Step-by-step guide for evaluating multi-environment parametric stability statistics including Eberhart & Russell linear regression, Wricke's Ecovalence, Shukla's Stability Variance, Francis CV, and Lin & Binns Superiority Index.
The Phenotypic Stability Models Module provides a comprehensive suite of parametric statistical stability procedures for evaluating factor performance across variable test environments. When conducting multi-site trials, identifying factor levels that exhibit high mean performance paired with consistent, predictable stability across environmental conditions is a primary objective.
This module computes classic linear regression stability parameters (Eberhart & Russell, Finlay & Wilkinson) alongside variance-based stability metrics (Wricke's Ecovalence, Shukla's Variance, Francis CV %, Lin & Binns Superiority Index).
Supported Stability Models:
The control panel and header toolbar provide options for mapping factors, selecting specific stability models, alpha levels, and precision:
| Control / Parameter | Description | Statistical Purpose | When to Select / Set |
|---|---|---|---|
| Primary Factor Column (Treatment) | Categorical column identifying treatment entries or sample entities. | Defines primary factor levels evaluated for stability metrics. | Required. Map to your treatment factor column. |
| Environment Column (Location / Site) | Categorical column identifying trial locations, testing sites, or environmental conditions. | Defines environmental testing sites for environmental index calculation. | 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 location. | Map column containing replicate/block tags. |
| Target Quantitative Traits | Selects continuous numeric response measurement columns. | Computes regression slopes, deviation mean squares, ecovalence, and superiority indices. | Select one or multiple quantitative outcome columns. |
| Alpha Level | Significance error threshold (5% / 0.05 or 1% / 0.01). |
Establishes critical limits for testing bi = 1.0 and S2di = 0.0 hypothesis tests. | Set to 5% for standard research or 1% for strict control. |
| Decimal Precision | Controls rounding precision for stability summary tables (1, 2, 3, or 4 places). | Ensures uniform display precision across output summary tables. | Set to 2 or 3 decimal places for general reporting. |
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, and continuous trait 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 |
The mathematical concepts behind stability models are defined in plain text below:
Plain Text Definition:
The average outcome value across all treatments in a specific environment minus the grand mean value across all treatments and environments, expressing environmental quality (favorable vs stress site).
Plain Text Definition:
The linear regression slope of a factor's mean performance plotted against environmental index values. A slope bi = 1.0 indicates average response sensitivity; bi > 1.0 indicates high sensitivity to favorable environments; bi < 1.0 indicates resistance to poor environments.
Plain Text Definition:
The mean square of deviations of a factor's performance from its linear regression slope across environments. A deviation S2di = 0.0 indicates predictable linear stability; significant S2di > 0 indicates unpredictable non-linear response.
Plain Text Definition:
The sum of squared interaction deviations attributable to a specific factor across all test environments. Lower Wi values reflect high stability and low interaction contribution.
Plain Text Definition:
An unbiased variance component estimate of the factor-by-environment interaction for a specific factor entry. Tested with an F-statistic against residual experimental error.
Plain Text Definition:
The mean squared distance between a factor's performance and the maximum performance achieved by any factor in each environment. Lower Pi values indicate general superiority across all environments.
Below is an example of a Unified Stability Parameters Summary Table:
| Treatment Entry | Mean Trait Value | Regression Slope (bi) | Deviation MS (S2di) | Wricke Ecovalence (Wi) | Shukla Variance (sig2i) | Lin & Binns Superiority (Pi) | Stability Diagnosis |
|---|---|---|---|---|---|---|---|
| Treatment_01 | 138.50 | 1.02 | 1.25 ns | 14.20 | 4.15 ns | 12.40 | Highly Stable & High Performing |
| Treatment_02 | 145.80 | 1.48 ** | 2.10 ns | 42.80 | 13.50 * | 8.50 | Adapted to High-Input Environments |
| Treatment_03 | 112.40 | 0.65 ** | 1.85 ns | 28.50 | 8.90 ns | 45.20 | Adapted to Stress Environments |
| Treatment_04 | 125.10 | 0.98 | 18.45 ** | 95.40 | 31.20 ** | 28.90 | Unstable / Unpredictable Performance |
Never select factor entries based on stability parameters alone; always evaluate stability parameters alongside overall mean performance.
Linear regression stability models (Eberhart & Russell) require evaluations across at least 4 to 5 distinct environmental sites to establish reliable regression slopes.
If you use the DATES Stability module for experimental data analysis in published scientific research, please cite it as follows: