POPULATION GENETICS SIMULATIONS
By F. Frey and C. Lively, Indiana University
How to get the program
Go to http://evolution.gs.washington.edu/popgen/popg.html (This is correct for 2008. Use a browser other than
Safari).
Download the appropriate version of the popgen program for your computer.
Software Notes
See “Running the program” in the url above
Purpose of this exercise
Drawing from past courses and interactions with other faculty (especially Dr. Fortier and Dr. Dudle), Frank Frey and
C. Lively developed this series of exercises. This program allows you to set parameter values (fitness of genotypes,
mutation & migration rates, population size, etc.) and watch allele frequencies change through time in a series of
simulated populations. These exercises should solidify your understanding of how selection, mutation, migration,
and drift affect the evolutionary process. Additionally, you should come away with an understanding of how
beneficial or deleterious recessive alleles may or may not persist in a population depending on the evolutionary
forces at work and understand the effects of interacting evolutionary forces on the evolutionary process.
How to set values in the program and start a simulation
In the menu, select run, then select “new run”.
With the mouse, click on the box neighboring the value you would like to set (or use the TAB button)
Type in the new value.
When all values are set, click the ‘run simulation’ button to start the simulation
Parameters and explanations (alleles are italicized in this exercise)
Initial frequency of allele A (not necessarily dominant – depends on relative fitness values)
wAA, wAa, waa: Relative fitness of each genotype in the population (may vary between 0 & 1)
Migration rate: Number of migrants from source population per generation to your population
Mutation rate of allele A to allele a. This may vary between 0 & 1
Mutation rate of allele a to allele A. This may vary between 0 & 1
Number of different populations to simulate at the same time (may vary between 1 & 10)
Number of generations the simulation will run through (may vary between 1 & 10000)
Population Size: Size of each simulated population (may vary between 1 & 10000)
1
NATURAL SELECTION
Consider a simple case of overdominance alone (no other evolutionary forces) using the parameters: p = 0.01, wAA
= 0.9, wAa = 1.0, and waa = 0.9, where p is the frequency of the A allele.
1) Why is this a case of overdominance?
2) Will allele A get more or less common through time?
3) Will allele A be fixed (p = 1), lost (p = 0), or maintained at some intermediate frequency?
4) On the figure below, graph your prediction of the frequency of allele A through time. Consider the shape of
the curve as you do so (e.g., Is the spread or loss of the allele constant? Does the rate of spread or loss of
the allele slow down or speed up over time?, etc.). Is the output from Popgen, the dashed line is the
analytical prediction, assuming an infinite population size.
1
Freq A
0
Time (generations)
Simulation
In the popgen simulation, set the number of populations to 1. Set Population Size to 10000 (so the effect of drift is
small). Set the initial frequency of the A allele to 0.01. Set the mutation and migration values to zero.
Now set wAA = 0.9, wAa = 1, waa = 0.9. Set the number of generations to 200.
Click Okay to run simulation.
5) Do your predictions above match the results of the popgen simulation?
6) In the space below, summarize how overdominance alone affects the evolutionary process.
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Now consider a case where allele A is recessive to allele a. Set p = 0.5 and waa = 1.0. All other parameters remain
the same.
7) How do the three fitness values (wAA, wAa, waa) show that allele A is recessive? Is it a beneficial or
deleterious allele?
8) Will allele A get more or less common through time?
9) Will allele A be fixed (p = 1), lost (p = 0), or maintained at some intermediate frequency?
10) On the figure below, graph your prediction of the frequency of allele A through time. Consider the shape of
the curve as you do so (e.g., Is the spread or loss of the allele constant? Does the rate of spread or loss of
the allele slow down or speed up over time?, etc.)
1
Freq A
0
Time (generations)
Simulation
Make sure p = 0.5, waa = 1.0, and all other parameters are the same as the previous simulation. Click on ‘run
simulation’.
11) On the figure above, sketch the results of the simulation. Do your predictions match the results?
12) In the space below, summarize how recessiveness alone affects the spread or loss of an allele in the
population.
13) How would you increase the strength of selection against allele A? Try simulating this situation. How does
the strength of selection affect the rate of spread or loss of a recessive allele?
14) How could you change the genotype fitness values to make allele A a beneficial recessive allele? Try
simulating this situation. Summarize the differences (at least 2) in evolutionary trajectory between a
situation where allele A is a beneficial recessive and where allele A is a deleterious recessive.
