Variance and covariance components and genetic parameters for fat and protein yield of first-lactation Holstein cows using random regression models

Background: the genetic parameters of the lactation curve in dairy cattle can be analyzed as longitudinal data using Random Regression Models (RRM). Objective: to estimate the (co) variance components and genetic parameters for fat (F) and protein (P) yield in first lactation Holstein cows of Antioquia (Colombia) by RRM based on Legendre polynomials. Methods: monthly F and P records (9,479) from 1,210 first-lactation Holstein cows were used. Twenty-two and 24 RRM were used for F and P, respectively, with different orthogonal Legendre-polynomial orders to estimate the fixed-curve population coefficients and predict direct-genetic additive and permanent environment effects. The models considered homogeneous and heterogeneous residual variances of 5, 7, and 10 classes. Results: the best fit for F was the fourth order model for the population fixed-curve and the additive genetic effect, and the third order for the permanent environment with seven heterogeneous variances. The best fit for P was the fifth order model for the population fixed-curve and the additive genetic and permanent environmental effects with five heterogeneous variances. The variance for the animals' genetic, phenotypic, permanent environment, and residual effects for both F and P decreased as lactation progressed. F and P heritabilities were between 0.13 and 0.38, and 0.12 and 0.32, respectively. Conclusion: first-birth animals can be selected in Antioquia for F and P characteristics. Selection should be done preferably at the beginning of lactation since they reach the highest heritability values at this time