Combining different functions to describe milk, fat, and protein yield in goats using Bayesian multiple-trait random regression models

We proposed multiple-trait random regression models (MTRRM) combining different functions to describe milk yield (MY) and fat (FP) and protein (PP) percentage in dairy goat genetic evaluation by using Bayesian inference. A total of 3,856 MY, FP, and PP test-day records, measured between 2000 and 2014, from 535 first lactations of Saanen and Alpine goats, including their cross, were used in this study. The initial analyses were performed using the following single-trait random regression models (STRRM): third-and fifth-order Legendre polynomials (Leg3 and Leg5), linear B-splines with 3 and 5 knots, the Ali and Schaeffer function (Ali), and Wilmink function. Heterogeneity of residual variances was modeled considering 3 classes. After the selection of the best STRRM to describe each trait on the basis of the deviance information criterion (DIC) and posterior model probabilities (PMP), the functions were combined to compose the MTRRM. All combined MTRRM presented lower DIC values and higher PMP, showing the superiority of these models when compared to other MTRRM based only on the same function assumed for all traits. Among the combined MTRRM, those considering Ali to describe MY and PP and Leg5 to describe FP (Ali_Leg5_Ali model) presented the best fit. From the Ali_Leg5_Ali model, heritability estimates over time for MY, FP. and PP ranged from 0.25 to 0.54, 0.27 to 0.48, and 0.35 to 0.51, respectively. Genetic correlation between MY and FP, MY and PP, and FP and PP ranged from -0.58 to 0.03, -0.46 to 0.12, and 0.37 to 0.64, respectively. We concluded that combining different functions under a MTRRM approach can be a plausible alternative for joint genetic evaluation of milk yield and milk constituents in goats.