AMMI vs GGE biplot: which one and why

Both biplots are graphs of the same SVD-style decomposition of a genotype by environment matrix. They look superficially identical: a cloud of genotype points, a cloud of environment vectors, two principal axes. But they answer different questions. Pick the wrong one and the visual story misleads.

What gets decomposed

AMMI takes the residual after removing genotype main effect and environment main effect, and decomposes only the GxE interaction. So AMMI shows the structure of the interaction.

GGE (Yan and Hunt, 2000) takes the environment-centred matrix and decomposes G plus GxE together. So GGE shows which genotype wins where, with environment differences already absorbed.

Worked example: 8 genotypes, 4 environments

Mean grain yield (t/ha) for 8 wheat lines tested in 4 sites:

genotype,E1,E2,E3,E4
G1,4.21,3.88,5.62,4.05
G2,4.55,4.12,5.31,4.62
G3,3.95,3.71,5.84,3.88
G4,5.12,4.66,5.05,5.21
G5,4.78,4.34,5.42,4.71
G6,5.31,4.88,4.92,5.45
G7,4.02,3.65,5.71,3.92
G8,4.62,4.21,5.18,4.55

What AMMI surfaces

IPCA1 vs IPCA2 of the GxE residuals. Genotypes near the origin are stable across environments. Environments far from the origin have strong differential effects on genotypes. G3 and G7 sit far from the origin and far from G4 and G6: the AMMI biplot says these groups react differently to E1 and E3.

What GGE surfaces

PC1 vs PC2 of the environment-centred matrix. PC1 mostly captures genotype mean performance, PC2 captures crossover. The which-won-where polygon connects the genotypes farthest from the origin and partitions environments into mega-environment sectors. G6 wins the sector covering E1, E2, E4. G3 wins the sector covering E3.

Pick AMMI when

You want a clean ANOVA-style decomposition of the GxE term, you want an AMMI stability value (ASV) or similar single-number stability metric, or you are writing the results section of a paper that already reports G and E main effects in the ANOVA table.

Pick GGE when

You want to identify mega-environments, decide which variety to recommend in each cluster of locations, or have one chart that tells the breeding team which line to advance for which target zone.

Both can be right

Many MET papers report both. AMMI for the partitioning and stability metrics, GGE for the which-won-where polygon. They are complementary, not competitive. The mistake is treating them as interchangeable visualisations of the same thing.

What partitioning to expect

In a typical MET, AMMI splits the total SS as roughly G = 25 to 50 percent, E = 30 to 60 percent, GxE = 10 to 25 percent. The GxE share is then further split across IPCA1, IPCA2 and onwards. The first two IPCAs together usually capture 70 to 90 percent of the GxE structure in a real trial. If they capture less than 50 percent, the GxE is diffuse and biplot interpretation gets fragile.

GGE rolls G plus GxE into one matrix. PC1 typically captures 50 to 80 percent and is dominated by the genotype mean signal. PC2 captures 10 to 25 percent and carries the crossover information. That is why GGE looks cleaner than AMMI on the same data: the strong G axis hides the noisier residuals.

Reading the polygon

On a GGE biplot, draw a polygon around the genotypes farthest from the origin. From the origin, draw perpendicular lines to each side of the polygon. These lines partition the biplot into sectors. Each sector belongs to the genotype at its vertex. Environments falling in a sector are the ones for which that genotype performed best. That single visual answers the breeder's actual question: which line wins where.

Common mistakes

Reporting an AMMI biplot but interpreting it as if it were GGE (saying genotype G has the highest mean because it sits far on IPCA1, when AMMI does not encode mean at all). Cropping the biplot before plotting all genotypes (the polygon vertices then mislead). Reading axes as if they had units (they are scaled scores, not yields).