ESTIMATING VARIANCE COMPONENTS FOR TEST DAY MILK RECORDS BY RESTRICTED MAXIMUM LIKELIHOOD WITH A RANDOM REGRESSION ANIMAL MODEL

Variance components for weekly averages of daily milk yield were estimated by restricted maximum likelihood (REML) using a random regression animal model. Additive genetic (σ2a) and permanent environmental (σ2pe) covariances were modelled with orthogonal polynomial regressions of varying order, while residual variance (σ2e) was assumed to be constant for yields in all or some weeks of lactation. The data comprised records of 488 first lactation Holstein–Friesian cows in one herd. The results indicate that the log likelihood increased as the order of polynomial regression in both the fixed and random part of the model increased from 3 to 5. However, only the first three eigenvalues of the additive covariance coefficient matrix were greater than zero in all models. Estimates of σ2a and σ2pe did not show any trend due to the increase in the order of the covariance function. Additive genetic variance declined from about 9 kg2 in week 4 to 6 kg2 in week 10 and increased linearly afterwards to peak at about 16 kg2 in week 35. Permanent environmental variance was relatively constant at about 12 kg2 in the first 35 weeks of lactation for most models. Estimates of residual variance (σ2e) in all stages of lactation declined as the order of fit of the other variance components increased and depended on the assumption about variation in measurement error across lactation. When assumed constant throughout lactation, σ2e was estimated as 3.2, 2.8 and 2.6 kg2 for the quadratic, cubic and quartic models, respectively.