Genomic Prediction of Single Crosses in the Early Stages of a Maize Hybrid Breeding Pipeline

Genomic selection in plant breeding: Key factors shaping two decades of progress

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

Maximizing efficiency in sunflower breeding through historical data optimization

Genomic selection (GS) has become an increasingly popular tool in plant breeding programs, propelled by declining genotyping costs, an increase in computational power, and rediscovery of the best linear unbiased prediction methodology over the past two decades. This development has led to an accumulation of extensive historical datasets with genotypic and phenotypic information, triggering the question of how to best utilize these datasets. Here, we investigate whether all available data or a subset should be used to calibrate GS models for across-year predictions in a 7-year dataset of a commercial hybrid sunflower breeding program. We employed a multi-objective optimization approach to determine the ideal years to include in the training set (TRS). Next, for a given combination of TRS years, we further optimized the TRS size and its genetic composition. We developed the Min_GRM size optimization method which consistently found the optimal TRS size, reducing dimensionality by 20% with an approximately 1% loss in predictive ability. Additionally, the Tails_GEGVs algorithm displayed potential, outperforming the use of all data by using just 60% of it for grain yield, a high-complexity, low-heritability trait. Moreover, maximizing the genetic diversity of the TRS resulted in a consistent predictive ability across the entire range of genotypic values in the test set. Interestingly, the Tails_GEGVs algorithm, due to its ability to leverage heterogeneity, enhanced predictive performance for key hybrids with extreme genotypic values. Our study provides new insights into the optimal utilization of historical data in plant breeding programs, resulting in improved GS model predictive ability.

Portability of genomic predictions trained on sparse factorial designs across two maize silage breeding cycles

KEY MESSAGE

We validated the efficiency of genomic predictions calibrated on sparse factorial training sets to predict the next generation of hybrids and tested different strategies for updating predictions along generations. Genomic selection offers new prospects for revisiting hybrid breeding schemes by replacing extensive phenotyping of individuals with genomic predictions. Finding the ideal design for training genomic prediction models is still an open question. Previous studies have shown promising predictive abilities using sparse factorial instead of tester-based training sets to predict single-cross hybrids from the same generation. This study aims to further investigate the use of factorials and their optimization to predict line general combining abilities (GCAs) and hybrid values across breeding cycles. It relies on two breeding cycles of a maize reciprocal genomic selection scheme involving multiparental connected reciprocal populations from flint and dent complementary heterotic groups selected for silage performances. Selection based on genomic predictions trained on a factorial design resulted in a significant genetic gain for dry matter yield in the new generation. Results confirmed the efficiency of sparse factorial training sets to predict candidate line GCAs and hybrid values across breeding cycles. Compared to a previous study based on the first generation, the advantage of factorial over tester training sets appeared lower across generations. Updating factorial training sets by adding single-cross hybrids between selected lines from the previous generation or a random subset of hybrids from the new generation both improved predictive abilities. The CDmean criterion helped determine the set of single-crosses to phenotype to update the training set efficiently. Our results validated the efficiency of sparse factorial designs for calibrating hybrid genomic prediction experimentally and showed the benefit of updating it along generations.

Genome-Wide Association Study and Prediction of Tassel Weight of Tropical Maize Germplasm in Multi-Parent Population

Tassel weight (TW) is a crucial agronomic trait that significantly affects pollen supply and grain yield development in maize breeding. To improve maize yield and develop new varieties, a comprehensive understanding of the genetic mechanisms underlying tassel weight is essential. In this study, tropical maize inbred lines, namely CML312, CML373, CML444, and YML46, were selected as female parents and crossed with the elite maize inbred line Ye107, which served as the common male parent, to develop a multi-parent population comprising four F8 recombinant inbred line (RIL) subpopulations. Using 6616 high-quality single nucleotide polymorphism (SNP) markers, we conducted genome-wide association analysis (GWAS) and genomic selection (GS) on 642 F8 RILs in four subpopulations across three different environments. Through GWAS, we identified 16 SNPs that were significantly associated with TW, encompassing two stable loci expressed across multiple environments. Furthermore, within the candidate regions of these SNPs, we discovered four novel candidate genes related to TW, namely Zm00001d044362, Zm00001d011048, Zm00001d011049, and Zm00001d031173 distributed on chromosomes 1, 3, and 8, which have not been previously reported. These genes are involved in processes such as signal transduction, growth and development, protein splicing, and pollen development, all of which play crucial roles in inflorescence meristem development, directly affecting TW. The co-localized SNP, S8_137379725, on chromosome 8 was situated within a 16.569 kb long terminal repeat retrotransposon (LTR-RT), located 22.819 kb upstream and 26.428 kb downstream of the candidate genes (Zm00001d011048 and Zm00001d011049). When comparing three distinct GS models, the BayesB model demonstrated the highest accuracy in predicting TW. This study establishes the theoretical foundation for future research into the genetic mechanisms underlying maize TW and the efficient breeding of high-yielding varieties with desired tassel weight through GS.

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.

Reciprocal testcross design for genome-wide prediction of maize single-cross performance

KEY MESSAGE

A reciprocal testcross design increases the relatedness among single crosses and testcrosses, thereby increasing the effectiveness of genome-wide prediction in maize. A reciprocal testcross design uses parental inbreds in an opposite heterotic group as testers in maize (Zea mays L.) inbred development. In particular, doubled haploids from the A × B cross are testcrossed with inbreds Y and Z, and doubled haploids from Y × Z are testcrossed with inbreds A and B. Our objective was to determine if a reciprocal testcross design is superior to a traditional, non-reciprocal testcross design. A total of 700 Iowa Stiff Stalk Synthetic (BSSS) doubled haploids and 231 non-BSSS doubled haploids were developed from 10 breeding populations and had data on 11,032 single nucleotide polymorphism markers. Each doubled haploid was testcrossed to one to five testers from the opposite heterotic group, and the resulting 1642 testcrosses were evaluated in multilocation yield trials in 2019. Divergent selection for yield/moisture, on the basis of genome-wide predictions according to a reciprocal testcross design, led to significant responses (in 2020) in all 10 populations for yield/moisture and moisture and in three populations for yield. Predictive ability for yield/moisture and moisture was 0.11 to 0.26 higher with a reciprocal testcross design than with a testcross design. This higher predictive ability was attributed to a stronger relatedness between the training and test populations. No significant difference in predictive ability was found for yield, for which predictive ability was lower. Differences among genetic models that included and excluded specific combining ability were small. Overall, the empirical results supported the usefulness of a reciprocal testcross design in maize breeding.

