Key message We propose the utilisation of environmental covariates in random coefficient models to predict the genotype performances in new locations. Abstract Multi-environment trials (MET) are conducted to assess the performance of a set of genotypes in a target population of environments. From a grower’s perspective, MET results must provide high accuracy and precision for predictions of genotype performance in new locations, i.e. the grower’s locations, which hardly ever coincide with the locations at which the trials were conducted. Linear mixed modelling can provide predictions for new locations. Moreover, the precision of the predictions is of primary concern and should be assessed. Besides, the precision can be improved when auxiliary information is available to characterize the targeted locations. Thus, in this study, we demonstrate the benefit of using environmental information (covariates) for predicting genotype performance in some new locations for Swedish winter wheat official trials. Swedish MET locations can be stratified into zones, allowing borrowing information between zones when best linear unbiased prediction (BLUP) is used. To account for correlations between zones, as well as for intercepts and slopes for the regression on covariates, we fitted random coefficient (RC) models. The results showed that the RC model with appropriate covariate scaling and model for covariate terms improved the precision of predictions of genotypic performance for new locations. The prediction accuracy of the RC model was competitive compared to the model without covariates. The RC model reduced the standard errors of predictions for individual genotypes and standard errors of predictions of genotype differences in new locations by 30–38% and 12–40%, respectively.

The principal goals of a plant breeding program are to provide breeders with cultivar information for selection purposes and to provide farmers with high‐yielding and stable cultivars. For that reason, multi‐environment trials need to be done to predict future cultivar yield, and a robust statistical procedure is needed to provide reliable information on the tested cultivars. In Sweden, the statistical procedure follows the tradition of modeling cultivar effects as fixed. Moreover, the analysis is performed separately by zone and level of fungicide treatment, and so the factorial information regarding cultivar × zone × fungicide combinations is not explored. Thus, the question arose whether the statistical method could be improved to increase accuracy in zone‐based cultivar prediction, since the cultivar recommendation is zone based. In this paper, the performance of empirical best linear unbiased estimation (E‐BLUE) and empirical best linear unbiased prediction (E‐BLUP) are compared using cross‐validation for winter wheat (Triticum aestivum L.) and spring barley (Hordeum vulgare L.), in single‐year and multiyear series of trials. Data were obtained from three agricultural zones of Sweden. Several linear mixed models were compared, and model performance was evaluated using the mean squared error of prediction criterion. The E‐BLUP method outperformed the E‐BLUE method in both crops and series. The prediction accuracy for zone‐based yield was improved by using E‐BLUP because the random‐effects assumption for cultivar × zone interaction allows information to be borrowed across zones. We conclude that E‐BLUP should replace the currently used E‐BLUE approach to predict zone‐based cultivar yield.

In cultivar testing, linear mixed models have been used routinely to analyze multienvironment trials. A single‐stage analysis is considered as the gold standard, whereas two‐stage analysis produces similar results when a fully efficient weighting method is used, namely when the full variance–covariance matrix of the estimated means from Stage 1 is forwarded to Stage 2. However, in practice, this may be hard to do and a diagonal approximation is often used. We conducted a cross‐validation with data from Swedish cultivar trials on winter wheat (Triticum aestivum L.) and spring barley (Hordeum vulgare L.) to assess the performance of single‐stage and two‐stage analyses. The fully efficient method and two diagonal approximation methods were used for weighting in the two‐stage analyses. In Sweden, cultivar recommendation is delineated by zones (regions), not individual locations. We demonstrate the use of best linear unbiased prediction (BLUP) for cultivar effects per zone, which exploits correlations between zones and thus allows information to be borrowed across zones. Complex variance–covariance structures were applied to allow for heterogeneity of cultivar × zone variance. The single‐stage analysis and the three weighted two‐stage analyses all performed similarly. Loss of information caused by a diagonal approximation of the variance–covariance matrix of adjusted means from Stage 1 was negligible. As expected, BLUP outperformed best linear unbiased estimation. Complex variance–covariance structures were dispensable. To our knowledge, this study is the first to use cross‐validation for comparing single‐stage analyses with stagewise analyses.

Key message We propose a simulation approach to compute response to genomic selection on a multi-environment framework to provide breeders the number of entries that need to be selected from the population to have a defined probability of selecting the truly best entry from the population and the probability of obtaining the truly best entries when some top-ranked entries are selected. Abstract The goal of any plant breeding program is to maximize genetic gain for traits of interest. In classical quantitative genetics, the genetic gain can be obtained from what is known as “Breeder’s equation”. In the past, only phenotypic data were used to compute the genetic gain. The advent of genomic prediction (GP) has opened the door to the utilization of dense markers for estimating genomic breeding values or GBV. The salient feature of GP is the possibility to carry out genomic selection with the assistance of the kinship matrix, hence improving the prediction accuracy and accelerating the breeding cycle. However, estimates of GBV as such do not provide the full information on the number of entries to be selected as in the classical response to selection. In this paper, we use simulation, based on a fitted mixed model for GP in a multi-environmental framework, to answer two typical questions of a plant breeder: (1) How many entries need to be selected to have a defined probability of selecting the truly best entry from the population; (2) what is the probability of obtaining the truly best entries when some top-ranked entries are selected.