The used data set included the records of 131990 Iranian Holstein dairy cattle for first three lactations that were collected from 1981 to 2008 time period by Animal Breeding Center, Iran. The traits which were considered for 305 days of lactation included milk, fat and protein yield and percentages of milk fat and protein. Variance components were estimated using average information restricted maximum likelihood (AI-REML) algorithm using AIREMLF90 software under single trait and repeatability models and Bayesian method by using a Gibbs sampling technique (BAGS) and by MTGSAM and GIBBS3F90 software by same models. The linear statistical models of the analyses included herd-year-season and lactations as fixed effects, age at calving as covariate and animal and permanent environment as random effects. The ranges of heritabilities estimates for lactations 1 to 3 by animal single and repeatability models using AI-REML and BAGS methods were 0.19 to 0.29, 0.17 to 0.26, 0.20 to 0.25, 0.21 to 0.25 and 0.19 to 0.35 for milk, fat and protein yield and percentage of milk fat and protein respectively. Repeatability estimates by using BAGS method were 0.44, 0.35, 0.43 and by AI-REML method the values were 0.43, 0.34, 0.39 for milk, fat and protein yield, respectively. The results showed that estimated genetic parameter values by AI-REML analyses for all traits and lactations in both models were smaller than BAGS method. In addition, estimated heritability values for later lactations were lower in comparison with the first lactation.

Key words: AI-REML, BAGS, Iranian Holstein dairy cattle, Variance components