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.

Genome-Wide Association Study and Genomic Prediction on Plant Architecture Traits in Sweet Corn and Waxy Corn

Sweet corn and waxy corn has a better taste and higher accumulated nutritional value than regular maize, and is widely planted and popularly consumed throughout the world. Plant height (PH), ear height (EH), and tassel branch number (TBN) are key plant architecture traits, which play an important role in improving grain yield in maize. In this study, a genome-wide association study (GWAS) and genomic prediction analysis were conducted on plant architecture traits of PH, EH, and TBN in a fresh edible maize population consisting of 190 sweet corn inbred lines and 287 waxy corn inbred lines. Phenotypic data from two locations showed high heritability for all three traits, with significant differences observed between sweet corn and waxy corn for both PH and EH. The differences between the three subgroups of sweet corn were not obvious for all three traits. Population structure and PCA analysis results divided the whole population into three subgroups, i.e., sweet corn, waxy corn, and the subgroup mixed with sweet and waxy corn. Analysis of GWAS was conducted with 278,592 SNPs obtained from resequencing data; 184, 45, and 68 significantly associated SNPs were detected for PH, EH, and TBN, respectively. The phenotypic variance explained (PVE) values of these significant SNPs ranged from 3.50% to 7.0%. The results of this study lay the foundation for further understanding the genetic basis of plant architecture traits in sweet corn and waxy corn. Genomic selection (GS) is a new approach for improving quantitative traits in large plant breeding populations that uses whole-genome molecular markers. The marker number and marker quality are essential for the application of GS in maize breeding. GWAS can choose the most related markers with the traits, so it can be used to improve the predictive accuracy of GS.

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.

Genomic prediction for the Germplasm Enhancement of Maize project

The Germplasm Enhancement of Maize (GEM) project was initiated in 1993 as a cooperative effort of public- and private-sector maize (Zea mays L.) breeders to enhance the genetic diversity of the U.S. maize crop. The GEM project selects progeny lines with high topcross yield potential from crosses between elite temperate lines and exotic parents. The GEM project has released hundreds of useful breeding lines based on phenotypic selection within selfing generations and multienvironment yield evaluations of GEM line topcrosses to elite adapted testers. Developing genomic selection (GS) models for the GEM project may contribute to increases in the rate of genetic gain. Here we evaluated the prediction ability of GS models trained on 6 yr of topcross evaluations from the two GEM programs in Raleigh, NC, and Ames, IA, documenting prediction abilities ranging from 0.36 to 0.75 for grain yield and from 0.78 to 0.96 for grain moisture when models were cross-validated within program and heterotic group. Predicted genetic gain from GS ranged from 0.95 to 2.58 times the gain from phenotypic selection. Prediction ability across program and heterotic group was generally poorer than within groups. Based on observed genomic relationships between GEM breeding lines and their tropical ancestors, GS for either yield or moisture would reduce recovery of exotic germplasm only slightly. Using GS models trained within program, the GEM programs should be able to more effectively deliver on its mission to broaden the genetic base of U.S. germplasm.

Genome-wide identification of genes enabling accurate prediction of hybrid performance from parents across environments and populations for gene-based breeding in maize

Accurate prediction of hybrid offspring complex trait phenotype from parents is paramount to enhanced plant breeding, animal breeding, and human medicine. Here we report genome-wide identification of genes enabling accurate prediction of hybrid offspring complex traits from parents using maize grain yield as the target trait. We identified 181 ZmF1GY genes enabling prediction of maize (Zea mays L.) F₁ hybrid grain yield from parents and tested their utility and efficiency for predicting F₁ hybrid grain yields from parents using their expressions, genic SNPs, and number of favorable alleles (NFAs), respectively. The ZmF1GY genes predicted hybrid grain yields from parents at an accuracy of 0.86, presented by correlation coefficient between predicted and observed phenotypes, within an environment, 0.74 across environments, and 0.64 across populations, outperforming genomic prediction by 27-406%, 23%, and 40%, respectively. Furthermore, we identified nine of the ZmF1GY genes containing SNPs or InDels in parents that increased or decreased hybrid grain yields by 14-46%. When the NFAs of these nine ZmF1GY genes were used for hybrid grain yield prediction from parents, they predicted hybrid grain yields at an accuracy of 0.79, outperforming genomic prediction by 21% that was based on up to tens of thousands of genome-wide SNPs. These results demonstrate the feasibility of developing a gene toolkit for a species enabling gene-based breeding across environments and populations that is much more powerful and efficient than current breeding, thereby helping secure the world's food production. The methodology is applicable to all crops, livestock, and humans.

Genomic prediction of hybrid performance: comparison of the efficiency of factorial and tester designs used as training sets in a multiparental connected reciprocal design for maize silage

Calibrating a genomic selection model on a sparse factorial design rather than on tester designs is advantageous for some traits, and equivalent for others. In maize breeding, the selection of the candidate inbred lines is based on topcross evaluations using a limited number of testers. Then, a subset of single-crosses between these selected lines is evaluated to identify the best hybrid combinations. Genomic selection enables the prediction of all possible single-crosses between candidate lines but raises the question of defining the best training set design. Previous simulation results have shown the potential of using a sparse factorial design instead of tester designs as the training set. To validate this result, a 363 hybrid factorial design was obtained by crossing 90 dent and flint inbred lines from six segregating families. Two tester designs were also obtained by crossing the same inbred lines to two testers of the opposite group. These designs were evaluated for silage in eight environments and used to predict independent performances of a 951 hybrid factorial design. At a same number of hybrids and lines, the factorial design was as efficient as the tester designs, and, for some traits, outperformed them. All available designs were used as both training and validation set to evaluate their efficiency. When the objective was to predict single-crosses between untested lines, we showed an advantage of increasing the number of lines involved in the training set, by (1) allocating each of them to a different tester for the tester design, or (2) reducing the number of hybrids per line for the factorial design. Our results confirm the potential of sparse factorial designs for genomic hybrid breeding.

