A generalized statistical framework to assess mixing ability from incomplete mixing designs using binary or higher order variety mixtures and application to wheat

There has been recently a renewed interest for variety mixtures due to their potential capacity to stabilize production through buffering abiotic and biotic stresses. Part of this results from complementarity and/or compensation between varieties which can be assessed under mixed stands only. Mixing ability of varieties can be partitioned into General and Specific Mixing Abilities (GMA and SMA) that have been estimated so far through the evaluation of binary mixtures in complete diallel designs. However, the number of mixtures increases exponentially with the number of studied varieties, and the only feasible devices are incomplete designs. Despite the long history of statistical analysis of variety mixtures, such incomplete design analysis has rarely been addressed so far. To fill the gap, we proposed a generalized statistical framework to assess mixing abilities based on mixed models and BLUP method, with an original modeling of plant-plant interactions. The approach has been applied to a panel of 25 winter wheat genotypes observed in two contrasted experimental designs: (i) an incomplete diallel of 75 binary mixtures, and (ii) a trial including higher order mixtures (four and eight components). The use of mixing ability models improved prediction accuracy (of modeled values for observed traits) in comparison to predictions from the mean of the pure stand components, especially in the first experiment. Genetic variability was detected for the GMA of yield and its components, whereas variability for SMA was lower. GMA predictions based on the diallel trial were highly correlated with the GMA of the second trial providing accurate inter-trial predictions. A new model has been proposed to jointly account for inter and intra-genotypic interactions for specific mixing ability, thus contributing to a better understanding of mixture functioning. This framework constitutes a step forward to the screening for mixing ability, and could be further integrated into breeding programs for the development of intra- or inter-specific crop mixtures.