Principles of Plant Genetics and Breeding

112 CHAPTER 7
of genes as 1 : n : n–1 of free : heterozygotic potential :
homozygotic potential.
Another level of complexity may be factored in by
considering dominance and non-allelic interactions
(AA = Aa = BB = Bb). If this is so, the nine genotypes
previously observed will produce only three phenotypic
classes ([AABB, 4AaBb, 2AaBB, 2AABb] + [2Aabb,
2aaBb, AAbb, aaBB] + [aabb], in a frequency of 9 : 6 :
1. A key difference is that 50% of the visible variability is
now in the heterozygous potential state that cannot be
fixed by selection. The heterozygotes now contribute to
the visible variability instead of the cryptic variability.
From the plant breeding standpoint, its effect is to
reduce the rate of response to phenotypic selection at
least in the same direction as the dominance effect. This
is because the fixable homozygotes are indistinguishable
from the heterozygotes without a further breeding test
(e.g., progeny row). Also, the classifications are skewed
(9 : 6 : 1) in the positive (or negative) direction.
Key plant breeding information to be gained from the
above discussion is that in outbreeding populations,
polygenic systems are capable of storing large amounts
of cryptic variability. This can be gradually released for
selection to act on through crossing, segregation, and
recombination. The flow of this cryptic variability to the
free state depends on the rate of recombination (which
also depends on the linkage of genes on the chromosomes
and the breeding system).
Given a recombination value of r between two linked
genes, the segregation in the second generation
depends on the initial cross, as M. D. Haywood and
E. L. Breese demonstrated:
Initial cross Free Homozygous potential
AABB × aabb 1(1 − r) 2r
AAbb × aaBB 2r 2(r − 1)
The second cross shows genes linked in the repulsion
phase. The flow of variability from the homozygous
potential to the free state depends on how tight a linkage
exists between the genes. It will be at its maximum
when r = 0.5 and recombination is free, and will diminish
with diminishing r. This illustration shows that with
more than two closely linked loci on the same chromosome,
the flow of variability would be greatly restricted.
In species where selfing is the norm (or when a breeder
enforces complete inbreeding), the proportion of heterozygotes
will be reduced by 50% in each generation,
dwindling to near zero by the eighth or ninth generation.
The open system of pollination in cross-pollinated
species allows each plant in the gene pool to have both
homozygous and heterozygous loci. Plant breeders exploit
this heterozygous genetic structure of individuals
in population improvement programs. In a natural
environment, the four factors of genetic change mentioned
previously are operational. Fitness or adaptive
genes will be favored over non-adaptive ones. Plant
breeders impose additional selection pressure to hasten
the shift in the population genetic structure toward
adaptiveness as well as to increase the frequencies of
other desirable genes.
An example of a breeding application of
Hardy–Weinberg equilibrium
In disease-resistance breeding, plant breeders cross
an elite susceptible cultivar with one that has disease
resistance. Consider a cross between two populations,
susceptible × resistant. If the gene frequencies of an
allele A in the two populations are represented by P1 and
P2 , the gene frequency in the F1 = (P1 + P2 )/2 = p.
Assuming the frequency of the resistance gene in the
resistant cultivar is P1 = 0.7 and that in the susceptible
elite cultivar it is P2 = 0.05, the gene frequency in the
progeny of the cross p would be obtained as follows:
p = (P 1 + P 2 )/2 = (0.7 + 0.05)/2 = 0.375
Consequently, the gene frequency for the resistant trait
is reduced by about 50% (from 0.7 to 0.375).
Issues arising from Hardy–Weinberg
equilibrium
In order for Hardy–Weinberg equilibrium to be true,
several conditions must be met. However, some situations
provide approximate conditions to satisfy the
requirements.
The issue of population size
The Hardy–Weinberg equilibrium requires a large random
mating population (among other factors as previously
indicated) to be true. However, in practice, the
law has been found to be approximately true for most of
the genes in most cross-pollinated species, except when
non-random mating (e.g., inbreeding and assortative
mating, discussed below on p. 116) occur. Whereas
inbreeding is a natural feature of self-pollinated species,
assortative mating can occur when cross-pollinated
species are closely spaced in the field.