Novel Insights into the Inheritance of Gibberella Ear Rot (GER), Deoxynivalenol (DON) Accumulation, and DON Production

Gibberella ear rot (GER) is an important fungal ear pathogen of maize that causes ear rot and toxin contamination. Most previous works have only dealt with the visual symptoms, but not with the toxins of GER. As food and feed safety rankings depend on toxin contamination, including deoxynivalenol (DON), without toxins, nothing can be said about the risks involved in food and feed quality. Therefore, three susceptible, three medium-susceptible, and three medium-resistant mother lines were crossed with three testers with differing degrees of resistance and tested between 2017–2020. Two plot replicates and two fungal strains were used separately. The highest heterosis was found at the GER% with a 13% increase across 27 hybrids, including 7 hybrids showing negative heterosis (a higher hybrid performance above the parental mean), with a variance ranging between 63.5 and −55.4. For DON, the mean heterosis was negative at −35%, and only 10 of the 27 hybrids showed a positive heterosis. The mean heterosis for DON contamination, at 1% GER, was again negative (−19.6%, varying between 85% and 224%). Only 17 hybrids showed heterosis, while that of the other 17 was rated higher than the parental mean. A positive significant correlation was found only for GER% and DON; the other factors were not significant. Seven hybrids were identified with positive (2) or negative (5) heterosis for all traits, while the rest varied. For DON and GER, only 13 provided identical (positive or negative) heteroses. The majority of the hybrids appeared to diverge in the regulation of the three traits. The stability of GER and DON (variance across eight data sets) did not agree—only half of the genotypes responded similarly for the two traits. The genetic background for this trait is unknown, and there was no general agreement between traits. Thus, without toxin analyses, the evaluation of food safety is not possible. The variety in degrees of resistance to toxigenic fungi and resistance to toxin accumulation is an inevitable factor.

Oil Palm Breeding in the Modern Era: Challenges and Opportunities

Oil palm, a cross-pollinated crop with long generation time, poses a lot of challenges in achieving sustainable oil palm with high yield and quality. The African oil palm (Elaeis guineensis Jacq.) is the most productive and versatile oil-yielding crop in the world, producing more than any other oil-yielding crop. Despite recent challenges, such as stress tolerance, superior oil quality, disease tolerance, and the need for new market niches, there is a growing need to explore and develop new varieties with high yield potential and the genetic diversity required to maintain oil palm yield stability. Breeding is an indispensable part of producing high-quality planting materials to increase oil palm yield. Biotechnological technologies have transformed conventional plant breeding approaches by introducing novel genotypes for breeding. Innovative pre-breeding and breeding approaches, such as identifying candidate genes in wild or land races using genomics tools, can pave the way for genetic improvement in oil palm. In this review, we highlighted the modern breeding tools, including genomics, marker-assisted breeding, genetic engineering, and genome editing techniques in oil palm crops, and we explored certain concerns connected to the techniques and their applications in practical breeding.

Building a Calibration Set for Genomic Prediction, Characteristics to Be Considered, and Optimization Approaches

The efficiency of genomic selection strongly depends on the prediction accuracy of the genetic merit of candidates. Numerous papers have shown that the composition of the calibration set is a key contributor to prediction accuracy. A poorly defined calibration set can result in low accuracies, whereas an optimized one can considerably increase accuracy compared to random sampling, for a same size. Alternatively, optimizing the calibration set can be a way of decreasing the costs of phenotyping by enabling similar levels of accuracy compared to random sampling but with fewer phenotypic units. We present here the different factors that have to be considered when designing a calibration set, and review the different criteria proposed in the literature. We classified these criteria into two groups: model-free criteria based on relatedness, and criteria derived from the linear mixed model. We introduce criteria targeting specific prediction objectives including the prediction of highly diverse panels, biparental families, or hybrids. We also review different ways of updating the calibration set, and different procedures for optimizing phenotyping experimental designs.

Improving genomic predictions with inbreeding and nonadditive effects in two admixed maize hybrid populations in single and multienvironment contexts

Genetic admixture, resulting from the recombination between structural groups, is frequently encountered in breeding populations. In hybrid breeding, crossing admixed lines can generate substantial nonadditive genetic variance and contrasted levels of inbreeding which can impact trait variation. This study aimed at testing recent methodological developments for the modeling of inbreeding and nonadditive effects in order to increase prediction accuracy in admixed populations. Using two maize (Zea mays L.) populations of hybrids admixed between dent and flint heterotic groups, we compared a suite of five genomic prediction models incorporating (or not) parameters accounting for inbreeding and nonadditive effects with the natural and orthogonal interaction approach in single and multienvironment contexts. In both populations, variance decompositions showed the strong impact of inbreeding on plant yield, height, and flowering time which was supported by the superiority of prediction models incorporating this effect (+0.038 in predictive ability for mean yield). In most cases dominance variance was reduced when inbreeding was accounted for. The model including additivity, dominance, epistasis, and inbreeding effects appeared to be the most robust for prediction across traits and populations (+0.054 in predictive ability for mean yield). In a multienvironment context, we found that the inclusion of nonadditive and inbreeding effects was advantageous when predicting hybrids not yet observed in any environment. Overall, comparing variance decompositions was helpful to guide model selection for genomic prediction. Finally, we recommend the use of models including inbreeding and nonadditive parameters following the natural and orthogonal interaction approach to increase prediction accuracy in admixed populations.

Genomic Prediction Methods Accounting for Nonadditive Genetic Effects

The use of genomic information for prediction of future phenotypes or breeding values for the candidates to selection has become a standard over the last decade. However, most procedures for genomic prediction only consider the additive (or substitution) effects associated with polymorphic markers. Nevertheless, the implementation of models that consider nonadditive genetic variation may be interesting because they (1) may increase the ability of prediction, (2) can be used to define mate allocation procedures in plant and animal breeding schemes, and (3) can be used to benefit from nonadditive genetic variation in crossbreeding or purebred breeding schemes. This study reviews the available methods for incorporating nonadditive effects into genomic prediction procedures and their potential applications in predicting future phenotypic performance, mate allocation, and crossbred and purebred selection. Finally, a brief outline of some future research lines is also proposed.

