Improving hybrid rice breeding programs via stochastic simulations: number of parents, number of hybrids, tester update, and genomic prediction of hybrid performance

KEY MESSAGE

Schemes that use genomic prediction outperform others, updating testers increases hybrid genetic gain, and larger population sizes tend to have higher genetic gain and less depletion of genetic variance One of the most common methods to improve hybrid performance is reciprocal recurrent selection (RRS). Genomic prediction (GP) can be used to increase genetic gain in RRS by reducing cycle length, but it is also possible to use GP to predict single-cross hybrid performance. The impact of the latter method on genetic gain has yet to be previously reported. Therefore, we compared via stochastic simulations various phenotypic and genomics-assisted RRS breeding schemes which used GP to predict hybrid performance rather than reducing cycle length, which allows minimal changes to traditional breeding schemes. We also compared three breeding sizes scenarios that varied the number of genotypes crossed within heterotic pools, the number of genotypes crossed between heterotic pools, the number of hybrids evaluated, and the number of genomic predicted hybrids. Our results demonstrated that schemes that used genomic prediction of hybrid performance outperformed the others for the average interpopulation hybrid population and the best hybrid performance. Furthermore, updating the testers increased hybrid genetic gain with phenotypic RRS. As expected, the largest breeding size tested had the highest rates of genetic improvement and the lowest decrease in additive genetic variance due to the drift. Therefore, this study demonstrates the usefulness of single-cross prediction, which may be easier to implement than rapid-cycling RRS and cyclical updating of testers. We also reiterate that larger population sizes tend to have higher genetic gain and less depletion of genetic variance.

Construction and genetic characterization of an interspecific raspberry hybrids panel aiming resistance to late leaf rust and adaptation to tropical regions

Raspberries (Rubus spp) are temperate climate fruits with profitable high returns and have the potential for diversification of fruit growing in mid to low-latitude regions. However, there are still no cultivars adapted to climatic conditions and high pressure of diseases that occurs in tropical areas. In this context, our objective was to evaluate the genetic diversity from a 116 raspberry genotypes panel obtained from interspecific crosses in a testcross scheme with four cultivars already introduced in Brazil. The panel was genotyped via genotyping-by-sequencing. 28,373 and 27,281 SNPs were obtained, using the species R. occidentalis and R. idaeus genomes as references, respectively. A third marker dataset was constructed consisting of 41,292 non-coincident markers. Overall, there were no differences in the results when using the different marker sets for the subsequent analyses. The mean heterozygosity was 0.54. The average effective population size was 174, indicating great genetic variability. The other analyses revealed that the half-sibling families were structured in three groups. It is concluded that the studied panel has great potential for breeding and further genetic studies. Moreover, only one of the three marker matrices is sufficient for diversity studies.

On the usefulness of mock genomes to define heterotic pools, testers, and hybrid predictions in orphan crops

The advances in genomics in recent years have increased the accuracy and efficiency of breeding programs for many crops. Nevertheless, the adoption of genomic enhancement for several other crops essential in developing countries is still limited, especially for those that do not have a reference genome. These crops are more often called orphans. This is the first report to show how the results provided by different platforms, including the use of a simulated genome, called the mock genome, can generate in population structure and genetic diversity studies, especially when the intention is to use this information to support the formation of heterotic groups, choice of testers, and genomic prediction of single crosses. For that, we used a method to assemble a reference genome to perform the single-nucleotide polymorphism (SNP) calling without needing an external genome. Thus, we compared the analysis results using the mock genome with the standard approaches (array and genotyping-by-sequencing (GBS)). The results showed that the GBS-Mock presented similar results to the standard methods of genetic diversity studies, division of heterotic groups, the definition of testers, and genomic prediction. These results showed that a mock genome constructed from the population's intrinsic polymorphisms to perform the SNP calling is an effective alternative for conducting genomic studies of this nature in orphan crops, especially those that do not have a reference genome.

Enviromic-based kernels may optimize resource allocation with multi-trait multi-environment genomic prediction for tropical Maize

BACKGROUND

Success in any genomic prediction platform is directly dependent on establishing a representative training set. This is a complex task, even in single-trait single-environment conditions and tends to be even more intricated wherein additional information from envirotyping and correlated traits are considered. Here, we aimed to design optimized training sets focused on genomic prediction, considering multi-trait multi-environment trials, and how those methods may increase accuracy reducing phenotyping costs. For that, we considered single-trait multi-environment trials and multi-trait multi-environment trials for three traits: grain yield, plant height, and ear height, two datasets, and two cross-validation schemes. Next, two strategies for designing optimized training sets were conceived, first considering only the genomic by environment by trait interaction (GET), while a second including large-scale environmental data (W, enviromics) as genomic by enviromic by trait interaction (GWT). The effective number of individuals (genotypes × environments × traits) was assumed as those that represent at least 98% of each kernel (GET or GWT) variation, in which those individuals were then selected by a genetic algorithm based on prediction error variance criteria to compose an optimized training set for genomic prediction purposes.

RESULTS

The combined use of genomic and enviromic data efficiently designs optimized training sets for genomic prediction, improving the response to selection per dollar invested by up to 145% when compared to the model without enviromic data, and even more when compared to cross validation scheme with 70% of training set or pure phenotypic selection. Prediction models that include G × E or enviromic data + G × E yielded better prediction ability.

CONCLUSIONS

Our findings indicate that a genomic by enviromic by trait interaction kernel associated with genetic algorithms is efficient and can be proposed as a promising approach to designing optimized training sets for genomic prediction when the variance-covariance matrix of traits is available. Additionally, great improvements in the genetic gains per dollar invested were observed, suggesting that a good allocation of resources can be deployed by using the proposed approach.

