HARDY-WEINBERG AND EVOLUTION
The Hardy-Weinberg principle is straightforward: if p + q = 1, then p2 + 2pq +q2 = 1.
Arithmetically, this is trivial. Biologically it is astonishingly profound. This is a lab exercise in
which your lab class will become a population of fishes. In becoming this population, you will
learn that by simple, straightforward exchange of gametes, several remarkable evolutionary
processes can occur: genetic drift, mutation, natural selection, gene-flow, and nonrandom
mating. You will even gain insights into the processes that can lead to speciation.
Summary:
The biological principle illustrated by the Hardy-Weinberg equation is this: If a population has
only two alleles at a given locus, and their frequencies are known, we can call those frequencies
p and q. Since there are only two alleles, it must be true that p + q=1. For example, let’s say we
have a population of 100 diploid individuals. Among them they have 200 alleles at the locus of
interest; 120 are of one form and 80 are of the other form. The frequency of the first allele form
is 120/200 (p = 0.6), and the frequency of the second is 80/200 (q = 0.4). Note that it doesn’t
really matter which allele gets described by p and which by q. However, a common convention
is to give the p label to the frequency of the more common allele.
In a diploid population, every individual has two copies of each gene (two alleles). Since the
probability that an individual has one copy of the first allele is p, then the probability that it is
homozygous for that allele is p2. This is just an illustration of the law of independent
probabilities. The same argument can be used to describe the probability that an individual is
homozygous for the second allele, q2, or in fact that the individual is heterozygous, 2pq. The
point is this: if you know p and q, you can predict what the frequency of each genotype will be in
the population using the law of independent probabilities. Predicting the future of populations is
the brass ring of ecology and conservation biology, and in population genetics, we have captured
that ring. Since there are only three possible genotypes, then the sum of those three frequencies
must equal one. Thus we come by a biological argument to the same equation, p2 + 2pq +q2 = 1.
Here a numerical example is very helpful.
Say we have a population of 100 diploid individuals. Among them, there are 200 alleles of the
gene we are interested in (because each individual has two copies). If we know that the first
allele, let’s call it A, occurs with a frequency p = 0.6, and the second, a, with a frequency q = 0.4,
then we can predict that in that population, 0.36 will have the genotype AA (0.62), 0.16 will be
aa (0.42), 0.48 will be Aa (2 x 0.6 x 0.4). At this point, students usually yawn, bored stiff,
knowing that this is ridiculously obvious. Unfortunately, it isn’t. If you go to that population of
100 individuals, and count the number of homozygotes of each kind and the number of
heterozygotes, the proportions of each may not be the proportions predicted above. For example,
a population with 60 AA and 40 aa individuals does not meet the predictions of HardyWeinberg. Populations do not have to be in Hardy-Weinberg proportions, and in fact they
usually aren’t. In this demonstration, p = 0.6 and q = 0.4, but the frequency of AA is not the
predicted 0.16, instead it is a whopping 0.6. This is why Hardy-Weinberg equilibrium is
interesting: A population can have other-than-predicted frequencies of genotypes. In fact, when
a population deviates from the expected proportions of genotypes, when it is out of HardyWeinberg equilibrium, we have proof of evolution acting on the population. Proof of evolution
is a wonderful thing because many don’t think that this kind of proof is easy to come by. In fact,
many people are under the impression that evolution is not demonstrable. But here we have it: if
a population is out of Hardy-Weinberg equilibrium, it is because something (evolution) has
interfered with the law of probabilities which govern that equilibrium. There is another
interesting consequence of the Hardy-Weinberg law: if a population is out of Hardy-Weinberg
equilibrium in one generation, it will be back in equilibrium in the next generation (if generations
are non-overlapping, which is to say that everyone mates and then dies before its offspring are
mature). That means that in every generation we can look for evidence of evolution, because
every time we expect the population’s genotypes to be in Hardy-Weinberg proportions. So how
can populations find themselves out of Hardy-Weinberg equilibrium? There are five
qualitatively different ways, and each is considered an evolutionary process. These ways are:
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Genetic drift (sampling error in alleles getting from one generation to the next)
