Probability of Net Gain of Favorable Alleles for Improving an Elite Single Cross
1994
Metz, Grant
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 (Iw) possessing favorable dominant alleles not present in the elite single cross (I₁ × I₂). This paper evaluates the probability of Iw to improve I₁ × I₂. Assuming complete dominance, μG' estimates the relative number of loci with favorable alleles in Iw but not in I₁ or I₂. The estimates μD' and μF' are the relative number of loci with favorable alleles in I₁ or I₂, respectively, but not in Iw. Thus, the probability of a net gain of favorable alleles (PNGg) from Iw = max[μG'/(μG' + μ μG'/(μG' + μF')], 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 ca be either gained or lost. The PNGg can be estimated from phenotypic values of I₁ × Iw, I₂ × Iw, I₁ × I₂, I₁, and I₂. Iw per se need not be evaluated. If partial dominance and/or complementary epistasis is prevalent, μE' and μC' estimate additional loci where favorable alleles could be gained from Iw to improve I₁ and I₂, respectively, while μD', μF', and μB' estimate additional loci where favoralbe alleles could be lost from I₁, I₂, or both I₁ and I₂, respectively. Thus, the probability of a net gain of favorable alleles (PNGccg) from Iw = max[(μE + μG)'/(μB + μD + μE + μG)',(μC + μG)'/(μB + μ + μF + μG)']. In this case, Iw needs to be evaluated. The statistics PNGg and PNGccg can be used to estimate the genetic probability to success of a donor (Iw) to improve an elite hybrid.
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