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Population Genetics • Hardy-Weinberg Equilibrium
• Mutation and Selection
• Balanced Polymorphism
• Founder Effect
• Consanguinity
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Hardy-Weinberg Equilibrium • large population
• no mutation
• no selection
• random mating
• no migration
[A] = p [a] = q p + q =1 [AA] = p2 [Aa] = 2pq [aa] = q2 frequencies remain stable
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AA Aa
aA aa
p pq
pq q 2
2
sperm
eggs
A
a
A a
p
p
q
q
=
= =
=
allele frequency
allele
frequency
Hardy-Weinberg
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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
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How Long Does It Take To Reach Equilibrium?
Population 1 all AA
Population 2 all aa
[AA] = x [aa] = y x + y = 1
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[AA] = x2 = p2 [Aa] = 2xy = 2pq [aa] = y2 = q2
Equilibrium in achieved in one generation for an autosomal trait
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Autosomal Recessive
Cystic fibrosis: 1/2,500 = q2 q = 1/50 2pq = 2(1/50)(49/50) ≈ 1/25
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Multiple Alleles (p + q + r + s + t +….) = 1
(p + q + r)2 = p2 + 2pq + 2pr + 2qr + q2 + r2 Consider alleles a, b, c [a] = p [b] = q [c] = r
aa ab ac bc bb cc
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• Selection: relative reduction in ability to reproduce (fitness)
• Mutation: alteration of allele from “wild type” state to “mutant”
Selection and Mutation
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Selection: Genetic Lethal
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AA! aa Aa
p q
0.5 0.5 1
0.66 0.33 2
0.75 0.25 3 AA
AA
Aa
Aa aa
aa
generation
gene pool
gene pool
Genetic Lethal
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0
0.1
0.2
0.3
0.4
0.5
0.6
generation
q
Change in Gene Frequency with Genetic Lethal
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Mutation-Selection Equilibrium 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
A A
A
a a selection
a mutation
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0
0.1
0.2
0.3
0.4
0.5
0.6
generation
q
selection
mutation
Mutation-Selection Equilibrium
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“new q” = q1 = 2p0q0
2(p02+2p0q0)
= 2p0q0
2p0 (p0+2q0) =
q0
1-q0+2q0 =
q0
1+q0
q2 = q1
1+q1
=
q0
1+q0
q0
1+q0
1+
=
q0
1+2q0
generally, qn =
q0
1+nq0
Rate of Decline of q
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How long does it take to reduce q by one-half?
qn =
q0
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
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Fitness
fitness: proportion of offspring compared with “normal”
F = 1, s = 0 if normal number of offspring F = 0, s = 1 if lethal
coefficient of selection = 1 - F
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Mutation-Selection BalanceAutosomal Recessive
AA Aa aa
Before p 2 2pq q 2
Fitness 1 1 1-s
After p 2 2pq q 2 (1-s)
lose 2sq2 alleles each generation at equilibrium, 2µ = 2sq2 q =
µ
s
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AR Example
consider an autosomal recessive disorder with a population frequency of 1/90,000 and a reproductive fitness of 20%
q2
s µ = = 1/90,000
0.8 = 1.39 x 10-5
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Mutation-Selection BalanceAutosomal Dominant
lose 2ps alleles each generation at equilibrium, 2µ = 2ps p = µ/s
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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
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Polymorphism • Multiple alleles not accounted for by mutation
• Frequency of minor allele at least 1%
• Maintenance
• balancing selection
• neutral (genetic drift)
• founder effect
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Balanced Polymorphism
• Maintenance of otherwise deleterious allele in heterozygotes
• “Heterozygote advantage”
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Worldwide Distribution of Globin Disorders
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Malaria AA
Globin Disorder aa
AA
Aa
Balanced Polymorphism
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Balanced Polymorphism
AA Aa aa
Before p2 2pq q2
Fitness 1-s 1 1-t
After p2(1-s) 2pq q2(1-t)
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at equilibrium q1 - q = 0 or q1 = q
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Genetic Drift
• Fluctuation in gene frequency due to small size of breeding population
• Fixation or extinction of allele possible
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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
Genetic Drift
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Founder Effect
• high frequency of gene in distinct population
• introduction at time when population is small
• continued relatively high frequency due to population being “closed”
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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
initial population
"bottleneck" where new population is derived from small sample
new population with high frequency of mutant allele
Founder Effect
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Population Screening
• Globin disorders
• Tay-Sachs disease
• Cystic fibrosis
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Thalassemia in Sardinia
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Tay-Sachs Disease
• Devastating neurological disorder
• Hexosaminidase A deficiency
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CF Carrier Screening
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36
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