Random Regression Test-Day Model for Milk Yield in Sahiwal Cattle, Kenya
##article.abstract##
A total of 19,313 test-day milk yield records for 1,892 Sahiwal cattle from first three lactations were used to describe variation in milk yield using Random Regression Model (RRM) with Legendre Polynomials (LP). Data were recorded between 1978 and 2002. Variance components were estimated by Restricted Maximum Likelihood method. Thirty models from first to fourth order Legendre Polynomials were used to describe additive genetic and permanent environmental effects in each parity. Both heterogeneous and homogeneous models were considered. Heterogeneous residual variances were modeled by considering eight classes. Most suitable LP order was selected based on Logarithm of likelihood function (-2logL), Akaike Information (AIC) and Schwarz's Bayesian Information (BIC) criterion. Different error covariance structures were compared using Likelihood ratio test with significance of differences between models obtained using a chi-square test. Model LP (5,5RV8) with 5 additive genetic and 5 permanent environmental random regression coefficients was sufficient to model variability in milk yield across the three parities. The first three Eigen values and first four Eigen values, respectively, explained over 98% of total variation of random regression coefficients for additive genetic and permanent environmental effects. Heritability estimates for daily milk yield in parities one, two and three ranged from 0.15 to 0.27, 0.05 to 0.17 and 0.16 to 0.38, respectively. Genetic correlations between daily milk yields in parities one, two and three ranged from 0.332 to 0.995, 0.13 to 0.996197 and 0.092 to 0.988, respectively. Average heritability estimates for lactation milk yield for parities one two and three, respectively, were 0.309, 0.144 and 0.422. Sire Rank correlations between model LP(5,5RV8) and the lower models in parities one, two and three ranged from -0.089 to 0.222, -0.132 to 0.295 and -0.100 to 0.177, respectively. Product moment correlations between model LP(5,5RV8) and lower models ranged from 0.773 to 0.984, 0.805 to 0.958 and 0.919 to 0.989 in parities one, two and three, respectively.
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