Genomewide predictions from maize single-cross data

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.

Genomic prediction in multi-environment trials in maize using statistical and machine learning methods

In the context of multi-environment trials (MET), genomic prediction is proposed as a tool that allows the prediction of the phenotype of single cross hybrids that were not tested in field trials. This approach saves time and costs compared to traditional breeding methods. Thus, this study aimed to evaluate the genomic prediction of single cross maize hybrids not tested in MET, grain yield and female flowering time. We also aimed to propose an application of machine learning methodologies in MET in the prediction of hybrids and compare their performance with Genomic best linear unbiased prediction (GBLUP) with non-additive effects. Our results highlight that both methodologies are efficient and can be used in maize breeding programs to accurately predict the performance of hybrids in specific environments. The best methodology is case-dependent, specifically, to explore the potential of GBLUP, it is important to perform accurate modeling of the variance components to optimize the prediction of new hybrids. On the other hand, machine learning methodologies can capture non-additive effects without making any assumptions at the outset of the model. Overall, predicting the performance of new hybrids that were not evaluated in any field trials was more challenging than predicting hybrids in sparse test designs.

Haplotype blocks for genomic prediction: a comparative evaluation in multiple crop datasets

In modern plant breeding, genomic selection is becoming the gold standard for selection of superior genotypes. The basis for genomic prediction models is a set of phenotyped lines along with their genotypic profile. With high marker density and linkage disequilibrium (LD) between markers, genotype data in breeding populations tends to exhibit considerable redundancy. Therefore, interest is growing in the use of haplotype blocks to overcome redundancy by summarizing co-inherited features. Moreover, haplotype blocks can help to capture local epistasis caused by interacting loci. Here, we compared genomic prediction methods that either used single SNPs or haplotype blocks with regards to their prediction accuracy for important traits in crop datasets. We used four published datasets from canola, maize, wheat and soybean. Different approaches to construct haplotype blocks were compared, including blocks based on LD, physical distance, number of adjacent markers and the algorithms implemented in the software "Haploview" and "HaploBlocker". The tested prediction methods included Genomic Best Linear Unbiased Prediction (GBLUP), Extended GBLUP to account for additive by additive epistasis (EGBLUP), Bayesian LASSO and Reproducing Kernel Hilbert Space (RKHS) regression. We found improved prediction accuracy in some traits when using haplotype blocks compared to SNP-based predictions, however the magnitude of improvement was very trait- and model-specific. Especially in settings with low marker density, haplotype blocks can improve genomic prediction accuracy. In most cases, physically large haplotype blocks yielded a strong decrease in prediction accuracy. Especially when prediction accuracy varies greatly across different prediction models, prediction based on haplotype blocks can improve prediction accuracy of underperforming models. However, there is no "best" method to build haplotype blocks, since prediction accuracy varied considerably across methods and traits. Hence, criteria used to define haplotype blocks should not be viewed as fixed biological parameters, but rather as hyperparameters that need to be adjusted for every dataset.

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.

Modeling the influence of phenotypic plasticity on maize hybrid performance

Phenotypic plasticity, the ability of an individual to alter its phenotype in response to changes in the environment, has been proposed as a target for breeding crop varieties with high environmental fitness. Here, we used phenotypic and genotypic data from multiple maize (Zea mays L.) populations to mathematically model phenotypic plasticity in response to the environment (PPRE) in inbred and hybrid lines. PPRE can be simply described by a linear model in which the two main parameters, intercept a and slope b, reflect two classes of genes responsive to endogenous (class A) and exogenous (class B) signals that coordinate plant development. Together, class A and class B genes contribute to the phenotypic plasticity of an individual in response to the environment. We also made connections between phenotypic plasticity and hybrid performance or general combining ability (GCA) of yield using 30 F₁ hybrid populations generated by crossing the same maternal line with 30 paternal lines from different maize heterotic groups. We show that the parameters a and b from two given parental lines must be concordant to reach an ideal GCA of F₁ yield. We hypothesize that coordinated regulation of the two classes of genes in the F₁ hybrid genome is the basis for high GCA. Based on this theory, we built a series of predictive models to evaluate GCA in silico between parental lines of different heterotic groups.

Genomic prediction of hybrid performance in grain sorghum (Sorghum bicolor L.)

Genomic selection is expected to improve selection efficiency and genetic gain in breeding programs. The objective of this study was to assess the efficacy of predicting the performance of grain sorghum hybrids using genomic information of parental genotypes. One hundred and two public sorghum inbred parents were genotyped using genotyping-by-sequencing. Ninty-nine of the inbreds were crossed to three tester female parents generating a total of 204 hybrids for evaluation at two environments. The hybrids were sorted in to three sets of 77,59 and 68 and evaluated along with two commercial checks using a randomized complete block design in three replications. The sequence analysis generated 66,265 SNP markers that were used to predict the performance of 204 F1 hybrids resulted from crosses between the parents. Both additive (partial model) and additive and dominance (full model) were constructed and tested using various training population (TP) sizes and cross-validation procedures. Increasing TP size from 41 to 163 increased prediction accuracies for all traits. With the partial model, the five-fold cross validated prediction accuracies ranged from 0.03 for thousand kernel weight (TKW) to 0.58 for grain yield (GY) while it ranged from 0.06 for TKW to 0.67 for GY with the full model. The results suggest that genomic prediction could become an effective tool for predicting the performance of sorghum hybrids based on parental genotypes.

