Key message Including additive and additive-by-additive epistasis in a NOIA parametrization did not yield orthogonal partitioning of genetic variances, nevertheless, it improved predictive ability in a leave-one-out cross-validation for wheat grain yield. Abstract Additive-by-additive epistasis is the principal non-additive genetic effect in inbred wheat lines and is potentially useful for developing cultivars based on total genetic merit; nevertheless, its practical benefits have been highly debated. In this article, we aimed to (i) evaluate the performance of models including additive and additive-by-additive epistatic effects for variance components (VC) estimation of grain yield in a wheat-breeding population, and (ii) to investigate whether including additive-by-additive epistasis in genomic prediction enhance wheat grain yield predictive ability (PA). In total, 2060 sixth-generation (F6) lines from Nordic Seed A/S breeding company were phenotyped in 21 year-location combinations in Denmark, and genotyped using a 15 K-Illumina-BeadChip. Three models were used to estimate VC and heritability at plot level: (i) “I-model” (baseline), (ii) “I + GA-model”, extending I-model with an additive genomic effect, and (iii) “I + GA + GAA-model”, extending I + GA-model with an additive-by-additive genomic effects. The I + GA-model and I + GA + GAA-model were based on the Natural and Orthogonal Interactions Approach (NOIA) parametrization. The I + GA + GAA-model failed to achieve orthogonal partition of genetic variances, as revealed by a change in estimated additive variance of I + GA-model when epistasis was included in the I + GA + GAA-model. The PA was studied using leave-one-line-out and leave-one-breeding-cycle-out cross-validations. The I + GA + GAA-model increased PA significantly (16.5%) compared to the I + GA-model in leave-one-line-out cross-validation. However, the improvement due to including epistasis was not observed in leave-one-breeding-cycle-out cross-validation. We conclude that epistatic models can be useful to enhance predictions of total genetic merit. However, even though we used the NOIA parameterization, the variance partition into orthogonal genetic effects was not possible.

Epistasis is the principal non-additive genetic effect in inbred wheat lines and can be used to develop cultivars based on total genetic merit. Correct models for variance components (VCs) estimation are needed to disentangle the genetic architecture of complex traits in wheat. We aimed to i) evaluate the performance of extended genomic best linear unbiased prediction (EG-BLUP) and the natural and orthogonal interactions approach (NOIA) for VCs estimation in a commercial wheat-breeding population, and ii) investigate whether including epistasis in genomic prediction enhance predictive ability (PA) for wheat breeding lines. In total, 2,060 sixth-generation (F6) lines from Nordic Seed A/S breeding company were phenotyped for grain yield over 21-year-x-location combinations in Denmark, and genotyped using 15K Illumina-BeadChip. Four models were used to estimate VCs and heritability at plot level: i) Baseline, ii) Genomic best linear unbiased prediction (G-BLUP), iii) EG-BLUP, and iv) NOIA. Narrow- and broad-sense heritabilities estimated with G-BLUP were 0.15 and 0.31, respectively. EG-BLUP and NOIA failed to achieve orthogonal partition of genetic variances. Even though NOIA removed Hardy-Weinberg equilibrium assumption, both models yielded very similar estimates, indicating that linkage disequilibrium causes the lack of orthogonality. The PA was studied using leave-one-line-out and leave-one-breeding-cycle-out cross-validations. Both EG-BLUP and NOIA increased PA significantly (16.5%) compared to G-BLUP in leave-one-line-out cross-validation. However, the improvement for including epistasis was not observed in the leave-one-breeding-cycle-out cross-validation. We conclude that although the variance partition into orthogonal genetic effects was not possible, epistatic models can be useful to enhance predictions of total genetic merit.

Multi-trait and multi-environment analyses can improve genomic prediction by exploiting between-trait correlations and genotype-by-environment interactions. In the context of reaction norm models, genotype-by-environment interactions can be described as functions of high-dimensional sets of markers and environmental covariates. However, comprehensive multi-trait reaction norm models accounting for marker × environmental covariates interactions are lacking. In this article, we propose to extend a reaction norm model incorporating genotype-by-environment interactions through (co)variance structures of markers and environmental covariates to a multi-trait reaction norm case. To do that, we propose a novel methodology for characterizing the environment at different growth stages based on growth degree-days (GDD). The proposed models were evaluated by variance components estimation and predictive performance for winter wheat grain yield and protein content in a set of 2,015 F6-lines. Cross-validation analyses were performed using leave-one-year-location-out (CV1) and leave-one-breeding-cycle-out (CV2) strategies. The modeling of genomic [SNPs] × environmental covariates interactions significantly improved predictive ability and reduced the variance inflation of predicted genetic values for grain yield and protein content in both cross-validation schemes. Trait-assisted genomic prediction was carried out for multi-trait models, and it significantly enhanced predictive ability and reduced variance inflation in all scenarios. The genotype by environment interaction modeling via genomic [SNPs] × environmental covariates interactions, combined with trait-assisted genomic prediction, boosted the benefits in predictive performance. The proposed multi-trait reaction norm methodology is a comprehensive approach that allows capitalizing on the benefits of multi-trait models accounting for between-trait correlations and reaction norm models exploiting high-dimensional genomic and environmental information.

