BackgroundBarley, globally the fourth most important cereal, provides food and beverages for humans and feed for animal husbandry. Maximizing grain yield under varying climate conditions largely depends on the optimal timing of flowering. Therefore, regulation of flowering time is of extraordinary importance to meet future food and feed demands. We developed the first barley nested association mapping (NAM) population, HEB-25, by crossing 25 wild barleys with one elite barley cultivar, and used it to dissect the genetic architecture of flowering time.ResultsUpon cultivation of 1,420 lines in multi-field trials and applying a genome-wide association study, eight major quantitative trait loci (QTL) were identified as main determinants to control flowering time in barley. These QTL accounted for 64% of the cross-validated proportion of explained genotypic variance (pG). The strongest single QTL effect corresponded to the known photoperiod response gene Ppd-H1. After sequencing the causative part of Ppd-H1, we differentiated twelve haplotypes in HEB-25, whereof the strongest exotic haplotype accelerated flowering time by 11 days compared to the elite barley haplotype. Applying a whole genome prediction model including main effects and epistatic interactions allowed predicting flowering time with an unmatched accuracy of 77% of cross-validated pG.ConclusionsThe elaborated causal models represent a fundamental step to explain flowering time in barley. In addition, our study confirms that the exotic biodiversity present in HEB-25 is a valuable toolbox to dissect the genetic architecture of important agronomic traits and to replenish the elite barley breeding pool with favorable, trait-improving exotic alleles.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-015-1459-7) contains supplementary material, which is available to authorized users.

If regression tasks are sampled from a distribution, then the expected error for a future task can be estimated by the average empirical errors on the data of a finite sample of tasks, uniformly over a class of regularizing or pre-processing transformations. The bound is dimension free, justifies optimization of the pre-processing feature-map and explains the circumstances under which learning-to-learn is preferable to single task learning.

HighlightThe genetic control of plant development was investigated in a multi-parental wild barley NAM population. We found that major flowering genes control plant development and highlight trait-improving exotic alleles.

This paper presents a general coding method where data in a Hilbert space are represented by finite dimensional coding vectors. The method is based on empirical risk minimization within a certain class of linear operators, which map the set of coding vectors to the Hilbert space. Two results bounding the expected reconstruction error of the method are derived, which highlight the role played by the codebook and the class of linear operators. The results are specialized to some cases of practical importance, including K-means clustering, nonnegative matrix factorization and other sparse coding methods.

Producing sufficient food for nine billion people by 2050 will be constrained by soil salinity, especially in irrigated systems. To improve crop yield, greater understanding of the genetic control of traits contributing to salinity tolerance in the field is needed. Here, we exploit natural variation in exotic germplasm by taking a genome-wide association approach to a new nested association mapping population of barley called HEB-25. The large population (1,336 genotypes) allowed cross-validation of loci, which, along with two years of phenotypic data collected from plants irrigated with fresh and saline water, improved statistical power. We dissect the genetic architecture of flowering time under high salinity and we present genes putatively affecting this trait and salinity tolerance. In addition, we identify a locus on chromosome 2H where, under saline conditions, lines homozygous for the wild allele yielded 30% more than did lines homozygous for the Barke allele. Introgressing this wild allele into elite cultivars could markedly improve yield under saline conditions.