Читать книгу Principles of Plant Genetics and Breeding - George Acquaah - Страница 287

The goal of crossing for generating variability for selection is to produce a large number of gene recombinations from the parents used in the cross. In hybrid seed programs, the F₁ is the end product for commercial use. However, in other crosses, the F₂ and subsequent generations are evaluated to select genotypes that represent the most desirable recombination of parental genes. The F₂ generation has the largest number of different gene combinations of any generation following a cross. The critical question in plant breeding is the size of F₂ population to generate in order to have the chance of including that ideal recombinant this is homozygous for all the desirable genes in the parent. Three factors determine the number of gene recombination that would be observed in an F₂ 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.