PROBABILITY OF NET GAIN OF FAVORABLE ALLELES FOR IMPROVING AN ELITE SINGLE CROSS

Choice of donor to improve an elite single cross maize (Zea maize L.) hybrid is critical to the success of a breeding program. Theory has been developed to identify lines (I-w) possessing favorable dominant alleles not present in the elite single cross (I-1 x I-2). This paper evaluates the probability of I-w to improve I-1 x I-2. Assuming complete dominance, mu G' estimates the relative number of loci with favorable alleles in I-w but not in I-1 or I-2. The estimates mu D' and mu F' are the relative number of loci with favorable alleles in I-1 or I-2, respectively, but not in I-w. Thus, the probability of a net gain of favorable alleles (PNG(g)) from I-w = max[mu G'/(mu G' + mu D'),mu G'/(mu G' + mu F')], which estimates the relative number of loci where favorable alleles can be gained as a proportion of the relative number of loci where favorable alleles can be either gained or lost. The PNG(g) can be estimated from phenotypic values of I-1 x I-w, I-2 x I-w, I-1 x I-2, I-1, and I-2. I-w per se need not be evaluated. If partial dominance and/or complementary epistasis is prevalent, mu E' and mu C' estimate additional loci where favorable alleles could be gained from I-w to improve I-1 and I-2, respectively, while mu D', mu F', and mu B' estimate additional loci where favorable alleles could be lost from I-1, I-2, or both I-1 and I-2, respectively. Thus, the probability of a net gain of favorable alleles (PNG(ceg)) from I-w = max[(mu E + mu G)'/ (mu B + mu D + mu E + mu G)',(mu C + mu G)'/(mu B + mu C + mu F + mu G)']. In this case, I-w needs to be evaluated. The statistics PNG(g) and PNG(ceg) can be used to estimate the genetic probability of success of a donor (I-w) to improve an elite hybrid.