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

Phenomic Selection for Hybrid Rapeseed Breeding

Phenomic selection is a recent approach suggested as a low-cost, high-throughput alternative to genomic selection. Instead of using genetic markers, it employs spectral data to predict complex traits using equivalent statistical models. Phenomic selection has been shown to outperform genomic selection when using spectral data that was obtained within the same generation as the traits that were predicted. However, for hybrid breeding, the key question is whether spectral data from parental genotypes can be used to effectively predict traits in the hybrid generation. Here, we aimed to evaluate the potential of phenomic selection for hybrid rapeseed breeding. We performed predictions for various traits in a structured population of 410 test hybrids, grown in multiple environments, using near-infrared spectroscopy data obtained from harvested seeds of both the hybrids and their parental lines with different linear and nonlinear models. We found that phenomic selection within the hybrid generation outperformed genomic selection for seed yield and plant height, even when spectral data was collected at single locations, while being less affected by population structure. Furthermore, we demonstrate that phenomic prediction across generations is feasible, and selecting hybrids based on spectral data obtained from parental genotypes is competitive with genomic selection. We conclude that phenomic selection is a promising approach for rapeseed breeding that can be easily implemented without any additional costs or efforts as near-infrared spectroscopy is routinely assessed in rapeseed breeding.

Optimizing selection based on BLUPs or BLUEs in multiple sets of genotypes differing in their population parameters

KEY MESSAGE

Selection response in truncation selection across multiple sets of candidates hinges on their post-selection proportions, which can deviate grossly from their initial proportions. For BLUPs, using a uniform threshold for all candidates maximizes the selection response, irrespective of differences in population parameters. Plant breeding programs typically involve multiple families from either the same or different populations, varying in means, genetic variances and prediction accuracy of BLUPs or BLUEs for true genetic values (TGVs) of candidates. We extend the classical breeder's equation for truncation selection from single to multiple sets of genotypes, indicating that the expected overall selection response ( Δ G Tot ) for TGVs depends on the selection response within individual sets and their post-selection proportions. For BLUEs, we show that maximizingΔ G Tot requires thresholds optimally tailored for each set, contingent on their population parameters. For BLUPs, we prove thatΔ G Tot is maximized by applying a uniform threshold across all candidates from all sets. We provide explicit formulas for the origin of the selected candidates from different sets and show that their proportions before and after selection can differ substantially, especially for sets with inferior properties and low proportion. We discuss implications of these results for (a) optimum allocation of resources to training and prediction sets and (b) the need to counteract narrowing the genetic variation under genomic selection. For genomic selection of hybrids based on BLUPs of GCA of their parent lines, selecting distinct proportions in the two parent populations can be advantageous, if these differ substantially in the variance and/or prediction accuracy of GCA. Our study sheds light on the complex interplay of selection thresholds and population parameters for the selection response in plant breeding programs, offering insights into the effective resource management and prudent application of genomic selection for improved crop development.

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.

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.

Genomic prediction in hybrid breeding: I. Optimizing the training set design

Training sets produced by maximizing the number of parent lines, each involved in one cross, had the highest prediction accuracy for H0 hybrids, but lowest for H1 and H2 hybrids. Genomic prediction holds great promise for hybrid breeding but optimum composition of the training set (TS) as determined by the number of parents (nTS) and crosses per parent (c) has received little attention. Our objective was to examine prediction accuracy ([Formula: see text]) of GCA for lines used as parents of the TS (I1 lines) or not (I0 lines), and H0, H1 and H2 hybrids, comprising crosses of type I0 × I0, I1 × I0 and I1 × I1, respectively, as function of nTS and c. In the theory, we developed estimates for [Formula: see text] of GBLUPs for hybrids: (i)[Formula: see text] based on the expected prediction accuracy, and (ii) [Formula: see text] based on [Formula: see text] of GBLUPs of GCA and SCA effects. In the simulation part, hybrid populations were generated using molecular data from two experimental maize data sets. Additive and dominance effects of QTL borrowed from literature were used to simulate six scenarios of traits differing in the proportion (τSCA = 1%, 6%, 22%) of SCA variance in σG2 and heritability (h2 = 0.4, 0.8). Values of [Formula: see text] and [Formula: see text] closely agreed with [Formula: see text] for hybrids. For given size NTS = nTS × c of TS, [Formula: see text] of H0 hybrids and GCA of I0 lines was highest for c = 1. Conversely, for GCA of I1 lines and H1 and H2 hybrids, c = 1 yielded lowest [Formula: see text] with concordant results across all scenarios for both data sets. In view of these opposite trends, the optimum choice of c for maximizing selection response across all types of hybrids depends on the size and resources of the breeding program.

