Estimating Response To Selection

Abstract

For any trait the difference between the average phenotype of the animals used as parents and the average phenotype of all animals born that year can be calculated. This difference can be symbolized as . However, in only very specific cases is the expected genetic change (ΔG) in the trait between one generation and the next equal to heritability times . If selection is completely on the trait being considered, then ΔG=heritability times . In this case has traditionally been called selection differential. However, in any case where selection is on the basis of more than one trait, e.g., trait 1 and trait 2, then ΔG₁ is not equal to heritability₁ times , but rather is equal to . The b_i values are determined by the index used in selection, I=b₁P₁+b₂P₂. Since in this case ΔG₁ is not equal to heritability times , it seems unwise to describe as a selection differential. Lush (Personal communication) has proposed this be called a secondary selection differential. Examples are given in the text of the inaccuracy which may be involved by always calling a selection differential and then estimating ΔG as heritability times the selection differential. In cases where the bi values were not used in the actual selection, they can sometimes be estimated. A method of estimating the b_i values which were actually used in selection is given in the text. However, if records are not available on all traits used in selecting the animals, the estimated b_i values will be biased. If accurate estimates of b_i values cannot be made, estimates of the ΔG_i values should not be made.