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MUTATION
Consider a simple case of mutation alone. Things will happen extremely slowly if we use realistic mutation rates, so
pretend our study population is at Love Canal, Chernobyl, or Three Mile Island. Set u (Ato a) = 0.1, u (a to A) =
0.01, p = 0, wAA = wAa = waa = 1. All other parameters remain the same.
15) Is mutation from allele A to allele a deleterious, beneficial or neutral?
16) Is mutation from allele a to allele A deleterious, beneficial or neutral?
17) Will allele A get more or less common through time?
18) Will allele A be fixed (p = 1), lost (p = 0), or maintained at some intermediate frequency?
19) On the figure below, graph your prediction of the frequency of allele A through time. Consider the shape of
the curve as you do so (e.g., Is the spread or loss of the allele constant? Does the rate of spread or loss of
the allele slow down or speed up over time?, etc.)
1
Freq A
0
Time (generations)
Simulation
Make sure all parameter values are set as described above. Click on ‘run simulation’.
20) On the figure above, sketch the results of the simulation. Do your predictions match the results? Press
control C to continue the simulation for another 200 generations.
21) In the space below, summarize how mutation alone affects the spread or loss of an allele in the population.
22) Try some more simulations with lower mutation rates. For example, try u (A to a) = 0.01 & u (a to A) =
0.001. How do decreased mutation rates affect the time it takes for an allele to reach an intermediate
frequency?
Compare the results of the mutation simulations to the selection simulations. Note that mutation alone is a very
weak evolutionary force relative to natural selection.
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NATURAL SELECTION AND MUTATION
Even though mutation alone is a weak evolutionary force, mutation is an extremely important evolutionary force.
These next two examples will illustrate the effects of mutation when combined with selection on the evolutionary
process.
CASE I
Consider a case of mutation – selection balance and the loss of deleterious recessive alleles. Set p = 0.5, wAA = 1,
wAa = 1, waa = 0.5, u (A to a) = 0.001, u (a to A) = 0. All other parameters remain the same as before.
23) Will allele A be fixed (p = 1), lost (p = 0), or maintained at some intermediate frequency?
24) On the figure below, graph your prediction of the frequency of allele A through time. Consider the shape of
the curve as you do so (e.g., Is the spread or loss of the allele constant? Does the rate of spread or loss of
the allele slow down or speed up over time?, etc.)
1
Freq A
0
Time (generations)
Simulation
Make sure all parameter values are set as described above. Click on ‘run simulation’.
25) On the figure above, sketch the results of the simulation. Do your predictions match the results?
There are two possible reasons why allele A was not fixed in this population (note: these are not mutually exclusive).
First, mutation from A to a may be recreating allele a faster than selection takes it out. Second, allele a is
‘completely recessive’. This means that heterozygotes do not suffer a fitness cost because they have one copy of
allele a. These next two simulations will test two hypotheses for the maintenance of allele a in this population.
Hypothesis I: Mutation prevents the rapid fixation of allele A
26) Set the mutation rates to zero, leaving all other parameters the same. Re-run the simulation and compare
your results to the previous simulation (with mutation rate A to a = 0.001). Does mutation alone explain
the maintenance of allele a in the population?
Hypothesis II: Allele A is not fixed in the population because allele a is completely recessive
27) Leaving the mutation rates at zero, change wAa to 0.9. This makes allele a ‘partially dominant’, meaning
that one copy of allele a has a small deleterious effect on the heterozygote. Re-run the simulation and
compare your results to the above two simulations. Does the ‘complete recessiveness’ of allele a alone
explain the maintenance of allele a in the population?
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28) In terms of evolutionary dynamics, what is the difference between a ‘completely recessive’ allele and a
‘partially dominant’ allele?
To understand the importance of mutation, reset the mutation rates to u (A to a) = 0.001 and u (a to A) = 0. Leave
all other parameters the same (allele a is still ‘partially dominant’). Re-run the simulation.
29) Compare these results to the prior situation of ‘partial dominance’ and no mutation. How does mutation
affect the evolutionary dynamics?
Re-run several simulations altering the mutation rate.
30) Can mutation alone always prevent the rapid fixation of allele A?
Reset wAA = 1, wAa = 1, and waa = 0.5 leaving all other parameters the same (note: allele a is now completely
recessive). Re-run several simulations altering the mutation rate (leave u (a to A) = 0).
31) How does the mutation rate affect the equilibrium frequency of allele A?
