comparison of legendre polynomials in random regression model for production traits in holstein dairy cattle of iran

in order to estimate the genetic parameters and comparison legendre polynomials for production traits of iranian holstein dairy cattle test-day records of first lactation cows for milk yield, fat yield, protein yield, fat percentage and protein percentage traits were used. these records collected from 2006 to 2010, by the animal breeding center of iran. the genetic parameters were estimated using reml algorithm by random regression model with legendre polynomials of order 3 to 5. according to the results, order 5 of legendre polynomials were proposed for fitting permanent environment and additive genetic effects for the milk yield, fat and protein percentages traits, and order 4 of legendre polynomials for the fat and protein yields. residual variances were considered homogeneous over the lactation period. the phenotypic variance of the considered traits during lactation was not constant and it was higher at the beginning and the end of lactation. additionally, the estimated permanent environment variance was larger than genetic variances throughout the lactation. estimates of heritability were found to be lowest during early lactation. the additive genetic correlation between lactation adjacent days were more than between distant test days. the genetic trend of milk yield was showed an increasing phase during the10 past years, while this genetic trend for fat and protein percentages declined