Gene flow (migration of alleles into or out of the population)
Mutation (spontaneous change of alleles within the population)
Natural selection (differential success of one allele over another)
Nonrandom mating (preferential mating of some allele combinations over others)
Description of lab exercise:
In this laboratory, we will use the understanding of Hardy-Weinberg to see how evolutionary
forces work to drive populations away from predicted allele and genotype frequencies. You will
observe how allele frequencies can change over time in a population of fish. The lake the fish
live in is the classroom, and each of you will carry one fish around the lake. Thus there are as
many fish in the lake as there are students in the class. Each fish is represented by a card that
shows its genotype. Each fish in the population has two traits that we will pay attention to, and
each trait is controlled by two alleles at one locus. Your fish will exchange genes with other fish
in the population, produce offspring, and then die. (In your fish population, fish die after they
mate. Salmon really do this, as do many non-fish species.) The offspring will also produce
offspring. Thus, as a class, you will participate in the evolution of the fish population over
several generations. In doing this, you will be able to integrate the ideas you have learned about
Mendelian inheritance with the ideas you have learned about the evolution of populations. You
will discover what some of the great geneticists and mathematicians discovered in the 1930s:
Mendelian genetics and Darwinian evolution are two sides of the same coin.
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Activity 1. Characterizing a population:
Each student should have at his/her bench an index card that describes the genotype of an
individual fish. On the card you will see three characteristics:
1. Mating type. There are two mating types, XX and XY. Individuals can only exchange
genes with individuals that have a different mating type.
2. Blue locus. This locus controls one trait in your individual (such as fin shape). There are
two kinds of alleles (light blue and dark blue) in the population at this locus.
3. Green locus. This locus controls another trait in your individual (mouth size). As with
the blue locus, there are two kinds of alleles (light green and dark green).
Count the alleles at each locus in your class population, and answer the three questions below.
You will need these data for subsequent activities.
 What is the population size?
 How many alleles are there at the blue locus?
 What is the relationship between population size and number of alleles?
 What are the frequencies of each allele? (Complete Table 2, columns labeled 1 only.)
 What are the frequencies of each genotype? (Complete Table 3.)
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Activity 2. Hardy-Weinberg proportions:
Hardy-Weinberg proportions are the frequencies of genotypes that we expect in a population
with a given set of allele frequencies. If, at any locus, a population is not in Hardy-Weinberg
proportions, this is evidence of evolution. What genotype frequencies do we expect in a
population? In a population with only two kinds of alleles at a locus, the frequency of one allele
can be symbolized by p, and the frequency of the other can be symbolized by q. It is always true
that p + q = 1, no matter what values p and q have. The probability that any individual has one
copy of the first allele is p. The probability that that individual has two copies of the first allele
is p2. This is because the probability that two events occur simultaneously is the product of their
independent probabilities. By the same logic, the probability that an individual has two copies of
the second allele is q2. What is the probability that an individual has one of each allele? At first
you might say pq. That is the product of their independent probabilities. But there is another
way that an individual can have one of each allele, that is, by qp. Thus there are two ways of
being heterozygote, pq or qp. The probability that two events occur alternatively is the sum of
their independent probabilities. Thus, the chance that an individual is heterozygous is pq + qp =
2pq. Thus, we expect the genotype frequencies in a population to be p2, 2pq, and q2. The sum
of these three frequencies equals one because they represent 100% of the population.
Work with the students at your lab bench (group of three or four students) to fill in the following
table.
 What are the Hardy-Weinberg proportions of each genotype? (Complete Table 4.)
 Compare the expected genotype frequencies with your actual genotype frequencies for the
blue locus and for the green locus.
 Is the blue locus actually in Hardy-Weinberg proportions?
