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North Star Academy College Preparatory High School

Name: ______________________________ Team_____________________

EDUCATION IS FREEDOM! Date__________/Mr. McIntire

AP Biology

Homework: The Hardy Weinberg Equilibrium Challenge

Making calculations for Hardy Weinberg equilibrium is not a new concept for you. However, because these calculations are critical to your success on the AP exam, you must demonstrate mastery of them. This assignment is unique, so read the following instructions carefully.

This assignment is graded on accuracy and will count as a quiz grade for Quarter 1. Accordingly, it is considered a long-term assignment that must be completed and checked by me before October 26, the Friday before exam week. For your answer to each question, you must show all your work and be able to explain your solution to me. If you answer all of the questions correctly, you will earn a 100% on your quiz. If you are unable to answer a question (or questions), you will lose the points assigned to them. This assignment is graded out of 40 points, with “Easy” questions worth 1 point each, “Medium” questions worth 2 points each, and “Hard” questions worth 3 points each.

You may work on this assignment anytime, as long as it is completed on or before the date above. Additionally, this assignment does NOT need to be completed all at once; you are permitted to complete a question (or group of questions), check your solutions with me, and I will give you feedback on your progress. If there is evidence that you have copied solutions from a peer and fail to be able to explain your answer to me, then you will automatically get a zero on this assignment. You must show your work for all problems; correct answers without correct work will not receive credit.

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Easy (1 point each)

1. You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

a. The frequency of the aa genotype.b. The frequency of the “a” allele.c. The frequency of the “A” allele.d. The frequencies of the two genotypes AA and Aa.

2. Consider a population with two alleles for a given gene, A and a. We experimentally determine that the population is 20% AA, 20% Aa and 60% aa. What is the frequency of the dominant allele?

3. In a population that meets the H-W equilibrium assumptions, 81% of the individuals are homozygous for a recessive gene. What percentage of the individuals would be expected to be heterozygous for this gene in the next generation?

4. Sickle-cell anemia is an interesting genetic disease. Normal homozygous individuals (SS) have normal blood cells that are easily infected with the malarial parasite. Thus, many of these individuals become very ill from the parasite and many die. Individuals homozygous for the sickle-cell trait (ss) have red blood cells that readily collapse when deoxygenated. Although malaria cannot grow in these red blood cells, individuals often die because of the genetic defect. However, individuals with the heterozygous condition (Ss) have some sickling of red blood cells, but generally not enough to cause mortality. In addition, malaria cannot survive well within these "partially defective" red blood cells. Thus, heterozygotes tend to survive better than either of the homozygous conditions. If 9% of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous (Ss) for the sickle-cell gene?

5. Many cattle breeders obtain bulls of one breed to sire calves with cows of another breed. One of the most common crosses is black angus bulls with hereford cows. Purebred herefords all have a white face that is caused by a dominant allele. As a result of being inbred you can assume that they are all homozygous. Purebred black angus never have a white face. What percentage of the offspring in such a herd will have a white face?

_____ / 5 points total

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Medium (2 points each)

6. Coloration in a species of scarlet tiger moth species (Panaxia dominula) had been previously shown to behave as a single-locus, two-allele system with incomplete dominance. Data for the wing coloration of 1612 individuals are given below:

White-spotted (AA) =1469 Intermediate (Aa) = 138 Little spotting (aa) =5

Calculate the frequencies of the recessive allele.

7. Attached ears are an autosomal recessive trait in humans. Assume that there are 400 people with attached ears in a population of 10000. How many individuals would be expected to be homozygous dominant?

8. In humans, albinism is a recessive condition caused by mutations in genes involved in the production of melanin, a skin pigment. In Americans of European ancestry, albino individuals occur at a frequency of about 1 in 10,000 (or 0.0001). If you assume Hardy-Weinberg equilibrium in this population, what percentage of them do you expect to be carriers (heterozygotes) for albinism?

