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Teacher Guide: Hardy-Weinberg Equilibrium
Learning Objectives
Students will …
 Determine that the ratios of alleles tend to remain nearly constant in a randomly-mating
population.
 Determine that the ratios of genotypes also tend to remain nearly constant in a
randomly-mating population.
 Measure the ratio of heterozygous to homozygous individuals in a population, and see
that this ratio remains fairly constant over time.
 Use the Hardy-Weinberg equation to calculate the percentages of genotypes in a
population.
Vocabulary
allele, genotype, Hardy-Weinberg equation, Hardy-Weinberg principle, heterozygous,
homozygous, Punnett square
Lesson Overview
Many factors can influence the frequencies of different alleles
and genotypes in a population. Predation, sexual selection,
immigration, disease, competition, or natural selection may
cause some alleles to become more common and others to
become less common.
To understand if a population is being influenced by one of these
factors, it is first necessary to understand how a population
reacts if none of these factors are present. The Hardy-Weinberg
Equilibrium Gizmo™ allows students to explore how the
proportions of alleles and genotypes change over time in a
A population of proud parrot
population that is not undergoing any form of selection.
parents preparing for progeny
The Student Exploration sheet contains two activities:

Activity A – Students discover that in normal circumstances allele and genotype
percentages tend to remain stable over time.

Activity B – Students derive the Hardy-Weinberg equation and use it to calculate
genotype and allele percentages.
Suggested Lesson Sequence
1. Pre-Gizmo activities
( 10 – 20 minutes)
The Hardy-Weinberg Equilibrium Gizmo explores the mathematical laws that govern
allele and genotype percentages in a population. Before beginning the Gizmo, review
basic genetic terms such as allele, genotype, phenotype, homozygous, and
heterozygous. Practice filling in Punnett squares for various combinations of parent
genotypes, and predict the percentages of each offspring genotype and phenotype. The
Mouse Genetics (One Trait) Gizmo provides a helpful review of these topics.
2. Prior to using the Gizmo
( 10 – 15 minutes)
Before students are at the computers, pass out the Student Exploration sheets and ask
students to complete the Prior Knowledge Questions. Discuss student answers as a
class, but do not provide correct answers at this point. Afterwards, if possible, use a
projector to introduce the Gizmo and demonstrate its basic operations. Demonstrate how
to take a screenshot and paste the image into a blank document.
3. Gizmo activities
( 15 – 20 minutes per activity)
Assign students to computers. Students can work individually or in small groups. Ask
students to work through the activities in the Student Exploration using the Gizmo.
Alternatively, you can use a projector and do the Exploration as a teacher-led activity.
4. Discussion questions
( 15 – 30 minutes)
As students are working or just after they are done, discuss the following questions:

Suppose there is a rare recessive allele in a large population. If the allele confers
no advantage or disadvantage, what would you expect to happen over time? [If
the population is in equilibrium, the proportion of the rare allele should remain
constant over time.]

The Hardy-Weinberg Equilibrium Gizmo focuses on a population that is in
equilibrium. How could you determine if a population is affected by natural or
artificial selection?

Suppose the green and yellow (Dd) parrots were particularly popular in the illegal
pet trade. How could you determine if a wild parrot population was affected by
poachers? [In a normal population, the ratios of DD, Dd, and dd parrots should
be p2: 2pq: q2, where p is equal to the proportion of DD parrots plus half the
proportion of Dd parrots, and q is equal to the proportion of dd parrots plus half
the proportion of Dd parrots. If the parrot population is affected by poachers, the
Dd population will be smaller than what this proportion predicts.]
5. Follow-up activity: Microevolution
( 30 – 60 minutes)
The Hardy-Weinberg Equilibrium Gizmo focuses on a population of parrots that is not
under any directed selection pressures. To explore what happens when selection is
occurring, have students work through the Microevolution Gizmo. In this Gizmo, the
parrot population lives in a grove of trees and is predated on by hawks. Wellcamouflaged parrots are less likely to be eaten and will tend to reproduce and pass on
their alleles to the next generation. This Gizmo allows students to explore scenarios
such as a deleterious recessive gene and heterozygote superiority.
Scientific Background
The early 1900s was an important time in biology. Just as Charles Darwin’s theory of evolution
by natural selection was gaining wide acceptance among scientists, Gregor Mendel’s laws of
heredity were rediscovered. Elements of both of these revolutionary ideas were incorporated
into a new field of science called population genetics.
Population geneticists sought to understand how natural selection and other factors would affect
allele and genotype frequencies over time. The first step in this process was to determine what
a population would look like when no natural selection or other disturbing factors were present.
The Hardy-Weinberg principle states that in the absence of natural selection and other factors
both allele and genotype frequencies will remain constant over time. This applies to populations
that satisfy the following conditions:



The population is large.
Mating is random.
All individuals mate, and all mated pairs
produce the same number of offspring.



There is no immigration or emigration.
There is no mutation.
There is no selection pressure for or
against any particular trait.
The Hardy-Weinberg principle also allows one to predict the genotype
frequencies that result from a particular distribution of alleles. This is
illustrated on the Punnett square at right. If the proportion of the dominant
allele (D) is p and the proportion of the recessive allele (d) is q, then the
probability of genotype DD is p 2, the probability of genotype dd is q 2, and
the probability of genotype Dd is 2pq.
The genotype frequencies predicted by Hardy-Weinberg can be arranged as follows:
Dd  Dd 2 pq  2 pq

4
DD  dd
p2q2
This arrangement provides a quick way to test if natural selection or another disturbing factor is
present. If the ratio of Dd 2 to DD·dd is not close to 4, then one of the conditions listed above
must not be true for the population.
Historical Connection: Discovery of the Hardy-Weinberg principle
In the early days of population genetics, some scientists believed that the “stronger” dominant
genes would eventually overwhelm the “weak” recessive genes in a population, causing traits
such as blond hair to go extinct. This phenomenon was called genophagy, or “gene-eating.” If
that was the case, how did recessive genes survive at all?
In 1908, the Cambridge geneticist Reginald Punnett mentioned this conundrum to his colleague
G. H. Hardy. Hardy was a pure mathematician who boasted, “Nothing I have ever done is of the
slightest practical use.” Surprised that this “simple problem” had not been solved already, Hardy
quickly worked out the rule and published his discovery in the July, 1908, issue of Science.
In fact, the principle had been previously discovered by the German physician Wilhelm
Weinberg. Weinberg presented his version of the Hardy-Weinberg principle in a January 1908
lecture to the Württemberg Natural History Society. Weinberg’s work was unknown to Englishspeaking scientists until the oversight was finally noticed in 1943.
Selected Web Resources
Hardy-Weinberg principle: http://anthro.palomar.edu/synthetic/synth_2.htm
History of Hardy-Weinberg principle: http://www.genetics.org/cgi/content/full/179/3/1143
G. H. Hardy’s letter to Science: http://www.vacadsci.org/jsr/hardy.htm
Related Gizmos:
Mouse Genetics (One Trait): http://www.explorelearning.com/gizmo/id?449
Microevolution: http://www.explorelearning.com/gizmo/id?521