We compared the goodness of fit of three mathematical functions (including: Legendre polynomials, Lidauer-Mäntysaari function and Wilmink function) for describing the lactation curve of primiparous Iranian Holstein cows by using multipletrait random regression models (MT-RRM). Lactational submodels provided the largest daily additive genetic (AG) and permanent environmental (PE) variance estimates at the end and at the onset of lactation, respectively, as well as low genetic correlations between peripheral test-day records. For all models, heritability estimates were highest at the end of lactation (245 to 305 days) and ranged from 0.05 to 0.26, 0.03 to 0.12 and 0.04 to 0.24 for milk, fat and protein yields, respectively. Generally, the genetic correlations between traits depend on how far apart they are or whether they are on the same day in any two traits. On average, genetic correlations between milk and fat were the lowest and those between fat and protein were intermediate, while those between milk and protein were the highest. Results from all criteria (Akaike’s and Schwarz’s Bayesian information criterion, and −2*logarithm of the likelihood function) suggested that a model with 2 and 5 coefficients of Legendre polynomials for AG and PE effects, respectively, was the most adequate for fitting the data.