Genotyping marker density and prediction models effects in long-term breeding schemes of cross-pollinated crops

In genomic recurrent selection, the more markers, the better because they buffer the linkage disequilibrium losses caused by recombination over cycles, and consequently, provide higher responses to selection. Reductions of genotyping marker density have been extensively evaluated as potential strategies to reduce the genotyping costs of genomic selection (GS). Low-density marker panels are appealing in GS because they entail lower multicollinearity and computing time and allow more individuals to be genotyped for the same cost. However, statistical models used in GS are usually evaluated with empirical data, using "static" training sets and populations. This may be adequate for making predictions during a breeding program's initial cycles but not for the long-term. Moreover, studies that focus on long selective breeding cycles generally do not consider GS models with the effect of dominance, which is particularly important for breeding outcomes in cross-pollinated crops. Hence, dominance effects are important and unexplored in GS for long-term programs involving allogamous species. To address it, we employed two approaches: analysis of empirical maize datasets and simulations of long-term breeding applying phenotypic and genomic recurrent selection (intrapopulation and reciprocal schemes). In both schemes, we simulated twenty breeding cycles and assessed the effect of marker density reduction on the population mean, the best crosses, additive variance, selective accuracy, and response to selection with models [additive, additive-dominant, general (GCA), and this plus specific combining ability (GCA + SCA)]. Our results indicate that marker reduction based on linkage disequilibrium levels provides useful predictions only within a cycle, as accuracy significantly decreases over cycles. In the long-term, without training set updating, high-marker density provides the best responses to selection. The model to be used depends on the breeding scheme: additive for intrapopulation and additive-dominant or GCA + SCA for reciprocal.

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.

Optimizing self-pollinated crop breeding employing genomic selection: From schemes to updating training sets

Long-term breeding schemes using genomic selection (GS) can boost the response to selection per year. Although several studies have shown that GS delivers a higher response to selection, only a few analyze which stage GS produces better results and how to update the training population to maintain prediction accuracy. We used stochastic simulation to compare five GS breeding schemes in a self-pollinated long-term breeding program. Also, we evaluated four strategies, using distinct methods and sizes, to update the training set. Finally, regarding breeding schemes, we proposed a new approach using GS to select the best individuals in each F2 progeny, based on genomic estimated breeding values and genetic divergence, to cross them and generate a new recombination event. Our results showed that the best scenario was using GS in F2, followed by the phenotypic selection of new parents in F4. For TS updating, adding new data every cycle (over 768) to update the TS maintains the prediction accuracy at satisfactory levels for more breeding cycles. However, only the last three generations can be kept in the TS, optimizing the genetic relationship between TS and the targeted population and reducing the computing demand and risks. Hence, we believe that our results may help breeders optimize GS in their programs and improve genetic gain in long-term schemes.

Partial Least Squares Enhances Genomic Prediction of New Environments

In plant breeding, the need to improve the prediction of future seasons or new locations and/or environments, also denoted as “leave one environment out,” is of paramount importance to increase the genetic gain in breeding programs and contribute to food and nutrition security worldwide. Genomic selection (GS) has the potential to increase the accuracy of future seasons or new locations because it is a predictive methodology. However, most statistical machine learning methods used for the task of predicting a new environment or season struggle to produce moderate or high prediction accuracies. For this reason, in this study we explore the use of the partial least squares (PLS) regression methodology for this specific task, and we benchmark its performance with the Bayesian Genomic Best Linear Unbiased Predictor (GBLUP) method. The benchmarking process was done with 14 real datasets. We found that in all datasets the PLS method outperformed the popular GBLUP method by margins between 0% (in the Indica data) and 228.28% (in the Disease data) across traits, environments, and types of predictors. Our results show great empirical evidence of the power of the PLS methodology for the prediction of future seasons or new environments.

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.

Genetic Trends Estimation in IRRIs Rice Drought Breeding Program and Identification of High Yielding Drought-Tolerant Lines

Estimating genetic trends using historical data is an important parameter to check the success of the breeding programs. The estimated genetic trends can act as a guideline to target the appropriate breeding strategies and optimize the breeding program for improved genetic gains. In this study, 17 years of historical data from IRRI's rice drought breeding program was used to estimate the genetic trends and assess the breeding program's success. We also identified top-performing lines based on grain yield breeding values as an elite panel for implementing future population improvement-based breeding schemes. A two-stage approach of pedigree-based mixed model analysis was used to analyze the data and extract the breeding values and estimate the genetic trends for grain yield under non-stress, drought, and in combined data of non-stress and drought. Lower grain yield values were observed in all the drought trials. Heritability for grain yield estimates ranged between 0.20 and 0.94 under the drought trials and 0.43-0.83 under non-stress trials. Under non-stress conditions, the genetic gain of 0.21% (10.22 kg/ha/year) for genotypes and 0.17% (7.90 kg/ha/year) for checks was observed. The genetic trend under drought conditions exhibited a positive trend with the genetic gain of 0.13% (2.29 kg/ha/year) for genotypes and 0.55% (9.52 kg/ha/year) for checks. For combined analysis showed a genetic gain of 0.27% (8.32 kg/ha/year) for genotypes and 0.60% (13.69 kg/ha/year) for checks was observed. For elite panel selection, 200 promising lines were selected based on higher breeding values for grain yield and prediction accuracy of > 0.40. The breeding values of the 200 genotypes formulating the core panel ranged between 2366.17 and 4622.59 (kg/ha). A positive genetic rate was observed under all the three conditions; however, the rate of increase was lower than the required rate of 1.5% genetic gain. We propose a recurrent selection breeding strategy within the elite population with the integration of modern tools and technologies to boost the genetic gains in IRRI's drought breeding program. The elite breeding panel identified in this study forms an easily available and highly enriched genetic resource for future recurrent selection programs to boost the genetic gains.

