Hardy-Weinberg Lab
Background: In 1908, two scientists, Godfrey H. Hardy, an English mathematician, and Wilhelm
Weinberg, a German physician, independently worked out a mathematical relationship that
related genotypes to allele frequencies.
Godfrey H. Hardy
Wilhelm Weinberg
Their mathematical concept, called the Hardy-Weinberg principle, is a crucial concept in
population genetics. It predicts how gene frequencies will be inherited from generation to
generation given a specific set of assumptions. 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. This
principle is important because it gives biologists a standard from which to measure changes in
allele frequency in a population.
The Hardy-Weinberg principle can be illustrated mathematically with the equation:
p2+2pq+q2 = 1
p+q=1
Where ‘p’ and ‘q’ represent the frequencies of alleles. It is important to note that p added to q
always equals one (100%).
To illustrate how the Hardy-Weinberg principle works, let us consider the MN blood group.
Humans inherit either the M or the N antigen, which is determined by two different alleles at the
same gene locus. If we let the frequency of allele M equal “p” (p = M) and the frequency of the
other allele N equal “q” (q = N), then the next
generation's genotypes will occur as follows:
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

Frequency of MM genotype = p2
Frequency of MN genotype = 2pq
Frequency of NN genotype = q2
Remember: Each offspring gets one
allele from mom and one from dad!
We can take a sample of the population and count the number of people with each genotype. For
example, a sample of 5000 from Forensic Town, USA, has:
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

1460 individuals of type MM, that is 1460/5000 or 29.2%
2550 of type MN, that is 2550/5000 or 51%
990 of type NN, that is 990/5000 or 19.8%
Remember:
allele frequency =
# of specific allele/# of
total alleles
If we apply the Hardy-Weinberg equation (p2 + 2pq + q2 = 1) we
can calculate the allele frequencies as:


Frequency of M = p2 + 0.5 (2pq) = 0.292 + (0.5 x 0.51) = 0.547
Frequency of N = q = 1 - p = 1 - 0.547 = 0.453
We can now calculate our expected genotype frequencies:
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
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MM = p2 = 0.5472 = 0.299, or 1496 individuals in the sample
MN = 2pq = 2 x 0.547 x 0.453 = 0.496, or 2478 individuals
NN = q2 = 0.4532 = 0.205, or 1026 individuals
Our expected genotype frequencies are not identical to our actual sample from Forensic Town,
USA suggesting this population is evolving.
Source: National Forensic Science Technology Center (www.nfstc.org)
Procedure: Assume you are dealing with a single gene that has two allele alternatives, A and a.
“A” is dominant over “a”. Red suits (diamonds and hearts) represent “A”. Black suits (clubs and
spades) represent “a”. Jokers, since they are printed in black ink, will also represent “a”.
To begin each simulation, each student must have one red-suited and one black-suited card. This
represents the heterozygous (Aa) genotype.
When mating, pass one of your cards face down to your partner. They will give you one of their
cards in return. NO peeking at your cards until told to do so. Unlike real human mating
(hopefully!), all mating will be random. This means if someone asks you, you have to mate with
him or her. Same sex, opposite sex…it doesn’t matter.
Simulation 1: Begin by counting the number of students in the class. Count the number of each
genotype (AA, Aa, or aa) in the class and then calculate the frequency of alleles, A and a. Record
this information in your Data Table.
Each member will mate (exchange a card) with another member of the class. After the exchange,
each student will now represent the newest generation and will be ready to mate with another
member of the class.
You must mate with a different person each time, and you must mate five times. No peeking at
your cards in-between romantic encounters!
After everyone in the class has mated five times, count the number of each genotype (AA, Aa, aa)
in the class and calculate the frequency of the alleles, A and a. Record this information in your
Data Table.
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