Training set designs for prediction of yield and moisture of maize test cross hybrids with unreplicated trials

Unreplicated field trials and genomic prediction are both used to enhance the efficiency in early selection stages of a hybrid maize breeding program. No results are available on the optimal experimental design when combining both approaches. Our objectives were to investigate the effect of the training set design on the accuracy of genomic prediction in unreplicated maize test crosses. We carried out a cross validation study on basis of an experimental data set consisting of 1436 hybrids evaluated for yield and moisture for which genotyping information of 461 SNP markers were available. Training set designs of different size, implementing within environment prediction, within year prediction, across year prediction, and combinations of data sources across years and environments were compared with respect to their prediction accuracy. Across year prediction did not reach prediction accuracies that are useful for genomic selection. Within year prediction across environments provided useful correlations between observed and predicted breeding values. The prediction accuracies did not improve when adding to the training set data from previous years. We conclude that using all data available from unreplicated tests of the current breeding cycle provides a good accuracy of predicting test crosses, whereas adding data from previous breeding cycles, in which the genotypes are less related to the tested material, has only limited value for increasing the prediction accuracy.

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.

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.

Prediction ability of genome-wide markers in Pinus taeda L. within and between population is affected by relatedness to the training population and trait genetic architecture

Genomic prediction has the potential to significantly increase the rate of genetic gain in tree breeding programs. In this study, a clonally replicated population (n = 2063) was used to train a genomic prediction model. The model was validated both within the training population and in a separate population (n = 451). The prediction abilities from random (20% vs 80%) cross validation within the training population were 0.56 and 0.78 for height and stem form, respectively. Removal of all full-sib relatives within the training population resulted in ∼50% reduction in their genomic prediction ability for both traits. The average prediction ability for all 451 individual trees was 0.29 for height and 0.57 for stem form. The degree of genetic linkage (full-sib family, half sib family, unrelated) between the training and validation sets had a strong impact on prediction ability for stem form but not for height. A dominant dwarfing allele, the first to be reported in a conifer species, was discovered via genome-wide association studies on linkage Group 5 that conferred a 0.33-m mean height reduction. However, the QTL was family specific. The rapid decay of linkage disequilibrium, large genome size, and inconsistencies in marker-QTL linkage phase suggest that large, diverse training populations are needed for genomic selection in Pinus taeda L.

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.

Calibration and validation of predicted genomic breeding values in an advanced cycle maize population

Model training on data from all selection cycles yielded the highest prediction accuracy by attenuating specific effects of individual cycles. Expected reliability was a robust predictor of accuracies obtained with different calibration sets. The transition from phenotypic to genome-based selection requires a profound understanding of factors that determine genomic prediction accuracy. We analysed experimental data from a commercial maize breeding programme to investigate if genomic measures can assist in identifying optimal calibration sets for model training. The data set consisted of six contiguous selection cycles comprising testcrosses of 5968 doubled haploid lines genotyped with a minimum of 12,000 SNP markers. We evaluated genomic prediction accuracies in two independent prediction sets in combination with calibration sets differing in sample size and genomic measures (effective sample size, average maximum kinship, expected reliability, number of common polymorphic SNPs and linkage phase similarity). Our results indicate that across selection cycles prediction accuracies were as high as 0.57 for grain dry matter yield and 0.76 for grain dry matter content. Including data from all selection cycles in model training yielded the best results because interactions between calibration and prediction sets as well as the effects of different testers and specific years were attenuated. Among genomic measures, the expected reliability of genomic breeding values was the best predictor of empirical accuracies obtained with different calibration sets. For grain yield, a large difference between expected and empirical reliability was observed in one prediction set. We propose to use this difference as guidance for determining the weight phenotypic data of a given selection cycle should receive in model retraining and for selection when both genomic breeding values and phenotypes are available.

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.

Genomic Prediction across Structured Hybrid Populations and Environments in Maize

Genomic prediction (GP) across different populations and environments should be enhanced to increase the efficiency of crop breeding. In this study, four populations were constructed and genotyped with DNA chips containing 55,000 SNPs. These populations were testcrossed to a common tester, generating four hybrid populations. Yields of the four hybrid populations were evaluated in three environments. We demonstrated by using real data that the prediction accuracies of GP across structured hybrid populations were lower than those of within-population GP. Including relatives of the validation population in the training population could increase the prediction accuracies of GP across structured hybrid populations drastically. G × E models (including main and genotype-by-environment effect) had better performance than single environment (within environment) and across environment (including only main effect) GP models in the structured hybrid population, especially in the environment where yields had higher heritability. GP by implementing G × E models in two cross-validation schemes indicated that, to increase the prediction accuracy of a new hybrid line, it would be better to field-test the hybrid line in at least one environment. Our results would be helpful for designing training population and planning field testing in hybrid breeding.

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.