Genome and Environment Based Prediction Models and Methods of Complex Traits Incorporating Genotype × Environment Interaction

Genomic-enabled prediction models are of paramount importance for the successful implementation of genomic selection (GS) based on breeding values. As opposed to animal breeding, plant breeding includes extensive multienvironment and multiyear field trial data. Hence, genomic-enabled prediction models should include genotype × environment (G × E) interaction, which most of the time increases the prediction performance when the response of lines are different from environment to environment. In this chapter, we describe a historical timeline since 2012 related to advances of the GS models that take into account G × E interaction. We describe theoretical and practical aspects of those GS models, including the gains in prediction performance when including G × E structures for both complex continuous and categorical scale traits. Then, we detailed and explained the main G × E genomic prediction models for complex traits measured in continuous and noncontinuous (categorical) scale. Related to G × E interaction models this review also examine the analyses of the information generated with high-throughput phenotype data (phenomic) and the joint analyses of multitrait and multienvironment field trial data that is also employed in the general assessment of multitrait G × E interaction. The inclusion of nongenomic data in increasing the accuracy and biological reliability of the G × E approach is also outlined. We show the recent advances in large-scale envirotyping (enviromics), and how the use of mechanistic computational modeling can derive the crop growth and development aspects useful for predicting phenotypes and explaining G × E.

Unravelling Rubber Tree Growth by Integrating GWAS and Biological Network-Based Approaches

Hevea brasiliensis (rubber tree) is a large tree species of the Euphorbiaceae family with inestimable economic importance. Rubber tree breeding programs currently aim to improve growth and production, and the use of early genotype selection technologies can accelerate such processes, mainly with the incorporation of genomic tools, such as marker-assisted selection (MAS). However, few quantitative trait loci (QTLs) have been used successfully in MAS for complex characteristics. Recent research shows the efficiency of genome-wide association studies (GWAS) for locating QTL regions in different populations. In this way, the integration of GWAS, RNA-sequencing (RNA-Seq) methodologies, coexpression networks and enzyme networks can provide a better understanding of the molecular relationships involved in the definition of the phenotypes of interest, supplying research support for the development of appropriate genomic based strategies for breeding. In this context, this work presents the potential of using combined multiomics to decipher the mechanisms of genotype and phenotype associations involved in the growth of rubber trees. Using GWAS from a genotyping-by-sequencing (GBS) Hevea population, we were able to identify molecular markers in QTL regions with a main effect on rubber tree plant growth under constant water stress. The underlying genes were evaluated and incorporated into a gene coexpression network modelled with an assembled RNA-Seq-based transcriptome of the species, where novel gene relationships were estimated and evaluated through in silico methodologies, including an estimated enzymatic network. From all these analyses, we were able to estimate not only the main genes involved in defining the phenotype but also the interactions between a core of genes related to rubber tree growth at the transcriptional and translational levels. This work was the first to integrate multiomics analysis into the in-depth investigation of rubber tree plant growth, producing useful data for future genetic studies in the species and enhancing the efficiency of the species improvement programs.

Population-tailored mock genome enables genomic studies in species without a reference genome

Based on molecular markers, genomic prediction enables us to speed up breeding schemes and increase the response to selection. There are several high-throughput genotyping platforms able to deliver thousands of molecular markers for genomic study purposes. However, even though its widely applied in plant breeding, species without a reference genome cannot fully benefit from genomic tools and modern breeding schemes. We used a method to assemble a population-tailored mock genome to call single-nucleotide polymorphism (SNP) markers without an available reference genome, and for the first time, we compared the results with standard genotyping platforms (array and genotyping-by-sequencing (GBS) using a reference genome) for performance in genomic prediction models. Our results indicate that using a population-tailored mock genome to call SNP delivers reliable estimates for the genomic relationship between genotypes. Furthermore, genomic prediction estimates were comparable to standard approaches, especially when considering only additive effects. However, mock genomes were slightly worse than arrays at predicting traits influenced by dominance effects, but still performed as well as standard GBS methods that use a reference genome. Nevertheless, the array-based SNP markers methods achieved the best predictive ability and reliability to estimate variance components. Overall, the mock genomes can be a worthy alternative for genomic selection studies, especially for those species where the reference genome is not available.

On the genetic architecture in a public tropical maize panel of the symbiosis between corn and plant growth-promoting bacteria aiming to improve plant resilience

Exploring the symbiosis between plants and plant growth-promoting bacteria (PGPB) is a new challenge for sustainable agriculture. Even though many works have reported the beneficial effects of PGPB in increasing plant resilience for several stresses, its potential is not yet widely explored. One of the many reasons is the differential symbiosis performance depending on the host genotype. This opens doors to plant breeding programs to explore the genetic variability and develop new cultivars with higher responses to PGPB interaction and, therefore, have higher resilience to stress. Hence, we aimed to study the genetic architecture of the symbiosis between PGPB and tropical maize germplasm, using a public association panel and its impact on plant resilience. Our findings reveal that the synthetic PGPB population can modulate and impact root architecture traits and improve resilience to nitrogen stress, and 37 regions were significant for controlling the symbiosis between PGPB and tropical maize. In addition, we found two overlapping SNPs in the GWAS analysis indicating strong candidates for further investigations. Furthermore, genomic prediction analysis with genomic relationship matrix computed using only significant SNPs obtained from GWAS analysis substantially increased the predictive ability for several traits endorsing the importance of these genomic regions for the response of PGPB. Finally, the public tropical panel reveals a significant genetic variability to the symbiosis with the PGPB and can be a source of alleles to improve plant resilience.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11032-021-01257-6.

