The genetic architecture of a phenotype plays a critical role in determining phenotypic evolution through its effects on patterns of genetic variation. Genetic architecture is often considered to be constant in evolutionary quantitative genetic models. However, genetic architecture may be variable and itself evolve when there are dominance and epistatic interactions among alleles at the same and different loci, respectively. The evolution of genetic architecture by genetic drift is examined here by testing the breeding value of four standard inbred mouse strains mated across a set of 26 related recombinant quasi-inbred (RqI) lines generated from the intercross of the Large (LG/J) and Small (SM/J) inbred mouse strains. Phenotypes of interest include age-specific body weights, growth, and adult body composition. If the genetic architecture of these traits has differentiated by genetic drift during the production of the RqI strains, we should observe interactions between tester strain and RqI strain. The breeding values of the tester strains will change relative to one another depending on which RqI strain they are crossed to. The study included an average of 15.1 offspring per cross, over a total of 100 different crosses. Multivariate and univariate analyses of variance indicate that there is strongly significant interaction for all traits. Interaction is more pronounced in males than in females and accounted for an average of about 40% of the explained variation in males and 30% in females. These results indicate that the genetic architecture of these traits has differentiated by genetic drift in the RqI strains since their isolation from a common founder population. Further analysis indicates that this differentiation results in changes in the order of tester strain effects so that common patterns of selection in these differentiated populations could result in the fixation of different alleles.