Models for genetic evaluation of growth of Brazilian Bonsmara cattle

The purpose of this study was to demonstrate the usefulness of different multi-trait models and random regression models (RRM) using Legendre polynomials for the genetic evaluation of growth in Brazilian Bonsmara cattle. Data comprised 54,039 weight records of Bonsmara cattle, from birth to adult age (614 days of age). A standard multi-trait model (SMT); reduced rank analyses fitting the first 2 genetic principal components (PC2), reduced rank analyses fitting the first direct additive genetic and maternal principal components (PC22), reduced rank analyses fitting the first direct additive genetic, maternal, and maternal permanent environmental principal components (PC222), were carried out. For all traits, genetic additive direct and maternal, and maternal permanent environmental were considered as random effects. Furthermore, linear and quadratic effects of age of the animal at recording (except for birth weight), and dam age at calving were included as covariates. The analyses were performed using a single-trait RRM. Fourth-order Legendre polynomials to model trends in the population mean. Additive direct, animal permanent environmental effects, maternal genetic, and maternal permanent environmental effects were modeled with Legendre polynomials. In addition, contemporary group as fixed effects, dam age at calving (linear and quadratic), age at recording (linear) as covariates were included. Genetic parameters from different approaches were similar, when the optimal number of PC was fitted. The model PC222 (reduced rank analyses fitting the first direct additive genetic, maternal, and maternal permanent environmental principal components) allows a reduction of the number of parameters to be estimated, and this methods was sufficient to describe the genetic covariance structure adequately.