EXPECTED GENETIC ADVANCE FOR COMBINING ABILITY. MULTIPLE-ALLELE MODEL AND HOMOZYGOUS TESTERS

Abstract

The model for two alleles at a locus might be limited for the theoretical study of open pollinated populations and populations derived from the crosses among three or more parents. Ignoring this drawback in such model can mislead the plant breeders in their programs. On the other hand, the classical theory of breeding for combining ability was derived from the basis of models of two alleles per locus. This study was designed to derive the response to selection for combining ability of a population of lines with multiple alleles, an inbreeding coefficient F, and homozygous testers. It was found that the response to selection (R) and F are directly related and that R depends on the additive variance ( σ ² _A  ) and the covariance between additive values and dominance deviations of the testcrosses ( σ _A,DMu ) . In addition, it was determined that σ _A,DMu can produce a negative response to selection and a zero value for the genetic variance of the testcrosses. The minimun value for σ _A,DMu is − (1/ 4)σ ²_A − (1/ 2)σ ²_DMu , where σ ²_DMu is the genotypic variance of the testcrosses. It was also found that when the results derived in this study were expressed in terms of the model for two alleles, there was a complete agreement relative to those already obtained for the twoallele model with a different approach. Particularly, it was found that R is negative when, with positive overdominance, d = ka (k>1), [(k1)/(2k)]<q<1, and when with negative overdominance, d = ka (k<- 1), 0<q<[(k+1)/(2k)]. Here q, d, and a are the frequency of A₂ and the genotypic values of A₁A₂ and A₁A₁, respectively.