Hardy-Weinberg I
DIRECTIONS: solve the ENTIRE equation for each problem. Then answer the specific question provided for each
problem. Set up the table below for each question AND show the math in the space below on how you solved each part
of the table.
What do each of the following variables represent in the Hardy-Weinberg equations (define in terms of homozygous
dominant, homozygous recessive, etc.)?
p
q
P2
2pq
q2
Frequency of dominant allele
Frequency of recessive allele
Frequency of homozygous dominant genotype
Frequency of heterozygous genotype
Frequency of homozygous recessivet genotype
Why use this formula? -- The Hardy Weinberg formulas are used to determine the allele or genotype frequencies for a
population of organisms that is not evolving. Helpful Videos- Click here (Bozeman Biology — Solving Hardy Weinberg
Problems)
Formula
P2 + 2pq + q2 = 1
p+q=1
Additional Information from the Formula Sheet
p= frequency of the dominant allele in a population
q = frequency of the recessive allele in a population
1. If 250 people out of a population of 1,000 are born with sickle-cell anemia, how many people in
the population will be more resistant to malaria because they are heterozygous for the sicklecell gene? Express your answer to the question below as a whole number.
250/1000 = 0.25 = aa = q2
q = 0.5, p = 1 - q = 0.5
2pq = 0.5; heterozygous= 0.5 x 1000 = 500
2. In a population of 250 peas, 16% of the peas are homozygous recessive wrinkled and the rest
are smooth,. What is the frequency of the dominant allele for smooth peas? Express your
answer as a decimal between 0 and 1 to the nearest hundredth.
16% = 0.16 = ss = q2
q = 0.4, p = 1 - q = 0.6
3. Some people have the ability to taste a bitter chemical called phenylthiocarbamide (PTC). The
ability to taste PTC is due to the presence of at least one dominant allele for the PTC taste
gene. The incidence of non-tasters in North America is approximately 45%. Assuming the
population is in Hardy-Weinberg equilibrium, what percent of the North American population
is homozygous dominant for the ability to taste PTC? Provide your answer as a number
between 0 and 1 to the nearest hundredth.
Any value from 0.09 to 0.11, inclusive, or any value from 9/100 to 11/100, inclusive
4. In a population of certain frogs in which the allele for brown skin is dominant to the allele for
green skin, a drought leads to selection against green-skinned frogs. When the drought ends,
12 percent of the remaining frogs exhibit the green- kin phenotype. If the population is now in
Hardy-Weinberg equilibrium, what will be the frequency of the green-skin allele in the next
generation? Provide your answer to the nearest hundredth
5. Seventy percent of the population shows the dominant trait while 30% are recessive. What percent of the
population are carriers (heterozygous for dominant trait)? Fill the table below. 50%
Allele Frequencies
p
q
0.45
0.55
p2
0.20
Hardy-Weinberg Equations:
p +q = 1
and
Use any letters: DD and Dd = 70% and dd = 30%
Genotype Frequencies
2pq
0.50
p2 + 2pq + q2 =1
q2
0.30
6. It is determined in a certain population that 1% of the people do not have freckles. Not having freckles is a recessive
characteristic. What percentage of the population are carriers for this trait? 18%
Allele Frequencies
p
q
0.9
0.1
p2
0.81
Genotype Frequencies
2pq
0.18
q2
0.01
7. Pea seeds can be round (R dominant) or wrinkled (r recessive.) In a field of wild peas ninety-six percent of the peas
are round. What percent of the population are carriers (heterozygous for dominant trait)? 32%
Allele Frequencies
p
q
0.8
0.2
p2
0.64
Genotype Frequencies
2pq
0.32
q2
0.04
8. Below is a classic data set on wing coloration in the scarlet-tiger moth (Panaxia dominula). Coloration In this species
has been previously shown to behave as a single locus, two-allele system with incomplete dominance. Data for 1612
individuals are given below:
White-spotted (AA) = 1469
Intermediate (Aa) = 138
What are the recessive allelic frequency?
p = 0.95 and q = 0.05
Allele Frequencies
p
0.95
q
0.05
Little-spotting (aa) = 5
2
p
0.91
Genotype Frequencies
2pq
0.09
q2
0.003
9. If 98 out of 200 individuals in a population express the recessive phenotype, what percent of
the population are homozygous dominant?
9%
Allele Frequencies
p
0.3
q
0.7
2
p
0.09
Genotype Frequencies
2pq
0.42
q2
0.49
10. Brown hair (B) is dominant to blond hair, (b). If there are 168 brown hair individuals in a
population of 200, what is the predicted frequency of heterozygotes?
Bb = 0.48
Allele Frequencies
p
q
0.6
0.4
p2
0.36
Genotype Frequencies
2pq
0.48
q2
0.16