Designs for balanced observation of plant competition

Symmetric designs, for exploring the effect of competition between two varieties or plant species planted on a triangular lattice of hill plots, are discussed and the class of m-fold symmetric Beehive designs, based on certain symmetry properties of a regular hexagon, is introduced. The designs considered by Martin (1973) and Veevers and Boffey (1975) belong to the family arising when m = 6. Optimal designs for m = 2 and 3 are presented and, although not balanced, improvements in the sense of being nearer to balanced are achieved.Taking an alternative approach, a simple technique for constructing balanced, essentially rectangular, designs of arbitrary size is developed, based upon a set of twelve symmetric elementary arrays which possess a remarkable self-building property. The experimenter is at liberty to choose a balanced design to suit restrictions on space and material or to meet his desired degree of replication whilst the actual planting technique requires only that complete rows of each variety be suitably juxtaposed.