Abstract
Optimum allocation of locations (sj, subscript j designating stage), replications within locations (uj), fraction of selection (pj) and field area per stage (αj) in three-stage yield selection is discussed on the principle of maximizing the probability of success (S) that an entry with the highest yielding ability is selected from a population of candidate entries. Monte Carlo calculations of S with practically possible conditions of the parameters concerned confirm that the total number and allocation of locations, not of replications, determine S. With the same total number of locations, a uniform allocation s1 = s2 =s3 (or, s1 > s2 > s3 in the presence of a high magnitude of genotype × location interaction) is nearly if not exactly the best. If circumstances permit, the locations should be chosen newly in each stage from the target region. As to selection fraction and field area, allocations directed as p1 < p 2 < p3 and α1 > α2 > α3 will be appropriate in most practical conditions. Replications uj should be allocated in accordance with the total available field area and such directed allocations of sj, pj and αj. The previously proposed and widely adopted allocation of locations, i.e., 1(=s1) < s2 < s3, is not advantageous except when multiple locations cannot be allocated to the first stage for some reason, as would be the case when testing many entries with a severely limited capacity of field area. An allocation directed as p1 > p2 > p3 instead of p 1 < p2 < p3 is appropriate when genotype × year interaction is the major error component in the yield scores of entries.
