Multispectral and thermal infrared data, visual scores for severity of common rust symptoms, and genotypic single nucleotide polymorphism data of three F2-derived biparental doubled-haploid maize populations

Three F2-derived biparental doubled haploid (DH) maize populations were generated for genetic mapping of resistance to common rust. Each of the three populations has the same susceptible parent, but a different resistance donor parent. Population 1 and 3 consist of 320 lines each, population 2 consists of 260 lines. The DH lines were evaluated for their susceptibility to common rust in two years and with two replications in each year. For phenotyping, a visual score (VS) for susceptibility was assigned. Additionally, unmanned aerial vehicle (UAV) derived multispectral and thermal infrared data was recorded and combined in different vegetation indices ("remote sensing", RS). The DH lines were genotyped with the DarTseq method, to obtain data on single nucleotide polymorphisms (SNPs). After quality control, 9051 markers remained. Missing values were "imputed" by the empirical mean of the marker scores of the respective locus. We used the data for comparison of genome-wide association studies and genomic prediction when based on different phenotyping methods, that is either VS or RS data. The data may be interesting for reuse for instance for benchmarking genomic prediction models, for phytopathological studies addressing common rust, or for specifications of vegetation indices.

Use of remote sensing for linkage mapping and genomic prediction for common rust resistance in maize

Breeding for disease resistance is a central component of strategies implemented to mitigate biotic stress impacts on crop yield. Conventionally, genotypes of a plant population are evaluated through a labor-intensive process of assigning visual scores (VS) of susceptibility (or resistance) by specifically trained staff, which limits manageable volumes and repeatability of evaluation trials. Remote sensing (RS) tools have the potential to streamline phenotyping processes and to deliver more standardized results at higher through-put. Here, we use a two-year evaluation trial of three newly developed biparental populations of maize doubled haploid lines (DH) to compare the results of genomic analyses of resistance to common rust (CR) when phenotyping is either based on conventional VS or on RS-derived (vegetation) indices. As a general observation, for each population × year combination, the broad sense heritability of VS was greater than or very close to the maximum heritability across all RS indices. Moreover, results of linkage mapping as well as of genomic prediction (GP), suggest that VS data was of a higher quality, indicated by higher - log p values in the linkage studies and higher predictive abilities for genomic prediction. Nevertheless, despite the qualitative differences between the phenotyping methods, each successfully identified the same genomic region on chromosome 10 as being associated with disease resistance. This region is likely related to the known CR resistance locus Rp1. Our results indicate that RS technology can be used to streamline genetic evaluation processes for foliar disease resistance in maize. In particular, RS can potentially reduce costs of phenotypic evaluations and increase trialing capacities.

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.

Multispectral-derived genotypic similarities from budget cameras allow grain yield prediction and genomic selection augmentation in single and multi-environment scenarios in spring wheat

With abundant available genomic data, genomic selection has become routine in many plant breeding programs. Multispectral data captured by UAVs showed potential for grain yield (GY) prediction in many plant species using machine learning; however, the possibilities of utilizing this data to augment genomic prediction models still need to be explored. We collected high-throughput phenotyping (HTP) multispectral data in a genotyped multi-environment large-scale field trial using two cost-effective cameras to fill this gap. We tested back to back the prediction ability of GY prediction models, including genomic (G matrix), multispectral-derived (M matrix), and environmental (E matrix) relationships using best linear unbiased predictor (BLUP) methodology in single and multi-environment scenarios. We discovered that M allows for GY prediction comparable to the G matrix and that models using both G and M matrices show superior accuracies and errors compared with G or M alone, both in single and multi-environment scenarios. We showed that the M matrix is not entirely environment-specific, and the genotypic relationships become more robust with more data capture sessions over the season. We discovered that the optimal time for data capture occurs during grain filling and that camera bands with the highest heritability are important for GY prediction using the M matrix. We showcased that GY prediction can be performed using only an RGB camera, and even a single data capture session can yield valuable data for GY prediction. This study contributes to a better understanding of multispectral data and its relationships. It provides a flexible framework for improving GS protocols without significant investments or software customization.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11032-024-01449-w.

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.

Prediction of near-term climate change impacts on UK wheat quality and the potential for adaptation through plant breeding

Wheat is a major crop worldwide, mainly cultivated for human consumption and animal feed. Grain quality is paramount in determining its value and downstream use. While we know that climate change threatens global crop yields, a better understanding of impacts on wheat end-use quality is also critical. Combining quantitative genetics with climate model outputs, we investigated UK-wide trends in genotypic adaptation for wheat quality traits. In our approach, we augmented genomic prediction models with environmental characterisation of field trials to predict trait values and climate effects in historical field trial data between 2001 and 2020. Addition of environmental covariates, such as temperature and rainfall, successfully enabled prediction of genotype by environment interactions (G × E), and increased prediction accuracy of most traits for new genotypes in new year cross validation. We then extended predictions from these models to much larger numbers of simulated environments using climate scenarios projected under Representative Concentration Pathways 8.5 for 2050-2069. We found geographically varying climate change impacts on wheat quality due to contrasting associations between specific weather covariables and quality traits across the UK. Notably, negative impacts on quality traits were predicted in the East of the UK due to increased summer temperatures while the climate in the North and South-west may become more favourable with increased summer temperatures. Furthermore, by projecting 167,040 simulated future genotype-environment combinations, we found only limited potential for breeding to exploit predictable G × E to mitigate year-to-year environmental variability for most traits except Hagberg falling number. This suggests low adaptability of current UK wheat germplasm across future UK climates. More generally, approaches demonstrated here will be critical to enable adaptation of global crops to near-term climate change.

Genetic analyses of tropical maize lines under artificial infestation of fall armyworm and foliar diseases under optimum conditions

