Multiple trait breeding programs with genotype-by-environment interactions based on reaction norms, with application to genetic improvement of disease resilience

Background Genotype-by-environment interactions for a trait can be modeled using multiple-trait, i.e. character-state, models, that consider the phenotype as a different trait in each environment, or using reaction norm models based on a functional relationship, usually linear, between phenotype and a quantitative measure of the quality of the environment. The equivalence between character-state and reaction norm models has been demonstrated for a single trait. The objectives of this study were to extend the equivalence of the reaction norm and character-state models to a multiple-trait setting and to both genetic and environmental effects, and to illustrate the application of this equivalence to the design and optimization of breeding programs for disease resilience. Methods Equivalencies between reaction norm and character-state models for multiple-trait phenotypes were derived at the genetic and environmental levels, which demonstrates how multiple-trait reaction norm parameters can be derived from multiple-trait character state parameters. Methods were applied to optimize selection for a multiple-trait breeding goal in a target environment based on phenotypes collected in a healthy and disease-challenged environment, and to optimize the environment in which disease-challenge phenotypes should be collected. Results and conclusions The equivalence between multiple-trait reaction norm and multiple-trait character-state parameters allow genetic improvement for a multiple-trait breeding goal in a target environment to be optimized without recording phenotypes and estimating parameters for the target environment.