Identifying populations useful for improving parents of a single cross based on net transfer of alleles

Theory and methods for identifying populations (P y ) with the highest frequency of favorable dominant alleles not present in an elite single cross (I 1× I 2) have been developed recently. During selection, new favorable alleles can be transferred from P y to either I 1 or I 2 only at the risk of losing favorable alleles already present in the single cross. A "net improvement" (NI) statistic, which estimates the relative number of favorable alleles that can be gained from P y minus the relative number of favorable alleles that can be lost from I 1 or I 2, is presented. NI is calculated as maximum [(I 1×P y -I 1×I 2)/2,(I 2×P y -I 1×I 2)/2]. Because I 1 × I 2 is constant in an experiment, the method reduces to choosing P y populations with the best mean performance in combination with either I 1 or I 2. For a set of maize (Zea mays L.) grain yield data, NI was highly correlated to three other statistics proposed for choosing populations, namely: (1) minimally biased estimate (l [Formula: see text]μ') of the relative number of favorable dominant alleles present in P y but not in I 1 and I 2; (2) minimum upper bound on l [Formula: see text]μ; and (3) predicted performance of the three-way cross [P y (I 1× I 2)]. While l [Formula: see text]μ' estimates potential improvement likely to be achieved only through long-term recurrent selection, NI is probably a better predictor of short-term improvement in single-cross performance.