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2p
0.0001
or
p
0.00005.
In conclusion, the allele frequency (p) of the Huntington dis-
ease gene is
0.00005
or
1 in 20,000.
IV. HARDY-WEINBERG AND AUTOSOMAL RECESSIVE
A.
In autosomal recessive disorders, homozygosity (aa) produces the disorder. A good example
of this is
sickle cell anemia
. Homozygosity (aa) for sickle cell anemia produces the disorder in
individuals. Therefore, individuals in the population with sickle cell anemia are homozy-
gotes (rr) and the heterozygotes (Rr) are normal but carriers.
Example 8-1. Sickle Cell Anemia
Question:
A recent study of sickle cell anemia documented 10 new cases out of 6,250 in the
African American population. What is the allele frequency (q) of the sickle cell disease gene
in the African American population? What is the allele frequency (p) of the sickle cell nor-
mal gene in the African American population? What is the frequency of heterozygote carri-
ers in the African American population?
Solution:
1.
10 new cases out of 6,250 means that sickle cell anemia occurs in the African American
population at a
disease frequency of 1 in 625 or 0.0016
(10/6,250).
2.
All the genotypes containing the sickle cell disease gene include the homozygotes (rr; q
2
)
and heterozygotes (Rr; 2pq). The only genotype that produces sickle cell anemia is the
homozygote (rr) so that
q
2
0.0016.
Taking the square root, gives
q
0.04.
In conclusion,
the allele frequency (q) of the sickle cell disease gene is
0.04
or
1 in 25.
3.
The allele frequency (p) of the sickle cell normal gene is
1-q.
This means that
p
1.00
0.04
0.96.
In conclusion, the allele frequency (p) of the sickle cell normal gene is
0.96
or
1 in 1.04.
4.
The frequency of heterozygote carriers is
2pq.
This means that
2pq
2(0.96)(0.04)
0.0768.
In conclusion, the frequency of heterozygote carriers is
0.0768
or
1 in 13.
B.
In rare autosomal recessive disorders, the allele frequency (q) is very small and allele fre-
quency (p) is
1. In these circumstances, the frequency of heterozygous carriers is approxi-
mately equal to 2p.
Example 8-2. Congenital Deafness
Question:
A recent study of congenital deafness caused by a connexin 26 mutation docu-
mented 1 case out of 4,356 in the U.S. population. What is the allele frequency (q) of the
connexin 26 mutation in the U.S. population? What is the allele frequency (p) of the con-
nexin 26 normal gene in the U.S. population? What is the frequency of heterozygote carri-
ers in the U.S. population?
Solution:
1.
One case out 4,356 means that congenital deafness caused by the connexin 26 mutation
occurs in the U.S. population at a
disease frequency of 1 in 4,356 or 0.00023
(1/4356).
2.
All the genotypes containing the connexin 26 mutation include the homozygotes (rr;q
2
)
and heterozygotes (Rr; 2pq). The only genotype that produces congenital deafness is the
homozygote (rr) so that
q
2
0.00023.
Taking the square root gives q
0.0151
.
In conclu-
sion, the allele frequency (q) of the connexin 26 mutation is
0.0151
or
1 in 66.
3.
The allele frequency (p) of the connexin 26 normal gene is 1
q
.
This means that
p
1
0.0151 0.9848 (or 1).
In conclusion, the allele frequency (p) of the connexin 26 nor-
mal gene is
0.9849
or
1 in 1.02.
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Population Genetics
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4.
The frequency of heterozygote carriers is 2pq. This means that 2pq
2(1) (0.0151) 0.0302.
In conclusion, the frequency of heterozygote carries for the connexin 26 mutation is
0.0302
or 1 in 33.
C.
Because only a small proportion of recessive alleles are present in homozygotes selection does
not have much affect on allele frequencies. Even if f
0, it would take many generations to
reduce a mutant allele frequency appreciably. In some cases, the heterozygotes have a selective
advantage. For example, heterozygous carriers of sickle cell trait have resistance to malaria.
