Honors Biology
KEY
Hardy-Weinberg Calculations Practice Sheet 2
Give the Hardy-Weinberg equation:
p2+2pq+q2=1
For alleles
For organisms
p
= frequency of the dominant
allele
p2
q
= frequency of the recessive
allele
2pq
q2
= frequency of homozygous
dominant organisms
= frequency of heterozygotes
= frequency of homozygous
recessive organisms
1. In a population of frogs in Hardy-Weinberg equilibrium, a single gene controls the skin
color. Green is dominant to brown. You sample the frog’s gene pool, and find that the
frequency of the dominant green allele is 0.678.
What is the frequency of the recessive allele? p + q =1, if p= 0.678  q= 0.322
What is the frequency of homozygous dominant frogs? p2 = 0.6782 = 0.46, or 46%
What is the frequency of heterozygous frogs? 2pq = (2)(0.678)(0.322) = 0.44, or 44%
What is the frequency of homozygous recessive frogs? q2 = 0.3222 = 0.10, or 10%
2. In a group of pine trees in Hardy-Weinberg equilibrium, smooth bark is dominant to
rough bark. You obtain a DNA sample of many trees, and find that of 486 different
alleles, 312 encode for smooth bark.
What are the allele frequencies?
p = 312/486 = 0.642
p + q =1, if p= 0.642  q= 0.358
If this sample came from 243 different trees, how many would you expect to be:
Heterozygous? 2pq = 0.46; 0.46 * 243 trees = 112 trees
Homozygous recessive? q2 = 0.13; 0.13 * 243 trees = 32 trees
3. You study a population of lizards in Hardy-Weinberg equilibrium. You are interested in
the gene that controls the production of a toxin in their venom. The dominant allele
causes instant death; the recessive allele causes a slow, lingering, painful death. After a
very difficult survey of the lizards, you find that 49 of the 678 lizards have bites that
cause a slow, painful death.
What are the allele frequencies?
**You are talking about organisms, so you are dealing with q2 here, not q!**
q2 = 49/678 = 0.0723
q = √0.0723 = 0.2689  p= 0.7311
How many heterozygous lizards would you expect? 2pq = 0.3932*678 lizards = 267
How many would you expect to be homozygous dominant? p2 = 0.5345*678 = 362
4. You go back in time 6 000 years and survey a population of perch (a fish) in a lake. You
are interested in a gene that controls fin size. The dominant allele encodes for large fins.
The recessive allele encodes for small fins. You find that 1 237 out of 10 087 fish have
small fins.
Today, you survey the same gene in the same fish and find that 687 out of 2 344 fish have
small fins. Has evolution occurred concerning fin size? Back up your answer.
6,000 years ago
= 1237/10087 = 0.1226
q = √0.1226 = 0.3501
p = 0.6499
q2
Today
= 687/2344 = 0.2931
q = √0.2931 = 0.5414
p = 0.4586
q2
Yes—the allele
frequencies have changed
over time.
5. You are studying a population of gnus. The allele frequency for a trait you are interested
in is p= 0.0612 and q = 0.9388. In the wild you, count and study all of the gnus in the
group, and get this count:
2% homozygous dominant, 78% heterozygous, 20% homozygous recessive.
What do you find about these results?
If you calculate out the percentages, you would get 0.4% homozygous dominant,
11% heterozygous, 88% homozygous recessive. The actual results are inconsistent
with the expected results.
Propose a mechanism to explain these data.
The biggest difference is in the low numbers of homozygous recessive organisms
compared to the number you would expect. One possible explanation is that
homozygous recessive organisms are selected against, and are dying out quickly.
Because the real numbers do not agree with the actual animals, evolution or genetic
drift must be occurring.