Development and deployment of high-yielding maize varieties with native resistance to Fall armyworm (FAW), turcicum leaf blight (TLB), and gray leaf spot (GLS) infestation is critical for addressing the food insecurity in sub-Saharan Africa. The objectives of this study were to determine the inheritance of resistance for FAW, identity hybrids which in addition to FAW resistance, also show resistance to TLB and GLS, and investigate the usefulness of models based on general combining ability (GCA) and SNP markers in predicting the performance of new untested hybrids. Half-diallel mating scheme was used to generate 105 F₁ hybrids from 15 parents and another 55 F₁ hybrids from 11 parents. These were evaluated in two experiments, each with commercial checks in multiple locations under FAW artificial infestation and optimum management in Kenya. Under artificial FAW infestation, significant mean squares among hybrids and hybrids x environment were observed for most traits in both experiments, including at least one of the three assessments carried out for foliar damage caused by FAW. Interaction of GCA x environment and specific combining ability (SCA) x environment interactions were significant for all traits under FAW infestation and optimal conditions. Moderate to high heritability estimates were observed for GY under both management conditions. Correlation between GY and two of the three scorings (one and three weeks after infestation) for foliar damage caused by FAW were negative (-0.27 and -0.38) and significant. Positive and significant correlation (0.84) was observed between FAW-inflicted ear damage and the percentage of rotten ears. We identified many superior-performing hybrids compared to the best commercial checks for both GY and FAW resistance associated traits. Inbred lines CML312, CML567, CML488, DTPYC9-F46-1-2-1-2, CKDHL164288, CKDHL166062, and CLRCY039 had significant and positive GCA for GY (positive) and FAW resistance-associated traits (negative). CML567 was a parent in four of the top ten hybrids under optimum and FAW conditions. Both additive and non-additive gene action were important in the inheritance of FAW resistance. Both GCA and marker-based models showed high correlation with field performance, but marker-based models exhibited considerably higher correlation. The best performing hybrids identified in this study could be used as potential single cross testers in the development of three-way FAW resistance hybrids. Overall, our results provide insights that help breeders to design effective breeding strategies to develop FAW resistant hybrids that are high yielding under FAW and optimum conditions.

DNNGP, a deep neural network-based method for genomic prediction using multi-omics data in plants

Genomic prediction is an effective way to accelerate the rate of agronomic trait improvement in plants. Traditional methods typically use linear regression models with clear assumptions; such methods are unable to capture the complex relationships between genotypes and phenotypes. Non-linear models (e.g., deep neural networks) have been proposed as a superior alternative to linear models because they can capture complex non-additive effects. Here we introduce a deep learning (DL) method, deep neural network genomic prediction (DNNGP), for integration of multi-omics data in plants. We trained DNNGP on four datasets and compared its performance with methods built with five classic models: genomic best linear unbiased prediction (GBLUP); two methods based on a machine learning (ML) framework, light gradient boosting machine (LightGBM) and support vector regression (SVR); and two methods based on a DL framework, deep learning genomic selection (DeepGS) and deep learning genome-wide association study (DLGWAS). DNNGP is novel in five ways. First, it can be applied to a variety of omics data to predict phenotypes. Second, the multilayered hierarchical structure of DNNGP dynamically learns features from raw data, avoiding overfitting and improving the convergence rate using a batch normalization layer and early stopping and rectified linear activation (rectified linear unit) functions. Third, when small datasets were used, DNNGP produced results that are competitive with results from the other five methods, showing greater prediction accuracy than the other methods when large-scale breeding data were used. Fourth, the computation time required by DNNGP was comparable with that of commonly used methods, up to 10 times faster than DeepGS. Fifth, hyperparameters can easily be batch tuned on a local machine. Compared with GBLUP, LightGBM, SVR, DeepGS and DLGWAS, DNNGP is superior to these existing widely used genomic selection (GS) methods. Moreover, DNNGP can generate robust assessments from diverse datasets, including omics data, and quickly incorporate complex and large datasets into usable models, making it a promising and practical approach for straightforward integration into existing GS platforms.

Modeling genotype × environment interaction for single and multitrait genomic prediction in potato (Solanum tuberosum L.)

In this study, we extend research on genomic prediction (GP) to polysomic polyploid plant species with the main objective to investigate single-trait (ST) and multitrait (MT) multienvironment (ME) models using field trial data from 3 locations in Sweden [Helgegården (HEL), Mosslunda (MOS), Umeå (UM)] over 2 years (2020, 2021) of 253 potato cultivars and breeding clones for 5 tuber weight traits and 2 tuber flesh quality characteristics. This research investigated the GP of 4 genome-based prediction models with genotype × environment interactions (GEs): (1) ST reaction norm model (M1), (2) ST model considering covariances between environments (M2), (3) ST M2 extended to include a random vector that utilizes the environmental covariances (M3), and (4) MT model with GE (M4). Several prediction problems were analyzed for each of the GP accuracy of the 4 models. Results of the prediction of traits in HEL, the high yield potential testing site in 2021, show that the best-predicted traits were tuber flesh starch (%), weight of tuber above 60 or below 40 mm in size, and the total tuber weight. In terms of GP, accuracy model M4 gave the best prediction accuracy in 3 traits, namely tuber weight of 40-50 or above 60 mm in size, and total tuber weight, and very similar in the starch trait. For MOS in 2021, the best predictive traits were starch, weight of tubers above 60, 50-60, or below 40 mm in size, and the total tuber weight. MT model M4 was the best GP model based on its accuracy when some cultivars are observed in some traits. For the GP accuracy of traits in UM in 2021, the best predictive traits were the weight of tubers above 60, 50-60, or below 40 mm in size, and the best model was MT M4, followed by models ST M3 and M2.

Envirome-wide associations enhance multi-year genome-based prediction of historical wheat breeding data

Linking high-throughput environmental data (enviromics) to genomic prediction (GP) is a cost-effective strategy for increasing selection intensity under genotype-by-environment interactions (G × E). This study developed a data-driven approach based on Environment-Phenotype Association (EPA) aimed at recycling important G × E information from historical breeding data. EPA was developed in two applications: (1) scanning a secondary source of genetic variation, weighted from the shared reaction-norms of past-evaluated genotypes and (2) pinpointing weights of the similarity among trial-sites (locations), given the historical impact of each envirotyping data variable for a given site. These results were then used as a dimensionality reduction strategy, integrating historical data to feed multi-environment GP models, which led to the development of four new G × E kernels considering genomics, enviromics, and EPA outcomes. The wheat trial data used included 36 locations, 8 years, and three target populations of environments (TPEs) in India. Four prediction scenarios and six kernel models within/across TPEs were tested. Our results suggest that the conventional GBLUP, without enviromic data or when omitting EPA, is inefficient in predicting the performance of wheat lines in future years. Nevertheless, when EPA was introduced as an intermediary learning step to reduce the dimensionality of the G × E kernels while connecting phenotypic and environmental-wide variation, a significant enhancement of G × E prediction accuracy was evident. EPA revealed that the effect of seasonality makes strategies such as "covariable selection" unfeasible because G × E is year-germplasm specific. We propose that the EPA effectively serves as a "reinforcement learner" algorithm capable of uncovering the effect of seasonality over the reaction-norms, with the benefits of better forecasting the similarities between past and future trialing sites. EPA combines the benefits of dimensionality reduction while reducing the uncertainty of genotype-by-year predictions and increasing the resolution of GP for the genotype-specific level.

Sparse kernel models provide optimization of training set design for genomic prediction in multiyear wheat breeding data

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.

Sparse testing using genomic prediction improves selection for breeding targets in elite spring wheat

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.