9. A farmer bought a herd of 600 sheep, taken from a freely breeding population, and later found that 150 of the animals had an economically undesirable feature, crinkly-hair, caused by the recessive allele cr? What is the frequency of this undesirable allele in the herd?

10. The alleles for red and white coat color in cattle show absence of dominance, the heterozygote being roan. In a freely breeding herd of 1000 head how many would you expect to be of each coat color if the allele for white coat has a frequency of 0.4?

11. In a sample of 2400 births at a maternity hospital, six babies died shortly after birth from the effects of a recessive gene (co) for colonic obstruction. What proportion of the population is heterozygous and what proportion is homozygous for the normal allele?

12. A recessive lethal gene in chickens causes circulatory failure and death of the embryo at 70 hours. A commercial hatchery finds that a hatching failure due to this gene of greater than 4% is unacceptable. What is the upper limit for the frequency of this allele in the breeding population of fowls that is acceptable to the hatchery managers?

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13. There are 100 students in a class. Ninety-six did well in the course whereas four blew it totally and received a grade of F. Sorry. In the highly unlikely event that these traits are genetic rather than environmental, if these traits involve dominant and recessive alleles, and if the four (4%) represent the frequency of the homozygous recessive condition, please calculate the frequency of the heterozygous individuals.

14. Within a population of butterflies, the color brown (B) is dominant over the color white (b). And, 40% of all butterflies are white. Given this simple information, which is something that is very likely to be on an exam, calculate the frequency of dominant individuals.

15. After graduation, you and 19 of your closest friends (lets say 10 males and 10 females) charter a plane to go on a round-the-world tour. Unfortunately, you all crash land (safely) on a deserted island. No one finds you and you start a new population totally isolated from the rest of the world. Two of your friends carry (i.e. are heterozygous for) the recessive cystic fibrosis allele (c). Assuming that the frequency of this allele does not change as the population grows, what will be the incidence of cystic fibrosis on your island?


4


Hard (3 points each)

16. I had a room full of 666 cockroaches which included 24 albinos. These albinos were so scary looking that I squashed them and let the remaining cockroaches breed. The next generation of cute little baby cockroaches totaled 13,485. Assuming that the allele for albinism is recessive how many of these youngsters were albino.

17. The gene for color blindness is on the X chromosome. Men have one X chromosome (and a Y). Women have two X chromosomes. I have personally tested a large number of students for color-blindness and have found that, on average, one male will be color-blind in a class of 30. Assuming that such a class is 1/2 male and 1/2 female, how many women would I have to test before I found one who was color-blind?

18. Among a group of 1000 British expatriates, the number of individuals with each of the following MN antigen phenotypes was as follows M: 298, MN: 489, N: 213. What is the M allele frequency? What is the N allele frequency? What number of each of the genotypes would be expected with random mating?

19. A human trait involving finger length in humans is recessive in males but dominant in females (This is true!). A survey of 938 college students found that 385 of 438 males and 104 of 500 females had dominant phenotypes. What are the allele frequencies?

20. The dry type of ear cerumen ("wax") is due to homozygosity for a simple Mendelian recessive. Among American Indians the frequency of dry-cerumen individual is 66 percent. What is the frequency of the recessive allele? What is the overall frequency of heterozygotes? Among individuals with the wet type of cerumen, what is the frequency of heterozygotes? (Hint: to answer this question you must assume that the population is in Hardy-Weinberg equilibrium).


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Challenge Yourself

If you really think that you understand how these problems work, enjoy a challenge and have some spare time, try question #21. If you are able to solve this question correctly, show and explain your work, you will earn extra credit (trust me, it’ll be worth it) AND a mystery prize Good luck!

21. The City of Angels has a population of 106. Their blood types are:

B = 4.5 x 105

O = 3.6 x 105

A = 1.3 x 105

AB = 6.0 x 104

What are the allele frequencies in this population?

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