SSI computes the Simultaneous Selection Index for Yield and Stability
(SSI) according to the methods specified in the argument method.
SSI(y, sp, gen, method = c("farshadfar", "rao"), a = 1)A numeric vector of the mean yield/performance of genotypes.
A numeric vector of the stability parameter/index of the genotypes.
A character vector of the names of the genotypes.
The method for the computation of simultaneous selection index.
Either "farshadfar" or "rao" (See Details).
The ratio of the weights given to the stability components for
computation of SSI when method = "rao" (See Details).
A data frame with the following columns:
The stability parameter values.
The computed values of simultaneous selection index for yield and stability.
The ranks of the stability parameter.
The ranks of the mean yield of genotypes.
The mean yield of the genotypes.
The names of the genotypes are indicated as the row names of the data frame.
The SSI according to Rao and Prabhakaran (2005) (\(I_{i}\)) is computed as follows:
\[I_{i} = \frac{\overline{Y}_{i}}{\overline{Y}_{..}} + \alpha \frac{\frac{1}{SP_{i}}}{\frac{1}{T}\sum_{i=1}^{T}\frac{1}{SP_{i}}}\]
Where \(SP_{i}\) is the stability measure of the \(i\)th genotype under AMMI procedure; \(\overline{Y}_{i}\) is mean performance of \(i\)th genotype; \(\overline{Y}_{..}\) is the overall mean; \(T\) is the number of genotypes under test and \(\alpha\) is the ratio of the weights given to the stability components (\(w_{2}\)) and yield (\(w_{1}\)) with a restriction that \(w_{1} + w_{2} = 1\). The weights can be specified as required.
| \(\alpha\) | \(w_{1}\) | \(w_{2}\) |
| 1.00 | 0.5 | 0.5 |
| 0.67 | 0.6 | 0.4 |
| 0.43 | 0.7 | 0.3 |
| 0.25 | 0.8 | 0.2 |
The SSI proposed by Farshadfar (2008) is called the Genotype stability index (\(GSI\)) or Yield stability index (\(YSI\)) (Farshadfar et al. 2011) and is computed by summation of the ranks of the stability index/parameter and the ranks of the mean yields.
\[GSI = YSI = R_{SP} + R_{Y}\]
Where, \(R_{SP}\) is the stability parameter/index rank of the genotype and \(R_{Y}\) is the mean yield rank of the genotype.
Farshadfar E (2008).
“Incorporation of AMMI stability value and grain yield in a single non-parametric index (GSI) in bread wheat.”
Pakistan Journal of biological sciences, 11(14), 1791.
Farshadfar E, Mahmodi N, Yaghotipoor A (2011).
“AMMI stability value and simultaneous estimation of yield and yield stability in bread wheat (Triticum aestivum L.).”
Australian Journal of Crop Science, 5(13), 1837--1844.
Rao AR, Prabhakaran VT (2005).
“Use of AMMI in simultaneous selection of genotypes for yield and stability.”
Journal of the Indian Society of Agricultural Statistics, 59, 76--82.
library(agricolae)
data(plrv)
model <- with(plrv, AMMI(Locality, Genotype, Rep, Yield, console=FALSE))
yield <- aggregate(model$means$Yield, by= list(model$means$GEN),
FUN=mean, na.rm=TRUE)[,2]
stab <- DZ.AMMI(model)$DZ
genotypes <- rownames(DZ.AMMI(model))
# With default ssi.method (farshadfar)
SSI(y = yield, sp = stab, gen = genotypes)
#> SP SSI rSP rY means
#> 102.18 0.26393535 37 14 23 26.31947
#> 104.22 0.22971564 21 8 13 31.28887
#> 121.31 0.32031744 34 19 15 30.10174
#> 141.28 0.39838535 23 22 1 39.75624
#> 157.26 0.53822924 33 28 5 36.95181
#> 163.9 0.26659011 42 15 27 21.41747
#> 221.19 0.19563325 29 3 26 22.98480
#> 233.11 0.25167755 27 10 17 28.66655
#> 235.6 0.46581370 28 24 4 38.63477
#> 241.2 0.21481887 28 6 22 26.34039