Automated Machine Learning: A Case Study of Genomic "Image-Based" Prediction in Maize Hybrids

Machine learning methods such as multilayer perceptrons (MLP) and Convolutional Neural Networks (CNN) have emerged as promising methods for genomic prediction (GP). In this context, we assess the performance of MLP and CNN on regression and classification tasks in a case study with maize hybrids. The genomic information was provided to the MLP as a relationship matrix and to the CNN as "genomic images." In the regression task, the machine learning models were compared along with GBLUP. Under the classification task, MLP and CNN were compared. In this case, the traits (plant height and grain yield) were discretized in such a way to create balanced (moderate selection intensity) and unbalanced (extreme selection intensity) datasets for further evaluations. An automatic hyperparameter search for MLP and CNN was performed, and the best models were reported. For both task types, several metrics were calculated under a validation scheme to assess the effect of the prediction method and other variables. Overall, MLP and CNN presented competitive results to GBLUP. Also, we bring new insights on automated machine learning for genomic prediction and its implications to plant breeding.

The statistical theory of linear selection indices from phenotypic to genomic selection

A linear selection index (LSI) can be a linear combination of phenotypic values, marker scores, and genomic estimated breeding values (GEBVs); phenotypic values and marker scores; or phenotypic values and GEBVs jointly. The main objective of the LSI is to predict the net genetic merit (H), which is a linear combination of unobservable individual traits' breeding values, weighted by the trait economic values; thus, the target of LSI is not a parameter but rather the unobserved random H values. The LSI can be single-stage or multi-stage, where the latter are methods for selecting one or more individual traits available at different times or stages of development in both plants and animals. Likewise, LSIs can be either constrained or unconstrained. A constrained LSI imposes predetermined genetic gain on expected genetic gain per trait and includes the unconstrained LSI as particular cases. The main LSI parameters are the selection response, the expected genetic gain per trait, and its correlation with H. When the population mean is zero, the selection response and expected genetic gain per trait are, respectively, the conditional mean of H and the genotypic values, given the LSI values. The application of LSI theory is rapidly diversifying; however, because LSIs are based on the best linear predictor and on the canonical correlation theory, the LSI theory can be explained in a simple form. We provided a review of the statistical theory of the LSI from phenotypic to genomic selection showing their relationships, advantages, and limitations, which should allow breeders to use the LSI theory confidently in breeding programs.

Using an incomplete block design to allocate lines to environments improves sparse genome-based prediction in plant breeding

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.

Response to Early Generation Genomic Selection for Yield in Wheat

We investigated increasing genetic gain for grain yield using early generation genomic selection (GS). A training set of 1,334 elite wheat breeding lines tested over three field seasons was used to generate Genomic Estimated Breeding Values (GEBVs) for grain yield under irrigated conditions applying markers and three different prediction methods: (1) Genomic Best Linear Unbiased Predictor (GBLUP), (2) GBLUP with the imputation of missing genotypic data by Ridge Regression BLUP (rrGBLUP_imp), and (3) Reproducing Kernel Hilbert Space (RKHS) a.k.a. Gaussian Kernel (GK). F2 GEBVs were generated for 1,924 individuals from 38 biparental cross populations between 21 parents selected from the training set. Results showed that F2 GEBVs from the different methods were not correlated. Experiment 1 consisted of selecting F2s with the highest average GEBVs and advancing them to form genomically selected bulks and make intercross populations aiming to combine favorable alleles for yield. F4:6 lines were derived from genomically selected bulks, intercrosses, and conventional breeding methods with similar numbers from each. Results of field-testing for Experiment 1 did not find any difference in yield with genomic compared to conventional selection. Experiment 2 compared the predictive ability of the different GEBV calculation methods in F2 using a set of single plant-derived F2:4 lines from randomly selected F2 plants. Grain yield results from Experiment 2 showed a significant positive correlation between observed yields of F2:4 lines and predicted yield GEBVs of F2 single plants from GK (the predictive ability of 0.248, P < 0.001) and GBLUP (0.195, P < 0.01) but no correlation with rrGBLUP_imp. Results demonstrate the potential for the application of GS in early generations of wheat breeding and the importance of using the appropriate statistical model for GEBV calculation, which may not be the same as the best model for inbreds.

Juvenile Heat Tolerance in Wheat for Attaining Higher Grain Yield by Shifting to Early Sowing in October in South Asia

Farmers in northwestern and central India have been exploring to sow their wheat much earlier (October) than normal (November) to sustain productivity by escaping terminal heat stress and to utilize the available soil moisture after the harvesting of rice crop. However, current popular varieties are poorly adapted to early sowing due to the exposure of juvenile plants to the warmer temperatures in the month of October and early November. Therefore, a study was undertaken to identify wheat genotypes suited to October sowing under warmer temperatures in India. A diverse collection of 3322 bread wheat varieties and elite lines was prepared in CIMMYT, Mexico, and planted in the 3rd week of October during the crop season 2012-2013 in six locations (Ludhiana, Karnal, New Delhi, Indore, Pune and Dharwad) spread over northwestern plains zone (NWPZ) and central and Peninsular zone (CZ and PZ; designated as CPZ) of India. Agronomic traits data from the seedling stage to maturity were recorded. Results indicated substantial diversity for yield and yield-associated traits, with some lines showing indications of higher yields under October sowing. Based on agronomic performance and disease resistance, the top 48 lines (and two local checks) were identified and planted in the next crop season (2013-2014) in a replicated trial in all six locations under October sowing (third week). High yielding lines that could tolerate higher temperature in October sowing were identified for both zones; however, performance for grain yield was more promising in the NWPZ. Hence, a new trial of 30 lines was planted only in NWPZ under October sowing. Lines showing significantly superior yield over the best check and the most popular cultivars in the zone were identified. The study suggested that agronomically superior wheat varieties with early heat tolerance can be obtained that can provide yield up to 8 t/ha by planting in the third to fourth week of October.

Multi-generation genomic prediction of maize yield using parametric and non-parametric sparse selection indices

Genomic prediction models are often calibrated using multi-generation data. Over time, as data accumulates, training data sets become increasingly heterogeneous. Differences in allele frequency and linkage disequilibrium patterns between the training and prediction genotypes may limit prediction accuracy. This leads to the question of whether all available data or a subset of it should be used to calibrate genomic prediction models. Previous research on training set optimization has focused on identifying a subset of the available data that is optimal for a given prediction set. However, this approach does not contemplate the possibility that different training sets may be optimal for different prediction genotypes. To address this problem, we recently introduced a sparse selection index (SSI) that identifies an optimal training set for each individual in a prediction set. Using additive genomic relationships, the SSI can provide increased accuracy relative to genomic-BLUP (GBLUP). Non-parametric genomic models using Gaussian kernels (KBLUP) have, in some cases, yielded higher prediction accuracies than standard additive models. Therefore, here we studied whether combining SSIs and kernel methods could further improve prediction accuracy when training genomic models using multi-generation data. Using four years of doubled haploid maize data from the International Maize and Wheat Improvement Center (CIMMYT), we found that when predicting grain yield the KBLUP outperformed the GBLUP, and that using SSI with additive relationships (GSSI) lead to 5-17% increases in accuracy, relative to the GBLUP. However, differences in prediction accuracy between the KBLUP and the kernel-based SSI were smaller and not always significant.

