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.

Optimized breeding strategies to harness genetic resources with different performance levels.

BACKGROUND: The narrow genetic base of elite germplasm compromises long-term genetic gain and increases the vulnerability to biotic and abiotic stresses in unpredictable environmental conditions. Therefore, an efficient strategy is required to broaden the genetic base of commercial breeding programs while not compromising short-term variety release. Optimal cross selection aims at identifying the optimal set of crosses that balances the expected genetic value and diversity. We propose to consider genomic selection and optimal cross selection to recurrently improve genetic resources (i.e. pre-breeding), to bridge the improved genetic resources with elites (i.e. bridging), and to manage introductions into the elite breeding population. Optimal cross selection is particularly adapted to jointly identify bridging, introduction and elite crosses to ensure an overall consistency of the genetic base broadening strategy. RESULTS: We compared simulated breeding programs introducing donors with different performance levels, directly or indirectly after bridging. We also evaluated the effect of the training set composition on the success of introductions. We observed that with recurrent introductions of improved donors, it is possible to maintain the genetic diversity and increase mid- and long-term performances with only limited penalty at short-term. Considering a bridging step yielded significantly higher mid- and long-term genetic gain when introducing low performing donors. The results also suggested to consider marker effects estimated with a broad training population including donor by elite and elite by elite progeny to identify bridging, introduction and elite crosses. CONCLUSION: Results of this study provide guidelines on how to harness polygenic variation present in genetic resources to broaden elite germplasm.

Genomic prediction with a maize collaborative panel: identification of genetic resources to enrich elite breeding programs.

KEY MESSAGE: Collaborative diversity panels and genomic prediction seem relevant to identify and harness genetic resources for polygenic trait-specific enrichment of elite germplasms. In plant breeding, genetic diversity is important to maintain the pace of genetic gain and the ability to respond to new challenges in a context of climatic and social expectation changes. Many genetic resources are accessible to breeders but cannot all be considered for broadening the genetic diversity of elite germplasm. This study presents the use of genomic predictions trained on a collaborative diversity panel, which assembles genetic resources and elite lines, to identify resources to enrich an elite germplasm. A maize collaborative panel (386 lines) was considered to estimate genome-wide marker effects. Relevant predictive abilities (0.40-0.55) were observed on a large population of private elite materials, which supported the interest of such a collaborative panel for diversity management perspectives. Grain-yield estimated marker effects were used to select a donor that best complements an elite recipient at individual loci or haplotype segments, or that is expected to give the best-performing progeny with the elite. Among existing and new criteria that were compared, some gave more weight to the donor-elite complementarity than to the donor value, and appeared more adapted to long-term objective. We extended this approach to the selection of a set of donors complementing an elite population. We defined a crossing plan between identified donors and elite recipients. Our results illustrated how collaborative projects based on diversity panels including both public resources and elite germplasm can contribute to a better characterization of genetic resources in view of their use to enrich elite germplasm.

Improving Short- and Long-Term Genetic Gain by Accounting for Within-Family Variance in Optimal Cross-Selection.

The implementation of genomic selection in recurrent breeding programs raises the concern that a higher inbreeding rate could compromise the long-term genetic gain. An optimized mating strategy that maximizes the performance in progeny and maintains diversity for long-term genetic gain is therefore essential. The optimal cross-selection approach aims at identifying the optimal set of crosses that maximizes the expected genetic value in the progeny under a constraint on genetic diversity in the progeny. Optimal cross-selection usually does not account for within-family selection, i.e., the fact that only a selected fraction of each family is used as parents of the next generation. In this study, we consider within-family variance accounting for linkage disequilibrium between quantitative trait loci to predict the expected mean performance and the expected genetic diversity in the selected progeny of a set of crosses. These predictions rely on the usefulness criterion parental contribution (UCPC) method. We compared UCPC-based optimal cross-selection and the optimal cross-selection approach in a long-term simulated recurrent genomic selection breeding program considering overlapping generations. UCPC-based optimal cross-selection proved to be more efficient to convert the genetic diversity into short- and long-term genetic gains than optimal cross-selection. We also showed that, using the UCPC-based optimal cross-selection, the long-term genetic gain can be increased with only a limited reduction of the short-term commercial genetic gain.

Usefulness Criterion and Post-selection Parental Contributions in Multi-parental Crosses: Application to Polygenic Trait Introgression.