Introgression of Maize Diversity for Drought Tolerance: Subtropical Maize Landraces as Source of New Positive Variants

Current climate change models predict an increased frequency and intensity of drought for much of the developing world within the next 30 years. These events will negatively affect maize yields, potentially leading to economic and social instability in many smallholder farming communities. Knowledge about the genetic resources available for traits related to drought tolerance has great importance in developing breeding program strategies. The aim of this research was to study a maize landrace introgression panel to identify chromosomal regions associated with a drought tolerance index. For that, we performed Genome-Wide Association Study (GWAS) on 1326 landrace progenies developed by the CIMMYT Genetic Resources Program, originating from 20 landraces populations collected in arid regions. Phenotypic data were obtained from early testcross trials conducted in three sites and two contrasting irrigation environments, full irrigation (well-watered) and reduced irrigation (drought). The populations were genotyped using the DArTSeq^® platform, and a final set of 5,695 SNPs markers was used. The genotypic values were estimated using spatial adjustment in a two-stage analysis. First, we performed the individual analysis for each site/irrigation treatment combination. The best linear unbiased estimates (BLUEs) were used to calculate the Harmonic Mean of Relative Performance (HMRP) as a drought tolerance index for each testcross. The second stage was a joint analysis, which was performed using the HMRP to obtain the best linear unbiased predictions (BLUPs) of the index for each genotype. Then, GWAS was performed to determine the marker-index associations and the marker-Grain Yield (GY) associations for the two irrigation treatments. We detected two significant markers associated with the drought-tolerance index, four associated with GY in drought condition, and other four associated with GY in irrigated conditions each. Although each of these markers explained less than 0.1% of the phenotypic variation for the index and GY, we found two genes likely related to the plant response to drought stress. For these markers, alleles from landraces provide a slightly higher yield under drought conditions. Our results indicate that the positive diversity delivered by landraces are still present on the backcrosses and this is a potential breeding strategy for improving maize for drought tolerance and for trait introgression bringing new superior allelic diversity from landraces to breeding populations.

EnvRtype: a software to interplay enviromics and quantitative genomics in agriculture

Envirotyping is an essential technique used to unfold the nongenetic drivers associated with the phenotypic adaptation of living organisms. Here, we introduce the EnvRtype R package, a novel toolkit developed to interplay large-scale envirotyping data (enviromics) into quantitative genomics. To start a user-friendly envirotyping pipeline, this package offers: (1) remote sensing tools for collecting (get_weather and extract_GIS functions) and processing ecophysiological variables (processWTH function) from raw environmental data at single locations or worldwide; (2) environmental characterization by typing environments and profiling descriptors of environmental quality (env_typing function), in addition to gathering environmental covariables as quantitative descriptors for predictive purposes (W_matrix function); and (3) identification of environmental similarity that can be used as an enviromic-based kernel (env_typing function) in whole-genome prediction (GP), aimed at increasing ecophysiological knowledge in genomic best-unbiased predictions (GBLUP) and emulating reaction norm effects (get_kernel and kernel_model functions). We highlight literature mining concepts in fine-tuning envirotyping parameters for each plant species and target growing environments. We show that envirotyping for predictive breeding collects raw data and processes it in an eco-physiologically smart way. Examples of its use for creating global-scale envirotyping networks and integrating reaction-norm modeling in GP are also outlined. We conclude that EnvRtype provides a cost-effective envirotyping pipeline capable of providing high quality enviromic data for a diverse set of genomic-based studies, especially for increasing accuracy in GP across untested growing environments.

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.

Genome-Wide Association Study Reveals Genomic Regions Associated with Fusarium Wilt Resistance in Common Bean

Fusarium wilt (Fusarium oxysporum f. sp. phaseoli, Fop) is one of the main fungal soil diseases in common bean. The aim of the present study was to identify genomic regions associated with Fop resistance through genome-wide association studies (GWAS) in a Mesoamerican Diversity Panel (MDP) and to identify potential common bean sources of Fop's resistance. The MDP was genotyped with BARCBean6K_3BeadChip and evaluated for Fop resistance with two different monosporic strains using the root-dip method. Disease severity rating (DSR) and the area under the disease progress curve (AUDPC), at 21 days after inoculation (DAI), were used for GWAS performed with FarmCPU model. The p-value of each SNP was determined by resampling method and Bonferroni test. For UFV01 strain, two significant single nucleotide polymorphisms (SNPs) were mapped on the Pv05 and Pv11 for AUDPC, and the same SNP (ss715648096) on Pv11 was associated with AUDPC and DSR. Another SNP, mapped on Pv03, showed significance for DSR. Regarding IAC18001 strain, significant SNPs on Pv03, Pv04, Pv05, Pv07 and on Pv01, Pv05, and Pv10 were observed. Putative candidate genes related to nucleotide-binding sites and carboxy-terminal leucine-rich repeats were identified. The markers may be important future tools for genomic selection to Fop disease resistance in beans.

EnvRtype: a software to interplay enviromics and quantitative genomics in agriculture

Envirotyping is an essential technique used to unfold the nongenetic drivers associated with the phenotypic adaptation of living organisms. Here, we introduce the EnvRtype R package, a novel toolkit developed to interplay large-scale envirotyping data (enviromics) into quantitative genomics. To start a user-friendly envirotyping pipeline, this package offers: (1) remote sensing tools for collecting (get_weather and extract_GIS functions) and processing ecophysiological variables (processWTH function) from raw environmental data at single locations or worldwide; (2) environmental characterization by typing environments and profiling descriptors of environmental quality (env_typing function), in addition to gathering environmental covariables as quantitative descriptors for predictive purposes (W_matrix function); and (3) identification of environmental similarity that can be used as an enviromic-based kernel (env_typing function) in whole-genome prediction (GP), aimed at increasing ecophysiological knowledge in genomic best-unbiased predictions (GBLUP) and emulating reaction norm effects (get_kernel and kernel_model functions). We highlight literature mining concepts in fine-tuning envirotyping parameters for each plant species and target growing environments. We show that envirotyping for predictive breeding collects raw data and processes it in an eco-physiologically smart way. Examples of its use for creating global-scale envirotyping networks and integrating reaction-norm modeling in GP are also outlined. We conclude that EnvRtype provides a cost-effective envirotyping pipeline capable of providing high quality enviromic data for a diverse set of genomic-based studies, especially for increasing accuracy in GP across untested growing environments.