Genomic Prediction of Complex Traits in an Allogamous Annual Crop: The Case of Maize Single-Cross Hybrids

For many plant and animal species, commercial products are hybrids between individuals from different genetic groups. For allogamous plant species such as maize, the breeding objective is to produce single-cross hybrid varieties from two inbred lines each selected in complementary groups. Efficient hybrid breeding requires methods that (1) quickly generate homozygous and homogeneous parental lines with high combining abilities, (2) efficiently choose among the large number of available parental lines the most promising ones, and (3) predict the performances of sets of non-phenotyped single-cross hybrids, or hybrids phenotyped in a limited number of environments, based on their relationship with another set of hybrids with known performances. The maize breeding community has been developing model-based prediction of hybrid performances well before the genomic era. This chapter (1) provides a reminder of the maize breeding scheme before the genomic era; (2) describes how genomic data were incorporated in the prediction models involved in different steps of genomic-based single-cross maize hybrid breeding; and (3) reviews factors affecting the accuracy of genomic prediction, approaches for optimizing GP-based single-cross maize hybrid breeding schemes, and ensuring the long-term sustainability of genomic selection.

Genomic Selection in Sugarcane: Current Status and Future Prospects

Sugarcane is a C4 and agro-industry-based crop with a high potential for biomass production. It serves as raw material for the production of sugar, ethanol, and electricity. Modern sugarcane varieties are derived from the interspecific and intergeneric hybridization between Saccharum officinarum, Saccharum spontaneum, and other wild relatives. Sugarcane breeding programmes are broadly categorized into germplasm collection and characterization, pre-breeding and genetic base-broadening, and varietal development programmes. The varietal identification through the classic breeding programme requires a minimum of 12-14 years. The precise phenotyping in sugarcane is extremely tedious due to the high propensity of lodging and suckering owing to the influence of environmental factors and crop management practices. This kind of phenotyping requires data from both plant crop and ratoon experiments conducted over locations and seasons. In this review, we explored the feasibility of genomic selection schemes for various breeding programmes in sugarcane. The genetic diversity analysis using genome-wide markers helps in the formation of core set germplasm representing the total genomic diversity present in the Saccharum gene bank. The genome-wide association studies and genomic prediction in the Saccharum gene bank are helpful to identify the complete genomic resources for cane yield, commercial cane sugar, tolerances to biotic and abiotic stresses, and other agronomic traits. The implementation of genomic selection in pre-breeding, genetic base-broadening programmes assist in precise introgression of specific genes and recurrent selection schemes enhance the higher frequency of favorable alleles in the population with a considerable reduction in breeding cycles and population size. The integration of environmental covariates and genomic prediction in multi-environment trials assists in the prediction of varietal performance for different agro-climatic zones. This review also directed its focus on enhancing the genetic gain over time, cost, and resource allocation at various stages of breeding programmes.

Training Set Optimization for Sparse Phenotyping in Genomic Selection: A Conceptual Overview

Genomic selection (GS) is becoming an essential tool in breeding programs due to its role in increasing genetic gain per unit time. The design of the training set (TRS) in GS is one of the key steps in the implementation of GS in plant and animal breeding programs mainly because (i) TRS optimization is critical for the efficiency and effectiveness of GS, (ii) breeders test genotypes in multi-year and multi-location trials to select the best-performing ones. In this framework, TRS optimization can help to decrease the number of genotypes to be tested and, therefore, reduce phenotyping cost and time, and (iii) we can obtain better prediction accuracies from optimally selected TRS than an arbitrary TRS. Here, we concentrate the efforts on reviewing the lessons learned from TRS optimization studies and their impact on crop breeding and discuss important features for the success of TRS optimization under different scenarios. In this article, we review the lessons learned from training population optimization in plants and the major challenges associated with the optimization of GS including population size, the relationship between training and test set (TS), update of TRS, and the use of different packages and algorithms for TRS implementation in GS. Finally, we describe general guidelines to improving the rate of genetic improvement by maximizing the use of the TRS optimization in the GS framework.

Heterotic quantitative trait loci analysis and genomic prediction of seedling biomass-related traits in maize triple testcross populations

BACKGROUND

Heterosis has been widely used in maize breeding. However, we know little about the heterotic quantitative trait loci and their roles in genomic prediction. In this study, we sought to identify heterotic quantitative trait loci for seedling biomass-related traits using triple testcross design and compare their prediction accuracies by fitting molecular markers and heterotic quantitative trait loci.

RESULTS

A triple testcross population comprised of 366 genotypes was constructed by crossing each of 122 intermated B73 × Mo17 genotypes with B73, Mo17, and B73 × Mo17. The mid-parent heterosis of seedling biomass-related traits involved in leaf length, leaf width, leaf area, and seedling dry weight displayed a large range, from less than 50 to ~ 150%. Relationships between heterosis of seedling biomass-related traits showed congruency with that between performances. Based on a linkage map comprised of 1631 markers, 14 augmented additive, two augmented dominance, and three dominance × additive epistatic quantitative trait loci for heterosis of seedling biomass-related traits were identified, with each individually explaining 4.1-20.5% of the phenotypic variation. All modes of gene action, i.e., additive, partially dominant, dominant, and overdominant modes were observed. In addition, ten additive × additive and six dominance × dominance epistatic interactions were identified. By implementing the general and special combining ability model, we found that prediction accuracy ranged from 0.29 for leaf length to 0.56 for leaf width. Different number of marker analysis showed that ~ 800 markers almost capture the largest prediction accuracies. When incorporating the heterotic quantitative trait loci into the model, we did not find the significant change of prediction accuracy, with only leaf length showing the marginal improvement by 1.7%.

CONCLUSIONS

Our results demonstrated that the triple testcross design is suitable for detecting heterotic quantitative trait loci and evaluating the prediction accuracy. Seedling leaf width can be used as the representative trait for seedling prediction. The heterotic quantitative trait loci are not necessary for genomic prediction of seedling biomass-related traits.

