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# Teaching Hardy Weinberg in the classroom

Candace Berkeley
Product Developer

The Hardy-Weinberg principle states that allele and genotype frequencies remain stable in a population over generations if certain conditions are met:

1. The population is very large.
2. Mating is random.
3. There is no immigration or emigration.
4. There are no mutations.
5. Natural selection is not occurring.

When all of these conditions are met, the population is said to be in Hardy-Weinberg equilibrium. If the allele or genotype frequencies do change over time, then scientists assume that 1 or more of the conditions is not being met and the population may be evolving.

The Hardy-Weinberg equation allows scientists to estimate the allele and genotype frequencies in a population. The frequencies can be compared across generations to determine whether evolution may be occurring. Assuming that a population includes only 2 alleles for a given trait, the proportion of dominant alleles (p) plus the proportion of recessive alleles (q) is equal to 1 (i.e., 100% of the population). Squaring both sides of the equation p + q = 1 produces the equation p2 + 2pq + q2 = 1. Here p2 is the number of individuals with a homozygous dominant genotype, 2pq is the number of individuals with a heterozygous genotype, and q2 is the number of individuals with a homozygous recessive genotype.

The Hardy-Weinberg principle is often hard for students to understand. Evolution is difficult to observe in nature, but modeling an evolving population of edible treats effectively engages your students in the Hardy-Weinberg principle and demonstrates what happens when Hardy-Weinberg conditions are not met. The following 2 activities generally take no more than 30 min of class time. Class data will likely indicate stable genotype frequencies in Activity 1 but varying frequencies in Activity 2.

### Materials

• 2 Bags of Cheese Goldfish® Crackers
• 2 Bags of Pretzel Goldfish® Crackers
• Plates or Napkins
• Student Data Sheet (optional)

### Preparation and procedure

1. Pour the contents of all 4 bags of Goldfish® snacks into a large bowl—the lake.
2. Depending on class size, you may wish to divide your class into pairs or allow them to work individually.
3. Give each student or pair a copy of the Student Data Sheet, if desired, and a plate or napkin; have them wash their hands before beginning.
4. Explain that brown (pretzel) Goldfish® are homozygous recessive individuals (gg) and that orange (cheese) Goldfish® display the dominant phenotype and therefore may be either homozygous dominant (GG) or heterozygous (Gg).

### Activity 1: Hardy-Weinberg Equilibrium

1. Have each student or pair remove 10 Goldfish® from the lake and place them on the plate or napkin. In order to ensure random choice, have students close their eyes.
2. Students record the number of orange and brown Goldfish® in Table 1 as Generation 1.
3. Instruct students to close their eyes and to select and eat 3 of their 10 Goldfish® at random. (It is important that this step be random; students must not introduce bias.)
4. Have students return to the lake, close their eyes, and randomly select 3 new Goldfish® to replace those that were eaten.
5. Students then record their new count of orange and brown Goldfish® in Table 1 as Generation 2.
6. Have students repeat steps 3–5 until they have data for 5 generations.
7. After data have been collected, have students use the Hardy-Weinberg equation to calculate p, q, p2, q2, and 2pq for each generation.
8. Collect class data.

### Activity 2: Hardy-Weinberg and Natural Selection

1. Have each student or pair remove 10 Goldfish® from the lake and place them on the plate or napkin. In order to ensure random choice, have students close their eyes.
2. Students record the number of orange and brown Goldfish® in Table 2 as Generation 1.
3. Instruct students to select and eat 3 of their brown Goldfish®. (If they do not have 3 brown ones on their plate, have them substitute an orange one. The point, though, is to select against the brown phenotype over a few generations.)
4. Have students return to the lake, close their eyes, and randomly select 3 new Goldfish® to replace those that were eaten. It is important that this step be random; students must not introduce bias.
5. Students then record their new count of orange and brown Goldfish® in Table 2 as Generation 2, and then, as before, select 3 brown ones to eat.
6. Have students repeat steps 3–5 until they have data for 5 generations.
7. After data have been collected, have students use the Hardy-Weinberg equation to calculate p, q, p2, q2, and 2pq.
8. Collect class data.

### Conclusion

Once class data are collected, have students compare the genotype frequencies in both simulations. The class data from the first activity should result in fairly constant frequencies over the 5 generations. When selection is introduced in the second activity, the genotype frequencies should vary over the 5 generations. Discuss what conditions must exist for frequencies to remain stable over multiple generations. What do changing frequencies indicate in a population? Have students discuss whether Hardy-Weinberg equilibrium is possible in nature.