Predicting the usefulness of crosses in terms of expected genetic gain and genetic diversity is of interest to secure performance in the progeny and to maintain long-term genetic gain in plant breeding. A wide range of crossing schemes are possible including large biparental crosses, backcrosses, four-way crosses, and synthetic populations. In silico progeny simulations together with genome-based prediction of quantitative traits can be used to guide mating decisions. However, the large number of multi-parental combinations can hinder the use of simulations in practice. Analytical solutions have been proposed recently to predict the distribution of a quantitative trait in the progeny of biparental crosses using information of recombination frequency and linkage disequilibrium between loci. Here, we extend this approach to obtain the progeny distribution of more complex crosses including two to four parents. Considering agronomic traits and parental genome contribution as jointly multivariate normally distributed traits, the usefulness criterion parental contribution (UCPC) enables to (i) evaluate the expected genetic gain for agronomic traits, and at the same time (ii) evaluate parental genome contributions to the selected fraction of progeny. We validate and illustrate UCPC in the context of multiple allele introgression from a donor into one or several elite recipients in maize (Zea mays L.). Recommendations regarding the interest of two-way, three-way, and backcrosses were derived depending on the donor performance. We believe that the computationally efficient UCPC approach can be useful for mate selection and allocation in many plant and animal breeding contexts.

Assessment of breeding programs sustainability: application of phenotypic and genomic indicators to a North European grain maize program.

KEY MESSAGE: We review and propose easily implemented and affordable indicators to assess the genetic diversity and the potential of a breeding population and propose solutions for its long-term management. Successful plant breeding programs rely on balanced efforts between short-term goals to develop competitive cultivars and long-term goals to improve and maintain diversity in the genetic pool. Indicators of the sustainability of response to selection in breeding pools are of key importance in this context. We reviewed and proposed sets of indicators based on temporal phenotypic and genotypic data and applied them on an early maize grain program implying two breeding pools (Dent and Flint) selected in a reciprocal manner. Both breeding populations showed a significant positive genetic gain summing up to 1.43 qx/ha/year but contrasted evolutions of genetic variance. Advances in high-throughput genotyping permitted the identification of regions of low diversity, mainly localized in pericentromeric regions. Observed changes in genetic diversity were multiple, reflecting a complex breeding system. We estimated the impact of linkage disequilibrium (LD) and of allelic diversity on the additive genetic variance at a genome-wide and chromosome-wide scale. Consistently with theoretical expectation under directional selection, we found a negative contribution of LD to genetic variance, which was unevenly distributed between chromosomes. This suggests different chromosome selection histories and underlines the interest to recombine specific chromosome regions. All three sets of indicators valorize in house data and are easy to implement in the era of genomic selection in every breeding program.

Genetic Gain Increases by Applying the Usefulness Criterion with Improved Variance Prediction in Selection of Crosses.

A crucial step in plant breeding is the selection and combination of parents to form new crosses. Genome-based prediction guides the selection of high-performing parental lines in many crop breeding programs which ensures a high mean performance of progeny. To warrant maximum selection progress, a new cross should also provide a large progeny variance. The usefulness concept as measure of the gain that can be obtained from a specific cross accounts for variation in progeny variance. Here, it is shown that genetic gain can be considerably increased when crosses are selected based on their genomic usefulness criterion compared to selection based on mean genomic estimated breeding values. An efficient and improved method to predict the genetic variance of a cross based on Markov chain Monte Carlo samples of marker effects from a whole-genome regression model is suggested. In simulations representing selection procedures in crop breeding programs, the performance of this novel approach is compared with existing methods, like selection based on mean genomic estimated breeding values and optimal haploid values. In all cases, higher genetic gain was obtained compared with previously suggested methods. When 1% of progenies per cross were selected, the genetic gain based on the estimated usefulness criterion increased by 0.14 genetic standard deviation compared to a selection based on mean genomic estimated breeding values. Analytical derivations of the progeny genotypic variance-covariance matrix based on parental genotypes and genetic map information make simulations of progeny dispensable, and allow fast implementation in large-scale breeding programs.

Genomic models with genotype × environment interaction for predicting hybrid performance: an application in maize hybrids.

KEY MESSAGE: A new genomic model that incorporates genotype × environment interaction gave increased prediction accuracy of untested hybrid response for traits such as percent starch content, percent dry matter content and silage yield of maize hybrids. The prediction of hybrid performance (HP) is very important in agricultural breeding programs. In plant breeding, multi-environment trials play an important role in the selection of important traits, such as stability across environments, grain yield and pest resistance. Environmental conditions modulate gene expression causing genotype × environment interaction (G × E), such that the estimated genetic correlations of the performance of individual lines across environments summarize the joint action of genes and environmental conditions. This article proposes a genomic statistical model that incorporates G × E for general and specific combining ability for predicting the performance of hybrids in environments. The proposed model can also be applied to any other hybrid species with distinct parental pools. In this study, we evaluated the predictive ability of two HP prediction models using a cross-validation approach applied in extensive maize hybrid data, comprising 2724 hybrids derived from 507 dent lines and 24 flint lines, which were evaluated for three traits in 58 environments over 12 years; analyses were performed for each year. On average, genomic models that include the interaction of general and specific combining ability with environments have greater predictive ability than genomic models without interaction with environments (ranging from 12 to 22%, depending on the trait). We concluded that including G × E in the prediction of untested maize hybrids increases the accuracy of genomic models.

