Modelling non-additive genetic effects using ridge regression for an Angus–Nellore crossbred population

Data from 294045 records from a crossbred Angus × Nellore population were used to estimate fixed genetic effects (both additive and non-additive) and to test different non-additive models using ridge regression. The traits studied included weaning gain (WG), postweaning gain (PG), phenotypic scores for weaning (WC) and postweaning (PC) conformation, weaning (WP) and postweaning (PP) precocity, weaning (WM) and postweaning (PM) muscling and scrotal circumference (SC). All models were compared using the likelihood-ratio test. The model including all fixed genetic effects (breed additive and complementarity, heterosis and epistatic loss non-additive effects, both direct and maternal) was the best option to analyse this crossbred population. For the complete model, all effects were statistically significant (P < 0.01) for weaning traits, except the direct breed additive effects for WP and WM; direct complementarity effect for WP, WM, PP and PM and maternal epistatic loss for PG. Direct breed additive effect was positive for weaning traits and negative for postweaning. Maternal breed additive effect was negative for SC and WP. Direct complementarity and heterosis were positive for all traits and maternal complementarity and heterosis were also positive for all traits, except for PG. Direct and maternal epistatic loss effects were negative for all traits. We conclude that the fixed genetic effects are mostly significant. Thus, it is important to include them in the model when evaluating crossbred animals, and the model that included breed additive effects, complementarity, heterosis and epistatic loss differed significantly from all reduced models, allowing to infer that it was the best model. The model with only breed additive and heterosis was parsimonious and could be used when the structure or amount of data does not allow the use of complete model.

Comparing methodologies to estimate fixed genetic effects and to predict genetic values for an Angus × Nellore cattle population

The study assesses the need for and effectiveness of using ridge regression when estimating regression coefficients of covariates representing genetic effects due to breed proportion in a crossbreed genetic evaluation. It also compares 2 ways of selecting the ridge parameters. A large crossbred Angus × Nellore population with 294,045 records for weaning gain and 148,443 records for postweaning gain was used. Phenotypic visual scores varying from 1 to 5 for weaning and postweaning conformation, weaning and postweaning precocity, weaning and postweaning muscling, and scrotal circumference were analyzed. Three models were used to assess the need for ridge regression, having 4, 6, and 8 genetic covariates. All 3 models included the fixed contemporary group effect and random animal, maternal, and permanent environment effects. Model AH included fixed direct and maternal breed additive and the direct and maternal heterosis covariates, model AHE also included direct and maternal epistatic loss covariates, and model AHEC further included direct and maternal complementarity effects. The normal approach is to include these covariates as fixed effects in the model. However, being all derived from breed proportions, they are highly collinear and, consequently, may be poorly estimated. Ridge regression has been proposed as a method of reducing the collinearity. We found that collinearity was not a problem for models AH and AHE. We found a high variance inflation factor, >20, associated with some maternal covariates in the AHEC model reflecting instability of the regression coefficients and that this instability was well addressed by using ridge regression using a ridge parameter calculated from the variance inflation factor.

Bioeconomic model and selection indices in Aberdeen Angus cattle

A bioeconomic model was developed to calculate economic values for biological traits in full-cycle production systems and propose selection indices based on selection criteria used in the Brazilian Aberdeen Angus genetic breeding programme (PROMEBO). To assess the impact of changes in the performance of the traits on the profit of the production system, the initial values ​​of the traits were increased by 1%. The economic values for number of calves weaned (NCW) and slaughter weight (SW) were, respectively, R$ 6.65 and R$ 1.43/cow/year. The selection index at weaning showed a 44.77% emphasis on body weight, 14.24% for conformation, 30.36% for early maturing and 10.63% for muscle development. The eighteen-month index showed emphasis of 77.61% for body weight, 4.99% for conformation, 11.09% for early maturing, 6.10% for muscle development and 0.22% for scrotal circumference. NCW showed highest economic impact, and SW had important positive effect on the economics of the production system. The selection index proposed can be used by breeders and should contribute to greater profitability.