Comparison of different orders of Legendre polynomials in random regression model for estimation of genetic parameters and breeding values of milk yield in the Chinese Holstein population

Random regression test-day model has become the most commonly adopted model for routine genetic evaluations for different dairy populations, which allows accurately accounting for genetic and environmental effects at different periods during lactation. The objective of this study was to explore appropriate random regression test-day model for genetic evaluation of milk yield in Chinese Holstein population. Data included 419,567 test-day records from 54,417 cows in the first lactation. Variance components and breeding values were estimated using random regression test-day model with different order (first order to fifth order) of Legendre polynomials, and accounted for homogeneous or heterogeneous residual variance across the lactation. The goodness of fit of the models was evaluated by total residual variance (TRV) and − 2 logL . Further, the predictive ability of the models was assessed by Spearman’s rank correlation between estimated breeding values for 305d milk yield (EBV 305 ) from the full data set and reduced data set in which the records from the last calving year were masked. The results showed that random regression models using third order Legendre polynomials (LP3) with heterogeneous residual variance achieved the lower TRV and − 2 logL value and the highest correlation for EBV 305 between full data and reduced data. Heritability estimated by this model was 0.250 for 305d milk yield and ranged from 0.163 to 0.304 for test-day milk yield. We suggest random regression model with Legendre polynomial of order 3 and accounting for heterogeneous residual variances could be an appropriate model to be used for genetic evaluation of milk yield for Chinese Holstein population.