In this article, we imagine a breeding scenario with a population of individuals that have been genotyped but not phenotyped. We derived a computationally efficient statistic that uses this genetic information to measure the reliability of genomic estimated breeding values (GEBV) for a given set of individuals (test set) based on a training set of individuals. We used this reliability measure with a genetic algorithm scheme to find an optimized training set from a larger set of candidate individuals. This subset was phenotyped to create the training set that was used in a genomic selection model to estimate GEBV in the test set. Our results show that, compared to a random sample of the same size, the use of a set of individuals selected by our method improved accuracies. We implemented the proposed training selection methodology on four sets of data on Arabidopsis, wheat, rice and maize. This dynamic model building process that takes genotypes of the individuals in the test sample into account while selecting the training individuals improves the performance of genomic selection models.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-015-0116-6) contains supplementary material, which is available to authorized users.

Selection in breeding programs can be done by using phenotypes (phenotypic selection), pedigree relationship (breeding value selection) or molecular markers (marker assisted selection or genomic selection). All these methods are based on truncation selection, focusing on the best performance of parents before mating. In this article we proposed an approach to breeding, named genomic mating, which focuses on mating instead of truncation selection. Genomic mating uses information in a similar fashion to genomic selection but includes information on complementation of parents to be mated. Following the efficiency frontier surface, genomic mating uses concepts of estimated breeding values, risk (usefulness) and coefficient of ancestry to optimize mating between parents. We used a genetic algorithm to find solutions to this optimization problem and the results from our simulations comparing genomic selection, phenotypic selection and the mating approach indicate that current approach for breeding complex traits is more favorable than phenotypic and genomic selection. Genomic mating is similar to genomic selection in terms of estimating marker effects, but in genomic mating the genetic information and the estimated marker effects are used to decide which genotypes should be crossed to obtain the next breeding population.

Key message We found two loci on chromosomes 2BS and 6AL that significantly contribute to stripe rust resistance in current European winter wheat germplasm. Abstract Stripe or yellow rust, caused by the fungus Puccinia striiformis Westend f. sp. tritici, is one of the most destructive wheat diseases. Sustainable management of wheat stripe rust can be achieved through the deployment of rust resistant cultivars. To detect effective resistance loci for use in breeding programs, an association mapping panel of 230 winter wheat cultivars and breeding lines from Northern and Central Europe was employed. Genotyping with the Illumina® iSelect® 25 K Infinium® single nucleotide polymorphism (SNP) genotyping array yielded 8812 polymorphic markers. Structure analysis revealed two subpopulations with 92 Austrian breeding lines and cultivars, which were separated from the other 138 genotypes from Germany, Norway, Sweden, Denmark, Poland, and Switzerland. Genome-wide association study for adult plant stripe rust resistance identified 12 SNP markers on six wheat chromosomes which showed consistent effects over several testing environments. Among these, two marker loci on chromosomes 2BS (RAC875_c1226_652) and 6AL (Tdurum_contig29607_413) were highly predictive in three independent validation populations of 1065, 1001, and 175 breeding lines. Lines with the resistant haplotype at both loci were nearly free of stipe rust symptoms. By using mixed linear models with those markers as fixed effects, we could increase predictive ability in the three populations by 0.13–0.46 compared to a standard genomic best linear unbiased prediction approach. The obtained results facilitate an efficient selection for stripe rust resistance against the current pathogen population in the Northern and Central European winter wheat gene pool.