Agriculture Reference
In-Depth Information
in a population not in equilibrium. It is because of this
unequal mode of transmission of sex-linked genes to male
and female offspring that if the equilibrium is disturbed,
the time required to reach equilibrium will usually be more
than one generation.
Table 4.5
Genotypes and their frequency,
phenotype, genotypic value, and sum.
Genotype of goats
BB
Bb
bb
2
(1 −
q
)
2
Genotypic frequency
q
2
q
(1 −
q
)
Phenotype
P
BB
P
Bb
P
bb
QUANTITATIVE GENETICS
Quantitative traits observed in the phenotype of the animal
are affected by many factors; some are genetic in origin
while others are environmental in nature. Many such traits
are measurable on some numeric scale (for example,
weights, milk yield, or body dimensions). Some quantita-
tive traits may have binary outcomes, such as survival or
death, but the outcome for an individual animal is due to
an underlying scale of risk, which has genetic and envi-
ronmental effects. An individual past a certain threshold
on the scale of risk dies. The genetic effect on a quantita-
tive trait is, in most practical situations, a result of many
genes. The number and effects of genes are often unknown,
although in recent times, more and more genes and their
effects on phenotype are being discovered. The purpose of
this section is to illustrate how genotype translates into
phenotype for a quantitative trait, using a simple one-locus
model for most of the development. Concepts such as
breeding value, important for quantitative traits, will be
developed here.
Genotypic value
u
au
−
u
Sum
uq
2
2
auq
(1
−
q
)
−
u
(1
−
q
)
2
q
) are the frequencies of
B
and
b
alleles,
u
is the genotypic value for the
b
allele, and
a
is
the level of dominance.
Note:
q
and (1
−
Table 4.6
Average effect of a gene.
Genotype of parents
BB
Bb
bb
Genotypic frequency
q
2
2
q
(1
−
q
)
(1
−
q
)
2
Effect of adding
b
to
BB
×
b
B b
×
b
b b
×
b
the genotype of
offspring
↓
↓
↓
Bb
Bb, bb
none
Note:
q
and (1 −
q
) are the frequencies of
B
and
b
alleles.
The population mean is the sum of the product of the
frequency and the genotypic value for all classes of geno-
types =
uq
2
+ 2
auq
(1
q
)
2
. Note that the mid-
point of homozygotes should be added to this result to give
the actual mean. The population mean is calculated as a
weighted average of genotypic values.
−
q
)
−
u
(1
−
Phenotypic Value, Genotypic Value, and
Population Mean
In the present development, phenotypes are observed for
individuals of different genotypes, and environmental
effects are considered to be not important. In a population
represented by three genotypes,
bb
,
Bb
, and
BB
, with mea-
sures of average phenotypic performance as
P
bb
,
P
Bb
, and
P
BB
, respectively, the midpoint of the two homozygotes,
m
= (
P
bb
+
P
BB
)/2. Defi ning
u
as follows:
u
=
P
bb
Breeding Value and Selection
Parents transmit genes to their offspring. Therefore, it is
desirable to obtain a measure of the effects of these genes
on their offspring. This is known as the “transmitting
ability” of the individual and is equal to one-half of a
goat's breeding value. The average effect of a gene will
help explain this concept (Table 4.6).
Shown in Table 4.6 is the effect of adding the
b
allele
to a population of
BB
,
Bb
, and
bb
individuals. The average
value of the
b
allele can be derived from the product of
genotypic frequencies and their value.
The average effect of an allele can be defi ned in a
random breeding population where individuals receive an
allele from one parent while the allele received from the
other parent will be at random (Table 4.7). The average
effect is expressed as a deviation from the population
mean. It is important to note that the average effect of a
gene substitution is greater when the frequency of the
unfavorable gene increases.
m
. Now
let the genotypic value of genotypes,
bb
,
Bb
, and
BB
be
P
bb
−
m
=
au
and
P
BB
=
u
, respectively. Note
that with this formulation, the genotypic value increases
by
u
for every addition of a
B
allele to the genotype
(depending on degree of dominance), and the heterozygote
is allowed to show varying degrees of dominance. With
the level of dominance
a
= 0, for example, the heterozy-
gote is exactly intermediate in value to the two homozy-
gotes, denoting gene action known as codominance. When
a
= 1, the heterozygote
Bb
is equal to the homozygote
BB
,
denoting complete dominance.
Consider the
dwarf
gene in goats which is recessive (
b
)
to normal size (
B
) and responsible for a decrease in body
size (Table 4.5 ).
−
m
=
−
u
,
P
Bb
−
