@article{12787,
  abstract     = {Populations evolve in spatially heterogeneous environments. While a certain trait might bring a fitness advantage in some patch of the environment, a different trait might be advantageous in another patch. Here, we study the Moran birth–death process with two types of individuals in a population stretched across two patches of size N, each patch favouring one of the two types. We show that the long-term fate of such populations crucially depends on the migration rate μ
 between the patches. To classify the possible fates, we use the distinction between polynomial (short) and exponential (long) timescales. We show that when μ is high then one of the two types fixates on the whole population after a number of steps that is only polynomial in N. By contrast, when μ is low then each type holds majority in the patch where it is favoured for a number of steps that is at least exponential in N. Moreover, we precisely identify the threshold migration rate μ⋆ that separates those two scenarios, thereby exactly delineating the situations that support long-term coexistence of the two types. We also discuss the case of various cycle graphs and we present computer simulations that perfectly match our analytical results.},
  author       = {Svoboda, Jakub and Tkadlec, Josef and Kaveh, Kamran and Chatterjee, Krishnendu},
  issn         = {1471-2946},
  journal      = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  number       = {2271},
  publisher    = {The Royal Society},
  title        = {{Coexistence times in the Moran process with environmental heterogeneity}},
  doi          = {10.1098/rspa.2022.0685},
  volume       = {479},
  year         = {2023},
}