HARDY-WEINBERG PRINCIPLE
I. Introduction -
The Hardy-Weinberg Principle deals with the frequency, or percentage, of alleles in a population. It states that the frequency of an allele, or rather the number of times an allele is present in a population, is constant from one generation to the next. In order for this to occur certain conditions must be met. The conditions are:
1. The population must mate at random.
2. Alleles cannot be lost through migration.
3. Alleles are not changed by mutation.
4. Alleles are not lost by selective pressure or discrimination.
II. Procedure -
1. To investigate the Hardy-Weinberg Principle you will be working in a group with 3 other students. Each group should have 60 red beans, 40 white beans, and 2 bags (one marked male and the other marked female).
2. Assume that a red bean represents a dominant allele and a white bean represents a recessive allele. Therefore, the homozygous dominant individual would be represented by 2 red beans, the homozygous recessive individual would be represented by 2 white beans, and the heterozygous individual would be represented by one red bean and one white bean.
ACTIVITY I:
PART I: Calculate the frequency of the dominant and the recessive alleles.
1. p = frequency of dominant allele = # of red beans = total # of beans
2. q = frequency of recessive allele = # of white beans = total # of beans
PART II: Calculate p + q
1. Take the values for p and q as determined in PART I and add them together:
p + q =
2. Extension: Multiply and calculate (p + q)2 =
PART III: Determine the frequency of p2 (homozygous dominant), q2 (homozygous recessive), and 2pq (heterozygote).
1. Students place 30 red beans and 20 white beans in the bag marked male.
2. Students place 30 red beans and 20 white beans in the bag marked female.
3. One bean from each bag is drawn until all beans have been drawn. Tally the combinations in the table below.
Red/Red Red/White White/White
Total:
4. Calculate the frequencies of p2, q2, and 2pq:
p2 = # of beans in the double red bean drawing = Total # of beans
q2 = # of beans in the double white bean drawing =
Total # of beans
2pq = # of red beans and white beans drawn together = Total # of beans
5. Gather class data in a table on the board and copy the data into the following table:
Class Data
Red/Red Red/White White/White
Total:
Calculate the class total frequencies of p2, q2, 2pq.
p2 = # of beans in the double red bean drawing =
total # of beans
q2 = # of beans in the double white bean drawing =
total # of beans
2pq = # of red beans and white beans drawn together =
total # of beans
Analysis Questions
1. What is the value of p + q? _____________________________________
2. What is the value of (p + q)2? ___________________________________
3. For this activity p = 0.6, what is the value of p2? _______________________
How close did your answer for p2 come to this value? ____________
4. For this activity q = 0.4, what is the value of q2? ______________________
How close did your answer for q2 come to this value? ____________
5. What is the value for 2pq? _________________________________
How close did your answer for 2pq come to this value? ______________
__________________________________________________________
6. Why must the value for p + q be equal to 1? _______________________
________________________________________________________
ACTIVITY II: This activity will demonstrate that even a small migration of the
population will effect the frequencies of the alleles.
Procedure
Repeat the procedure of Part III in ACTIVITY I except this time draw only 10 pairs of beans from the respective bags. This bean population represents a migration. Now the Hardy-Weinberg Principle will no longer apply. The new frequencies should be different from those in ACTIVITY I.
Red/Red Red/White White/White
Total:
2. Determine the frequencies of p, q, p2, q2, and 2pq of this new population.
p = # of red beans =
total # of beans
q = # of white beans =
total # of beans
p2 = # of beans in a double red bean drawing =
total # of beans
q2 = # of beans in a double white bean drawing =
total # of beans
2pq = # of red and white beans drawn together =
total # of beans
Analysis Questions
1. Compare the value you obtained for p in this activity with the value you obtained in ACTIVITY I.
________________________________________________
2. Compare the value you obtained for q in this activity with the value you obtained in ACTIVITY I. _________________________________________________
3. How have these values affected 2pq? ___________________________
Compare your values with the rest of the class. ___________________
__________________________________________________________
4. Have the number of homozygous dominant, homozygous recessive, or heterozygous individuals been altered significantly by this migration of a
few individuals?
______________________________________________________________
5. What is the value of p + q? _____________________________________
6. What is the value of (p + q)2?____________________________________
ACTIVITY III: This activity will demonstrate the effect that selection or discrimination upon a certain allele combination will have on the frequencies of all the alleles.
Procedure
Repeat the procedure in Part III of ACTIVITY I. Use all of the beans in the bags for this activity, but this time remove or discard all the homozygous recessive (white/white) bean combinations. Recount the allele combinations to determine the new frequencies for p, q, p2, q2, and 2pq.
Red/Red Red/White White/White
0
Total:
p = # of red beans =
total # of beans
q = # of white beans =
total # of beans
p2 = # of beans in a double red bean drawing =
total # of beans
q2 = # of beans in a double white bean drawing = 0
total # of beans
2pq = # of red beans and white beans drawn together =
total # of beans
Analysis questions -
1. Compare the p value you obtained in this activity with the p value in ACTIVITY I.
_________________________________________________________________
2. Compare the q value you obtained in this activity with the q value in ACTIVITY I.
_________________________________________________________________
3. The value for q should be much less than the value you obtained for q in the first activity. Explain why that is.
_____________________________________________________________
4. What happens to the p value? Explain. ______________________________
__________________________________________________________________
Procedure
Now refill the bags with equal amounts of the colored beans from the red/red drawing and red/white drawing. In other words, divide the red beans and the remaining white beans equally between the two bags. Again draw the beans from each bag and tally the pairs in the table. Again discard the white/white bean combinations. Calculate the new values of p, q, p2, q2, and 2pq.
Red/Red Red/White White/White
0
Total:
p = # of red beans =
total # of beans
q = # of white beans =
total # of beans
p2 = # of beans in a double red bean drawing =
total # of beans
q2 = # of beans in a double white bean drawing =
total # of beans
2pq = # of red beans and white beans drawn together =
total # of beans
4. What has happened to q?
Why is q not 0? __________________________________________
Will q ever be 0? __________Why? ______________________________
5. Predict what would happen if the selection or discrimination occurred against the individuals expressing the dominant gene.
____________________________________________________________
What would happen to the value of p? ______________________
What is the value of p + q? _______________________________
6. Can you deduce why harmful human alleles are usually recessive rather than dominant?
_________________________________________________________