Abstract
The incorporation of modern animal models become imperative for planning breeding strategies of dairy populations. The present study was designed to compare between single-trait and multi-traits animal models in estimating genetic parameters and breeding values for some milk yield and reproductive traits of Holstein-Friesian dairy cattle. A total of 9450 records of dairy cows calved in the period between 2007 and 2018 were included in the analyses by using the datasets of the first four lactations. Mixed model methodologies have been applied through applications of restricted maximum likelihood estimation algorithms. The heritability estimates for investigated traits were found be 0.26 for lactation milk yield (LMY), 0.42 (0.45) for milk fat percentage, 0.41 (0.44) for milk protein percentage, 0.13 (0.14) for lactation length (LL), 0.14 (0.15) for age at first calving, 0.17 (0.18) for calving interval, and 0.10 (0.13) for days open as denoted by single-trait (multi-traits) models, respectively. The genetic correlations between lactation milk yield and fertility traits ranged from 0.41 to -0.74. The highest genetic correlation was found between LMY and LL which was 0.84. The Akaike Information Criteria (AIC), the model evaluation measure were estimated for both models and its values were 59245.56 and 58598.23 for single-trait model and multi-traits model, respectively. Therefore, the multi-traits model, the model with the lowest value of AIC was selected as the model of choice for model’s evaluation and preference. In conclusion, the current estimates and results indicate the possibility of genetic improvements for studied traits of Holstein-Friesian cows. Moreover, the multi-traits models are highly recommended for future analyses of complex livestock traits and for construction of selection plans.

Key words: Holstein-Friesian cattle, animal models, milk yield traits, fertility traits, Akaike Information Criterion, Model fitting