A novel way to validate UAS-based high-throughput phenotyping protocols using in silico experiments for plant breeding purposes

It is possible to make inferences regarding the feasibility and applicability of plant high-throughput phenotyping via computer simulations. Protocol validation has been a key challenge to the establishment of high-throughput phenotyping (HTP) in breeding programs. We add to this matter by proposing an innovative way for designing and validating aerial imagery-based HTP approaches with in silico 3D experiments for plant breeding purposes. The algorithm is constructed following a pipeline composed of the simulation of phenotypic values, three-dimensional modeling of trials, and image rendering. Our tool is exemplified by testing a set of experimental setups that are of interest in the context of maize breeding using a comprehensive case study. We report on how the choice of (percentile of) points in dense clouds, the experimental repeatability (heritability), the treatment variance (genetic variability), and the flight altitude affect the accuracy of high-throughput plant height estimation based on conventional structure-from-motion (SfM) and multi-view stereo (MVS) pipelines. The evaluation of both the algorithm and the case study was driven by comparisons of the computer-simulated (ground truth) and the HTP-estimated values using correlations, regressions, and similarity indices. Our results showed that the 3D experiments can be adequately reconstructed, enabling inference-making. Moreover, it suggests that treatment variance, repeatability, and the choice of the percentile of points are highly influential over the accuracy of HTP. Conversely, flight altitude influenced the quality of reconstruction but not the accuracy of plant height estimation. Therefore, we believe that our tool can be of high value, enabling the promotion of new insights and further understanding of the events underlying the practice of high-throughput phenotyping.

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.

Population structure analysis and identification of genomic regions under selection associated with low-nitrogen tolerance in tropical maize lines

Increasing low nitrogen (N) tolerance in maize is an important goal for food security and agricultural sustainability. In order to analyze the population structure of tropical maize lines and identify genomic regions associated with low-N tolerance, a set of 64 inbred lines were evaluated under low-N and optimal-N conditions. The low-N Agronomic Efficiency index (LNAE) of each line was calculated. The maize lines were genotyped using 417,112 SNPs markers. The grouping based on the LNAE values classified the lines into two phenotypic groups, the first comprised by genotypes with high LNAE (named H_LNAE group), while the second one comprised genotypes with low LNAE (named L_LNAE group). The H_LNAE and L_LNAE groups had LNAE mean values of 3,304 and 1,644, respectively. The population structure analysis revealed a weak relationship between genetic and phenotypic diversity. Pairs of lines were identified, having at the same time high LNAE and high genetic distance from each other. A set of 29 SNPs markers exhibited a significant difference in allelic frequencies (Fst > 0.2) between H_LNAE and L_LNAE groups. The Pearson's correlation between LNAE and the favorable alleles in this set of SNPs was 0.69. These SNPs could be useful for marker-assisted selection for low-N tolerance in maize breeding programs. The results of this study could help maize breeders identify accessions to be used in the development of low-N tolerant cultivars.

Nonlinear kernels, dominance, and envirotyping data increase the accuracy of genome-based prediction in multi-environment trials

Modern whole-genome prediction (WGP) frameworks that focus on multi-environment trials (MET) integrate large-scale genomics, phenomics, and envirotyping data. However, the more complex the statistical model, the longer the computational processing times, which do not always result in accuracy gains. We investigated the use of new kernel methods and modeling structures involving genomics and nongenomic sources of variation in two MET maize data sets. Five WGP models were considered, advancing in complexity from a main-effect additive model (A) to more complex structures, including dominance deviations (D), genotype × environment interaction (AE and DE), and the reaction-norm model using environmental covariables (W) and their interaction with A and D (AW + DW). A combination of those models built with three different kernel methods, Gaussian kernel (GK), Deep kernel (DK), and the benchmark genomic best linear-unbiased predictor (GBLUP/GB), was tested under three prediction scenarios: newly developed hybrids (CV1), sparse MET conditions (CV2), and new environments (CV0). GK and DK outperformed GB in prediction accuracy and reduction of computation time (~up to 20%) under all model-kernel scenarios. GK was more efficient in capturing the variation due to A + AE and D + DE effects and translated it into accuracy gains (~up to 85% compared with GB). DK provided more consistent predictions, even for more complex structures such as W + AW + DW. Our results suggest that DK and GK are more efficient in translating model complexity into accuracy, and more suitable for including dominance and reaction-norm effects in a biologically accurate and faster way.

On the usefulness of parental lines GWAS for predicting low heritability traits in tropical maize hybrids

Genome-wide association studies (GWAS) is one of the most popular methods of studying the genetic control of traits. This methodology has been intensely performed on inbred genotypes to identify causal variants. Nonetheless, the lack of covariance between the phenotype of inbred lines and their offspring in cross-pollinated species (such as maize) raises questions on the applicability of these findings in a hybrid breeding context. To address this topic, we incorporated previously reported parental lines GWAS information into the prediction of a low heritability trait in hybrids. This was done by marker-assisted selection based on significant markers identified in the lines and by genomic prediction having these markers as fixed effects. Additive-dominance GWAS of hybrids, a non-conventional procedure, was also performed for comparison purposes. Our results suggest that incorporating information from parental inbred lines GWAS led to decreases in the predictive ability of hybrids. Correspondingly, inbred lines and hybrids-based GWAS yielded different results. These findings do not invalidate GWAS on inbred lines for selection purposes, but mean that it may not be directly useful for hybrid breeding.

