Download Hardy-Weinberg Principle

Hardy‐Weinberg Principle
• Population genetics ‐ study of properties of genes in populations
• Hardy‐Weinberg ‐ original proportions of genotypes in a population will remain constant from generation to generation
– Sexual reproduction (meiosis and fertilization) alone will not change allelic (genotypic) proportions.
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Hardy‐Weinberg Principle
• Necessary assumptions
Allelic frequencies would remain constant if…
– population size is very large
– random mating
– no mutation
– no gene input from external sources
– no selection occurring
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FREQUENCY OF ALLELES IN THE POPULATIONS ≈ FREQUENCY OF ALLELES IN GAMETES A
a
A
AA
Aa
a
Aa
aa
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FREQUENCY OF ALLELES IN THE POPULATIONS ≈ FREQUENCY OF ALLELES IN GAMETES A
a
0,9
A
AA
0,9
Aa
0,81
Aa
a
0,1
0,1
0,09
aa
0,09
0,01
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FREQUENCY OF ALLELES IN THE POPULATIONS ≈ FREQUENCY OF ALLELES IN GAMETES A
a
0,9
0,1
p
A
Aa
AA
0,9
q
0,09
0,81
p2
p
a
Aa
0,1
aa
0,09
q
pq
0,01
pq
q2
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FREQUENCY OF ALLELES IN THE POPULATIONS ≈ FREQUENCY OF ALLELES IN GAMETES a
A
0,9
0,1
p
A
Aa
AA
0,9
q
0,09
0,81
p2
p
a
Aa
0,1
aa
0,09
q
0,01
pq
AA 2Aa aa pq
0,81 p2
0,18 2pq
0,01 q2
q2
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Hardy‐Weinberg Equilibrium
Population of cats
n=100
16 white and 84 black
bb = white
B_ = black
Can we figure out the allelic frequencies of individuals BB and Bb?
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Hardy‐Weinberg Principle
• Calculate genotype frequencies with a binomial expansion
(p+q)2 = p2 + 2pq + q2
• p2 = individuals homozygous for first allele
• 2pq = individuals heterozygous for alleles
• q2 = individuals homozygous for second allele
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Hardy‐Weinberg Principle
2
2
p + 2pq + q
and
p+q = 1 (always two alleles)
16 cats white = 16bb then (q2 = 0.16)
This we know we can see and count!!!!!
If p + q = 1 then we can calculate p from q2
square root of q2 = q √.16 q=0.4
p + q = 1 then p=1‐q p = .6 (.6 +.4 = 1)
p2 = .36
All we need now are those that are heterozygous (2pq) (2 x .6 x .4)=0.48
• .36 + .48 + .16 = 1 •
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•
•
•
•
•
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Hardy‐Weinberg Equilibrium
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Five Agents of Evolutionary Change
• 1‐Mutation
– Mutation rates are generally so low they have little effect on Hardy‐Weinberg proportions of common alleles.
• ultimate source of genetic variation
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Severe Autosomal Recessive disease
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• 2‐Gene flow
– movement of alleles from one population to another
• tend to homogenize allele frequencies
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Migrations
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Five Agents of Evolutionary Change
• 3‐Nonrandom mating
– assortative mating ‐ phenotypically similar individuals mate
• Causes frequencies of particular genotypes to differ from those predicted by Hardy‐Weinberg.
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Five Agents of Evolutionary Change
• 4‐Genetic drift – statistical accidents.
•
Random fluctuations in the frequency of the appearance of a gene in a small isolated population, presumably owing to chance rather than natural selection.
– Frequencies of particular alleles may change by chance alone.
• important in small populations
– founder effect ‐ few individuals found new population (small allelic pool)
– bottleneck effect ‐ drastic reduction in population, and gene pool size
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Genetic Drift ‐ Bottleneck Effect
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5‐Five Agents of Evolutionary Change
• Selection – Only agent that produces adaptive
evolutionary change
– artificial ‐ breeders exert selection – natural ‐ nature exerts selection
• variation must exist among individuals
• variation must result in differences in numbers of viable offspring produced
• variation must be genetically inherited
– natural selection is a process, and evolution is an outcome
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Five Agents of Evolutionary Change
• Selection pressures:
– avoiding predators
– matching climatic condition
– pesticide resistance
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Natural Selection
Biston Betularia
1848
Rare black
animals
1900
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Severe Autosomal Recessive disease
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Next
generation
Severe
Autosomal
Recessive
disease
A
a
A
a
AA
81
162
‐‐
162
Aa
18
18
18
18
‐‐
2 ‐‐
180
20
180
18
180/200
20/200
180/198
18/198
.9
.1
.91
.09
aa
1 lethal
100
AA
.91 x .91
.828
Aa
2 x .91 x .09
.164
aa
.09 x .09
.008
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Heterozygote Advantage
• Heterozygote advantage will favor heterozygotes, and maintain both alleles instead of removing less successful alleles from a population.
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Measuring Fitness
• Fitness is defined by evolutionary biologists as the number of surviving offspring left in the next generation.
– relative measure
• Selection favors phenotypes with the greatest fitness.
