Ancestral covariance and the Bulmer effect.

An n-generation pedigree is set up and selection is carried out generation by generation. The influence of this procedure on the covariances in subsequent generations is assessed and, ultimately, Bulmer's general recursion formula for the reduction in genetic variance due to selection is obtained. The results are extended to assess the effect of selection of one or more characters on the genetic covariance matrix of a number of characters. The concept of ancestral regression is also used to provide a different insight into the selection process and to justify some models used in the analysis of assortative mating.