The importance of dominance and genotype-by-environment interactions on grain yield variation in a large-scale public cooperative maize experiment

High-dimensional and high-throughput genomic, field performance, and environmental data are becoming increasingly available to crop breeding programs, and their integration can facilitate genomic prediction within and across environments and provide insights into the genetic architecture of complex traits and the nature of genotype-by-environment interactions. To partition trait variation into additive and dominance (main effect) genetic and corresponding genetic-by-environment variances, and to identify specific environmental factors that influence genotype-by-environment interactions, we curated and analyzed genotypic and phenotypic data on 1918 maize (Zea mays L.) hybrids and environmental data from 65 testing environments. For grain yield, dominance variance was similar in magnitude to additive variance, and genetic-by-environment variances were more important than genetic main effect variances. Models involving both additive and dominance relationships best fit the data and modeling unique genetic covariances among all environments provided the best characterization of the genotype-by-environment interaction patterns. Similarity of relative hybrid performance among environments was modeled as a function of underlying weather variables, permitting identification of weather covariates driving correlations of genetic effects across environments. The resulting models can be used for genomic prediction of mean hybrid performance across populations of environments tested or for environment-specific predictions. These results can also guide efforts to incorporate high-throughput environmental data into genomic prediction models and predict values in new environments characterized with the same environmental characteristics.

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.

Genomic prediction of hybrid crops allows disentangling dominance and epistasis

We revisited, in a genomic context, the theory of hybrid genetic evaluation models of hybrid crosses of pure lines, as the current practice is largely based on infinitesimal model assumptions. Expressions for covariances between hybrids due to additive substitution effects and dominance and epistatic deviations were analytically derived. Using dense markers in a GBLUP analysis, it is possible to split specific combining ability into dominance and across-groups epistatic deviations, and to split general combining ability (GCA) into within-line additive effects and within-line additive by additive (and higher order) epistatic deviations. We analyzed a publicly available maize data set of Dent × Flint hybrids using our new model (called GCA-model) up to additive by additive epistasis. To model higher order interactions within GCAs, we also fitted "residual genetic" line effects. Our new GCA-model was compared with another genomic model which assumes a uniquely defined effect of genes across origins. Most variation in hybrids is accounted by GCA. Variances due to dominance and epistasis have similar magnitudes. Models based on defining effects either differently or identically across heterotic groups resulted in similar predictive abilities for hybrids. The currently used model inflates the estimated additive genetic variance. This is not important for hybrid predictions but has consequences for the breeding scheme-e.g. overestimation of the genetic gain within heterotic group. Therefore, we recommend using GCA-model, which is appropriate for genomic prediction and variance component estimation in hybrid crops using genomic data, and whose results can be practically interpreted and used for breeding purposes.

Diversifying maize genomic selection models

Genomic selection (GS) is one of the most powerful tools available for maize breeding. Its use of genome-wide marker data to estimate breeding values translates to increased genetic gains with fewer breeding cycles. In this review, we cover the history of GS and highlight particular milestones during its adaptation to maize breeding. We discuss how GS can be applied to developing superior maize inbreds and hybrids. Additionally, we characterize refinements in GS models that could enable the encapsulation of non-additive genetic effects, genotype by environment interactions, and multiple levels of the biological hierarchy, all of which could ultimately result in more accurate predictions of breeding values. Finally, we suggest the stages in a maize breeding program where it would be beneficial to apply GS. Given the current sophistication of high-throughput phenotypic, genotypic, and other -omic level data currently available to the maize community, now is the time to explore the implications of their incorporation into GS models and thus ensure that genetic gains are being achieved as quickly and efficiently as possible.

Multi-omics-based prediction of hybrid performance in canola

Complementing or replacing genetic markers with transcriptomic data and use of reproducing kernel Hilbert space regression based on Gaussian kernels increases hybrid prediction accuracies for complex agronomic traits in canola. In plant breeding, hybrids gained particular importance due to heterosis, the superior performance of offspring compared to their inbred parents. Since the development of new top performing hybrids requires labour-intensive and costly breeding programmes, including testing of large numbers of experimental hybrids, the prediction of hybrid performance is of utmost interest to plant breeders. In this study, we tested the effectiveness of hybrid prediction models in spring-type oilseed rape (Brassica napus L./canola) employing different omics profiles, individually and in combination. To this end, a population of 950 F₁ hybrids was evaluated for seed yield and six other agronomically relevant traits in commercial field trials at several locations throughout Europe. A subset of these hybrids was also evaluated in a climatized glasshouse regarding early biomass production. For each of the 477 parental rapeseed lines, 13,201 single nucleotide polymorphisms (SNPs), 154 primary metabolites, and 19,479 transcripts were determined and used as predictive variables. Both, SNP markers and transcripts, effectively predict hybrid performance using (genomic) best linear unbiased prediction models (gBLUP). Compared to models using pure genetic markers, models incorporating transcriptome data resulted in significantly higher prediction accuracies for five out of seven agronomic traits, indicating that transcripts carry important information beyond genomic data. Notably, reproducing kernel Hilbert space regression based on Gaussian kernels significantly exceeded the predictive abilities of gBLUP models for six of the seven agronomic traits, demonstrating its potential for implementation in future canola breeding programmes.

Utility of Climatic Information via Combining Ability Models to Improve Genomic Prediction for Yield Within the Genomes to Fields Maize Project

Genomic prediction provides an efficient alternative to conventional phenotypic selection for developing improved cultivars with desirable characteristics. New and improved methods to genomic prediction are continually being developed that attempt to deal with the integration of data types beyond genomic information. Modern automated weather systems offer the opportunity to capture continuous data on a range of environmental parameters at specific field locations. In principle, this information could characterize training and target environments and enhance predictive ability by incorporating weather characteristics as part of the genotype-by-environment (G×E) interaction component in prediction models. We assessed the usefulness of including weather data variables in genomic prediction models using a naïve environmental kinship model across 30 environments comprising the Genomes to Fields (G2F) initiative in 2014 and 2015. Specifically four different prediction scenarios were evaluated (i) tested genotypes in observed environments; (ii) untested genotypes in observed environments; (iii) tested genotypes in unobserved environments; and (iv) untested genotypes in unobserved environments. A set of 1,481 unique hybrids were evaluated for grain yield. Evaluations were conducted using five different models including main effect of environments; general combining ability (GCA) effects of the maternal and paternal parents modeled using the genomic relationship matrix; specific combining ability (SCA) effects between maternal and paternal parents; interactions between genetic (GCA and SCA) effects and environmental effects; and finally interactions between the genetics effects and environmental covariates. Incorporation of the genotype-by-environment interaction term improved predictive ability across all scenarios. However, predictive ability was not improved through inclusion of naive environmental covariates in G×E models. More research should be conducted to link the observed weather conditions with important physiological aspects in plant development to improve predictive ability through the inclusion of weather data.

