Statistical analysis of a linkage experiment in barley involving quantitative trait loci for height and ear-emergence time and two genetic markers on chromosome 4

Abstract

The quantitative traits height and ear-emergence date were analyzed in the F₂ progeny of a cross between a tall winter barley cultivar (Gerbel) and a short spring barley cultivar (Heriot). The trait distributions were found to be related to the genotypes at two biochemical loci, β-amylase (Bmy1) and water-soluble protein (Wsp3), which are known to lie on the long arm of chromosome 4. Linkages between each trait and the markers were investigated using normal mixture models. The two parental phenotypes and the heterozygote phenotype of Bmy1 were distinguishable so the model could be used directly to estimate linkage between Bmy1 and a quantitative trait locus (QTL) for height (Height). The Gerbel homozygote and heterozygote phenotype of Wsp3 could not be distinguished and the model was adapted accordingly. The proportion of plants requiring vernalization was consistent with control by two independent genes acting epistatically, and a normal mixture model based on a two-gene hypothesis was fitted to the distribution of ear-emergence date to estimate linkage between the marker loci and a QTL for ear-emergence date (Vrn1). The parameters of each model were the recombination fraction between the marker locus and the QTL and the means and standard deviations associated with each QTL genotype; these were estimated by maximum likelihood. The fitted distributions correspond well to those observed and the order of the loci along the chromosome is inferred to be Height — Vrn1 — Bmy1 — Wsp3, with Wsp3 being the most distal.