Agriculture Reference
In-Depth Information
Selection with dominance will change allelic frequency
by acting against the recessive allele (1
gene frequency has a variance equal to
qq
N
e
(
2
−
1
)
. The
q
). This will
decrease the frequency of the recessive allele (1
−
−
q
) and
change in mean performance from one generation to the
next has variance due to genetic drift (
ˆ
the genotype (1
q
)
2
and increase the frequency of the
dominant allele
q
and genotype
q
2
. The change will be
gradual and steady with the greatest change occurring at
intermediate frequencies (Table 4.3 ).
−
σ
2
) which can be
estimated as
ˆ
σ
g
2
, where
ˆ
σ
2
is additive genetic variance.
This can be rewritten as
ˆ
N
e
ˆ
σ
2
=Δ
2
F
σ
2
.
d
g
Extension of the Hardy - Weinberg Equilibrium
The Hardy-Weinberg equilibrium also applies to situations
where there are more than two alleles in a locus, more than
a single locus, and sex-linked loci in the absence of muta-
tion, migration, selection and genetic drift. Under equilib-
rium conditions with a large random mating population,
the genotype and gene frequencies will remain unchanged
from generation to generation. These extensions are
beyond the scope of the present chapter, but reference to
them can be found in a text such as Falconer and MacKay
(1996) .
G
ENETIC
D
RIFT
Dispersive forces of evolutionary signifi cance infl uence
gene frequencies during the assortment of chromosomes at
meiosis, and in other processes involved in the transmis-
sion of genes from one generation to the next. The theoreti-
cal basis of genetic drift is the sampling of families from
populations, individual animals from families, and genes
within those individuals that cause the gene frequencies to
vary in either direction from their initial values in each
generation. The effect of genetic drift is most pronounced
in small populations.
In closed populations with a limited number of parents,
the sampling variance increases homozygosity above that
in the initial population. This effect is a result of the effec-
tive number of parents (
N
e
), which is a function of the
number of breeding bucks
N
m
and does
N
f
in the popula-
tion. When mating is random, each parent has an “equal
chance” of contributing to the next generation. It has been
shown, however, that the number of kids per parent follows
a Poisson distribution in many cases. The effective number
of parents (
N
e
) will be
4
NN
NN
S
EX
-
LINKED
L
OCI
There are two sex chromosomes in mammals denoted by
X
and
Y
. The sex chromosome makeup of females is
XX
referred to as the homogametic sex, and of males is
XY
the
heterogametic sex. Of genes found on the sex chromo-
somes, most are associated with the
X
chromosome, very
few with the
Y
chromosome. In referring to sex-linked loci
it is usually loci on the
X
chromosome that are being con-
sidered, and that is the case here. Note that females have
two
X
chromosomes, and the behavior of a sex-linked
character in females will be the same as for characters
affected by genes on autosomes (that is, the genotype will
be composed of two alleles). Gene action such as domi-
nance or additivity can contribute to the phenotype. With
males, on the other hand, they possess only one
X
chromo-
some, so the phenotype will be the result of only one allele,
and gene action such as dominance will play no role. This
difference between males and females thus affects the
behavior of gene and genotype frequencies. Suppose a
sex-linked character has two alleles in a population,
B
and
b
, with frequencies
p
and
q
, respectively. At Hardy-
Weinberg equilibrium, females will have genotypes,
X
B
X
B
(
p
2
),
X
B
X
b
(2
pq
) and
X
b
X
b
(
q
2
). Males in the population will
be
X
B
Y
(
p
) and
X
b
Y
(
q
).
Transmission of genes from male and female parents
to male and female offspring is also different. Females
receive one
X
chromosome from each parent, while males
receive their
X
chromosome only from their female parent.
Gene frequencies may differ between males and females
mf
which can be rewritten
+
m
f
as
1
1
1
=
+
(Wright, 1931). In a random
NN N
e
4
4
m
f
breeding population the change in inbreeding level (
F
)
per generation depends upon the effective population size
Δ
1
2
N
e
1
NN
m
1
and is equal to
which can be rewritten as
.
+
8
f
This change in inbreeding level,
F
, is a measure of the
increase in homozygosity in the population.
Example: In a population of goats consisting of 10 bucks
and 100 does that produces kids, the effective population
size (
N
e
) will be
4
Δ
NN
NN
410100
10
××
+
mf
=
=
36 4
.
. Also
+
100
m
f
1
1
2364
0 0138
Δ
F
=
=
=
.
per generation, indicating
2
N
e
×
.
that 1.38% more will become homozygous for a given
locus in this generation.
When
q
is the gene frequency of the favorable allele
and
N
e
is the effective number of parents, the change in
