Step-by-step guide for running Hayman's diallel cross analysis to evaluate additive vs dominance genetic variance components, Vr-Wr array regression graphs, directional dominance, and gene distribution symmetry.
The Diallel Analysis — Hayman Approach Module provides a rigorous graphical and numerical framework for evaluating full diallel crossing matrices (all possible pairwise combinations among a set of parent entries). In genetics, plant/animal breeding, material synthesis, and multi-factor combination trials, understanding whether trait variation is governed by additive gene action or dominance gene action is critical for strategic decision-making.
Hayman's approach combines an itemized ANOVA breakdown with array variance (Vr) and array covariance (Wr) graphical regression techniques to determine the degree of dominance, dominant vs recessive allele frequencies, and narrow-sense heritability.
Primary Analytical Capabilities:
The control panel and header toolbar provide complete options for parent mapping, alpha significance, decimal precision, and transformations:
| Control / Parameter | Description | Statistical Purpose | When to Select / Set |
|---|---|---|---|
| Parent 1 (First Factor Level) | Categorical column identifying the first parent entry in each pairwise cross pair. | Identifies the primary parent entry for array variance/covariance grouping. | Required. Map to your Parent 1 column. |
| Parent 2 (Second Factor Level) | Categorical column identifying the second parent entry in each pairwise cross pair. | Identifies the secondary parent entry in the diallel matrix grid. | Required. Map to your Parent 2 column. |
| Replication Column | Categorical column identifying trial replication blocks (e.g., Rep_1, Rep_2). | Isolates environmental block error variance across diallel trial plots. | Required. Map to your replicate/block column. |
| Target Outcome Traits | Selects continuous numeric response measurement columns. | Computes Hayman ANOVA, Vr-Wr regression, genetic parameters, and plots for selected traits. | Select one or multiple quantitative response variables. |
| Alpha Level | Significance error threshold (5% / 0.05 or 1% / 0.01). |
Establishes significance limits for Hayman ANOVA F-tests and genetic parameters. | Set to 5% for standard research or 1% for strict control. |
| Decimal Precision | Controls rounding precision for output matrices and tables (1, 2, 3, or 4 places). | Ensures uniform formatting across summary tables and export files. | Set to 2 or 3 decimal places for genetic parameters. |
Datasets must follow a tidy tabular structure (.xlsx or .csv). Every pair of parent entries (including selfs/parents where Parent 1 equals Parent 2) should be represented across replications:
| 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 Hayman's diallel analysis are defined in plain text below:
Plain Text Definition:
Measures the component of variation due to additive gene effects among parent entries, derived from the variance of parental means minus error variance.
Plain Text Definition:
H1 measures total dominance variance component across all loci; H2 measures dominance variance adjusted for asymmetrical allele frequencies. When H1 equals H2, dominant and recessive alleles are present in equal proportions (0.5 each).
Plain Text Definition:
The F value indicates the relative frequency of dominant versus recessive alleles across parents (positive F indicates excess of dominant alleles). The h2 value quantifies overall dominance effect across all heterozygous loci.
Plain Text Definition:
Array variance (Vr) measures variance within off-spring arrays of each parent; array covariance (Wr) measures covariance between parents and off-spring array means. The slope of the Wr on Vr regression line tests adequacy of the additive-dominance model (unit slope = 1.0), and the Y-intercept location indicates degree of dominance.
Plain Text Definition:
Calculated as the square root of the ratio of H1 to D. A value less than 1 indicates partial dominance; equal to 1 indicates complete dominance; greater than 1 indicates overdominance.
Plain Text Definition:
The proportion of total phenotypic variance driven strictly by additive genetic variance (D), reflecting the proportion of variance transferable to subsequent selection generations.
Below is an example of a Hayman Diallel Genetic Parameter Summary Table:
| Genetic Parameter | Symbol | Estimated Value | Standard Error (SE) | Biological / Analytical Interpretation |
|---|---|---|---|---|
| Additive Component | D | 48.500 | 3.120 | ** Significant Additive Variance |
| Dominance Component 1 | H1 | 32.400 | 2.850 | ** Significant Dominance Component |
| Dominance Component 2 | H2 | 28.100 | 2.410 | Asymmetrical Gene Distribution (H2 < H1) |
| Allele Frequency Covariance | F | +12.300 | 1.950 | Excess of Dominant Alleles (F > 0) |
| Overall Dominance Effect | h2 | 18.600 | 1.820 | ** Significant Heterozygote Dominance |
| Degree of Dominance | (H1 / D)^0.5 | 0.817 | — | Partial Dominance (< 1.0) |
| Narrow-Sense Heritability | h2_n | 0.542 | — | 54.2 % Transmissable Additive Variance |
Verify that the Vr-Wr regression slope does not significantly deviate from 1.0 (unit slope) to ensure the basic assumptions of Hayman's additive-dominance model are satisfied.
Hayman's approach requires a complete diallel matrix including both direct crosses, reciprocal crosses (or assumed equal), and parental selfs.
If you use the DATES Diallel Hayman module for experimental data analysis in published scientific research, please cite it as follows: