Background: Despite the importance of relationships between somatic cell score (SCS) and currently selected traits (milk, fat and protein yield) of Holstein cows, there was a lack of comprehensive literature for it in Iran. Therefore we tried to examine heritabilities and relationships between these traits using a fixed-regression animal model and Bayesian inference. The data set consisted of 1,078,966 test-day observations from 146,765 primiparous daughters of 1930 sires, with calvings from 2002 to 2013. Results: Marginal posterior means of heritability estimates for SCS (0.03 ± 0.002) were distinctly lower than those for milk (0.204 ± 0.006), fat (0.096 ± 0.004) and protein (0.147 ± 0.005) yields. In the case of phenotypic correlations, the relationships between production and SCS were near zero at the beginning of lactation but become increasingly negative as days in milk increased. Although all environmental correlations between production and SCS were negative (−0.177 ± 0.007, −0.165 ± 0.008 and −0.152 ± 0.007 between SCS and milk, fat, and protein yield, respectively), slightly antagonistic genetic correlations were found; with posterior mean of relationships ranging from 0.01 ± 0.039 to 0.11 ± 0.036. This genetic opposition was distinctly higher for protein than for fat. Conclusion: Although small, the positive genetic correlations suggest some genetic antagonism between desired increased milk production and reduced SCS (i.e., single-trait selection for increased milk production will also increase SCS).
