ASI.AMMI computes the AMMI Stability Index (ASI)
(Jambhulkar et al. 2014; Jambhulkar et al. 2015; Jambhulkar et al. 2017)
considering the first two interaction principal components (IPCs) in the AMMI
model. Using ASI, the Simultaneous Selection Index for Yield and Stability
(SSI) is also calculated according to the argument ssi.method.
ASI.AMMI(model, ssi.method = c("farshadfar", "rao"), a = 1)A data frame with the following columns:
The ASI values.
The computed values of simultaneous selection index for yield and stability.
The ranks of ASI values.
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 AMMI Stability Index (\(ASI\)) (Jambhulkar et al. 2014; Jambhulkar et al. 2015; Jambhulkar et al. 2017) is computed as follows:
\[ASI = \sqrt{\left [ PC_{1}^{2} \times \theta_{1}^{2} \right ]+\left [ PC_{2}^{2} \times \theta_{2}^{2} \right ]}\]
Where, \(PC_{1}\) and \(PC_{2}\) are the scores of 1st and 2nd IPCs respectively; and \(\theta_{1}\) and \(\theta_{2}\) are percentage sum of squares explained by the 1st and 2nd principal component interaction effect respectively.
Jambhulkar NN, Bose LK, Pande K, Singh ON (2015).
“Genotype by environment interaction and stability analysis in rice genotypes.”
Ecology, Environment and Conservation, 21(3), 1427--1430.
Jambhulkar NN, Bose LK, Singh ON (2014).
“AMMI stability index for stability analysis.”
In Mohapatra T (ed.), CRRI Newsletter, January-March 2014, volume 35(1), 15.
Central Rice Research Institute, Cuttack, Orissa.
Jambhulkar NN, Rath NC, Bose LK, Subudhi HN, Biswajit M, Lipi D, Meher J (2017).
“Stability analysis for grain yield in rice in demonstrations conducted during rabi season in India.”
Oryza, 54(2), 236--240.
library(agricolae)
data(plrv)
# AMMI model
model <- with(plrv, AMMI(Locality, Genotype, Rep, Yield, console = FALSE))
# ANOVA
model$ANOVA
#> Analysis of Variance Table
#>
#> Response: Y
#> Df Sum Sq Mean Sq F value Pr(>F)
#> ENV 5 122284 24456.9 257.0382 9.08e-12 ***
#> REP(ENV) 12 1142 95.1 2.5694 0.002889 **
#> GEN 27 17533 649.4 17.5359 < 2.2e-16 ***
#> ENV:GEN 135 23762 176.0 4.7531 < 2.2e-16 ***
#> Residuals 324 11998 37.0
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# IPC F test
model$analysis
#> percent acum Df Sum.Sq Mean.Sq F.value Pr.F
#> PC1 56.3 56.3 31 13368.5954 431.24501 11.65 0.0000
#> PC2 27.1 83.3 29 6427.5799 221.64069 5.99 0.0000
#> PC3 9.4 92.7 27 2241.9398 83.03481 2.24 0.0005
#> PC4 4.3 97.1 25 1027.5785 41.10314 1.11 0.3286
#> PC5 2.9 100.0 23 696.1012 30.26527 0.82 0.7059
# Mean yield and IPC scores
model$biplot
#> type Yield PC1 PC2 PC3 PC4
#> 102.18 GEN 26.31947 -1.50828851 1.258765244 -0.19220309 0.48738861
#> 104.22 GEN 31.28887 0.32517729 -1.297024517 -0.63695749 -0.44159957
#> 121.31 GEN 30.10174 0.95604605 1.143461054 -1.28777348 2.22246913
#> 141.28 GEN 39.75624 2.11153737 0.817810467 1.45527701 0.25257620
#> 157.26 GEN 36.95181 1.05139017 2.461179974 -1.97208942 -1.96538800
#> 163.9 GEN 21.41747 -2.12407441 -0.284381234 -0.21791137 -0.50743629
