Population Genetics
Medical Genetics
Population genetics investigates genetic
structure and genetic variation among
individuals within groups.
Mendelian population is a group of
interbreeding individuals,who live in the
same place and share a common set of
genes (gene pool).
Allelic frequency,a proportion or a
percent of allele.
Genotypic frequency,the number of
individuals with one particular genotype
divided by the total number of individuals
in the population.
Gene Frequency &
Genotypic Frequency
Gene Frequency &
Genotypic Frequency
M
N
Genotype,MM 5; MN 7; NN 4
Allelic frequency of M,p ＝ (2× 5＋ 7)/(2× 16)＝ 0.5312
Allelic frequency of N,q ＝ (2× 4＋ 7)/(2× 16)＝ 0.4688
Law of Genetic Equilibrium
Hardy-Weinberg law
Hardy GH Weinberg W
Explains how Mendelian segregation
influences allelic and genotypic frequencies
in a population.
Law of Genetic Equilibrium
Hardy-Weinberg law
Law of Genetic Equilibrium
Assumptions
Large population
Random mating
No natural selection
No mutation
No migration
If assumptions are met,population will be
in genetic equilibrium.
Hardy-Weinberg law
Allele frequencies do not change over
generations.
p＋ q＝ 1
p2＋ 2pq＋ q2＝ 1
p2,frequency of AA
2pq,frequency of Aa
q2,frequency of aa
Law of Genetic Equilibrium
Hardy-Weinberg law
Genotypic frequencies will remain in
the following proportions:
Law of Genetic Equilibrium
Hardy-Weinberg law
Allele frequencies do not change over
generations.
Genotypic frequencies do not change
over generations.
After only one generation of random
mating,population will be in genetic
equilibrium.
f (a) = q
f (A) = 1－ q
= q2
Law of Genetic Equilibrium
p＋ q＋ r＝ 1
(p＋ q＋ r)2＝ p2＋ 2pq＋ q2＋ 2pr＋ r2＋ 2qr＝ 1
Multiple allele (IA,IB,i)
f (IA) = p
f (IB) = q
f (i) = r
Law of Genetic Equilibrium
Blood group A B O AB
Genotype IAIA,IAi IBIB,IBi ii IAIB
Genotypic frequency p2＋ 2pr q2＋ 2qr r2 2pq
Law of Genetic Equilibrium
Females,f(XA)＝ 2/3p
Males,f(XA)＝ 1/3p; f(Xa) ＝ 1/3q
f(Xa)＝ 2/3q＝ 2/3q(p＋ q)＝ 2/3q2＋ 2/3pq
XAY XaY
XAXA＝ 2/3p2 ; XAXa ＝ 4/3pq; XaXa ＝ 2/3q2
＝ 2/3p(p＋ q)＝ 2/3p2＋ 2/3pq
X-linked alleles
XA (p) Xa (q) Y
XA (p) XAXA (p2) XAXa (pq) XAY (p)
Xa (q) XAXa (pq) XaXa (q2) XaY (q)
Females,Frequencies are the same for any
other locus,(p2 +2pq + q2 )
Males,Genotype frequencies are the same
as allele frequencies,(p + q)
Law of Genetic Equilibrium
X-linked alleles
Affected
2pq
p2 ＋ 2pq ≈ 1
Derivation
AD diseases
Affected of Heterozygote
Almost all of the affected are heterozygote
2pq ＝ 2q － 2q2＝ 2q(1－ q) ≈ 2q
2pq ≈ 2q
The heterozygote carrier frequency is twice
the frequency of the mutant allele.
Derivation
AR diseases
2pq
q2 ≈
2q
q2 ＝
2
q
The number of heterozygote carriers in the
population is much larger than the affected.
The ratio increases as the disease frequency
decreases.
Derivation
AR diseases
p
p2 ＋ 2pq ≈
1
2＝
1
p ＋ 2q ＝
1
p ＋ 2(1－ p) ＝
1
2－ p
The ratio of affected females to the males
is approximately 2 to 1.
Derivation
XD diseases
The ratio increases as the disease frequency
decreases.
q
q2 ＝
1
q
More affected males than affected females
Derivation
XR diseases
Mutation
Selection
Genetic Drift
Isolation
Migration
Consanguineous Marriage
Factors that Alter
Genetic Equilibrium
Genetic Load
The reduction in fitness due to deleterious
or lethal genes in a population.
Indicated by the number of deleterious
genes that individual’s possess.
Genetic Load
The reduction in fitness due to
deleterious or lethal mutations in a
population.
Mutation load
Mutation rate
Selection coefficient (S)
Genetic Load
The genetic disability sustained by a
population due to genes segregating from
advantageous heterozygotes to less fit
homozygotes.