Effect of F1 and F2 generations on genetic variability and working steps of doubled haploid production in maize

For doubled haploid (DH) production in maize, F1 generation has been the most frequently used for haploid induction due to facility in the process. However, using F2 generation would be a good alternative to increase genetic variability owing to the additional recombination in meiosis. Our goals were to compare the effect of F1 and F2 generations on DH production in tropical germplasm, evaluating the R1-navajo expression in seeds, the working steps of the methodology, and the genetic variability of the DH lines obtained. Sources germplasm in F1 and F2 generations were crossed with the tropicalized haploid inducer LI-ESALQ. After harvest, for both induction crosses were calculated the haploid induction rate (HIR), diploid seed rate (DSR), and inhibition seed rate (ISR) using the total number of seeds obtained. In order to study the effectiveness of the DH working steps in each generation, the percentage per se and the relative percentage were verified. In addition, SNP markers were obtained for genetic variability studies. Results showed that the values for HIR, ISR, and DSR were 1.23%, 23.48%, and 75.21% for F1 and 1.78%, 15.82%, and 82.38% for F2, respectively. The effectiveness of the DH working step showed the same percentage per se value (0.4%) for F1 and F2, while the relative percentage was 27.2% for F1 and 22.4% for F2. Estimates of population parameters in DH lines from F1 were higher than F2. Furthermore, population structure and kinship analyses showed that one additional generation was not sufficient to create new genotype subgroups. Additionally, the relative efficiency of the response to selection in the F1 was 31.88% higher than F2 due to the number of cycles that are used to obtain the DH. Our results showed that in tropical maize, the use of F1 generation is recommended due to a superior balance between time and genetic variability.

Expected Genotype Quality and Diploidized Marker Data from Genotyping-by-Sequencing of Urochloa spp. Tetraploids

Introduced concept of expected genotype quality (EGQ) and software to calculate it Provided read depth guidelines for GBS in tetraploids Developed software to generate diploidized genotype calls from VCF files Demonstrated value of aligning GBS reads to a mock reference genome for SNP discovery Recommend filtering based on GQ and read depth to prevent genotype bias Although genotyping-by-sequencing (GBS) is a well-established marker technology in diploids, the development of best practices for tetraploid species is a topic of current research. We determined the theoretical relationship between read depth and the phred-scaled probability of genotype misclassification conditioned on the true genotype, which we call expected genotype quality (EGQ). If the GBS method has 0.5% allelic error, then 17 reads are needed to classify simplex tetraploids as heterozygous with 95% accuracy (EGQ = 13) vs. 61 reads to determine allele dosage. We developed an R script to convert tetraploid GBS data in variant call format (VCF) into diploidized genotype calls and applied it to 267 interspecific hybrids of the tetraploid forage grass Urochloa. When reads were aligned to a mock reference genome created from GBS data of the Urochloa brizantha (Hochst. ex A. Rich.) R. D. Webster cultivar Marandu, 25,678 biallelic single nucleotide polymorphism (SNPs) were discovered, compared with ∼3000 SNPs when aligning to the closest true reference genomes, Setaria viridis (L.) P. Beauv. and S. italica (L.) P. Beauv. Cross-validation revealed that missing genotypes were imputed by the random forest method with a median accuracy of 0.85 regardless of heterozygote frequency. Using the Urochloa spp. hybrids, we illustrated how filtering samples based only on genotype quality (GQ) creates genotype bias; a depth threshold based on EGQ is also needed regardless of whether genotypes are called using a diploidized or allele dosage model.

Relative importance of gene effects for nitrogen-use efficiency in popcorn

The objective of this study was to evaluate the effects of additive and non-additive genes on the efficiency of nitrogen (N) use and N responsiveness in inbred popcorn lines. The parents, hybrids and reciprocal crosses were evaluated in a 10x10 triple lattice design at two sites and two levels of N availability. To establish different N levels in the two experiments, fertilization was carried out at sowing, according to soil analysis reports. However, for the experiments with ideal nitrogen availability, N was sidedressed according to the crop requirement, whereas for the N-poor experiments sidedressing consisted of 30% of that applied in the N-rich environment. Two indices were evaluated, the Harmonic Mean of the Relative Performance (HMRP) and Agronomic Efficiency under Low Nitrogen Availability (AELN), both based on grain yield at both N levels. Both additive and non-additive gene effects were important for selection for N-use efficiency. Moreover, there was allelic complementarity between the lines and a reciprocal effect for N-use efficiency, indicating the importance of the choice of the parents used as male or female. The best hybrids were obtained from inbred popcorn lines with contrasting N-use efficiency and N responsiveness.

Additive and heterozygous (dis)advantage GWAS models reveal candidate genes involved in the genotypic variation of maize hybrids to Azospirillum brasilense

Maize genotypes can show different responsiveness to inoculation with Azospirillum brasilense and an intriguing issue is which genes of the plant are involved in the recognition and growth promotion by these Plant Growth-Promoting Bacteria (PGPB). We conducted Genome-Wide Association Studies (GWAS) using additive and heterozygous (dis)advantage models to find candidate genes for root and shoot traits under nitrogen (N) stress and N stress plus A. brasilense. A total of 52,215 Single Nucleotide Polymorphism (SNP) markers were used for GWAS analyses. For the six root traits with significant inoculation effect, the GWAS analyses revealed 25 significant SNPs for the N stress plus A. brasilense treatment, in which only two were overlapped with the 22 found for N stress only. Most were found by the heterozygous (dis)advantage model and were more related to exclusive gene ontology terms. Interestingly, the candidate genes around the significant SNPs found for the maize-A. brasilense association were involved in different functions previously described for PGPB in plants (e.g. signaling pathways of the plant's defense system and phytohormone biosynthesis). Our findings are a benchmark in the understanding of the genetic variation among maize hybrids for the association with A. brasilense and reveal the potential for further enhancement of maize through this association.