Exploiting genetic diversity in two European maize landraces for improving Gibberella ear rot resistance using genomic tools

KEY MESSAGE

High genetic variation in two European maize landraces can be harnessed to improve Gibberella ear rot resistance by integrated genomic tools. Fusarium graminearum (Fg) causes Gibberella ear rot (GER) in maize leading to yield reduction and contamination of grains with several mycotoxins. This study aimed to elucidate the molecular basis of GER resistance among 500 doubled haploid lines derived from two European maize landraces, "Kemater Landmais Gelb" (KE) and "Petkuser Ferdinand Rot" (PE). The two landraces were analyzed individually using genome-wide association studies and genomic selection (GS). The lines were genotyped with a 600-k maize array and phenotyped for GER severity, days to silking, plant height, and seed-set in four environments using artificial infection with a highly aggressive Fg isolate. High genotypic variances and broad-sense heritabilities were found for all traits. Genotype-environment interaction was important throughout. The phenotypic (r) and genotypic ([Formula: see text]) correlations between GER severity and three agronomic traits were low (r =  - 0.27 to 0.20; [Formula: see text]=  - 0.32 to 0.22). For GER severity, eight QTLs were detected in KE jointly explaining 34% of the genetic variance. In PE, no significant QTLs for GER severity were detected. No common QTLs were found between GER severity and the three agronomic traits. The mean prediction accuracies ([Formula: see text]) of weighted GS (wRR-BLUP) were higher than [Formula: see text] of marker-assisted selection (MAS) and unweighted GS (RR-BLUP) for GER severity. Using KE as the training set and PE as the validation set resulted in very low [Formula: see text] that could be improved by using fixed marker effects in the GS model.

Heterosis and Hybrid Crop Breeding: A Multidisciplinary Review

Although hybrid crop varieties are among the most popular agricultural innovations, the rationale for hybrid crop breeding is sometimes misunderstood. Hybrid breeding is slower and more resource-intensive than inbred breeding, but it allows systematic improvement of a population by recurrent selection and exploitation of heterosis simultaneously. Inbred parental lines can identically reproduce both themselves and their F1 progeny indefinitely, whereas outbred lines cannot, so uniform outbred lines must be bred indirectly through their inbred parents to harness heterosis. Heterosis is an expected consequence of whole-genome non-additive effects at the population level over evolutionary time. Understanding heterosis from the perspective of molecular genetic mechanisms alone may be elusive, because heterosis is likely an emergent property of populations. Hybrid breeding is a process of recurrent population improvement to maximize hybrid performance. Hybrid breeding is not maximization of heterosis per se, nor testing random combinations of individuals to find an exceptional hybrid, nor using heterosis in place of population improvement. Though there are methods to harness heterosis other than hybrid breeding, such as use of open-pollinated varieties or clonal propagation, they are not currently suitable for all crops or production environments. The use of genomic selection can decrease cycle time and costs in hybrid breeding, particularly by rapidly establishing heterotic pools, reducing testcrossing, and limiting the loss of genetic variance. Open questions in optimal use of genomic selection in hybrid crop breeding programs remain, such as how to choose founders of heterotic pools, the importance of dominance effects in genomic prediction, the necessary frequency of updating the training set with phenotypic information, and how to maintain genetic variance and prevent fixation of deleterious alleles.

How the pan-genome is changing crop genomics and improvement

Crop genomics has seen dramatic advances in recent years due to improvements in sequencing technology, assembly methods, and computational resources. These advances have led to the development of new tools to facilitate crop improvement. The study of structural variation within species and the characterization of the pan-genome has revealed extensive genome content variation among individuals within a species that is paradigm shifting to crop genomics and improvement. Here, we review advances in crop genomics and how utilization of these tools is shifting in light of pan-genomes that are becoming available for many crop species.

How the pan-genome is changing crop genomics and improvement

Crop genomics has seen dramatic advances in recent years due to improvements in sequencing technology, assembly methods, and computational resources. These advances have led to the development of new tools to facilitate crop improvement. The study of structural variation within species and the characterization of the pan-genome has revealed extensive genome content variation among individuals within a species that is paradigm shifting to crop genomics and improvement. Here, we review advances in crop genomics and how utilization of these tools is shifting in light of pan-genomes that are becoming available for many crop species.

Applications of Support Vector Machine in Genomic Prediction in Pig and Maize Populations

Genomic prediction (GP) has revolutionized animal and plant breeding. However, better statistical models that can improve the accuracy of GP are required. For this reason, in this study, we explored the genomic-based prediction performance of a popular machine learning method, the Support Vector Machine (SVM) model. We selected the most suitable kernel function and hyperparameters for the SVM model in eight published genomic data sets on pigs and maize. Next, we compared the SVM model with RBF and the linear kernel functions to the two most commonly used genome-enabled prediction models (GBLUP and BayesR) in terms of prediction accuracy, time, and the memory used. The results showed that the SVM model had the best prediction performance in two of the eight data sets, but in general, the predictions of both models were similar. In terms of time, the SVM model was better than BayesR but worse than GBLUP. In terms of memory, the SVM model was better than GBLUP and worse than BayesR in pig data but the same with BayesR in maize data. According to the results, SVM is a competitive method in animal and plant breeding, and there is no universal prediction model.

Testing methods and statistical models of genomic prediction for quantitative disease resistance to Phytophthora sojae in soybean [Glycine max (L.) Merr] germplasm collections

KEY MESSAGE

Genomic prediction of quantitative resistance toward Phytophthora sojae indicated that genomic selection may increase breeding efficiency. Statistical model and marker set had minimal effect on genomic prediction with > 1000 markers. Quantitative disease resistance (QDR) toward Phytophthora sojae in soybean is a complex trait controlled by many small-effect loci throughout the genome. Along with the technical and rate-limiting challenges of phenotyping resistance to a root pathogen, the trait complexity can limit breeding efficiency. However, the application of genomic prediction to traits with complex genetic architecture, such as QDR toward P. sojae, is likely to improve breeding efficiency. We provide a novel example of genomic prediction by measuring QDR to P. sojae in two diverse panels of more than 450 plant introductions (PIs) that had previously been genotyped with the SoySNP50K chip. This research was completed in a collection of diverse germplasm and contributes to both an initial assessment of genomic prediction performance and characterization of the soybean germplasm collection. We tested six statistical models used for genomic prediction including Bayesian Ridge Regression; Bayesian LASSO; Bayes A, B, C; and reproducing kernel Hilbert spaces. We also tested how the number and distribution of SNPs included in genomic prediction altered predictive ability by varying the number of markers from less than 50 to more than 34,000 SNPs, including SNPs based on sequential sampling, random sampling, or selections from association analyses. Predictive ability was relatively independent of statistical model and marker distribution, with a diminishing return when more than 1000 SNPs were included in genomic prediction. This work estimated relative efficiency per breeding cycle between 0.57 and 0.83, which may improve the genetic gain for P. sojae QDR in soybean breeding programs.

