Title: Diagrammatic expressions for the steady-state distribution and static responses in evolving populations
Abstract:
Responses of biological quantities are fundamental for understanding and controlling populations. In particular, the steady-state distribution and mean fitness are important quantities, since they characterize how well each species and the whole population adapt to the environment, respectively. However, how these quantities and their responses can be expressed in terms of experimentally accessible observables remains unclear, even in simple models.
In this talk, I will study the parallel mutation–reproduction model, which describes population dynamics through a nonlinear master equation. Using a diagrammatic approach, I will derive expressions for the steady-state distribution and static responses of mean fitness in terms of accessible observables. In these diagrams, self-loops represent reproduction, while directed edges represent mutations. Our results extend the Markov chain tree theorem, which provides the steady-state distribution of a linear master equation. I will also demonstrate how our results can be used to derive approximations in limiting regimes and develop strategies for controlling harmful populations. This talk is based on "our paper" (https://journals.aps.org/prresearch/abstract/10.1103/fc35-47fs).