Sickle cell trait has its highest carrier frequency in West Africa where malaria is prevalent.
V. HARDY-WEINBERG AND X-LINKED DOMINANT INHERITANCE
In X-linked dominant disorders, the disorder is observed in twice the number of females
than males. Males usually die (a genetic lethal). In X-linked dominant disorders, females who
receive the mutant gene on the X chromosome have the disorder. The genotype of a normal
female is XX and the genotype of an affected female is X
D
X. A good example of this is classic
Rett syndrome.
Example: Classic Rett Syndrome
Question:
A recent study of classic Rett syndrome documented 10 new cases out of 180,000
over the last 10 years in the female U.S. population. What is the allele frequency (q) of the
classic Rett syndrome disease gene in the U.S. population? What is the allele frequency (p)
of the classic Rett syndrome normal gene in the U.S. population?
Solution:
1.
10 new cases out of 180,000 means that classic Rett syndrome occurs in the U.S. popula-
tion at a
disease frequency of 1 in 18,000 or 0.00006
(1/18,000).
2.
In X-linked dominant disorders, the allele frequency (q) of the classic Rett syndrome dis-
ease gene equals the disease frequency. This means that
q
0.00001.
In conclusion, the
allele frequency (q) of the classic Rett syndrome disease gene is
0.00001 or 1 in 100,000.
3.
The allele frequency (p) of the classic Rett syndrome normal gene is
1
q.
This means
that
p
1.00 0.00001 0.99999 (or 1).
In conclusion, the allele frequency (p) of the
classic Rett syndrome normal gene is
0.99999 or 1 in 1.00001.
VI. HARDY-WEINBERG AND X-LINKED RECESSIVE INHERITANCE
In X-linked recessive disorders, the disorder is observed only in males (affected homozygous
females are rare). In X-lined recessive disorders, males who receive the mutant gene on the X
chromosome have the disorder. The genotype of a normal male is XY and the genotype of an
affected male is X
r
Y. A good example of this is
Hunter syndrome (mucopolysaccharidosis II)
.
Example: Hunter Syndrome
Question:
A recent study of Hunter syndrome documented 10 new cases out of 1,000,000
over the last 5 years in the U.S. population. What is the allele frequency (q) of the Hunter
syndrome disease gene in the U.S. population? What is the allele frequency (p) of the
Hunter syndrome normal gene in the U.S. population? What is the frequency of female het-
erozygote carriers?
Solution:
1.
10 new cases out of 1,000,000 means that Hunter syndrome occurs in the U.S. popula-
tion at a
disease frequency of 1 in 100,000 or 0.00001
(1/100,000).
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2.
In X-linked recessive disorders, the allele frequency (q) of the Hunter syndrome disease
gene equals the disease frequency. This means that
q
0.00001.
In conclusion, the allele
frequency (q) of the Hunter syndrome disease gene is
0.00001 or 1 in 100,000.
3.
The allele frequency (p) of the Hunter syndrome normal gene is
1
q.
This means that
p
1.00 0.00001 0.99999 (or 1).
In conclusion, the allele frequency (p) of the Hunter
syndrome normal gene is
0.99999 or 1 in 1.00001.
4.
The frequency of female heterozygote carriers is
2pq,
where p
1. This means that
2pq
2 (1) (0.00001 ) 0.00002.
In conclusion, the frequency of female heterozygote carri-
ers is
0.00002 or 1 in 50,000 females.
VII. MUTATION-SELECTION EQUILIBRIUM
According to the mutation-selection equilibrium theory, gene frequencies in a population are
maintained in equilibrium by mutations that replace disease genes that are selectively lost in
the population by death (e.g., a genetic lethal disease) or reproduction failure (e.g., sterility).
A. Autosomal Dominant Disorders.
If every carrier of a disease gene dies or cannot reproduce,
then every new case of the autosomal dominant disorder arises from a new mutation.
