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Random regression models (RRM) were used to estimate covariance functions for 2,155 first-lactation milk yields of native Brazilian Caracu heifers. The models included contemporary group (defined as year-month of test and paddock) fixed effects, and quadratic effect of age of cow at calving. Genetic and permanent environmental effects were fitted by a random regression model and Legendre polynomials of days in milk (DIM). Schwarz's Bayesian information criteria (BIC) indicated that the best RRM assumed a six coefficient function for both random effects and a sixth order variance function for residual structure. Akaike's information criteria suggested a model with the same number of coefficients for both effects and a residual structure fitted by a step function with 15 variances. Phenotypic, additive genetic, permanent environmental and residual variances were higher at the beginning and declined during lactation. The RRM heritability estimates were 0.09 to 0.26 and generally higher at the beginning and end of lactation. Some unexpected negative genetic correlations emerged when higher order covariance functions were used. A model with four coefficients for additive genetic covariance function explains more parsimoniously the changes in genetic variation with DIM since the genetic parameter was more acceptable and BIC was close to that for a six coefficient covariance function

Variance component estimates applying random regression models for test-day milk yield in Caracu heifers (Bos taurus Artiodactyla, Bovidae)