This thesis presents a statistical approach which incorporates pedigree information in the form of relationship matrices into the analysis of standard agricultural genetic trials, where elite lines are tested. Allowing for the varying levels of inbreeding of the lines which occur in these types of trials, the approach involves the partitioning of the genetic effect of lines into additive genetic effects and non-additive genetic effects. The current methodology for creating relationship matrices is developed and in particular an approach to create the dominance matrix under full inbreeding in a more efficient manner is presented. A new method for creating the dominance matrix assuming no inbreeding is also presented. The application of the approach to the single site analyses of wheat breeding trials is shown. The wheat lines evaluated in these trials are inbred lines so that the total genetic effect of each of the lines is partitioned into an additive genetic effect and an epistatic genetic effect. Multi-environment trial analysis is also explored through the application of the approach to a sugarcane breeding trial. The sugarcane lines are hybrids and therefore the total genetic effect of each hybrid is partitioned into an additive genetic effect, a heterozygous dominance genetic effect and a residual non-additive genetic effect. Finally, the approach for inbred lines is examined in a simulations study where the levels of heritability and the genetic variation as a proportion of total trial variation is explored in single site analyses. / Thesis (Ph.D.) - University of Adelaide, School of Agriculture, Food and Wine, 2008