Choice of optimality criteria for the design of crossbreeding experiments

Crossbreeding experiments carried out over several generations and analyzed using genetic models including additive, dominance, and epistatic effects deserve careful planning. Designs should be optimized with respect to the specific aim of the experiment. Using an experiment with guinea pigs as an example, designs were optimized for three different criteria: D-optimality, where the determinant of the variance-covariance matrix of all parameters in the genetic model is minimized, DS-optimality, where a specific subset of parameters is of special interest and the respective determinant is minimized, and DA-optimality, where a linear function or a set of linear functions of the parameters in the model is of interest. The linear function used in this particular case relates to the comparison of a composite line of two breeds and a rotational crossbreeding system at equilibrium. The designs produced by a sequential design algorithm depend very much on the optimality criterion. Designs that are optimal for the comparison of composites and rotations are very inefficient for the estimation of the whole set of parameters in the model or the specific subset of special interest in this case. Assuming that the underlying genetic model is correct, composites and rotations at equilibrium may be compared extremely efficiently using only crosses arising in the first three generations of crossbreeding.