Integrated genomic selection for rapid improvement of crops

An increase in the rate of crop improvement is essential for achieving sustained food production and other needs of ever-increasing population. Genomic selection (GS) is a potential breeding tool that has been successfully employed in animal breeding and is being incorporated into plant breeding. GS promises accelerated breeding cycles through a rapid selection of superior genotypes. Numerous empirical and simulation studies on GS and realized impacts on improvement in the crop yields are recently being reported. For a holistic understanding of the technology, we briefly discuss the concept of genetic gain, GS methodology, its current status, advantages of GS over other breeding methods, prediction models, and the factors controlling prediction accuracy in GS. Also, integration of speed breeding and other novel technologies viz. high throughput genotyping and phenotyping technologies for enhancing the efficiency and pace of GS, followed by its prospective applications in varietal development programs is reviewed.

Optimization of training sets for genomic prediction of early-stage single crosses in maize

Training population optimization algorithms are useful for efficiently training genomic prediction models for single-cross performance, especially if the population is extended beyond only realized crosses to all possible single crosses. Genomic prediction of single-cross performance could allow effective evaluation of all possible single crosses between all inbreds developed in a hybrid breeding program. The objectives of the present study were to investigate the effect of different levels of relatedness on genomic predictive ability of single crosses, evaluate the usefulness of deterministic formula to forecast prediction accuracy in advance, and determine the potential for TRS optimization based on prediction error variance (PEVmean) and coefficient of determination (CDmean) criteria. We used 481 single crosses made by crossing 89 random recombinant inbred lines (RILs) belonging to the Iowa stiff stalk synthetic group with 103 random RILs belonging to the non-stiff stalk synthetic heterotic group. As expected, predictive ability was enhanced by ensuring close relationships between TRSs and target sets, even when TRS sizes were smaller. We found that designing a TRS based on PEVmean or CDmean criteria is useful for increasing the efficiency of genomic prediction of maize single crosses. We went further and extended the sampling space from that of all observed single crosses to all possible single crosses, providing a much larger genetic space within which to design a training population. Using all possible single crosses increased the advantage of the PEVmean and CDmean methods based on expected prediction accuracy. This finding suggests that it may be worthwhile using an optimization algorithm to select a training population from all possible single crosses to maximize efficiency in training accurate models for hybrid genomic prediction.

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.

How Population Structure Impacts Genomic Selection Accuracy in Cross-Validation: Implications for Practical Breeding

Over the last two decades, the application of genomic selection has been extensively studied in various crop species, and it has become a common practice to report prediction accuracies using cross validation. However, genomic prediction accuracies obtained from random cross validation can be strongly inflated due to population or family structure, a characteristic shared by many breeding populations. An understanding of the effect of population and family structure on prediction accuracy is essential for the successful application of genomic selection in plant breeding programs. The objective of this study was to make this effect and its implications for practical breeding programs comprehensible for breeders and scientists with a limited background in quantitative genetics and genomic selection theory. We, therefore, compared genomic prediction accuracies obtained from different random cross validation approaches and within-family prediction in three different prediction scenarios. We used a highly structured population of 940 Brassica napus hybrids coming from 46 testcross families and two subpopulations. Our demonstrations show how genomic prediction accuracies obtained from among-family predictions in random cross validation and within-family predictions capture different measures of prediction accuracy. While among-family prediction accuracy measures prediction accuracy of both the parent average component and the Mendelian sampling term, within-family prediction only measures how accurately the Mendelian sampling term can be predicted. With this paper we aim to foster a critical approach to different measures of genomic prediction accuracy and a careful analysis of values observed in genomic selection experiments and reported in literature.

Advancing crested wheatgrass [Agropyron cristatum (L.) Gaertn.] breeding through genotyping-by-sequencing and genomic selection

Crested wheatgrass [Agropyron cristatum (L.) Gaertn.] provides high quality, highly palatable forage for early season grazing. Genetic improvement of crested wheatgrass has been challenged by its complex genome, outcrossing nature, long breeding cycle, and lack of informative molecular markers. Genomic selection (GS) has potential for improving traits of perennial forage species, and genotyping-by-sequencing (GBS) has enabled the development of genome-wide markers in non-model polyploid plants. An attempt was made to explore the utility of GBS and GS in crested wheatgrass breeding. Sequencing and phenotyping 325 genotypes representing 10 diverse breeding lines were performed. Bioinformatics analysis identified 827, 3,616, 14,090 and 46,136 single nucleotide polymorphism markers at 20%, 30%, 40% and 50% missing marker levels, respectively. Four GS models (BayesA, BayesB, BayesCπ, and rrBLUP) were examined for the accuracy of predicting nine agro-morphological and three nutritive value traits. Moderate accuracy (0.20 to 0.32) was obtained for the prediction of heading days, leaf width, plant height, clump diameter, tillers per plant and early spring vigor for genotypes evaluated at Saskatoon, Canada. Similar accuracy (0.29 to 0.35) was obtained for predicting fall regrowth and plant height for genotypes evaluated at Swift Current, Canada. The Bayesian models displayed similar or higher accuracy than rrBLUP. These findings show the feasibility of GS application for a non-model species to advance plant breeding.

