AP Biology—Unit 8
Hardy-Weinberg Equilibrium
Name:
Introduction
Evolution occurs in populations of organisms and involves variation in the population, heredity, and differential
survival and reproduction. One way to study evolution is to study how the frequency of alleles in a population
changes from generation to generation. In other words, you can ask “What are the inheritance patterns of
alleles, not just from two parental organisms, but also in a population?” You can then explore how allele
frequencies change in populations and how these changes might predict what will happen to a population in the
future.
Mathematical models and computer simulations are tools used to explore the complexity of biological systems
that might otherwise be difficult or impossible to study. In 1908, one such scheme, whereby evolution could be
viewed as changes in the frequency of alleles in a population of organisms, was independently suggested by
G.H. Hardy and W. Weinberg.
In this scheme, if A and a are alleles for a particular gene locus and each diploid individual has two such loci,
then p can be designated as the frequency of the A allele and q as the frequency of the a allele. In a population
of 100 individuals (each with two loci/alleles) in which 60% of the alleles are A, 40% of the alleles would be a.
Consequently, the frequencies for these alleles would be as such:
p = 0.6
q = 0.4
These are referred to as the allele frequencies in the population and we can conclude that:
p+q=1
(Allele Frequency Equation)
The frequencies of the possible genotypic / diploid combinations of these alleles (AA, Aa, aa) can be expressed
by an equation, but let’s first develop a Punnet square to see the possibilities.
p = 0.6
q = 0.4
p = 0.6
q = 0.4
The probability of two A alleles combining in one organism in the next generation is p2. The probability of two
a alleles combining in one organism in the next generation is q2. The probability of a combination of Aa is p*q,
as is the probability of aA , for a total of 2pq. Consequently, the formula that predicts the genotypic frequencies
for the next generation in a population is:
(p + q)2 = 1, which works out to be
p2 + 2pq + q2 = 1 (Genotypic Frequency Equation)
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If p = 0.6 and q = 0.4, what are the frequencies for the following genotypes?
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Homozygous Dominant _______________________
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Heterozygous ________________________
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Homozygous Recessive ________________________
Hardy and Weinberg also argued that if five conditions are met, the population’s allele and genotype
frequencies will remain constant from generation to generation. These conditions are as follows:
1.
2.
3.
4.
5.
The breeding population is large.
Mating is random.
There is no mutation of the alleles.
No differential migration occurs.
There is no selection.
Overall Objectives of the Lab
1. Explain Hardy-Weinberg Equilibrium in terms of allelic and genotypic frequencies and relate these to
the expression (p + q)2 = p2 + 2pq + q2 = 1.
2. Describe the conditions necessary to maintain the Hardy-Weinberg Equilibrium.
3. Use a bead model to demonstrate conditions for evolution.
Part 1—Testing the Hardy-Weinberg Equilibrium
You will test the Hardy-Weinberg Equilibrium by simulating a population using colored beads. The bag of
beads represents the gene pool for the population. Each bead should be regarded as a single gamete, the two
colors representing different alleles of a single gene. Each bag should contain 100 beads total of the two colors.
You may start with 50 and 50, 40 and 60, etc.
Hypothesis—Write a null hypothesis for this experiment, using the principles of the Hardy-Weinberg Theorem.
Procedure—
1. Determine how many beads of each color with which your population will begin and place them in your
bag.
2. Before beginning Steps 3-5, record the following information in your results section:
a. What color is representing A, and what is the initial allelic frequency of A?
b. What color is representing a, and what is the initial allelic frequency of a?
c. How many diploid individuals are represented in this population?
d. What would be the color of the beads for a homozygous dominant individual, a heterozygous
individual, and a homozygous recessive individual?
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3. Without looking, randomly remove two beads from the bag. This represents one diploid individual in
the next generation. Record the diploid genotype (AA, Aa, aa) of the individual formed from these two
gametes in the results section of this packet.
4. Return the beads to the bag and shake the bag to reinstate the gene pool. By replacing the beads each
time, the size of the gene pool remains constant and the probability of selecting any alleles should
remain equal to its frequency.
5. Repeat Steps 3-4 until you have recorded the genotype for 50 individuals who will form the next
generation of the population.
Results—Record your initial data in the space below.
Data Analysis:
1. Calculate and record the total number of diploid individuals for each genotype in the space below.
2. Calculate and record the genotypic frequencies for AA, Aa, and aa as well as the allelic frequencies for
A and a. These values are the observed frequencies for both the genotypic and allelic frequencies in the
new population and their sum should equal 1.
a. Observed genotypic frequencies:
b. Observed allelic frequencies:
3. Calculate and record the expected genotypic and allelic frequencies for the new population. Use the
original allelic frequencies for the parent population. Remember, the frequency of A = p and the
frequency of a = q.
a. Expected genotypic frequencies:
b. Expected allelic frequencies:
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4. Calculate the number of individuals expected for each genotype by multiplying 50 (total population size)
by the expected frequencies.
5. Compare your observed number of individuals for each genotype with your expected number of
individuals with each genotype by completing a chi-square statistical analysis. Your equation is:
x2 = The sum of (o – e)2
e
x2 = _________________________
6. Use the chart to determine if the difference between your observed and expected results is statistically
significant. In the space below, please write if you fail to reject your null hypothesis OR if you reject
your null hypothesis and explain why.
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Discussion Questions
1. What proportion of the population was homozygous dominant, heterozygous, homozygous recessive at
the beginning of the simulation and the end of the simulation?
2. Were your observed results consistent with the expected results based on your statistical analysis? If
yes, why? If not, can you suggest an explanation?
3. Is this population evolving? Explain.
4. Does this model meet all of the conditions for the Hardy-Weinberg model? Explain.
Part II—Simulation of Genetic Drift
You will simulate genetic drift, and more specifically, the Bottleneck Effect using 100 beads—50 of two colors.
Hypothesis—Propose a hypothesis that addresses the bottleneck effect specifically, or state the H-W theorem
as your hypothesis.
Procedure—
1. Establish a population containing 50 individuals with a frequency of 0.5 for each allele.
2. By sampling with replacement, remove five pairs of alleles (10% of the population) to determine the
allelic frequencies for the next generation. Record the number of individuals, allelic frequencies, and
genotypic frequencies for each generation in the results section.
3. Reestablish the gene pool to 50 individuals using the new allelic frequencies and continue to select only
five pairs of alleles in each successive generation.
4. Continue the simulation until one of the alleles becomes fixed in the population for several generations.
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Results—
1. You can record initial data in the space below, but make a neat data table recording your data and attach
to this packet before turning in your lab.
2. Prepare a graph of the change in p and q over time. Attach the graph to this packet.
Discussion Questions
1. Compare the pattern of change for p and q. Is there a consistent trend or do the changes suggest chance
events? Look at the graphs of other teams to help inform you conclusion.
2. Explain your observations of genetic fixation for the replicated simulations completed by the class.
What would you expect if you simulated bottleneck effect 100 times?
3. How might your results have differed if you had started with different allelic frequencies, for example,
p = 0.2 and q = 0.8?
4. Since only chance events—that is the effect of small population size—are responsible for the change in
gene frequencies, would you say that evolution has occurred? Explain.
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Part III—Design Your Own Experiment
Using beads for your population. Develop your own procedure that would illustrate if one of the other
conditions for H-W Equilibrium were to be violated.
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


Pick your condition.
Write a hypothesis.
Write a procedure. (This procedure should contain enough detail for anyone to follow.)
Write what you would expect to happen and why.
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