Table 6 This table summarizes the TRS optimization methods employed in this study, indicating their purpose (either optimization of size or composition) and type (whether genetic-based, phenotypic-based, or mixed and targeted or untargeted)
From: Maximizing efficiency in sunflower breeding through historical data optimization
Method | Purpose | Type | Mechanism |
|---|---|---|---|
\(\begin{array}{cc} \text {PCA\_CDmean/} \\ \text {PLS\_CDmean} \end{array}\) | Composition | \(\begin{array}{cc} \text {Genetic/Mixed} \\ \text {targeted} \end{array}\) | \(\begin{array}{cc} D_1 = diag(X_{TS;All}X'_{TS;All}) \\ X_1 = X'_{TRS;All}X_{TRS;All};\\ X_2 = (X_1+I\lambda )^{-1} \\ D_2 = diag(X_{TS;All}X_2X_1X_2X'_{TS;All}) \\ \text {\textit{CDmean}} = -sum(D_2/D_1)/n_{TS} \\ argmax(CDmean) \end{array}\) |
Avg_GRM_self | Composition | \(\begin{array}{cc} \text {Genetic} \\ \text {untargeted} \end{array}\) | \(\begin{array}{cc} \text {\textit{Avg\_GRM\_self}} = -mean(G_{TRS;TRS})\\ argmax(\text {\textit{Avg\_GRM\_self}}) \end{array}\) |
Avg_GRM_MinMax | Composition | \(\begin{array}{cc} \text {Genetic} \\ \text {targeted} \end{array}\) | \(\begin{array}{cc} \text {\textit{Avg\_GRM\_MinMax}} = mean(G_{TRS;TS}) -mean(G_{TRS;TRS})\\ argmax(\text {\textit{Avg\_GRM\_MinMax}}) \end{array}\) |
Avg_GRM | Composition | \(\begin{array}{cc} \text {Genetic} \\ \text {targeted} \end{array}\) | \(\begin{array}{cc} \text {\textit{Avg\_GRM}}_i = mean(G_{i;TS}) \end{array}\) \(\begin{array}{l} \text {1) Compute \textit{Avg\_GRM} for all hybrids in the candidate set} \\ \text {2) Select for the TRS the } n_{TRS} \text { hybrids with the highest} \\ \text {\textit{Avg\_GRM} values} \end{array}\) |
\(\begin{array}{c} \text {Min\_GRM} \end{array}\) | Composition | \(\begin{array}{cc} \text {Genetic} \\ \text {targeted} \end{array}\) | \(\begin{array}{cc} \text {\textit{Min\_GRM}}_i = min(G_{i;TS}) \end{array}\) \(\begin{array}{l} \text {1) Compute \textit{Min\_GRM} for all hybrids in the candidate set} \\ \text {2) Select for the TRS the } n_{TRS} \text { hybrids with the highest} \\ \text {\textit{Min\_GRM} values} \end{array}\) |
Size | \(\begin{array}{cc} \text {Genetic} \\ \text {targeted} \end{array}\) | \(\begin{array}{l} \text {1) Optimize composition of training sets of increasing size using} \\ \text {\textit{Min\_GRM}. Sizes tested range from 1 to entire candidate set} \\ \text {2) The \textit{fitness} value for every TRS is the smallest \textit{Min\_GRM}} \\ \text {value among its hybrids} \\ \text {3) Plot \textit{TRS size} against \textit{-fitness} as in Figure S9} \\ \text {4) Fit sigmoidal function to the plot} \\ \text {5) Optimal TRS size is the one corresponding to the second} \\ \text {inflexion point of the sigmoidal} \end{array}\) | |
Tails | Composition | \(\begin{array}{cc} \text {Phenotypic} \\ \text {untargeted} \end{array}\) | \(\begin{array}{l} \text {1) Rank hybrids according to their genotypic values} \\ \text {2) Select } \frac{n_{TRS}}{2} \text { hybrids with highest genotypic values} \\ \text {and } \frac{n_{TRS}}{2} \text { hybrids with lowest genotypic values} \end{array}\) |
Tails_GEGVs | Composition | \(\begin{array}{cc} \text {Mixed} \\ \text {untargeted} \end{array}\) | \(\begin{array}{l} \text {1) Rank hybrids according to their GEGVs} \\ \text {2) Select } \frac{n_{TRS}}{2} \text { hybrids with highest GEGVs} \\ \text {and } \frac{n_{TRS}}{2} \text { hybrids with lowest GEGVs} \end{array}\) |
Tails_GEGVs_sd1 | Composition and size | \(\begin{array}{cc} \text {Mixed} \\ \text {untargeted} \end{array}\) | \(\begin{array}{l} \text {1) Scale GEGVs distribution to have } \mu = 0, sd = 1 \\ \text {2) Select hybrids whose scaled GEGVs are lower than } -\alpha \cdot sd \\ \text {and hybrids with scaled GEGVs higher than } \alpha \cdot sd \end{array}\) |