Multi-type branching processes
This board comes from the office of Peter Keller, a new postdoc working at the University of Edinburgh. He is currently thinking about multi-type branching processes in biology and wanted to draw some pictures on the board to help him figure out what was going on. In a branching process you have a population of individuals who each produce a random number of offspring, and you want to ask questions like “How big will the population be at a certain time in the future?”, or “What is the chance of the population ever becoming extinct?”. In a multi-type branching process, there are different types of individuals. For example, when bacteria reproduce, they may either replicate themselves, or they may produce a mutant form. Mutants can then only replicate into mutants. We can then ask what the proportion of mutants to normal individuals is likely to be after a certain amount of time.
I have no idea what the reference to martingales and larks is. Please leave a comment if you think you know!