Variance components (VC) for milk yield of Holstein cows were estimated and the effects of increasing of the number of animals in the numerator relationship matrix (NRM) were evaluated on VC estimates obtained by REML and Bayesian inference via Gibbs sampling (GS). Data were obtained from herds in the states of Minas Gerais, São Paulo, Paraná, Santa Catarina, and Rio Grande do Sul. Two data sets were created for each state. In the first set, the NRM included only the pedigree of the animals of the state under consideration (PEDR). In the second, the NRM included animals from the five states (PEDA). An animal model including the effects of herd-year, parity, season, genetic group, effects of additive genetic and permanent environment was used. The REML estimates of VC and heritability in each state obtained from PEDR and PEDA were similar. The heritability in Minas Gerais, São Paulo, Paraná, Santa Catarina, and Rio Grande do Sul was 0.19, 0.18, 0.26, 0.43, and 0.48, respectively. There was evidence that the posterior means of the genetic variance of PEDA analyses were significantly greater than PEDR. Heritability and standard deviations estimated by GS in Minas Gerais, São Paulo, Paraná, Santa Catarina, and Rio Grande do Sul, using PEDR (PEDA), were 0.21 ± 0.032 (0.40 ± 0.025), 0.20 ± 0.017 (0.27 ± 0.017), 0.28 ± 0.014 (0.31 ± 0.014), 0.42 ± 0.041 (0.56 ± 0.021) and 0.43 ± 0.039 (0.55 ± 0.019), respectively. The genetic variance of each state increased significantly when animals from the other states were incorporated in its NRM. The smallest standard deviations and VC credibility intervals were estimated in the states with more records, which suggested that the precision of the VC estimates was higher in those states.
convergence; dairy cattle; Gibbs sampling; heritability; relationship
