stab_interpret(x = am , higher_better =TRUE , top =5 )
AMMI analysis
AMMI8: 8 interaction axes are significant; the first two axes explain 20.1%
and 17.3% of the interaction.
Findings:
- The interaction is significant (p < 0.001).
- Genotypes with a mean above average and the smallest first-axis scores
(stable): NIBGE GANDUM3, PR119, V14154, V14170 and TWS12464.
- Environments with the strongest interaction (largest first-axis scores):
Gujranwala, FSD and KSK; the weakest: FSDR, Sahiwal and Khanewal.
- Genotypes and environments with first-axis scores of the same sign interact
positively (the genotype does better there than its mean predicts).
Recommendations:
- Use AMMI8 for predictions and the stability indices (stab_asv(),
stab_masv() with .m = 8).
- Look at the AMMI1 biplot (plot(x, which = "ammi1")) to see mean and
interaction together.
Cautions:
- The first two axes explain less than half of the interaction; biplots show
it only partly.
3 Biplots
ab <-ammi_biplot(.data = ge_data , .y = Yield , .rep = Rep , .gen = Gen , .env = Env )plot(x = ab, which ="ammi1")
plot(x = ab, which ="ammi2")
4 Stability values
asv <-stab_asv(.data = ge_data , .y = Yield , .rep = Rep , .gen = Gen , .env = Env )head(x = asv$ASD, n =6)
stab_masv() is the MASV of Zali et al. (2012). The earlier versions computed it on two axes; the function now takes any number of axes .m, from 2 to the number of non-zero interaction axes. The ratio of the sums of squares of each axis to the next weighs the first axes heavily. stab_dist() is the AMMI stability distance developed by the package author: the Euclidean distance from the origin over the first .m axes of the AMMI scores, in which every axis enters only through its scores. Use for .m the number of significant axes found by ammi().
stab_interpret(x = masv , higher_better =TRUE , top =5 )
Modified AMMI stability value
Best on the yield stability index (yield and stability ranks together):
V14154, PR115, 013BT034, LOCAL CHECK and UOS1.
Findings:
- Smallest modified AMMI stability value (most stable in the AMMI sense):
V14154, NIBGE GANDUM4, 013BT034, PR119 and V14225.
- 17 genotype(s) combine a mean above average with a modified AMMI stability
value below the median.
- The rank correlation between mean and modified AMMI stability value is
0.03.
Recommendations:
- Consider V14154, PR115 and 013BT034; check their adaptation in the AMMI or
GGE biplot.
Cautions:
- The index rests on the AMMI axes it uses; when more axes are significant
(see ammi()), stab_masv() with more axes is more complete.
5 Summary
Many significant axes mean the interaction has several independent patterns; the first two show only part of it, and indices over more axes (stab_masv()) describe the stability more fully.
6 References
Gauch, H. G. (1992). Statistical Analysis of Regional Yield Trials: AMMI Analysis of Factorial Designs. Elsevier, Amsterdam.
Gollob, H. F. (1968). A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika, 33(1), 73–115.
Purchase, J. L., Hatting, H. and van Deventer, C. S. (2000). Genotype x environment interaction of winter wheat in South Africa: II. Stability analysis of yield performance. South African Journal of Plant and Soil, 17(3), 101–107.
Zali, H., Farshadfar, E., Sabaghpour, S. H. and Karimizadeh, R. (2012). Evaluation of genotype x environment interaction in chickpea using measures of stability from AMMI model. Annals of Biological Research, 3(7), 3126–3136.
