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Hardy Weinberg Law v1/04
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Prerequisites: Monohybrid Cross, Human genetics, Blood type inheritance
I. Introduction
By now you have probably realized that when we speak of gene frequency we are not considering
whether an allele is dominant or recessive. Some dominant alleles seem to be more frequent than their
recessive allele "partner"; for example, the allele for right-handedness is more frequent at LincolnSudbury than the allele for left-handedness. However, the allele for type O blood is recessive and yet
type O blood is the most common in our population. Here are some interesting human alleles that are
dominant, but not frequent:
no iris in eye
congenital cataracts
split feet
no incisor teeth
Obviously these genetic defects are very rare (infrequent) in the human population.
In this study we are no longer considering simply the inheritance of a trait by a set of offspring from
certain parents. we are considering the frequency of genes in a population. A "population" is considered
to be a stable group of individuals in which mating occurs at random. We also will assume that:
1. there is no mutuation of the gene;
2. there is no selection for or against the gene.
In 1908, an English mathematician, G. H. Hardy and a German physician, W. Weinberg each formulated
a theorem that describes the gene frequencies in a population. We call it the Hardy-Weinberg Law:
It states that in a single generation of random mating within a population, the binomial distribution of
genes is approximated by the equation: p2 + 2pq + q2 = 1.
where:
p2
= frequency of the homozygous dominant genotype
2pq = frequency of the heterozygous genotype
q2
= frequency of the homozygous recessive genotype
The sum of the genotypes equals 1, or 100% of the population. It is also given to you that
p = dominant allele frequency
q = recessive allele frequency
p+q=1
( 1 = 100% or the entire population )
Now what can you do with this wealth of information? You are walking around in a beautiful valley in
the Himalayan mountains. This society has been genetically stable for centuries, but where do you start?
You look into their eyes for the answer. You see a person with blue eyes.
1. Do you know his genotype for eye color?
Blue eyes must be homozygous recessive; so to find the number that are homozygous recessive for eye
color, you simply walk around and count the number of individuals with blue eyes and brown eyes.
Hardy Weinberg Law
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After taking your census, you find that about 9% of your population has blue eyes. Therefore, 9% of
your population is homozygous recessive or:
9% = q2
Knowing the value of q2, you can find the value of q:
9% = 0.09
q = 0.09
q = 0.3
Knowing the value of q, you can find the value of p:
q+p
0.3 + p
p
p
=
=
=
=
1
1
1 - 0.3
0.7
(remember, the sum of the frequency
of the dominant allele plus the
frequency of the recessive allele equals
1, or 100% of the population.)
Now you know the values of your p's and q's, you can plug these into the original equation and find the
distribution of genotypes for eye color in this stable society.
p = 0.7
q = 0.3
p2+ 2 pq + q2 = 1
Substituting values for letters:
p2 = (0.7) 2
2pq = 2(0.3)(0.7)
q2 = (0.3) 2
p2 = homozygous dominant = 0.49 or 49%
2pq = heterozygous = 0.42 or 42%
q2 = homozygous recessive =0.09 or 9%
(Recall that these three frequencies should total 100% or 1)
With this equation you can determine the probable proportions of genotypes and alleles in a stable
population. Answer the following questions and then check the answer sheet at the end of the packet.
Question 1. What percent of population has the allele for blue eyes?
Questlon 2. What percent of population has allele for brown eyes?
Question 3. If you set out to eliminate an allele, which would be easier to eliminate in the population,
the dominant or recessive allele? Why?
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Hardy-Weinberg Law Sample Problem
In the sophomore class of 400 students you find that 100 students cannot taste PTC paper. Three
hundred students, when tested, do taste PTC. The allele for PTC tasting is dominant. Using the HardyWeinberg Law, find:
1. What is the frequency of the homozygous recessive genotype?
2. What is the frequency of the non-tasting allele in this population?
3. What is the frequency of the tasting allele?
4. What is the frequency of the homozygous dominant genotype?
5. What is the frequency of the heterozygous genotype?
6. If your sophomore friend tells you he is a PTC taster, is he likely to have a homozygous genotype or a
heterozygous genotype?
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Hardy-Weinberg Law Answer Sheet
Question 1. 30% of the population has the allele for blue eyes.
Question 2. 70% of the population has the allele for brown eyes.
Question 3. It would be easier to eliminate the dominant allele from the population, because the
dominant allele is always expressed in the phenotype.
For instance, the king of this Himalayan mountain valley could decree that all brown-eyed people could
not have children. Within a generation, the brown-eyed people would die, Since the only individual s
that would have reproduced would have been blue-eyed, there would only be blue-eyed people left.
Hardy-Weinberg Problem on tasting PTC.
1. Frequency of the homozygous recessive genotype.
non-tasters = 100 /400 = 1/4 = 0.25
q2 = 0.25
2. Frequency of non-tasting allele
2
q = 0.25
q = 0.5
3. Frequency of the tasting allele
p+q = 1
p + 0.5 = 1
p = 1 - 0.5
p = 0.5
4. Frequency of the homozygous dominant genotype
p = 0.5
2
p = 0.25
5. Frequency of the heterozygous genotype
2 pq = 2(0.5)(0.5)
= 0.50
6. The frequency of the heterozygous genotype is 0.50. The frequency of the dominant homozygous
genotype is 0.25. Therefore, it is more likely that your friend is a heterozygote.
Hardy Weinberg Law
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