Population Genetics - Simulations with PopG¶
PopG is a one-locus, two-allele (A and a) genetic simulation program written in Java. With PopG you can simulate evolving populations. In the setting window you specify the parameters. The output shows the allele frequency over time (generations) for the different populations. The goal of the simulations is not to get it done but to get a feeling for the evolutionary forces. For this reason think about the possible outcome before you run it.
The PopG website helps with the installation. It also provided a short tutorial and a list of suggestions. Please also read the credits and respect copyright.
Note
Be careful not do open more than one parameter setting widow at a time!
A - Random Genetic Drift¶
A1 - Get started
Run a first simulations using the default parameters.
- Try to understand the graphical output.
- Can you predict the outcome of the simulation?
Tip
You can use [Run]▸[Restart] to repeat the simulations. This is recommended because it shows you different outcomes of the same simulation. You see how much variation you can expect.
A2 - Random Seed
Set parameter
- What did change?
A3 - Random but not arbitrary
Exchange the
- Compare the results?
- What does the seed parameter do and what could be the reason for using it?
- Can we still considered the silulation to be random if we use a seed?
A4 - Increase the number of evolving populations from default 10 to 100. Run 5 simulations and record the number (or %) of populations where the allele A got fixed (P(A)=1) or got lost (P(A)=0).
| Sim | Pop-Size | fixed | lost |
|---|---|---|---|
| #1 | 100 | ? | ? |
| #2 | 100 | ? | ? |
| #3 | 100 | ? | ? |
| #4 | 100 | ? | ? |
| #5 | 100 | ? | ? |
- Can you predict the fate of the allele A in a population?
A5 - Continue the last simulation for 500 more generations by steps of 100 generations (Run > Continue w/ 100). The x-axis keeps track of the time (generation time) passed since the simulation started.
| Gen | Pop-Size | fixed | lost |
|---|---|---|---|
| 100 | 100 | ? | ? |
| 200 | 100 | ? | ? |
| 300 | 100 | ? | ? |
| 400 | 100 | ? | ? |
| 500 | 100 | ? | ? |
- What happen to allele A?
- Based on this observation, what can you say about the genetic diversity in a population over time?
A6 - Repeat the previous simulation but increase the initial population size to 500.
| Gen | Pop-Size | fixed | lost |
|---|---|---|---|
| 100 | 500 | ? | ? |
| 200 | 500 | ? | ? |
| 300 | 500 | ? | ? |
| 400 | 500 | ? | ? |
| 500 | 500 | ? | ? |
- Can you see a difference between the previous simulations with population size 100?
A7 - Run new simulations with the same parameters but increase the number of generation.
| Gen | Pop-Size | fixed | lost |
|---|---|---|---|
| 1000 | 100 | ? | ? |
| 1000 | 500 | ? | ? |
| 5000 | 100 | ? | ? |
| 5000 | 500 | ? | ? |
| 10000 | 100 | ? | ? |
| 10000 | 500 | ? | ? |
- How does population size influence allele frequency over time?
- Can you predict the fate of genetic diversity?
A8 - Probability for fixation - Run a few more simulations but use different initial allele frequency (Feq(A)). Population size (Size), number of generation (N(Gen)), and number of population (N(Pop)) are constant.
| Size | Feq(A) | N(Gen) | N(Pop) | fixed | lost |
|---|---|---|---|---|---|
| 100 | 0.10 | 1000 | 1000 | ? | ? |
| 100 | 0.20 | 1000 | 1000 | ? | ? |
| 100 | 0.30 | 1000 | 1000 | ? | ? |
| 100 | 0.40 | 1000 | 1000 | ? | ? |
| 100 | 0.50 | 1000 | 1000 | ? | ? |
| 100 | 0.60 | 1000 | 1000 | ? | ? |
| 100 | 0.70 | 1000 | 1000 | ? | ? |
| 100 | 0.80 | 1000 | 1000 | ? | ? |
| 100 | 0.90 | 1000 | 1000 | ? | ? |
| 100 | 0.95 | 1000 | 1000 | ? | ? |
| 100 | 0.99 | 1000 | 1000 | ? | ? |
- In Summary - What did you learn from the simulations above in terms of allele frequency changes and predictability of genetic diversity within and between populations over time?
B - Mutation¶
Mutations are the sources of all genetic variation. A single mutation can have a large effect, but in many cases, evolutionary change is based on the accumulation of many mutations. In this simulation we assume that allele A mutates to a and back at different mutation rates.
