Table 1 List of frequently used symbols
Symbol | Explanation |
|---|---|
General | |
\(\mathcal{Y}\) | Space of phenotypes |
Set of environments | |
\(\mathcal{E}\) | Space of environments |
\({\mathcal{E}}_{b}^{c}\subset \mathcal{E}\) | Current niche of breed \(b\) |
\({\mathcal{E}}_{b}\subset \mathcal{E}\) | Potential niche of breed \(b\) |
\(\mathcal{D}\) | Space of owner desires. Each component of \(\mathcal{D}\) assesses the extent to which the animal should be suitable for satisfying a certain desire |
\(\mathcal{V}\) | Space of influencing variables |
Potential breeding goals | |
\(\mathcal{P}\) | Set of potential breeding goals |
\({\mathcal{S}}_{b}\subset \mathcal{P}\) | Search area in which the optimum breeding goal of breed \(b\) is searched |
\({\mathcal{U}}_{b}\subset {\mathcal{S}}_{b}\) | Set of permissible breeding goals for breed \(b\) |
\({{\varvec{\upmu}}}_{tb}\in \mathcal{P}\) | State of the breeding program of breed \(b\) at time \(t\) |
\({{\varvec{\upmu}}}_{b}^{c}\in \mathcal{P}\) | Current state of the breeding program |
\({{\varvec{\upmu}}}_{b}\in \mathcal{P}\) | Putative breeding goal of breed \(b\) |
\({\dot{{\varvec{\upmu}}}}_{b}^{i}\in {\mathcal{U}}_{b}\) | Optimum intermediate breeding goal of breed \(b\) |
\({\dot{{\varvec{\upmu}}}}_{b}^{s}\in {\mathcal{S}}_{b}\) | Optimum breeding goal of breed \(b\) in the search area |
Key parameters | |
\({\mathfrak{m}}_{t}\left({\mathcal{E}}_{b}\right)\) | Expected size of the breed’s envisaged niche \({\mathcal{E}}_{b}\) at time \(t\) |
\(a\left({{\varvec{\upmu}}}_{b},\mathbf{e}\right)\) | Adaptedness of breed \(b\) to environment \(\mathbf{e}\in \mathcal{E}\) |
\({a}_{t}\left({{\varvec{\upmu}}}_{b},{\mathcal{E}}_{b}\right)\) | Adaptedness of breed \(b\) to its envisaged niche \({\mathcal{E}}_{b}\subset \mathcal{E}\) at time \(t\) |
\({\mathrm{TM}}_{\mathbf{e}}\left(\mathbf{y}\right)\) | Total merit of an animal with phenotype vector \(\mathbf{y}\) in environment \(\mathbf{e}\) |
\({\phi }_{\mathbf{v}}\left(\mathbf{y}\right)\) | Monetary profit the owner has from keeping an animal with phenotype \(\mathbf{y}\) |
\({\mathrm{R}}_{\mathbf{e}}\left(\mathbf{y}\right)\) | Non-monetary reward the owner perceives he has |
\({\mathrm{C}}_{\mathbf{e}}\left(\mathbf{y}\right)\) | Non-monetary costs the owner perceives he has |
\({\alpha }_{p}\), \({\alpha }_{n}\),\({\alpha }_{c}\) | Weights given to the total merits of an animal and its products for the producers, owners, and consumers, respectively |
\({\lambda }_{\mathbf{e}}\) | Weight given to non-monetary rewards and costs |