#> 221.19 GEN 22.98480 -0.84981828 0.347983673 -0.82400783 -0.11451944
#> 233.11 GEN 28.66655 0.07554203 -1.046497338 1.04040485 0.22868362
#> 235.6 GEN 38.63477 1.20102029 -2.816581184 0.80975361 1.02013062
#> 241.2 GEN 26.34039 -0.79948495 0.220768053 -0.98538801 0.30004421
#> 255.7 GEN 30.58975 -1.49543817 -1.186549449 0.92552519 -0.32009239
#> 314.12 GEN 28.17335 1.39335380 -0.332786322 -0.73226877 0.05987348
#> 317.6 GEN 35.32583 1.05170769 0.002555823 -0.81561907 0.58180433
#> 319.20 GEN 38.75767 3.08338144 1.995946966 0.87971668 -1.11908943
#> 320.16 GEN 26.34808 -1.55737097 0.732314249 -0.41432567 1.32097009
#> 342.15 GEN 26.01336 -1.35880873 -0.741980068 0.87480105 -1.12013125
#> 346.2 GEN 23.84175 -2.48453928 -0.397045286 1.07091711 -0.90974484
#> 351.26 GEN 36.11581 1.22670345 1.537183139 1.79835728 -0.03516368
#> 364.21 GEN 34.05974 0.27328985 -0.447941156 0.03139543 0.77920500
#> 402.7 GEN 27.47748 -0.12907269 -0.080086669 0.01934016 -0.36085862
#> 405.2 GEN 28.98663 -1.90936369 0.309047963 0.57682642 0.51163370
#> 406.12 GEN 32.68323 0.90781100 -1.733433781 -0.24223050 -0.38596144
#> 427.7 GEN 36.19020 0.42791957 -0.723190970 -0.85381724 -0.53089914
#> 450.3 GEN 36.19602 1.38026196 1.279525147 0.16025163 0.61270137
#> 506.2 GEN 33.26623 -0.33054261 -0.302588536 -1.58471588 -0.04659416
#> Canchan GEN 27.00126 1.47802905 0.380553178 1.67423900 0.07718375
#> Desiree GEN 16.15569 -3.64968796 1.720025405 0.43761089 0.04648011
#> Unica GEN 39.10400 1.25331924 -2.817033826 -0.99510845 -0.64366599
#> Ayac ENV 23.70254 -2.29611851 0.966037760 1.95959116 2.75548057
#> Hyo-02 ENV 45.73082 3.85283195 -5.093371615 1.16967118 -0.08985538
#> LM-02 ENV 34.64462 -1.14575146 -0.881093222 -4.56547274 0.55159099
#> LM-03 ENV 53.83493 5.34625518 4.265275487 -0.14143931 -0.11714533
#> SR-02 ENV 14.95128 -2.58678337 0.660309540 0.89096920 -3.25055305
#> SR-03 ENV 11.15328 -3.17043379 0.082842050 0.68668051 0.15048221
#> PC5
#> 102.18 -0.04364115
#> 104.22 0.95312506
#> 121.31 -1.30661916
#> 141.28 -0.25996142
#> 157.26 -0.59719268
#> 163.9 0.18563390
#> 221.19 -0.57504816
#> 233.11 0.65754266
#> 235.6 -0.40273415
#> 241.2 0.07555258
#> 255.7 -0.46344763
#> 314.12 0.54406154
#> 317.6 0.39627052
#> 319.20 0.29657050
#> 320.16 2.29506737
#> 342.15 -0.10776433
#> 346.2 -0.12738693
#> 351.26 0.30191335
#> 364.21 -0.95811256
#> 402.7 -0.28473777
#> 405.2 -0.34397623
#> 406.12 -0.49796296
#> 427.7 1.00677993
#> 450.3 -0.34325251
#> 506.2 0.87807441
#> Canchan 0.49381313
#> Desiree -0.86767477
#> Unica -0.90489253
#> Ayac 1.67177210
#> Hyo-02 0.01540152
#> LM-02 0.52350416
#> LM-03 -0.40285728
#> SR-02 1.37283488
#> SR-03 -3.18065538
# G*E matrix (deviations from mean)
array(model$genXenv, dim(model$genXenv), dimnames(model$genXenv))
#> ENV
#> GEN Ayac Hyo-02 LM-02 LM-03 SR-02
#> 102.18 5.5726162 -12.4918224 1.7425251 -2.7070438 2.91734869
#> 104.22 -2.8712076 7.1684102 3.9336218 -4.0358373 0.47881580
#> 121.31 0.3255230 -3.8666836 4.3182811 10.4366135 -11.88343843