Maize responsiveness to Azospirillum brasilense: Insights into genetic control, heterosis and genomic prediction

Several studies have shown differences in the abilities of maize genotypes to facilitate or impede Azospirillum brasilense colonization and to receive benefits from this association. Hence, our aim was to study the genetic control, heterosis effect and the prediction accuracy of the shoot and root traits of maize in response to A. brasilense. For that, we evaluated 118 hybrids under two contrasting scenarios: i) N stress (control) and ii) N stress plus A. brasilense inoculation. The diallel analyses were performed using mixed model equations, and the genomic prediction models accounted for the general and specific combining ability (GCA and SCA, respectively) and the presence or not of G×E effects. In addition, the genomic models were fitted considering parametric (G-BLUP) and semi-parametric (RKHS) kernels. The genotypes showed significant inoculation effect for five root traits, and the GCA and SCA were significant for both. The GCA in the inoculated treatment presented a greater magnitude than the control, whereas the opposite was observed for SCA. Heterosis was weakly influenced by the inoculation, and the heterozygosity and N status in the plant can have a role in the benefits that can be obtained from this Plant Growth-Promoting Bacteria (PGPB). Prediction accuracies for N stress plus A. brasilense ranged from 0.42 to 0.78, depending on the scenario and trait, and were higher, in most cases, than the non-inoculated treatment. Finally, our findings provide an understanding of the quantitative variation of maize responsiveness to A. brasilense and important insights to be applied in maize breeding aiming the development of superior hybrids for this association.

Modeling copy number variation in the genomic prediction of maize hybrids

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

Bayesian analysis and prediction of hybrid performance

BACKGROUND

The selection of hybrids is an essential step in maize breeding. However, evaluating a large number of hybrids in field trials can be extremely costly. However, genomic models can be used to predict the expected performance of un-tested genotypes. Bayesian models offer a very flexible framework for hybrid prediction. The Bayesian methodology can be used with parametric and semi-parametric assumptions for additive and non-additive effects. Furthermore, samples from the posterior distribution of Bayesian models can be used to estimate the variance due to general and specific combining abilities even in cases where additive and non-additive effects are not mutually orthogonal. Also, the use of Bayesian models for analysis and prediction of hybrid performance has remained fairly limited.

RESULTS

We provided an overview of Bayesian parametric and semi-parametric genomic models for prediction of agronomic traits in maize hybrids and discussed how these models can be used to decompose the genotypic variance into components due to general and specific combining ability. We applied the methodology to data from 906 single cross tropical maize hybrids derived from a convergent population. Our results show that: (1) non-additive effects make a sizable contribution to the genetic variance of grain yield; however, the relative importance of non-additive effects was much smaller for ear and plant height; (2) genomic prediction can achieve relatively high accuracy in predicting phenotypes of un-tested hybrids and in pre-screening.

CONCLUSIONS

Genomic prediction can be a useful tool in pre-screening of hybrids and could contribute to the improvement of the efficiency and efficacy of maize hybrids breeding programs. The Bayesian framework offers a great deal of flexibility in modeling hybrid performance. The methodology can be used to estimate important genetic parameters and render predictions of the expected hybrid performance as well measures of uncertainty about such predictions.

Genomic Selection in Rubber Tree Breeding: A Comparison of Models and Methods for Managing G×E Interactions

Several genomic prediction models combining genotype × environment (G×E) interactions have recently been developed and used for genomic selection (GS) in plant breeding programs. G×E interactions reduce selection accuracy and limit genetic gains in plant breeding. Two data sets were used to compare the prediction abilities of multienvironment G×E genomic models and two kernel methods. Specifically, a linear kernel, or GB (genomic best linear unbiased predictor [GBLUP]), and a nonlinear kernel, or Gaussian kernel (GK), were used to compare the prediction accuracies (PAs) of four genomic prediction models: 1) a single-environment, main genotypic effect model (SM); 2) a multienvironment, main genotypic effect model (MM); 3) a multienvironment, single-variance G×E deviation model (MDs); and 4) a multienvironment, environment-specific variance G×E deviation model (MDe). We evaluated the utility of genomic selection (GS) for 435 individual rubber trees at two sites and genotyped the individuals via genotyping-by-sequencing (GBS) of single-nucleotide polymorphisms (SNPs). Prediction models were used to estimate stem circumference (SC) during the first 4 years of tree development in conjunction with a broad-sense heritability (H ²) of 0.60. Applying the model (SM, MM, MDs, and MDe) and kernel method (GB and GK) combinations to the rubber tree data revealed that the multienvironment models were superior to the single-environment genomic models, regardless of the kernel (GB or GK) used, suggesting that introducing interactions between markers and environmental conditions increases the proportion of variance explained by the model and, more importantly, the PA. Compared with the classic breeding method (CBM), methods in which GS is incorporated resulted in a 5-fold increase in response to selection for SC with multienvironment GS (MM, MDe, or MDs). Furthermore, GS resulted in a more balanced selection response for SC and contributed to a reduction in selection time when used in conjunction with traditional genetic breeding programs. Given the rapid advances in genotyping methods and their declining costs and given the overall costs of large-scale progeny testing and shortened breeding cycles, we expect GS to be implemented in rubber tree breeding programs.

