A mixed-model approach to mapping quantitative trait loci in barley on thebasis of multiple environment data

In this article, I propose a mixed-model method to detect QTL with signific ant mean effect across environments and to characterize the stability of ef fects across multiple environments. I demonstrate the method using the barl ey dataset by the North American Barley Genome Mapping Project. The analysi s raises the need for mixed modeling in two different ways. First, it is re asonable to regard environments as a random sample from a population of tar get environments. Thus, environmental main effects and QTL-by-environment i nteraction effects are regarded as random. Second, I expect a genetic corre lation among pairs of environments caused by undetected QTL. I show how ran dom QTL-by-environment effects as well as genetic correlations are straight forwardly handled in a mixed-model framework. The main advantage of this me thod is the ability to assess the stability of QTL effects. Moreover, the m ethod allows valid statistical inferences regarding average QTL effects.