Evaluation of an average numerator relationship matrix model and a Bayesian hierarchical model for growth traits in Nellore cattle with uncertain paternity

The objective of this work was to compare a model based on the use of an average numerator relationship matrix (ANRM) and a hierarchical animal model (HIER) to indicate the most appropriate statistical procedure to better estimate the genetic value of Nellore animals that have unknown paternity. The data set contained records of 62,212 Nellore animals. The pedigree file contained a total of 75,088 animals. Two approaches were adopted for the treatment of uncertain paternity. In the model based on the use of the ANRM probabilities were attributed to each of the possible parents of the animals with uncertain paternity. The other method adopted in the present study, i.e., the HIER, considers uncertainty in the assignment of paternity of animals participating in the multiple-sire (MS) system. Within this context, a priori probabilities are assigned to each possible sire of animals with uncertain paternity, which are altered according to information present in the data for the generation of posterior probabilities. Univariate analyses were carried out under Bayesian approach via Markov Chain Monte Carlo (MCMC) methods, implementing a chain of 400,000 rounds where the first 10,000 rounds were discarded (burn-in period). Models were compared by deviance information criteria (DIC) and pseudo Bayes factors (PBF). The model that best fits the data for estimating genetic parameter of animals with uncertain paternity is the Bayesian hierarchical model. Nevertheless, for genetic evaluation, the choice between these models would have no impact on genetic value classification of animals for selection.