Chickpea MET pooled ANOVA then Eberhart-Russell stability for a release candidate
Ten chickpea genotypes across eight environments. Pooled ANOVA confirms GxE, then the Eberhart-Russell regression reads bi and S squared d to decide if the candidate is widely adapted.
Farhan is finalising a chickpea variety for release. He has ten genotypes (G1 to G10), one of which, G4, is his release candidate. They were grown across eight environments (E1 to E8) that span irrigated, rainfed and late-sown conditions over two years. The release committee wants to know whether G4 is genuinely widely adapted or just lucky in a few sites.
Question
Is the genotype by environment interaction significant, and if so, does G4 have a regression slope close to 1 and a small deviation from regression, the Eberhart-Russell signature of a stable, widely adapted variety?
Data, in StatVeda format
One genotype per line, eight environment means (seed yield kg/ha scaled to per-plot kg for compactness). The pooled ANOVA is run first on the replicated data; the environment means below feed the Eberhart-Russell regression.
G1: 1.82, 2.41, 1.55, 2.98, 2.10, 1.40, 2.75, 2.20 G2: 2.05, 2.62, 1.78, 3.21, 2.34, 1.62, 2.95, 2.41 G3: 1.55, 2.10, 1.32, 2.61, 1.85, 1.20, 2.45, 1.95 G4: 2.31, 2.74, 2.05, 3.18, 2.55, 1.98, 3.02, 2.62 G5: 1.95, 2.50, 1.70, 3.05, 2.22, 1.52, 2.85, 2.30 G6: 1.70, 2.28, 1.45, 2.80, 2.00, 1.32, 2.60, 2.08 G7: 2.18, 2.70, 1.92, 3.30, 2.46, 1.78, 3.05, 2.52 G8: 1.88, 2.45, 1.62, 2.95, 2.15, 1.46, 2.80, 2.25 G9: 2.42, 2.60, 2.30, 2.90, 2.55, 2.28, 2.78, 2.60 G10: 1.60, 2.95, 1.20, 3.55, 2.05, 1.05, 3.20, 2.10
What he does in StatVeda
First, Pooled Analysis to confirm GxE on the replicated data. Then open Plant Breeding, pick Stability Analysis (Eberhart-Russell), paste the environment-mean format above, and run the regression.
Pooled ANOVA: Environments highly significant (the sites really do differ), Genotypes significant, Genotype x Environment significant (p < 0.001). GxE is real, so a single mean ranking is not enough; stability analysis is justified.
Eberhart-Russell partitions GxE into Environment (linear), G x E (linear), the regression slopes, and pooled deviation.
Stability parameters per genotype, mean yield, bi, S squared d:
G4: mean 2.56, bi = 0.98, S squared d = 0.004 (ns)
G7: mean 2.49, bi = 1.07, S squared d = 0.006 (ns)
G9: mean 2.55, bi = 0.41, S squared d = 0.010 (ns)
G10: mean 2.21, bi = 1.84, S squared d = 0.071 (significant)
G3: mean 1.88, bi = 0.95, S squared d = 0.005 (ns)
Grand mean across genotypes 2.29. The regression slope bi is tested against 1; S squared d is tested against zero using pooled error.
What it means
The Eberhart-Russell ideal is a genotype with high mean, bi not different from 1, and S squared d not different from zero. G4 fits almost exactly: the highest mean of the set (2.56), a slope of 0.98 that is statistically indistinguishable from 1, and a tiny, non-significant deviation. It tracks the environment as expected and its performance is predictable. G7 is similar but slightly less stable. G9 has a comparable mean but bi = 0.41, meaning it barely responds to better environments: a below-average responder, useful only for poor sites. G10 is the cautionary case: high deviation and bi = 1.84, a genotype that swings wildly between sites and cannot be recommended broadly despite a respectable looking mean in good years.
Recommend G4 for general release: highest mean yield, bi close to 1, deviation from regression not significant. This is the textbook stable, widely adapted variety.
Position G9 (bi well below 1) only for consistently low-yielding environments, where its flat response is an advantage.
Do not release G10 as a general variety. The significant S squared d means its performance is not predictable from the environment, which is exactly what general release cannot tolerate.
Farhan writes the stability section with the pooled ANOVA, the bi and S squared d table, and the regression plot. The release committee approves G4 because the two stability parameters, not just the mean, support a general recommendation.
Why pooled ANOVA before stability
If the GxE interaction had not been significant, stability analysis would have been unnecessary: one mean ranking would describe every site and the highest-mean genotype would simply win. The pooled ANOVA is the gate. Only because GxE is significant does it make sense to ask how each genotype responds to the environmental gradient, which is precisely the question the Eberhart-Russell regression answers.
What he will not over-claim
Eberhart-Russell uses the environment mean as the index, so a genotype can look stable simply because the environments tested were narrow. Farhan notes in the report that the eight environments span two years and three management systems, which is the evidence that the stability of G4 is meaningful and not an artefact of a narrow test range. If a future year adds a very different environment, the regression will be rerun.