Generating Improved Experimental Designs with Spatially and Genetically Correlated Observations Using Mixed Models

The aim of this study was to generate and evaluate the efficiency of improved field experiments while simultaneously accounting for spatial correlations and different levels of genetic relatedness using a mixed models framework for orthogonal and non-orthogonal designs. Optimality criteria and a search algorithm were implemented to generate randomized complete block (RCB), incomplete block (IB), augmented block (AB) and unequally replicated (UR) designs. Several conditions were evaluated including size of the experiment, levels of heritability, and optimality criteria. For RCB designs with half-sib or full-sib families, the optimization procedure yielded important improvements under the presence of mild to strong spatial correlation levels and relatively low heritability values. Also, for these designs, improvements in terms of overall design efficiency (ODE%) reached values of up to 8.7%, but these gains varied depending on the evaluated conditions. In general, for all evaluated designs, higher ODE% values were achieved from genetically unrelated individuals compared to experiments with half-sib and full-sib families. As expected, accuracy of prediction of genetic values improved as levels of heritability and spatial correlations increased. This study has demonstrated that important improvements in design efficiency and prediction accuracies can be achieved by optimizing how the levels of a treatment are assigned to the experimental units.