Chapter 23
Population Genetics
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Chapter Outline
The Theory of Allele Frequencies
Natural Selection
Random Genetic Drift
Populations in Genetic Equilibrium
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Population Genetics
Population genetics studies genes in groups
of individual.
It focuses on
– Allelic variation among individuals
– Transmission of allelic variants from parents to
offspring generation after generation
– Temporal changes in the genetic makeup of a
population due to systematic and random
evolutionary forces
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The Theory of Allele Frequencies
…to predict the frequencies of the genotypes
…frequency of each of the gene’s alleles
…the frequencies of the different types of
homogozygotes and heterozygotes of genes
Random mating (no selection)
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Estimating Allele Frequencies:
The MN Blood Type
MN blood groups (glycophorin A=antigen)
The M allele encodes Ser at position 1 (Ser-1) and Gly at position 5 (Gly-5)
The N allele encodes Leu-1 and Glu-5
The M-N blood type is determined by two
alleles of a gene on chromosome 4.
– LM produces the M blood type.
– LN produces the N blood type.
– LMLN heterozygotes have the MN blood type.
After the MN blood groups have been
determined for a sample, allele frequencies
can be calculated.
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Allele : It is the alternative form of a gene for a character producing different effects.
Number of copies of a particular allele
Frequencies of an allele:
Number of copies of ALL alleles at the locus
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Estimation of Allele Frequencies
The total number of alleles is two times
the sample size: 2  6129 = 12,258.
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The frequency of the LM allele is 2 times the
number of LMLM homozygotes plus the
number of LMLN heterozygotes, all divided by
the total number of alleles: [(2  1787) +
3039] / 12,258 = 0.5395.
f (LM) =
2n LM LM + n LM LN
2N
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The frequency of the LN allele is 2 times
the number of LNLN homozygotes plus
the number of LMLN heterozygotes, all
divided by the total number of alleles:
[(2  1303) + 3039] / 12,258 = 0.4605.
f (LN) =
2n LN LN + n LM LN
2N
Allele Frequencies
Letting p represent the frequency of the LM
allele and letting q represent the frequency of
the LN allele, we estimate that p = 0.5395 and
q = 0.4605, which is the variation of these
alleles in this particular population.
Because LM and LN represent 100% of the
alleles of this gene, p + q = 1.
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The Hardy-Weinberg Principle
The Hardy-Weinberg principle
--describes a mathematical relationship
between allele frequencies and
genotype frequencies.
--allows the prediction of a population’s
genotype frequencies from its allele
frequencies.
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Assume that in a population, a
particular gene segregates two alleles,
A and a, with frequencies of p and q,
respectively.
If members of the population mate
randomly, the diploid genotypes of the
next generation will be formed by the
random union of haploid eggs and
haploid sperm.
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The probability of producing an AA
homozygote is p  p = p2.
The probability of producing an aa
homozygote is q  q = q2.
A heterozygote may be produced by
– an A sperm uniting with an a egg and
– an a sperm uniting with an A egg
Each of these events occurs with probability
p  q, so the total probability of forming an Aa
zygote is 2pq.
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Genotypic Frequencies
The predicted frequencies of the
genotypes in the population are
– AA, …..f (AA)=p2
– Aa,….f (Aa)=2pq
– aa,….f (AA)=q2
These predicted frequencies can be
obtained by expanding the binomial
expression (p + q)2 = p2 + 2pq + q2
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allele frequencies
p+q = 100 %=1
genotype frequencies
M
p= f (L ) =
q= f (LN) =
2n LM LM + n LM LN
2N
2n LN LN + n LM LN
2N
f (AA)=p2
f (Aa)=2pq
f (AA)=q2
Hardy-Weinberg Equilibrium
The key assumption underlying the HardyWeinberg principle is random mating.
… and no differential survival or
reproduction exists among members of the
population, the Hardy-Weinberg genotype
frequencies persist generation after
generation…the genotype is expected to
produce p2 + 2pq + q2 the population is at
equilibrium….
 This condition is Hardy-Weinberg
equilibrium. © John Wiley & Sons, Inc.
Predicting Genotype Frequencies
With the Hardy-Weinberg principle, allele
frequencies can be used to predict the
genotype frequencies.
For the MN blood type example, p = 0.5395
and q = 0.4605
The predicted genotype frequencies are
LMLM p2 = (0.5395)2 = 0.2911
LMLN 2pq = 2 (0.5395) (0.4605) = 0.4968
LNLN q2 = (0.4605)2 = 0.2121
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Do these predictions fit the data?
First we must calculate the predicted
genotype numbers by multiplying the HardyWeinberg frequencies by the sample size
(6129).
Genotype
LMLM
LMLN
LNLN
Predicted Number
0.2911  6129 = 1784.2
0.4968  6129 = 3044.8
0.2121  6129 = 1300.0
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Next, we check for agreement between
the observed and predicted numbers by
calculating a chi-square statistic.
1787 1784.2 3039  3044.8 1303 1300.0

