Download Hardy-Weinberg Equilibrium

Name: ____________________________________________ Date: __________________
Hardy-Weinberg Equilibrium - “Goldfish Evolution”
In order to consider the mechanisms that cause a population to evolve, it is helpful to examine, for
comparison, the genetic structure of a non-living population. Such a gene pool is described by the HardyWeinberg principle. It states that allele frequencies in a population will remain constant unless one or
more factors cause those frequencies to change. The sexual shuffling of alleles due to meiosis and random
fertilization has no effect on the overall genetic structure of a population. The situation when allele
frequencies remain constant is called genetic equilibrium, and the population will not evolve. You can
quantify this principle using the Hardy-Weinberg equation, which shows that the genetic structure of a
non-evolving population will remain constant over generations. Genotype proportions can be calculated from
allele frequency and should remain constant. If p is the frequency of dominant allele for a trait and q is
the frequency of recessive allele for the same trait, then genotype proportions are given by
p2 + 2pq + q2 = 1. Genotype proportions must add up to 1. The Hardy-Weinberg principle requires five
conditions for genetic equilibrium to be maintained in a population:
1. Very large population size (in small populations, genetic drift, which is chance fluctuation in the
gene pool, can change the allele frequencies)
2. Isolation from other populations (there can be no movement into or out of the population)
3. No net mutations (by changing one allele into another, mutations alter the gene pool)
4. Random mating (if individuals select mates having certain heritable traits, then random mixing of
gametes does not occur)
5. No natural selection (differential survival and differential reproductive success alters the gene
pool by favoring some alleles at the expense of others)
These five conditions required to maintain Hardy-Weinberg provide a framework for understanding the
process of evolution. There are five potential agents for evolution: genetic drift, gene flow, mutation,
nonrandom mating and natural selection.
In this activity, students will represent predators, a shark that eats goldfish, which selectively preys upon
(eats) goldfish in a small population. There are two kinds of fish that you like to eat: gold fish (cheese
flavored) and brown fish (pretzel flavored). The goldfish are easy for you to see, so they are easy for you
to catch and eat. Brown fish travel more quickly and can evade capture more easily. Because of this, you
eat only goldfish, unless there are no goldfish around, in which case you eat brown fish. Fish are replaced
with individuals randomly selected from an ocean (mixing bowl full of crackers). Brown fish are determined
by the presence of a dominant allele (B), and gold fish by a recessive allele (b).
Materials
Several large bowls
paper plates
Several packages of cheese flavored goldfish crackers
Several packages of pretzel flavored goldfish crackers
graph paper
calculator
Procedures
1. Empty one bag of each type of crackers (cheese and pretzel) into a large bowl and mix.
2. Send one student from your group to collect a random population of 10 fish (crackers) from the
large bowls “ocean”, place them on a paper plate and take them back to your lab group. It is
important that the population be random, so don’t look while you are grabbing the fish.
3. In data table 1, for generation 1, record the number of gold and brown fish in the random
population. You can calculate your frequencies later.
4. Brown fish (pretzel flavored) express the dominant allele (B) and gold fish (cheese flavored)
express the recessive allele (b).
Name: ____________________________________________ Date: __________________
5. Choose three gold fish from the first generation and eat them. If you do not have three gold fish,
fill in the missing number by eating brown fish, for a total of three fish eaten.
6. Send one student choose, at random, three fish from the “ocean” and add them to your population.
Again, be careful to choose your fish randomly, DON’T LOOK!
7. In data table 1, for generation 2, record the number of gold and brown fish.
8. Repeat steps 5 to 7 until you have data for all five generations.
9. In table 2, calculate the allele and genotype frequencies for each generation using the data in data
table 1.
Using the information from the data table above, plot your data on a graph below to show how your
population changed over time. For each generation, plot two separate points: use one color to represent
the percent population of gold fish, use another color to plot the percent population of brown fish.
Name: ____________________________________________ Date: __________________
How did the frequency of brown fish change from generation 1 to generation 5? ____________________
How did the frequency of gold fish change from generation 1 to generation 5?
____________________
Using the information in data table 1, calculate the allele frequencies for each generation.
Since you know the gold color trait is recessive, the gold fish must be homozygous recessive (bb). Brown
fish may be either homozygous dominant (BB) or heterozygous (Bb).
If you know that 36% of the fish in a population express the recessive allele (bb), then the q2 value is 0.36,
and q equals the square root of 0.36, or 0.6. Thus the frequency of the b allele is 0.6. Since the sum of B
and b must be 1, the frequency of the B allele must be 0.4. Using Hardy-Weinberg equation,
(p2 + 2pq + q2 = 1), you can assume that in the population there are 0.16 BB (0.4 X 0.4) or p2. There are
0.48 Bb (2 X 0.4 X 0.6) or 2pq.
Remember:
P2 + 2pq + q2 = 1
p+q=1
%PP
%Pp
%pp
Analysis questions:
1. Which phenotype frequency was reduced in this population over time? Why?
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2. What event is occurring if there is a change in the frequencies of p and q, over time?
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3. Explain what would happen over time if the brown fish were easier to catch.
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4. What would happen if both fish were equally easy to catch?
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5. Explain why the recessive allele never disappears from the population.
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