AMMI Multi-Environment Analysis User Guide

1. INTRODUCTION

The AMMI Multi-Environment Analysis Module combines standard Analysis of Variance (ANOVA) for main factor effects with Principal Component Analysis (PCA via Singular Value Decomposition) for factor-by-environment interaction effects. In multi-location field trials, multi-batch industrial testing, clinical multi-center studies, and environmental monitoring, treatment factors often exhibit differential performance across test locations (Factor x Environment Interaction).

AMMI isolates main treatment effects and main environment effects in the ANOVA phase, then decomposes remaining interaction variation into orthogonal Interaction Principal Component Axes (IPCA 1, IPCA 2, etc.) to diagnose specific adaptation patterns.

Primary Analytical Capabilities:

Partitioned AMMI ANOVA: Separates total observed variation into Main Treatment Effect, Main Environment Effect, and Interaction (GEI).
IPCA Decomposition & Significance: Extracts orthogonal Interaction Principal Components (IPCA 1, IPCA 2, etc.) and tests significance using Gollob F-tests.
AMMI1 Biplot (Mean vs IPCA 1): Plots overall mean trait performance against IPCA 1 interaction scores to evaluate general performance alongside interaction magnitude.
AMMI2 Biplot (IPCA 1 vs IPCA 2): Plots IPCA 1 scores against IPCA 2 scores to diagnose specific environmental adaptation vectors and location groupings.
AMMI Stability Value (ASV) & Indices: Computes the AMMI Stability Value (ASV) and Yield/Performance Stability Index (YSI / PSI) to rank entries by combined high performance and stability.

2. AVAILABLE OPTIONS & SETTINGS

The control panel and top header controls provide full options for mapping factors, selecting IPCA axes, alpha limits, and precision:

Control / Parameter	Description	Statistical Purpose	When to Select / Set
Primary Factor Column (Treatment)	Categorical column identifying primary treatment entries or sample entities.	Defines primary treatment groups evaluated across environments.	Required. Map to your treatment factor column.
Environment Column (Location / Site)	Categorical column identifying trial locations, testing sites, or environmental conditions.	Defines environmental testing locations for interaction modeling.	Required. Map to your environment/site column.
Replication Column	Categorical column identifying trial replication blocks (e.g., Rep_1, Rep_2).	Isolates environmental block error variance within each testing site.	Map column containing replicate/block tags if available.
Target Quantitative Traits	Selects continuous numeric response measurement columns.	Computes AMMI ANOVA, IPCA scores, biplots, and stability tables for selected traits.	Select one or multiple quantitative outcome columns.
Number of IPCA Axes	Selects how many interaction axes (e.g., 2, 3, or Auto) to extract in the biplot.	Determines the cumulative interaction percentage explained by the biplot model.	Set to 2 axes for standard 2D biplots.
Alpha Level	Significance error threshold (`5% / 0.05` or `1% / 0.01`).	Establishes critical threshold for Gollob F-tests on IPCA axes.	Set to 5% for standard research or 1% for strict control.

3. INPUT DATA FORMAT REQUIREMENT

Datasets must follow a tidy tabular structure (.xlsx or .csv). Each row represents an individual observation plot or trial unit containing treatment labels, environment site tags, replication numbers, and outcome measurements:

Replicate	Treatment_Group	Environment_Site	Response_Metric_1	Response_Metric_2
Rep_1	Treatment_01	Location_Alpha	124.50	18.20
Rep_2	Treatment_01	Location_Alpha	127.10	18.90
Rep_1	Treatment_01	Location_Beta	110.40	15.80
Rep_2	Treatment_01	Location_Beta	112.80	16.30
Rep_1	Treatment_02	Location_Alpha	145.80	23.40
Rep_2	Treatment_02	Location_Alpha	148.20	24.10

4. STATISTICAL FOUNDATIONS & METRICS (PLAIN TEXT DEFINITIONS)

The mathematical concepts behind AMMI analysis are defined in plain text below:

Main Treatment & Environment Effects

Plain Text Definition:

Calculated in the additive ANOVA step as the average deviation of a treatment group mean or environment site mean from the grand overall trial mean across all locations.