#> 255.7 0.30862904 31 17 14 30.58975
#> 314.12 0.22603261 25 7 18 28.17335
#> 317.6 0.20224771 14 5 9 35.32583
#> 319.20 0.50675112 29 26 3 38.75767
#> 320.16 0.23280596 30 9 21 26.34808
#> 342.15 0.25989774 36 12 24 26.01336
#> 346.2 0.37125512 45 20 25 23.84175
#> 351.26 0.43805896 31 23 8 36.11581
#> 364.21 0.07409309 12 2 10 34.05974
#> 402.7 0.02004533 20 1 19 27.47748
#> 405.2 0.26238837 29 13 16 28.98663
#> 406.12 0.28179394 28 16 12 32.68323
#> 427.7 0.20176581 11 4 7 36.19020
#> 450.3 0.25465368 17 11 6 36.19602
#> 506.2 0.30899851 29 18 11 33.26623
#> Canchan 0.37201039 41 21 20 27.00126
#> Desiree 0.52005815 55 27 28 16.15569
#> Unica 0.48083049 27 25 2 39.10400
# With ssi.method = "rao"
SSI(y = yield, sp = stab, gen = genotypes, method = "rao")
#> SP SSI rSP rY means
#> 102.18 0.26393535 1.5536988 14 23 26.31947
#> 104.22 0.22971564 1.8193399 8 13 31.28887
#> 121.31 0.32031744 1.5545939 19 15 30.10174
#> 141.28 0.39838535 1.7570779 22 1 39.75624
#> 157.26 0.53822924 1.5459114 28 5 36.95181
#> 163.9 0.26659011 1.3869397 15 27 21.41747
#> 221.19 0.19563325 1.6878048 3 26 22.98480
#> 233.11 0.25167755 1.6641025 10 17 28.66655
#> 235.6 0.46581370 1.6538090 24 4 38.63477
#> 241.2 0.21481887 1.7134093 6 22 26.34039
#> 255.7 0.30862904 1.5922105 17 14 30.58975
#> 314.12 0.22603261 1.7307783 7 18 28.17335
#> 317.6 0.20224771 2.0595024 5 9 35.32583
#> 319.20 0.50675112 1.6259792 26 3 38.75767
#> 320.16 0.23280596 1.6476346 9 21 26.34808
#> 342.15 0.25989774 1.5545233 12 24 26.01336
#> 346.2 0.37125512 1.2718506 20 25 23.84175
#> 351.26 0.43805896 1.5966462 23 8 36.11581
#> 364.21 0.07409309 3.5881882 2 10 34.05974
#> 402.7 0.02004533 10.0539968 1 19 27.47748
#> 405.2 0.26238837 1.6447637 13 16 28.98663
#> 406.12 0.28179394 1.7171135 16 12 32.68323
#> 427.7 0.20176581 2.0898536 4 7 36.19020
#> 450.3 0.25465368 1.9010808 11 6 36.19602
#> 506.2 0.30899851 1.6787677 18 11 33.26623
#> Canchan 0.37201039 1.3738642 21 20 27.00126
#> Desiree 0.52005815 0.8797586 27 28 16.15569
#> Unica 0.48083049 1.6568004 25 2 39.10400
# Changing the ratio of weights for Rao's SSI
SSI(y = yield, sp = stab, gen = genotypes, method = "rao", a = 0.43)
#> SP SSI rSP rY means
#> 102.18 0.26393535 1.1572429 14 23 26.31947
#> 104.22 0.22971564 1.3638258 8 13 31.28887
#> 121.31 0.32031744 1.2279220 19 15 30.10174
#> 141.28 0.39838535 1.4944208 22 1 39.75624
#> 157.26 0.53822924 1.3514985 28 5 36.95181
#> 163.9 0.26659011 0.9944318 15 27 21.41747
#> 221.19 0.19563325 1.1529329 3 26 22.98480
#> 233.11 0.25167755 1.2483375 10 17 28.66655
#> 235.6 0.46581370 1.4291726 24 4 38.63477
#> 241.2 0.21481887 1.2263072 6 22 26.34039
#> 255.7 0.30862904 1.2531668 17 14 30.58975
#> 314.12 0.22603261 1.2678419 7 18 28.17335
#> 317.6 0.20224771 1.5421234 5 9 35.32583
#> 319.20 0.50675112 1.4194898 26 3 38.75767
#> 320.16 0.23280596 1.1981670 9 21 26.34808
#> 342.15 0.25989774 1.1519083 12 24 26.01336
#> 346.2 0.37125512 0.9899993 20 25 23.84175
#> 351.26 0.43805896 1.3577771 23 8 36.11581
#> 364.21 0.07409309 2.1759278 2 10 34.05974
#> 402.7 0.02004533 4.8338929 1 19 27.47748
#> 405.2 0.26238837 1.2459704 13 16 28.98663
#> 406.12 0.28179394 1.3457828 16 12 32.68323
#> 427.7 0.20176581 1.5712389 4 7 36.19020
#> 450.3 0.25465368 1.4901748 11 6 36.19602
#> 506.2 0.30899851 1.3401295 18 11 33.26623
#> Canchan 0.37201039 1.0925852 21 20 27.00126
#> Desiree 0.52005815 0.6785528 27 28 16.15569
#> Unica 0.48083049 1.4391795 25 2 39.10400