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.

Revisiting hybrid breeding designs using genomic predictions: simulations highlight the superiority of incomplete factorials between segregating families over topcross designs

Simulations showed that hybrid performances issued from an incomplete factorial between segregating families of two heterotic groups enable to calibrate genomic predictions of hybrid value more efficiently than tester-based designs. Genomic selection offers new opportunities to revisit hybrid breeding by replacing extensive phenotyping of hybrid combinations by genomic predictions. A key question remains to identify the best design to calibrate genomic prediction models. We proposed to use single-cross hybrids issued from an incomplete factorial design between segregating populations and compared this strategy with a conventional approach based on topcross evaluation. Two multiparental segregating populations of lines, each specific of one heterotic group, were simulated. Hybrids considered as training sets were generated using either (1) a parental line from the opposite group as tester or (2) following an incomplete factorial design. Different specific combining ability (SCA) proportions were simulated by considering different levels of group divergence and dominance effects for the simulated QTL. For the incomplete factorial design, for a same number of hybrids, we considered different numbers of parental lines and different contributions of lines (one to four) to calibration hybrids. We evaluated for different training set sizes prediction accuracies of new hybrids and genetic gains along three generations. At a given training set size, factorial design was as efficient (considering accuracy) as tester design in additive scenarios, but significantly outperformed tester design when SCA was present. The contribution number of each parental line to the incomplete factorial design had a small impact on accuracies. Our simulations confirmed experimental results and showed that calibrating models on hybrids between two multiparental populations is a cost-efficient way to perform genomic predictions in both groups, opening prospects for revisiting reciprocal recurrent selection schemes.

Dominance Effects and Functional Enrichments Improve Prediction of Agronomic Traits in Hybrid Maize

Single-cross hybrids have been critical to the improvement of maize (Zea mays L.), but the characterization of their genetic architectures remains challenging. Previous studies of hybrid maize have shown the contribution of within-locus complementation effects (dominance) and their differential importance across functional classes of loci. However, they have generally considered panels of limited genetic diversity, and have shown little benefit from genomic prediction based on dominance or functional enrichments. This study investigates the relevance of dominance and functional classes of variants in genomic models for agronomic traits in diverse populations of hybrid maize. We based our analyses on a diverse panel of inbred lines crossed with two testers representative of the major heterotic groups in the U.S. (1106 hybrids), as well as a collection of 24 biparental populations crossed with a single tester (1640 hybrids). We investigated three agronomic traits: days to silking (DTS), plant height (PH), and grain yield (GY). Our results point to the presence of dominance for all traits, but also among-locus complementation (epistasis) for DTS and genotype-by-environment interactions for GY. Consistently, dominance improved genomic prediction for PH only. In addition, we assessed enrichment of genetic effects in classes defined by genic regions (gene annotation), structural features (recombination rate and chromatin openness), and evolutionary features (minor allele frequency and evolutionary constraint). We found support for enrichment in genic regions and subsequent improvement of genomic prediction for all traits. Our results suggest that dominance and gene annotations improve genomic prediction across diverse populations in hybrid maize.

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).

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.

Genomic Prediction of Pumpkin Hybrid Performance

Genomic prediction has become an increasingly popular tool for hybrid performance evaluation in plant breeding mainly because that it can reduce cost and accelerate a breeding program. In this study, we propose a systematic procedure to predict hybrid performance using a genomic selection (GS) model that takes both additive and dominance marker effects into account. We first demonstrate the advantage of the additive-dominance effects model over the only additive effects model through a simulation study. Based on the additive-dominance model, we predict genomic estimated breeding values (GEBVs) for individual hybrid combinations and their parental lines. The GEBV-based specific combining ability (SCA) for each hybrid and general combining ability (GCA) for its parental lines are then derived to quantify the degree of midparent heterosis (MPH) or better-parent heterosis (BPH) of the hybrid. Finally, we estimate the variance components resulting from additive and dominance gene action effects and heritability using a genomic best linear unbiased predictor (g-BLUP) model. These estimates are used to justify the results of the genomic prediction study. A pumpkin ( spp.) data set is given to illustrate the provided procedure. The data set consists of 320 parental lines with 61,179 collected single nucleotide polymorphism (SNP) markers; 119, 120, and 120 phenotypic values of hybrids on three quantitative traits within maxima Duchesne; and 89, 111, and 90 phenotypic values of hybrids on the same three quantitative traits within Dechesne.

Use of F2 Bulks in Training Sets for Genomic Prediction of Combining Ability and Hybrid Performance

Developing training sets for genomic prediction in hybrid crops requires producing hybrid seed for a large number of entries. In autogamous crop species (e.g., wheat, rice, rapeseed, cotton) this requires elaborate hybridization systems to prevent self-pollination and presents a significant impediment to the implementation of hybrid breeding in general and genomic selection in particular. An alternative to F1 hybrids are bulks of F2 seed from selfed F1 plants (F1:2). Seed production for F1:2 bulks requires no hybridization system because the number of F1 plants needed for producing enough F1:2 seed for multi-environment testing can be generated by hand-pollination. This study evaluated the suitability of F1:2 bulks for use in training sets for genomic prediction of F1 level general combining ability and hybrid performance, under different degrees of divergence between heterotic groups and modes of gene action, using quantitative genetic theory and simulation of a genomic prediction experiment. The simulation, backed by theory, showed that F1:2 training sets are expected to have a lower prediction accuracy relative to F1 training sets, particularly when heterotic groups have strongly diverged. The accuracy penalty, however, was only modest and mostly because of a lower heritability, rather than because of a difference in F1 and F1:2 genetic values. It is concluded that resorting to F1:2 bulks is, in theory at least, a promising approach to remove the significant complication of a hybridization system from the breeding process.