Segregation load
Mutation
Mutation rate
The mutation rate of each gene is expressed
by the number of mutation per million genes per
generation (n× 10－ 6/gene/generation).
A pair of alleles A and a
f(A) is p,the mutation rate is u
f(a) is q,the mutation rate is v
Mutation
q ＝ uu ＋ v p ＝ vu ＋ v
p ＝ qv;?q ＝ pu
Back
Mutation
Neutral mutation
A mutation that has no effect on the
Darwinian fitness of its carriers.
A mutation that has no phenotypic
effect.
Selection
Selection represents the action of environmental
factors on a particular phenotype,and hence its
genotype,and may be positive or negative,It is the
consequence of differences in the fitness of
individual phenotypes.
Fitness ( f ),One can survive and contribute to the
gene pool of the succeeding generation,It is a measure
of relative fertility.
Selection coefficient (S) means
reducing fitness under the action of
selection,
S＝ 1－ f
Selection
Selection
Selection pressure
Mutation pressure
The effectiveness of natural selection
in altering the genetic composition of a
population over a series of generations.
The continued production of an allele
by mutation.
Mutation
Selection
Selection
0 1 2 3 4 5 6 7 8 9 10 11
Number of Deleterious Mutations
Fr
eq
ue
nc
y
Mutation will push the mean of this
distribution up
Selection will push the mean down.
AD disease v ＝ Sp ＝ S × 1/2H
Action of Selection
AR disease u ＝ Sq2
XR disease u ＝ Sq/3
XD disease v ＝ Sp
Increasing of Selection Pressure
n 1q
n
＝ 1q－
AD disease
AR disease
XR disease
XD disease
Decreasing of Selection Pressure
q ＋ M× 10－ 6 × n = 2q
q
M× 10－ 6n ＝
AD disease
AR disease
XR disease
XD disease
Polymorphism
Polymorphism
The existence of two or more
genetically different classes in the
same interbreeding population.
A polymorphic locus at which the
rarer allele has a frequency more than
0.01.
Polymorphism
Back
Polymorphism
Balanced polymorphism
Genetic polymorphism maintained in a
population because the heterozygotes for
the alleles under consideration have a
higher adaptive than either homozygore.
Random Genetic Drift
Genetic drift is the random change in
allele frequency from one generation to
the next due to chance fluctuations (as
opposed to due to selection pressure).
Isolated Island Model
Random Genetic Drift
AA× Aa
aa× AA
Aa× Aa
aa× aa
AA Aa Aa aa
AA
Aa
Aa
aa ×
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Generation
25
Fr
eq
uen
cy
of
al
lel
e A
2500
250
Random Genetic Drift
Back
Random Genetic Drift
ABO frequency of American indians
North America,IA 0.018; IB 0.009; i 0.973
Blackfeet,IA 0.5
Isolation
Geographic isolation
Social isolation
Founder effect
Back
A high frequency of a mutant gene in a
population founded by a small ancestral
group.
Migration
The difference of allele frequency
between two populations
Gene flow,gradual diffusion of genes from
one population to another by
migration and intermarriage.
Number of immigrators (gene)
Back
Migration pressure
Consanguineous Marriage
Inbreeding coefficient (F)
The probability that an individual has a
pair of alleles that are identical by descent
from a common ancestor
F of Brother-Sister Marriage
S
A1A2 A3A4
A1A1
A2A2
A3A3
A4A4
F of Uncle-Niece Marriage
S
A1A2 A3A4
A1A1
A2A2
A3A3
A4A4
F of Half-Sib Marriage
A1A2A3A4
A1A1
A2A2
A5A6
S
F of Consanguineous Marriage
F ＝ 4 × (1/2)n & F ＝ 2 × (1/2)n
4 ×,two common ancestor (4 chromosomes)
n ＝ 2× generations
2 ×,one common ancestor (2 chromosomes)
n,steps of alleles by descent
n ＝ generation1＋ generation2
X-linked allele
Only female has the inbreeding coefficient (Fx)
Consanguineous Marriage
One Married
with Daughter of Maternal Aunt
X1Y X2X3
X1X1
X2X2
X3X3
S
One Married
with Daughter of Maternal Uncle
S
X1Y X2X3
X1X1
X2X2
X3X3
One Married
with Daughter of Paternal Aunt
X1Y X2X3
X1X1
X2X2
X3X3
S
One Married
with Daughter of Paternal Uncle
X1Y X2X3
X1X1
X2X2
X3X3
S
In X-linked allele,marriage with
maternal cousin has more risk than
paternal cousin.
Consanguineous Marriage
Average inbreeding coefficient (a)
a = ΣMi?FiN
a ＞ 0.01
Back
Consanguineous Marriage
Medical Genetics
Population genetics investigates genetic
structure and genetic variation among
individuals within groups.
