The paradigm called genomic selection (GS) is a revolutionary way of developing new plants and animals. This is a predictive methodology, since it uses learning methods to perform its task. Unfortunately, there is no universal model that can be used for all types of predictions; for this reason, specific methodologies are required for each type of output (response variables). Since there is a lack of efficient methodologies for multivariate count data outcomes, in this paper, a multivariate Poisson deep neural network (MPDN) model is proposed for the genomic prediction of various count outcomes simultaneously. The MPDN model uses the minus log-likelihood of a Poisson distribution as a loss function, in hidden layers for capturing nonlinear patterns using the rectified linear unit (RELU) activation function and, in the output layer, the exponential activation function was used for producing outputs on the same scale of counts. The proposed MPDN model was compared to conventional generalized Poisson regression models and univariate Poisson deep learning models in two experimental data sets of count data. We found that the proposed MPDL outperformed univariate Poisson deep neural network models, but did not outperform, in terms of prediction, the univariate generalized Poisson regression models. All deep learning models were implemented in Tensorflow as back-end and Keras as front-end, which allows implementing these models on moderate and large data sets, which is a significant advantage over previous GS models for multivariate count data.

Synthetic hexaploid wheat (SHW) has shown effective resistance to a diversity of diseases and insects, including tan spot, which is caused by Pyrenophora tritici-repentis, being an important foliar disease that can attack all types of wheat and several grasses. In this study, 443 SHW plants were evaluated for their resistance to tan spot under controlled environmental conditions. Additionally, a genome-wide association study was conducted by genotyping all entries with the DArTSeq technology to identify marker-trait associations for tan spot resistance. Of the 443 SHW plants, 233 showed resistant and 183 moderately resistant reactions, and only 27 were moderately susceptible or susceptible to tan spot. Durum wheat (DW) parents of the SHW showed moderately susceptible to susceptible reactions. A total of 30 significant marker-trait associations were found on chromosomes 1B (4 markers), 1D (1 marker), 2A (1 marker), 2D (2 markers), 3A (4 markers), 3D (3 markers), 4B (1 marker), 5A (4 markers), 6A (6 markers), 6B (1 marker) and 7D (3 markers). Increased resistance in the SHW in comparison to the DW parents, along with the significant association of resistance with the A and B genome, supported the concept of activating epistasis interaction across the three wheat genomes. Candidate genes coding for F-box and cytochrome P450 proteins that play significant roles in biotic stress resistance were identified for the significant markers. The identified resistant SHW lines can be deployed in wheat breeding for tan spot resistance.

Spot blotch (SB) caused by Bipolaris sorokiniana (Sacc.) Shoem is a destructive fungal disease affecting wheat and many other crops. Synthetic hexaploid wheat (SHW) offers opportunities to explore new resistance genes for SB for introgression into elite bread wheat. The objectives of our study were to evaluate a collection of 441 SHWs for resistance to SB and to identify potential new genomic regions associated with the disease. The panel exhibited high SB resistance, with 250 accessions showing resistance and 161 showing moderate resistance reactions. A genome-wide association study (GWAS) revealed a total of 41 significant marker–trait associations for resistance to SB, being located on chromosomes 1B, 1D, 2A, 2B, 2D, 3A, 3B, 3D, 4A, 4D, 5A, 5D, 6D, 7A, and 7D; yet none of them exhibited a major phenotypic effect. In addition, a partial least squares regression was conducted to validate the marker–trait associations, and 15 markers were found to be most important for SB resistance in the panel. To our knowledge, this is the first GWAS to investigate SB resistance in SHW that identified markers and resistant SHW lines to be utilized in wheat breeding.