Genome-enabled prediction for sparse testing in multi-environmental wheat trials

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.

Assessing combining abilities, genomic data, and genotype × environment interactions to predict hybrid grain sorghum performance

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.

Application of a Poisson deep neural network model for the prediction of count data in genome-based prediction

Genomic selection (GS) is revolutionizing conventional ways of developing new plants and animals. However, because it is a predictive methodology, GS strongly depends on statistical and machine learning to perform these predictions. For continuous outcomes, more models are available for GS. Unfortunately, for count data outcomes, there are few efficient statistical machine learning models for large datasets or for datasets with fewer observations than independent variables. For this reason, in this paper, we applied the univariate version of the Poisson deep neural network (PDNN) proposed earlier for genomic predictions of count data. The model was implemented with (a) the negative log-likelihood of Poisson distribution as the loss function, (b) the rectified linear activation unit as the activation function in hidden layers, and (c) the exponential activation function in the output layer. The advantage of the PDNN model is that it captures complex patterns in the data by implementing many nonlinear transformations in the hidden layers. Moreover, since it was implemented in Tensorflow as the back-end, and in Keras as the front-end, the model can be applied to moderate and large datasets, which is a significant advantage over previous GS models for count data. The PDNN model was compared with deep learning models with continuous outcomes, conventional generalized Poisson regression models, and conventional Bayesian regression methods. We found that the PDNN model outperformed the Bayesian regression and generalized Poisson regression methods in terms of prediction accuracy, although it was not better than the conventional deep neural network with continuous outcomes.

Increased ranking change in wheat breeding under climate change

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 strategies¹. The collaborator test sites are experiencing climate change, with new implications for how wheat genotypes are bred and selected². 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.

Optimizing Genomic-Enabled Prediction in Small-Scale Maize Hybrid Breeding Programs: A Roadmap Review

The usefulness of genomic prediction (GP) for many animal and plant breeding programs has been highlighted for many studies in the last 20 years. In maize breeding programs, mostly dedicated to delivering more highly adapted and productive hybrids, this approach has been proved successful for both large- and small-scale breeding programs worldwide. Here, we present some of the strategies developed to improve the accuracy of GP in tropical maize, focusing on its use under low budget and small-scale conditions achieved for most of the hybrid breeding programs in developing countries. We highlight the most important outcomes obtained by the University of São Paulo (USP, Brazil) and how they can improve the accuracy of prediction in tropical maize hybrids. Our roadmap starts with the efforts for germplasm characterization, moving on to the practices for mating design, and the selection of the genotypes that are used to compose the training population in field phenotyping trials. Factors including population structure and the importance of non-additive effects (dominance and epistasis) controlling the desired trait are also outlined. Finally, we explain how the source of the molecular markers, environmental, and the modeling of genotype-environment interaction can affect the accuracy of GP. Results of 7 years of research in a public maize hybrid breeding program under tropical conditions are discussed, and with the great advances that have been made, we find that what is yet to come is exciting. The use of open-source software for the quality control of molecular markers, implementing GP, and envirotyping pipelines may reduce costs in an efficient computational manner. We conclude that exploring new models/tools using high-throughput phenotyping data along with large-scale envirotyping may bring more resolution and realism when predicting genotype performances. Despite the initial costs, mostly for genotyping, the GP platforms in combination with these other data sources can be a cost-effective approach for predicting the performance of maize hybrids for a large set of growing conditions.

Application of Genomic Selection at the Early Stage of Breeding Pipeline in Tropical Maize

In maize, doubled haploid (DH) line production capacity of large-sized maize breeding programs often exceeds the capacity to phenotypically evaluate the complete set of testcross candidates in multi-location trials. The ability to partially select DH lines based on genotypic data while maintaining or improving genetic gains for key traits using phenotypic selection can result in significant resource savings. The present study aimed to evaluate genomic selection (GS) prediction scenarios for grain yield and agronomic traits of one of the tropical maize breeding pipelines of CIMMYT in eastern Africa, based on multi-year empirical data for designing a GS-based strategy at the early stages of the pipeline. We used field data from 3,068 tropical maize DH lines genotyped using rAmpSeq markers and evaluated as test crosses in well-watered (WW) and water-stress (WS) environments in Kenya from 2017 to 2019. Three prediction schemes were compared: (1) 1 year of performance data to predict a second year; (2) 2 years of pooled data to predict performance in the third year, and (3) using individual or pooled data plus converting a certain proportion of individuals from the testing set (TST) to the training set (TRN) to predict the next year's data. Employing five-fold cross-validation, the mean prediction accuracies for grain yield (GY) varied from 0.19 to 0.29 under WW and 0.22 to 0.31 under WS, when the 1-year datasets were used training set to predict a second year's data as a testing set. The mean prediction accuracies increased to 0.32 under WW and 0.31 under WS when the 2-year datasets were used as a training set to predict the third-year data set. In a forward prediction scenario, good predictive abilities (0.53 to 0.71) were found when the training set consisted of the previous year's breeding data and converting 30% of the next year's data from the testing set to the training set. The prediction accuracy for anthesis date and plant height across WW and WS environments obtained using 1-year data and integrating 10, 30, 50, 70, and 90% of the TST set to TRN set was much higher than those trained in individual years. We demonstrate that by increasing the TRN set to include genotypic and phenotypic data from the previous year and combining only 10-30% of the lines from the year of testing, the predicting accuracy can be increased, which in turn could be used to replace the first stage of field-based screening partially, thus saving significant costs associated with the testcross formation and multi-location testcross evaluation.

Scalable Sparse Testing Genomic Selection Strategy for Early Yield Testing Stage

To enable a scalable sparse testing genomic selection (GS) strategy at preliminary yield trials in the CIMMYT maize breeding program, optimal approaches to incorporate genotype by environment interaction (GEI) in genomic prediction models are explored. Two cross-validation schemes were evaluated: CV1, predicting the genetic merit of new bi-parental populations that have been evaluated in some environments and not others, and CV2, predicting the genetic merit of half of a bi-parental population that has been phenotyped in some environments and not others using the coefficient of determination (CDmean) to determine optimized subsets of a full-sib family to be evaluated in each environment. We report similar prediction accuracies in CV1 and CV2, however, CV2 has an intuitive appeal in that all bi-parental populations have representation across environments, allowing efficient use of information across environments. It is also ideal for building robust historical data because all individuals of a full-sib family have phenotypic data, albeit in different environments. Results show that grouping of environments according to similar growing/management conditions improved prediction accuracy and reduced computational requirements, providing a scalable, parsimonious approach to multi-environmental trials and GS in early testing stages. We further demonstrate that complementing the full-sib calibration set with optimized historical data results in improved prediction accuracy for the cross-validation schemes.

