Agriculture Reference
In-Depth Information
described as:
q
1
=
mq
m
+ (1
m
)
q
0
. Consider a population
of 100 goats consisting of 10 migrant and 90 native goats.
Let the frequency of alleles in the migrant (
q
m
) and native
(
q
0
) populations be 0.5 and 0.01, respectively. The allelic
frequency of the population in one generation (
q
1
) follow-
ing the introduction of migrant goats will be:
−
s
) is equal to the proportion of the
bb
genotype parents which reproduced in each generation,
also known as their fi tness. The proportion of the total
population in generation 0, which survives to reproductive
age is = 1
The term (1
−
q
0
)
2
. The genetic contribution of the
offspring shows a loss of
s
(1
−
s
(1
−
−
q
)
2
as a result of
selection.
The frequency of alleles in survivors of generation 0 is
the same as the allele frequencies in their offspring at birth
in generation 1. Individuals selected to become parents for
the next generation result in offspring that have a new gene
frequency. Let the new allelic frequency of
b
following
one generation of selection be (1
10
100
90
100
(
qmq
=+−
1
mq
)
=×+×=
05
.
0 01
.
0 059
.
.
1
m
0
The expression for the frequency of allele in the mixed
population after one generation can be simplifi ed as:
qmq
=+( ) =+−
=−+= −
1
mqmq qmq
1
m
0
m
0
0
q
1
). This is equal to the
genetic contribution from all the recessive individuals
(
bb
) and one half of the heterozygotes (
Bb
) as follows:
−
.
The change in allelic frequency from one generation to
another (
mq
mq
q
m q
(
q
) +
q
m
0
0
m
0
0
2
(
11
−
s
)
(
−
q
) +−
q
(
1
q
)
q
) is the difference in the frequency of the alleles
before (
q
0
) and after migration (
q
1
).
Δ
0
0
0
1
(
−
q
) =
. The change in allelic
1
2
Δ
q
=
q
1
−
q
0
=
m
(
q
m
−
11
−−
s
(
q
)
0
q
0
) +
q
0
0.01) = 0.049.
The rate of change in allelic frequency depends on the
proportion of migrants and the difference in allelic fre-
quencies of migrant and native populations. Therefore, the
change in gene frequency of the population as a result of
migration is 0.049.
−
q
0
=
m
(
q
m
−
q
0
) = 0.10
×
(0.5
−
frequency following one generation of selection is the dif-
ference between the previous and the new allelic freq
uencies as follows:
(
(
(
Δ
1
−
q
) =−
1
q
) −−
1
q
)
.
1
0
Substituting (1
−
q
1
) from the earlier equation,
Δ
(1
−
q
)
S
ELECTION
When goats in a population contribute unequally to the next
generation, selection occurs. The reason for this unequal
contribution is that goats differ in their reproductive fi tness,
and some leave no offspring while others leave many.
Consider fi tness to be infl uenced by a single locus repre-
sented by two alleles,
B
and
b
, with allele frequencies of
q
0
and (1
2
2
(
11
−
s
)
(
−
q
) +−
q
(
1
q
)
1
11
sq
−( )
−−
q
0
0
0
0
0
=
−−
(
1
q
) =
0
2
2
11
−−
s
(
q
)
s
(
q
)
The change in allelic frequency is dependent on the
initial gene frequency (1
0
0
−
q
0
) and the intensity of
selection(
s
).
Fitness of genotypes may be described in terms of
complete, partial, no, and overdominance. With incom-
plete or partial dominance a heterozygous individual has
a phenotype intermediate to the two homozygous. The
q
0
) in generation 0. Table 4.2 describes a situation
where selection is against the
bb
genotype, with a propor-
tion,
s
, of the
bb
individuals unable to reproduce.
−
Table 4.2
Genotype of goats and their frequencies, relative fi tness, genetic contribution, and
genotype frequency in survivors.
Genotype of goats
BB
Bb
bb
q
0
2
(1 −
q
0
)
2
Genotypic frequency
2
q
0
(1 −
q
0
)
Relative fi tness
1
1
(1 −
s
)
q
0
2
0
)
2
Genetic contribution
2q
0
(1 −
q
0
)
(1 −
s
)(1 −
q
Frequency in survivors
2
−
(
)
−−
(
) −
(
)
−−
q
2
21
11
qq
s
11
11
−
s
q
0
0
0
2
2
2
11
−−
s
(
q
)
(
q
)
s
(
q
)
0
0
0
Note:
q
and (1 −
q
) are the frequencies of
B
and
b
alleles; (1 −
s
) is the proportion of the
bb
genotype parents
which reproduced in each generation.
