Calculation of multiple-trait sire reliability for traits included in a dairy cattle fertility index

The advent of genetic evaluations for fertility traits in the UK offers valuable information to farmers that can be used to control fertility problems and safeguard against involuntary culling. In addition to estimated genetic merit, proof reliabilities are required to make correct use of this genetic information. Exact reliabilities, based on the inverse of the coefficient matrix, cannot be estimated for large data sets because of computational restrictions. A method to calculate approximate reliabilities was implemented based on a six-trait sire model. Traits considered were interval between first and second calving, interval between first calving and first service, non-return rate 56 days post first service, number of inseminations per conception, daily milk yield at test nearest day 110 and body condition score. Sire reliabilities were calculated in four steps. Firstly, the number of effective daughters was calculated for each bull, separately for each trait, based on total number of daughters and daughter distribution across herd-year-seasons. Secondly, multiple-trait reliabilities were calculated, based on bull daughter contribution, applying selection index theory on independent daughter groups. Thirdly, (great-) grand-daughter contribution was added to the reliability of each bull, using daughter-based reliability of sons and maternal grandsons. An adjustment was made to account for the probability of bull and son or grandson having daughters in the same herd-year-season. Without the adjustment, reliabilities were inflated by proportionately 0·15 to 0·25. Finally, parent (sire and maternal grandsire) contribution was added to the reliability of each bull. The procedure was first tested on a data subset of 28 061 cow records from 285 bulls. Approximate reliabilities were compared with exact estimates based on the inverse of the coefficient matrix. Mean absolute differences ranged from 0·014 to 0·020 for the six traits and correlation between exact and approximate estimates neared unity. In a full-scale application, sire reliability for the fertility traits increased by proportionately 0·47 to 0·79 over single-trait estimates and the number of bulls with a reliability of 0·60 or more increased by 42 to 115%.