Individuals within a common environment experience variations due to unique and non-identifiable micro-environmental factors. Genetic sensitivity to micro-environmental variation (i.e. micro-environmental sensitivity) can be identified in residuals, and genotypes with lower micro-environmental sensitivity can show greater resilience towards environmental perturbations. Micro-environmental sensitivity has been studied in animals; however, research on this topic is limited in plants and lacking in wheat. In this article, we aimed to (i) quantify the influence of genetic variation on residual dispersion and the genetic correlation between genetic effects on (expressed) phenotypes and residual dispersion for wheat grain yield using a double hierarchical generalized linear model (DHGLM); and (ii) evaluate the predictive performance of the proposed DHGLM for prediction of additive genetic effects on (expressed) phenotypes and its residual dispersion. Analyses were based on 2,456 advanced breeding lines tested in replicated trials within and across different environments in Denmark and genotyped with a 15K SNP-Illumina-BeadChip. We found that micro-environmental sensitivity for grain yield is heritable, and there is potential for its reduction. The genetic correlation between additive effects on (expressed) phenotypes and dispersion was investigated, and we observed an intermediate correlation. From these results, we concluded that breeding for reduced micro-environmental sensitivity is possible and can be included within breeding objectives without compromising selection for increased yield. The predictive ability and variance inflation for predictions of the DHGLM and a linear mixed model allowing heteroscedasticity of residual variance in different environments (LMM-HET) were evaluated using leave-one-line-out cross-validation. The LMM-HET and DHGLM showed good and similar performance for predicting additive effects on (expressed) phenotypes. In addition, the accuracy of predicting genetic effects on residual dispersion was sufficient to allow genetic selection for resilience. Such findings suggests that DHGLM may be a good choice to increase grain yield and reduce its micro-environmental sensitivity.

Fusarium head blight (FHB) and stem rust (SR) threaten the sustainability of wheat production worldwide. Fhb1 and Sr2 confer partial durable resistance to FHB and SR, respectively. Despite resistant alleles of both genes are linked in repulsion, lines with Fhb1-Sr2 in coupling were developed at the University of Minnesota, USA. Marker-assisted backcrossing was used to incorporate the coupled Fhb1-Sr2 into four elite INIA-Uruguay spring wheat varieties lacking both genes and expressing different levels of FHB and SR resistance. In each case, the initial cross between the donor line and recurrent parent was backcrossed three times. Genotypes carrying Fhb1-Sr2 were selected using the molecular marker UMN10. In BC3F3 families, retention of Fhb1-Sr2 was further confirmed with the markers SNP3BS-8 and Sr2-ger9 for Fhb1 and Sr2, respectively. BC3F3 homozygous lines contrasting at UMN10, SNP3BS-8 and Sr2-ger9 were obtained to quantify the effect of Fhb1-Sr2 on the resistance to FHB under controlled conditions and to SR under field conditions. After 26 months period, successful introgression of Fhb1-Sr2 into the four cultivars was achieved, representing novel wheat genetic resources. Lines homozygous for the resistant alleles of Fhb1 were significantly more resistant to FHB as reflected by an 18% reduction of average FHB area under the disease progress curve. A significant effect of Sr2 on SR field resistance was observed in lines derived from the most susceptible cultivar ‘Génesis 2375’. The most resistant lines to both diseases are expected to be valuable genetic resources in breeding for durable resistance to FHB and SR.

Accelerating the rate of genetic gain of major crops is required to meet the projected global demand for food. Genomic selection (GS) has made valuable contributions to the genetic progress of different species and is currently a routine procedure in most wheat (Triticum aestivum L.) breeding programs (WBP). Accounting for gene × gene (G × G) and genotype × environment interactions (G × E) in GS can significantly enhance genetic improvement by increasing the rate of genetic gain and adaptation of wheat cultivars. However, a comprehensive and updated knowledge of G × G and G × E methodologies is required to define the appropriate breeding strategy. In this review, we start by briefly describing the current situation and relevance of wheat breeding, then we focus on the central concepts of G × G and G × E and discuss the implications, challenges, and opportunities for the implementation of interactions in GS and wheat breeding. This review is primarily intended to be a reference material for wheat breeders and researchers. Nevertheless, most of the concepts exposed are transferable to any other autogamous or clonal crops, and are therefore useful in a much broader scope. We expect to encourage and facilitate the implementation of GS models accounting for interactions in plant breeding.