Genetic dissection of Striga hermonthica (Del.) Benth. resistance via genome-wide association and genomic prediction in tropical maize germplasm

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.

Additive genetic variance and covariance between relatives in synthetic wheat crosses with variable parental ploidy levels

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.

Enviromic Assembly Increases Accuracy and Reduces Costs of the Genomic Prediction for Yield Plasticity in Maize

Quantitative genetics states that phenotypic variation is a consequence of the interaction between genetic and environmental factors. Predictive breeding is based on this statement, and because of this, ways of modeling genetic effects are still evolving. At the same time, the same refinement must be used for processing environmental information. Here, we present an "enviromic assembly approach," which includes using ecophysiology knowledge in shaping environmental relatedness into whole-genome predictions (GP) for plant breeding (referred to as enviromic-aided genomic prediction, E-GP). We propose that the quality of an environment is defined by the core of environmental typologies and their frequencies, which describe different zones of plant adaptation. From this, we derived markers of environmental similarity cost-effectively. Combined with the traditional additive and non-additive effects, this approach may better represent the putative phenotypic variation observed across diverse growing conditions (i.e., phenotypic plasticity). Then, we designed optimized multi-environment trials coupling genetic algorithms, enviromic assembly, and genomic kinships capable of providing in-silico realization of the genotype-environment combinations that must be phenotyped in the field. As proof of concept, we highlighted two E-GP applications: (1) managing the lack of phenotypic information in training accurate GP models across diverse environments and (2) guiding an early screening for yield plasticity exerting optimized phenotyping efforts. Our approach was tested using two tropical maize sets, two types of enviromics assembly, six experimental network sizes, and two types of optimized training set across environments. We observed that E-GP outperforms benchmark GP in all scenarios, especially when considering smaller training sets. The representativeness of genotype-environment combinations is more critical than the size of multi-environment trials (METs). The conventional genomic best-unbiased prediction (GBLUP) is inefficient in predicting the quality of a yet-to-be-seen environment, while enviromic assembly enabled it by increasing the accuracy of yield plasticity predictions. Furthermore, we discussed theoretical backgrounds underlying how intrinsic envirotype-phenotype covariances within the phenotypic records can impact the accuracy of GP. The E-GP is an efficient approach to better use environmental databases to deliver climate-smart solutions, reduce field costs, and anticipate future scenarios.

Maximizing efficiency of genomic selection in CIMMYT's tropical maize breeding program

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.

Target Population of Environments for Wheat Breeding in India: Definition, Prediction and Genetic Gains

In this study, we defined the target population of environments (TPE) for wheat breeding in India, the largest wheat producer in South Asia, and estimated the correlated response to the selection and prediction ability of five selection environments (SEs) in Mexico. We also estimated grain yield (GY) gains in each TPE. Our analysis used meteorological, soil, and GY data from the international Elite Spring Wheat Yield Trials (ESWYT) distributed by the International Maize and Wheat Improvement Center (CIMMYT) from 2001 to 2016. We identified three TPEs: TPE 1, the optimally irrigated Northwestern Plain Zone; TPE 2, the optimally irrigated, heat-stressed North Eastern Plains Zone; and TPE 3, the drought-stressed Central-Peninsular Zone. The correlated response to selection ranged from 0.4 to 0.9 within each TPE. The highest prediction accuracies for GY per TPE were derived using models that included genotype-by-environment interaction and/or meteorological information and their interaction with the lines. The highest prediction accuracies for TPEs 1, 2, and 3 were 0.37, 0.46, and 0.51, respectively, and the respective GY gains were 118, 46, and 123 kg/ha/year. These results can help fine-tune the breeding of elite wheat germplasm with stable yields to reduce farmers' risk from year-to-year environmental variation in India's wheat lands, which cover 30 million ha, account for 100 million tons of grain or more each year, and provide food and livelihoods for hundreds of millions of farmers and consumers in South Asia.

Genome-Wide Association Mapping and Genomic Prediction of Anther Extrusion in CIMMYT Hybrid Wheat Breeding Program via Modeling Pedigree, Genomic Relationship, and Interaction With the Environment

Anther extrusion (AE) is the most important male floral trait for hybrid wheat seed production. AE is a complex quantitative trait that is difficult to phenotype reliably in field experiments not only due to high genotype-by-environment effects but also due to the short expression window in the field condition. In this study, we conducted a genome-wide association scan (GWAS) and explored the possibility of applying genomic prediction (GP) for AE in the CIMMYT hybrid wheat breeding program. An elite set of male lines (n = 603) were phenotype for anther count (AC) and anther visual score (VS) across three field experiments in 2017–2019 and genotyped with the 20K Infinitum is elect SNP array. GWAS produced five marker trait associations with small effects. For GP, the main effects of lines (L), environment (E), genomic (G) and pedigree relationships (A), and their interaction effects with environments were used to develop seven statistical models of incremental complexity. The base model used only L and E, whereas the most complex model included L, E, G, A, and G × E and A × E. These models were evaluated in three cross-validation scenarios (CV0, CV1, and CV2). In cross-validation CV0, data from two environments were used to predict an untested environment; in random cross-validation CV1, the test set was never evaluated in any environment; and in CV2, the genotypes in the test set were evaluated in only a subset of environments. The prediction accuracies ranged from −0.03 to 0.74 for AC and −0.01 to 0.54 for VS across different models and CV schemes. For both traits, the highest prediction accuracies with low variance were observed in CV2, and inclusion of the interaction effects increased prediction accuracy for AC only. In CV0, the prediction accuracy was 0.73 and 0.45 for AC and VS, respectively, indicating the high reliability of across environment prediction. Genomic prediction appears to be a very reliable tool for AE in hybrid wheat breeding. Moreover, high prediction accuracy in CV0 demonstrates the possibility of implementing genomic selection across breeding cycles in related germplasm, aiding the rapid breeding cycle.

Genome-based prediction of multiple wheat quality traits in multiple years

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.