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Selection and H-W population analysis
• Natural selection is caused by differential fitness
• Fitness (w) is a measure of a genotype’s success
at contributing to the next generation
Survival or viability (v)
Reproduction or fecundity (f)
Fitness
w = (v)(f)
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Single locus, 2 alleles
Alleles
A1
A2
Genotype
A1A1
A1A2
A2A2
Frequency
p2
2pq
q2
Absolute fitness*
w11
w12
w22
Mean fitness
of population
w = p2 w11 + 2pq w12
+ q2 w22
*calculated directly from survival and viability data
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Result if
w11 < w12 > w22
Heterozygous advantage
(overdominance)
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Heterozygous Advantage
w11=0.60
w12=1.00
w22=0.60
Intense selection without
change in allele frequency!
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Heterozygote Advantage in man
– Sickle cell anemia
• Homozygotes exhibit severe anemia, have abnormal blood cells, and usually die before reproductive age.
• Heterozygotes are less susceptible to malaria. 29
The Plasmodium life cycle
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Sickle Cell and Malaria
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Deleterious recessive alleles may, in some cases,
provide a small benefit to heterozygotes
Phenylketonuria
(PKU) autosomal
recessive
Heterozygous advantage in
PKU seems to operate via
protection against mycotoxins
produced by Aspergillus and
Penicillium that infest stored
foods.
Mild, wet climate of Ireland and
W Scotland encourages mold
growth; these areas have
suffered
repeated
famines
during which moldy food were
eaten.
Heterozygous (PKU) women
have
lower
spontaneous
abortion rate.
Solution? Test early.
Treat w/ low-protein diet.
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Classic PKU is caused by a complete or near-complete
Deficiency of phenylalanine hydroxylase activity;
without dietary restriction of phenylalanine, most
Children with PKU develop profound and irreversible
intellectual disability.
PAH deficiency can be diagnosed by newborn screening
in virtually 100% of cases based on detection of
hyperphenylalaninemia using the Guthrie assay on a
blood spot obtained from a heel prick.
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PKU
Diet >> No mental retardation
- aa will reproduce
1/10.000 incidence of the disease
Aa 1/50 in the population
aa x AA >>>>
Aa 100%
Expected phenotype >>> normal, but
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Aa x AA >>> Aa
the Maternal PKU Collaborative Study reports that
even at maternal plasma Phe concentrations of
120-360 µmol/L, 6% of infants are born with
microcephaly and 4% with postnatal growth retardation.
If maternal plasma Phe concentrations are greater than
900 µmol/L, the risk is 85% for microcephaly,
51% for postnatal growth retardation, and 26% for
intrauterine growth retardation.
The risk for these abnormalities is
both dose and time dependent.
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The abnormalities that result from exposure
of a fetus to high maternal plasma Phe concentration
are the result of 'maternal HPA/PKU' .
The likelihood that the fetus will have congenital
heart disease, Intrauterine and postnatal growth
retardation, microcephaly, and intellectual disability
depends upon the severity of the maternal HPA and
the effectiveness of the mother's dietary management.
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Population
PAH Deficiency
in Live Births
Carrier Rate
Citation
Turks
1/2,600
1/26
Ozalp et al [1986]
Irish
1/4,500
1/33
DiLella et al
[1986]
Northern European
heritage,
East Asian
1/10,000
1/50
Scriver &
Kaufman [2001]
Japanese
1/143,000
1/200
Aoki & Wada
[1988]
Finnish, Ashkenazi
Jewish
1/200,000
1/225
Scriver &
Kaufman [2001]
African
~1/100,000
?
Anecdotal
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Cystic fibrosis, (CF), AR disease, affects lungs, sweat glands and digestive
system.
It is caused by the malfunction of the CFTR protein, which controls intermembrane transport of chloride ions, which is vital to maintaining equilibrium
of water in the body.
The malfunctioning protein causes viscous mucus to form in the lungs and
intestinal tract.
In the past children born with CF had a life expectancy of only a few years,
now increased to adulthood. However, even in these individuals, male and
female, CF typically causes sterility.
It is the most common genetic disease among people of European descent.
Approximately 1/25 persons of European descent is a carrier, and 1 in 2500 to
3000 children born is affected by cystic fibrosis.
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In CF carriers, survivorship is influenced in relation to diseases
involving loss of body fluid, typically due to diarrhea.
The most common of them is cholera, patients often die of
dehydration due to intestinal water losses.
In a mouse model of CF the heterozygote (carrier) mouse had less
secretory diarrhea than normal, non-carrier mice.
Thus resistance to cholera explained the selective advantage to
being a carrier for CF and why the carrier state was so frequent.
A second theory is that CF mutation provides resistance to
tuberculosis, which was responsible for 20% of all European
deaths between 1600 and 1900, so even partial protection against
the disease could account for the current high gene frequency.
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Aa frequency
Risk for affected
children
Incidence of
disease
1/30
1/30 x 1/30 x 1/4
1/3,600
1/50
1/50 x 1/50 x 1/4
1/10,000
1/100
1/100 x 1/100 x 1/4 1/40,000
If I know the incidence of the disease, I can
calculate easily the number of Aa in the
population
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I
I:1
I:2
II
II:1
II:2
II:3
II:2
II:3
1/10,000
1 x 1/50 x 1/4
1/200 affected
II:3
II:2 status not
known
199/200 unaffected
1/10,000
2/3 x 1/50 x1/4
1/300
affected
299/300
unaffected
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