Combination of Linkage Mapping, GWAS, and GP to Dissect the Genetic Basis of Common Rust Resistance in Tropical Maize Germplasm

Common rust (CR) caused by Puccina sorghi is one of the destructive fungal foliar diseases of maize and has been reported to cause moderate to high yield losses. Providing CR resistant germplasm has the potential to increase yields. To dissect the genetic architecture of CR resistance in maize, association mapping, in conjunction with linkage mapping, joint linkage association mapping (JLAM), and genomic prediction (GP) was conducted on an association-mapping panel and five F₃ biparental populations using genotyping-by-sequencing (GBS) single-nucleotide polymorphisms (SNPs). Analysis of variance for the biparental populations and the association panel showed significant genotypic and genotype x environment (GXE) interaction variances except for GXE of Pop4. Heritability (h²) estimates were moderate with 0.37-0.45 for the individual F₃ populations, 0.45 across five populations and 0.65 for the association panel. Genome-wide association study (GWAS) analyses revealed 14 significant marker-trait associations which individually explained 6-10% of the total phenotypic variances. Individual population-based linkage analysis revealed 26 QTLs associated with CR resistance and together explained 14-40% of the total phenotypic variances. Linkage mapping revealed seven QTLs in pop1, nine QTL in pop2, four QTL in pop3, five QTL in pop4, and one QTL in pop5, distributed on all chromosomes except chromosome 10. JLAM for the 921 F3 families from five populations detected 18 QTLs distributed in all chromosomes except on chromosome 8. These QTLs individually explained 0.3 to 3.1% and together explained 45% of the total phenotypic variance. Among the 18 QTL detected through JLAM, six QTLs, qCR1-78, qCR1-227, qCR3-172, qCR3-186, qCR4-171, and qCR7-137 were also detected in linkage mapping. GP within population revealed low to moderate correlations with a range from 0.19 to 0.51. Prediction correlation was high with r = 0.78 for combined analysis of the five F₃ populations. Prediction of biparental populations by using association panel as training set reveals positive correlations ranging from 0.05 to 0.22, which encourages to develop an independent but related population as a training set which can be used to predict diverse but related populations. The findings of this study provide valuable information on understanding the genetic basis of CR resistance and the obtained information can be used for developing functional molecular markers for marker-assisted selection and for implementing GP to improve CR resistance in tropical maize.

Performance prediction of crosses in plant breeding through genotype by environment interactions

Performance prediction of potential crosses plays a significant role in plant breeding, which aims to produce new crop varieties that have higher yields, require fewer resources, and are more adaptable to the changing environments. In the 2020 Syngenta crop challenge, Syngenta challenged participants to predict the yield performance of a list of potential breeding crosses of inbreds and testers based on their historical yield data in different environments. They released a dataset that contained the observed yields for 294,128 corn hybrids through the crossing of 593 unique inbreds and 496 unique testers across multiple environments between 2016 and 2018. To address this challenge, we designed a new predictive approach that integrates random forest and an optimization model for G [Formula: see text] E interaction detection. Our computational experiment found that our approach achieved a relative root-mean-square-error (RMSE) of 0.0869 for the validation data, outperforming other state-of-the-art models such as factorization machine and extreme gradient boosting tree. Our model was also able to detect genotype by environment interactions that are potentially biologically insightful. This model won the first place in the 2020 Syngenta crop challenge in analytics.

Hybrid breeding in wheat: how shaping floral biology can offer new perspectives

Hybrid breeding in wheat (Triticum aestivum L.) has the potential to deliver major yield increases. This is a requisite to guarantee food security for increasing population demands and to counterbalance the effects of extreme environmental conditions. Successful hybrid breeding in wheat relies on forced outcrossing while preventing self-pollination. To achieve this, research has been directed towards identifying and improving fertility control systems. To maximise cross-pollination and seed set, however, fertility control systems need to be complemented by breeding phenotypically distinct male and female lines. This review summarises existing and novel male sterility systems for wheat hybridisation. We also consider the genetic resources that can be used to alter wheat's floral development and spike morphology, with a focus on the genetic variation already available. Exploiting these resources can lead to enhanced outcrossing, a key requirement in the progress towards hybrid wheat breeding.

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.

Hybrid Breeding for MLN Resistance: Heterosis, Combining Ability, and Hybrid Prediction

Prior knowledge on heterosis and quantitative genetic parameters on maize lethal necrosis (MLN) can help the breeders to develop numerous resistant or tolerant hybrids with optimum resources. Our objectives were to (1) estimate the quantitative genetic parameters for MLN disease severity, (2) investigate the efficiency of the prediction of hybrid performance based on parental per se and general combining ability (GCA) effects, and (3) examine the potential of hybrid prediction for MLN resistance or tolerance based on markers. Fifty elite maize inbred lines were selected based on their response to MLN under artificial inoculation. Crosses were made in a half diallel mating design to produce 307 F1 hybrids. All hybrids were evaluated in MLN quarantine facility in Naivasha, Kenya for two seasons under artificial inoculation. All 50 inbreds were genotyped with genotyping-by-sequencing (GBS) SNPs. The phenotypic variation was significant for all traits and the heritability was moderate to high. We observed that hybrids were superior to the mean performance of the parents for disease severity (−14.57%) and area under disease progress curve (AUDPC) (14.9%). Correlations were significant and moderate between line per se and GCA; and mean of parental value with hybrid performance for both disease severity and AUDPC value. Very low and negative correlation was observed between parental lines marker based genetic distance and heterosis. Nevertheless, the correlation of GCA effects was very high with hybrid performance which can suggests as a good predictor of MLN resistance. Genomic prediction of hybrid performance for MLN is high for both traits. We therefore conclude that there is potential for prediction of hybrid performance for MLN. Overall, the estimated quantitative genetic parameters suggest that through targeted approach, it is possible to develop outstanding lines and hybrids for MLN resistance.