On Hadamard and Kronecker products in covariance structures for genotype × environment interaction

When including genotype × environment interactions (G × E) in genomic prediction models, Hadamard or Kronecker products have been used to model the covariance structure of interactions. The relation between these two types of modeling has not been made clear in genomic prediction literature. Here, we demonstrate that a certain model based on a Hadamard formulation and another using the Kronecker product lead to exactly the same statistical model. Moreover, we illustrate how a multiplication of entries of covariance matrices is related to modeling locus × environmental-variable interactions explicitly. Finally, we use a wheat and a maize data set to illustrate that the environmental covariance E can be specified easily, also if no information on environmental variables - such as temperature or precipitation - is available. Given that lines have been tested in different environments, the corresponding environmental covariance can simply be estimated from the training set as phenotypic covariance between environments. To achieve a high level of increase in predictive ability, the environmental covariance has to be defined appropriately and records on the performance of the lines of the test set under different environmental conditions have to be included in the training set.

Genome-based trait prediction in multi- environment breeding trials in groundnut

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.

Approximate Genome-Based Kernel Models for Large Data Sets Including Main Effects and Interactions

The rapid development of molecular markers and sequencing technologies has made it possible to use genomic prediction (GP) and selection (GS) in animal and plant breeding. However, when the number of observations (n) is large (thousands or millions), computational difficulties when handling these large genomic kernel relationship matrices (inverting and decomposing) increase exponentially. This problem increases when genomic × environment interaction and multi-trait kernels are included in the model. In this research we propose selecting a small number of lines m(m < n) for constructing an approximate kernel of lower rank than the original and thus exponentially decreasing the required computing time. First, we describe the full genomic method for single environment (FGSE) with a covariance matrix (kernel) including all n lines. Second, we select m lines and approximate the original kernel for the single environment model (APSE). Similarly, but including main effects and G × E, we explain a full genomic method with genotype × environment model (FGGE), and including m lines, we approximated the kernel method with G × E (APGE). We applied the proposed method to two different wheat data sets of different sizes (n) using the standard linear kernel Genomic Best Linear Unbiased Predictor (GBLUP) and also using eigen value decomposition. In both data sets, we compared the prediction performance and computing time for FGSE versus APSE; we also compared FGGE versus APGE. Results showed a competitive prediction performance of the approximated methods with a significant reduction in computing time. Genomic prediction accuracy depends on the decay of the eigenvalues (amount of variance information loss) of the original kernel as well as on the size of the selected lines m.

Genomic prediction across years in a maize doubled haploid breeding program to accelerate early-stage testcross testing

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.

Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution

The expectation and variance of the estimator of the maximized index selection response allow the breeders to construct confidence intervals and to complete the analysis of a selection process. The maximized selection response and the correlation of the linear selection index (LSI) with the net genetic merit are the main criterion to compare the efficiency of any LSI. The estimator of the maximized selection response is the square root of the variance of the estimated LSI values multiplied by the selection intensity. The expectation and variance of this estimator allow the breeder to construct confidence intervals and determine the appropriate sample size to complete the analysis of a selection process. Assuming that the estimated LSI values have normal distribution, we obtained those two parameters as follows. First, with the Fourier transform, we found the distribution of the variance of the estimated LSI values, which was a Gamma distribution; therefore, the expectation and variance of this distribution were the expectation and variance of the variance of the estimated LSI values. Second, with these results, we obtained the expectation and the variance of the estimator of the selection response using the Delta method. We validated the theoretical results in the phenotypic selection context using real and simulated dataset. With the simulated dataset, we compared the LSI efficiency when the genotypic covariance matrix is known versus when this matrix is estimated; the differences were not significant. We concluded that our results are valid for any LSI with normal distribution and that the method described in this work is useful for finding the expectation and variance of the estimator of any LSI response in the phenotypic or genomic selection context.

Genomic Prediction with Genotype by Environment Interaction Analysis for Kernel Zinc Concentration in Tropical Maize Germplasm

Zinc (Zn) deficiency is a major risk factor for human health, affecting about 30% of the world's population. To study the potential of genomic selection (GS) for maize with increased Zn concentration, an association panel and two doubled haploid (DH) populations were evaluated in three environments. Three genomic prediction models, M (M1: Environment + Line, M2: Environment + Line + Genomic, and M3: Environment + Line + Genomic + Genomic x Environment) incorporating main effects (lines and genomic) and the interaction between genomic and environment (G x E) were assessed to estimate the prediction ability (rMP ) for each model. Two distinct cross-validation (CV) schemes simulating two genomic prediction breeding scenarios were used. CV1 predicts the performance of newly developed lines, whereas CV2 predicts the performance of lines tested in sparse multi-location trials. Predictions for Zn in CV1 ranged from -0.01 to 0.56 for DH1, 0.04 to 0.50 for DH2 and -0.001 to 0.47 for the association panel. For CV2, rMP values ranged from 0.67 to 0.71 for DH1, 0.40 to 0.56 for DH2 and 0.64 to 0.72 for the association panel. The genomic prediction model which included G x E had the highest average rMP for both CV1 (0.39 and 0.44) and CV2 (0.71 and 0.51) for the association panel and DH2 population, respectively. These results suggest that GS has potential to accelerate breeding for enhanced kernel Zn concentration by facilitating selection of superior genotypes.

Combined Multistage Linear Genomic Selection Indices To Predict the Net Genetic Merit in Plant Breeding

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.

Regularized selection indices for breeding value prediction using hyper-spectral image data

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.

On-farm performance and farmers' participatory assessment of new stress-tolerant maize hybrids in Eastern Africa

The development and deployment of high-yielding stress tolerant maize hybrids are important components of the efforts to increase maize productivity in eastern Africa. This study was conducted to: i) evaluate selected, stress-tolerant maize hybrids under farmers' conditions; ii) identify farmers' selection criteria in selecting maize hybrids; and iii) have farmers evaluate the new varieties according to those criteria. Two sets of trials, one with 12 early-to-intermediate maturing and the other with 13 intermediate-to-late maturing hybrids, improved for tolerance to multiple stresses common in farmers' fields in eastern Africa (drought, northern corn leaf blight, gray leaf spot, common rust, maize streak virus), were evaluated on-farm under smallholder farmers' conditions in a total of 42 and 40 environments (site-year-management combinations), respectively, across Kenya, Uganda, Tanzania and Rwanda in 2016 and 2017. Farmer-participatory variety evaluation was conducted at 27 sites in Kenya and Rwanda, with a total of 2025 participating farmers. Differential performance of the hybrids was observed under low-yielding (<3 t ha^-1) and high-yielding (>3 t ha^-1) environments. The new stress-tolerant maize hybrids had a much better grain-yield performance than the best commercial checks under smallholder farmer growing environments but had a comparable grain-yield performance under optimal conditions. These hybrids also showed better grain-yield stability across the testing environments, providing an evidence for the success of the maize-breeding approach. In addition, the new stress- tolerant varieties outperformed the internal genetic checks, indicating genetic gain under farmers' conditions. Farmers gave high importance to grain yield in both farmer-stated preferences (through scores) and farmer-revealed preferences of criteria (revealed by regressing the overall scores on the scores for the individual criteria). The top-yielding hybrids in both maturity groups also received the farmers' highest overall scores. Farmers ranked yield, early maturity, cob size and number of cobs as the most important traits for variety preference. The criteria for the different hybrids did not differ between men and women farmers. Farmers gave priority to many different traits in addition to grain yield, but this may not be applicable across all maize-growing regions. Farmer-stated importance of the different criteria, however, were quite different from farmer- revealed importance. Further, there were significant differences between men and women in the revealed-importance of the criteria. We conclude that incorporating farmers' selection criteria in the stage-gate advancement process of new hybrids by the breeders is useful under the changing maize-growing environments in sub-Saharan Africa, and recommended to increase the turnover of new maize hybrids.

