Fig. 3

Illustration of the state space of breeding programs. Illustrative example with a one-dimensional space \(\mathcal{E}\) of environments, and a one-dimensional space \(\mathcal{Y}\) of phenotypes, so there is only one trait under selection. The current state of the breeding program for breed \(b\) is described by a function \({\mu }_{b}^{c}\in \mathcal{P}\) that provides for each environment \(e\) the trait mean of the breed in that environment. The phenotypic variance is assumed to be constant. The breeding goal of the breed is defined by function \({\dot{\mu }}_{b}\in \mathcal{P}\). The red arrows symbolize that the trait mean \({\mu }_{b}^{c}\left(e\right)\) is expected to approach the breeding goal \({\dot{\mu }}_{b}\left(e\right)\) in the course of the breeding program for all relevant environments \(e\)