In this study, the effects of varying order of Legendre polynomials (LP) for permanent environmental (Pe) variance structure on the estimates of genetic parameters for first-lactation milk yield were evaluated fitting random regression (RR) test-day animal models. The total data set included 6850 test-day milk yield records from 800 first-lactation Holstein Friesian cows that calved between 1997 and 2013 and the pedigree file with total of 1779 animals. Four different random regression models (RR1, RR2, RR3 and RR4) all with second order LP for additive genetic effects but with varying order (intercept, 1st, 2nd and 3rd, respectively) of LP for modelling the Pe variances structure were tested for estimation of variance components and corresponding genetic parameters for milk yield. Variance components were estimated by average information restricted maximum likelihood method. The performances of competing RR models in the estimation of variance components were compared using estimates of log-likelihoods and the size of residual variances. Results showed that the estimates of log-likelihoods were higher and residual variances were lower for models that fitted second (RR3) and third order (RR4) LP for Pe effects. Heritability (h2) and genetic correlations from RR3 and RR4 models ranged from 0.13 to 0.29 and 0.45 to 0.98, respectively. Models with lower order fits (RR1 and RR2) with either a constant or a linear term for Pe resulted in oscillatory trend for variance components and highly erratic h2 estimates ranged from 0.18 to 0.52. Genetic correlations from these models were also implausible biologically indicating that models with lower order fits for the Pe effects were not robust enough to accurately model the variance structure at different stages of lactation. It is therefore suggested that at least a second or higher order polynomial fits are needed to model the Pe variance structure for the accurate estimation of genetic parameters for milk yield in first-lactation Ethiopian Holsteins.
Key words: Dairy cows, milk yield, random regression model, genetic parameters, test-day.
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