 Is the green locus actually in Hardy-Weinberg proportions?
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What does it mean if a locus is in Hardy-Weinberg proportions?
Can one locus be in Hardy-Weinberg proportions, and the other not?
Why or why not?
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Activity 3. The next generation & genetic drift
Before we begin, venture a guess to the following questions:
 Do allele frequencies change from one generation to the next?
 Do genotype frequencies change from one generation to the next?
Take your fish to one of the spawning grounds and find someone who is carrying a fish with a
different mating type. If you can’t find anyone, wait out this turn until the second round. Failure
to find a mate is common in many species.
1) Determine the genotype of the first offspring.
a) Write down the genotype of your parental fish before you begin (Table 5).
b) Put the two alleles from the blue locus of your fish in each of your fists. The person
carrying your fish’s mate should blindly select one of your fists. The allele he/she
chooses will be the first allele of the first offspring.
c) You should do the same with the alleles of your fish’s mate to select the second allele of
the first offspring.
d) You now have two selected alleles that represent the blue locus genotype of your first
offspring.
e) On your gene exchange worksheet (Table 5) write in the new blue-locus genotype of the
first offspring.
f) Replace the alleles from your fists into your fish’s genotype card to restore it to its
original parental state (refer to your written notes if necessary).
g) Repeat the same procedure for the green locus alleles.
h) Determine the mating type of the first offspring using the same procedure.
2) Determine the genotype of the second off spring. Use the same method as above.
3) Allow your parental fish to die.
a) Remove the alleles and mating type labels from the genotype cards.
b) Put these alleles and labels into the various containers around the room that hold the
extras. Allow your fishes’ offspring to be born by filling your empty genotype cards with
their new identities.
c) Note that your fish’s new genotype may have a different mating type and different alleles
than it had in the preceding generation.
d) Use the necessary alleles from the allele containers to make the new genotypes.
e) Your new fish is now a member of the next generation.
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When the whole class has reached the new generation, return to the spawning grounds with your
new fish, and find it a new mate. You may not choose a mate carried by someone with whom
you have exchanged genes in the previous generation. This will avoid inbreeding. (If you did
not avoid this, your fish might mate with a brother or sister. Nonrandom mating of this sort is an
evolutionary process in its own right. We will not consider it in this lab.) Repeat the cycle
through the second and third generations.
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At the end of three generations, what are the new frequencies of each allele? (Complete
Table 2, columns labeled 3 only.)
What are the frequencies of each genotype? (Complete Table 3, columns labeled 2 only.)
Have the allele frequencies changed at the blue locus?
Have the allele frequencies changed at the green locus?
Why?
Have the genotype frequencies changed at the blue locus?
Have the genotype frequencies changed at the green locus?
Is there a difference in how the genotype frequencies have changed at the two loci?
Why?
The number of successful breeding individuals is the effective population size. Is the
effective population size equal to the total population size?
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Activity 4. Mutation & selection
Until now, the different alleles have had no distinctive effect on fitness. That is to say that they
did not differ in their influence on the survival or reproductive success of the fish that carried
them. Now, a new allele will arise in your population (by mutation) that enhances fitness. The
new allele, “mutant B1,” will be introduced at the blue locus. Remember that the blue locus has
alleles that influence fin shape. Offspring with the new “mutant B1” allele have a new fin shape
that enables them to evade predators more effectively. These offspring will have a muchimproved chance of surviving their first few minutes of life compared to new offspring without
this allele.
 What do you predict will happen to the new mutant B1 allele in the fish population over
three generations?
A new allele will arise at the green locus too, “mutant G1.” Recall that the green locus
influences mouth size, and this new mutation changes mouth size by making the gape wider.
Because the lake is full of nutritious food sources for the fish, this new mutation does not
increase fish fitness. The fishes without this mutation can get all the food resources that they
need, even though their mouths are smaller. Thus, this mutation is considered neutral.
 What do you predict will happen to the new mutant G1 allele in the fish population over
three generations?