Variable-Selection Emerges on Top in Empirical Comparison of Whole-Genome Complex-Trait Prediction Methods.

Accurate prediction of complex traits based on whole-genome data is a computational problem of paramount importance, particularly to plant and animal breeders. However, the number of genetic markers is typically orders of magnitude larger than the number of samples (p >> n), amongst other challenges. We assessed the effectiveness of a diverse set of state-of-the-art methods on publicly accessible real data. The most surprising finding was that approaches with feature selection performed better than others on average, in contrast to the expectation in the community that variable selection is mostly ineffective, i.e. that it does not improve accuracy of prediction, in spite of p >> n. We observed superior performance despite a somewhat simplistic approach to variable selection, possibly suggesting an inherent robustness. This bodes well in general since the variable selection methods usually improve interpretability without loss of prediction power. Apart from identifying a set of benchmark data sets (including one simulated data), we also discuss the performance analysis for each data set in terms of the input characteristics.

A comparison of methods for whole-genome QTL mapping using dense markers in four livestock species.

BACKGROUND: With dense genotyping, many choices exist for methods to detect quantitative trait loci (QTL) in livestock populations. However, no across-species study has been conducted on the performance of different methods using real data. We compared three methods that correct for relatedness either implicitly or explicitly: linkage and linkage disequilibrium haplotype-based analysis (LDLA), efficient mixed-model association (EMMA) analysis, and Bayesian whole-genome regression (BayesC). We analyzed one chromosome in each of five datasets (dairy cattle, beef cattle, sheep, horses, and pigs) using real genotypes based on dense single nucleotide polymorphisms and phenotypes. The P values corrected for multiple testing or Bayes factors greater than 150 were considered to be significant. To complete the real data study, we also simulated quantitative trait loci (QTL) for the same datasets based on the real genotypes. Several scenarios were chosen, with different QTL effects and linkage disequilibrium patterns. A pseudo-null statistical distribution was chosen to make the significance thresholds comparable across methods. RESULTS: For the real data, the three methods generally agreed within 1 or 2 cM for the locations of QTL regions and disagreed when no signals were significant (e.g. in pigs). For certain datasets, LDLA had more significant signals than EMMA or BayesC, but they were concentrated around the same peaks. Therefore, the three methods detected approximately the same number of QTL regions. For the simulated data, LDLA was slightly less powerful and accurate than either EMMA or BayesC but this depended strongly on how thresholds were set in the simulations. CONCLUSIONS: All three methods performed similarly for real and simulated data. No method was clearly superior across all datasets or for any particular dataset. For computational efficiency and ease of interpretation, EMMA is recommended, but using more than one method is suggested.

Statistical distributions of test statistics used for quantitative trait association mapping in structured populations.

BACKGROUND: Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the classical statistical methods used: simple regression, two approximate methods of mixed models involving the effect of a single nucleotide polymorphism (SNP) and a random polygenic effect (GRAMMAR and FASTA) and the transmission/disequilibrium test for quantitative traits and nuclear families. Analytical formulae were derived using matrix algebra for the first and second moments of the statistical tests, assuming a true mixed model with a polygenic effect and SNP effects. RESULTS: The expectation and variance of the test statistics and their marginal expectations and variances according to the distribution of genotypes and estimators of variance components are given as a function of the relationship matrix and of the heritability of the polygenic effect. These formulae were used to compute type 1 error rate and power for any kind of relationship matrix between phenotyped and genotyped individuals for any level of heritability. For the regression method, type 1 error rate increased with the variability of relationships and with heritability, but decreased with the GRAMMAR method and was not affected with the FASTA and quantitative transmission/disequilibrium test methods. CONCLUSIONS: The formulae can be easily used to provide the correct threshold of type 1 error rate and to calculate the power when designing experiments or data collection protocols. The results concerning the efficacy of each method agree with simulation results in the literature but were generalized in this work. The power of the GRAMMAR method was equal to the power of the FASTA method at the same type 1 error rate. The power of the quantitative transmission/disequilibrium test was low. In conclusion, the FASTA method, which is very close to the full mixed model, is recommended in association mapping studies.