Genomic prediction of hybrid crops allows disentangling dominance and epistasis

Simulation of functional additive and non-additive genetic effects using statistical estimates from quantitative genetic models

Stochastic simulation software is commonly used to aid breeders designing cost-effective breeding programs and to validate statistical models used in genetic evaluation. An essential feature of the software is the ability to simulate populations with desired genetic and non-genetic parameters. However, this feature often fails when non-additive effects due to dominance or epistasis are modeled, as the desired properties of simulated populations are estimated from classical quantitative genetic statistical models formulated at the population level. The software simulates underlying functional effects for genotypic values at the individual level, which are not necessarily the same as effects from statistical models in which dominance and epistasis are included. This paper provides the theoretical basis and mathematical formulas for the transformation between functional and statistical effects in such simulations. The transformation is demonstrated with two statistical models analyzing individual phenotypes in a single population (common in animal breeding) and plot phenotypes of three-way hybrids involving two inbred populations (observed in some crop breeding programs). We also describe different methods for the simulation of functional effects for additive genetics, dominance, and epistasis to achieve the desired levels of variance components in classical statistical models used in quantitative genetics.

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.

Assessing the potential of genetic resource introduction into elite germplasm: a collaborative multiparental population for flint maize

KEY MESSAGE

Implementing a collaborative pre-breeding multi-parental population efficiently identifies promising donor x elite pairs to enrich the flint maize elite germplasm. Genetic diversity is crucial for maintaining genetic gains and ensuring breeding programs' long-term success. In a closed breeding program, selection inevitably leads to a loss of genetic diversity. While managing diversity can delay this loss, introducing external sources of diversity is necessary to bring back favorable genetic variation. Genetic resources exhibit greater diversity than elite materials, but their lower performance levels hinder their use. This is the case for European flint maize, for which elite germplasm has incorporated only a limited portion of the diversity available in landraces. To enrich the diversity of this elite genetic pool, we established an original cooperative maize bridging population that involves crosses between private elite materials and diversity donors to create improved genotypes that will facilitate the incorporation of original favorable variations. Twenty donor × elite BC1S2 families were created and phenotyped for hybrid value for yield related traits. Crosses showed contrasted means and variances and therefore contrasted potential in terms of selection as measured by their usefulness criterion (UC). Average expected mean performance gain over the initial elite material was 5%. The most promising donor for each elite line was identified. Results also suggest that one more generation, i.e., 3 in total, of crossing to the elite is required to fully exploit the potential of a donor. Altogether, our results support the usefulness of incorporating genetic resources into elite flint maize. They call for further effort to create fixed diversity donors and identify those most suitable for each elite program.

Prediction of additive, epistatic, and dominance effects using models accounting for incomplete inbreeding in parental lines of hybrid rye and sugar beet

Genomic models for prediction of additive and non-additive effects within and across different heterotic groups are lacking for breeding of hybrid crops. In this study, genomic prediction models accounting for incomplete inbreeding in parental lines from two different heterotic groups were developed and evaluated. The models can be used for prediction of general combining ability (GCA) of parental lines from each heterotic group as well as specific combining ability (SCA) of all realized and potential crosses. Here, GCA was estimated as the sum of additive genetic effects and within-group epistasis due to high degree of inbreeding in parental lines. SCA was estimated as the sum of across-group epistasis and dominance effects. Three models were compared. In model 1, it was assumed that each hybrid was produced from two completely inbred parental lines. Model 1 was extended to include three-way hybrids from parental lines with arbitrary levels of inbreeding: In model 2, parents of the three-way hybrids could have any levels of inbreeding, while the grandparents of the maternal parent were assumed completely inbred. In model 3, all parental components could have any levels of inbreeding. Data from commercial breeding programs for hybrid rye and sugar beet was used to evaluate the models. The traits grain yield and root yield were analyzed for rye and sugar beet, respectively. Additive genetic variances were larger than epistatic and dominance variances. The models' predictive abilities for total genetic value, for GCA of each parental line and for SCA were evaluated based on different cross-validation strategies. Predictive abilities were highest for total genetic values and lowest for SCA. Predictive abilities for SCA and for GCA of maternal lines were higher for model 2 and model 3 than for model 1. The implementation of the genomic prediction models in hybrid breeding programs can potentially lead to increased genetic gain in two different ways: I) by facilitating the selection of crossing parents with high GCA within heterotic groups and II) by prediction of SCA of all realized and potential combinations of parental lines to produce hybrids with high total genetic values.

Robotized indoor phenotyping allows genomic prediction of adaptive traits in the field

Breeding for resilience to climate change requires considering adaptive traits such as plant architecture, stomatal conductance and growth, beyond the current selection for yield. Robotized indoor phenotyping allows measuring such traits at high throughput for speed breeding, but is often considered as non-relevant for field conditions. Here, we show that maize adaptive traits can be inferred in different fields, based on genotypic values obtained indoor and on environmental conditions in each considered field. The modelling of environmental effects allows translation from indoor to fields, but also from one field to another field. Furthermore, genotypic values of considered traits match between indoor and field conditions. Genomic prediction results in adequate ranking of genotypes for the tested traits, although with lesser precision for elite varieties presenting reduced phenotypic variability. Hence, it distinguishes genotypes with high or low values for adaptive traits, conferring either spender or conservative strategies for water use under future climates.

