If phenotypic response equals the product of the selection pressure and the strict-sense heritability, then any systematic difference between predicted and realised heritability estimates is due to a bias in the former. Sire estimates of the predicted heritability for quantitative economic traits on commercial Large White pigs are obtained under two assumptions: random mating, and that there are no non-additive genetic and environmental causes of similarity between sire family members. Analysis of variance estimates of the sire family, dam family and within dam family variance components are computed for each sex by season (end of test) cell. Significant linear and non-linear time trends in these variance component estimates occur, but only for a minority of the traits. Estimates of genetic parameters for the Large White and Landrace breeds are compared. The average relationship between full sib, half sib and nonsib pairs are calculated for each sex by season (end of test) cell. Highly significant linear and non-linear time trends are found in the average proportion of genes shared by sire and dam family members respectively. Heritability estimates are corrected for non-random mating. A simple technique is designed for detecting non-additive genetic and environmental causes of similarity between sire family members finishing test. It is concluded that, under certain conditions, these perhaps unexpected causes of similarity are present. Estimators of genetic parameters, based on tentative models incorporating terms due to non-random mating and non-additive genetic and environmental causes of similarity, are derived. Galton's law is generalised to include terms due to the nonadditive genetic and environmental causes of similarity between parent and offspring. It is concluded, as a consequence of this generalisation, that agreement between realised and predicted response may occur even when a biased predicted heritapility estimate is used.