engleski

Covariance functions for weights of young dual purpose Simmental bulls using splines

Phenotypic, genetic and environmental covariance functions were estimated for weight of young dual purpose Simmental bulls. Data consisted of the records of 1360 young bulls measured monthly from 6 to 12 mo. Covariance functions were estimated by using polynomial (POL), piecewise cubic spline (PCS) and cubic smoothing spline (CSS) random regressions on Legendre polynomials of weight easurements. Age, season and year of birth and their interactions were defined as fixed, while animal and permanent environment due to repeated measurements were defined as random effects. The parameters were estimated by REML, and the model fits were analyzed using Akaike information criteria (AIC). The shape of the overall covariance functions (phenotypic) and partial functions (additive genetic and environmental) were analyzed. By comparing models using AIC, the POL models with degrees 2 and 3 showed slightly better overall fit than other models, however, they had more parameters and consequently were more computationally demanding. Further, the fit of the partial random effects was not satisfactory. The CSS showed moderate overall and partial fit, but they tend to smooth the original data showing average increase in variability. The PCS showed the best partial fit, and good overall fit, although slightly worse than the other models. Their performance depended on defined degree and position of knots. The heritability estimates ranged from 0.37 to 0.40 for PCS, 0.40 to 0.44 for CSS, and 0.40 to 0.49 for POL. The choice of the models, including the defined degree of the overall and spline polynomials, and position and numbers of knots, depends not only on overall fit but also on the fit of genetic and environmental components. This can be verified by looking at graphs of partial covariance functions. Splines fit on Legendre polynomials, which reduces possible estimation numerical problems, proved to be very good method for estimating changes in genetic parameters over age in dual purpose Simmental cattle.

Random regression; Simmental cattle; Spline

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