Student A
I chose Evolutionary Graph Theory to start off and he asked me what this models and how we model it. I told him that it has an underlying moran process. He asked me how we model the interactions in the graph and it took me a while to understand that he meant the transition probabilities. We went on to talk about spatial models and he asked me what this models and what kind of model we used there. He asked me what the shape of the process is in the end and I said a sphere. He asked me how we can solve spatial models analytically and I said via a diffusion approximation as Fisher’s equaiton. He asked me then what we assumed in order to solve this and I didn’t know that we assumed a diminishing behaviour. He went on to ask me how to approximate it (Gillespie Algorithm) and how this works. He asked me as well whether that is computationally efficient which I said yes, we only need to set up the SDEs and follow the procedure that I mentioned before that. In the end we went to the last topic, evolutionary escape. When asked about the model I said WF, even though it would have been a branching process. NB was helpful in my case, I thought the exam would be worse tbh, the things he asked were mostly high level and due to the situation via Zoom, I could only describe things rather than write them down. This lead to even more high level discussion I believe.
Student B
The exam happened online using Zoom because of the covid pandemic. He asked me what was my favorite subject and I wanted to start by talking about Quasispecies. I said we can bring together mutation and selection in this model, and we only look at genotype frequencies, therefore we can use quasispecies to model infinitely large populations. He didn’t like that I used the word “infinite” because of course a population size has to be finite. We moved on and he asked me about the equation used in quasispecies. I described the equation in matrix form x’ = xW - phi x and said that W is the mutation-selection matrix and that it is used to find the equilibrium frequency by solving an eigenvalue problem. He asked what is phi about. I answer that phi is the average fitness of the population. He then asked me what we can determine using the quasispecies model and how exactly we worked our way toward that goal. The answer is that we can define an error threshold, and we used a simplified model with only two different types: wild type and mutated, with moderate fitness value an small mutation rate we can find that u_c = 1/L. He asked me what the mutation rate of a specific species was (i don’t remember which one, maybe he even asked about human?!) which I didn’t expect at all. I said I didn’t know but that most organism except some viruses have a mutation rate below the error threshold.
We then moved to Branching Processes. I started by saying that we use the Glaton-Watson process, and at each generation we have a random number of offsprings given by a probability generation function, which wasn’t totally correct since the number of offsprings is given by the the transition probability (which can be derived from the pgf though). He asked me the exact formula of the pgf, which I didn’t remember (it is f(s) = E[s^Z] = Sum p_k s^k, so he described me the Sum and asked me what p_k was. I wasn’t sure anymore and a bit stressed so he simply told me that it was the probability of having k offsprings. This was the worst time of the exam as I didn’t expect those precise questions, I said I didn’t remember but that I remembered clearly the graph used to illustrate the properties of the pgf so we finally move to that. I talked about what the different slopes m = f’(1) tell us. He asked me what was f(s) again which confused me but he simply wanted to check if I listened to him earlier so I simply said that f(s) was the pgf.
Finally, he asked me about Evolutionary Escape. He asked what we were trying to used it for. I took the example of cancer treatment: we want to know if the treatment will be successful i.e. if we kill the cancerous cells before an escape type is generated. He asked what model we used for that, which made the link with the previous part about branching processes. He then wanted me to give the exact formula for the risk of escape xi_0 \approx xi_1 f_0 Pi mu_e R(G,f), and then asked what was the risk polynomial about. I said that the risk polynomial gave use all the different paths that we can take from wild type to escape type along the genotype lattice. We ended up there. He said the witness and him would talk in private for a second before coming back. Once they came back on my screen he told me it wasn’t perfect but definitely a pass.
My advice: Reading the book from Nowak helped a lot understanding transition between different part of the course. During the oral exam, I’d advice to talk as long as he doesn’t interrupt you with an other question. I think it helps to show that you know stuff and that you are confident/excited to share your knowledge (but remember to answer the question!)