Data comprising8,183 test day records of 1,273 first lactations of Gyr cows from herds supervisedby ABCZ were used to estimate variance components and genetic parameters formilk yield using repeatability and random regression animal models by REML.Genetic modelling of logarithmic (FAS), exponential (FW) curves was comparedto orthogonal Legendre polynomials (LP) of order 3 to 5. Residual variance wasassumed to be constant in all (ME=1) or some periods of lactation (ME=4). Lactationmilk yield in 305-d was also adjusted by an animal model. Genetic variance,heritability and repeatability for test day milk yields estimated by a repeatabilityanimal model were 1.74 kg2, 0.27, and 0.76, respectively. Genetic variance andheritability estimates for lactation milk yield were respectively 121,094.6and 0.22. Heritability estimates from FAS and FW, respectively, decreased from0,59 and 0.74 at the beginning of lactation to 0.20 at the end of the period.Except for a fifth-order LP with ME=1, heritability estimates decreased fromaround 0,70 at early lactation to 0,30 at the end of lactation. Residual varianceestimates were slightly smaller for logarithimic than for exponential curvesboth for homogeneous and heterogeneous variance assumptions. Estimates of residualvariance in all stages of lactation decreased as the order of LP increased anddepended on the assumption about ME. Estimates of genetic and permanent environmentvariances did not show any trend due to the increase in the order of LP. Geneticcorrelation estimates between TD were largest for LP and larger for FW thanfor FAS. Except for FAS, a similar pattern in genetic correlation estimateswas observed for all curves decreasing from values close to unity between adjacentTD at early lactation to negative values for TD in the beginning and the endof lactation. The Legendre polynomial of order five and the FAS under ME4 bestfitted the data. There is a potential for using random regression to model animalgenetic and permanent environmental effects using test day information of Gyrcows.
