Correcting overestimation of approximate traditional reliabilities with herd-sire interactions when young genomic bulls are used in few herds.

Background: Differential treatment of daughters of the same sire within a herd is modelled as the herd-sire effect. Recent changes in management practices may have led to the extensive use of certain bulls in a limited number of herds. In that case, although the effect can be well accounted for in genetic evaluation models, some approximation methods for reliabilities do not consider it correctly, leading to an overestimation of some sires' approximated reliabilities. This study assessed the potential bias of these approximated reliabilities due to the herd-sire effect in both simulated and real dairy cattle records. Two existing methods were tested: Misztal-Wiggans, which includes a specific modification for herd-sire, and Tier-Meyer, which does not. We also modified and tested a Tier-Meyer method considering the herd-sire effect.

Results: We observed that in the presence of the herd-sire effect, reliabilities obtained by approximations were overestimated by the Tier-Meyer method for sires with many daughters in a limited number of herds. This was true even for sires with a large number of daughters. The Misztal-Wiggans method performed correctly. We introduced a modified Tier-Meyer method that weighs the information transmitted by the daughter to the sire as a function of the herd-sire information. As a result, the modified Tier-Meyer method performed well in both simulated and real data. For cows, the inclusion of the herd-sire effect had minimal impact.

Conclusions: This study identified possible overestimation of approximated reliabilities of sires with daughters concentrated in a few herds when there is a herd-sire effect. This bias occurs when the herd-sire effect is not correctly modeled in reliability approximation methods. Methods that specifically accounted for the herd-sire effect produced unbiased reliability estimates.