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Probability of Net Gain of Favorable Alleles for Improving an Elite Single Cross

ICI Seeds, Sleepy Eye Research Center, RR 4 Box 46, Sleepy Eye, MN 56085.

^* Corresponding author.

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 (I₁ x I₂). This paper evaluates the probability of I_w to improve I₁ x I₂. Assuming complete dominance, µG' estimates the relative number of loci with favorable alleles in I_w 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 I_w. Thus, the probability of a net gain of favorable alleles (PNG_g) from I_w = 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 PNG_g can be estimated from phenotypic values of I₁ x I_w, I₂ x I_w, I₁ x I₂, I₁, and I₂. I_w 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 I_w 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 (PNG_ccg) from I_w = max[(µE + µG)'/(µB + µD + µE + µG)',(µC + µG)'/(µB + µ + µF + µG)']. In this case, I_w needs to be evaluated. The statistics PNG_g and PNG_ccg can be used to estimate the genetic probability to success of a donor (I_w) to improve an elite hybrid.

Received for publication April 12, 1993.

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