1.
The
disease frequency
is the frequency that a genetic disorder is observed in a population.
The disease frequency is expressed as, for example, 1 in 150,000 people. Therefore, if the
number of affected people in the population studied is
D
and number of people in the
population studied is
N
,
then the
disease frequency
D/N.
2.
The
mutation frequency
is the frequency that a mutation occurs in the DNA. The mutation
frequency is expressed as the number of new mutations per locus or the number of new
mutations per gamete. Therefore, if the number of affected people in the population stud-
ied is
D
and number of people in the population studied is
N
,
then the
mutation frequency
D/2N.
The denominator is 2N because a mutation of either allele at the autosomal locus
could result in the disorder.
Example: Achondroplasia Dwarfism
Question:
A recent study of achondroplasia dwarfism documented 7 new cases out of
250,000 in the U.S. population. In achondroplasia dwarfism, homozygosity is generally a
genetic lethal. What is the disease frequency? What is the mutation frequency?
Solution:
1.
The disease frequency
D/N 7/250,000 0.000028 2.8 10
5
0.0028%. Dividing
100/0.0028
35,714. Therefore, the disease frequency is 0.000028, 2.8 10
5
, 0.0028%,
or 1 in 35,714 people.
2.
The mutation frequency
D/2N 7/2(250,000) 0.000014 1.4 10
5
0.0014%.
Dividing 100/0.000014
71,428. Therefore, the mutation frequency is 0.000014, 1.4
10
5
, 0.0014%, or 1 new mutation per 71,428 loci or 1 new mutation per 71,428 gametes.
B. X-linked Recessive Disorders.
If every carrier of a disease gene dies or cannot reproduce,
then every new case of the X-linked recessive disorder arises from a new mutation.
1.
The
disease frequency
is the frequency that a genetic disorder is observed in the popula-
tion. The disease frequency is expressed as, for example, 1 in 150,000 people. Therefore, if
the number of affected people in the population studied is
D
and number of people in the
population studied is
N
,
then the
disease frequency
D/N.
2.
The
mutation frequency
is the frequency that a mutation occurs in the DNA. The mutation
frequency is expressed as the number of new mutations per locus or the number of new
mutations per gamete. Therefore, if the number of affected people in the population stud-
ied is
D
and number of people in the population studied is
N
,
then the
mutation frequency
D/3N.
The denominator is 3N because in a population of equal numbers of females and
males, only 1/3 of the X chromosomes occur in the male. An X-linked recessive disorder is
observed only in males. Heterozygous females are generally clinically normal.
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Population Genetics
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Example: Fragile X Syndrome
Question:
In a recent study of fragile X syndrome, 15 new cases in boys were documented
among 250,000 births. What is the disease frequency? What is the mutation frequency?
Solution:
1.
The disease frequency
D/N 15/250,000 0.00006 6.0 10
5
0.006%. Dividing
100/0.006
16,666. Therefore, the disease frequency is 0.00006, 6.0 10
5
, 0.006%, or 1
in 16,666 people.
2.
The mutation frequency
D/3N 15/3(250,000) 0.00002 2.0 10
5
0.002%.
Dividing 100/0.002
50,000. Therefore, the mutation frequency is 0.00002, 2.0 10
5
,
0.002%, or 1 new mutation per 50,000 loci or 1 new mutation per 50,000 gametes.
Linkage is the closeness of two or more loci on a chromosome that sort together during
meiosis. Linkage refers to loci, not alleles. Linkage occurs because crossover rarely occurs
between loci that are close together.
Crossover
is the exchange of DNA between homologous
chromosomes that occurs in meiosis I during
chiasma (i.e., the crossover point)
formation.
Linkage is measured only in family pedigrees because meiosis that is required to demon-
strated linkage occurs only during gametogenesis. Consequently, only family members can
be used to determine linkage. The units of measurement of linkage include the following:
A. Recombination Fraction (
) or Recombination %.