As before, your individuals will undergo three bouts of gene exchange, but the methods are
slightly different, so please follow these new instructions. Take your individual to one of the
spawning grounds, and find someone who is carrying an individual with a different mating type.
If you can’t find anyone, wait out this turn until the second round. During this time, your
professor will introduce one mutation at the blue locus and one mutation at the green locus (one
mutation in each of two arbitrarily selected fishes).
1) Determine the blue locus genotype of the first offspring.
a) Write down the genotype of your parental fish before you begin.
b) Put the alleles from the blue locus of your fish in your fists as before, and determine the
genotype of the first offspring.
c) If your offspring has one of the new mutant alleles, it survives.
d) If your offspring lacks one of the new mutant alleles (mutant B1), it may not survive.
Flip a coin to determine whether it lives or dies (heads = lives; tails = dies). This coin
flip corresponds to a probability of mortality in nonmutant genotypes that the mutant
genotype does not suffer. The nonmutant may, for example, be more susceptible to a
predator than the mutant.
e) If it dies, return the alleles to your fists, and determine a new genotype of the first
offspring. (Repeat the coin flip if it still does not have the mutant B1 allele.)
f) If your offspring lives, or if it has one of the mutant alleles, proceed.
g) On your gene exchange worksheet, write the new blue locus genotype of the first
offspring. Replace the alleles from your fists into your fish’s genotype card to restore it
to its original parental state.
2) Determine the green locus genotype of the first offspring.
a) Put the alleles from the green locus of your fish in each of your fists, and have the person
carrying your fish’s mate select one fist. Now you select an allele from the fists of this
person.
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3)
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5)
6)
b) No matter what genotype the offspring gets at the green locus, it lives, since the mutant
G1 does not alter the fitness of the fish.
c) On your gene exchange worksheet, write in the new green locus genotype of the
offspring.
d) Replace the alleles from your fists into your fish’s genotype card to restore it to its
original state.
Determine the mating type of the first offspring as you did in Activity 3.
Determine the genotype and mating type of the second offspring. Use the same method as in
1, 2, and 3 above.
Allow your fish to die. (In this fish population, as before, fish die after they mate.) Follow
the instructions in Activity 3 for this task.
Allow your offspring to be born by taking on their new identities. Follow the instructions in
Activity 3 for this task.
When the whole class has reached the new generation, return to the spawning grounds with your
fish, and find it a new mate. Your professor will not introduce further mutations during this
activity. As before, you may not choose a fish carried by someone whom you have exchanged
genes with in the most recent generation. Repeat the cycle through the second and third
generations.
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The difference between this activity and the last is that the number of alleles in the population
has probably changed. Though each individual still only carries two alleles at each locus, there
may be three different alleles if you examine the whole population at a particular locus. At the
blue locus, the new allele B1 improves the probability of reproductive success of your fish (so
the old alleles, by comparison, reduce reproductive success.) At the green locus, the new allele
G1 has no effect on reproductive success. It is neutral.
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What are the new frequencies of each allele? (Complete Table 2, columns labeled 4 only.)
Have the allele frequencies changed at the blue locus?
Why?
Have the allele frequencies changed at the green locus?
Why?
What happened to the new B1 allele?
What happened to the new G1 allele?
What does a fitness advantage do for a mutation?
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Activity 5. Population size & divergence
Sometimes a population can get subdivided as a result of a change in geography. For instance, a
river may change course and cut through the middle of a terrestrial population, isolating the two
halves from one another. In this activity, you will explore the consequences of this kind of
event. The lake in which your fish lives has suffered from a prolonged drought, and the lake
level has become so low that it now forms two smaller pools with a dry land area dividing the
middle. Half the fish live in one pool, and the remainder in the other.
