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 (I₁× I₂) have been developed recently. During selection, new favorable alleles can be transferred from P_yto either I₁ or I₂ 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_yminus the relative number of favorable alleles that can be lost from I₁ or I₂, is presented. NI is calculated as maximum [(I₁×P_y-I₁×I₂)/2,(I₂×P_y-I₁×I₂)/2]. Because I₁ × I₂ is constant in an experiment, the method reduces to choosing P_ypopulations with the best mean performance in combination with either I₁ or I₂. 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 {Mathematical expression}μ′) of the relative number of favorable dominant alleles present in P_ybut not in I₁ and I₂; (2) minimum upper bound on l {Mathematical expression}μ; and (3) predicted performance of the three-way cross [P_y(I₁× I₂)]. While l {Mathematical expression}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.