Principles of Plant Genetics and Breeding. George Acquaah

population:

      1 The number of gene loci for which the parents in a cross differ;

      2 The number of alleles at each locus;

      3 The linkage of the gene loci.

Plant breeders are often said to play the numbers game. Table 6.1 summarizes the challenges of breeding in terms of size of the F₂ population to grow. If the parents differ by only one pair of allelic genes, the breeder needs to grow at least 16 plants in the F₂ to have the chance to observe all the possible gene combinations (according to Mendel's laws). On the other hand, if the parents differ in 10 allelic pairs, the F₂ population size needed is 59 049 (obtained by the formula 3ⁿ, where n = the number of loci). The frequencies illustrate how daunting a task it is to select for quantitative traits.

Table 6.1 The variability in an F₂ population as affected by the number of genes that are different between the two parents.

Number of heterozygous loci	Number of heterozygous in the F2	Number of different genotypes in the F2	Minimum population size for a chance to include each genotype
n	2n	3n	4n
1	2	3	4
2	4	9	16
6	64	729	4096
10	1024	59 049	1 048 576
15	32 768	14 348 907	1 076 741 824

      The total possible genotypes in the F₂ based on the number of alleles per locus is given by the relationship [k (k + 1)/2]ⁿ where k = number of alleles at each locus, and n = number of heterozygous loci. With 1 heterozygote and 2 alleles, there will be only 3 kinds of genotypes in the F₂, while with 1 heterozygote and 4 alleles, there will be 10. The effect on gene recombination by linkage is more important than for the number of alleles. Linkage may be desirable or undesirable. Linkage reduces the frequency of gene recombination (it increases parental types). The magnitude of reduction depends on the phase (coupling phase – with both dominant gene loci in one parent, e.g. AB/ab, and repulsion phase – with one dominant and one recessive loci in one parent, e.g. Ab/aB). The effect of linkage in the F₂ may be calculated as ¼ (1‐P)² × 100 for the coupling phase, and ¼ P² × 100 for the repulsion phase, for the proportion of AB/AB or ab/ab genotypes in the F₂ from a cross between AB/ab × Ab/aB. Given, for example, a crossing over value of 0.10, the percentage of the homozygotes will be 20.25% in the coupling versus only 0.25% in the repulsion phase. If two genes were independent (crossing over value = 0.50), only 6.25% homozygotes would occur. The message here is that the F₂ population should be as large as possible.

      With every advance in generation, the heterozygosity in the segregating population decreases by 50%. The chance of finding a plant that combines all the desirable alleles decreases as the generations advance, making it practically impossible to find such a plant in advanced generations. Some calculations by J. Sneep will help clarify this point. Assuming 21 independent gene pairs in wheat, he calculated that the chance of having a plant with all desirable alleles (either homozygous or heterozygous) are 1 in 421 in the F₂, 1 in 49 343 in the F₃, and 1 in 176 778 in the F₄, and so on. However, to be certain of finding such a plant, he recommended that the breeder grow four times as many plants.

      Another genetic consequence of hybridization is the issue of linkage drag. As previously noted, genes that occur in the same chromosome constitute a linkage block. However, the phenomenon of crossing over provides an opportunity for linked genes to be separated and not inherited together. Sometimes, a number of genes are so tightly linked they are resistant to the effect of recombination. Gene transfer by hybridization is subject to the phenomenon of linkage drag, the unplanned transfer of other genes associated with those targeted. If a desired gene is strongly linked with other undesirable genes, a cross to transfer the desired gene will invariably be accompanied by the linked undesirable genes.

6.10 Types of populations generated through hybridization

      A breeding program starts with an initial population that is obtained from previous programs, and existing variable populations (e.g. landraces), or is created through a planned cross. Hybridization may be used to generate a wide variety of populations in plant breeding, ranging from the very basic two‐parent cross (single cross) to very complex populations in which hundreds of parents could be involved. Single crosses are the most widely used in breeding. Commercial hybrids are mostly produced by single crosses. Complex crosses are important in breeding programs where the goal is population improvement. Hybridization may be used to introgress new alleles from wild relatives into breeding lines. Because the initial population is critical to the success of the breeding program, it cannot be emphasized enough that it be generated with much planning and thoughtfulness.

Various mating designs and arrangements are used by breeders and geneticists to generate plant populations. These designs require some type of cross to be made. Factors that affect the choice of a mating design include: (i) the predominant type of pollination (self‐ or cross‐pollinated); (ii) type of crossing used (artificial or natural); (iii) type of pollen dissemination (wind or insect); (iv) presence of male sterility system; (v) purpose of the project (for breeding or genetic studies); and (vi) size of the population required. In addition, the breeder should be familiar with how to analyze and interpret or use the data to be generated from the mating.

      The primary purpose of crossing is to expand genetic variability by combining genes from the parents involved in the cross to produce offspring that contain genes they never had before. Sometimes, multiple crosses are conducted to generate the variability in the base population to begin the selection process in the program. Based on how the crosses are made and their effects on the genetic structure of the plants or the population, methods of crossing may be described as either divergent or convergent.

      6.10.1 Divergent crossing

Genetically divergent parents are crossed for recombination of their desirable genes. To optimize results, parents should be carefully selected to have a maximum number of positive traits and a minimum number of negative traits with no negative traits in common (i.e. elite × elite cross). This way, recombinants that possess both sets of desirable traits will occur in significant numbers in the F₂. The F₁ contains the maximum number of desirable genes from both parents. There are several ways to conduct divergent crosses (Figure 6.2):

       Single crossIf two elite lines are available that together possess all desired traits at adequate levels, one cross (single cross [A × B]) may be all that is needed in the breeding program.

       Three‐way crossSometimes, for combining all desirable traits several cultivars or elite germplasm are required, since each pair may have some negative traits in common. In this case,