EXPECTED GENETIC ADVANCE FOR COMBINING ABILITY. MÚLTIPLE-ALLELES MODEL AND HETEROZYGOUSTESTERS

Abstract

Theory of prediction of response to selection for combining ability (R) has been derived from a two-allele model. When there is no
correspondence between the population under improvement and this model, prediction of R may be misleading and can cancel the opportunity to study the gene action mechanism associated to multiallelism. In this study R was derived according to a model with multiple alleles, the base population (BP) and a heterozygous genotype (H) as testers. It was found that: 1) For BP the covariance of the regression of progeny produced by the recombination of selected times (PR) on the testcrosses (M) and the genetic variance of the testcrosses ( σ ²_M ) were equal, involving only additive variance ( σ ²_A ) and R was always positive; 2) For H the covariances of the regression included σ ²_A and two covariances between additive values and dominance deviations from testcrosses. These covariances may cause negative values of R. Resides the three previous parameters, σ²_M was composed by two variances of testccross dominance deviations ( σ²_DMu and σ²_DMv ) and the covariance of these deviations; 3) With only additive gene action R was the same for the two testers, and 4) When the results from multiallelism were reduced to the case of two apeles, in general the

information already known for this case was obtained. In addition, it was found that R is negative if with positive overdominance, d = ka (k > 1), [(1+k)/(2k)] < p < 1 and if with negative overdominance, d = ka (k <-1), 0 < p < [(1 + k)/(2k)]. Here p, d, and a are the frequency of Al, and the genotypic values of A_lA₂ and A₁A₁, respectively.