Taylor Pruett
AP biology
3rd block
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British mathematician Godfery H. Hardy and
German physician Wilhelm Weinberg.
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In 1908, Hardy and Weinberg came up with a
mathematical model to estimate the
genotypic frequencies of a population that is
in genetic equilibrium.
Genetic Equilibrium: where allele frequencies
do not change.
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The Hardy-Weinberg principle states that in a
large randomly breeding population, allelic
frequencies will remain the same from
generation to generation assuming that there
is no mutation, gene migration, selection or
genetic drift.
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Genetic equilibrium is referred to as HardyWeinberg equilibrium.
This describes a stable, nonevolving
population; allelic frequencies do not change.
Requirements:
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Population must be large
Population must be isolated
No mutations
Mating must be random
No natural selection
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The Hardy-Weinberg principle is illustrated in
a mathmatical equation:
p²+2pq+q²=1
p+q=1
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p = frequency of the dominant allele in the
population
q = frequency of the recessive allele in the
population
p2 = percentage of homozygous dominant
individuals
q2 = percentage of homozygous recessive
individuals
2pq = percentage of heterozygous
individuals
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Example:
◦ D= p
◦ d= q
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So, set up your equation like:
◦D²+2Dd+d²=1
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D²= frequency of DD
2Dd= frequency of Dd
d²= frequency of dd
D= frequency of the D allele
d= frequency of the d allele
◦ You have sampled a population in which you know
that the percentage of the homozygous recessive
genotype (aa) is 36%. Using that 36%, calculate the
following:
◦ The frequency of the "aa" genotype.
◦ The frequency of the "a" allele.
◦ The frequency of the "A" allele.
◦ The frequency for the “AA” allele.
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36%, as given in the problem itself
If q² = 0.36, then q = 0.6, again by
definition. Since q equals the frequency of the
“a” allele, then the frequency is 60%.
Since q = 0.6, and p + q = 1, then p = 0.4;
the frequency of A is by definition equal to p,
so the answer is 40%.
Since p=0.4, to find p², (0.4)²=0.16. So the
frequency of the “AA” genotype is 16%.
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A census of albatrosses nesting on a
Galapagos Island revealed that 24 of them
showed a rare recessive condition that
affected beak formation. The other 63 show
no beak defect. What is the frequency of the
dominant allele? Give your answer to the
nearest hundreth.
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24+63= 87 total birds.
24/87=0.28
Take the square root
You get 0.53
1-0.53= 0.47
P= 0.47