RANDOM REGRESSION MODELS FOR ESTIMATION OF COVARIANCE FUNCTIONS, GENETIC PARAMETERS AND PREDICTION OF BREEDING VALUES FOR RIB EYE AREA IN A COLOMBIAN BOS INDICUS-BOS TAURUS MULTIBREED CATTLE POPULATION MODELOS DE REGRESIóN ALEATORIA PARA LA ESTIMACIóN DE FUNCIONES DE COVARIANZA, PARáMETROS GENéTICOS Y PREDICCIóN DE VALORES GENéTICOS EN UNA POBLACIóN BOVINA MULTIRRACIAL BOS INDICUS-BOS TAURUS EN COLOMBIA

In this paper we present an application of random regression models (RRM) to obtain restricted maximum likelihood estimates of covariance functions and predictions of breeding values for longitudinal records of rib eye area measured by ultrasound (REA) in a Colombian multibreed cattle population. The dataset contained 708 records from 340 calves progeny of 37 sires from nine breeds mated to Gray Brahman Cows. The mixed model was a RRM that used Legendre polynomials (LP) of order 1 to 3. Fixed effects were age of animal, dam parity, contemporary group (herd*year*season*sex), breed additive genetic and heterosis, whereas direct and maternal additive genetic and maternal permanent environment were random effects. Residual variances were modeled either as constant or changing across the growth trajectory. Models were compared with two Information Criteria, the corrected Akaike’s and the Schwartz’s Bayesian. According to these criteria the best model was the one with first order LP and constant residual variance. Given that with this model estimated maternal additive genetic and permanent environment covariance functions showed that these effects were not accurately disentangled, a parsimonious model without maternal additive genetic effects was used to obtain genetic parameters and breeding values. Direct additive genetic variance decreased until 150 days and then increased. Maternal permanent environment variance increased with age. Direct heritability estimates for REA at 4 months, weaning, 12 and 15 months (considered as target ages), were 0.003, 0.007, 0.034 and 0.058, respectively. Direct additive correlations ranged from -0.7 to 1. Maternal permanent environmental correlations were close to unity across the entire range of ages. Estimates of (co)variance components showed the need to validate results with larger multigenerational multibreed populations before implement RRM in regional or national genetic evaluation procedures in Colombia. En este trabajo presentamos una aplicación de modelos de regresión aleatoria (RRM) para obtener estimadores de máxima verosimilitud restringida de funciones de covarianza y predicciones del valor genético para datos longitudinales de área de ojo del lomo medidos por ultrasonido (REA) en una población bovina multirracial en Colombia. El conjunto de datos contenía 708 registros de 340 animales descendientes de 37 toros de 9 razas apareados con hembras Brahman Gris. Los modelos mixtos empleados fueron RRM que usaron polinomios de Legendre (LP) de orden 1 a 3. Los efectos fijos fueron edad del animal, número de partos de