The analysis of QTL and QTL x treatment experiments using spatial models for marker effects

The continued increase in the availability of markers has led to much interest in their use in genetic improvement programs of crop species, such as wheat and maize. There is a large amount of literature on this topic and much of the focus has turned from marker assisted selection and the identification of quantitative trait loci (QTL) to genomic selection. The basic idea in marker assisted selection is to exploit statistical dependencies (linkage disequilibrium, LD) existing in the joint distribution of marker and QTLs. Linkage disequilibrium between markers and QTL has two main objectives, and in some way these are not disjoint and not surprisingly the statistical models used in these two applications are similar. We refer to these objectives as (i) QTL analysis in which the aim is to infer genomic locations and effects (i.e. QTLs) which affect a (quantitative) trait and (ii) genomic selection in which the aim is to obtain predictions of genetic merit of individuals for selection as parents in a breeding program. Since the seminal paper of Meuwissen et al. (2001) there has been significant progress made in the second objective where there was a realisation that unravelling the genetic architecture of a trait via identification of (major) QTLs is not necessary for prediction of genetic merit. This concept built on the idea that a trait is the result of the influences of many, possibly small QTLs which would be very difficult if not impossible, to detect and hence routinely use within a breeding program