Principles of Plant Genetics and Breeding

However, in other crosses, the F 2 and subsequent generations
are evaluated to select genotypes that represent
the most desirable recombination of parental genes. The
F 2 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 F 2 population
to generate in order to have the chance of including
the ideal homozygous recombinant for all the
desirable genes in the parent. Three factors determine
the number of gene recombinations that would be
observed in an F 2 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 10.1 summarizes the challenges of breeding in
terms of size of the F 2 population to grow. If the parents
differ by only one pair of allelic genes, the breeder needs
to grow at least four plants in the F 2 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 minimum F 2 population size
needed is 1,048,576 (obtained by the formula 4 n , where
n is the number of loci). The frequencies illustrate how
daunting a task it is to select for quantitative traits.
The total possible genotypes in the F 2 based on the
number of alleles per locus is given by the relationship
[k(k + 1)/2] n where k is the number of alleles at each
locus, and n is the number of heterozygous loci. With
one heterozygote and two alleles, there will be only
three kinds of genotypes in the F 2 , while with one heterozygote
and four 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
SEXUAL HYBRIDIZATION AND WIDE CROSSES IN PLANT BREEDING 169
or undesirable. Linkage reduces the frequency of gene
recombination (it increases parental types). The magnitude
of reduction depends on the phase: the coupling
phase (with both dominant gene loci in one parent,
e.g., AB/ab) and the repulsion phase (with one
dominant and one recessive locus in one parent, e.g.,
Ab/aB). The effect of linkage in the F 2 may be calculated
as 1 / 4 (1 − P) 2 × 100 for the coupling phase, and
1 /4 P 2 × 100 for the repulsion phase, for the proportion
of AB/AB or ab/ab genotypes in the F 2 from a cross
between AB/ab × Ab/aB. Given, for example, a crossing
over value (P) of 0.10, the percentage of the
homozygotes will be 20.25% in the coupling phase
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 F 2 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 the desirable alleles (either homozygous
or heterozygous) are one in 421 in the F 2 , one in 49,343
in the F 3 , and one in 176,778 in the F 4 , 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
Table 10.1 The variability in an F 2 population as affected by the number of genes that are different between the two
parents.
Number of Number of heterozygous Number of different Minimum population size for a
heterozygous loci (n) in F 2 (2 n ) genotypes in F 2 (3 n ) chance to include each genotype (4 n )
1 2 3 4
2 4 9 16
6 64 729 4,096
10 1,024 59,049 1,048,576
15 32,768 14,348,907 1,076,741,824