Genetic prediction models and heritability estimates for functional longevity in dairy cattle

Longevity is a major component of the breeding objective for dairy cattle in many countries because of its high economic value. The trait has been recommended for inclusion in the breeding objective for dairy cattle in South Africa. Linear models, random regression (RR) models, threshold models (TMs) and proportional hazard models (PH) have been used to evaluate longevity. This paper discusses these methodologies and their advantages and disadvantages. Heritability estimates obtained from these models are also reviewed. Linear methodologies can model binary and actual longevity, while RR and TM methodologies model binary survival. PH procedures model the hazard function of a cow at time t derived from survival from first calving to culling, death or censoring. It is difficult to compare methodologies for sire evaluation and ranking across countries because of the variation in the definition of longevity and the choice of model. Sire estimated breeding values (EBVs) are derived differently for the models. Sire EBVs from PH models are expressed as deviations of the culling risk from the mean of the base sires, expected percentage of daughters still alive after a given number of lactations, expected length of productive life in absolute terms or as standard deviation units. In linear, TM and RR modelling, sire EBVs for longevity have been expressed as deviations of survival from the mean estimated with Best Linear Unbiased Prediction (BLUP). Appropriate models should thus be developed to evaluate functional longevity for possible inclusion in the overall breeding objective for South African dairy cattle. Keywords: Dairy Cattle, Proportional Hazards, Random Regression, Survival Analysis