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MET

Multi-Environment Trials (GxE, AMMI, Finlay–Wilkinson)

Decompose genotype-by-environment interaction so you can ship cultivars that hold up across locations.

How it works

Our MET module ingests phenotype data measured across multiple environments and decomposes the variance into main effects and GxE interaction. AMMI (Additive Main effects and Multiplicative Interaction) extracts the dominant interaction patterns. Finlay–Wilkinson regression characterizes stability: a slope near 1 means a genotype adapts proportionally to environment quality, while flatter slopes identify broadly stable winners. We also report Wricke's ecovalence and Shukla's stability variance.

Formula

AMMI: y_ij = μ + g_i + e_j + Σ_k λ_k γ_ik δ_jk + ε_ij. Finlay–Wilkinson: y_ij = a_i + b_i·μ_j + ε_ij.

What you get

  • ▸GxE heatmap of genotype × environment yields
  • ▸AMMI biplot (PC1 vs PC2 of the interaction matrix)
  • ▸Finlay–Wilkinson slopes and intercepts per genotype
  • ▸Wricke ecovalence and Shukla stability variance rankings

When to use it

  • ▸You have multi-location or multi-year trial data
  • ▸You want to release cultivars with predictable performance
  • ▸You're zoning your variety portfolio by mega-environment

Inputs

Long-format trial data
CSV with columns: genotype, environment, replicate, trait
Environment metadata (optional)
CSV keyed by environment (location, year, rainfall zone)

Parameters

NameDefaultDescription
AMMI PCs2Number of interaction PCs to retain; captures the dominant GxE patterns.
Stability metricWricke + ShuklaAny combination of Wricke ecovalence, Shukla variance, and FW slope.
Spatial adjustmenton2D smoother over plot coordinates before BLUPs.

Workflow

  1. 1. Per-environment BLUPs
    Mixed model per site with spatial adjustment; row and column effects removed.
  2. 2. Cross-site alignment
    Common check panel aligns BLUPs across environments.
  3. 3. AMMI decomposition
    SVD of the residual GxE matrix returns interaction PCs.
  4. 4. FW regression
    Per-genotype slope against the site mean; slope, intercept, R² reported.
  5. 5. Stability rankings
    Wricke ecovalence and Shukla variance surfaced as final ranking table.

Interpreting results

  • ▸AMMI biplot near-origin = broadly adapted; extreme along a PC = specialist for that pattern.
  • ▸FW slope ≈ 1: proportional response. Slope < 1: stable across environments. Slope > 1: exploits good years.
  • ▸Wricke and Shukla agree in most cases; disagreement flags outlier environments worth inspecting.

Common pitfalls

  • ✕Missing check varieties makes cross-site BLUPs incomparable and biases the AMMI biplot.
  • ✕Treating years as environments hides year-specific weather signal — model them separately when possible.
  • ✕Ranking on main effect alone ignores stability and picks specialists that fail elsewhere.

Worked example

12-site maize network
12 sites × 3 years × 84 hybrids. AMMI PC1 captures 42% of GxE variance; a hybrid with FW slope 0.9 and low Shukla emerges as the best stable performer for the dry zone.

Try it — interactive example

Compute broad-sense heritability on an entry-mean basis for a multi-environment trial: H² = σ²g / (σ²g + σ²ge/e + σ²e/(r·e)).

Expected outputs
Entry-mean H²
0.816
Approx. selection accuracy (√H²)
0.904
Total phenotypic variance
2.7
σ²g + σ²ge + σ²e on a plot basis.

Numbers are quick analytical estimates for planning — actual runs incorporate the full data, covariates, and QC pipeline.

References

Run MET on your data

Open the module and upload a CSV.

Open module