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 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.

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.

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.

Optimizing the setup of multienvironmental hybrid wheat yield trials for boosting the selection capability

The accuracy of genomic prediction increases with increasing heritability, and thus the challenge of optimizing the design of multienvironment yield trials under a limited budget arises. With this in mind, we aimed to find the best of several options to sparsely distribute a fixed number of plots across different environments to increase the accuracy of hybrid performance prediction. We used a comprehensive published genomic and phenotypic data set of 1,604 winter wheat (Triticum aestivum L.) hybrids and compared several commonly used biometric models for phenotypic data analysis in a resampling study to identify the one that most accurately estimated the hybrid performance in different imbalanced trials. Our results showed that when using information about genotypic relationships, genotypic values were more strongly associated with the reference values than when this information was ignored. In addition, a balanced environmental sampling resulted in an adequate characterization of each environment and increased the accuracy for estimating the hybrid performance. One promising design involved dividing the genotypes into equally sized subgroups that were tested in a subset of environments, with the constraint that the subgroups overlapped with respect to the environments. This scenario appears to be particularly appropriate, as it provided both high accuracies in the estimates of genotypic values and had low variability resulting from the data sample used. Thus, we were able to clearly demonstrate the utility for optimizing the design of multienvironment hybrid wheat yield trials in times of genomic selection.

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.

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.

Why and How to Switch to Genomic Selection: Lessons From Plant and Animal Breeding Experience

The present study is a transversal analysis of the interest in genomic selection for plant and animal species. It focuses on the arguments that may convince breeders to switch to genomic selection. The arguments are classified into three different “bricks.” The first brick considers the addition of genotyping to improve the accuracy of the prediction of breeding values. The second consists of saving costs and/or shortening the breeding cycle by replacing all or a portion of the phenotyping effort with genotyping. The third concerns population management to improve the choice of parents to either optimize crossbreeding or maintain genetic diversity. We analyse the relevance of these different bricks for a wide range of animal and plant species and sought to explain the differences between species according to their biological specificities and the organization of breeding programs.

Back to the future: Implications of genetic complexity for the structure of hybrid breeding programs

Commercial hybrid breeding operations can be described as decentralized networks of smaller, more or less isolated breeding programs. There is further a tendency for the disproportionate use of successful inbred lines for generating the next generation of recombinants, which has led to a series of significant bottlenecks, particularly in the history of the North American and European maize germplasm. Both the decentralization and the disproportionate contribution of inbred lines reduce effective population size and constrain the accessible genetic space. Under these conditions, long-term response to selection is not expected to be optimal under the classical infinitesimal model of quantitative genetics. In this study, we therefore aim to propose a rationale for the success of large breeding operations in the context of genetic complexity arising from the structure and properties of interactive genetic networks. For this, we use simulations based on the NK model of genetic architecture. We indeed found that constraining genetic space through program decentralization and disproportionate contribution of parental inbred lines, is required to expose additive genetic variation and thus facilitate heritable genetic gains under high levels of genetic complexity. These results introduce new insights into why the historically grown structure of hybrid breeding programs was successful in improving the yield potential of hybrid crops over the last century. We also hope that a renewed appreciation for “why things worked” in the past can guide the adoption of novel technologies and the design of future breeding strategies for navigating biological complexity.

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.

Advances in Breeding for Mixed Cropping - Incomplete Factorials and the Producer/Associate Concept

Mixed cropping has been suggested as a resource-efficient approach to meet high produce demands while maintaining biodiversity and minimizing environmental impact. Current breeding programs do not select for enhanced general mixing ability (GMA) and neglect biological interactions within species mixtures. Clear concepts and efficient experimental designs, adapted to breeding for mixed cropping and encoded into appropriate statistical models, are lacking. Thus, a model framework for GMA and SMA (specific mixing ability) was established. Results of a simulation study showed that an incomplete factorial design combines advantages of two commonly used full factorials, and enables to estimate GMA, SMA, and their variances in a resource-efficient way. This model was extended to the Producer (Pr) and Associate (As) concept to exploit additional information based on fraction yields. It was shown that the Pr/As concept allows to characterize genotypes for their contribution to total mixture yield, and, when relating to plant traits, allows to describe biological interaction functions (BIF) in a mixed crop. Incomplete factorial designs show the potential to drastically improve genetic gain by testing an increased number of genotypes using the same amount of resources. The Pr/As concept can further be employed to maximize GMA in an informed and efficient way. The BIF of a trait can be used to optimize species ratios at harvest as well as to extend our understanding of competitive and facilitative interactions in a mixed plant community. This study provides an integrative methodological framework to promote breeding for mixed cropping.