On-farm performance and farmers' participatory assessment of new stress-tolerant maize hybrids in Eastern Africa

The development and deployment of high-yielding stress tolerant maize hybrids are important components of the efforts to increase maize productivity in eastern Africa. This study was conducted to: i) evaluate selected, stress-tolerant maize hybrids under farmers' conditions; ii) identify farmers' selection criteria in selecting maize hybrids; and iii) have farmers evaluate the new varieties according to those criteria. Two sets of trials, one with 12 early-to-intermediate maturing and the other with 13 intermediate-to-late maturing hybrids, improved for tolerance to multiple stresses common in farmers' fields in eastern Africa (drought, northern corn leaf blight, gray leaf spot, common rust, maize streak virus), were evaluated on-farm under smallholder farmers' conditions in a total of 42 and 40 environments (site-year-management combinations), respectively, across Kenya, Uganda, Tanzania and Rwanda in 2016 and 2017. Farmer-participatory variety evaluation was conducted at 27 sites in Kenya and Rwanda, with a total of 2025 participating farmers. Differential performance of the hybrids was observed under low-yielding (<3 t ha-1) and high-yielding (>3 t ha-1) environments. The new stress-tolerant maize hybrids had a much better grain-yield performance than the best commercial checks under smallholder farmer growing environments but had a comparable grain-yield performance under optimal conditions. These hybrids also showed better grain-yield stability across the testing environments, providing an evidence for the success of the maize-breeding approach. In addition, the new stress- tolerant varieties outperformed the internal genetic checks, indicating genetic gain under farmers' conditions. Farmers gave high importance to grain yield in both farmer-stated preferences (through scores) and farmer-revealed preferences of criteria (revealed by regressing the overall scores on the scores for the individual criteria). The top-yielding hybrids in both maturity groups also received the farmers' highest overall scores. Farmers ranked yield, early maturity, cob size and number of cobs as the most important traits for variety preference. The criteria for the different hybrids did not differ between men and women farmers. Farmers gave priority to many different traits in addition to grain yield, but this may not be applicable across all maize-growing regions. Farmer-stated importance of the different criteria, however, were quite different from farmer- revealed importance. Further, there were significant differences between men and women in the revealed-importance of the criteria. We conclude that incorporating farmers' selection criteria in the stage-gate advancement process of new hybrids by the breeders is useful under the changing maize-growing environments in sub-Saharan Africa, and recommended to increase the turnover of new maize hybrids.

Enhancing Hybrid Prediction in Pearl Millet Using Genomic and/or Multi-Environment Phenotypic Information of Inbreds

Genomic selection (GS) is an emerging methodology that helps select superior lines among experimental cultivars in plant breeding programs. It offers the opportunity to increase the productivity of cultivars by delivering increased genetic gains and reducing the breeding cycles. This methodology requires inexpensive and sufficiently dense marker information to be successful, and with whole genome sequencing, it has become an important tool in many crops. The recent assembly of the pearl millet genome has made it possible to employ GS models to improve the selection procedure in pearl millet breeding programs. Here, three GS models were implemented and compared using grain yield and dense molecular marker information of pearl millet obtained from two different genotyping platforms (C [conventional GBS RAD-seq] and T [tunable GBS tGBS]). The models were evaluated using three different cross-validation (CV) schemes mimicking real situations that breeders face in breeding programs: CV2 resembles an incomplete field trial, CV1 predicts the performance of untested hybrids, and CV0 predicts the performance of hybrids in unobserved environments. We found that (i) adding phenotypic information of parental inbreds to the calibration sets improved predictive ability, (ii) accounting for genotype-by-environment interaction also increased the performance of the models, and (iii) superior strategies should consider the use of the molecular markers derived from the T platform (tGBS).

Strategies for Effective Use of Genomic Information in Crop Breeding Programs Serving Africa and South Asia

Much of the world's population growth will occur in regions where food insecurity is prevalent, with large increases in food demand projected in regions of Africa and South Asia. While improving food security in these regions will require a multi-faceted approach, improved performance of crop varieties in these regions will play a critical role. Current rates of genetic gain in breeding programs serving Africa and South Asia fall below rates achieved in other regions of the world. Given resource constraints, increased genetic gain in these regions cannot be achieved by simply expanding the size of breeding programs. New approaches to breeding are required. The Genomic Open-source Breeding informatics initiative (GOBii) and Excellence in Breeding Platform (EiB) are working with public sector breeding programs to build capacity, develop breeding strategies, and build breeding informatics capabilities to enable routine use of new technologies that can improve the efficiency of breeding programs and increase genetic gains. Simulations evaluating breeding strategies indicate cost-effective implementations of genomic selection (GS) are feasible using relatively small training sets, and proof-of-concept implementations have been validated in the International Maize and Wheat Improvement Center (CIMMYT) maize breeding program. Progress on GOBii, EiB, and implementation of GS in CIMMYT and International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) breeding programs are discussed, as well as strategies for routine implementation of GS in breeding programs serving Africa and South Asia.