BGGE: A New Package for Genomic-Enabled Prediction Incorporating Genotype × Environment Interaction Models

One of the major issues in plant breeding is the occurrence of genotype × environment (GE) interaction. Several models have been created to understand this phenomenon and explore it. In the genomic era, several models were employed to improve selection by using markers and account for GE interaction simultaneously. Some of these models use special genetic covariance matrices. In addition, the scale of multi-environment trials is getting larger, and this increases the computational challenges. In this context, we propose an R package that, in general, allows building GE genomic covariance matrices and fitting linear mixed models, in particular, to a few genomic GE models. Here we propose two functions: one to prepare the genomic kernels accounting for the genomic GE and another to perform genomic prediction using a Bayesian linear mixed model. A specific treatment is given for sparse covariance matrices, in particular, to block diagonal matrices that are present in some GE models in order to decrease the computational demand. In empirical comparisons with Bayesian Genomic Linear Regression (BGLR), accuracies and the mean squared error were similar; however, the computational time was up to five times lower than when using the classic approach. Bayesian Genomic Genotype × Environment Interaction (BGGE) is a fast, efficient option for creating genomic GE kernels and making genomic predictions.

Correction to: Accuracy of genomic selection to predict maize single-crosses obtained through different mating designs

Unfortunately, the first author name of the above-mentioned article was incorrectly published in the original publication. The complete correct name should read as follows.

Accuracy of genomic selection to predict maize single-crosses obtained through different mating designs

Testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II. Even though many papers have been published about genomic prediction (GP) in maize, the best mating design to build the training population has not been defined yet. Such design must maximize the accuracy given constraints on costs and on the logistics of the crosses to be made. Hence, the aims of this work were: (1) empirically evaluate the effect of the mating designs, used as training set, on genomic selection to predict maize single-crosses obtained through full diallel and North Carolina design II, (2) and identify the possibility of reducing the number of crosses and parents to compose these training sets. Our results suggest that testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II. Moreover, North Carolina design II is the best training set to predict hybrids taken from full diallel. However, hybrids from full diallel and North Carolina design II can be well predicted using optimized training sets, which also allow reducing the total number of crosses to be made. Nevertheless, the number of parents and the crosses per parent in the training sets should be maximized.

Genomic-Enabled Prediction Kernel Models with Random Intercepts for Multi-environment Trials

In this study, we compared the prediction accuracy of the main genotypic effect model (MM) without G×E interactions, the multi-environment single variance G×E deviation model (MDs), and the multi-environment environment-specific variance G×E deviation model (MDe) where the random genetic effects of the lines are modeled with the markers (or pedigree). With the objective of further modeling the genetic residual of the lines, we incorporated the random intercepts of the lines ([Formula: see text]) and generated another three models. Each of these 6 models were fitted with a linear kernel method (Genomic Best Linear Unbiased Predictor, GB) and a Gaussian Kernel (GK) method. We compared these 12 model-method combinations with another two multi-environment G×E interactions models with unstructured variance-covariances (MUC) using GB and GK kernels (4 model-method). Thus, we compared the genomic-enabled prediction accuracy of a total of 16 model-method combinations on two maize data sets with positive phenotypic correlations among environments, and on two wheat data sets with complex G×E that includes some negative and close to zero phenotypic correlations among environments. The two models (MDs and MDE with the random intercept of the lines and the GK method) were computationally efficient and gave high prediction accuracy in the two maize data sets. Regarding the more complex G×E wheat data sets, the prediction accuracy of the model-method combination with G×E, MDs and MDe, including the random intercepts of the lines with GK method had important savings in computing time as compared with the G×E interaction multi-environment models with unstructured variance-covariances but with lower genomic prediction accuracy.

Accuracy of genomic selection to predict maize single-crosses obtained through different mating designs

KEY MESSAGE

Testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II. Even though many papers have been published about genomic prediction (GP) in maize, the best mating design to build the training population has not been defined yet. Such design must maximize the accuracy given constraints on costs and on the logistics of the crosses to be made. Hence, the aims of this work were: (1) empirically evaluate the effect of the mating designs, used as training set, on genomic selection to predict maize single-crosses obtained through full diallel and North Carolina design II, (2) and identify the possibility of reducing the number of crosses and parents to compose these training sets. Our results suggest that testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II. Moreover, North Carolina design II is the best training set to predict hybrids taken from full diallel. However, hybrids from full diallel and North Carolina design II can be well predicted using optimized training sets, which also allow reducing the total number of crosses to be made. Nevertheless, the number of parents and the crosses per parent in the training sets should be maximized.

Effects of using phenotypic means and genotypic values in GGE biplot analyses on genotype by environment studies on tropical maize (Zea mays)

The objective of this study was to examine the effects of the type and intensity of nutritional stress, and of the statistical treatment of the data, on the genotype x environment (G x E) interaction for tropical maize (Zea mays). For this purpose, 39 hybrid combinations were evaluated under low- and high-nitrogen and -phosphorus availability. The plants were harvested at the V6 stage, and the shoot dry mass was estimated. The variance components and genetic values were assessed using the restricted maximum likelihood/best linear unbiased prediction method, and subsequently analyzed using the GGE biplot method. We observed differences in the performances of the hybrids depending on both the type and intensity of nutritional stress. The results of relationship between environments depended on whether genotypic values or phenotypic means were used. The selection of tropical maize genotypes against nutritional stress should be performed for each nutrient availability level within each type of nutritional stress. The use of phenotypic means for this purpose provides greater reliability than do genotypic values for the analysis of the G x E interaction using GGE biplot.