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Simultaneous improvement of protein content and grain yield by index selection is possible but its efficiency largely depends on the weighting of the single traits. The genetic architecture of these indices is similar to that of the primary traits. Grain yield and protein content are of major importance in durum wheat breeding, but their negative correlation has hampered their simultaneous improvement. To account for this in wheat breeding, the grain protein deviation (GPD) and the protein yield were proposed as targets for selection. The aim of this work was to investigate the potential of different indices to simultaneously improve grain yield and protein content in durum wheat and to evaluate their genetic architecture towards genomics-assisted breeding. To this end, we investigated two different durum wheat panels comprising 159 and 189 genotypes, which were tested in multiple field locations across Europe and genotyped by a genotyping-by-sequencing approach. The phenotypic analyses revealed significant genetic variances for all traits and heritabilities of the phenotypic indices that were in a similar range as those of grain yield and protein content. The GPD showed a high and positive correlation with protein content, whereas protein yield was highly and positively correlated with grain yield. Thus, selecting for a high GPD would mainly increase the protein content whereas a selection based on protein yield would mainly improve grain yield, but a combination of both indices allows to balance this selection. The genome-wide association mapping revealed a complex genetic architecture for all traits with most QTL having small effects and being detected only in one germplasm set, thus limiting the potential of marker-assisted selection for trait improvement. By contrast, genome-wide prediction appeared promising but its performance strongly depends on the relatedness between training and prediction sets.

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