If the crossover point does not occur between
the two loci under consideration, then a
parental chromosome
is formed. If the crossover
point does occur between the two loci under consideration, then a
recombinant chromosome
is formed. This is measured by the recombination fraction (
) and the recombination % and
is best illustrated by the example below.
Example:
A mother and father have a family of 8 children. A chromosomal analysis revealed
that 7 children had parental chromosomes, which means the crossover point did not occur
between the two loci under consideration during meiosis. However, 1 child had a recombi-
nant chromosome, which means the crossover point occurred between the two loci under
consideration during meiosis. What is the recombinant fraction (
)? What is the recombi-
nation %?
B. Centimorgan (cM).
cM defines the distance between two loci. 1cM is defined as the distance
between two loci that produces a recombination fraction (
) 0.01 or a recombination % 1%.
1. High linkage.
If two loci are
0.1cM apart,
then the
recombinant fraction (
) 0.001
,
and the
recombinant %
0.1%.
This means there is a
0.1% chance
(i.e., 1 in a 1,000 chance) of
recombination occurring between these loci during crossover. Therefore, if a 1,000
gametes are produced during gametogenesis, 1 gamete will contain a recombinant chro-
mosome.
2. Intermediate linkage.
If two loci are
1cM apart
,
then the
recombinant fraction (
)
0.01,
and the
recombinant %
1.0%.
This means there is a 1% chance (i.e., 1 in a 100 chance) of
recombination occurring between these loci during crossover. Therefore, if a 100
gametes are produced during gametogenesis, 1 gamete will contain a recombinant chro-
mosome.
3. Low linkage.
If two loci are
50cM apart,
then the
recombinant fraction (
) 0.50
,
and the
recombinant %
50%
.
This means there is a 50% chance (i.e., 50 in 100 chance) of recom-
Recombination %
# of recombinant chromosomes
total number of children
100 1/8 0.13 100 13%
Recombination Fraction (
)
# of recombinant chromosomes
total number of children
1/8 0.13
78
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Chapter 8
Population Genetics
79
t a b l e
8-1
Summary Table of Population Genetics
Hardy-Weinberg Calculations
Important Equations: p
2
2pq q
2
1
p
q 1
Autosomal dominant inheritance
Allele frequency (p) of disease gene (D)
Allele frequency (q) of normal gene (d)
1 – p
Autosomal recessive inheritance
Allele frequency (q) of disease gene (r)
Allele frequency (p) of normal gene (R)
1 q
Frequency of heterozygote carriers
2pq
X-linked dominant inheritance
Allele frequency (q) of disease gene (X
D
)
disease frequency
Allele frequency (p) of normal gene (X
d
)
1 q
X-linked recessive inheritance
Allele frequency (q) of disease gene (X
r
)
disease frequency
Allele frequency (p) of normal gene (X
R
)
1 q
Frequency of heterozygote carriers
2pq
Mutation-Selection Equilibrium
Autosomal dominant disorders
Disease frequency
D/N
Mutation frequency
D/2N
X-linked recessive Disorders
Disease frequency
D/N
Mutation frequency
D/3N
Linkage
1cM
0.01 1% recombination %
LOD
log
10
Probability that 2 loci are linked
Probability that 2 loci are not linked
Recombination %
# of recombinant chromosomes
total number of children
100
Recombination fraction (
)
# of recombinant chromosomes
total number of children
2disease frequency
disease frequency
2
bination occurring between these loci during crossover. Therefore, if a 100 gametes are
produced during gametogenesis, 50 gametes will contain a recombinant chromosome.
C. Logarithm of the Odds (LOD) Score (or Z).
A LOD score of
3 indicates definite evidence FOR linkage between two loci.
A LOD score of
2 indicates definite evidence AGAINST linkage between two loci
LOD
log
10
probability that 2 loci are linked
probability that 2 loci are not linked
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