Daily milk yield over the course of the lactation follows a curvilinear pattern, so a suitable function is required to model this curve. In this study, 7 functions (Wood, Wilmink, Ali and Schaeffer, cubic splines, and 3 Legendre polynomials) were used to model the lactation curve at the phenotypic level, using both daily observations and data from commonly used recording schemes. The number of observations per lactation varied from 4 to 11. Several criteria based on the analysis of the real error were used to compare models. The performance of models showed few discrepancies in the comparison criteria when daily or 4-weekly (with first test at days in milk 8) data by lactation were used. The performance of the Wood, Wilmink, and Ali and Schaeffer models were highly affected by the reduction of the sample dimension. The results of this work support the idea that the performance of these models depends on the sample properties but also shows considerable variation within the sampling groups.

A spline animal model was fitted to 152,103 test-day milk, fat, and protein yield records from 14,423 first-lactation cows. The models included age at calving and the herd-test-month as fixed effects. Model fitting was carried out using Restricted Maximum Likelihood with ASREML. For milk yield, the heritability at 18 d in milk was 0.19, which increased to the maximum estimated value of 0.23 at midlactation and then decreased. On average, milk, fat, and protein yield heritabilities were 0.22, 0.14, and 0.19, respectively. For milk yield, all correlations were positive and ranged from 0.54 to 0.99 for the genetic component and from 0.32 to 0.78 for the phenotypic component. Genetic correlations were higher than phenotypic ones. For fat and protein yields, all genetic correlations were positive, ranging from 0.43 to 0.99. The phenotypic correlations for fat yield had the lowest correlations of the 3 traits. Curves of estimated breeding values for milk, fat, and protein over lactation had positive deviations from mean curves for sires with high genetic merit, but there was considerable variability in the shapes of the curves for different sires. More research is needed to compare the spline function with other mathematical functions used as submodels of lactation curve.