On the use of multiple lattice designs and α-designs in plant breeding trials

Plant breeders in Germany often use multiple lattice designs to test a large number of entries that are to be directly compared for selection. Comparison among entries from different lattices is accommodated by the use of checks. While this design has some practical merits, it is statistically expected to be less efficient than alternative designs for a large number of entries. In this note a study is made of the gain in efficiency by using a single large alpha-design in place of multiple lattices. The comparison for a number of settings shows that the efficiency gain in terms of sample size or variance may be appreciable. It is concluded that plant breeders should seriously consider using alpha-designs in place of multiple lattices. A simple method is described which allows breeders to study the potential gain for their particular design. Practical considerations leading to a preference of multiple lattices are critically discussed.