Diallel methods 1 to 4 (Griffing): which one fits your crosses?

Griffing (1956) defined four methods for analysing a diallel cross, differing in which crosses are included. The choice is not a statistical preference; it is determined by what you actually planted. Picking the wrong method either wastes information or, worse, attempts an analysis the data cannot support.

The four methods

For p parents, the diallel set can include parents (p), F1 hybrids (p(p-1)/2 in one direction or p(p-1) including reciprocals).

Method  Includes                          Number of entries (p=5)
1       Parents + F1 + reciprocals        25
2       Parents + F1 (no reciprocals)     15
3       F1 + reciprocals (no parents)     20
4       F1 only (no parents, no recip.)   10

How to pick

Walk through the field at flowering. Did you plant the parents? Did you make crosses both ways round (A by B and B by A) or only one way? That decides the method.

Method 1

Parents in the trial, F1 hybrids in both directions. Largest information set: estimates GCA, SCA, reciprocal effects, and maternal effects. Use when reciprocal effects are biologically plausible (some species, some traits show maternal cytoplasmic effects). Heaviest crossing programme.

Method 2

Parents in the trial, F1 in one direction only. The most common Griffing analysis in agricultural research. Estimates GCA and SCA, no reciprocal effects. Use when reciprocal effects are not expected (most field crops, most agronomic traits) and you want to keep the crossing programme manageable.

Method 3

F1 in both directions, parents not planted. Estimates SCA and reciprocal effects but cannot separate GCA from inbreeding effects. Use when parents were not available for sowing in the same season as the F1 set.

Method 4

F1 only, in one direction. Smallest crossing programme. Estimates SCA and a combined GCA-like effect. Use when seed of parents and reciprocals is not available, or when the breeder explicitly wants to focus on hybrid performance and combining ability of crosses, not on parental per-se evaluation.

Models I (fixed) versus II (random)

Each method comes with two models. Model I treats parents as fixed (a defined set the breeder cares about). Model II treats parents as a random sample from a population (used to estimate variance components and predict gain in a wider breeding population). For most applied breeding decisions Model I is the right choice. For genetic-parameter estimation in a breeding population, Model II.

One-line cheat

Method 2 covers most agronomic crops where reciprocal effects do not matter and parents were planted. Use Method 1 only if you have a biological reason to estimate reciprocals. Use Method 3 or 4 only if the parents or one direction of crosses was unavailable.

Common mistakes

Picking Method 1 to look thorough when reciprocals were never made (the analysis runs but the reciprocal MS is meaningless). Picking Method 4 when parents were planted (the parental information is thrown away, narrow-sense heritability cannot be estimated cleanly). Mixing Models I and II in the same write-up without saying which results came from which.

What StatVeda surfaces

For every Griffing method, the tool produces the ANOVA partitioning (treatments split into GCA, SCA, and reciprocal where applicable), the GCA effects per parent with standard errors, the SCA effects for each cross combination, the variance components sigma squared GCA and sigma squared SCA, and the predictability ratio 2 sigma squared GCA over (2 sigma squared GCA plus sigma squared SCA). The AI explainer translates the table into a one-paragraph recommendation about which parents to retain.

Reading GCA effects

A GCA effect is a deviation from the grand mean. Positive GCA means the parent consistently produces above-average crosses across all partners. Negative GCA means the opposite. Ranking parents by GCA and retaining the top two or three is the standard combining-ability decision rule, valid as long as variance is dominated by additive effects (sigma squared GCA much greater than sigma squared SCA).

When SCA matters more than GCA

If sigma squared SCA is comparable to or larger than sigma squared GCA, dominance and epistasis dominate. Then GCA-based parent ranking misleads, and the breeding strategy should pivot to identifying specific high-SCA crosses and producing those as hybrids directly. The diallel still tells you what to do; you just read the SCA matrix instead of the GCA vector.