Population genetics exercisesBILD 3; created by Dr. Sarah Stockwell
Do part 1 of this problem set in your discussion section, collaborating with your group.
Do part 2 as homework, on your own. Part 2 should be entirely your own work.
Parts 1 AND 2 will be due by the start of your discussion section the following week.
Show all your work for full credit.
Part 1: In your discussion section
1 (2 point) Given the many ways in which real populations may deviate from the HardyWeinberg model, why is the model useful to evolutionary biologists?
Bromeliads are plants that grow on the side of rainforest trees. Water collects in the
hollows of their leaves and forms long-lived pools, in which tree frogs lay their eggs and tinier
organisms live out many generations.
In one such pool, a population of 105 Phantasmagoric Water Fleas is happily swimming
about. Peering into the pool, you notice that 88 of them have short antennae and 17 have long
antennae. You hypothesize that long antennae might help their owners find food better and
might be increasing in frequency in the population due to natural selection.
A literature search reveals that in the closely related species Fantastical Water Fleas, the
gene Ant controls antenna length. You return and sequence the Ant gene in 105 Phantasmagoric
Water Fleas. You find 2 alleles for this gene, which you name A1 and A2. The genotypes in the
population are:
17 Fleas with A1A1, all with long antennae
48 Fleas with A1A2, all with short antennae
40 Fleas with A2A2, all with short antennae
Critical thinking question:
2 (1 point). Do you think the Ant gene controls antenna length in the Phantasmagoric Water
Flea? Justify your reasoning using the terms “genotype” and “phenoype.”
Copyright 2021 Sarah Stockwell. Do not distribute without permission.
Hardy-Weinberg Equilibrium hypothesis testing:
To investigate your hypothesis (see second paragraph in the description above) about the
selective advantage of long antennae, you decide to find out whether this population is in HardyWeinberg equilibrium.
3 (1 point). Calculate the observed allele frequencies. Show your work.
Note: to avoid rounding error compounding over the rest of the problem, report p and q with 4
decimal places of precision. Use those values as you do the rest of the calculations.
4 (1 point). Calculate the genotype frequencies you’d expect if the population were in HardyWeinberg equilibrium. Show your work. Give 4 decimal places of precision in your answers.
Use those values in later calculations.
5 (1 point). Using the expected genotype frequencies, calculate the number of Fleas with each
genotype you’d expect in a sample this size (105 Fleas). Show your work. Round to the first
decimal point.
6 (2 point). Calculate X2 for your data. Show your work.
The X2 equation is X2 = Σ [(Oi – Ei)2 / Ei ]
Then compare your X2 value to the significance cutoff: is X2 ≥ 3.841? What can you conclude
from this about whether the population is in Hardy-Weinberg equilibrium?
Copyright 2021 Sarah Stockwell. Do not distribute without permission.
7 (2 point). What do you conclude about your selection hypothesis? Why?
Part 2: Homework. THIS SECTION SHOULD BE COMPLETED ON YOUR OWN,
WITHOUT COLLABORATING WITH OTHER STUDENTS.
Arctic foxes on the island of Jan Mayen exhibit three coat colors: white, black, and gray. You are
a graduate student interested in studying the evolution and population genetics of the coat color.
A collaborator doing field work on the island sends you data on genotype and coat color
phenotype for a random sample of the foxes. You suspect that natural selection plays a role in
coat color on the island, but your advisor is skeptical. You show your advisor the new data and
she says, “The first thing you need to do to convince me about your ‘selection’ hypothesis is
check for Hardy-Weinberg equilibrium!”
Arctic Fox Data: Jan Mayen Island
Genotype
Color
Number
AA
White
132
Aa
Gray
287
aa
Black
100
Critical thinking question:
1 (1 point). Briefly explain why your advisor wants to know about Hardy-Weinberg equilibrium
in this population. Why would this help you understand whether your hypothesis about natural
selection on fox coat color is correct?
Copyright 2021 Sarah Stockwell. Do not distribute without permission.
Hardy-Weinberg Equilibrium hypothesis testing:
2 (1 point). Being the dutiful grad student that you are, you immediately do as your advisor
suggests. Calculate the observed allele frequencies in the fox data. Show your work. Note: to
avoid rounding error compounding over the rest of the problem, report p and q with 4 decimal
places of precision. Use those values as you do the rest of the calculations.
3 (1 point). Using those allele frequencies, calculate the genotype frequencies expected under
Hardy-Weinberg equilibrium. Show your work. Give 4 decimal places of precision in your
answers. Use those values in later calculations.
4 (1 point). Calculate the number of each kind of genotype you would expect under HWE in this
sample of foxes. Show your work. Round to the first decimal place.
5 (1 point). How do observed and expected numbers of genotypes differ?
Copyright 2021 Sarah Stockwell. Do not distribute without permission.
6 (1 point). Calculate X2 for your data. Show your work. Report your answers with 3 decimal
places.
The X2 equation is X2 = Σ [(Oi – Ei)2 / Ei ]
7 (2 point). How does your X2 value compare to the significance cutoff of 3.841? Is the fox
population is in Hardy-Weinberg equilibrium?
8 (2 point). Does this support your assertion about natural selection acting on fox populations, or
your advisor’s skepticism about it? If you found a pattern consistent with natural selection,
which phenotype(s) appear to have higher fitness? Are there other explanation(s) that are
consistent with your results?
Copyright 2021 Sarah Stockwell. Do not distribute without permission.
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