Several functions were used to model fixed and random part of the lactation curve in Iranian primiparous Holstein cows using random regression analysis. Legendre polynomials of orders three and four as well as parametric lactation curve for the random part of the first lactation milk production were compared to find the best model. The models differed in fixed regression lactation curve part and residual variance assumed heterogeneous during lactation. Based on eigenvalue, associated eigenfunction and residual variance, third order polynomial Quadratic form for random effects and Ali and Schaefer model for fixed part AS33 model is optimal and make parsimonious less parameters for adjustment of test day milk yield records. The maximum residual and permanent environmental variances were obtained at the beginning and at the end of lactation respectively. The greatest additive genetic variance was in the middle of lactation and residual variance decreased during lactation. The highest heritability observed in middle of lactation (170 to 205 d) and ranged from 0.06 to 0.40. The genetic, permanent environmental and phenotypic correlation between extreme parts of lactation was 0.519, 0.317 and 0.240 respectively.

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