Comparison of breeding values for growth traits in Nellore cattle predicted by finite or infinite dimension model

Data consisting of 20,065 weights of 3,016 Nellore animals recorded from birth to 630 days of age were used to compare random regression on Legendre polynomials of age (LP) and on Legendre polynomials associated to a parametric correlation structure (PC) models for breeding value prediction of growth traits. Results from Standard bivariate analyses (SBA) using weights at standard ages were also compared to those from random regression models. Dependent variables in random regression analyses were Legendre polynomials of age at recording and the models included contemporary groups as fixed effects, and age of dam with linear and quadratic components as covariates. Mean trends were modeled through a cubic regression on orthogonal polynomials of age and genetic direct and maternal and direct and maternal permanent environmental effects were modeled by polynomials of order of 4, 4, 6 and 3 respectively. Measurement errors were modeled through a variance function or by SBA differed from those predicted by infinite dimension models. Rank correlations between breeding values predicted using LP for animal permanent environmental effects and those predicted using PC were close to unity.