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The aim of this research was to compare different polynomial functions including Legendre polynomials (LP), Wilmink (WRR) and Ali-Schaeffer (ARR) functions, in random regression model (RRM) for estimation of genetic parameters for milk production traits of Iranian Holstein dairy cattle. For this purpose the performance records obtained from test-day (TD) regarding milk yield, fat and protein contents of the cows calving for the first time were used. The numbers of records for the above mentioned traits were 701212, 657004, and 560775, respectively. These records were collected from the years 2006 to 2010 by the National Breeding Center of Iran. The genetic parameters were estimated using Restricted Maximum Likelihood (REML) method by applying RRM. Residual variances were considered homogeneous over the lactation period. To compare the model, different criteria (-2Logl, AIC, BIC and RV) were used for considered traits. Based on the results obtained, for all traits, RRM with LP function (2,5) were chosen as the best model. Considering residual variance (RV), LP (2,2) was proved to be a model which has the lowest performance, while using -2Logl, AIC, BIC criteria, RRM with ARR function was the worst model. According to the results, it is recommended to use LP with low orders for the additive genetic effects and with more orders for the permanent environment effects in the RRM for Iranian Holstein cattle. Permanent environment variance was higher in early lactation than during lactation and additive genetic variance in the early lactation was lower than at the end of lactation. Heritability range of milk yield, fat and protein contents was estimated to be from 0.08 to 0.23, 0.05 to 0.20 and 0.08 to 0.14, respectively. Phenotypic variance of the considered traits during lactation was not constant and it was higher at the beginning and the end of lactation. The additive genetic correlation between adjacent test days was higher than between distant test days.

Comparison of different polynomial functions in Random Regression Model for milk production traits of Iranian Holstein dairy cattle