Population Genetics
Subfield of Genetics
Subject is genetic differences within and
between populations
Part of evolutionary biology
Population Genetics
Genetics definition
• Genetics is the study of genes, genetic
variation, and heredity in living
organisms.
Genes
A gene is a sequence of DNA or RNA
It codes for a molecule that has a
biological function
Alleles
• An allele is a variant form of a given gene
• Different alleles can result in different observable
phenotypic traits, e.g. different pigmentation and
color variation in Gregor Mendel's discovery that
the white and purple flower colors in pea plants
were the result of "pure line" traits which could
be used as a control for future experiments
• Many genetic variations result in little or no
observable variation. The word "allele" is a short
form
Population Genetics
Examine phenomena
• population structure
• adaptation
• speciation
Population Genetics
• Founders were Sewall Wright, J. B. S.
Haldane and Ronald Fisher
• Evolutionary synthesis
• Mathematical discipline
• Theoretical
• Laboratory
• Field
Population Genetics
• Models are used both for statistical
inference from DNA sequence data and
for proof/disproof of concept
• Phenotypic approaches to modelling
evolution
• Evolutionary game theory
• Adaptive dynamics
Population Genetics
• Genetic phenomena
• Dominance
• Epistasis
• Genetic recombination and linkage
disequilibrium
Epistasis
• Phenomenon that consists of the effect
of one gene being dependent on the
presence of one or more 'modifier
genes' (genetic background)
• Epistatic mutations have different
effects in combination than individually
• Concept from genetics, biochemistry,
population genetics, computational
biology and evolutionary biology
Epistasis
• The gene for total
baldness is
epistatic to those
for blond hair or
red hair. The haircolour genes are
hypostatic to the
baldness gene.
The baldness
phenotype
supersedes genes
for hair colour
and so the effects
are non-additive
Population Genetics
• Population genetics began as a reconciliation of
Mendelian inheritance and biostatistics models.
Natural selection will only cause evolution if there is
enough genetic variation in a population.
• The Hardy–Weinberg principle provides the solution
to how variation is maintained in a population with
Mendelian inheritance.
• According to this principle, the frequencies of alleles
(variations in a gene) will remain constant in absence
of selection, mutation, migration or genetic drift.
Key Points
 What is population genetics?
 How to describe genetic structures?
 The Hardy-Weinberg Law.
 Factors that disturb Hardy-Weinberg
equilibrium.
 Consanguinity.
Population Genetics
• genetic structure of a population
• alleles
• genotypes
group of individuals
of the same species
that can interbreed
Population Genetics
• Is the quantitative study of the
distribution of genetic variation in
populations and of how the
frequencies of genes and genotypes
are maintained or change.
Describing genetic structure
• genotype frequencies
• allele frequencies
rr = white
Rr = pink
RR = red
Describing genetic structure
• genotype frequencies
• allele frequencies
200 white
500 pink
genotype
frequencies:
200/1000 = 0.2 rr
500/1000 = 0.5 Rr
300 red
total = 1000 flowers
300/1000 = 0.3 RR
Describing genetic structure
• genotype frequencies
• allele frequencies
200 rr = 400 r
500 Rr = 500 r
= 500 R
300 RR = 600 R
allele
frequencies:
900/2000 = 0.45 r
1100/2000 = 0.55 R
total = 2000 alleles (gene pool)
• Gene pool is a collection of all the
alleles at a particular locus for the
entire population.
• For autosomal loci, the size of the
gene pool at one locus is twice the
number of individuals in the
population.
For example: HIV resistance---ΔCCR5
Number of
People
Observed Relative
Genotype Frequency
Allele
CCR5/CCR5
647
647/788=0.821
CCR5
CCR5/ ΔCCR5
134
134/788=0.170
Genotype
ΔCCR5/ ΔCCR5
Total
7
788
7/788=0.009
1.000
Derived Allele
Frequencies
(2X647)+(1X134)
788X2
=0.906
ΔCCR5
(2X7)+(1X134)
788X2
=0.094
another way to calculate
allele frequencies:
• from genotype frequency
• F(CCR5)=0.821+0.170/2=0.906
• F(ΔCCR5)=0.009+0.170/2=0.094
• Can we calculate the proportion of the
population with various genotypes once
we know the allele frequencies ?
The Hardy-Weinberg Law
Geoffrey Hardy
Wilhelm Weinberg
An English mathematician
A German physician
The Hardy-Weinberg Law
The frequency of the three genotypes AA,
Aa and aa is given by the terms of the
binomial expansion of (p+q)2=p2+2pq+q2.
The population genotype frequencies from
generation to generation will remain constant,
at equilibrium, if the allele frequencies p and q
remain constant.
Where p = frequency of “dominant” allele
and q = frequency of “recessive” allele
Proof of the equilibrium
•
•
•
•
Gametes
A (p)
a (q)
A (p)
AA (pXp)
Aa (pXq)
a (q)
Aa (pXq)
Aa (qXq)
Frequency of AA offspring is then p2;
Frequency of aa offspring is then q2 ;
Frequency of Aa offspring then 2pq ;
Frequency of an allele being present is = 1.
