Since the nineteenth century, animal breeders have been selecting animals with more and more efficient tools. The improvement of statistical methods as well as computation facilities has led to highly efficient livestock selection programmes generating rapid genetic change. But a high selection pressure also implies a reduction in the effective size of the selected population as the number of mating animals is reduced. For example, intensive use of elite bulls through artificial insemination in cattle has led to a sharp decrease in the effective population size (e.g. Nomura et al. 2001). Therefore, the price paid for selection efficiency can be a reduction in the genetic variance of selected populations.