The present study aimed to estimate the genetic parameters of first lactation milk yield (FLMY), first lactation period (FLP), first dry period (FDP) and first calving interval (FCI) and inclusion these studied traits in selection indices through different animal models. The data utilized in this study were obtained from 1821 normal first lactation of Friesian cows belong to Sakha and EI-Karada Experimental stations of Animal Production Research Institute (APRI), Dokki, Cairo, Egypt. Data were collected during the period from 1990 to 2016 and analyzed using the MTDFREML program. Covariance components were used to construct the different selection indices for FLMY kg, FLP day, FDP day and FCI day with four multiple animal models. Means for FLMY, FLP, FDP and FCI were 2425 kg, 304 d, 170 d and 474 d, respectively. Direct heritability (h 2 a) for the above-mentioned traits were 0.32, 0.29, 0.27 and 0.18, respectively. The corresponding estimates of the maternal heritability (h 2 m) for the same traits were 0.25, 0.22, 0.30 and 0.27, successively. Estimates of direct genetic correlations among studied traits ranged from -0.52 to 0.61. The phenotypic correlations among investigated traits were ranging from -0.20 to 0.23. Animal model number two that included the additive and permanent effects had the highest accuracy. On the contrary, model number three that included additive and maternal effects. The ranking correlations among four animal models were higher than 0.93. This indicates that using one of the studied models can be achieved the genetic improvement. We would however recommend that included the permanent environmental effects on analytical models when selection for these traits in Friesian cows under Egyptian condition.
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