B1 - Different mutation rates
| Size | N(Gen) | N(Pop) | A ➜ a | a ➜ A | f(AA) | f(Aa) | f(aa) |
|---|---|---|---|---|---|---|---|
| 100 | 500 | 100 | 0.0001 | 0 | ? | ? | ? |
| 100 | 500 | 100 | 0.001 | 0 | ? | ? | ? |
| 100 | 500 | 100 | 0.01 | 0 | ? | ? | ? |
| 100 | 500 | 100 | 0.1 | 0 | ? | ? | ? |
| 100 | 500 | 100 | 0.01 | 0.01 | ? | ? | ? |
B2 - Mutation over time
| Size | N(Gen) | N(Pop) | A ➜ a | a ➜ A | f(AA) | f(Aa) | f(aa) |
|---|---|---|---|---|---|---|---|
| 100 | 100 | 100 | 0 | 0 | ? | ? | ? |
| 100 | 100 | 100 | 0.001 | 0 | ? | ? | ? |
| 100 | 500 | 100 | 0.001 | 0 | ? | ? | ? |
B3 - Population size and mutation rate
| Size | N(Gen) | N(Pop) | A ➜ a | a ➜ A | f(AA) | f(Aa) | f(aa) |
|---|---|---|---|---|---|---|---|
| 10 | 500 | 100 | 0.001 | 0 | ? | ? | ? |
| 100 | 500 | 100 | 0.001 | 0 | ? | ? | ? |
| 1000 | 500 | 100 | 0.001 | 0 | ? | ? | ? |
- What is considered a high mutation rate?
- How is the mutation rate influencing genetic diversity over time?
- What are the limitations of this simulation?
C - Gene Flow / Migration¶
C1 - Different migration rates
| Size | N(Gen) | N(Pop) | m | f(AA) | f(Aa) | f(aa) |
|---|---|---|---|---|---|---|
| 100 | 500 | 100 | 0.0 | ? | ? | ? |
| 100 | 500 | 100 | 0.01 | ? | ? | ? |
| 100 | 500 | 100 | 0.001 | ? | ? | ? |
C2 - Migration rate and population size
| Size | N(Gen) | N(Pop) | m | f(AA) | f(Aa) | f(aa) |
|---|---|---|---|---|---|---|
| 10 | 500 | 100 | 0.01 | ? | ? | ? |
| 100 | 500 | 100 | 0.01 | ? | ? | ? |
| 1000 | 500 | 100 | 0.01 | ? | ? | ? |
C3 - Migration and mutation rate
| Size | N(Gen) | N(Pop) | m | A ➜ a | f(AA) | f(Aa) | f(aa) |
|---|---|---|---|---|---|---|---|
| 100 | 500 | 100 | 0.01 | 0.001 | ? | ? | ? |
| 100 | 500 | 100 | 0.05 | 0.001 | ? | ? | ? |
| 100 | 500 | 100 | 0.10 | 0.001 | ? | ? | ? |
- Describe the influence of migration on the genotype frequency.
- Describe the interaction between migration rate, genetic drift and mutation rate.
- What factors can influence the migration rate?
D - Selection / Fitness¶
Natural selection is the differential success of genotypes in contributing to the next generation. The effect of natural selection on genotypes is measured by fitness.
- w: relative fitness (w=1-s)
- s: selection coefficient (s=1-w)
- f(xx): genotype frequency
Before you start a simulation think about the possible outcome of your simulation!
| w(AA) | w(Aa) | w(aa) | s | f(AA) | f(Aa) | f(aa) | Fitness |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | - | ? | ? | ? | neutral |
| 1 | 1 | 0 | - | ? | ? | ? | complete dominance |
| 1 | 0 | 1 | - | ? | ? | ? | complete underdominance |
| 0 | 1 | 0 | - | ? | ? | ? | complete overdominance |
| 1 | 1 | 1-s | 0.01 | ? | ? | ? | recessive |
| 1 | 1 | 1-s | 0.1 | ? | ? | ? | recessive |
| 1 | 1-s/2 | 1-s | 0.1 | ? | ? | ? | additive |
| 1-s | 1 | 1-s | 0.05 | ? | ? | ? | overdominance |
| 1-s | 1 | 1-s | 0.1 | ? | ? | ? | overdominance |
| 1+s | 1 | 1+s | 0.05 | ? | ? | ? | underdominance |
| 1+s | 1 | 1+s | 0.1 | ? | ? | ? | underdominance |
- How does fitness influence diversity within and between populations?
- How much fitness does a population need to outrun genetic drift?
E - Simulations Explained¶
Find the setting used for the following simulations. Set population size, number of generations, and number of population to 100.
E1 - Stable Populations
E2 - Swift Shift
E3 - We All Go Down
E4 - Get Stable
E5 - You Are Not Getting Rid of Me
Possible Solutions
