Random regression test‐day models to describe milk production and fatty acid traits in first lactation Walloon Holstein cows

We investigated the use of different Legendre polynomial orders to estimate genetic parameters for milk production and fatty acid (FA) traits in the first lactation Walloon Holstein cows. The data set comprised 302,684 test‐day records of milk yield, fat and protein contents, and FAs generated by mid‐infrared (MIR) spectroscopy, C16:0 (palmitic acid), C18:1 cis‐9 (oleic acid), LCFAs (long‐chain FAs), SFAs (saturated FAs) and UFAs (unsaturated FAs) were studied. The models included random regression coefficients for herd‐year of calving (h), additive genetic (a) and permanent environment (p) effects. The selection of the best random regression model (RRM) was based on the deviance information criterion (DIC), and genetic parameters were estimated via a Bayesian approach. For all analysed random effects, DIC values decreased as the order of the Legendre polynomials increased. Best‐fit models had fifth‐order (degree 4) for the p effect and ranged from second‐ to fifth‐order (degree 1–4) for the a and h effects (LEGhap: LEG555 for milk yield and protein content; LEG335 for fat content and SFA; LEG545 for C16:0 and UFA; and LEG535 for C18:1 cis‐9 and LCFA). Based on the best‐fit models, an effect of overcorrection was observed in early lactation (5–35 days in milk [DIM]). On the contrary, third‐order (LEG333; degree 2) models showed flat residual trajectories throughout lactation. In general, the estimates of genetic variance tended to increase over DIM, for all traits. Heritabilities for milk production traits ranged from 0.11 to 0.58. Milk FA heritabilities ranged from low‐to‐high magnitude (0.03–0.56). High Spearman correlations (>0.90 for all bulls and >0.97 for top 100) were found among breeding values for 155 and 305 DIM between the best RRM and LEG333 model. Therefore, third‐order Legendre polynomials seem to be most parsimonious and sufficient to describe milk production and FA traits in Walloon Holstein cows.