Читать книгу Principles of Plant Genetics and Breeding - George Acquaah - Страница 195

A complete diallele mating design is one that allows the parents to be crossed in all possible combinations, including selfs and reciprocals. This is the kind of mating scheme required to achieve Hardy‐Weinberg equilibrium in a population. However, in practice, a diallele with selfs and reciprocals is neither practical nor useful for several reasons. Selfing does not contribute to recombination of genes between parents. Furthermore, recombination is achieved by crossing in one direction, making reciprocals unnecessary. Because of the extensive mating patterns, the number of parents that can be mated this way is limited. For p entries, a complete diallele will generate p² crosses. Without selfs and reciprocals, the number is p(p − 1)/2 crosses.

When the number of entries is large, a partial diallele mating design, which allows all parents to be mated to some but not all other parents in the set, is used. A diallele design is most commonly used to estimate combining abilities (both general and specific). It is also widely used for developing breeding populations for recurrent selection.

Nursery arrangements for application of complete and partial diallele are varied. Because a large number of crosses are made, diallele mating takes a large amount of space, seed, labor, and time to conduct. Because all possible pairs are contained in one half of a symmetric Latin square, this design may be used to address some of the space needs.

There are four basic methods developed by Griffing that vary in either the omission of parents or the omission of reciprocals in the crosses. The number of progeny families (pf) for methods 1 through 4 are: pf = n², pf = ½ n(n + 1), pf = n(n − 1), and pf = ½ n(n − 1), respectively. The ANOVA for method 4, for example, is as follows:

Source	dr	EMS
GCA	n1 − 1	σ2e + rσ2g + r(n − 2)σ2
SCA	[n(n − 3)]/2	σ2e + rσ2g
Reps × Crosses	(r − 1){[n(n − 1)/2] − 1}	σ2e