Habitat loss-induced tipping points in metapopulations with facilitation

Habitat loss is known to pervade extinction thresholds in metapopulations. Such thresholds result from a loss of stability that can eventually lead to collapse. Several models have been developed to understand the nature of these transitions and how they are affected by the locality of interactions, fluctuations or external drivers. Most models consider the impact of grazing or aridity as a control parameter that can trigger sudden shifts, once critical values are reached. Others explore instead the role played by habitat loss and fragmentation. Here we consider a minimal model incorporating facilitation between the individuals of the same species along with habitat destruction, with the aim of understanding how local cooperation and habitat loss interact with each other. A mathematical model incorporating facilitation and habitat destruction is derived, along with a spatially explicit simulation model. It is found that a catastrophic shift is expected for increasing levels of habitat loss, but the bifurcation becomes continuous when dispersal is local. Under these conditions, spatial patchiness is found and the qualitative change from discontinuous to continuous results are in agreement with previous studies on ecological systems. Our results suggest that species exhibiting facilitation and displaying short-range dispersal will be markedly more capable of avoiding catastrophic tipping points.