Random regression models to estimate genetic parameters for milk yield, fat, and protein contents in Tunisian Holsteins

Abstract This study aimed to find the parsimonious random regression model (RRM) to evaluate the genetic potential for milk yield (MY), fat content (FC), and protein content (PC) in Tunisian Holstein cows. For this purpose, 551,139; 331,654; and 302,396 test day records for MY, FC, and PC were analysed using various RRMs with different Legendre polynomials (LP) orders on additive genetic (AG) and permanent environmental (PE) effects, and different types of residual variances (RV). The statistical analysis was performed in a Bayesian framework with Gibbs sampling, and the model performances were assessed, mainly, on the predictive ability criteria. The study found that the optimal model for evaluating these traits was an RRM with a third LP order and nine classes of heterogeneous RV. In addition, the study found that heritability estimates for MY, FC, and PC ranged from 0.11 to 0.22, 0.11 to 0.17, and 0.12 to 0.18, respectively, indicating that genetic improvement should be accompanied by improvements in the production environment. The study also suggested that new selection rules could be used to modify lactation curves by exploiting the canonical transformation of the random coefficient covariance (RC) matrix or by using the combination of slopes of individual lactation curves and expected daily breeding values.