Reaction norm model with unknown environmental covariate to analyze heterosis by environment interaction

Abstract

Crossbreeding is currently increasing in dairy cattle production. Several studies have shown an environment-dependent heterosis [i.e., an interaction between heterosis and environment (H × E)]. An H × E interaction is usually estimated from a few discrete environment levels. The present study proposes a reaction norm model to describe H × E interaction, which can deal with a large number of environment levels using few parameters. In the proposed model, total heterosis consists of an environment-independent part, which is described as a function of heterozygosity, and an environment-dependent part, which is described as a function of heterozygosity and environmental value (e.g., herd-year effect). A Bayesian approach is developed to estimate the environmental covariates, the regression coefficients of the reaction norm, and other parameters of the model simultaneously in both linear and non-linear reaction norms. In the nonlinear reaction norm model, the H × E is approximated using linear splines. The approach was tested using simulated data, which were generated using an animal model with a reaction norm for heterosis. The simulation study includes 4 scenarios (the combinations of moderate vs. low heritability and moderate vs. low herd-year variation) of H × E interaction in a nonlinear form. In all scenarios, the proposed model predicted total heterosis very well. The correlation between true heterosis and predicted heterosis was 0.98 in the scenarios with low herd-year variation and 0.99 in the scenarios with moderate herd-year variation. This suggests that the proposed model and method could be a good approach to analyze H × E interactions and predict breeding values in situations in which heterosis changes gradually and continuously over an environmental gradient. On the other hand, it was found that a model ignoring H × E interaction did not significantly harm the prediction of breeding value under the simulated scenarios in which the variance for environment-dependent heterosis effects was small (as it generally is), and sires were randomly used over production environments. © American Dairy Science Association, 2009.