Active-to-absorbing-state phase transition in an evolving population with mutation

We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the significance of mutation and highlights the connection of this model with the well-known directed percolation universality class. Our model should be a useful starting point to study how mutation may affect extinction or survival of a species.

Figure 1

A schematic DRG flow diagram showing the stable and unstable fixed points (FPs) of our model in the parameter space $u^R-m^R-t^R$. The stable FP is FPIV given by the red thick dot and the unstable FPs are given by thick green dots. All the FPs correspond to weak dynamic scaling. Note that the flow is from the unstable FPs to the stable FPIV.