Remember, there is a simple equation that determines the equilibrium frequency of a completely recessive allele
given a constant mutation rate and constant selection differential.
32) Set the genotype fitness values to reflect any selection coefficient you choose (be sure that allele a remains
completely recessive and deleterious). Set the mutation rate, u (A to a), to any value you choose. Run the
simulation and determine if the equilibrium frequency of allele a in the population seems to match the
expectation given by the equation. Remember, the y-axis of the graph is the frequency of allele A. The
frequency of allele a is simply (1 – frequency of allele A).
CASE II
Consider another case of mutation – selection balance and the spread of beneficial recessive alleles. Set the
following parameters: p = 1.0, wAA = 0.5, wAa = 0.5, waa = 1.0, u (A to a) = 0.0001, u (a to A) = 0, Ngen = 1000,
population size = 10000.
How do the fitness values show that allele a is a beneficial recessive?
33) Will allele A get more or less common through time?
34) Will allele A be fixed (p = 1), lost (p = 0), or maintained at some intermediate frequency?
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35) On the figure below, graph your prediction of the frequency of allele A through time. Consider the shape of
the curve as you do so (e.g., Is the spread or loss of the allele constant? Does the rate of spread or loss of
the allele slow down or speed up over time?, etc.)
1
Freq A
0
Time (generations)
Simulation
Make sure all parameter values are set as described above. Click on ‘run simulation’.
36) On the figure above, sketch the results of the simulation. Do your predictions match the results?
37) Why does it take allele a so long to make it into the population even though it is an extremely beneficial
allele?
Set wAa = 0.6. This makes allele a ‘partially dominant’ because one copy of allele a has a small beneficial effect on
the heterozygote. All other parameters remain the same. Re-run the simulation.
38) What is the effect of ‘partial dominance’ compared to ‘complete recessiveness’ on the evolutionary
dynamics when a beneficial recessive allele is considered? (how is this simulation different from the
previous one)
Three important things to notice from these mutation – selection exercises.
 Mutation can counter-balance selection. Equilibrium allele frequencies may change depending on
the mutation rate and the strength of selection (Case I).
 Mutation provides the raw genetic variation that selection can act on (Case II).
 The degree to which an allele is dominant or recessive in a population (from completely dominant
to completely recessive and everything in between) affects evolutionary dynamics. The
‘effectiveness’ of selection in eliminating or fixing alleles in a population depends not only on the
strength of selection but also on how alleles are expressed in the heterozygote (degree of
dominance)
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GENETIC DRIFT
Popgen allow you to examine up to 10 different populations in the same simulation. We now want to look at the
differences among populations over time for different population sizes. Genetic drift (sampling error) should
increase as population sizes get smaller.
Set p = 0.5, wAA = wAa = waa = 1, mutation rates = 0, migration = 0, Ngens = 100. Number of populations =8.
39) Predict what will happen if the population size = 1000 (will allele frequencies change from their initial
values)? Run the simulation.
40) Explain why the dashed line remains at p = 0.5 throughout the simulation and the eight lighter lines
‘wiggle’ around the dark line.
41) Next, we’ll reduce the population size by ½ over the course of 5 more simulations (500, 250, 125, 64, 32).
Predict how these simulations will differ from one another. Run the simulation.
42) Notice how in each of the above simulations the dashed line (infinite population size) remains steady on p
= 0.5. When the population sizes get smaller the frequency of allele A goes to either 0 or 1 in the 8 lighter,
single-population lines. Is the rate of fixation or loss of allele A related to population size?
43) Is genetic drift a creative force (creates genetic variation) or a destructive force (reduces genetic variation)
within a population?
Next, we’ll look at the effect of population size on the spread of a beneficial, ‘completely recessive’ allele in the
population. Set wAA = 1.0, wAa = 0.9, waa = 0.9 and p = 0.3. Leave all other parameters as before.
44) Set the population size = 1000. Roughly how long does it take allele A to fix in the population?
45) Reduce the population size to 400, 80, 40 and 20. Compared to the previous simulation, what effect does
reducing population size have on the spread of allele A in the population?
46) Now run the same simulation 10 times with a population size of 20. Why doesn’t allele A always get
fixed?
47) Now make allele A ‘partially dominant’ (e.g., set wAa = 0.95) and re-run the same simulation 10 times with
a population size of 20 and compare the results to the previous simulation. How does changing the degree
of dominance affect the spread of allele A in the population?
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