Interaction Residual Matrix

Plain Text Definition:

The cell matrix remaining after subtracting both grand mean, main treatment effect, and main environment effect from observed cell means, representing factor-by-environment interaction noise.

Interaction Principal Component Axes (IPCA)

Plain Text Definition:

Orthogonal axes extracted from the interaction matrix using singular value decomposition. IPCA 1 captures the largest proportion of interaction variation, followed sequentially by IPCA 2, IPCA 3, and remaining axes.

AMMI Stability Value (ASV)

Plain Text Definition:

A distance metric calculated as the square root of the sum of the weighted IPCA 1 score squared (weighted by the ratio of IPCA 1 sum of squares to IPCA 2 sum of squares) and the IPCA 2 score squared. Lower ASV scores indicate higher stability across environments.

Performance-Stability Index (PSI)

Plain Text Definition:

A composite ranking index computed by adding the rank of a factor's overall mean performance to its rank in AMMI Stability Value (ASV), identifying entries with both high performance and low interaction variability.

5. STEP-BY-STEP WORKFLOW

Upload Dataset: Open the sidebar panel and upload your multi-environment spreadsheet (.xlsx or .csv).
Map Factor Columns: Assign categorical dataset columns to Primary Factor (Treatment) and Environment (Location/Site).
Map Replication Column: Select your trial replication/block column (e.g., Rep_1, Rep_2).
Select Outcome Traits: Check one or more continuous response measurement columns from the variable list.
Set Header Controls: Select alpha level (5% or 1%), decimal places, and number of IPCA axes (e.g., 2).
Run AMMI Analysis: Click the bold Run Analysis button.
Inspect AMMI Tables & Biplots: Review the AMMI ANOVA table, IPCA variance breakdown, AMMI1 (Mean vs IPCA 1) biplot, AMMI2 (IPCA 1 vs IPCA 2) biplot, and ASV stability rankings table.
Export Reports: Download formatted reports in Excel (.xlsx), Word (.docx), PowerPoint (.pptx), or high-res chart images.

6. SAMPLE RESULTS & INTERPRETATION

Below is an example of an AMMI ANOVA & IPCA Decomposition Summary Table:

Source of Variation	Degrees of Freedom (df)	Sum of Squares (SS)	Mean Square (MS)	F-Statistic	p-Value	Interaction Explained (%)
Main Treatment Factor	9	458.200	50.911	16.850	0.0001	—
Main Environment Site	4	1240.500	310.125	102.690	0.0001	—
Treatment x Environment	36	312.400	8.678	2.870	0.0002	100.00 %
IPCA 1 Axis	12	198.600	16.550	5.480	0.0001	63.57 %
IPCA 2 Axis	10	78.400	7.840	2.600	0.0084	25.10 %
AMMI Residual Noise	14	35.400	2.529	—	—	11.33 %

How to Read AMMI Output:

Cumulative IPCA Coverage (88.67%): IPCA 1 (63.57%) and IPCA 2 (25.10%) explain nearly 89% of interaction variation, confirming the AMMI2 biplot is highly representative.
AMMI1 Biplot Position: Entries positioned near the zero line on the IPCA 1 axis exhibit general stability across testing sites; entries far from zero show specific environmental adaptation.
ASV Stability Ranking: Lower AMMI Stability Value (ASV) indicates consistent treatment performance across variable environments.

7. BEST PRACTICES & TIPS

Interpreting Biplot Distance

Treatments positioned close to a specific environment vector on the AMMI2 biplot perform exceptionally well in that specific testing site.

Balanced Site Replications

Ensure every treatment level is evaluated across all environmental locations to maintain full AMMI matrix balance.

Cite DATES in Research Papers

If you use the DATES AMMI module for experimental data analysis in published scientific research, please cite it as follows:

@software{dates_app_2026, author = {DATES Development Team}, title = {DATES: Data Analysis and Trial Evaluation System}, year = {2026}, url = {https://dates-app.org}, note = {Multi-Environment Analysis — AMMI Analysis Module} }