Mendelian population is a group of
interbreeding individuals,who live in the
same place and share a common set of
genes (gene pool).
Allelic frequency,a proportion or a
percent of allele.
Genotypic frequency,the number of
individuals with one particular genotype
divided by the total number of individuals
in the population.
Gene Frequency &
Genotypic Frequency
Gene Frequency &
Genotypic Frequency
M
N
Genotype,MM 5; MN 7; NN 4
Allelic frequency of M,p ＝ (2× 5＋ 7)/(2× 16)＝ 0.5312
Allelic frequency of N,q ＝ (2× 4＋ 7)/(2× 16)＝ 0.4688
Law of Genetic Equilibrium
Hardy-Weinberg law
Hardy GH Weinberg W
Explains how Mendelian segregation
influences allelic and genotypic frequencies
in a population.
Law of Genetic Equilibrium
Hardy-Weinberg law
Law of Genetic Equilibrium
Assumptions
Large population
Random mating
No natural selection
No mutation
No migration
If assumptions are met,population will be
in genetic equilibrium.
Hardy-Weinberg law
Allele frequencies do not change over
generations.
p＋ q＝ 1
p2＋ 2pq＋ q2＝ 1
p2,frequency of AA
2pq,frequency of Aa
q2,frequency of aa
Law of Genetic Equilibrium
Hardy-Weinberg law
Genotypic frequencies will remain in
the following proportions:
Law of Genetic Equilibrium
Hardy-Weinberg law
Allele frequencies do not change over
generations.
Genotypic frequencies do not change
over generations.
After only one generation of random
mating,population will be in genetic
equilibrium.
f (a) = q
f (A) = 1－ q
= q2
Law of Genetic Equilibrium
p＋ q＋ r＝ 1
(p＋ q＋ r)2＝ p2＋ 2pq＋ q2＋ 2pr＋ r2＋ 2qr＝ 1
Multiple allele (IA,IB,i)
f (IA) = p
f (IB) = q
f (i) = r
Law of Genetic Equilibrium
Blood group A B O AB
Genotype IAIA,IAi IBIB,IBi ii IAIB
Genotypic frequency p2＋ 2pr q2＋ 2qr r2 2pq
Law of Genetic Equilibrium
Females,f(XA)＝ 2/3p
Males,f(XA)＝ 1/3p; f(Xa) ＝ 1/3q
f(Xa)＝ 2/3q＝ 2/3q(p＋ q)＝ 2/3q2＋ 2/3pq
XAY XaY
XAXA＝ 2/3p2 ; XAXa ＝ 4/3pq; XaXa ＝ 2/3q2
＝ 2/3p(p＋ q)＝ 2/3p2＋ 2/3pq
X-linked alleles
XA (p) Xa (q) Y
XA (p) XAXA (p2) XAXa (pq) XAY (p)
Xa (q) XAXa (pq) XaXa (q2) XaY (q)
Females,Frequencies are the same for any
other locus,(p2 +2pq + q2 )
Males,Genotype frequencies are the same
as allele frequencies,(p + q)
Law of Genetic Equilibrium
X-linked alleles
Affected
2pq
p2 ＋ 2pq ≈ 1
Derivation
AD diseases
Affected of Heterozygote
Almost all of the affected are heterozygote
2pq ＝ 2q － 2q2＝ 2q(1－ q) ≈ 2q
2pq ≈ 2q
The heterozygote carrier frequency is twice
the frequency of the mutant allele.
Derivation
AR diseases
2pq
q2 ≈
2q
q2 ＝
2
q
The number of heterozygote carriers in the
population is much larger than the affected.
The ratio increases as the disease frequency
decreases.
Derivation
AR diseases
p
p2 ＋ 2pq ≈
1
2＝
1
p ＋ 2q ＝
1
p ＋ 2(1－ p) ＝
1
2－ p
The ratio of affected females to the males
is approximately 2 to 1.
Derivation
XD diseases
The ratio increases as the disease frequency
decreases.
q
q2 ＝
1
q
More affected males than affected females
Derivation
XR diseases
Mutation
Selection
Genetic Drift
Isolation
Migration
Consanguineous Marriage
Factors that Alter
Genetic Equilibrium
Genetic Load
The reduction in fitness due to deleterious
or lethal genes in a population.
Indicated by the number of deleterious
genes that individual’s possess.
Genetic Load
The reduction in fitness due to
deleterious or lethal mutations in a
population.
Mutation load
Mutation rate
Selection coefficient (S)
Genetic Load
The genetic disability sustained by a
population due to genes segregating from
advantageous heterozygotes to less fit
homozygotes.