AA ：Aa ：aa
= p2 ：2pq：q2
Proof of the equilibrium
Types of Matings
Mother
Father
AA
AA
AA
Offspring
Frequency
AA
Aa
p2X p2= p4
(p4)
Aa
p2X2pq= 2p3q
½(2p3q)
½(2p3q)
Aa
AA
2pqXp2= 2p3q
½(2p3q)
½(2p3q)
AA
aa
p2Xq2= p2q2
(p2q2)
aa
AA
q2Xp2 = p2q2
(p2q2)
Aa
Aa
2pqX2pq=4p2q2
Aa
aa
aa
aa
¼(4p2q2)
aa
½(4p2q2)
¼(4p2q2)
2pqXq2=2pq3
½(2pq3)
½(2pq3)
Aa
q2X2pq=2pq3
½(2pq3)
½(2pq3)
aa
q2Xq2=q4
AA：p4+2p3q+p2q2=p2(p2+2pq+q2)=p2
Aa： 2p3q +2p2q2 + 2p2q2 + 2pq3 =2pq (p2+2pq+q2)=2pq
aa： p2q2 +2pq3+q4=q2(p2+2pq+q2)=q2
(q4)
Hardy-Weinberg Equilibrium
AA ：Aa ：aa = p2 ：2pq：q2
Conditions or assumptions for the Hardy –
Weinberg law to be true…
• Infinitely large population
• Randomly mating population
• No mutation
• No migration
• No natural selection
• Frequencies of alleles do not change over time
The Hardy-Weinberg Law in Autosomal
Recessive Disease
• For example, the frequency of Albinism is
approximately 1/10000.
• Q: What are the gene frequency and the
heterozygote frequency of it?
• The frequency of affected individuals=1/10000=q2
• q=1/100=0.01 (the frequency of allele a)
• p=1-q=0.99 (the frequency of allele A)
• 2pq = 2X0.99X0.01 ≈ 0.02 (the carrier frequency)
There would be an approximately 2% chance
that a parent known to be a carrier of Albunism.
The Hardy-Weinberg Law in Autosomal
Dominant Disease
• For example, the frequency of retinoblastoma is
approximately 1/10000.
• Q: What are the gene frequency of mutant rb?
• The frequency of dominant allele in AD disease is very
low, so p2 is too small to be estimated.
• The frequency of affected individuals=1/10000=2pq
• 2p ≈1/10000 (because q≈1)
• p=1/20000 (the frequency of mutant rb allele)
The Hardy-Weinberg Law in X-linked
Dominant Disease
• Affected male: XAY (p)
• Affected female: XAXA (p2) and XAXa (2pq)
• P2+2pq ≈ 2p
• So, the affected incidence in female is twice than
in male.
The Hardy-Weinberg Law in X-linked
Recessive Disease
• For example, the frequency of red-green color
blindness is approximately 8% in males.
Sex
Genotype
Phenotype
Male
X+
Normal
Xcb
Color blind
X+/X+
Normal
X+/Xcb
Normal
Xcb/Xcb
Color blind
Female
Incidence (Approximate)
q=0.08
The Hardy-Weinberg Law in X-linked
Recessive Disease
Sex
Genotype
Phenotype
Incidence (Approximate)
Male
X+
Normal
p=0.92
Xcb
Color blind
q=0.08
X+/X+
Normal
p2=(0.92)2
X+/Xcb
Normal
2pq=2(0.92)(0.08)
Xcb/Xcb
Color blind
q2=(0.08)2
Female
Factors that disturb Hardy-Weinberg
equilibrium
• mutation
• migration
• natural selection
• genetic drift
• non-random mating
Factors that disturb Hardy-Weinberg
equilibrium
• mutation
spontaneous change in DNA
• migration
• natural selection
• creates new alleles
• ultimate source of all
genetic variation
• genetic drift
• non-random mating
Factors that disturb Hardy-Weinberg
equilibrium
• mutation
• migration
individuals move into population
new alleles
• natural selection • introduces
“gene flow”
• genetic drift
• non-random mating
Factors that disturb Hardy-Weinberg
equilibrium
• mutation
• migration
certain genotypes produce
more offspring
• natural selection
• genetic drift
• differences in survival
or reproduction
differences in“fitness”
• leads to adaptation
• non-random mating
Fitness and Coefficient of Seletion
• Fitness is the chief factor that determines whether
a mutation is lost immediately, becomes stable in the
population, or even becomes, over time, the
predominant allele at the locus concerned.
• Whether an allele is transmitted to the succeeding
generation depends on its fitness (f).
Fitness and Coefficient of Seletion
Fitness (f)--- is a measure of the number
of offspring of affected persons who survive
to reproductive age, compared with an
appropriate control group.
Coefficient of selection (s) --- is a
measure of the loss of fitness and is defined
as 1-f, that is, the proportion of mutant
alleles that are not passed on and are
therefore lost as a result of selection.
Selection on sickle-cell allele
aa – abnormal ß hemoglobin very low
fitness
sickle-cell anemia
AA – normal ß hemoglobin
vulnerable to malaria
Aa – both ß hemoglobins
resistant to malaria
intermed.
fitness
high
fitness
Selection favors heterozygotes (Aa).
Both alleles maintained in population (a at low level).
Factors that disturb Hardy-Weinberg
equilibrium
• mutation
• migration
genetic change by chance alone
• natural selection
• genetic drift
• non-random mating
• sampling error
• misrepresentation
• small populations
Genetic Drift
Genetic drift
Before:
8 RR
0.50 R
8 rr
0.50 r
After:
2 RR
6 rr
0.25 R
0.75 r
Founder Effect
• The founder effect is the loss of genetic variation
that occurs when a new population is established
by a very small number of individuals from a larger
population.
• As a result of the loss of genetic variation, the
new population may be distinctively different,
both genetically and phenotypically, from the
parent population from which it is derived.
Founder Effect
Ellis-van Creveld syndrome
Factors that disturb Hardy-Weinberg
equilibrium
• mutation
• migration
• natural selection
• genetic drift
• non-random mating
cause changes in
allele frequencies
Factors that disturb Hardy-Weinberg
equilibrium
• mutation
• migration
• natural selection
mating combines alleles
into genotypes
• genetic drift
• non-random mating
• non-random mating
non-random
allele combinations
A A A
A A a A
A
a
A
A
0.8
AA
A
0.8 0.8 x 0.8
a
aA
0.2 0.2 x 0.8
aa x aa
aa
a
0.2
Aa
0.8 x 0.2
aa
0.2 x 0.2
AA x AA
AA
allele frequencies:
A = 0.8
A = 0.2
genotype frequencies:
AA = 0.8 x 0.8 = 0.64
Aa = 2(0.8 x0.2) = 0.32
aa = 0.2 x 0.2 = 0.04
Consanguinity
• Couples are related and have one or more
ancestors in common.
• Consanguinity is arbitrarily as a union of
individuals related to each other as close
as or closer than second cousins.
Coefficient of inbreeding
• Consanguinity is measured by the coefficient of
inbreeding (F) :
• Is the probability that a homozygote has
received both alleles at a locus from the same
ancestral source
Coefficient of inbreeding of AR genes
A 1A2
A3A4
A1A1 = （1/2）4
P2
P1
A2A2 = （1/2）4
A3A3 = （1/2）4
B2
B1
◇
A4A4 = （1/2）4
F = 4 ×（1/2）4 = 1 / 4
S
Brother-sister
Coefficient of inbreeding of AR genes
A1A2
A1A1 = （1/2）5
A3A4
P2
P1
A2A2 = （1/2）5
A3A3 = （1/2）5
B2
B1
C
◇
S
A4A4 = （1/2）5
F = 4 ×（1/2）5 = 1 / 8
Uncle-niece
Coefficient of inbreeding of AR genes
A1A2
P1
□
A3A4
○ P2
□
B1○
○B2
A1A1 = （1/2）6
□
A2A2 = （1/2）6
A3A3 = （1/2）6
C1□
○ C2
◇
S
A1A1
A2A2
A3A3
A4A4
A4A4 = （1/2）6
F = 4 ×（1/2）6 = 1 / 16
First cousins
Coefficient of inbreeding of X-linked genes
• Remember that sons receive their X
chromosome from their mother and
have to pass on their X chromosome
to their daughter.
Coefficient of inbreeding of X-linked genes
X1Y
P1
□
X2X3
○ P2
□
B1○
□B2
C1□
○ C2
○
S
X1X1
X2X2
X3X3
X1 X1 = 0
○
X2X2 = （1/2）4
X3X3 = （1/2）4
F = （1/2）4+（1/2）4= 1 / 8
Coefficient of inbreeding of X-linked genes
X 1Y
X2X3
P2
P1
X1X1 = （1/2）3
X2X2 = （1/2）5
B1
B2
C1
C2
S
X3X3 = （1/2）5
F = （1/2）3+（1/2）5 +（1/2）5
= 3 / 16
Coefficient of inbreeding of X-linked genes
F = 0
Key Points
 What is population genetics?
 How to destribe genetic structures?
 The Hardy-Weinberg Law.
 Factors that disturb Hardy-Weinberg
equilibrium.
 Consanguinity.
Question 9 (on p207)
• You are consulted by a couple, Abby and Andrew, who
tell you that Abby’s sister Anna has Hurler syndrome (an
AR disease) and that they are concerned that they
themselves might have a child with the same disorder.
The population incidence of Hurler syndrome is about
1/90000 in your community.
• A. If Abby and Andrew are not consanguineous, what is
the risk that Abby and Andrew’s first child will have
Hurler syndrome?
• B. If they are first cousins, what is the risk?
A
Abby: the chance of being a carrier = 2/3
Andrew: the chance of being a carrier = 1/150 (2pq)
The risk of having an affected child
= 2/3 X 1/150 X 1/4 = 1/900
B
Abby: the chance of being a carrier = 2/3
Andrew: the chance of being a carrier = 1/4
The risk of having an affected child
= 2/3 X 1/4 X 1/4 = 1/24