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).

Hybrid breeding of rice via genomic selection

Hybrid breeding is the main strategy for improving productivity in many crops, especially in rice and maize. Genomic hybrid breeding is a technology that uses whole-genome markers to predict future hybrids. Predicted superior hybrids are then field evaluated and released as new hybrid cultivars after their superior performances are confirmed. This will increase the opportunity of selecting true superior hybrids with minimum costs. Here, we used genomic best linear unbiased prediction to perform hybrid performance prediction using an existing rice population of 1495 hybrids. Replicated 10-fold cross-validations showed that the prediction abilities on ten agronomic traits ranged from 0.35 to 0.92. Using the 1495 rice hybrids as a training sample, we predicted six agronomic traits of 100 hybrids derived from half diallel crosses involving 21 parents that are different from the parents of the hybrids in the training sample. The prediction abilities were relatively high, varying from 0.54 (yield) to 0.92 (grain length). We concluded that the current population of 1495 hybrids can be used to predict hybrids from seemingly unrelated parents. Eventually, we used this training population to predict all potential hybrids of cytoplasm male sterile lines from 3000 rice varieties from the 3K Rice Genome Project. Using a breeding index combining 10 traits, we identified the top and bottom 200 predicted hybrids. SNP genotypes of the training population and parameters estimated from this training population are available for general uses and further validation in genomic hybrid prediction of all potential hybrids generated from all varieties of rice.

Genome-Wide Analyses and Prediction of Resistance to MLN in Large Tropical Maize Germplasm

Maize lethal necrosis (MLN), caused by co-infection of maize chlorotic mottle virus and sugarcane mosaic virus, can lead up to 100% yield loss. Identification and validation of genomic regions can facilitate marker assisted breeding for resistance to MLN. Our objectives were to identify marker-trait associations using genome wide association study and assess the potential of genomic prediction for MLN resistance in a large panel of diverse maize lines. A set of 1400 diverse maize tropical inbred lines were evaluated for their response to MLN under artificial inoculation by measuring disease severity or incidence and area under disease progress curve (AUDPC). All lines were genotyped with genotyping by sequencing (GBS) SNPs. The phenotypic variation was significant for all traits and the heritability estimates were moderate to high. GWAS revealed 32 significantly associated SNPs for MLN resistance (at p < 1.0 × 10⁻⁶). For disease severity, these significantly associated SNPs individually explained 3–5% of the total phenotypic variance, whereas for AUDPC they explained 3–12% of the total proportion of phenotypic variance. Most of significant SNPs were consistent with the previous studies and assists to validate and fine map the big quantitative trait locus (QTL) regions into few markers’ specific regions. A set of putative candidate genes associated with the significant markers were identified and their functions revealed to be directly or indirectly involved in plant defense responses. Genomic prediction revealed reasonable prediction accuracies. The prediction accuracies significantly increased with increasing marker densities and training population size. These results support that MLN is a complex trait controlled by few major and many minor effect genes.

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.

QTL mapping and genome-wide prediction of heat tolerance in multiple connected populations of temperate maize

Climate change will lead to increasing heat stress in the temperate regions of the world. The objectives of this study were the following: (I) to assess the phenotypic and genotypic diversity of traits related to heat tolerance of maize seedlings and dissect their genetic architecture by quantitative trait locus (QTL) mapping, (II) to compare the prediction ability of genome-wide prediction models using various numbers of KASP (Kompetitive Allele Specific PCR genotyping) single nucleotide polymorphisms (SNPs) and RAD (restriction site-associated DNA sequencing) SNPs, and (III) to examine the prediction ability of intra-, inter-, and mixed-pool calibrations. For the heat susceptibility index of five of the nine studied traits, we identified a total of six QTL, each explaining individually between 7 and 9% of the phenotypic variance. The prediction abilities observed for the genome-wide prediction models were high, especially for the within-population calibrations, and thus, the use of such approaches to select for heat tolerance at seedling stage is recommended. Furthermore, we have shown that for the traits examined in our study, populations created from inter-pool crosses are suitable training sets to predict populations derived from intra-pool crosses.

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.

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.

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.

When less can be better: How can we make genomic selection more cost-effective and accurate in barley?

