The random regression test-day models can accelerate the genetic improvement of Sahiwal cattle as test-day milk yield models offer a faster, accurate and economical approach of genetic evaluation. First three lactation monthly test-day records of Sahiwal cows calved between 1961 and 2012 at ICAR-National Dairy Research Institute, Karnal were used to fit random regression model (RRM) with various order of legendre polynomial, and a constant (RRM-HOM) or heterogeneous residual variance (RRM-HET). For both RRM-HOM and RRM-HET third order legendre polynomial for modelling additive genetic effects were found best. There was reduction in order of fit for modelling permanent environmental effects due to assumption of heterogeneous residual variance, as legendre polynomial of sixth order for RRM-HOM and fourth or fifth order for RRM-HET was found to be best, for modelling the permanent environmental effect. First two eigenvalues of additive genetic random regression coefficient matrix explained more than 99% of the additive genetic variation, whereas four eigenvalues explained ~98% of the permanent environment variations. First eigenfunction from both the models did not show any large change along lactation, suggesting most variation can be explained by genes that act in same way during lactation. The heritability estimates were generally low but moderate for some test-day milk yields, and it ranged from 0.007 to 0.088 for first, 0.044 to 0.279 for second, and 0.089 to 0.129 for third lactation from RRM-HOM. The values of genetic correlation between test-day milk yields ranged from 0.06 to 0.99 for first, 0.77 to 0.99 for second, and 0.07 to 0.99 for third lactation, from RRM-HOM. The value of permanent environment correlation ranged from 0.30 to 0.98 for first, 0.07 to 0.99 for second, and 0.16 to 0.98 for third lactation. The genetic correlations between two adjacent test-days were high (≥0.90). RRM-HET also gave similar heritability and correlation estimates. The rank correlation between sire breeding values for first, second, and third lactation, estimated using two models were 0.98, 1.00, and 0.99, respectively, indicating there was no difference in the ranking of animals using two models. Thus the random regression model with lower order of polynomial for modelling additive genetic effect and higher order polynomial for modelling animal permanent environmental effect was found suitable for genetic evaluation and both RRM-HOM and RRM-HET can be used for modelling test-day milk yield and breeding value prediction in Sahiwal cattle.
Impact of the Order of Legendre Polynomials in Random Regression Model on Genetic Evaluation for Milk Yield in Dairy Cattle Population
