Emergent Bistability and Mutualistic Behavior: How Interactions and Dispersal Rescue Diverse Ecosystems from Extinction

We study how migration and interactions can rescue species-rich, spatially structured ecosystems from extinction due to demographic noise. For a single species, one finds an extinction and a survival state depending on the strength of the demographic noise with respect to migration. The transition between these two regimes is a second-order out-of-equilibrium phase transition, which falls into the universality class of Directed Percolation. Here we show that the case of many species with heterogeneous interactions is different and richer. When the demographic fluctuations are strong enough, the transition is continuous and analogous to the single-species case. Ecological interactions play a secondary role in it. At small demographic noise, instead, we find novel features that are a signature of the complexity of the ecosystem. Thanks to interactions and migration, the metacommunity is able to thrive even when demographic noise would drive single species to extinction. This is accompanied by the development of mutualism between non-extinct species. The transition becomes discontinuous and a global bistability emerges. We present a way to predict the catastrophic shift from high diversity to extinction by probing responses to perturbations as early warning signal. Our analytical framework is grounded in statistical physics and focuses on a model of metacommunities based on Lotka-Volterra equations with random interactions.