AA = red & red
Aa = red & black
aa = black & black
Simulation 2: Everyone begins as a heterozygote again. Count the number of different
genotypes and the frequency of the alleles, A and a. Record this information in your Data Table.
Now mate as you did before, however, you will look at your cards after the first mating. If you
inherited the “aa” genotype, then you die and must sit down. Everyone that is still living will
mate four more times. No peeking in-between these encounters.
Before calculating the allele frequencies of A and a, hypothesize what will happen to these values
because the “aa” individuals died after the first mating. Will they be similar to Simulation 1 or
different? Why?
The genotypes of the survivors and the frequency of the alleles, A and a, should be determined.
Record this information in your Data Table.
Simulation 3: Everyone begins as a heterozygote again. Count the number of different
genotypes and the frequency of the alleles, A and a. Record this information in your Data Table.
Now mate as you did in Simulation 1. No peeking at your cards in-between romantic encounters!
At the end of five matings, sit down and your teacher will tell you if you survive or not. You see,
you may have been in the wrong place at the wrong time and chance alone (we call this genetic
drift) determined that you did not survive. The remaining students survive.
Before calculating the allele frequencies of A and a, hypothesize what will happen to these values
because genetic drift (chance). Will the allele frequencies change or stay the same? Why?
Count the different genotypes of the survivors and calculate the frequency of the alleles, A and a.
Record this information in your Data Table.
Names: ____________________________________________________ Date: ________________________ Period: _________
Hardy-Weinberg Lab
Background:
1. What does the Hardy-Weinberg Principle state? _____________________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
2. What is the Hardy-Weinberg equation? What does each variable represent? _____________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
Data Table:
Simulation
1
Simulation
2
Simulation
3
Beginning #
of AA
Beginning #
of Aa
Beginning #
of aa
Total # of
alleles
Beginning
frequency of
A
Beginning
frequency of
a
Ending # of
AA
Ending # of
Aa
Ending # of
aa
Total # of
surviving
alleles
Ending
frequency of
A
Ending
frequency of
a
Beginning #
of AA
Beginning #
of Aa
Beginning #
of aa
Total # of
alleles
Beginning
frequency of
A
Beginning
frequency of
a
Ending # of
AA
Ending # of
Aa
Ending # of
aa
Total # of
surviving
alleles
Ending
frequency of
A
Ending
frequency of
a
Beginning #
of AA
Beginning #
of Aa
Beginning #
of aa
Total # of
alleles
Beginning
frequency of
A
Beginning
frequency of
a
Ending # of
AA
Ending # of
Aa
Ending # of
aa
Total # of
surviving
alleles
Ending
frequency of
A
Ending
frequency of
a
Simulation 2 Prediction:
______________________________________________________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
Simulation 3 Prediction:
______________________________________________________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
Analysis & Conclusions
1. Explain why the allele frequencies in Simulation 1 did not change although the number of
different phenotypes did change. ______________________________________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
2. Why did the frequency of the alleles change in Simulation 2? _______________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
3. In Simulation 3, the allele frequencies should have hanged due to the random event that
removed a portion of the population.
a. How was Simulation 3 different from Simulation 2? _________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
b. If the class size had been 1,000 instead of our actual class size (which is much smaller
than 1,000), and the same number of students were randomly removed, do you think
the change in allele frequency would have been as different as the change your class
experienced? Explain your reasoning. _________________________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
4. Other than population size, what four factors might interfere with the H-W principle?
_______________________________________________________________________________________________________________
_______________________________________________________________________________________________________________
5. If you know that a population is 75% the dominant phenotype (p2 + 2pq) and 25% is the
recessive phenotype (q2), can you determine approximately how many of the dominant
phenotype are homozygous dominant (p2) and how many are heterozygous dominant (2pq)?
Show your math.
Hardy-Weinberg Lab Extra Credit – MUST SHOW ALL YOUR WORK TO EARN
CREDIT
1. Tall is dominant over short in pea plants. In a population of pea plants, 60 were tall (T) and 40
were short (t). (3 points)
a. What is the frequency (%) of short plants in the population?
b. Using your answer to part a, calculate the frequency of the short gene.
c. What is the frequency of the tall gene?
2. If all of the pea plants in question 1 reproduce and the next generation is 200 plants, who
many of those plants will be: (3 points)
a. Homozygous dominant:
b. Heterozygous:
c. Homozygous recessive:
3. If all the short (homozygous recessive) plants in question 2 die, what will be the new
frequency of the: (two points)
a. tall allele:
b. short allele:
4. If the short plants continue to die generation after generation, will the frequency of t ever
reach zero? Defend your answer. (2 points)