Agriculture Reference
In-Depth Information
Table 4.7 Genetic contribution of parents to their offspring, average effect of genotypes and breeding
value.
Gametes produced by parents
Genotypes produced in the
offspring
B allele
b allele
Genotype
Value
Frequency
Sum
Frequency
Sum
BB
u
q
uq
Bb
au
( 1
q )
au (1
q )
q
auq
Bb
u
( 1 − q )
u (1 − q )
Sum
uq + au (1 − q )
auq u (1 − q )
Average effect
α 1 = u (1 − q ){1 + a (1 − 2 q ) }
α 2 = − uq {1 + a (1 − 2 q )}
Genotype
BB
Bb
bb
Average effect of alleles
2
α
1
α
1 +
α
2
2
α
2
Breeding value
2(1
q )
α
( 1
2 q )
α
2 q
α
Note: q and (1 − q ) are the frequencies of B and b alleles, α 1 and
α
2 are average effect resulting from the
substitution of B and b alleles, and
α
is the average effect of the substitution =
α
1
α
2 .
Breeding value is derived from the mean value of an
animal's offspring, and is calculated as twice the average
deviation of the offspring mean from the population mean.
The deviation is multiplied by two because the individual
only transmits one-half of its genes to the offspring. The
remaining one-half is from a random sample of genes in
the population. The actual value is the sum of the breeding
value and population mean.
Breeding value defi ned in terms of average effects of
genes is equal to the sum of the average effects of all genes
that it carries as shown in Table 4.7.
50% because both the parents are common. On average
50% of the genes are common whereas the remaining 50%
differ.
When offspring X and Y receive 50% of their genes
from the buck, the probability that both offspring receive
the same gene from the buck is 0.5 × 0.5 = 0.25. If off-
spring X and Y receive 50% of their genes from the
doe, then the probability that both offspring receive the
same gene from the doe is equal to 0.5 × 0.5 = 0.25. In
full siblings, offspring X and Y have the same buck and
doe as parents. Therefore, the probability of receiving
the same genes from both the buck and doe parents is
the sum of the two frequencies which is 0.5 = (0.25 + 0.25)
or 50%. In half siblings, offspring X and Y have
one common parent. Therefore, the probability of receiv-
ing the same genes will be 0.25 or 25%. The relationship
between the parent and offspring is 0.5 or 50%. Therefore,
the probability of receiving the same genes will be 0.25 or
25%.
Inbreeding is a measure of increase in homozygosity in
individuals based on the relationship between the sire and
dam. It is denoted as F ×
Inbreeding and Relationships
Inbreeding is used to denote the mating of parents that are
more closely related to each other than the average of the
population. Related parents are more likely to transmit
the same genes to their offspring than unrelated parents.
Inbreeding has an infl uence on the genotype frequency
of the offspring such that there will be an increase in
homozygosity and reduction in heterozygosity. The term,
“inbreeding,” is used in another way in the “inbreeding
coeffi cient,” which is used to describe the level of homo-
zygosity resulting from the mating of related animals.
The degree of relationship between individuals can
be measured by the coeffi cient of relationship ( R XY ).
Relationship is expressed in terms of the probability that
two individuals have the same alleles by descent because
of common ancestry (Figure 4.1). Full sibs are related by
, which is known as Wright's coef-
fi cient of inbreeding and is one-half of the relationship
between parents. Inbreeding of an individual can be esti-
mated from the following equation:
)
nn
+
′ +
1
1
2
(
)
F
=
1
+
F
×
A
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