The objective of this study was to estimate genetic parameters including repeatability, heritability as well as genetic and environmental relationships between 305-day milk yield, milk fat and protein yield (Fat and Pro), milk fat and protein percentages (Fat% and Pro%), mastitis (Mast), number of mastitis occurrence and different measurements of somatic cell counts using linear and threshold animal as well as linear and threshold sire models in Holstein cows of Iran. Records of 33851 first lactation Holstein cows from five large dairy herds with calving dates from March 2002 to September 2014 were analysed, using Gibbs sampling methodology. Heritabilities of production traits estimated by linear animal model ranged from 0.14 (Fat%) to 0.29 (Pro%). Generally, udder health traits had low heritability (ranged from 0.005 to 0.10). Estimates of heritability for Mast using linear models were higher than those obtained with threshold models. However, in general estimates of heritabilities using threshold models were higher than those from linear models. There were unfavourable genetic correlations between production traits and Mast, which implies that breeding programs with emphasis on 305-day milk yield will experience deterioration in udder health. Despite low heritability of udder health traits, genetic variability exists for these traits that allow selecting superior animals and increasing resistance to Mast and animal welfare. Considering relatively high ratio of permanent environmental variance for Mast, culling decisions can be made with higher accuracy in order to reduce Mast incidence phenotypically over time.
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