Principles of Plant Genetics and Breeding. George Acquaah

Females n₂ – 1 MS₂ σ²w + rσ²_mf + rn₁σ²_f Males × females (n₁ – 1)(n₂ – 1) MS₃ σ²w + rσ²_mf Within progenies n₁n₂(r − 1) MS₄ σ²w

      The design also allows the breeder to measure not only GCA but also SCA.

       North carolina design III

In this design, a random sample of F₂ plants is backcrossed to the two inbred lines from which the F₂ was descended. It is considered the most powerful of all the three NC designs. However, it was made more powerful by the modifications made by Kearsey and Jinks that adds a third tester (not just the two inbreds) (Figure 4.7). The modification is called the triple test cross and is capable of testing for non‐allelic (epistatic) interactions that the other designs cannot, and also estimate additive and dominance variance.

Figure 4.7 North Carolina Design III. The conventional form (a), the practical layout (b), and the modification (c) are shown.

       Diallele cross

      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

       Comparative evaluation of mating designs

Hill, Becker, and Tigerstedt roughly summarized these mating designs in two ways:

      1 In terms of coverage of the population: BIPs > NCM‐I > Polycross > NCM‐III > NCM‐II > diallele, in that order of decreasing effectiveness.

      2 In terms of amount of information: Diallele > NCM‐II > NCM‐II > NCM‐I > BIPs.

      The diallele mating design is the most important for GCA and SCA. These researchers emphasized that it is not the mating design per se, but rather the breeder who breeds a new cultivar. The implication is that the proper choice and use of a mating design will provide the most valuable information for breeding.

4.3 The genetic architecture of quantitative traits

      Molecular quantitative genetics mainly focuses on evaluating the coupling association of the polymorphic DNA sites with the phenotypic variations of quantitative and complex traits. In addition, whereas classical quantitative genetics deals with the holistic status of all genes, molecular quantitative genetics dissects the genetic architectures of quantitative genes (concerned with the analytical status of the major genes and holistic status of the minor genes).

      The genetic architecture of quantitative traits entails the number of QTLs that influence a quantitative trait, the number of alleles that each QTL possesses, the frequencies of the alleles in the population, and the influence of each QTL and its alleles on the quantitative trait. Identifying and characterizing QTLs will provide a basis for selecting and improving plant species. The summation of QTL studies indicates that QTL alleles with large effects are rare; most quantitative traits are controlled by many loci with small effects.

      Researchers commonly use one of two fundamental approaches to design and study quantitative traits. In what is called the top‐down approach, they start with the trait of interest and then attempt to draw inferences about the underlying genetics from examining the degree of trait resemblance among related subjects. It is usually the first step taken to determine if there is any evidence for a genetic component. It is also described as the unmeasured genotype approach because it focuses on the inheritance pattern without measuring any genetic variations. Typical statistical analyses employed in this approach are heritability and segregational analysis.

      In the second approach, the bottom‐up (measured) approach, researchers actually measure QTLs and use the information to draw inferences about which genes might have a role in the genetic architecture of a quantitative trait. Typical statistical analyses employed in this approach are linkage analysis and association analysis. The second approach is becoming more assessable with the advent of newer, more efficient, and less expensive technologies to measure QTLs. These technologies include DNA microarrays and protein mass spectrometry. They allow researchers