Download ANTH 131: Evolutionary Forces

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Hardy-Weinberg Equilibrium sample problems
Hardy-Weinberg Principle
In order to assess whether gene frequencies are changing, scientists use a formula called the Hardy-Weinberg
equilibrium. Refer to pages 121-122 of your lab manual for an explanation of the Hardy-Weinberg formula and its
significance.
1. In a population of college students in San Diego County, 4% of the individuals cannot roll their tongues.
Tongue-rolling is transmitted as a dominant trait (R).
a. What is the frequency of the r allele? _____
b. What is the frequency of the R allele? _____
c. What proportion of the population is heterozygous for tongue-rolling? _____
2. 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 genotypes "AA" and "Aa."
E. The frequencies of the two possible phenotypes if "A" is completely dominant over "a."
3. MN blood types were assessed for a population that consists of 100 individuals: 25 have blood type M, 50
have blood type MN and 25 have blood type N. In the MN blood system, M and N are co-dominant, so both
would be expressed in the heterozygote.
What are the allele frequencies for M and N?
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What are the predicted genotype frequencies according to Hardy-Weinberg?
ANTH 131: Evolutionary Forces
Chapter 6 discusses the forces that cause evolution. Here, we define evolution as the change in gene frequencies
in a population over time, and we’ll model how some of these forces can cause populations to evolve.
Simulation 1: Effect of Natural Selection
In the first simulation, each group of students will get a bag
and put 70 white beans and 30 black beans into it for a total of
100 beans.
We will say that the white bean represents the allele for
normal hemoglobin, which carries oxygen on the surface of
the red blood cells.
The black bean represents the sickle cell gene, which has a
mutation that damages the hemoglobin and causes distortion
of the red blood cell and an inability to carry oxygen. Sickle
cell anemia is a recessive disorder. Therefore, in this
population, there is strong selection against the homozygous
recessive genotype.
Genotypes and Phenotypes
 White/White = homozygous dominant (healthy)
 White/Black= heterozygous (carrier of sickle cell trait but healthy)
 Black/Black = homozygous recessive (have sickle cell anemia)
1. But the beans in the bag and mix them together.
2. Without looking, randomly pull out pairs of beans until the can is empty. Place each pair separately on the
table. These represent the genotypes of the 50 individuals you are studying (50 individuals = 100 alleles)
3. Record the number of each type of bean pair in the generation 1 row, and record the frequency of the two
alleles. Remember, the frequency is the percentage of each allele out of the total population.
4. Because your black/black individuals have sickle cell anemia, they have a greater chance of dying before they
can reproduce. To demonstrate this, remove 90% of the black/black pairs from your gene pool. If you can't
remove exactly 90%, just remove a number close to that percentage. For example, if you have 5 black pairs,
remove either 4 (80%) or all 5 pairs (100%).
5. Place all the remaining beans in the bag and mix them.
6. Repeat steps 2 through 5 three more times. In the following table, record for each generation the number of
each genotype and the frequency of each allele. Remember, the allele frequency is calculated out of the total
remaining alleles. If you start with 100 alleles and remove 4 individuals (8 alleles), you will have 92 alleles in
your next generation.
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7. Answer questions 1-3 below when you are finished.
Number
White/White
Number
White/Black
Number
Black/Black
Generation 1
Frequency
(percent) White
Allele
70% (70/100)
Frequency
(percent) Black
Allele
30% (30/100)
Generation 2
Generation 3
Generation 4
1.
What happens to the frequency of the white bean allele over the generations?
2.
What happens to the frequency of the black bean allele?
3.
If you continued this exercise for another 10 generations, do you think you could eliminate the black
bean allele from the population? Why or why not?
Simulation 2: Effect of Genetic Drift
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Working in groups, count out 70 light bean alleles and 30 dark bean alleles for a total of 100 beans. The beans
represent an allele found in mountain gorillas that has a 2-allele system. Due to human encroachment and habitat
loss, the mountain gorilla now numbers about 600 individuals in the wild. The recent war in Rwanda put these
remaining individuals in even greater danger of extinction.
1. Put all the beans in the bag and mix them together.
2. Without looking in the bag, randomly pull out pairs of beans until the bag is empty. Place each pair
separately on the table. These represent the genotypes of the 50 gorillas you are studying (50 indiv, 100
alleles).
3. Record the number of each pair in the prewar row of the following chart.
4. Assume the war in Rwanda resulted in the random loss of some mountain gorillas. To demonstrate this,
randomly pull out 20 allele pairs, or 40% of the population.
5. Without mixing up the beans/alleles again, count the remaining allele pairs and record their frequencies in
the postwar row in the following chart. Remember, the allele frequency is calculated out of the total
remaining alleles. If you start with 100 alleles and remove 20 individuals (40 alleles), you will have 60
alleles in your next generation.
6. Then answer questions 4-6 below.
Number
White/White
Number
White/Black
Number
Black/Black
Prewar
Frequency
(percent) White
allele
70% (70/100)
Frequency
(percent) Black
allele
30% (30/100)
Postwar
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4.
What happened to the frequency of the white allele?
5.
What happened to the frequency of the black allele?
6.
How does this compare to what you saw in the previous sickle cell simulation? How and why do the two
simulations differ?