Transcript Hardy-Weinberg Principle

Hardy-Weinberg Principle
Hardy-Weinberg Principle
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Hardy-Weinberg Principle – enables us
to calculate and predict allelic and
genotypic frequencies
Allelic frequency – the frequency of an
allele in a population
Genotypic frequency – the frequency of
a genotype in a population
Hardy-Weinberg
 We use p to represent the dominant allele,
and q to represent the recessive allele
 For allelic frequency: p + q = 1
 So if the frequency of the dominant allele (p)
is 0.75, then the frequency of the recessive
allele (q) is…0.25
Hardy-Weinberg
 For genotypic frequency:
p2 + 2pq + q2 = 1
 Where:
p2 = frequency of homozygous dominant
2pq = frequency of heterozygous
q2 = frequency of homozygous recessive
Hardy-Weinberg
 SO…for example, if we know the frequency
of the homozygous recessive genotype (q2),
we can find the frequency of the recessive
allele [√(q2) = q]
 THEN…since we know q, we can find p,
then p2, then 2pq!
Hardy-Weinberg
 Hardy-Weinberg predicts that gene
frequencies will remain the same from one
generation to the next
 However, certain conditions must be met
Hardy-Weinberg
– the frequencies of the alleles do not change
and
– as long as the mating is random, the
genotypic frequencies will remain in the
proportions p2 (frequency of AA), 2pq
(frequency of Aa) and q2 (frequency of aa)
where p is the frequency of A and q is the
frequency of a
– The sum of the genotypic frequencies
should be:
p2 + 2pq + q2 = 1
Hardy-Weinberg Assumptions
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1) Large population
2) Random mating
3) No mutation
4) No migration (in or out of population)
5) No selective pressure
Brachydactyly and evolutionary
change
 We know the gene for
brachydactyl fingers is dominant
to normal fingers
 A man named Yule suggested
that short-fingered people
should become more common
through time
 Godfrey Hardy showed this
inference was wrong
 Wilhelm Weinberg derived the
same solution to the problem
independently
The Hardy-Weinberg Law - the most
important principle in population genetics
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 The law is divided into three parts: a
set of assumptions and two major
results
– In an infinitely large, randomly
mating population, free from
mutation, migration and natural
selection (note there are five
assumptions here)
The Hardy-Weinberg Law - the most
important principle in population genetics
 The incidence of albinism is remarkably common (0.0043 or 13
in every 3000 Hopis)
 Assuming Hardy-Weinberg equilibrium, we can calculate q as
the square root of 0.0043 = 0.066
 p is therefore equal to 0.934
 The frequency of heterozygotes in the population is 2pq = 0.123
 In other words, 1 in 8 Hopis carries the gene for albinism!
 Take-home Lesson: For a rare allele, heterozygotes can be
relatively common
Albinism in Hopi Native Americans
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The incidence of albinism is
remarkably common (0.0043 or
13 in every 3000 Hopis)
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Assuming Hardy-Weinberg
equilibrium, we can calculate q
as the square root of 0.0043 =
0.066
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p is therefore equal to 0.934
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The frequency of heterozygotes
in the population is 2pq = 0.123
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In other words, 1 in 8 Hopis
carries the gene for albinism!
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Take-home Lesson: For a rare
allele, heterozygotes can be
relatively common
Hardy Weinberg Problem I
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Sickle Cell Anemia
– SS = susceptible to malaria but no SCA
– ss = non-susceptible but SCA 􀃆 mortality
– Ss = non-susceptible and no SCA
What do we expect proportions of ss? Ss?
• E.g. 4% ss - what are proportions of Ss
– .04 = ss = q2 􀃆 q = √.04 = .2
– p = 1 - q = 1 - .2 = .8
– Ss = 2pq = 2(.8)(.2) = .32
Hardy Weinberg Problem II
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What would it take to increase Ss
proportion to 50% (from 32%)?
– Ss = 2pq = .5 􀃆 pq = .25
– q = 1 - p 􀃆 p (1-p) = .25 􀃆 p = .5
– Which means
aa goes to .25 from .04, over 6x
Hardy Weinberg Problem III
How many of you can roll your
tongues?
– A - Yes
–B-N
Hardy Weinberg Problem III
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What is the percentage of heterozygous
tongue-rollers?
– Yes = p2 + 2pq
– No = q2
– q = √No
– p = 1- q
– Heterozygous = 2pq