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 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.

Synthetic soil crusts against green-desert transitions: a spatial model

“…Also, facilitation processes (involving strong nonlinearities) are known to introduce important changes in spatial systems, as compared with well-mixed ones. In this sense, recent research has found a shift from catastrophic tipping points to continuous ones, due to local spatial processes [42,43]. Similar analyses to those presented in figure 2 for the mean-field model are displayed in figure 3 for the CA simulations.…”

“…This is a dynamical phenomenon that involves extremely long transients once the bifurcations has occurred, and the time trajectories experience a long bottleneck before rapidly achieving, in equations (3.5) and (3.6), another attractor (the full desert state in electronic supplementary material, figure S6(a) and (b)). These long transients [63] are typically found in systems with strong feedbacks, such as cooperation, catalytic processes [64,65] or metapopulations with facilitation [43]. Also, this dynamical delay tied to saddle-node bifurcations has been recently described in both deterministic and stochastic well-mixed approaches for the non-terraformed system explored in this article (see [19] for more details).…”

“…Under this potential scenario, it is important to develop strategies of intervention aimed at avoiding these transitions. Theoretical results on the nature of these shifts and the parameter values at which they take place suggest that some generic factors (such as noise and dispersal [42,43]) could be crucial. Can realistic interventions help preventing green-desert transitions?…”

“…Here, M k is the neighbourhood of site k and M N ¼ 8 the number of neighbour (using a Moore neighbourhood). The nature of local (spatial) interactions is known to largely influence ecological dynamics [40,43,67]. This is particularly important in drylands, where carbon and water limitation deeply constrains the outcome of nonlinear exchanges [14,59], leading to spatial patterning [48,68].…”

“…These spatial patterns have been extensively studied using computational models [39,40], for instance, models only considering competition [41]. Other models including both competition and facilitation processes also typically display self-organized patchiness [38,[42][43][44][45]. Such patterns are often remarkably organized in space [45].…”