Habitat loss-induced tipping points in metapopulations with facilitation

Abstract

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 are they 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 along with habitat destruction, with the aim of understanding how local cooperation and habitat loss interact with each other. An explicit mathematical model 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 breakpoint dynamics becomes continuous when dispersal is local. Under these conditions, spatial patchiness is found and the qualitative change from discontinuous to continuous results from a universal behaviour found in a broad class of nonlinear ecological systems (Weissmann and Shnerb, 2014; Martin et al. PNAS (2015) E1828-E1836). Our results suggest that species exhibiting facilitation and displaying short-range dispersal will be markedly more capable of dealing with habitat destruction, also avoiding catastrophic tipping points.