As in Activity 4, your fish will undergo three generations of offspring production, and in the first
generation, your professor will introduce new mutations at each locus (the old mutations
remain). The mutations in each subpopulation will be different because mutations are very
rarely identical. The front half of the room will get mutations B2 and G2, and the back half of the
room will get mutations B3 and G3 (as before, the professor will place one mutation in each of
two arbitrarily selected fishes within each subpopulation). These mutations have no effect on
fitness, so you will follow the instructions from Activity 3 to make offspring (unless B1 is
involved, then follow the instructions from Activity 4). The difference between this activity and
the last is that the fish population is subdivided. Each subpopulation has a smaller size. If you
sit in the back half of the room, go to the back spawning grounds to exchange genes; if you sit in
the front half of the room, go to the front spawning grounds. No gene exchange will occur
between front and back, only within these separate spawning grounds.
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When you have exchanged genes for three generations, answer the questions below.
 What is your subpopulation size?
 What are the new frequencies of each allele? (Complete Table 2, columns labeled 5.)
 Write these numbers down on the chalkboard. Then reconvene for a class discussion.
 What occurred within your subpopulation?
 How does this compare to what occurred in Activity 4?
 Did the two subpopulations end up with the same allele frequencies?
There are several mechanisms that can cause divergence between populations. The initial allele
frequencies in subdivided populations may differ, the allele frequencies may drift apart during
the generations that follow subdivision, and new mutations may arise that differ among the
subpopulations. Small populations face unique problems. Often, in very small populations, there
are not equal numbers of males and females. In fact, this sex-ratio bias can make the effective
population size even smaller.
 Did any of these processes cause divergence between your two class subpopulations?
 Do allele frequencies change faster or slower when population size is small?
 Given your answer, is divergence facilitated or hampered by decreases in population size?
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Activity 6. Secondary contact
Just as a geographic barrier may arise and cause a population to subdivide, it may also disappear,
move, or change and allow the subdivided groups to reunite. What happens then? Are the two
groups that were previously isolated now two new species that can no longer interchange genes?
Are they still the same species? This final activity is designed to help you answer these
questions. The long drought is finally over, and rains have replenished the lake to its original
size. The two subpopulations once again are able to interact. However, some of the new alleles
influence mating success. Individuals with mutation B2 can never mate with individuals with
B3, and individuals with G2 can never mate with individuals with G3. In the case of the B2-B3
incompatibility, the two kinds of individuals mate at different times of day, so never meet each
other in spawning grounds (this is a prezygotic isolating mechanism). In the case of the G2- G3
incompatibility, the two kinds of fish produce a zygote that always fails to develop properly (this
is a post-zygotic isolating mechanism). You don’t need to adopt these behaviors, just don’t let
your fish mate with someone else’s if they are incompatible.
The two subdivided populations reunite in the original spawning grounds, and proceed with three
final cycles of gene exchange. However, some allele combinations result in no viable offspring.
Take your fish to the central spawning grounds, and find someone who is carrying an individual
with a different mating type.
1) If your individual and its mate do not have incompatible alleles:
a) Proceed as you did in Activities 3 and 4 to produce two offspring.
b) Wait until everyone in the class is finished with the first round before proceeding to the
second.
2) If your individual and its mate are incompatible:
a) Try one more time to find another mate.
b) If you succeed, go to 1.
c) If you fail to find a compatible mate, wait out this round, and try again in the second
generation.
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What are the new frequencies of each allele? (Complete Table 2, columns labeled 6.)
Upon secondary contact, were the subpopulations capable of gene exchange?
Based on this answer, did the divergence from Activity 5 cause speciation?
What began to happen to the rejoined population over the final three generations (did the
reproductive isolation problem spread or dissipate)?
What do you predict will happen to the population in the future?
Did you change your behavior to help you find compatible mates?
Could behavioral change lead to reduced gene exchange between the fish that were once in
different subpopulations?
Acknowledgments:
Modified slightly from Winterer, J. 2001. A lab exercise explaining Hardy-Weinberg and
evolution effectively. American Biology Teacher 63:678-687
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