Two-step and random regression analyses of weight gain of station-tested beef bulls

Our objectives were to compare a two-step model and a joint procedure via random regression model for evaluating weight gain of beef bulls, weighed every 28 d on 140-d test, and to estimate genetic, environmental, and phenotypic parameters. Two-step analysis consisted of fitting fixed linear regressions to weights of each bull to determine weight gain on test. In the second step, gain on test was analyzed by a mixed model that included fixed effects of breed, test group, and starting age and random effects of weaning herd-year group and animal (additive genetic). The random regression model included the same effects as the two-step mixed-model analysis with an additional random animal permanent environment effect. Fourth-order Legendre polynomials of days on test were fitted for all fixed and random effects in the random regression model, except for breed. Breed effects and residual variances varied for each measurement period. Variance components and EBV for gain were obtained from the covariance function and estimates of random regression coefficients for weight, respectively. Random regression heritability estimates for gain on test increased over time, being maximum at end of test (0.38) and equal to two-step estimate. Permanent environment variance ratio estimates also increased over time and were greater than heritability estimates. Estimate of weaning herd-year variance ratio was approximately constant over time, being equal to 0.07 at end of test and similar to two-step estimate. Genetic correlations between gain through different periods on test given by random regression model were high (from 0.81, between 28 and 140-d gain on test, to 0.99, between 112 and 140-d gain on test). Genetic correlations between gain on discrete 28-d intervals were moderate to high (e.g., 0.49 and 0.99 between the last 28 d on test and the first and fourth 28 d, respectively). Rank correlations between EBV for 140-d gain by the two procedures were 0.98, 0.84, and 0.73 for all bulls and the 5% and 1% of bulls with highest random regression EBV, respectively. Results indicated that the two procedures rank top bulls quite differently for 140-d gain on test. Random regression model accounted for changes over time of genetic and environmental effects on the test weight gain curve of the bulls. Use of 112-d instead of a 140-d test provided similar ranking of bulls on the basis of EBV for gain on test.