GVaverage • TSDFGS

GVaverage is the mean genetic variance of the training individuals, the trace of their relationship matrix divided by $n$ (TSDFGS returns the trace).

Type	Genomic variation
Direction	Larger is better
Uses a test set	no (a test set given to `optTrain()` is ignored)
Score a given set	`gv_average_score()`
Search with it	`optTrain(method = "GVaverage")`

Definition

$\mathrm{tr}(G) = \lVert X\rVert_F^2/p$ . Maximizing it favors individuals far from the population center.

Use in TSDFGS

library(TSDFGS)
data(geno)
gv_average_score(geno[1:50, ])

## [1] 4012.101

fit <- optTrain(geno, cand = 1:404, n.train = 50, method = "GVaverage",
                 min.iter = 300, console = FALSE, seed = 1)
fit$OPTtrain

##  [1] 403 348 311 136 339 313 379  65  33 185 399  51 329 301 244  69 179 122 391
## [20] 335 350  97 382  18 298 323 216  12  27 296  20  44 312 305  10  40 189  52
## [39] 376  16  67 128 162  77  36 389 347 245  32  82

The search is a random-start exchange (hill-climbing) search; see How the scores are computed. Use min.iter larger than 300 on real data and check fit$converged.

Original work

Chen, S.-P., Sung, W.-H., & Liao, C.-T. (2024). Constructing training sets for genomic selection to identify superior genotypes in candidate populations. Theoretical and Applied Genetics, 137, 270. https://doi.org/10.1007/s00122-024-04766-y

Fernández-González, J., Akdemir, D., & Isidro y Sánchez, J. (2023). A comparison of methods for training population optimization in genomic selection. Theoretical and Applied Genetics, 136, 30. https://doi.org/10.1007/s00122-023-04265-6

Repository or website of the original authors: R package TSODBG of Chen et al. (2024): github.com/spcspin/TSODBG (GPL >= 3).

License review

Formulas and algorithms are ideas and methods, which copyright does not protect. Where an original package is under a GPL license, we read it to check our results and credit it; TSDFGS is GPL-3, which is compatible with GPL-3 and GPL (>= 3) code. This is our reading of the public record, not legal advice; see the license review.

Original software: TSODBG, GPL (>= 3); compared, not copied.
Verdict: included.

Reviewed 2026-11-04. All criteria and the ones left out.