Principles of Plant Genetics and Breeding

of interest. As Falconer indicated, in order for heterosis
to manifest for the breeder to exploit, some level of
dominance gene action must be present, in addition to
the presence of relative differences in gene frequency in
the two parents.
Assume two populations (A, B), in Hardy–Weinberg
equilibrium, with genotypic values and frequencies for
one locus with two alleles p and q for population A, and
r and s for population B as follows:
Gene frequency Genotypic Number of
Genotypes Pop. A Pop. B values A 1 alleles
A 1 A 1 p 2 r 2 +a 2
A 1 A 2 2pq 2rs d 1
A 2 A 2 q 2 s 2 –a 0
After a cross (A × B) between the populations in
Hardy–Weinberg equilibrium, the genotypic values and
frequencies in the cross are:
Genotypes Frequencies Genotypic values
A 1 A 1 pr +2
A 1 A 2 ps + qr d
A 2 A 2 qs −d
where p and r are the frequencies of allele A 1 , and q and s
are the frequencies of allele A 2 , in the two populations.
Also, q = 1 − p and s = 1 − r. The mean values of the
populations are P A and P B .
P A = [(p − q)a] + 2pqd
= [(2p − 1)a] + [2(p − q 2 )d]
P B = (r − s)a + 2rsd
= (2r − 1) + [2(r − r 2 )d]
F = [(pr − qs)a] + [(ps + qr)d]
= [(p + r − 1)a] + [(p + r − 2pr)d]
where F is the hybrid of P A × P B . Calculating heterosis as
a deviation from the midparent values is as follows:
H MP = F 1 − (P 1 + P 2 )/2
= [(p + r − 1)a + (p + r − 2pr)d]
− 1 / 2 [(2p − 1)a + 2(p − q 2 )d + (2r − 1)a
+ 2(r − 1)a + 2(r − r 2 )d] ...
= (p − r) 2 d
From the foregoing, if d = 0 (no dominance), then
heterosis is zero (i.e., F = MP, the mean of the midparents).
On the other hand, if in population A, p = 0 or 1,
and by the same token in population B, r = 0 or 1 for
the same locus, depending on whether the allele is in
homozygous recessive or dominant state, there will be a
BREEDING HYBRID CULTIVARS 341
heterotic response. In the first generation, the heterotic
response will be due to the loci where p = 1 and r = 0, or
vice versa. Consequently, the heterosis manifested will
depend on the number of loci that have contrasting
loci as well as the level of dominance at each locus. The
highest heterosis will occur when one allele is fixed
in one population and the other allele in the other. If
gene action is completely additive, the average response
would be equal to the midparent, and hence heterosis
will be zero. On the other hand, if there is dominance
and/or epistasis, heterosis will manifest.
Plant breeders develop cultivars that are homozygous
(according to the nature of the method of reproduction).
When there is complete or partial dominance,
the best genotypes to develop are homozygotes or heterozygotes,
where there could be opportunities to discover
transgressive segregates. On the other hand, when
non-allelic interaction is significant, the best genotype
to breed would be a heterozygote.
Some recent views on heterosis have been published.
Some maize researchers have provided evidence to the
effect that the genetic basis of heterosis is partial dominance
to complete dominance. A number of research data
supporting overdominance suggest that it resulted from
pseudo-overdominance arising from dominant alleles
in repulsion phase linkage. Yet other workers in maize
research have suggested epistasis between linked loci to
explain the observance of heterosis.
Concept of heterotic relationship
Genetic diversity in the germplasm used in a breeding
program affects the potential genetic gain that can
be achieved through selection. The most costly and
time-consuming phase in a hybrid program is the
identification of parental lines that would produce
superior hybrids when crossed. Hybrid production
exploits the phenomenon of heterosis, as already indicated.
Genetic distance between parents plays a role in
heterosis.
In general, heterosis is considered an expression of
the genetic divergence among cultivars. When heterosis
or some of its components are significant for all traits,
it may be concluded that there is genetic divergence
among the parental cultivars. Information on the
genetic diversity and distance among the breeding lines,
and the correlation between genetic distance and hybrid
performance, are important for determining breeding
strategies, classifying the parental lines, defining heterotic
groups, and predicting future hybrid performance.