Student A
I chose evolutionary graph theory to start off, he then went on to evolutionary game theory and we eventually ended up with diffusion theory.
The questions were almost all simple and high-level stuff, asking about the assumptions, premises and use-cases for each of the theories we discussed.
There were a few times where he specifically asked for (simple) equations (e.g. the rough structure of the Kolmogorov forward & backward equations, the fixation time distribution for a diffusion Wright-Fisher process or the transition probabilities for a directed circle graph).
In general, the atmosphere was very pleasant and he made sure to give you some hints if you went off in the wrong direction. From what I discussed with other people, I get the feeling that diffusion theory is definitely a favorite of his.
Student B
The exam took place in Niko Beerenwinkel’s office in Basel. One of the course assistants took notes but did not interact during the exam. The atmosphere was quite friendly. Niko Beerenwinkel was fair and helped me out during the exam when I could not come up with an answer right away.
You can choose the topic you want to start with. I chose evolutionary dynamics on graphs and he started to ask me what this models. I also had to explain what you need to model such a process and what kind of process it is (Moran). He asked me to draw several types of graphs and asked me how I can find the fixation probability. I also had to write down the formula of the fixation probabilities. I continued to explain how you could proof the isothermal theorem. He asked me about suppressors of selection and where they can be observed. My answer was that this is often in cancer for instance when there is only one or few stem cells.
This led to the second part of the exam. He asked me about oncogenes and the probability of fixation of an oncogene. I had to explain how we could model this dynamics using differential equations and I drew the dynamics with the different hits. Further, I had to explain what the conditions that one type reaches fixation before the other arises.
Finally, he asked me about branching processes. I explained what a Galton-Watson process is and what is models. He continued to ask me how this process behaves and what its properties are. I said that it either goes to infinity or to zero depending on the average number of offspring. He asked me how you can find this probability but I could not really give the answer but I could draw the plot of the roots of the pgf. At last, I had to write down the formula for the pgf. Then I left the room for a moment and when I came back he told me that I passed but not what grade I had.
I suggest that you prepare one topic really well and start with this. You might also want to think to wich other topic your choice can lead and also study this quite well. But it is very important that you know at least the basics of every topic and that you have an intuition of what is going on in general. I think the exam is very fair compared to the content of the course and you definitely don’t have to derive complicated formulas or redo some of the exercises.
Student C
There will be two topics/lectures discussed. You can choose the first one. I went for ED in Cancer.
How is an oncogene formed. What is the dynamics? Write down formula for the fixation probability of a oncogene. Write down rho, (1-1/r…)
How is a TSG formed. What is the dynamics? Draw the graphs for small, intermediate and large population. What is a small population in terms of maths? (Critical population size)
What is the Moran process? Define the transition matrix for the neutral case. (write down transitions for Pi,i+1, …
How does it change if fitness r is included
Explain branching process
What is the possible outcome of the Watson-Galton process: Extinction or infinite growth
Explain prob. generating function
Student D
Contrary to what you read above, NB did not help me out and towards the end let the time run out on one question, only to complain that we discussed 10% (!) of the usual material. His advice was to learn the basics verbatim, I guess.