Estimation of genetic parameters for calving ease by heifers and cows using multi-trait threshold animal models with Bayesian approach

Genetic parameters for birth weights (BWT), calving case scores observed from calves born by heifers (CEH), and calving ease scores observed from calves born by cows (CEC) were estimated using Bayesian methodology with Gibbs sampling in different threshold animal models, Data consisted of 77.458 records for calving ease scores and birth weights in Gelbvieh cattle. Gibbs samplers were used to obtain the parameters of interest for the categorical traits in two univariate threshold animal models, a bivariate threshold animal model. and a three-trait linear-threshold animal model. Samples of heritabilities and genetic correlations were calculated from the posterior means of dispersion parameters. In a univariate threshold animal model with CEH (model 1), the posterior means of heritabilities for calving case was 0.35 for direct genetic effects and 0,18 for maternal genetic effects. In the other univariate threshold model with CEC (model 2), the posterior means of heritabilities of CEC was 0.28 for direct genetic effects and 0.18 for maternal genetic effects, In a bivariate threshold model with CEH and CEC (model 3), heritability estimates were similar to those in unvariate threshold models. In this model, genetic correlation between heifer calving case and cow calving me was 0.89 and 0.87 for direct genetic effect and maternal genetic effects, respectively. In a three-trait animal model which contained two categorical traits (CEH and CEC) and one continuous trait (BWT) (model 4), heritability estimates of CEH and CEC for direct (maternal) genetic effects were 0.40 (0.23) and 0.23 (0.13), respectively. In this model, genetic correlation estimates between CEH and CEC were 0.89 and 0,66 for direct genetic effects and maternal effects, respectively, These estimates were greater than estimates between BWT and CEH (0,82 and 0.34) or BWT and CEC (0.85 and 0.26). This result indicates that CEH and CEC should be high correlated rather than estimates between calving case and birth weight. Genetic correlation estimates between direct genetic effects and maternal effects were -0.29, -0.31 and 0.15 for BWT, CEH and CEC, respectively. Correlation for permanent environmental effects between BWT and CEC was -0.83 in model 4. This study can provide genetic evaluation for calving case with other continuous traits jointly with assuming that calving ease from first calving was a same trait to calving case from later parities calving, Further researches for reliability of dispersion parameters would be needed even if the more correlated traits would be concerned in the model, the higher reliability could be obtained, especially on threshold model with property that categorical traits have little information.