QTL mapping

One individual of each RIL was genotyped with a selection of 384 BOPA single-nucleotide polymorphism (SNP) markers from the barley Consensus Map (Close et al. 2009) at the James Hutton Institute (Dundee, Scotland, UK) using the Illumina Golden Gate Assay system.

The markers were assigned to their positions on the POPSEQ map (Ariyadasa et al. 2014). The SNP markers were used to calculate the genetic predictors, i.e. the probabilities that a particular RIL at a given locus has the genotype of one of the five founders. The founder to offspring probabilities were calculated using a Hidden Markov Model (Rabiner 1989; Zheng et al. 2015), an extension of the inheritance vector approach as described in Huang et al. (2011).

The QTL-mapping was done using linear mixed models in Genstat 17 (VSN international). In the first step of the QTL analysis we used a genome scan, known as simple interval mapping (SIM) (Lander and Botstein 1989). Let y̲ik be the awn length for RIL i in cross k, then the following model can be given:

where μ_k is a fixed effect, the vector xikl=(xikl1,xikl2,…,xijl5)T contains the probabilities that RIL i in cross k for locus l has the genotype of wild barley line f (f = 1,…,4). The vector β̲l is a 4-dimensional vector of random founder effects corresponding to locus l. Finally, ε̲ik is the residual error for RIL i in cross k, with cross-specific variance Vε̲ik=σε,k2.

In the second step, we ran a genome scan using a multi-QTL model adjusting for background QTLs. The background QTL with the strongest effect was first added, then a new QTL-scan was performed to detect the second strongest QTL, and this procedure was repeated until no new QTLs were detected above the QTL significance threshold of −log10(P) = 3.2 (Huang et al. 2011). Each background QTL was modelled as a random effect, and the model is an extension of Eq. (1):

where C is a set of co-factors to correct for QTLs elsewhere in the genome, and l is the putative QTL. Co-factors within 10 cM of the putative QTL were excluded.

In the final step of the QTL-analyses all QTLs detected with model (2) were included in the model:

where Q is the set of selected QTLs. For each QTL the min log10(P)-values, the founder effects and the standard errors were estimated. Epistatic interactions between the 12 QTL were tested pairwise according to Huang et al. (2011).