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.

A major barrier to the wider use of supervised learning in emerging applications, such as genomic selection, is the lack of sufficient and representative labeled data to train prediction models. The amount and quality of labeled training data in many applications is usually limited and therefore careful selection of the training examples to be labeled can be useful for improving the accuracies in predictive learning tasks. In this paper, we present an R package, TrainSel, which provides flexible, efficient, and easy-to-use tools that can be used for the selection of training populations (STP). We illustrate its use, performance, and potentials in four different supervised learning applications within and outside of the plant breeding area.

No abstract

Genomic selection (GS) is becoming an essential tool in breeding programs due to its role in increasing genetic gain per unit time. The design of the training set (TRS) in GS is one of the key steps in the implementation of GS in plant and animal breeding programs mainly because (i) TRS optimization is critical for the efficiency and effectiveness of GS, (ii) breeders test genotypes in multi-year and multi-location trials to select the best-performing ones. In this framework, TRS optimization can help to decrease the number of genotypes to be tested and, therefore, reduce phenotyping cost and time, and (iii) we can obtain better prediction accuracies from optimally selected TRS than an arbitrary TRS. Here, we concentrate the efforts on reviewing the lessons learned from TRS optimization studies and their impact on crop breeding and discuss important features for the success of TRS optimization under different scenarios. In this article, we review the lessons learned from training population optimization in plants and the major challenges associated with the optimization of GS including population size, the relationship between training and test set (TS), update of TRS, and the use of different packages and algorithms for TRS implementation in GS. Finally, we describe general guidelines to improving the rate of genetic improvement by maximizing the use of the TRS optimization in the GS framework.

Spring barley (Hordeum vulgare L.) is the most important cereal in Iceland and its national breeding program aims to select barley genotypes adapted to its environment. A critical step to understand the adaptation of Nordic barley material to a cool maritime climate is to assess the genotype by environment interaction (GxE). In this study, we evaluated the yield and thousand-kernel weight (TKW) of 32 spring barley genotypes in seven Icelandic environments. We applied three methods to analyze GxE: the additive main effects and multiplicative interaction model, a factorial model, and a linear mixed model. For yield, GxE was mainly caused by a better response of six-row genotypes compared to two-row genotypes in high fertility soils. For TKW, GxE showed a pattern along a gradient of daily mean temperatures. This pattern translated into a divergent TKW response between the 2-row and 6-row genotypes, with substantial crossovers along the temperature gradient. This GxE pattern was disentangled using all three methods, illustrating the value of cross-analysis. As yield is the main trait of interest for barley cultivation in Iceland, and few crossovers of genotype performance have been observed between environments, the definition of one mega-environment was recommended for Icelandic cultivation and breeding. We identified promising genetic material for both traits and highlighted the superiority of six-row genotypes for yield.

Private and public breeding programs, as well as companies and universities, have developed different genomics technologies that have resulted in the generation of unprecedented amounts of sequence data, which bring new challenges in terms of data management, query, and analysis. The magnitude and complexity of these datasets bring new challenges but also an opportunity to use the data available as a whole. Detailed phenotype data, combined with increasing amounts of genomic data, have an enormous potential to accelerate the identification of key traits to improve our understanding of quantitative genetics. Data harmonization enables cross-national and international comparative research, facilitating the extraction of new scientific knowledge. In this paper, we address the complex issue of combining high dimensional and unbalanced omics data. More specifically, we propose a covariance-based method for combining partial datasets in the genotype to phenotype spectrum. This method can be used to combine partially overlapping relationship/covariance matrices. Here, we show with applications that our approach might be advantageous to feature imputation based approaches; we demonstrate how this method can be used in genomic prediction using heterogeneous marker data and also how to combine the data from multiple phenotypic experiments to make inferences about previously unobserved trait relationships. Our results demonstrate that it is possible to harmonize datasets to improve available information across gene-banks, data repositories, or other data resources.