The effect of repeated cycles of selection on genetic variance, heritability, and response.

The genetic variance of a quantitative trait decreases under directional selection due to generation of linkage disequilibrium. After a few cycles of selection on individual phenotype, a limit is reached where there is no further reduction in the genetic variance. Bulmer's model is extended to an animal breeding situation where selection is on information on relatives rather than on the individual's own performance. Algebraic expressions are derived to predict the decrease in genetic variance and associated reductions in heritability and response in the limit. Consequences of the results are discussed in the context of breeding strategies.