Dormancy: a trade-off between resilience and invasiveness

While most existing mathematical models of dormancy and catastrophic events consider bet-hedging dormancy strategies in a monostable stochastic environment, we investigate their impact in a bistable model incorporating the Allee effect, where a catastrophic event (or the introduction of a species into a new environment) is treated as a sudden change in the initial conditions. Using monotone dynamical systems theory, we analyze a two-compartment bistable model with active and dormant individuals. We characterize the separatrix and show that dormancy introduces an inherent trade-off for the population: while it increases resilience to catastrophic events, it also strengthens the Allee effect, thereby reducing the invasiveness of the species under consideration. In this sense, dormancy increases the inertia of the environment. Furthermore, we explore how density-dependent switching rates may optimize this trade-off. Finally, we extend these results to time-varying environments, showing that dormancy can also protect a population against rate-induced tipping caused by gradual environmental degradation following a catastrophe.