction accuracy compared to SNPs in intergenic regions. Since genotyping can represent an important cost in genomic selection, it is important to minimize it without compromising the accuracy of predictions. The objectives of the present study were to explore how a decrease in the unit cost of genotyping impacted: (1) the number of single nucleotide polymorphism (SNP) markers; (2) the accuracy of the resulting genotypic data; (3) the extent of coverage on both physical and genetic maps; and (4) the prediction accuracy (PA) for six important traits in barley. Variations on the genotyping by sequencing protocol were used to generate 16 SNP sets ranging from ~ 500 to ~ 35,000 SNPs. The accuracy of SNP genotypes fluctuated between 95 and 99%. Marker distribution on the physical map was highly skewed toward the terminal regions, whereas a fairly uniform coverage of the genetic map was achieved with all but the smallest set of SNPs. We estimated the PA using three statistical models capturing (or not) the epistatic effect; the one modeling both additivity and epistasis was selected as the best model. The PA obtained with the different SNP sets was measured and found to remain stable, except with the smallest set, where a significant decrease was observed. Finally, we examined if the localization of SNP loci (genic vs. intergenic) affected the PA. No gain in PA was observed using SNPs located in genic regions. In summary, we found that there is considerable scope for decreasing the cost of genotyping in barley (to capture ~ 2000 SNPs) without loss of PA.

New methods and algorithms are being developed for predicting untested phenotypes in schemes commonly used in genomic selection (GS). The prediction of disease resistance in GS has its own peculiarities: a) there is consensus about the additive nature of quantitative adult plant resistance (APR) genes, although epistasis has been found in some populations; b) rust resistance requires effective combinations of major and minor genes; and c) disease resistance is commonly measured based on ordinal scales (e.g., scales from 1-5, 1-9, etc.). Machine learning (ML) is a field of computer science that uses algorithms and existing samples to capture characteristics of target patterns. In this paper we discuss several state-of-the-art ML methods that could be applied in GS. Many of them have already been used to predict rust resistance in wheat. Others are very appealing, given their performance for predicting other wheat traits with similar characteristics. We briefly describe the proposed methods in the Appendix., (Copyright © 2018 Crop Science Society of America.)

In genomic-enabled prediction, the task of improving the accuracy of the prediction of lines in environments is difficult because the available information is generally sparse and usually has low correlations between traits. In current genomic selection, although researchers have a large amount of information and appropriate statistical models to process it, there is still limited computing efficiency to do so. Although some statistical models are usually mathematically elegant, many of them are also computationally inefficient, and they are impractical for many traits, lines, environments, and years because they need to sample from huge normal multivariate distributions. For these reasons, this study explores two recommender systems: item-based collaborative filtering (IBCF) and the matrix factorization algorithm (MF) in the context of multiple traits and multiple environments. The IBCF and MF methods were compared with two conventional methods on simulated and real data. Results of the simulated and real data sets show that the IBCF technique was slightly better in terms of prediction accuracy than the two conventional methods and the MF method when the correlation was moderately high. The IBCF technique is very attractive because it produces good predictions when there is high correlation between items (environment-trait combinations) and its implementation is computationally feasible, which can be useful for plant breeders who deal with very large data sets., (Copyright © 2018 Montesinos-Lopez et al.)

Genomic selection (GS) facilitates the rapid selection of superior genotypes and accelerates the breeding cycle. In this review, we discuss the history, principles, and basis of GS and genomic-enabled prediction (GP) as well as the genetics and statistical complexities of GP models, including genomic genotype×environment (G×E) interactions. We also examine the accuracy of GP models and methods for two cereal crops and two legume crops based on random cross-validation. GS applied to maize breeding has shown tangible genetic gains. Based on GP results, we speculate how GS in germplasm enhancement (i.e., prebreeding) programs could accelerate the flow of genes from gene bank accessions to elite lines. Recent advances in hyperspectral image technology could be combined with GS and pedigree-assisted breeding., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

When a plant scientist wishes to make genomic-enabled predictions of multiple traits measured in multiple individuals in multiple environments, the most common strategy for performing the analysis is to use a single trait at a time taking into account genotype × environment interaction (G × E), because there is a lack of comprehensive models that simultaneously take into account the correlated counting traits and G × E. For this reason, in this study we propose a multiple-trait and multiple-environment model for count data. The proposed model was developed under the Bayesian paradigm for which we developed a Markov Chain Monte Carlo (MCMC) with noninformative priors. This allows obtaining all required full conditional distributions of the parameters leading to an exact Gibbs sampler for the posterior distribution. Our model was tested with simulated data and a real data set. Results show that the proposed multi-trait, multi-environment model is an attractive alternative for modeling multiple count traits measured in multiple environments., (Copyright © 2017 Montesinos-López et al.)

