Phenotyping is the current bottleneck in plant breeding, especially because next-generation sequencing has decreased genotyping cost more than 100.000 fold in the last 20 years. Therefore, the cost of phenotyping needs to be optimized within a breeding program. When designing the implementation of genomic selection scheme into the breeding cycle, breeders need to select the optimal method for (1) selecting training populations that maximize genomic prediction accuracy and (2) to reduce the cost of phenotyping while improving precision. In this article, we compared methods for selecting training populations under two scenarios: Firstly, when the objective is to select a training population set (TRS) to predict the remaining individuals from the same population (Untargeted), and secondly, when a test set (TS) is first defined and genotyped, and then the TRS is optimized specifically around the TS (Targeted). Our results show that optimization methods that include information from the test set (targeted) showed the highest accuracies, indicating that apriori information from the TS improves genomic predictions. In addition, predictive ability enhanced especially when population size was small which is a target to decrease phenotypic cost within breeding programs.

The purpose of breeding programs is to obtain sustainable gains in multiple traits while controlling the loss of genetic variation. The decisions at each breeding cycle involve multiple, usually competing, objectives; these complex decisions can be supported by the insights that are gained by applying multi-objective optimization principles to breeding. The discussion in this manuscript includes the definition of several multi-objective optimized breeding approaches within the phenotypic or genomic breeding frameworks and the comparison of these approaches with the standard multi-trait breeding schemes such as tandem selection, independent culling and index selection. Proposed methods are demonstrated with two empirical data sets and simulations. In addition, we have described several graphical tools that can aid breeders in arriving at a compromise decision. The results show that the proposed methodology is a viable approach to answer several real breeding problems. In simulations, the newly proposed methods resulted in gains larger than the methods previously proposed including index selection: Compared to the best alternative breeding strategy, the gains from multi-objective optimized parental proportions approaches were about 20–30% higher at the end of long-term simulations of breeding cycles. In addition, the flexibility of the multi-objective optimized breeding strategies were displayed with methods and examples covering non-dominated selection, assignment of optimal parental proportions, using genomewide marker effects in producing optimal mating designs, and finally in selection of training populations for genomic prediction.

Core Ideas Optimum seeding rate on elite durum wheat depends on environment. Seeding rate had a significant positive relationship with grain yield, leaf area index, and carbon isotope discrimination. Seeding rate should be adjusted for environment and genotype for maximum yield. Seeding rate can be manipulated to optimize the ability of the crop to capture available resources and therefore increase yield. Seeding rate may vary between regions according to the climate conditions, soil type, sowing time, and other agronomic practices. Insufficient information is available for optimum seeding rate on durum wheat (Triticum turgidum L. var durum) for some production zones, and response to seeding rate is unknown for recently registered durum cultivars in Canada. The objective of this study was to determine the effect of seeding rate (SR) on performance of Canada Western Amber Durum wheat cultivars and study the underlying physiological response to a wide range of SRs. Eight durum wheat cultivars were sown at densities of 163, 217, 272, 326, and 380 seeds m−2 to study the effect of SR on several agronomic and physiological traits. Each experiment was planted as a factorial randomized complete block design with three replications near Swift Current and Regina in 2010 and 2011. High genetic and environmental response to SR was observed between cultivars. The results showed an increase in grain yield as the SR increased. The optimum SR for cultivars grown at Swift Current and Regina was 272 to 326 seeds m−2 and 217 to 272 seeds m−2. Grain yield showed a positive relationship with carbon isotope discrimination (CID) and leaf area index (LAI). In turn, LAI showed a linear increase with SR. Information generated from this study could enable producers to maximize crop grain profitability by optimizing plant density.

BackgroundIn statistical genetics, an important task involves building predictive models of the genotype–phenotype relationship to attribute a proportion of the total phenotypic variance to the variation in genotypes. Many models have been proposed to incorporate additive genetic effects into prediction or association models. Currently, there is a scarcity of models that can adequately account for gene by gene or other forms of genetic interactions, and there is an increased interest in using marker annotations in genome-wide prediction and association analyses. In this paper, we discuss a hybrid modeling method which combines parametric mixed modeling and non-parametric rule ensembles.ResultsThis approach gives us a flexible class of models that can be used to capture additive, locally epistatic genetic effects, gene-by-background interactions and allows us to incorporate one or more annotations into the genomic selection or association models. We use benchmark datasets that cover a range of organisms and traits in addition to simulated datasets to illustrate the strengths of this approach.ConclusionsIn this paper, we describe a new strategy for incorporating genetic interactions into genomic prediction and association models. This strategy results in accurate models, with sometimes significantly higher accuracies than that of a standard additive model.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-017-0348-8) contains supplementary material, which is available to authorized users.