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

Heterotic loci identified for maize kernel traits in two chromosome segment substitution line test populations

Heterosis has been widely used to increase grain quality and yield, but its genetic mechanism remains unclear. In this study, the genetic basis of heterosis for four maize kernel traits was examined in two test populations constructed using a set of 184 chromosome segment substitution lines (CSSLs) and two inbred lines (Zheng58 and Xun9058) in two environments. 63 and 57 different heterotic loci (HL) were identified for four kernel traits in the CSSLs × Zheng58 and CSSLs × Xun9058 populations, respectively. Of these, nine HL and six HL were identified for four kernel traits in the CSSLs × Zheng58 and CSSLs × Xun9058 populations, at the two locations simultaneously. Comparative analysis of the HL for the four kernel traits identified only 21 HL in the two test populations simultaneously. These results showed that most HL for the four kernel traits differed between the two test populations. The common HL were important loci from the Reid × Tangsipingtou heterotic model, and could be used to predict hybrid performance in maize breeding.

Accelerating genetic gains in legumes for the development of prosperous smallholder agriculture: integrating genomics, phenotyping, systems modelling and agronomy

Grain legumes form an important component of the human diet, provide feed for livestock, and replenish soil fertility through biological nitrogen fixation. Globally, the demand for food legumes is increasing as they complement cereals in protein requirements and possess a high percentage of digestible protein. Climate change has enhanced the frequency and intensity of drought stress, posing serious production constraints, especially in rainfed regions where most legumes are produced. Genetic improvement of legumes, like other crops, is mostly based on pedigree and performance-based selection over the past half century. To achieve faster genetic gains in legumes in rainfed conditions, this review proposes the integration of modern genomics approaches, high throughput phenomics, and simulation modelling in support of crop improvement that leads to improved varieties that perform with appropriate agronomy. Selection intensity, generation interval, and improved operational efficiencies in breeding are expected to further enhance the genetic gain in experimental plots. Improved seed access to farmers, combined with appropriate agronomic packages in farmers' fields, will deliver higher genetic gains. Enhanced genetic gains, including not only productivity but also nutritional and market traits, will increase the profitability of farming and the availability of affordable nutritious food especially in developing countries.

Beyond Genomic Prediction: Combining Different Types of omics Data Can Improve Prediction of Hybrid Performance in Maize

The ability to predict the agronomic performance of single-crosses with high precision is essential for selecting superior candidates for hybrid breeding. With recent technological advances, thousands of new parent lines, and, consequently, millions of new hybrid combinations are possible in each breeding cycle, yet only a few hundred can be produced and phenotyped in multi-environment yield trials. Well established prediction approaches such as best linear unbiased prediction (BLUP) using pedigree data and whole-genome prediction using genomic data are limited in capturing epistasis and interactions occurring within and among downstream biological strata such as transcriptome and metabolome. Because mRNA and small RNA (sRNA) sequences are involved in transcriptional, translational and post-translational processes, we expect them to provide information influencing several biological strata. However, using sRNA data of parent lines to predict hybrid performance has not yet been addressed. Here, we gathered genomic, transcriptomic (mRNA and sRNA) and metabolomic data of parent lines to evaluate the ability of the data to predict the performance of untested hybrids for important agronomic traits in grain maize. We found a considerable interaction for predictive ability between predictor and trait, with mRNA data being a superior predictor for grain yield and genomic data for grain dry matter content, while sRNA performed relatively poorly for both traits. Combining mRNA and genomic data as predictors resulted in high predictive abilities across both traits and combining other predictors improved prediction over that of the individual predictors alone. We conclude that downstream "omics" can complement genomics for hybrid prediction, and, thereby, contribute to more efficient selection of hybrid candidates.

Efficiency of genomic prediction of non-assessed single crosses

An important application of genomic selection in plant breeding is predicting untested single crosses (SCs). Most investigations on the prediction efficiency were based on tested SCs using cross-validation. The main objective was to assess the prediction efficiency by correlating the predicted and true genotypic values of untested SCs (accuracy) and measuring the efficacy of identification of the best 300 untested SCs (coincidence) using simulated data. We assumed 10,000 SNPs, 400 QTLs, two groups of 70 selected DH lines, and 4900 SCs. The heritabilities for the assessed SCs were 30, 60, and 100%. The scenarios included three sampling processes of DH lines, two sampling processes of SCs for testing, two SNP densities, DH lines from distinct and the same populations, DH lines from populations with lower LD, two genetic models, three statistical models, and three statistical approaches. We derived a model for genomic prediction based on SNP average effects of substitution and dominance deviations. The prediction accuracy is not affected by the linkage phase. The prediction of untested SCs is very efficient. The accuracies and coincidences ranged from ~0.8 and 0.5 at low heritability to 0.9 and 0.7 at high heritability, respectively. We also highlight the relevance of the overall LD and demonstrate that efficient prediction of untested SCs can be achieved for crops that show no heterotic pattern, for reduced training set size (10%), for SNP density of 1 cM, and for distinct sampling processes of DH lines based on random choice of the SCs for testing.