Across-years prediction of hybrid performance in maize using genomics

Inclusion of historical training data improved the genomics-based prediction of performance of maize hybrids, the extent depending on the phenotypic trait and genotype-by-year interaction. Prediction of hybrid performance using existing phenotypic data on previous hybrids combined with molecular data collected on the parent lines allows to identify the most promising candidates from a huge number of possible hybrids at an early stage. Phenotypic data on yield and dry matter of 1970 grain maize hybrids from 19 years of a public breeding program were aggregated considering the underlying structure of factorial sets of hybrids. Pedigree records and 50 K SNP data were collected on their 170 Dent and 127 Flint parent lines. The performance of untested hybrids was predicted by best linear unbiased predictors (BLUP) on basis of pedigree or genomic data. For composition of training sets (TRN) and test sets (TST), three schemes for collecting factorials from specific years were employed which resulted in 490 scenarios. For each scenario, the predictive ability and genomic relationship between TRN and TST hybrids were determined. For extended TRNs, where earlier years were successively added to the TRN, the maximum relationship increased and the predictive ability improved, with the extent of the latter depending on the phenotypic trait and its genotype-by-year interaction. Genomic BLUP outperformed pedigree BLUP and better utilized the early years' data, especially for prediction of hybrids from factorials in a more distant future. This study on hybrid prediction in grain maize illustrated that including historical phenotypic data for training, although consisting of less related genotypes, can improve genomic prediction and enables optimization of hybrid variety development.

Efficient genetic value prediction using incomplete omics data

Covering a subset of individuals with a quantitative predictor, while imputing records for all others using pedigree or genomic data, could improve the precision of predictions while controlling for costs. Predicting genetic values with high accuracy is pivotal for effective candidate selection in animal and plant breeding. Novel 'omics'-based predictors have been shown to improve upon established genome-based predictions of important complex traits but require laborious and expensive assays. As a consequence, there are various datasets with full genetic marker coverage of all studied individuals but incomplete coverage with other 'omics' data. In animal breeding, single-step prediction was introduced to efficiently combine pedigree information, collected on a large number of animals, with genomic information, collected on a smaller subset of animals, for breeding value estimation without bias. Using two maize datasets of inbred lines and hybrids, we show that the single-step framework facilitates imputing transcriptomic data, boosting forecasts when their predictive ability exceeds that of pedigree or genomic data. Our results suggest that covering only a subset of inbred lines with 'omics' predictors and imputing all others using pedigree or genomic data could enable breeders to improve trait predictions while keeping costs under control. Employing 'omics' predictors could particularly improve candidate selection in hybrid breeding because the success of forecasts is a strongly convex function of predictive ability.

Response Surface Analysis of Genomic Prediction Accuracy Values Using Quality Control Covariates in Soybean

An important and broadly used tool for selection purposes and to increase yield and genetic gain in plant breeding programs is genomic prediction (GP). Genomic prediction is a technique where molecular marker information and phenotypic data are used to predict the phenotype (eg, yield) of individuals for which only marker data are available. Higher prediction accuracy can be achieved not only by using efficient models but also by using quality molecular marker and phenotypic data. The steps of a typical quality control (QC) of marker data include the elimination of markers with certain level of minor allele frequency (MAF) and missing marker values and the imputation of missing marker values. In this article, we evaluated how the prediction accuracy is influenced by the combination of 12 MAF values, 27 different percentages of missing marker values, and 2 imputation techniques (IT; naïve and Random Forest (RF)). We constructed a response surface of prediction accuracy values for the two ITs as a function of MAF and percentage of missing marker values using soybean data from the University of Nebraska-Lincoln Soybean Breeding Program. We found that both the genetic architecture of the trait and the IT affect the prediction accuracy implying that we have to be careful how we perform QC on the marker data. For the corresponding combinations MAF-percentage of missing values we observed that implementing the RF imputation increased the number of markers by 2 to 5 times than the simple naïve imputation method that is based on the mean allele dosage of the non-missing values at each loci. We conclude that there is not a unique strategy (combination of the QCs and imputation method) that outperforms the results of the others for all traits.

Optimal Designs for Genomic Selection in Hybrid Crops

Improved capacity of genomics and biotechnology has greatly enhanced genetic studies in different areas. Genomic selection exploits the genotype-to-phenotype relationship at the whole-genome level and is being implemented in many crops. Here we show that design-thinking and data-mining techniques can be leveraged to optimize genomic prediction of hybrid performance. We phenotyped a set of 276 maize hybrids generated by crossing founder inbreds of nested association mapping populations for flowering time, ear height, and grain yield. With 10 296 310 SNPs available from the parental inbreds, we explored the patterns of genomic relationships and phenotypic variation to establish training samples based on clustering, graphic network analysis, and genetic mating scheme. Our analysis showed that training set designs outperformed random sampling and earlier methods that either minimize the mean of prediction error variance or maximize the mean of generalized coefficient of determination. Additional analyses of 2556 wheat hybrids from an early-stage hybrid breeding system and 1439 rice hybrids from an established hybrid breeding system validated the approaches. Together, we demonstrated that effective genomic prediction models can be established with a training set 2%-13% of the size of the whole set, enabling an efficient exploration of enormous inference space of genetic combinations.

Technological advances in maize breeding: past, present and future

Maize has for many decades been both one of the most important crops worldwide and one of the primary genetic model organisms. More recently, maize breeding has been impacted by rapid technological advances in sequencing and genotyping technology, transformation including genome editing, doubled haploid technology, parallelled by progress in data sciences and the development of novel breeding approaches utilizing genomic information. Herein, we report on past, current and future developments relevant for maize breeding with regard to (1) genome analysis, (2) germplasm diversity characterization and utilization, (3) manipulation of genetic diversity by transformation and genome editing, (4) inbred line development and hybrid seed production, (5) understanding and prediction of hybrid performance, (6) breeding methodology and (7) synthesis of opportunities and challenges for future maize breeding.

A Benchmarking Between Deep Learning, Support Vector Machine and Bayesian Threshold Best Linear Unbiased Prediction for Predicting Ordinal Traits in Plant Breeding

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

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.