Name: ________________ Per:_____
Thomases AP Biology Lab: Mathematical Modeling – using Hardy-Weinberg to
mathematically prove or disprove that a population is evolving
(When done, please hand in this packet for grading. After grading, tape it into your notebook).
Evolution occurs in populations of organisms and involves variation in the population, heredity and
differential survival. One way to study evolution is to study how the frequency of alleles in a population
changes from generation to generation. In other words, what are the inheritance patterns of alleles, not
just from 2 parental organisms but also in the population?
Hardy-Weinberg Equilibrium- Case 1: Stable population
1. Each table has two boxes of cards; each box has 48 of the same card. These are your Parent
generation.
2. The higher card is the dominant allele, the lower card is the recessive allele
3. Count how many there are of each type of card. Record this here: ___________________________
4. Calculate and record the allele frequencies (p and q) of the Parent generation.
p ____________
q ________________
5. Shuffle both decks of cards together several times. Then make two even piles.
6. Draw one card from each pile to simulate mating. Record the resulting F1 “offspring”, e.g.
King+Queen or King+King, etc. Continue drawing cards until you have drawn them all. Record the
results here:
7. Using the data you collected for the F1 generation, calculate the following, always showing your work:
a. Frequency of p2 (Homozygous dominant offspring)
b. Frequency of 2pq (Heterozygous offspring)
c.
Frequency of q2 (Homozygous recessive offspring)
d. Does your p2 + 2pq + q2 = 1?
e. Calculate the allele frequencies (the value of both p and q)
p ________________
f.
q __________________
Does p + q = 1?
8. Is this population evolving? How do you know?
9. Predict what would happen to the frequencies of p and q if you simulated another five generations
using the same cards. Would the allele frequencies change?
Hardy-Weinberg, Case 2 – Fatal genetic disease
10. Now shuffle and “mate” the F1 generation you just created in case 1, BUT conditions have changed. A
random mutation has occurred that kills off all homozygous recessive offspring of the F2 generation.
So set them aside and do not count them. Create your F2 generation by drawing and recording cards
as before. Record here:
11. For the F2 generation (with fatal mutation) calculate:
a. p2 (Homozygous dominant offspring)
b. 2pq (Heterozygous offspring)
c.
q2 (Homozygous recessive offspring)
d. Calculate the allele frequencies (the value of p and q)
p _______________________
e. Does p + q = 1?
q ______________________
12. Repeat the process by shuffling and mating the survivors of the F2 generation to create the F3
generation, recording your results. Remember to “kill off” the homozygous recessive offspring.
13. Calculate and compare the allele frequencies of generations Parent, F1, F2 and F3 here:
P stable generation
allele frequency of p_______________ allele frequency of q______________
F1 stable generation
allele frequency of p_______________ allele frequency of q _____________
F2 fatal mutation
allele frequency of p_________________ allele frequency of q _____________
F3 fatal mutation
allele frequency of p_________________ allele frequency of q _____________
14. Is evolution occurring? How do you know?
15. Predict what would happen to the frequencies of p and q if you simulated another five generations
with the fatal mutation.
16. Do you think the fatal recessive allele will be completely eliminated in case 2? Explain your answer.
Hardy-Weinberg, Case 3 Immigration
17. Shuffle all your cards and repeat what you did in case 1 BUT a new group of organisms has
immigrated into your population so add 10 joker cards that represent a new type of recessive allele.
Draw and record cards as before.
18. When done, calculate:
a. p2 frequency (Homozygous dominant offspring)
b. 2pq frequency (Heterozygous offspring)
c.
q2 frequency (Homozygous recessive offspring – there will be two kinds aren’t there? Let’s call
them q and q
1
2
19. Now calculate the allele frequencies of p, q1 and q2
20. Compare these to the allele frequencies of the Parent and F1 generation.
P stable generation
allele frequency of p_______________ allele frequency of q______________
F1 stable generation
allele frequency of p_______________ allele frequency of q _____________
Immigration generation allele frequency of p_______________ allele frequency of q______________
21. Has the frequency of q changed compared to case 1?
1
22. Has evolution occurred? How do you know?
23. Please re-sort your cards, separating the two types into separate boxes. Bring the joker cards to the
front.
Analysis (To receive credit, you must write thoughtful answers in complete sentences.
24. What are the five conditions required for Hardy-Weinberg equilibrium?
25. Is a population at equilibrium evolving? Why or why not.
26. What is the Hardy-Weinberg null hypothesis?
27. What is the importance of heterozygotes in maintaining variation in populations?
28. What major assumption(s) were not strictly followed in this simulation?
29. How would the effect of the homozygous recessive disease differ if the population was a tribe of 20
individuals? 3000 individuals?
30. Compare the effect of immigration (new trait) on a large population compared to a small one. (Genetic
drift)
31. What would be the effect if the new immigrants (jokers) and some of the heterozygous individuals
decided to move away and form their own colony? (Founder effect).
32. In a very large population, would it be possible to completely eliminate a deleterious recessive allele?
Explain.
Hardy-Weinberg Problems
33. Dark eyes are dominant to light eyes. In a population of 1000 individuals, 360 show the recessive
phenotype. How many individuals would you expect to be homozygous dominant and heterozygous
for this trait?
34. The ability to roll one’s tongue is dominant to a lack of ability. In a population of 500 individuals 25%
show the recessive phenotype. How many individuals would you expect to be homozygous dominant
and heterozygous for this trait?
35. Having a Widow’s peak is dominant to lacking a widow’s peak. In a population of 1000 individuals
510 show the dominant phenotype. How many individuals would you expect of each of the possible
three genotypes for this trait?
36. In the U.S. about 16% of the population is Rh-. Rh- is recessive to Rh+. If the student population of a
high school is 2000, how many students would you expect for each of the three possible genotypes?
37. In Nigeria, 4% of the newborn babies have sickle-cell anemia which is a recessive trait. Out of a
random population of 1000 newborn babies, how many would you expect for each of the three
possible genotypes?