Genes in Populations

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Genes in Populations
Dr John Loughlin
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Changes in gene frequency between generations
between populations
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Consider a locus with two alleles, A a
Allele A
Number of individuals N Number of copies of
gene 2N
Allele a
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Hardy-Weinberg (H-R) Rule
Frequency of allele A p Frequency of allele a
q p q 1 The probability of one allele
forming a zygote with any other allele is the
product of their two frequencies
Derived concurrently in the Edwardian era by a
Cambridge academic (Hardy) and a German
physician (Weinberg)
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Hardy-Weinberg Rule
a (q)
A (p)
Aa pq
AA p2
A (p)
aA pq
aa q2
a (q)
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Genotype frequencies
p 0.5 q 0.5 sum 1.0 p2 0.25 q2
0.25 2pq 0.5 sum 1.0
p 0.9 q 0.1 sum 1.0 p2 0.81 q2
0.01 2pq 0.18 sum 1.0
p 0.96 q 0.04 sum 1.0 p2 0.93
q2 0.0016 2pq 0.07 sum 1.0
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The HARDY-WEINBERG EQUILIBRIUM Allele and
genotype frequencies do not change from one
generation to the next
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Utility of the Hardy-Weinberg principle
Enables one to predict the incidence of diseased
individuals and unaffected carriers, if we know
p q
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An example

• Consider the autosomal recessive disease cystic
  fibrosis
• Two copies of the CF gene are needed for disease
  occurrence
• 1/2000 people have CF
• q2 therefore 1/2000 0.0005
• Therefore q v0.0005 0.022
• Therefore p 1-0.022 0.978
• Frequency of carriers (2pq) 2 X 0.978 X 0.022
  0.043
• i.e. 4.3 of the population

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When does the H-W equilibrium break down? i.e.
what factors alter allele frequencies?

• Non-random (assortive) mating
• Genetic drift
• Migration
• Selection
• New mutation

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Non-random mating for multifactorial traits
mate correlation
Trait
Intelligence 47 Waist size 38 Neurotic
tendency 30 Height 28 Eye colour 26
Increases frequency of extreme phenotypes above
expectation for random mating
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Non-random mating for rare recessive traits
Consanguinity
1) Heterozygotes more likely to mate than
expected by chance random mating 2) More
homozygotes (more disease) than predicted by
Hardy-Weinberg 3) Hastens selective removal of
bad recessive alleles and increase of good
ones
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Genetic Drift

• Drift is the effect of sampling fluctuations
• Small population - big influence
• Large population - small influence

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Drift in a small population
Ten heterozygotes
p 0.5 q 0.5
Gametes
Zygotes


p 0.6 q 0.4
Allele frequencies change due to
chance fluctuations in the sampling of gametes
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Genetic Drift

• Given time, one allele will be fixed and the
  other eliminated
• An alleles probability of fixation is equal to
  its frequency
• New alleles are at a great risk of elimination,
  especially in small populations

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Genetic Drift
p 0.25 q 0.75
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2
3
p 0.0 q 1.0
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Migration

• Genetic flow
• Movement of alleles from one population to
  another
• Will have most influence if the populations are
  small and if the allele frequency differences are
  large
• Founder affect
• Reduced genetic diversity in a population founded
  by a small number of individuals

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Population A joins population B to form
population C
p 0.5 q 0.5
A
C
B
p 0.65 q 0.35
p 0.72 q 0.28
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Founder effect
1
p 0.45 q 0.55
2
p 0.65 q 0.35
p 0.89 q 0.11
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New mutation

• Ultimate source of variation
• Most mutations will be detrimental
• Likely to be quickly eliminated unless there is a
  compensating advantage

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Achondroplasia
Gly380Arg mutation in transmembrane domain of
FGFR3

• Receptor signals in absence of ligand
• Bone growth attenuated

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Achondroplasia - autosomal dominant
FGFR3
80 of cases are new mutations New cases are
born to unaffected parents 1 in 30 000 births 1
in 60 000 or 17 per million gametes Frequency of
AD disorders in the population maintained by a
balance between new mutations and elimination by
selection
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Cystic fibrosis - autosomal recessive
CFTR
CFTR
CFTR
New mutations will initially be confined to
heterozygotes and not eliminated by
selection Must spread to high frequencies before
homozygotes begin to appear May achieve a high
frequency by Drift in small populations Consangui
nity Selective advantage to carriers
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Selection

• The vast majority of new mutations have no effect
  on gene activity or function (selectively
  neutral)
• The rest can either reduce or increase the
  fitness of the carrier
• Fitness is a measure of the ability of an
  individual to survive and reproduce

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Positive Selection

• If a mutation increases fitness it will be
  subjected to positive selection and will spread
  through the population
• So long as it survives drift!!

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Positive Selection
or
Elimination by drift
Achieved fixation
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Negative Selection

• Has most effect in a dominant disease - mutant
  alleles subject to selection in heterozygote
• Has least effect in a recessive disease - most
  mutant alleles are in carriers with only a small
  proportion in homozygotes
• i.e. 98 of cystic fibrosis alleles are in
  carriers

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Summarize
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Hardy-Weinberg Principle

• APPLIES STRICTLY PROVIDED
• there is random mating
• the population is large
• and closed
• and no mutation
• and no selection

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Polymorphism
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Definition - The existence of two or more
variants in a population in such proportion
that the rarest cannot be maintained by
recurrent mutation
An arbitary figure of 1 frequency for a DNA
sequence change
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Balanced polymorphism
Due to a balance of selection against both
homozygotes and for the heterozygote
(heterozygote advantage)
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Sickle cell anaemia
An autosomal recessive disease caused by mutation
in the b-globin gene Glutamic acid Valine
substitution
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Sickle cell anaemia and malaria show extensive
overlap
The purple colour indicates areas where both
malaria (pink) and sickle cell anaemia (blue) are
common
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Heterozygote advantage can lead to differences in
disease incidence between populations
Disease Selective Region Incidence per
Agent 10,000 births Sickle Cell Anaemia
Malaria West Africa 200 UK 0.5 Thalassae
mia Malaria SE Asia 200 UK 1 Cystic
Fibrosis Typhoid Europe 5 Fever Japan
0.1
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The end Next weeks lecture Mapping disease
loci