Genome-wide regression models considering general and specific combining ability predict hybrid performance in oilseed rape with similar accuracy regardless of trait architecture

Genomic prediction using the Brassica 60 k genotyping array is efficient in oilseed rape hybrids. Prediction accuracy is more dependent on trait complexity than on the prediction model. In oilseed rape breeding programs, performance prediction of parental combinations is of fundamental importance. Due to the phenomenon of heterosis, per se performance is not a reliable indicator for F₁-hybrid performance, and selection of well-paired parents requires the testing of large quantities of hybrid combinations in extensive field trials. However, the number of potential hybrids, in general, dramatically exceeds breeding capacity and budget. Integration of genomic selection (GS) could substantially increase the number of potential combinations that can be evaluated. GS models can be used to predict the performance of untested individuals based only on their genotypic profiles, using marker effects previously predicted in a training population. This allows for a preselection of promising genotypes, enabling a more efficient allocation of resources. In this study, we evaluated the usefulness of the Illumina Brassica 60 k SNP array for genomic prediction and compared three alternative approaches based on a homoscedastic ridge regression BLUP and three Bayesian prediction models that considered general and specific combining ability (GCA and SCA, respectively). A total of 448 hybrids were produced in a commercial breeding program from unbalanced crosses between 220 paternal doubled haploid lines and five male-sterile testers. Predictive ability was evaluated for seven agronomic traits. We demonstrate that the Brassica 60 k genotyping array is an adequate and highly valuable platform to implement genomic prediction of hybrid performance in oilseed rape. Furthermore, we present first insights into the application of established statistical models for prediction of important agronomical traits with contrasting patterns of polygenic control.

Systematic bias of correlation coefficient may explain negative accuracy of genomic prediction

Accuracy of genomic prediction is commonly calculated as the Pearson correlation coefficient between the predicted and observed phenotypes in the inference population by using cross-validation analysis. More frequently than expected, significant negative accuracies of genomic prediction have been reported in genomic selection studies. These negative values are surprising, given that the minimum value for prediction accuracy should hover around zero when randomly permuted data sets are analyzed. We reviewed the two common approaches for calculating the Pearson correlation and hypothesized that these negative accuracy values reflect potential bias owing to artifacts caused by the mathematical formulas used to calculate prediction accuracy. The first approach, Instant accuracy, calculates correlations for each fold and reports prediction accuracy as the mean of correlations across fold. The other approach, Hold accuracy, predicts all phenotypes in all fold and calculates correlation between the observed and predicted phenotypes at the end of the cross-validation process. Using simulated and real data, we demonstrated that our hypothesis is true. Both approaches are biased downward under certain conditions. The biases become larger when more fold are employed and when the expected accuracy is low. The bias of Instant accuracy can be corrected using a modified formula.

Genome-Based Identification of Heterotic Patterns in Rice

BACKGROUND

Hybrid rice breeding facilitates to increase grain yield and yield stability. Long-term success of hybrid breeding depends on the recognition of high-yielding complementary heterotic patterns, which is lacking in crops like rice.

RESULT

The main goal of this study was to evaluate the potential and limits to use genomics for establishing heterotic patterns in rice. For this purpose, data of a commercial hybrid rice breeding program targeted to India was analyzed, including 1,960 phenotyped hybrids from three market segments and 262 genotyped parental lines. Our cross-validation study revealed that grain yield of all potential single-crosses can be accurately predicted. Based on the full matrix of hybrid performances, high-yielding heterotic patterns were identified. These heterotic patterns increased grain yield up to 9% compared to the currently employed groups. Heterotic groups of around 14 individuals reflect a good compromise between long-term and short-term selection response.

CONCLUSIONS

Our findings clearly underlined the benefits of a genome-based establishment of heterotic patterns in rice as a requirement for a sustainable long-term success of hybrid rice breeding.

Effect of Trait Heritability, Training Population Size and Marker Density on Genomic Prediction Accuracy Estimation in 22 bi-parental Tropical Maize Populations

Genomic selection is being used increasingly in plant breeding to accelerate genetic gain per unit time. One of the most important applications of genomic selection in maize breeding is to predict and select the best un-phenotyped lines in bi-parental populations based on genomic estimated breeding values. In the present study, 22 bi-parental tropical maize populations genotyped with low density SNPs were used to evaluate the genomic prediction accuracy (rMG ) of the six trait-environment combinations under various levels of training population size (TPS) and marker density (MD), and assess the effect of trait heritability (h2 ), TPS and MD on rMG estimation. Our results showed that: (1) moderate rMG values were obtained for different trait-environment combinations, when 50% of the total genotypes was used as training population and ~200 SNPs were used for prediction; (2) rMG increased with an increase in h2 , TPS and MD, both correlation and variance analyses showed that h2 is the most important factor and MD is the least important factor on rMG estimation for most of the trait-environment combinations; (3) predictions between pairwise half-sib populations showed that the rMG values for all the six trait-environment combinations were centered around zero, 49% predictions had rMG values above zero; (4) the trend observed in rMG differed with the trend observed in rMG /h, and h is the square root of heritability of the predicted trait, it indicated that both rMG and rMG /h values should be presented in GS study to show the accuracy of genomic selection and the relative accuracy of genomic selection compared with phenotypic selection, respectively. This study provides useful information to maize breeders to design genomic selection workflow in their breeding programs.

