Step-by-step guide for analyzing diallel cross matrices using Griffing's Methods 1, 2, 3, and 4 under Model I (Fixed) and Model II (Random) to evaluate GCA, SCA, Reciprocal Effects, and Heterosis.
The Diallel Analysis — Griffing Methods Module implements Griffing's foundational combining ability framework. Diallel crossing designs evaluate all possible pairwise combinations among a selected set of parent entries. Depending on whether parents, direct crosses, and reciprocal crosses are included in the experimental evaluation, Griffing defined four distinct methods.
This module partitions total combination variation into General Combining Ability (GCA) (average parental transmission), Specific Combining Ability (SCA) (cross pair interaction), and Reciprocal Effects (RCA) (maternal vs paternal direction differences), supported under both Fixed Effects (Model I) and Random Effects (Model II).
Supported Griffing Methods:
The control panel and header toolbar provide full options for method selection, model type, parent mapping, mean comparisons, and transformations:
| Control / Parameter | Description | Statistical Purpose | When to Select / Set |
|---|---|---|---|
| Griffing Method (1, 2, 3, 4) | Selects Griffing experimental design mode: Method 1, Method 2, Method 3, or Method 4. |
Configures combining ability ANOVA equations based on inclusion of parents and reciprocals. | Match strictly to your trial matrix structure. |
| Model Type (Fixed / Random) | Selects model framework: Model I (Fixed Effects) or Model II (Random Effects). |
Model I estimates specific GCA/SCA contrast effects; Model II estimates GCA/SCA variance components. | Select Model I (Fixed) for specific parent selection; choose Model II (Random) for population variance components. |
| Parent 1 (First Factor Level) | Categorical column identifying the first parent entry in each cross pair. | Defines primary parent entry for GCA calculation. | Required. Map to your Parent 1 column. |
| Parent 2 (Second Factor Level) | Categorical column identifying the second parent entry in each cross pair. | Defines secondary parent entry for GCA calculation. | Required. Map to your Parent 2 column. |
| Replication Column | Categorical column identifying trial replication blocks (e.g., Rep_1, Rep_2). | Partition block variance away from residual error. | Required. Map to your replicate/block column. |
| Target Outcome Traits | Selects continuous numeric quantitative response measurement columns. | Computes Griffing ANOVA, GCA/SCA effects, reciprocal effects, heterosis, and plots. | Select one or multiple quantitative outcome variables. |
| Mean Separation Test | Selects post-hoc test for GCA/SCA means: LSD, Tukey, Duncan, or None. |
Identifies statistically significant differences among parent GCA values and cross SCA values. | Select Tukey or LSD for post-hoc grouping. |
Datasets must follow a tidy tabular structure (.xlsx or .csv) matching the chosen Griffing Method:
| Replicate | Parent_1 | Parent_2 | Response_Metric_1 | Response_Metric_2 |
|---|---|---|---|---|
| Rep_1 | Parent_A | Parent_A | 112.50 | 15.20 |
| Rep_2 | Parent_A | Parent_A | 114.10 | 15.80 |
| Rep_1 | Parent_A | Parent_B | 138.40 | 21.30 |
| Rep_2 | Parent_A | Parent_B | 140.20 | 21.90 |
| Rep_1 | Parent_B | Parent_A | 136.90 | 20.80 |
| Rep_2 | Parent_B | Parent_A | 139.10 | 21.40 |
| Rep_1 | Parent_B | Parent_B | 105.30 | 13.70 |
| Rep_2 | Parent_B | Parent_B | 107.50 | 14.10 |
The mathematical concepts behind Griffing's diallel analysis are defined in plain text below:
Plain Text Definition:
The average performance deviation of a parent entry across all its cross combinations in the diallel matrix, relative to the overall trial grand mean.
Plain Text Definition:
The performance deviation of a specific pairwise cross combination compared to the expected performance based on the sum of its individual parents' GCA effects.
Plain Text Definition:
The net difference between the mean of a direct cross (Parent A x Parent B) and its reciprocal cross (Parent B x Parent A), reflecting maternal or cytoplasmically inherited effects.
Plain Text Definition:
Calculated as twice the GCA mean square divided by twice the GCA mean square plus the SCA mean square. A ratio near 1.0 indicates that performance of cross progeny is predictable based on parent GCA values alone.
Plain Text Definition:
Mid-Parent Heterosis measures the percentage superiority of a cross over its mid-parent average; Heterobeltiosis measures percentage superiority over its top-performing parent entry.
Model I (Fixed Effects) for specific parent selection or Model II (Random Effects) for random sample variance components.Below is an example of a Griffing Combining Ability ANOVA & GCA Summary Table:
| Source of Variation / Entry | Degrees of Freedom (df) | Sum of Squares (SS) | Mean Square (MS) | F-Statistic | p-Value / Effect |
|---|---|---|---|---|---|
| General Combining Ability (GCA) | 4 | 214.800 | 53.700 | 18.450 | 0.0001 ** (Significant GCA) |
| Specific Combining Ability (SCA) | 10 | 85.200 | 8.520 | 2.930 | 0.0124 * (Significant SCA) |
| Residual Error | 28 | 81.480 | 2.910 | — | — |
| Parent_A GCA Effect | — | — | — | — | +5.420 ** (High Positive GCA) |
| Parent_B GCA Effect | — | — | — | — | -3.850 * (Negative GCA) |
| Baker's GCA Ratio | — | — | — | — | 0.926 (Predominantly Additive) |
Use Method 1 when reciprocal crosses are included to test for maternal effects. Use Method 2 when reciprocal differences are absent or assumed negligible.
Ensure your dataset contains observations for all required cells corresponding to the selected Griffing Method to avoid ANOVA matrix imbalance.
If you use the DATES Diallel Griffing module for experimental data analysis in published scientific research, please cite it as follows: