Population Genetics
•  Hardy-Weinberg Equilibrium
•  Mutation and Selection
•  Balanced Polymorphism
•  Founder Effect
•  Consanguinity
Hardy-Weinberg Equilibrium
•  large
population
•  no
mutation
•  no
selection
•  random
•  no
mating
migration
[A] = p
[a] = q
p + q =1
[AA] = p2
[Aa] = 2pq
[aa] = q2
frequencies remain stable
Hardy-Weinberg
eggs
A
a
frequency
=
=
p
q
=
allele
a
=
sperm
A
p
q
AA
p 2
allele
frequency
Aa
pq
aA
aa
pq
q
2
Data Checking
[MM] = 1787/6129
[MN] = 3037/6129
[NN] = 1305/6129
p = [M] = [2(2787)+3037]/12,258 = 0.5392
q = [N] = [2(1305)+3037]/12,258 = 0.4608
Observed
Expected
[MM] = p2
0.279
0.291
[MN] = 2pq
0.495
0.497
[NN] = q2
0.213
0.212
How Long Does It Take To
Reach Equilibrium?
Population 1
all AA
Population 2
all aa
[AA] = x
[aa] = y
x+y=1
[AA] = x2 = p2
[Aa] = 2xy = 2pq
[aa] = y2 = q2
Equilibrium in achieved in one
generation for an autosomal trait
Autosomal Recessive
Cystic fibrosis: 1/2,500 = q2
q = 1/50
2pq = 2(1/50)(49/50) ≈ 1/25
Multiple Alleles
(p + q + r + s + t +….) = 1
Consider alleles a, b, c
[a] = p
[b] = q
[c] = r
(p + q + r)2 = p2 + 2pq + 2pr + 2qr + q2 + r2
aa
ab
ac
bc
bb cc
Selection and Mutation
• 
Selection: relative reduction in ability
to reproduce (fitness)
•  Mutation: alteration of allele from
“wild type” state to “mutant”
Selection: Genetic Lethal
Genetic Lethal
p
generation
1
2
3
AA!
AA
AA
0.5
aa
Aa
gene pool
Aa
aa
q
0.5
0.66
0.33
0.75
0.25
gene pool
Aa
aa
Change in Gene Frequency with
Genetic Lethal
q
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
generation
Mutation-Selection Equilibrium
a
a
mutation
A
A
A
A
A
A
A
A
A
A
A
A A
A
A
A
A
A
a
A
A
A
A
A
A A
A
A
A
A
A
A
selection
A
A
A
a
Mutation-Selection Equilibrium
q
0.6
0.5
0.4
0.3
selection
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
generation
mutation
Rate of Decline of q
“new q” = q1 =
2p0q0
2+2p
2(p0
=
0q 0)
2p0q0
2p0 (p0+2q0)
q0
q2 =
q1
=
1+q1
q0
1+q0
1+
q0
generally, qn =
1+nq0
q0
1+q0
=
1+2q0
=
q0
1-q0+2q0
=
q0
1+q0
How long does it take to reduce
q by one-half?
q0
qn =
1+nq0
if qn/q0 = ½
then 1 = nq0 and so n = 1/q0
if q0 = 1/50, like CF, then need 50 generations, i.e., 1000 years
Fitness
fitness: proportion of offspring compared with “normal”
coefficient of selection = 1 - F
F = 1, s = 0 if normal number of offspring
F = 0, s = 1 if lethal
Mutation-Selection Balance
Autosomal Recessive
AA
2
Aa
aa
2
Before
p
2pq
q
Fitness
1
1
1-s
After
p
2pq
q (1-s)
2
2
lose 2sq2 alleles each generation
at equilibrium, 2µ = 2sq2
q=
µ
s
AR Example
consider an autosomal recessive disorder with a population
frequency of 1/90,000 and a reproductive fitness of 20%
µ=
q2
s
=
1/90,000
0.8
= 1.39 x 10-5
Mutation-Selection Balance
Autosomal Dominant
lose 2ps alleles each generation
at equilibrium, 2µ = 2ps
p = µ/s
Autosomal Dominant Example
NF1 has frequency of 1/3,000 and half of cases are new
mutations; what is the reproductive fitness?
2p = 1/3,000; hence = 1/6,000 and therefore µ = 1/12,000
s = µ/p = 1/2
Polymorphism
•  Multiple
alleles not accounted for by mutation
•  Frequency
of minor allele at least 1%
•  Maintenance
•  balancing
•  neutral
selection
(genetic drift)
•  founder
effect
Balanced Polymorphism
• 
Maintenance of otherwise deleterious
allele in heterozygotes
•  “Heterozygote advantage”
Worldwide Distribution of
Globin Disorders
Balanced Polymorphism
Globin Disorder
aa
Malaria
AA
AA
Aa
Balanced Polymorphism
AA
Aa
aa
Before
p2
2pq
q2
Fitness
1-s
1
1-t
After
p2(1-s)
2pq
q2(1-t)
at equilibrium q1 - q = 0 or q1 = q
Genetic Drift
• 
Fluctuation in gene frequency due
to small size of breeding population
•  Fixation or extinction of allele
possible
Genetic Drift
Aa
aa AA
Aa AA
aa Aa
Aa
Aa
Aa
Aa
Aa
AA
aa
Aa
Aa
Aa
Aa
AA
Aa
Aa
aa
aa AA
Aa AA
Aa
Aa
AA
aa AA
Aa AA
aa AA
AA
Aa
aa
Aa
Aa aa
aa Aa
Aa
aa AA
AA
Aa
Aa
aa
aa Aa
Aa
AA
Aa
Aa
aa
Aa
AA
aa
Aa
AA
AA
Aa
aa
aa AA
Aa AA
Aa aa
Aa
aa
AA
Aa
AA
Aa
Aa
Aa
AA
AA
Aa
aa
aa
Aa
Aa
AA
AA
AA
AA
AA
Founder Effect
•  high
frequency of gene in distinct population
•  introduction
•  continued
“closed”
at time when population is small
relatively high frequency due to population being
Founder Effect
aa
Aa
AA AA AA
AA
AA AA
AA
AA
AA
AA
Aa AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA AA
AA
AA AA
AA
AA AA
AA
AA AA AA
Aa
Aa AA Aa
Aa
AA
AA
AA
AA
AA
AA AA
AA
AA
AA
AA
AA
Aa
Aa
AA AA AA
AA
AA
new
population
with high
frequency of
mutant allele
initial
population
"bottleneck"
where
new population is
derived from
small
sample
Aa
AA
Aa
Aa
AA AA AA
AA
AA
Aa
AA
AA
Aa
AA
AA
Aa
AA
AA
AA
AA
AA
Population Screening
• 
• 
• 
Globin disorders
Tay-Sachs disease
Cystic fibrosis
Thalassemia in Sardinia
Tay-Sachs Disease
•  Devastating
disorder
neurological
•  Hexosaminidase
A deficiency
CF Carrier Screening
36