Bayesian inference for genetic parameter estimation on growth traits for Nelore cattle in Brazil, using the Gibbs sampler

Summary This data set consisted of over 29 245 field records from 24 herds of registered Nelore cattle born between 1980 and 1993, with calves sires by 657 sires and 12 151 dams. The records were collected in south-eastern and midwestern Brazil and animals were raised on pasture in a tropical climate. Three growth traits were included in these analyses: 205- (W205), 365- (W365) and 550-day (W550) weight. The linear model included fixed effects for contemporary groups (herd-year-season-sex) and age of dam at calving. The model also included random effects for direct genetic, maternal genetic and maternal permanent environmental (MPE) contributions to observations. The analyses were conducted using single-trait and multiple-trait animal models. Variance and covariance components were estimated by restricted maximum likelihood (REML) using a derivative-free algorithm (DFREML) for multiple traits (MTDFREML). Bayesian inference was obtained by a multiple trait Gibbs sampling algorithm (GS) for (co)variance component inference in animal models (MTGSAM). Three different sets of prior distributions for the (co)variance components were used: flat, symmetric, and sharp. The shape parameters (ν) were 0, 5 and 9, respectively. The results suggested that the shape of the prior distributions did not affect the estimates of (co)variance components. From the REML analyses, for all traits, direct heritabilities obtained from single trait analyses were smaller than those obtained from bivariate analyses and by the GS method. Estimates of genetic correlations between direct and maternal effects obtained using REML were positive but very low, indicating that genetic selection programs should consider both components jointly. GS produced similar but slightly higher estimates of genetic parameters than REML, however, the greater robustness of GS makes it the method of choice for many applications. Resumen Se analisaron datos de mas de 29245 registros de campo, colectados en 24 rebanos de vacuno Nelore registrados, nacidos entre 1980 y 1993, con becerros hijos de 657 toros y 12151 vacas. Los registros fueron originados en las regiones Sudeste y Centro-oeste del Brasil, en animales criados a pasto en un clima tropical. Se incluyeron en las analisis, tres caracteristicas del crecimiento siendo estas los pesos a los 205 (P205), 365 (P365) y 550 (P550) dias. El modelo lineal incluyo efectos fijos para los grupos contemporaneos (rebano-ano-estacion-sexo) y edad de la vaca al parto. El modelo tambien incluyo efectos aleatorios, tales como las contribuicones geneticas directas, maternas, y ambientales permanentes a las observaciones. Las analisis se llevaron a cabo utilizando modelos de una o dos variables. Los componentes de variancia y covariancia se estimaron a traves de la maxima verosimilitud restricta (Restricted Maximum Likelihood, REML), utilizandose un algoritmo libre de derivativas (Derivative-Free REML, DFREML) para caracteristicas multiplas. La Inferencia Bayesiana se obtuvo a traves de un algoritmo de muestreo Gibbs (Gibbs sampling, GS) para caracteristicas multiplas, especificamente para estimacion de los componentes de (co)variancia en modelos animales (MTGSAM). Se implementaron tres conjuntos de distribuciones previas (priors) de los componentes de (co)variancia: plana (flat), simetrica, y aguda (sharp). Los parametros de forma (ν) fueron 0, 5 y 9, respectivamente. Los resultados indican que la forma de las distribuciones previas no afectaron las estimativas de los componentes de (co)variancia. Las heredabilidades de todas las caracteristicas, obtenidas a traves del REML con el modelo de una sola caracteristica, fueron inferiores a aquellas obtenidas con el modelo bivariable. Las correlaciones geneticas entre los efectos directos y maternos, obtenidos con el metodo GS, indican que los programas de seleccion genetica deben considerar en conjunto los dos componentes. Esta conclusion tambien puede aplicarse a las estimaciones con REML, ya que estas correlaciones, aunque positivas, son demasiado bajas para asumir que los efectos directos puedaam incluir automaticamente los efectos maternos.