Genome-Wide Association Mapping and Genomic Prediction of Anther Extrusion in CIMMYT Hybrid Wheat Breeding Program via Modeling Pedigree, Genomic Relationship, and Interaction With the Environment

Anther extrusion (AE) is the most important male floral trait for hybrid wheat seed production. AE is a complex quantitative trait that is difficult to phenotype reliably in field experiments not only due to high genotype-by-environment effects but also due to the short expression window in the field condition. In this study, we conducted a genome-wide association scan (GWAS) and explored the possibility of applying genomic prediction (GP) for AE in the CIMMYT hybrid wheat breeding program. An elite set of male lines (n = 603) were phenotype for anther count (AC) and anther visual score (VS) across three field experiments in 2017-2019 and genotyped with the 20K Infinitum is elect SNP array. GWAS produced five marker trait associations with small effects. For GP, the main effects of lines (L), environment (E), genomic (G) and pedigree relationships (A), and their interaction effects with environments were used to develop seven statistical models of incremental complexity. The base model used only L and E, whereas the most complex model included L, E, G, A, and G × E and A × E. These models were evaluated in three cross-validation scenarios (CV0, CV1, and CV2). In cross-validation CV0, data from two environments were used to predict an untested environment; in random cross-validation CV1, the test set was never evaluated in any environment; and in CV2, the genotypes in the test set were evaluated in only a subset of environments. The prediction accuracies ranged from -0.03 to 0.74 for AC and -0.01 to 0.54 for VS across different models and CV schemes. For both traits, the highest prediction accuracies with low variance were observed in CV2, and inclusion of the interaction effects increased prediction accuracy for AC only. In CV0, the prediction accuracy was 0.73 and 0.45 for AC and VS, respectively, indicating the high reliability of across environment prediction. Genomic prediction appears to be a very reliable tool for AE in hybrid wheat breeding. Moreover, high prediction accuracy in CV0 demonstrates the possibility of implementing genomic selection across breeding cycles in related germplasm, aiding the rapid breeding cycle.

Genomic Prediction of Kernel Zinc Concentration in Multiple Maize Populations Using Genotyping-by-Sequencing and Repeat Amplification Sequencing Markers

Enriching of kernel zinc (Zn) concentration in maize is one of the most effective ways to solve the problem of Zn deficiency in low and middle income countries where maize is the major staple food, and 17% of the global population is affected with Zn deficiency. Genomic selection (GS) has shown to be an effective approach to accelerate genetic gains in plant breeding. In the present study, an association-mapping panel and two maize double-haploid (DH) populations, both genotyped with genotyping-by-sequencing (GBS) and repeat amplification sequencing (rAmpSeq) markers, were used to estimate the genomic prediction accuracy of kernel Zn concentration in maize. Results showed that the prediction accuracy of two DH populations was higher than that of the association mapping population using the same set of markers. The prediction accuracy estimated with the GBS markers was significantly higher than that estimated with the rAmpSeq markers in the same population. The maximum prediction accuracy with minimum standard error was observed when half of the genotypes were included in the training set and 3,000 and 500 markers were used for prediction in the association mapping panel and the DH populations, respectively. Appropriate levels of minor allele frequency and missing rate should be considered and selected to achieve good prediction accuracy and reduce the computation burden by balancing the number of markers and marker quality. Training set development with broad phenotypic variation is possible to improve prediction accuracy. The transferability of the GS models across populations was assessed, the prediction accuracies in a few pairwise populations were above or close to 0.20, which indicates the prediction accuracies across years and populations have to be assessed in a larger breeding dataset with closer relationship between the training and prediction sets in further studies. GS outperformed MAS (marker-assisted-selection) on predicting the kernel Zn concentration in maize, the decision of a breeding strategy to implement GS individually or to implement MAS and GS stepwise for improving kernel Zn concentration in maize requires further research. Results of this study provide valuable information for understanding how to implement GS for improving kernel Zn concentration in maize.

Empirical Comparison of Tropical Maize Hybrids Selected Through Genomic and Phenotypic Selections

Genomic selection predicts the genomic estimated breeding values (GEBVs) of individuals not previously phenotyped. Several studies have investigated the accuracy of genomic predictions in maize but there is little empirical evidence on the practical performance of lines selected based on phenotype in comparison with those selected solely on GEBVs in advanced testcross yield trials. The main objectives of this study were to (1) empirically compare the performance of tropical maize hybrids selected through phenotypic selection (PS) and genomic selection (GS) under well-watered (WW) and managed drought stress (WS) conditions in Kenya, and (2) compare the cost-benefit analysis of GS and PS. For this study, we used two experimental maize data sets (stage I and stage II yield trials). The stage I data set consisted of 1492 doubled haploid (DH) lines genotyped with rAmpSeq SNPs. A subset of these lines (855) representing various DH populations within the stage I cohort was crossed with an individual single-cross tester chosen to complement each population. These testcross hybrids were evaluated in replicated trials under WW and WS conditions for grain yield and other agronomic traits, while the remaining 637 DH lines were predicted using the 855 lines as a training set. The second data set (stage II) consists of 348 DH lines from the first data set. Among these 348 best DH lines, 172 lines selected were solely based on GEBVs, and 176 lines were selected based on phenotypic performance. Each of the 348 DH lines were crossed with three common testers from complementary heterotic groups, and the resulting 1042 testcross hybrids and six commercial checks were evaluated in four to five WW locations and one WS condition in Kenya. For stage I trials, the cross-validated prediction accuracy for grain yield was 0.67 and 0.65 under WW and WS conditions, respectively. We found similar responses to selection using PS and GS for grain yield other agronomic traits under WW and WS conditions. The top 15% of hybrids advanced through GS and PS gave 21%-23% higher grain yield under WW and 51%-52% more grain yield under WS than the mean of the checks. The GS reduced the cost by 32% over the PS with similar selection gains. We concluded that the use of GS for yield under WW and WS conditions in maize can produce selection candidates with similar performance as those generated from conventional PS, but at a lower cost, and therefore, should be incorporated into maize breeding pipelines to increase breeding program efficiency.

Optimum and Decorrelated Constrained Multistage Linear Phenotypic Selection Indices Theory

Some authors have evaluated the unconstrained optimum and decorrelated multistage linear phenotypic selection indices (OMLPSI and DMLPSI, respectively) theory. We extended this index theory to the constrained multistage linear phenotypic selection index context, where we denoted OMLPSI and DMLPSI as OCMLPSI and DCMLPSI, respectively. The OCMLPSI (DCMLPSI) is the most general multistage index and includes the OMLPSI (DMLPSI) as a particular case. The OCMLPSI (DCMLPSI) predicts the individual net genetic merit at different individual ages and allows imposing constraints on the genetic gains to make some traits change their mean values based on a predetermined level, while the rest of them remain without restrictions. The OCMLPSI takes into consideration the index correlation values among stages, whereas the DCMLPSI imposes the restriction that the index correlation values among stages be null. The criteria to evaluate OCMLPSI efficiency vs. DCMLPSI efficiency were that the total response of each index must be lower than or equal to the single-stage constrained linear phenotypic selection index response and that the expected genetic gain per trait values should be similar to the constraints imposed by the breeder. We used one real and one simulated dataset to validate the efficiency of the indices. The results indicated that OCMLPSI accuracy when predicting the selection response and expected genetic gain per trait was higher than DCMLPSI accuracy when predicting them. Thus, breeders should use the OCMLPSI when making a phenotypic selection.