Identifying QTLs involved in hybrid performance and heterotic group complementarity: new GWAS models applied to factorial and admixed diallel maize hybrid panels

KEY MESSAGE

An original GWAS model integrating the ancestry of alleles was proposed and allowed the detection of background specific additive and dominance QTLs involved in heterotic group complementarity and hybrid performance. Maize genetic diversity is structured into genetic groups selected and improved relative to each other. This process increases group complementarity and differentiation over time and ensures that the hybrids produced from inter-group crosses exhibit high performances and heterosis. To identify loci involved in hybrid performance and heterotic group complementarity, we introduced an original association study model that disentangles allelic effects from the heterotic group origin of the alleles and compared it with a conventional additive/dominance model. This new model was applied on a factorial between Dent and Flint lines and a diallel between Dent-Flint admixed lines with two different layers of analysis: within each environment and in a multiple-environment context. We identified several strong additive QTLs for all traits, including some well-known additive QTLs for flowering time (in the region of Vgt1/2 on chromosome 8). Yield trait displayed significant non-additive effects in the diallel panel. Most of the detected Yield QTLs exhibited overdominance or, more likely, pseudo-overdominance effects. Apparent overdominance at these QTLs contributed to a part of the genetic group complementarity. The comparison between environments revealed a higher stability of additive QTL effects than non-additive ones. Several QTLs showed variations of effects according to the local heterotic group origin. We also revealed large chromosomic regions that display genetic group origin effects. Altogether, our results illustrate how admixed panels combined with dedicated GWAS modeling allow the identification of new QTLs that could not be revealed by a classical hybrid panel analyzed with traditional modeling.

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 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.

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

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

Genomic Prediction: Progress and Perspectives for Rice Improvement

Genomic prediction can be a powerful tool to achieve greater rates of genetic gain for quantitative traits if thoroughly integrated into a breeding strategy. In rice as in other crops, the interest in genomic prediction is very strong with a number of studies addressing multiple aspects of its use, ranging from the more conceptual to the more practical. In this chapter, we review the literature on rice (Oryza sativa) and summarize important considerations for the integration of genomic prediction in breeding programs. The irrigated breeding program at the International Rice Research Institute is used as a concrete example on which we provide data and R scripts to reproduce the analysis but also to highlight practical challenges regarding the use of predictions. The adage "To someone with a hammer, everything looks like a nail" describes a common psychological pitfall that sometimes plagues the integration and application of new technologies to a discipline. We have designed this chapter to help rice breeders avoid that pitfall and appreciate the benefits and limitations of applying genomic prediction, as it is not always the best approach nor the first step to increasing the rate of genetic gain in every context.

Genomic Prediction Methods Accounting for Nonadditive Genetic Effects

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

Temporal and genomic analysis of additive genetic variance in breeding programmes

Genetic variance is a central parameter in quantitative genetics and breeding. Assessing changes in genetic variance over time as well as the genome is therefore of high interest. Here, we extend a previously proposed framework for temporal analysis of genetic variance using the pedigree-based model, to a new framework for temporal and genomic analysis of genetic variance using marker-based models. To this end, we describe the theory of partitioning genetic variance into genic variance and within-chromosome and between-chromosome linkage-disequilibrium, and how to estimate these variance components from a marker-based model fitted to observed phenotype and marker data. The new framework involves three steps: (i) fitting a marker-based model to data, (ii) sampling realisations of marker effects from the fitted model and for each sample calculating realisations of genetic values and (iii) calculating the variance of sampled genetic values by time and genome partitions. Analysing time partitions indicates breeding programme sustainability, while analysing genome partitions indicates contributions from chromosomes and chromosome pairs and linkage-disequilibrium. We demonstrate the framework with a simulated breeding programme involving a complex trait. Results show good concordance between simulated and estimated variances, provided that the fitted model is capturing genetic complexity of a trait. We observe a reduction of genetic variance due to selection and drift changing allele frequencies, and due to selection inducing negative linkage-disequilibrium.

Genomic Prediction and the Practical Breeding of 12 Quantitative-Inherited Traits in Cucumber (Cucumis sativus L.)

Genomic prediction is an effective way for predicting complex traits, and it is becoming more essential in horticultural crop breeding. In this study, we applied genomic prediction in the breeding of cucumber plants. Eighty-one cucumber inbred lines were genotyped and 16,662 markers were identified to represent the genetic background of cucumber. Two populations, namely, diallel cross population and North Carolina II population, having 268 combinations in total were constructed from 81 inbred lines. Twelve cucumber commercial traits of these two populations in autumn 2018, spring 2019, and spring 2020 were collected for model training. General combining ability (GCA) models under five-fold cross-validation and cross-population validation were applied to model validation. Finally, the GCA performance of 81 inbred lines was estimated. Our results showed that the predictive ability for 12 traits ranged from 0.38 to 0.95 under the cross-validation strategy and ranged from -0.38 to 0.88 under the cross-population strategy. Besides, GCA models containing non-additive effects had significantly better performance than the pure additive GCA model for most of the investigated traits. Furthermore, there were a relatively higher proportion of additive-by-additive genetic variance components estimated by the full GCA model, especially for lower heritability traits, but the proportion of dominant genetic variance components was relatively small and stable. Our findings concluded that a genomic prediction protocol based on the GCA model theoretical framework can be applied to cucumber breeding, and it can also provide a reference for the single-cross breeding system of other crops.

The utility of genomic prediction models in evolutionary genetics

Variation in complex traits is the result of contributions from many loci of small effect. Based on this principle, genomic prediction methods are used to make predictions of breeding value for an individual using genome-wide molecular markers. In breeding, genomic prediction models have been used in plant and animal breeding for almost two decades to increase rates of genetic improvement and reduce the length of artificial selection experiments. However, evolutionary genomics studies have been slow to incorporate this technique to select individuals for breeding in a conservation context or to learn more about the genetic architecture of traits, the genetic value of missing individuals or microevolution of breeding values. Here, we outline the utility of genomic prediction and provide an overview of the methodology. We highlight opportunities to apply genomic prediction in evolutionary genetics of wild populations and the best practices when using these methods on field-collected phenotypes.