Introduction Animal growth has been modelled using several mathematical functions (Logistic, Von Bertalanffy, Gompertz, etc.). These functions are described by a reduced number of parameters. In some cases, these parameters are assigned a biological interpretation (adult weight, maturing rate, etc.) and so the breeding goal can be closely related to the change of performance in these parameters, with the objective of altering the shape of the growth curve. In this sense, some studies have been focused on the estimation of (co)variance components of these parameters (B rown et al. 1976; F itzbugh 1976; D e N ise and B rinks 1985; K oenen and G roen 1996). These studies are based on a two‐step procedure. In the first step, a growth curve is fitted separately to the data of each individual animal, afterwards, a mixed model analysis is applied to obtain (co)variance components. In this second step the estimates of production function parameters from the previous step are taken as records. Recently, V arona et al. (1997, 1998) have described a Bayesian procedure which allows the particular parameters of any production function to be estimated jointly and the (co)variance components between them. This procedure provides a considerable advantage over Maximun Likelihood approaches to joint analysis (Z ucker et al. 1995) and makes use of all the available information. The aim of this study is to compare both procedures in a simulation scheme under the assumption of the Von Bertalanffy growth function.

a b s t r a c tReproductive traits as number of piglets born (NPB) and weaned (NWP) are directly related to the economic efficiency of swine production systems. Pig breeding programs seek to increase the number of weaned piglets per sow per year, and the NPB is among the factors that directly and indirectly influence the NWP. Thus, multi-trait evaluations are essential to estimate heritabilities and mainly genetic correlations between these traits over different farrowing orders. In general, Gaussian linear mixed models have been used to genetic evaluation of litter traits; however since these traits are characterized as count variables, Poisson models are also indicated. Some studies were carried out using Poisson mixed models in the area of Animal Breeding and Genetics, but they do not point out for a multi-trait scenario, as it should be for litter size at birth and weaning. Toward this orientation, we aimed to apply a multi-trait Poisson mixed model (MPM) for the genetic evaluation of the number of born and weaned piglets under a Bayesian framework. It was aimed also to compare the proposed model with the traditional multi-trait Gaussian model (MGM) by using posterior based goodness-of-fit measures. Two-trait analyses for NPB and NWP were performed separately by each considered farrowing order (first, second and third) using MPM and MGM fitted to data from a commercial Landrace population. Based on DIC (Deviance Information Criterion) and PMP (Posterior Model Probability) values, the MGM outperformed the MPM, but the genetic parameter and breeding values provided by both models were consistent and similar over the three first farrowing orders. Bayesian generalized a multi-trait mixed model approach is feasible for genetic evaluations in the animal breeding context and can be an alternative method for genetic evaluations assuming non-Normal phenotypes.