Segregation load
Mutation
Mutation rate
The mutation rate of each gene is expressed
by the number of mutation per million genes per
generation (n× 10－ 6/gene/generation).
A pair of alleles A and a
f(A) is p,the mutation rate is u
f(a) is q,the mutation rate is v
Mutation
q ＝ uu ＋ v p ＝ vu ＋ v
p ＝ qv;?q ＝ pu
Back
Mutation
Neutral mutation
A mutation that has no effect on the
Darwinian fitness of its carriers.
A mutation that has no phenotypic
effect.
Selection
Selection represents the action of environmental
factors on a particular phenotype,and hence its
genotype,and may be positive or negative,It is the
consequence of differences in the fitness of
individual phenotypes.
Fitness ( f ),One can survive and contribute to the
gene pool of the succeeding generation,It is a measure
of relative fertility.
Selection coefficient (S) means
reducing fitness under the action of
selection,
S＝ 1－ f
Selection
Selection
Selection pressure
Mutation pressure
The effectiveness of natural selection
in altering the genetic composition of a
population over a series of generations.
The continued production of an allele
by mutation.
Mutation
Selection
Selection
0 1 2 3 4 5 6 7 8 9 10 11
Number of Deleterious Mutations
Fr
eq
ue
nc
y
Mutation will push the mean of this
distribution up
Selection will push the mean down.
AD disease v ＝ Sp ＝ S × 1/2H
Action of Selection
AR disease u ＝ Sq2
XR disease u ＝ Sq/3
XD disease v ＝ Sp
Increasing of Selection Pressure
n 1q
n
＝ 1q－
AD disease
AR disease
XR disease
XD disease
Decreasing of Selection Pressure
q ＋ M× 10－ 6 × n = 2q
q
M× 10－ 6n ＝
AD disease
AR disease
XR disease
XD disease
Polymorphism
Polymorphism
The existence of two or more
genetically different classes in the
same interbreeding population.
A polymorphic locus at which the
rarer allele has a frequency more than
0.01.
Polymorphism
Back
Polymorphism
Balanced polymorphism
Genetic polymorphism maintained in a
population because the heterozygotes for
the alleles under consideration have a
higher adaptive than either homozygore.
Random Genetic Drift
Genetic drift is the random change in
allele frequency from one generation to
the next due to chance fluctuations (as
opposed to due to selection pressure).
Isolated Island Model
Random Genetic Drift
AA× Aa
aa× AA
Aa× Aa
aa× aa
AA Aa Aa aa
AA
Aa
Aa
aa ×
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Generation
25
Fr
eq
uen
cy
of
al
lel
e A
2500
250
Random Genetic Drift
Back
Random Genetic Drift
ABO frequency of American indians
North America,IA 0.018; IB 0.009; i 0.973
Blackfeet,IA 0.5
Isolation
Geographic isolation
Social isolation
Founder effect
Back
A high frequency of a mutant gene in a
population founded by a small ancestral
group.
Migration
The difference of allele frequency
between two populations
Gene flow,gradual diffusion of genes from
one population to another by
migration and intermarriage.
Number of immigrators (gene)
Back
Migration pressure
Consanguineous Marriage
Inbreeding coefficient (F)
The probability that an individual has a
pair of alleles that are identical by descent
from a common ancestor
F of Brother-Sister Marriage
S
A1A2 A3A4
A1A1
A2A2
A3A3
A4A4
F of Uncle-Niece Marriage
S
A1A2 A3A4
A1A1
A2A2
A3A3
A4A4
F of Half-Sib Marriage
A1A2A3A4
A1A1
A2A2
A5A6
S
F of Consanguineous Marriage
F ＝ 4 × (1/2)n & F ＝ 2 × (1/2)n
4 ×,two common ancestor (4 chromosomes)
n ＝ 2× generations
2 ×,one common ancestor (2 chromosomes)
n,steps of alleles by descent
n ＝ generation1＋ generation2
X-linked allele
Only female has the inbreeding coefficient (Fx)
Consanguineous Marriage
One Married
with Daughter of Maternal Aunt
X1Y X2X3
X1X1
X2X2
X3X3
S
One Married
with Daughter of Maternal Uncle
S
X1Y X2X3
X1X1
X2X2
X3X3
One Married
with Daughter of Paternal Aunt
X1Y X2X3
X1X1
X2X2
X3X3
S
One Married
with Daughter of Paternal Uncle
X1Y X2X3
X1X1
X2X2
X3X3
S
In X-linked allele,marriage with
maternal cousin has more risk than
paternal cousin.
Consanguineous Marriage
Average inbreeding coefficient (a)
a = ΣMi?FiN
a ＞ 0.01
Back
Consanguineous Marriage
