Use of Mixed Model Methodology in Analysis of Designed Experiments

Abstract

Applications of mixed model methods in the analysis of designed experiments are illustrated and discussed for purposes of: (1) increasing rate of selection response to create genetically diverse lines rapidly or to demonstrate feasibility of selection, (2) estimation of genetic parameters free of bias from selection and inbreeding, (3) estimation of response to selection with or without controls, and (4) verification of experimental design prior to the experiment. For traits controlled by a large number of additive loci, use of the numerator relationship matrix in the mixed model equations accounts for changes in additive genetic variance due to inbreeding, assortative mating and gametic disequilibrium resulting from selection. If the number of loci is small, non-normality of the genotypic distribution and changes in variance due to gene frequency changes (including fixation) are not accounted for but these seem to be of small consequence, at least for short-term selection. Use of mixed model methods do not require prior knowledge of base population heritability which can be estimated from the data unaltered by selection. If dominance effects are important, properties of the dominance relationship matrix and use of mixed model methods are not yet well understood in inbred and selected populations. Simulation results indicate that use of mixed model methods can be effective in randomly mated populations, even if the number of loci is small. There is evidence of bias in selected populations, however, particularly when gene frequencies are extreme. Properties of mixed model methods under dominance and other non-additive genetic models need more study.