#> 141.28 -0.9451837 5.6454825 -9.7806639 14.6463104 -4.80337115
#> 157.26 -10.3149711 -10.6241677 4.2336365 16.8683612 2.71710210
#> 163.9 3.0874931 -6.9416721 3.4963790 -12.5533271 7.01688164
#> 221.19 -0.6041752 -6.0090018 4.0648518 -2.6974743 1.27671246
#> 233.11 2.5837535 6.8277609 -3.4440645 -4.4985717 0.19989490
#> 235.6 -1.7541523 19.8225025 -2.2394463 -5.6643239 -8.11400542
#> 241.2 1.0710975 -5.3831118 5.4253097 -3.2588271 0.46433086
#> 255.7 2.4443155 1.3860497 -1.8857757 -12.9626594 4.31373929
#> 314.12 -3.8812099 6.2098482 2.3577759 5.9071782 -3.92419060
#> 317.6 -1.7450319 3.0388540 3.0448064 5.5211634 -4.79271565
#> 319.20 -6.0155949 2.8477540 -9.7697504 24.8850017 -1.82949467
#> 320.16 10.9481796 -10.2982108 4.9608280 -6.2233088 2.99984918
#> 342.15 0.8508002 -0.3338618 -2.4575390 -10.3783871 7.29753151
#> 346.2 4.7000495 -6.2178087 -2.2612391 -14.9700672 9.90123888
#> 351.26 2.6002030 -0.9918665 -10.8315931 12.7429121 -0.02713985
#> 364.21 -0.4533734 3.2864208 -0.1335527 -0.1592533 -4.82292664
#> 402.7 -1.2134573 -0.0387229 -0.2179557 -0.8774011 1.08032472
#> 405.2 6.6477681 -8.3071271 -0.6159895 -8.8927189 3.52179705
#> 406.12 -6.1296667 12.0703469 1.1195092 -2.2601009 -3.13776595
#> 427.7 -3.1340922 4.3967072 4.2792028 -1.0194744 0.76266844
#> 450.3 -0.5047010 -1.0720791 -3.2821761 12.8806007 -5.04562407
#> 506.2 -1.2991912 -1.5682154 8.3142802 -3.1819279 0.60021498
#> Canchan 1.2929442 5.7152780 -9.3713622 9.0803035 -1.65332869
#> Desiree 9.5767845 -22.3280421 0.2396387 -11.8935722 9.62433886
#> Unica -10.8355195 18.0569790 4.7604622 -4.7341684 -5.13878822
#> ENV
#> GEN SR-03
#> 102.18 4.9663762
#> 104.22 -4.6738028
#> 121.31 0.6697043
#> 141.28 -4.7625741
#> 157.26 -2.8799609
#> 163.9 5.8942454
#> 221.19 3.9690870
#> 233.11 -1.6687730
#> 235.6 -2.0505746
#> 241.2 1.6812008
#> 255.7 6.7043306
#> 314.12 -6.6694018
#> 317.6 -5.0670763
#> 319.20 -10.1179157
#> 320.16 -2.3873373
#> 342.15 5.0214562
#> 346.2 8.8478267
#> 351.26 -3.4925156
#> 364.21 2.2826853
#> 402.7 1.2672123
#> 405.2 7.6462704
#> 406.12 -1.6623226
#> 427.7 -5.2850119
#> 450.3 -2.9760204
#> 506.2 -2.8651608
#> Canchan -5.0638348
#> Desiree 14.7808522
#> Unica -2.1089651
# With default ssi.method (farshadfar)
ASI.AMMI(model)
#> ASI SSI rASI rY means
#> 102.18 0.91512303 43 20 23 26.31947
#> 104.22 0.39631322 19 6 13 31.28887
#> 121.31 0.62108102 25 10 15 30.10174
#> 141.28 1.20927797 26 25 1 39.75624
#> 157.26 0.89176583 22 17 5 36.95181
#> 163.9 1.19833464 51 24 27 21.41747
#> 221.19 0.48765291 34 8 26 22.98480
#> 233.11 0.28677206 21 4 17 28.66655
#> 235.6 1.01971997 25 21 4 38.63477
#> 241.2 0.45406877 29 7 22 26.34039
#> 255.7 0.90124720 33 19 14 30.58975
#> 314.12 0.78962523 30 12 18 28.17335
#> 317.6 0.59211183 18 9 9 35.32583
#> 319.20 1.81826161 30 27 3 38.75767
#> 320.16 0.89897900 39 18 21 26.34808
#> 342.15 0.79099371 37 13 24 26.01336
#> 346.2 1.40292793 51 26 25 23.84175
#> 351.26 0.80654291 22 14 8 36.11581
#> 364.21 0.19598368 12 2 10 34.05974
#> 402.7 0.07583976 20 1 19 27.47748
