Reduction of selection differentials in finite populations with a nested full-half sib family structure

The effect of family structure is of increasing importance in modern breeding schemes, because increased intraclass correlations between relatives due to improved breeding value estimation methods use all family information, and increased family sizes are possible with improved reproduction rates. In addition, reduction of the generation intervals in modern breeding schemes leads to increased intraclass (family) correlations, because young animals have little information on individual or on progeny performance. This paper derives an approximation for the selection differential in a population divided into families. The result is then extended to an approximation for the selection differentials in populations that are divided into full sib families within paternal half sib families. The approximation is compared with Monte Carlo results, from which it is concluded that the approximation is satisfactory (i.e., rarely more than 5% in error). In some practical situations the approximation is shown to be not more than 2% in error. With high intraclass correlations and few animals selected, the reduction of the selection differentials is maximal. When breeding values are based on family information and the family structure is not accounted for, overestimation of the selection differentials can be up to 61%.