Analysis of milk production traits in early lactation using a reaction norm model with unknown covariates

The reaction norm model is becoming a popular approach to study genotype x environment interaction (GxE), especially when there is a continuum of environmental effects. These effects are typically unknown, and an approximation that is used in the literature is to replace them by the phenotypic means of each environment. It has been shown that this method results in poor inferences and that a more satisfactory alternative is to infer environmental effects jointly with the other parameters of the model. Such a reaction norm model with unknown covariates and heterogeneous residual variances across herds was fitted to milk, protein, and fat yield of first-lactation Danish Holstein cows to investigate the presence of GxE. Data included 188,502 first test-day records from 299 herds and 3,775 herd-years in a time period ranging from 1991 to 2003. Variance components and breeding values were estimated with a Bayesian approach implemented using Markov chain Monte Carlo. The posterior distribution of the variance of genetic slopes was markedly shifted away from zero for all traits under study, supporting the presence of GxE. The ratio of the genetic slope variance to the genetic level variance was highest for fat yield, followed by protein and milk yields. Genetic correlations between environments that differ by plus and minus 1 standard deviation from the mean environmental effect were 0.93, 0.91, and 0.89 for milk, protein, and fat yield, respectively. Genetic variances and heritabilities increased with increasing level of environmental effects. The rank correlations between predicted breeding values at the 5th and 95th percentiles of the distribution of environmental effects were, respectively, equal to 0.91, 0.90, and 0.76, for milk, protein, and fat yield. Thus in this study, although GxE was detected, it has a small effect on reranking of candidates for selection.