Genotype x environment interaction for milk production in Guernsey cattle

International genetic evaluations that use national genetic evaluation results as input need to acknowledge country boundaries. The current model for international evaluation treats each country as a genetically separate trait, i.e., assumes milk production to be similar within country, but different between countries. The use of cow performance records does not require such restriction, and allows for other statistical models to consider genotype x environment interaction. First-lactation records from 40,000 Guernsey cows in four countries (Australia, Canada, United States, and South Africa) were used to detect and describe genotype x environment interaction for milk production traits. Five statistical models were considered: single-trait across-county (ST), single-trait across-country with heterogeneous residual variance (SThet), multiple-trait across-country (MT), multiple-trait herd cluster model (HC), and reaction norm model (RR). For the herd cluster model, herds were clustered into groups based on information on herd management, genetic composition, and climate. Reaction norms describe the phenotype expressed by a genotype as a function of the environment, and was modeled by random regression on the herd average for peak milk yield as the descriptor of production environment. Gibbs sampling was used to make inferences about the parameters of interest, and models were compared based on goodness of fit and deviance information criterion. Posterior mode of the heritability for the single-trait model was 0.32, and ranged from 0.15 to 0.53 for models SThet and MT. Posterior mode of the genetic correlations between countries estimated with model MT were generally high (0.78 to 0.90). However, posterior SD were high (up to 0.15 for Australia-South Africa), and values near unity for the genetic correlations were not unlikely. Model HC gave more precise inferences but lower goodness of fit compared with model MT. Results from model RR provided evidence for heterogeneity of genetic variances. This model was least supported by the data, probably because heterogeneity of residual variances was not considered. Among the models in this study, the one with homogeneous genetic and heterogeneous residual variances across countries fitted best to the data, and we expect a model for which the assumption of homogeneous genetic variance is relaxed to show an even better fit to the data.