More than 80% of the 19 million ha of maize ( L.) in tropical Asia is rainfed and prone to drought. The breeding methods for improving drought tolerance (DT), including genomic selection (GS), are geared to increase the frequency of favorable alleles. Two biparental populations (CIMMYT-Asia Population 1 [CAP1] and CAP2) were generated by crossing elite Asian-adapted yellow inbreds (CML470 and VL1012767) with an African white drought-tolerant line, CML444. Marker effects of polymorphic single-nucleotide polymorphisms (SNPs) were determined from testcross (TC) performance of F families under drought and optimal conditions. Cycle 1 (C1) was formed by recombining the top 10% of the F families based on TC data. Subsequently, (i) C2[PerSe_PS] was derived by recombining those C1 plants that exhibited superior per se phenotypes (phenotype-only selection), and (ii) C2[TC-GS] was derived by recombining a second set of C1 plants with high genomic estimated breeding values (GEBVs) derived from TC phenotypes of F families (marker-only selection). All the generations and their top crosses to testers were evaluated under drought and optimal conditions. Per se grain yields (GYs) of C2[PerSe_PS] and that of C2[TC-GS] were 23 to 39 and 31 to 53% better, respectively, than that of the corresponding F population. The C2[TC-GS] populations showed superiority of 10 to 20% over C2[PerSe-PS] of respective populations. Top crosses of C2[TC-GS] showed 4 to 43% superiority of GY over that of C2[PerSe_PS] of respective populations. Thus, GEBV-enabled selection of superior phenotypes (without the target stress) resulted in rapid genetic gains for DT., (Copyright © 2017 Crop Science Society of America.)

The phenomenon of genotype × environment (G × E) interaction in plant breeding decreases selection accuracy, thereby negatively affecting genetic gains. Several genomic prediction models incorporating G × E have been recently developed and used in genomic selection of plant breeding programs. Genomic prediction models for assessing multi-environment G × E interaction are extensions of a single-environment model, and have advantages and limitations. In this study, we propose two multi-environment Bayesian genomic models: the first model considers genetic effects [Formula: see text] that can be assessed by the Kronecker product of variance-covariance matrices of genetic correlations between environments and genomic kernels through markers under two linear kernel methods, linear (genomic best linear unbiased predictors, GBLUP) and Gaussian (Gaussian kernel, GK). The other model has the same genetic component as the first model [Formula: see text] plus an extra component, F: , that captures random effects between environments that were not captured by the random effects [Formula: see text] We used five CIMMYT data sets (one maize and four wheat) that were previously used in different studies. Results show that models with G × E always have superior prediction ability than single-environment models, and the higher prediction ability of multi-environment models with [Formula: see text] over the multi-environment model with only u occurred 85% of the time with GBLUP and 45% of the time with GK across the five data sets. The latter result indicated that including the random effect f is still beneficial for increasing prediction ability after adjusting by the random effect [Formula: see text]., (Copyright © 2017 Cuevas et al.)

There are a lot of methods developed to predict untested phenotypes in schemes commonly used in genomic selection (GS) breeding. The use of GS for predicting disease resistance has its own particularities: (a) most populations shows additivity in quantitative adult plant resistance (APR); (b) resistance needs effective combinations of major and minor genes; and (c) phenotype is commonly expressed in ordinal categorical traits, whereas most parametric applications assume that the response variable is continuous and normally distributed. Machine learning methods (MLM) can take advantage of examples (data) that capture characteristics of interest from an unknown underlying probability distribution (i.e., data-driven). We introduce some state-of-the-art MLM capable to predict rust resistance in wheat. We also present two parametric R packages for the reader to be able to compare.

In the last decade the breeding technology referred to as 'genomic selection' (GS) has been implemented in a variety of species, with particular success in animal breeding. Recent research shows the potential of GS to reshape wheat breeding. Many authors have concluded that the estimated genetic gain per year applying GS is several times that of conventional breeding. GS is, however, a new technology for wheat breeding and many programs worldwide are still struggling to identify the best strategy for its implementation. This article provides practical guidelines on the key considerations when implementing GS. A review of the existing GS literature for a range of species is provided and used to prime breeder-oriented considerations on the practical applications of GS. Furthermore, this article discusses potential breeding schemes for GS, genotyping considerations, and methods for effective training population design. The components of selection intensity, progress toward inbreeding in half- or full-sibs recurrent schemes, and the generation of selection are also presented., (Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.)