#> 405.2 1.07822942 39 23 16 28.98663
#> 406.12 0.69418710 23 11 12 32.68323
#> 427.7 0.31056699 12 5 7 36.19020
#> 450.3 0.85094150 22 16 6 36.19602
#> 506.2 0.20336120 14 3 11 33.26623
#> Canchan 0.83849670 35 15 20 27.00126
#> Desiree 2.10698168 56 28 28 16.15569
#> Unica 1.03956820 24 22 2 39.10400
# With ssi.method = "rao"
ASI.AMMI(model, ssi.method = "rao")
#> ASI SSI rASI rY means
#> 102.18 0.91512303 1.3832387 20 23 26.31947
#> 104.22 0.39631322 2.2326416 6 13 31.28887
#> 121.31 0.62108102 1.7551519 10 15 30.10174
#> 141.28 1.20927797 1.6936286 25 1 39.75624
#> 157.26 0.89176583 1.7436656 17 5 36.95181
#> 163.9 1.19833464 1.0993106 24 27 21.41747
#> 221.19 0.48765291 1.7347850 8 26 22.98480
#> 233.11 0.28677206 2.6102708 4 17 28.66655
#> 235.6 1.01971997 1.7309273 21 4 38.63477
#> 241.2 0.45406877 1.9170753 7 22 26.34039
#> 255.7 0.90124720 1.5305578 19 14 30.58975
#> 314.12 0.78962523 1.5271379 12 18 28.17335
#> 317.6 0.59211183 1.9633384 9 9 35.32583
#> 319.20 1.81826161 1.5279859 27 3 38.75767
#> 320.16 0.89897900 1.3936010 18 21 26.34808
#> 342.15 0.79099371 1.4556573 13 24 26.01336
#> 346.2 1.40292793 1.1198795 26 25 23.84175
#> 351.26 0.80654291 1.7733422 14 8 36.11581
#> 364.21 0.19598368 3.5623227 2 10 34.05974
#> 402.7 0.07583976 7.2317748 1 19 27.47748
#> 405.2 1.07822942 1.3907733 23 16 28.98663
#> 406.12 0.69418710 1.7578467 11 12 32.68323
#> 427.7 0.31056699 2.7272047 5 7 36.19020
#> 450.3 0.85094150 1.7448731 16 6 36.19602
#> 506.2 0.20336120 3.4475042 3 11 33.26623
#> Canchan 0.83849670 1.4534532 15 20 27.00126
#> Desiree 2.10698168 0.7548219 28 28 16.15569
#> Unica 1.03956820 1.7372299 22 2 39.10400
# Changing the ratio of weights for Rao's SSI
ASI.AMMI(model, ssi.method = "rao", a = 0.43)
#> ASI SSI rASI rY means
#> 102.18 0.91512303 1.0839450 20 23 26.31947
#> 104.22 0.39631322 1.5415455 6 13 31.28887
#> 121.31 0.62108102 1.3141619 10 15 30.10174
#> 141.28 1.20927797 1.4671376 25 1 39.75624
#> 157.26 0.89176583 1.4365328 17 5 36.95181
#> 163.9 1.19833464 0.8707513 24 27 21.41747
#> 221.19 0.48765291 1.1731344 8 26 22.98480
#> 233.11 0.28677206 1.6551898 4 17 28.66655
#> 235.6 1.01971997 1.4623334 21 4 38.63477
#> 241.2 0.45406877 1.3138836 7 22 26.34039
#> 255.7 0.90124720 1.2266562 19 14 30.58975
#> 314.12 0.78962523 1.1802765 12 18 28.17335
#> 317.6 0.59211183 1.5007728 9 9 35.32583
#> 319.20 1.81826161 1.3773527 27 3 38.75767
#> 320.16 0.89897900 1.0889326 18 21 26.34808
#> 342.15 0.79099371 1.1093959 13 24 26.01336
#> 346.2 1.40292793 0.9246517 26 25 23.84175
#> 351.26 0.80654291 1.4337564 14 8 36.11581
#> 364.21 0.19598368 2.1648057 2 10 34.05974
#> 402.7 0.07583976 3.6203374 1 19 27.47748
#> 405.2 1.07822942 1.1367545 23 16 28.98663
#> 406.12 0.69418710 1.3632981 11 12 32.68323
#> 427.7 0.31056699 1.8452998 5 7 36.19020
#> 450.3 0.85094150 1.4230055 16 6 36.19602
#> 506.2 0.20336120 2.1006861 3 11 33.26623
#> Canchan 0.83849670 1.1268084 15 20 27.00126
#> Desiree 2.10698168 0.6248300 28 28 16.15569
#> Unica 1.03956820 1.4737642 22 2 39.10400