2
 


 0.0223
1784.2
3044.8
1300.0
2
2
2

This chi-square has 3 –1 = 2 degree of
freedom
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2 = 0.0223
1 degree of freedom
The critical value for 2 degree of
freedom is 5.991.
Conclusions:
– The predicted genotype frequencies are in
agreement with the observed frequencies.
– In this population, the M-N genotypes are
in Hardy-Weinberg proportions.
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Predicting Allele Frequencies
from Genotype Frequencies
In the United States, the incidence of
the autosomal recessive disorder
phenylketonuria (PKU) is about 0.0001.
The incidence of PKU represents the
frequency of mutant homozygotes in the
population.
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Homozygous mutant individuals should occur with a
frequency equal to the square of the mutant allele
frequency, q.
q2 = 0.0001
Taking the square root, q = 0.01
Because p + q = 1, we know that p = 0.99.
p = 0.99 and q = 0.01
The frequency of heterozygous carriers is 2pq =
2(0.99)(0.01) = 0.0198.
p+q=100%, p=99%; q=1%;
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The Hardy-Weinberg Principle
for X-Linked Genes
For X-linked genes, allele frequencies
are estimated from the frequencies of
the genotypes in males.
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Example: Color Vision
Genotype
Sex Genotype
Frequency
Males X1Y f (X1Y)= p = 0.88
X2Y f (X2Y)= q = 0.12
Allele
Phenotype Frequency
Normal vision
Color blind
Females X1X1 f (X1X1)=p2 = 0.77
X1X2 f (X1X2)= 2pq = 0.21
f (X2X2)=q2 = 0.02
X2X2
Normal vision
Normal vision
Color blind
X1Y=C
X2Y=c
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f (X1)=p
f (X2)=q
Genes with Multiple Alleles
For genes with multiple alleles, the
Hardy-Weinberg genotype proportions
are obtained by expanding a binomial
expression.
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Example: A-B-O Blood Type
The A-B-O blood types are determined
by three alleles, IA, IB, and I, with
frequencies p, q, and r, respectively.
Genotypes can be calculated by
expanding the trinomial
(p + q + r)2 = p2 + q2 + r2 + 2pq + 2qr + 2pr
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Phenotype
Blood Type
A
B
AB
O
Genotype
IAIA
IAi
IBIB
IBi
IAIB
ii
G
Frequency
p2 =f (IAIA)
2pr
q2 =f (IBIB)
2qr
2pq
r2 =f (Ii Ii)
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A
Frequency
f (IA)=p
f (Ii)=r
f (Ib)=q
Exceptions to the HardyWeinberg Principle
Nonrandom mating
Unequal survival
Population subdivision
Migration
It will disrupt Hardy-Weinberg equilibrium
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Nonrandom Mating
 Nonrandom mating includes
– Consanguineous mating (mating between genetically related
individuals)
– Assortative individuals (mating between individuals with
similar phenotypes)
 Both consanguineous mating and assortative mating reduce the
frequency of heterozygotes and increase the frequency of
homozygotes compared to the Hardy-Weinberg genotype
frequencies.
 The effects of consanguineous mating can be quantified using
the inbreeding coefficient, F.
 F=1
Self-fertilization
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Unequal Survival
If zygotes produced by random mating have
different survival rates….
Heterozygotes == Homozygotes
A sample of 200 adults yielded the following
data:
Genotype
A1A1
A1A2
A2A2
Observed Number
26
140
34
Expected Number
46.1
99.8
54.1
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Population Subdivision
Single interbreeding unit,---non homogenous
There are no mating restrictions at all
It is panmictic.
Panmixis implies that any member of the
population is able to mate with any other
member.
In nature, populations may be subdivided due
to geographical or ecological barriers that
may be correlated with genetic differences.
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Migration
The introduction of genes by recent
migrations can alter allele and
genotype frequencies within a
population and disrupt Hardy-Weinberg
equilibrium.
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average
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Random Genetic Drift
Allele frequencies change unpredictably
in populations because of uncertainties
during reproduction.
Genetic drift, the random change of allele
frequencies in populations.
It is due to uncertainties in Mendelian
segregation.
Non-Mendelian inheritance:
Gene conversion: mismatch repair
Extranuclear DNA
Random Changes in Allele
Frequencies
C
c
C
CC
Cc
c
cC
cc
Offspring’s probability for CC is
1/2 x 1/2=1/4
2 offspring is 1/16
of population
Offspring’s probability for cc is
1/2 x 1/2=1/4
2 offspring is 1/16
Offspring’s probability for CC and Cc
is 1/4 x 1/2 x 2=1/4=4/16
Offspring’s probability for cc and Cc
is 1/2 x 1/4 x 2=1/4=4/16
Factors Contributing to
Random Genetic Drift
There is always uncertainty as to
which allele a given offspring will
receive.
There is random variation in the
number of offspring that a parent
produces.
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The Effects of Population Size
In large populations, the effect of genetic drift
is minimal.
In small populations, genetic drift may be the
primary evolutionary force.
The effect of population size is determined by
monitoring the frequency of heterozygotes, or
the heterozygosity of a population over time.
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H  1/2N
p=q=0.5
N=4
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