Download Hardy-Weinberg Principle • Population genetics

Hardy-Weinberg Principle
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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
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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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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
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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
p2 + 2pq + q2
and
p+q = 1 (always two alleles)
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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
Q = square root of q2 = q
√.16 q=0.4
p + q = 1 then 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
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Hardy-Weinberg Equilibrium
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Five Agents of Evolutionary Change
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Mutation
– Mutation rates are generally so low they
have little effect on Hardy-Weinberg
proportions of common alleles.
ƒ ultimate source of genetic variation
Gene flow
– movement of alleles from one population
to another
ƒ tend to homogenize allele frequencies
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Five Agents of Evolutionary Change
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Nonrandom mating
– assortative mating - phenotypically similar
individuals mate
ƒ Causes frequencies of particular
genotypes to differ from those predicted
by Hardy-Weinberg.
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Five Agents of Evolutionary Change
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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.
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Frequencies of particular alleles may
change by chance alone.
ƒ 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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Five Agents of Evolutionary Change
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Selection – Only agent that produces adaptive
evolutionary change
– artificial - breeders exert selection
– natural - nature exerts selection
ƒ variation must exist among individuals
ƒ variation must result in differences in
numbers of viable offspring produced
ƒ variation must be genetically inherited
™ natural selection is a process, and
evolution is an outcome
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Five Agents of Evolutionary Change
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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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Measuring Fitness
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Fitness is defined by evolutionary biologists
as the number of surviving offspring left in
the next generation.
– relative measure
ƒ Selection favors phenotypes with the
greatest fitness.
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Heterozygote Advantage
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Heterozygote advantage will favor
heterozygotes, and maintain both alleles
instead of removing less successful alleles
from a population.
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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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Sickle cell anemia
ƒ Homozygotes exhibit severe anemia,
have abnormal blood cells, and usually
die before reproductive age.
ƒ Heterozygotes are less susceptible to
malaria.
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Sickle Cell and Malaria
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The Plasmodium life cycle
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Deleterious recessive alleles may, in some cases,
provide a small benefit to heterozygotes
Heterozygous advantage in PKU
seems to operate via protection
against mycotoxins produced by
Aspergillus and Penicillium that
infest stored foods.
Phenylketonuria
(PKU) autosomal
recessive
Phenylketonuria (PKU) inherited error of
metabolism caused by deficiency in
enzyme phenylalanine hydroxylase.
Loss of PAH results in mental
retardation, organ damage, unusual
posture. In cases of maternal PKU, can
severely compromise pregnancy.
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.24
Cystic fibrosis, or CF, autosomal recessive disease, affects lungs, sweat glands and
digestive system. It is caused by the malfunction of the CFTR protein, which controls
inter-membrane 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.
Before modern times, children born with CF would have a life expectancy of only a few
years, but modern medicine has made it possible for these people to live into 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 in 25 persons of European descent is a carrier of the disease, and 1 in
2500 to 3000 children born is affected by cystic fibrosis.
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The presence of a single CF mutation may influence survivorship of people affected by
diseases involving loss of body fluid, typically due to diarrhea.
The most common of these maladies is cholera, which throughout history has killed many
Europeans. Those with cholera would often die of dehydration due to intestinal water
losses.
A mouse model of CF was used to study resistance to cholera, and the results were
published in Science in 1994 (Gabriel, et al.). The heterozygote (carrier) mouse had less
secretory diarrhea than normal, non-carrier mice. Thus it appeared for a time that
resistance to cholera explained the selective advantage to being a carrier for CF and why
the carrier state was so frequent.
Another theory for the prevalence of the CF mutation is that it provides resistance to
tuberculosis. Tuberculosis was responsible for 20% of all European deaths between 1600
and 1900, so even partial protection against the disease could account for the current gene
frequency[4].
As of 2007, the selective pressure for the high gene prevalence of CF mutations is still
uncertain. Approximately 1 in 25 persons of European descent is a carrier of the disease,
and 1 in 2500 to 3000 children born is affected by cystic fibrosis.
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Natural Selection Can Maintain Variation
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Frequency-dependent selection
– Phenotype fitness depends on its frequency
within the population.
ƒ Negative frequency-dependent selection
favors rare phenotypes.
ƒ Positive frequency-dependent selection
eliminates variation.
Oscillating selection
– Selection favors different phenotypes at
different times.
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