Choice of method for identifying germplasm with superior alleles : 1. Theoretical results.

Elite, adapted germplasm is not likely to contain all the favorable alleles available in a species. Three statistics were evaluated for screening populations for their ability to contribute favorable dominant alleles not available in an elite single cross: (1) a statistic proposed by Dudley (SD)=[(P x I1-I1)(I1 x I2-I2)-(P x I2-I2) (I1 x I2-I1)]/[2(I1-I2)]; (2) the upper bound minimum (P x I1-I1, P x I2-I2) ; and (3) the testcross to the single cross [TC(SC)]=P x (I1 x I2), where P is the population to be evaluated and I1 and I2 are homozygous parents of the elite single cross I1×I2. A superiority measure for a population was defined as the product of frequencies of favorable alleles and effects summed over loci where I1×I2 is homozygous unfavorable. Of the statistics considered, TC (SC) should have the highest genetic correlation with the superiority measure under the assumptions made, require the fewest testing resources and have the smallest standard error. Methods considered for screening inbreds were: (1) SDI proposed by Dudley=[(I1 x IW)+(I2 x IW)-I1-I2-IW-(I1 x I2)]/4 ; (2) TC(SC)=IW x (I1 xI2); and (3) UBND=minimum where Iw is the inbred to be evaluated. The superiority measure of an inbred Iw was defined as the relative number of loci where I1 and I2 are unfavorable and Iw is favorable. The genetic correlation with the superiority measure should be highest for SDI. The larger number of measurements used in calculation, the necessity of evaluating potentially unadapted inbreds and larger testing resources required for SDI suggest further research should be done to evaluate these statistics.