Line x Tester vs full Diallel: choosing a mating design for combining ability

A full diallel crosses every parent with every other parent. For p parents that is p(p-1)/2 crosses before reciprocals, which grows fast: 10 parents already mean 45 crosses. Line x Tester (Kempthorne 1957) is the practical alternative. A set of lines is crossed onto a small set of testers, and general and specific combining ability are still estimable. The choice is driven by how many crosses you can physically make and pollinate.

The decision in one sentence

Use a full diallel when the number of parents is small enough that all pairwise crosses are feasible and you want GCA for every parent on an equal footing. Use Line x Tester when the parent set is large, or when there is a natural split into females (lines) and a few well-characterised males (testers).

Crossing load compared

Parents / lines   Full diallel crosses   Line x Tester crosses
p = 6             15 (6 x 5 / 2)         depends on testers
8 lines, 3 test                          24 (8 x 3)
10 parents        45                     (not applicable)
10 lines, 3 test                         30 (10 x 3)
15 lines, 4 test                         60 (15 x 4)

Line x Tester scales with lines times testers, not with the square of the parent count. That is why it is the standard combining-ability design once the parent set passes roughly 8 to 10.

What each design estimates

A full diallel (Griffing) gives GCA for every parent, SCA for every cross, and, with the right method, reciprocal effects. Line x Tester gives GCA for the lines, GCA for the testers, and SCA for each line by tester combination. It also partitions the cross sum of squares into lines, testers, and line by tester, which maps directly onto additive and non-additive variance.

Worked example: 4 lines x 3 testers

Mean grain yield t/ha for the 12 crosses, lines L1 to L4 as rows, testers T1 to T3 as columns, in the matrix form StatVeda accepts:

        T1     T2     T3
L1     25.4   31.2   28.7
L2     27.1   29.8   30.5
L3     22.1   26.8   24.9
L4     30.5   32.1   29.3

The analysis splits the among-cross variation into the line effect (GCA of females), the tester effect (GCA of males), and the line by tester effect (SCA). From these, the variance due to GCA and the variance due to SCA are estimated, and their ratio indicates whether additive or non-additive gene action dominates.

Reading the partition

A large line and tester mean square relative to line by tester says additive effects dominate, so parent GCA ranking is a sound basis for selection. A large line by tester mean square says specific combinations matter more than parental averages, so the breeding plan should target high-SCA crosses directly. This is the same additive versus non-additive read a diallel gives, reached with far fewer crosses.

How to pick before you cross

If the parent set is small (up to roughly 6 to 8) and every parent is equally interesting as a potential parent, the full diallel gives the richest information. If the set is large, or the breeding scheme already separates a pool of lines from a few elite testers, Line x Tester gives the same combining-ability decision at a fraction of the crossing effort.

Common mistakes

Running a full diallel with so many parents that the crosses cannot all be pollinated in one season, leaving an incomplete matrix. Choosing testers that are too similar, which collapses the tester df and hides genetic differences. Reading line GCA when the line by tester term is large, where specific combinations, not parental averages, carry the signal. Treating Line x Tester GCA as comparable across studies that used different testers; GCA is always relative to the tester set.

When line by tester dominates

If the line by tester mean square is large relative to lines and testers, dominance and epistasis matter more than additive effects. GCA-based parent selection then misleads, and the right move is to identify the specific high-SCA crosses and advance those as hybrids. The design still answers the question; you read the SCA matrix instead of the GCA columns.