Multi-type birth-death processes are used to model evolutionary dynamics of a range of biological processes, on the level of cells as well as species. A drawback of many of those models is that they preclude interactions between individuals in order to guarantee tractability, which is not realistic from a biological perspective. For instance during B-cell maturation in germinal centers, which is our guiding example, selection depends on the frequency of each type and on the total number of cells present. In this talk I will introduce a multi-type birth death process with mean-field interactions, and analyse it in the limit where the number of initial cells converges to infinity. In the limit the interaction field converges to a deterministic limit, such that the individuals effectively decouple. I will then show numerical computations for a special case that is rich enough to model both carrying capacity and frequency-dependent selection. This is joint work with William S. DeWitt, Steven N. Evans and Sebastian Hummel.
