Student Exploration: Hardy-Weinberg Equilibrium (ANSWER KEY)

Student Exploration: Hardy-Weinberg Equilibrium
Vocabulary: allele, genotype, Hardy-Weinberg equation, Hardy-Weinberg principle, heterozygous, homozygous, incompletely dominant, Punnett square
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
A bird’s feather color is controlled by two alleles, D (dark feathers) and d (lighter feathers). Suppose two Dd birds mate. What percentages of DD, Dd, and dd offspring would you predict? Use the Punnett square at right to help determine your answer.
In this situation, what ratio of heterozygous (Dd) to homozygous (DD and dd) offspring would you expect to find?
Gizmo Warm-up
Many factors—immigration, natural selection, hunting, etc.—can influence the composition of a population. To determine if one of these factors is affecting a population, it is useful to know what a population looks like when none of these factors is present.
In 1908, Godfrey Hardy and Wilhelm Weinberg independently discovered the laws that govern such populations. These laws can be explored in the Hardy-Weinberg Equilibrium Gizmo™.
The parrots you see represent a population of 500 parrots. For these parrots, the Dallele is incompletely dominant over d, which means that Dd parrots are intermediate between DD and dd parrots. In the Gizmo, select the TABLE tab. How many parrots of each genotype are in the initial population?
Return to the DESCRIPTION tab. Click Begin, and then click Breed. What happens?
Click Hatch, and look on the TABLE tab. What are the parrot populations now? 
Activity A:

Alleles and genotypes
Get the Gizmo ready:
  • On the DESCRIPTION tab, click Reset.
  • Check that DD is 50% and dd is 30%.
 
Question: How will the proportion of genotypes and alleles change over time when mating is random, and no natural selection is occurring?
Predict: How do you expect the proportions of D and d alleles to change over time?
Gather data: Run a generation in the Gizmo. After clicking Hatch, fill in the allele and genotype percentages for generation 1. Repeat this process for 5 generations.
Analyze: What patterns do you see in your data?       
Interpret: Select the ALLELE GRAPH tab. What does this graph show?
Interpret: Select the GENOTYPE GRAPH tab. What does this graph show?
(Activity A continued on next page)
Activity A (continued from previous page)
Gather data: On the DESCRIPTION tab, click Reset. Set DDand dd to any values you like. Fill in the initial values in the table below, and then run the Gizmo for five generations. Record the allele and genotype percentages for each generation in the table below.
Analyze: Do the patterns you noticed in the first experiment appear in the second? Explain.
Draw conclusions: The Hardy-Weinberg principle states that the proportions of alleles and genotypes in a population will remain stable as long as the following criteria are satisfied:
Mating is random.
There is no immigration or emigration.
No natural or artificial selection is occurring.
There is no mutation.
The population is relatively large.
How well does the Hardy-Weinberg principle describe this population of parrots?
Think and discuss: Would you say that this parrot population is evolving? Explain.
Activity B:

Genotype ratios
Get the Gizmo ready:
  • Click Reset.
  • Set DD to 30% and dd to 70%.
 
Question: How do genotype percentages relate to allele percentages?
Calculate: You can use the laws of probability to predict how many DD, Dd, and ddoffspring will result from this parent population.
What is the current percentage of D alleles in the population?
What is the current percentage of d alleles in the population?
What is the probability of inheriting a D allele from a parent? (Hint: Convert the percentage of D alleles to a decimal.)
What is the probability of inheriting a d allele?
Explain: If a trait is determined by two alleles, the sum of p and q is 1. Why is this true?
Calculate: Fill in the current p and q values next to the D and d alleles around the Punnett square at right. Then calculate the probability of each offspring genotype. Write these values into the individual squares.
For example, the upper left box in the square represents the probability of a DDoffspring. The probability of inheriting a D allele from each parent is p, so the probability of DD is p 2.
What is the sum of the probabilities in the four squares?
Manipulate: Now determine an algebraic expression for the probability of each genotype in terms of p (the probability of inheriting D) and q (the probability of inheriting d). Use the Punnett square above as a guide.
In terms of p and q, what is the probability of a DD offspring?
In terms of p and q, what is the probability of a dd offspring?
In terms of p and q, what is the probability of a Dd offspring?
(Activity B continued on next page)
Activity B (continued from previous page)
Calculate: The Hardy-Weinberg equation states that the sum of the probabilities of each genotype is equal to 1:
Why is the probability of Dd equal to 2pq?
Predict: Check that DD is still set to 30% and dd is still set to 70%. With p = 0.3 and q= 0.7, what are the predicted percentages of DD, Dd, and dd offspring?
Predicted percentages:       DD              Dd              dd
Test: Click Begin, Breed, and Hatch. What are the resulting genotype percentages?
Actual percentages:       DD          Dd             dd
How close are these to the predicted values?
Apply: For a dominant/recessive gene, it is often difficult to determine the percentages of dominant and recessive alleles in a population because individuals that express the dominant trait may be either homozygous (DD) or heterozygous (Dd). The only thing that is known for certain is the percentage of individuals that are homozygous recessive (dd).
Suppose that 16% of a population is homozygous recessive (dd). According to the Hardy-Weinberg equation, what is the value of q 2?If you know q 2, you can calculate q. What is the value of q?
Recall that p + q is equal to 1. What is the value of p?
Based on the values of p and q, calculate the percentages of the DD and Ddgenotypes:   DD                  Dd
Check: If a population is in Hardy-Weinberg equilibrium, genotype percentages will remain stable over time. Set DDto the value given in part D above and dd to 16%. Run several generations in the Gizmo. Do the genotype percentages remain relatively constant? Explain.
Activity C:

A useful Hardy-Weinberg ratio
Get the Gizmo ready:
  • Click Reset. Set DD to 50% and dd to 50%.
  • Turn on Show Hardy-Weinberg quantities.
 
Question: How can you determine if a population is in Hardy-Weinberg equilibrium?
Manipulate: The Hardy-Weinberg equation is p 2 + 2pq + q 2 = 1, where p = probability of D, q = probability of d, p2 = probability of DD, 2pq = probability of Dd, and q2 = probability of dd.
Look under Show Hardy-Weinberg quantities. Notice there are two terms: Dd•Dd and DD•dd. Rewrite each of these in terms of the variables p and q.
The third line of the table is the ratio (Dd•Dd) / (DD•dd). Rewrite this ratio in terms of p and q, and then simplify the expression. Show your work.
If a population is in Hardy-Weinberg equilibrium, what would you expect to be the ratio of Dd•Dd / DD•dd?.
Experiment: With Dd set to 0%, the initial value of Dd•Dd / DD•dd is 0. Click Begin, Breed, and Hatch. Record the percentage of DD, Dd, dd, and Dd•Dd / DD•dd for 5 generations in the table below.
Calculate: What is the mean value of Dd•Dd / DD•dd?


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