SBI3U – Evolution
Date:
Name:
THE HARDY-WEINBERG EQUILIBRIUM
Assume all populations follow the Hardy-Weinberg principle.
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) frequency of the "aa" genotype; b) frequency of the "a" allele; c) frequency of the "A" allele;
d) frequencies of the genotypes "AA" and "Aa"; e) frequencies of the two possible phenotypes if "A" is completely
dominant over "a."
2. 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?
3. 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 following:
a) The percentage of butterflies in the population that are heterozygous.
b) The frequency of homozygous dominant individuals.
4. A very large population of randomly-mating laboratory mice contains 35% white mice. White colouring is caused by
the double recessive genotype, "aa". Calculate allele and genotypic frequencies for this population.
5. Cystic fibrosis is a recessive condition that affects about 1 in 2 500 babies in Canada. Please calculate the following.
a. The frequency of the recessive allele in the population.
b. The frequency of the dominant allele in the population.
c. The percentage of heterozygous individuals (carriers) in the population.
6. The ability to taste PTC is due to a single dominant allele (T). You sampled 215 individuals at school and determined
that 150 could detect the bitter taste of PTC and 65 could not. Calculate the percentages of all the genotypes.
7. For each of the following situations, explain whether the Hardy-Weinberg equilibrium would be maintained
generation after generation:
a) a population of African violets maintained by a plant breeder
b) the population of the black fly, Simulium venustum, in northern Ontario
c) a racoon population living in the Humber Valley in west Toronto
d) a newly discovered bird population on a remote island off the coast of British Columbia
Answers:
1. a) 0.36
b) 0.6 c) 0.4
2. 42%
3. a) 46.5%
6. 30.2%, 49.5% and 20.3%
d) 0.16 and 0.48
e) 0.64 and 0.36
b) 0.135
4. 0.59, 0.41, 0.35, 0.48, 0.17
5. a) 0.02
b) 0.98
c) 4%
SBI3U – Evolution
Date:
Name:
POPULATION GENETICS AND THE HARDY-WEINBERG PRINCIPLE
Example #1
A biologist has found that 10% of a population of Bats are hairless, which is a recessive trait. Assuming the population is
in Hardy-Weinberg equilibrium, determine the genetic structure (genotype and allele frequencies) of the population.
Example #2
In a population of 200 cats, 168 are black coloured and 32 are white coloured. Determine the allele frequencies of B and
b. Note: black coloured is dominant to white coloured. Calculate:
a) the frequency of each allele b) frequency of each genotype, and (c) the number of cats possessing each genotype.
A set of sampled data of cats was obtained and the following results were: p2 = 0.74, 2pq = 0.10 and q2 = 0.16.
How do you explain the data?
SBI3U – Evolution
Date:
Name:
POPULATION GENETICS AND THE HARDY-WEINBERG PRINCIPLE ANSWERS
Example #1
A biologist has found that 10% of a population of Bats are hairless, which is a recessive trait. Assuming the population is
in Hardy-Weinberg equilibrium, determine the genetic structure (genotype and allele frequencies) of the population.
q2 = 0.1
q= 0.32 – frequency of the recessive allele
p+q=1
p=1-q
= 1 – 0.32 = 0. 68  frequency of the dominant allele
p2 = (0.68)2 = 0.46  frequency of homozygous dominant
2pq = 2(0.68)(0.32) = 0.44  frequency of heterozygous dominant
Example #2
In a population of 200 cats, 168 are black coloured and 32 are white coloured. Determine the allele frequencies of B and
b. Note: black coloured is dominant to white coloured. Calculate:
a) the frequency of each allele b) frequency of each genotype, and (c) the number of cats possessing each genotype.
Let B and b be the alleles for black and white fur colour, respectively.
a) Since all the white cats are homozygous recessive (bb):
q2 = 32/200 = 0.16
q = 0.4  this represents the recessive allele (b) frequency
p+q=1
p = 1 – q = 1 – 0.4 = 0.6  this represents the dominant allele (B) frequency
b) BB: p2 = (0.6)2 = 0.36
Bb: 2pq = 2(0.6)(0.4) = 0.48
bb: q2 = (0.4)2 = 0.16
# of BB = (0.36)(200) = 96
# of Bb = (0.48)(200) = 96
# of bb = 32 (already given in the question)
A set of sampled data of cats was obtained and the following results were: p2 = 0.74, 2pq = 0.10 and q2 = 0.16.
How do you explain the data? (i.e. what conditions haven’t been
From answer (b) above: p2 = 0.36
From sample data:
p2 = 0.74
2pq = 0.48
2pq = 0.10
q2 = 0.16
q2 = 0.16
Reasons:
 Non-random mating – blacks selectively mating with themselves, same for whites.
 Heterozygous are weaker
 Immigration in from an external population that is p redominantly BB