Probability of Correct Selection of Sires Having Highest Transmitting Ability

In a young sire-sampling program, K young sires are progeny-tested each year, and the m sires having the highest daughter averages are retained for widespread use. The genetic superiority of the selected sires will depend on whether the sires with the highest daughter averages are also the sires having the highest transmitting abilities, i.e., on whether the number of daughters (N) included in the progeny test is large enough to ensure correct selection. The design and evaluation of young sire-sampling programs (and, indeed, of progeny testing and selection programs in general) are usually formulated in terms of the expected average performance of the future offspring of the selected parents, which is the most relevant practical consideration. However, it is also of some interest to know the probability that the sires with the highest transmitting abilities will also have the highest daughter averages and will thus be included in the selected group of sires.