Single and multitrait estimates of breeding values for survival using sire and animal models

Survival data were simulated under the Weibull model in a half-sib family design, and about 50% of the records were censored. The data were analysed using the proportional hazard model (PHM) and, after transformation to survival scores, using a linear and a binary (logit) model (LIN and BIN, respectively), where the survival scores are indicators of survival during time period t given survival up to period t – 1. Correlations between estimated and true breeding values of sires (accuracies of selection) were very similar for all three models (differences were smaller than 0·3%). Daughter effects were however less accurately predicted by the LIN model, i.e. taking proper account of the distribution of the survival data yields more accurate predictions of daughter effects. The estimated variance components and regressions of true on estimated breeding values were difficult to compare for the LIN models, because estimated breeding values were expressed as additive effects on survival scores while the simulated true breeding values were expressed on the underlying scale. Also the differences in accuracy of selection between sire and animal model breeding value estimates were small, probably due to the half-sib family design of the data. To estimate breeding values for functional survival, i.e. the component of survival that is genetically independent of production (here milk yield), two methods were compared: (i) breeding values were predicted by a single-trait linear model with a phenotypic regression on milk yield; and (ii) breeding values were predicted by a two-trait linear model for survival and milk yield, and breeding values for survival corrected for milk yield were obtained by a genetic regression on the milk yield breeding value estimates. Both methods yielded very similar accuracies of selection for functional survival, and are expected to be equivalent.