SinceVPis always greater than or equal toVG, the heritability of a trait can range from 0 to 1.
IfHis equal to one, then all variance is caused by genetic effects, and the breeder will be
very successful at selecting better plants. Such is the case for the imaginary melon trait
illustrated in Figure 3.1. However, ifHis zero, thenVGmust also be zero, and there is no
possibility of selecting plants that are genetically superior because all variation is environ-
mental. Most traits that breeders work with show intermediate levels of heritability,
between zero and one.
3.2.3 Mating Systems, Varieties, Landraces, and Pure Lines
The fundamental output of plant breeding is theplant variety, which is sometimes referred to
as acultivar(i.e., a cultivated variety). However, the genetic makeup of a variety, and the way
in which it is produced, maintained, and released depends critically on the type ofmating
systemfound in the species to which the variety belongs. Many plants can tolerateself-
pollination(or self-fertilization), and some of the most important crop species (including
most grain and oilseed crops) are naturally self-pollinated. An important exception is maize
(corn), which can tolerate self-pollination, but is normallycross-pollinated (or cross-
fertilized). Other plants cannot tolerate self-pollination, and have specific genetic mechanisms
to prevent this (see Chapter 2). Plants that normally cross-pollinate are subject to continual
recombination and selection after varieties are released, and thus strategies for breeding
and variety release can be quite different from those used in self-pollinating species.
For plant species that normally cross-pollinate, we often assume that mating occurs at
random. In reality, this is seldom the case because plants that are near to each other are
more likely to pollinate each other. Nevertheless, the assumption of random mating
allows the development of theories that often give good approximations of reality. The
most important theory regarding random mating is theHardy–Weinberg law, which pre-
dicts the frequency of genotypes that will occur according to the frequency of alleles.
Assume that there are two alleles, “A” and “a,” at a given locus, and that the alleles are
at frequenciespandq, wherepmust equal (1 2 q). The law states that the frequencies
of genotypes, as represented below, can be predicted as
AA:Aa:aa¼p^2 :2pq:q^2An important property of this law is that these frequencies are achieved after just one gen-
eration of random mating (the proof of this theory is shown in many textbooks). An import-
ant application of this theory is to identify whether random mating is occurring, or if other
factors such as selection or mixing of populations (immigration/emigration) are occurring.
Plant species that are highly self-pollinated usually exist in ahomozygousstate (i.e.,
alleles exist in identical pairs at most loci). To understand why, consider what happens
when ahybridis formed, through either a chance pollination or a deliberate hybridization
by a breeder. Figure 3.2 shows a cross between two homozygous genotypes. The product of
this mating (a hybrid) will beheterozygousat any locus that differs between the parents, and
all progeny will be identical. However, a mixture of genotypes will exist in the F 2 gener-
ation and beyond. Each generation of selfing reduces the level of heterozygosity by 50%,
such that the proportion of homozygotes (Phomo) at a particular locus in generation FX
can be predicted as
Phomo¼ 1 ^12 (X1):52 PLANT BREEDING