Exercise: effects of population size and mutation rate on population dynamics

We’ll go into this further in the next section, but a very important parameter is θ, which is equal to 2Nμ, where N is equal to the population size and μ is equal to mutations per generation. If there are 100 sites and a per-site per-gen mutation rate of 0.000025, then μ = 0.0025. If there are 200 individuals in the population, then θ = 2Nμ = 1.

This exercise can be completed by running the supplied Python script mutation-drift.py. To run the script with population size of 200, per-site per-gen mutation rate of 0.000025, 100 sites and 1000 generations, input:

python mutation-drift.py --pop_size 200 --mutation_rate 0.000025

This will output the file fig_mutation_drift.png that can be examined locally. Again, these parameters give θ = 1.

(1) Keeping the above parameters as baseline, adjust population size up and down to vary θ between ~0.2 and ~5. What happens to diversity, divergence and haplotype dynamics?

(2) Keeping the above parameters as baseline, adjust mutation rate up and down to vary θ between ~0.2 and ~5. Again, what happens to diversity, divergence and haplotype dynamics?

(3) Adjust N and μ up and down, while keeping θ = 1, to explore high N / low μ and low N / high μ scenarios. What happens to diversity, divergence and haplotype dynamics?

You might try increasing generations to something greater than 1000 to get a better feel for equilibrium divergence and diversity, say --generations 2500. In this case, it may be easier to not plot the haplotype trajectories. This can be done with --summary, like so:

python mutation-drift.py --pop_size 200 --mutation_rate 0.000025 --generations 2500 --summary

Alternatively, if you don’t have a working local Python install, you can run the mutation-drift.ipynb notebook or the mutation-drift.py script online with MyBinder: