Genetic analysis of herd life in Quebec Holsteins using Weibull models

Survival analysis methodologies were used to study herd life in Canadian Holstein cows. Herd life was defined as true herd life or the length of time between first calving and censoring. True herd life adjusted for 305-d milk production was defined as functional herd life. Lifetime records (censored or completed) were from 331,147 Holstein cows registered in the Programme d'Analyse des Troupeaux Laitiers du Quebec (PATLQ) that calved for the first time between March 1, 1981 and March 31, 1995. The Weibull (proportional hazards) model used to analyze true herd life and functional herd life contained a Weibull baseline hazard function and the time-dependent effects of year of first calving, lactation number by stage of lactation, annual change in herd size and herd-year (random), and the time-independent effects of the milk recording option (supervised or not) and age at first calving. The model for functional herd life included also the time-dependent effect of herd-year-parity class of 305-d milk production. Genetic differences between sires with regard to the hazard function of their daughters was clearly demonstrated. The hazard rate followed a different pattern in later lactations, particularly in the first 240 d in milk. Older age at first calving was found to be associated with higher risks of culling. Changes in herd size had a small impact on the hazard function of animals. The hazard decreased as production of the cow increased. Heritability in the log scale was 0.09 for true herd life and 0.08 for functional herd life, but when heritability was expressed on the original scale, the estimates for the two traits were 0.19 and 0.15, respectively. The difference in the median survival between a bull with an estimated transmitting ability of 0.6 and another bull with an estimated transmitting ability of 1.3 was 690 d or 1.7 lactations. Rank correlations between the official estimated transmitting abilities for true herd life and functional herd life and those obtained in this study were 0.62 and 0.66, respectively.