Constructing covariance functions for random regression models for growth in Gelbvieh beef cattle

Genetic parameters for a random regression model of growth in Gelbvieh beef cattle were constructed using existing estimates. Information for variances along ages was provided by parameters used for routine Gelbvieh multiple-trait evaluation, and information on correlations among different ages was provided by random regression model estimates from literature studies involving Nellore cattle. Both sources of information were combined into multiple-trait estimates; corrected for continuity, smoothness, and general agreement with literature estimates; and extrapolated to 730 d. Covariance functions using standardized Legendre polynomials were fit for the following effects: additive genetic (direct and maternal), and animal and maternal permanent environment. Residual variances at different ages were fitted using linear splines with three knots. Fit was by least squares. The order of polynomials was varied from third to sixth. Increasing the fit beyond cubic provided small improvements in R-2 and increased the number of small eigenvalues of covariance matrices, especially for the additive effect. Parameters for a random regression model in beef cattle can be constructed with negligible artifacts from literature estimates. Formulas can easily be modified for other types of polynomials and splines.