Population Genetics •  Hardy-Weinberg Equilibrium

•  Mutation and Selection

•  Balanced Polymorphism

•  Founder Effect

•  Consanguinity

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

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

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

(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

•  Selection: relative reduction in ability to reproduce (fitness)

•  Mutation: alteration of allele from “wild type” state to “mutant”

Selection and Mutation

Selection: Genetic Lethal

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

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

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

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

“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

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

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

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

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

Mutation-Selection BalanceAutosomal 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 selection

• neutral (genetic drift)

•  founder effect

Balanced Polymorphism

•  Maintenance of otherwise deleterious allele in heterozygotes

•  “Heterozygote advantage”

Worldwide Distribution of Globin Disorders

Malaria AA

Globin Disorder aa

AA

Aa

Balanced Polymorphism

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

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

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”

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

Population Screening

•  Globin disorders

•  Tay-Sachs disease

•  Cystic fibrosis

Thalassemia in Sardinia

Tay-Sachs Disease

• Devastating neurological disorder

• Hexosaminidase A deficiency

CF Carrier Screening

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