Avg_GRM • TSDFGS

The mean genomic relationship between the training set and the target.

Type	Relationship
Direction	Larger is better
Uses a test set	yes; without a test set, all candidates
Score a given set	`avg_grm_score()`
Search with it	`optTrain(method = "AvgGRM")`

Definition

$\mathrm{Avg\_GRM} = \mathbf{1}_n' G_{TP} \mathbf{1}_{n_P}/(n\,n_P)$ with $G = XX'/p$ . Without a test set, the target is the whole candidate set.

Use in TSDFGS

library(TSDFGS)
data(geno)
avg_grm_score(geno[1:50, ], geno[51:100, ])

## [1] -0.158039

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

##  [1] 403 303  74 339 142  71 307  85 277 304 330  51  12 244 321  60 117 240 392
## [20] 306 302 168 216 325 300  96 154  43  65 301  20  44 320 305 121 335 260 388
## [39]  82   3 152 298  16  77  36  17 349 246 348  97

# targeted: the test set is known
fit2 <- optTrain(geno, cand = 1:300, n.train = 50, test = 301:404,
                  method = "AvgGRM", min.iter = 300, console = FALSE, seed = 1)
fit2$OPTtrain

##  [1]  77 245 143  43 215  31  88 149 116 297 185 268  52 161  27  65 283  44 168
## [20] 121  40 244  10 282 296  39 162  20  12 246 142 195  71  18  74 256 216 299
## [39]  67  17  96 189 117 126 248 277   5 221 156 101

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

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: Code of Fernández-González et al. (2023): github.com/TheRocinante-lab/Publications. Package TrainSel: github.com/TheRocinante-lab/TrainSel.

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: the repository of Fernández-González et al. (2023) has no LICENSE file, and TrainSel carries an all-rights-reserved license with a patent notice. We did not read or copy either; the definition comes from the open-access article.
Article license: CC BY 4.0.
Verdict: included, written from the article.

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