ESTIMATION OF VARIANCE COMPONENTS WITH SELFED CROSSES AMONG INBRED UNRELATED PARENTS

Abstract

It is difficult to apply mating designs in self-pollinated crops to estimate variance components, because the obtention of crosses is not
easy and the amount of seeds produced for field evaluation is frequently limited. An alternative to produce enough seed is by selfing the crosses. The genotypic array of the selfed crosses, however, differs from the unselfed crosses, and the available theoretical studies are based on a two-loci model, which is not appropriate for populations formed by the crosses among three or more parents. This study was made to determine the estimator biases for the additive (σ²_A ) and dominance (σ²_D ) variances derived on the basis of a two-allele model and selfed crosses among p parents. For σ²_A the bias was 2FD₁+ (1/4) F²D₂ , where F is the inbreeding coefficient of the selfed crosses (F<1), D₁ is the covariance between the gene additive effects and the dominance deviations of the genotypes carrying alleles, which are identical by descent, and D₂ is the variance of these dominance deviations. For the two-allele case, this bias is zero if the allelic frequencies are 0.5, but it increases as p>q (p is the frequency of the most desirable allele). For σ²_D the two-allele-model estimator is unbiased. An additional component is the square mean of the inbreeding depression; its proposed estimator is a function of the error mean square and the mean of the parents and crosses.