Using the Hardy-Weinberg Principle
1. In humans, the ability to taste a substance known as PTC is a dominant trait. From a representative
sample it was found that 64% of the population could taste PTC while the remaining 36% could not.
A) Assuming no mutations or selection pressures, what is the frequency of the recessive allele?
Since 36% of the population has the recessive phenotype, q2 must equal 0.36 (or 36/100 if you
prefer to use fractions). Solving for q gives:
36
q 2  100
q 2  0.36
q2 
q 2  0.36
36
100

36
100
q  106
q  0.6
This means that the frequency of the recessive allele is 0.6 (or 6/10).
B) What is the frequency of the dominant allele?
p+ q = 1

p + 0.6 = 1
p = 1 – 0.6 = 0.4
So the frequency of the dominant allele is 0.4 (or 4/10).
2. Suppose a scientist studying the schmoo determines that blue fur is dominant over green fur. They
determine that 91% of the population has blue fur.
A) Assuming no mutations or selection pressures, what is the frequency of the recessive allele?
Blue fur is the dominant trait. You must first find the % of the population that has the recessive
phenotype. To do this, you need to subtract the 91% from 100%:
100% – 91% = 9%
You must change this % to a decimal (0.09) or a fraction (9/100). Set this equal q2 and solve:
q 2  0.09
q 2  0.09
q  0.3
9
q 2  100
q2 
9
100

9
100
q  103
So the frequency of the recessive allele is 0.3 or 3/10.

 dominant allele?
B) What is the frequency of the
To find the frequency of the dominant allele, solve the equation p+q=1, using 0.3 as the value of q:
p+q=1
p + (0.3) = 1
p = 1 – (0.3) = 0.7 or 7/10
3. In schmoos messy hair is dominant over neat hair. (Think of the bad hair days in that population!) In
a particular schmoo population 96% have messy hair.
A) Assuming no mutations or selection pressures, what is the frequency of the recessive allele?
Messy hair is the dominant trait. You must first find the % of the population that has the recessive
phenotype. To do this, you need to subtract the 96% from 100%:
100% – 96% = 4%
You must change this % to a decimal (0.04) or a fraction (4/100). Set this equal q2 and solve:
q 2  0.04
q 2  0.04
q  0.2
4
q 2  100
q2 
q  102
4
100

4
100
So the frequency of the recessive allele is 0.2 or 2/10.
B) What is the frequency of the dominant allele?
To find the frequency of the dominant allele, solve the equation p+q=1, using 0.2 as the value of q:
p+q=1
p + (0.2) = 1
p = 1 – (0.2) = 0.8 or 8/10
4. The schmow is a close relative of the schmoo. Scientists studying the schmow have determined that
long hair is dominant over short hair in schmows. In a certain schmow population, 19% of the
schmows have long hair.
A) Assuming no mutations or selection pressures, what is the frequency of the recessive allele?
Long hair is the dominant trait. You must first find the % of the population that has the recessive
phenotype. To do this, you need to subtract the 19% from 100%:
100% – 19% = 81%
You must change this % to a decimal (0.81) or a fraction (81/100). Set this equal q2 and solve:
q 2  0.81
q 2  0.81
q  0.9
81
q 2  100
q2 
81
100

81
100
q  109
So the frequency of the recessive allele is 0.9 or 9/10.
B) What is the frequency of the dominant allele?

To find the frequency of thedominant allele, solve the equation p+q=1, using 0.9 as the value of q:
p+q=1
p + (0.9) = 1
p = 1 – (0.9) = 0.1 or 1/10
C) How might these allele frequencies change if long-haired schmows survive and reproduce better
than short-haired schmows?
If the long-haired schmows survive and reproduce better than the short-haired schmows, we would
expect the value of p to increase while the value of q will decrease.
5. In a certain population, 99% of the individuals have the dominant phenotype.
A) What is the frequency of the recessive allele?
You must first find the % of the population that has the recessive phenotype. To do this, you need
to subtract the 99% from 100%:
100% – 99% = 1%
You must change this % to a decimal (0.01) or a fraction (1/100). Set this equal q2 and solve:
q 2  0.01
q 2  0.01
q  0.1
1
q 2  100
q2 
1
100

1
100
q  101
So the frequency of the recessive allele is 0.1 or 1/10.
 B) What is the frequency of the
dominant allele?
To find the frequency of the dominant allele, solve the equation p+q=1, using 0.1 as the value of q:
p+q=1
p + (0.1) = 1
p = 1 – (0.1) = 0.9 or 9/10
6. In a population of goldfish 51% of the fish have the dominant trait for a certain trait.
A) What is the frequency of the recessive allele?
You must first find the % of the population that has the recessive phenotype. To do this, you need
to subtract the 51% from 100%:
100% – 51% = 49%
You must change this % to a decimal (0.49) or a fraction (49/100). Set this equal q2 and solve:
q 2  0.49
q 2  0.49
q  0.7
49
q 2  100
q2 
49
100

49
100
q  107
So the frequency of the recessive allele is 0.1 or 1/10.
 B) What is the frequency of thedominant allele?
To find the frequency of the dominant allele, solve the equation p+q=1, using 0.7 as the value of q:
p+q=1
p + (0.7) = 1
p = 1 – (0.7) = 0.3 or 3/10
C) What fraction of the population would be heterozygous?
The fraction of the population that is heterozygous is represented by 2pq. You can simply
substitute the values of p(=.3) and q(-=.7) into this expression:
Fraction that is heterozygous = 2pq = 2 (0.3) (0.7) = 0.42.
7. In a population of wild flowers, yellow flowers are dominant over white flowers. 36% of the flowers
in the population have yellow flowers.
A) What is the frequency of the recessive allele?
You must first find the % of the population that has the recessive phenotype. To do this, you need
to subtract the 36% from 100%:
100% – 36% = 64%
You must change this % to a decimal (0.64) or a fraction (64/100). Set this equal q2 and solve:
q 2  0.64
q 2  0.64
q  0.8
64
q 2  100
q2 
64
100

64
100
q  108
So the frequency of the recessive allele is 0.1 or 1/10.
 B) What is the frequency of thedominant allele?
To find the frequency of the dominant allele, solve the equation p+q=1, using 0.8 as the value of q:
p+q=1
p + (0.8) = 1
p = 1 – (0.8) = 0.2 or 2/10