Genome-wide regression models considering general and specific combining ability predict hybrid performance in oilseed rape with similar accuracy regardless of trait architecture

KEY MESSAGE

Genomic prediction using the Brassica 60 k genotyping array is efficient in oilseed rape hybrids. Prediction accuracy is more dependent on trait complexity than on the prediction model. In oilseed rape breeding programs, performance prediction of parental combinations is of fundamental importance. Due to the phenomenon of heterosis, per se performance is not a reliable indicator for F₁-hybrid performance, and selection of well-paired parents requires the testing of large quantities of hybrid combinations in extensive field trials. However, the number of potential hybrids, in general, dramatically exceeds breeding capacity and budget. Integration of genomic selection (GS) could substantially increase the number of potential combinations that can be evaluated. GS models can be used to predict the performance of untested individuals based only on their genotypic profiles, using marker effects previously predicted in a training population. This allows for a preselection of promising genotypes, enabling a more efficient allocation of resources. In this study, we evaluated the usefulness of the Illumina Brassica 60 k SNP array for genomic prediction and compared three alternative approaches based on a homoscedastic ridge regression BLUP and three Bayesian prediction models that considered general and specific combining ability (GCA and SCA, respectively). A total of 448 hybrids were produced in a commercial breeding program from unbalanced crosses between 220 paternal doubled haploid lines and five male-sterile testers. Predictive ability was evaluated for seven agronomic traits. We demonstrate that the Brassica 60 k genotyping array is an adequate and highly valuable platform to implement genomic prediction of hybrid performance in oilseed rape. Furthermore, we present first insights into the application of established statistical models for prediction of important agronomical traits with contrasting patterns of polygenic control.

Genomic-based-breeding tools for tropical maize improvement

Maize has traditionally been the main staple diet in the Southern Asia and Sub-Saharan Africa and widely grown by millions of resource poor small scale farmers. Approximately, 35.4 million hectares are sown to tropical maize, constituting around 59% of the developing worlds. Tropical maize encounters tremendous challenges besides poor agro-climatic situations with average yields recorded <3 tones/hectare that is far less than the average of developed countries. On the contrary to poor yields, the demand for maize as food, feed, and fuel is continuously increasing in these regions. Heterosis breeding introduced in early 90 s improved maize yields significantly, but genetic gains is still a mirage, particularly for crop growing under marginal environments. Application of molecular markers has accelerated the pace of maize breeding to some extent. The availability of array of sequencing and genotyping technologies offers unrivalled service to improve precision in maize-breeding programs through modern approaches such as genomic selection, genome-wide association studies, bulk segregant analysis-based sequencing approaches, etc. Superior alleles underlying complex traits can easily be identified and introgressed efficiently using these sequence-based approaches. Integration of genomic tools and techniques with advanced genetic resources such as nested association mapping and backcross nested association mapping could certainly address the genetic issues in maize improvement programs in developing countries. Huge diversity in tropical maize and its inherent capacity for doubled haploid technology offers advantage to apply the next generation genomic tools for accelerating production in marginal environments of tropical and subtropical world. Precision in phenotyping is the key for success of any molecular-breeding approach. This article reviews genomic technologies and their application to improve agronomic traits in tropical maize breeding has been reviewed in detail.

Omics-based hybrid prediction in maize

Complementing genomic data with other "omics" predictors can increase the probability of success for predicting the best hybrid combinations using complex agronomic traits. Accurate prediction of traits with complex genetic architecture is crucial for selecting superior candidates in animal and plant breeding and for guiding decisions in personalized medicine. Whole-genome prediction has revolutionized these areas but has inherent limitations in incorporating intricate epistatic interactions. Downstream "omics" data are expected to integrate interactions within and between different biological strata and provide the opportunity to improve trait prediction. Yet, predicting traits from parents to progeny has not been addressed by a combination of "omics" data. Here, we evaluate several "omics" predictors-genomic, transcriptomic and metabolic data-measured on parent lines at early developmental stages and demonstrate that the integration of transcriptomic with genomic data leads to higher success rates in the correct prediction of untested hybrid combinations in maize. Despite the high predictive ability of genomic data, transcriptomic data alone outperformed them and other predictors for the most complex heterotic trait, dry matter yield. An eQTL analysis revealed that transcriptomic data integrate genomic information from both, adjacent and distant sites relative to the expressed genes. Together, these findings suggest that downstream predictors capture physiological epistasis that is transmitted from parents to their hybrid offspring. We conclude that the use of downstream "omics" data in prediction can exploit important information beyond structural genomics for leveraging the efficiency of hybrid breeding.

Identification of heterotic loci associated with grain yield and its components using two CSSL test populations in maize

Heterosis has widely been used to increase grain yield and quality. In this study, the genetic basis of heterosis on grain yield and its main components in maize were examined over 2 years in two locations in two test populations constructed from a set of 184 chromosome segment substitution lines (CSSLs) and two inbred lines (Zheng58 and Xun9058). Of the 169 heterotic loci (HL) associated with grain yield and its five components identified in CSSL × Zheng58 and CSSL × Xun9058 test populations, only 25 HL were detected in both populations. The comparison of quantitative trait loci (QTLs) detected in the CSSL population with HL detected in the two test populations revealed that only 15.46% and 17.35% of the HL in the given populations respectively, shared the same chromosomal regions as that of the corresponding QTLs and showed dominant effects as well as pleiotropism with additive and dominant effects. In addition, most of the HL (74.23% and 74.49%) had overdominant effects. These results suggest that overdominance is the main contributor to the effects of heterosis on grain yield and its components in maize, and different HL are associated with heterosis for different traits in different hybrids.