Mixed models including environmental covariables for studying QTL by environment interaction

The study of the phenotypic responses of a set of genotypes in their dependence on the environment has always been an important area of research in plant breeding. Non-parallelism of those responses is called genotype by environment interaction (GEI). GEI especially affects plant breeding strategies, when the phenotypic superiority of genotypes changes in relation to the environment. The study of the genetic basis of GEI involves the modelling of quantitative trait locus (QTL) expression in its dependence on environmental factors. We present a modelling framework for studying the interaction between QTL and environment, using regression models in a mixed model context. We integrate regression models for QTL main effect expression with factorial regression models for genotype by environment interaction, and, in addition, take care to model adequately the residual genetic variation. Factorial regression models describe GEI as differential genotypic sensitivity to one or more environmental covariables. We show how factorial regression models can be generalized to make also QTL expression dependent on environmental covariables. As an illustrative example, we reanalyzed yield data from the North American Barley Genome Project. QTL by environment interaction for yield, as identified at the 2H chromosome could be described as QTL expression in relation to the magnitude of the temperature range during heading.