Genetic modelling of daily milk yield using orthogonal polynomials and parametric curves

Random regression models have been advocated for the analysis of test day records in dairy cattle. The effectiveness of a random regression analysis depends on the function used to model the data. To investigate functions suitable for the analysis of daily milk yield, test day milk yields of 7860 first lactation Holstein Friesian cows were analysed using random regression models involving three types of curves. Each analysis fitted the same curve to model overall trends through a fixed regression and random deviations due to animals. Curves included orthogonal polynomials, fitted to order 3 (quadratic), 4 (cubic) and 5 (quartic), respectively, a three-parameter parametric curve and a five-parameter parametric curve. Sets of random regression coefficients were fitted to model both animals' genetic effects and permanent environmental effects. Temporary measurement errors were assumed independently but heterogeneously distributed, and assigned to one of 12 classes. Results showed that the measurement error variances were generally lowest around peak lactation, and higher at the beginning and end of lactation. Parametric curves yielded the highest likelihoods, but produced negative genetic associations between yield in early lactation and later lactation yields, while positive genetic correlations across the entire lactation were estimated with all models involving orthogonal polynomials. The fit of models using orthogonal polynomials to model test day yield was improved by including higher order fixed regressions.