Impact of the Order of Legendre Polynomials in Random Regression Model on Genetic Evaluation for Milk Yield in Dairy Cattle Population

The random regression test-day model has become the most commonly adopted model for routine genetic evaluations in dairy populations, which allows accurately accounting for genetic and environmental effects over lactation. The objective of this study was to explore appropriate random regression test-day models for genetic evaluation of milk yield in a Holstein population with a relatively small size, which is the common situation in regional or independent breeding companies to preform genetic evaluation. Data included 419,567 test-day records from 54,417 cows from the first lactation. Variance components and breeding values were estimated using a random regression test-day model with different orders (from first to fifth) of Legendre polynomials (LP) and accounted for homogeneous or heterogeneous residual variance across the lactation. Models were compared based on Akaike information criterion (AIC), Bayesian information criterion (BIC), and predictive ability. In general, models with a higher order of LP showed better goodness of fit based on AIC and BIC values. However, models with third, fourth, and fifth order of LP led to similar estimates of genetic parameters and predictive ability. Models with assumption of heterogeneous residual variances achieved better goodness of fit but yielded similar predictive ability compared with those with assumption of homogeneous residual variances. Therefore, a random regression model with third order of LP is suggested to be an appropriate model for genetic evaluation of milk yield in local Chinese Holstein populations.