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.A j A j E i + eA i P (σ; t) .

Phase Transitions in Virology

“…The positive solution starts at a value z * = Σ defining the minimal (critical) population size. This result is related to those found within the context of extinction thresholds in metapopulation models due to habitat loss and fragmentation including continuous (Bascompte and Solé 1996) and first-order (Sardanyés et al 2019) transitions. It thus connects the problem of reduced habitat and the persistence of viral associations requiring higher-order interactions (such as mutualism).…”

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

“…S6(a)-(b)). These transients are typically found in systems with strong feedbacks e.g., cooperation, such as catalytic hypercycles (see e.g., [32, 33]) or metapopulations with facilitation [41]. 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 [46] for more details).…”

“…Also, facilitation processes (involving strong nonlinearities) are known to introduce important changes in spatial systems, as compared to well-mixed ones. In this sense, recent research has found a shift from catastrophic tipping points to continuous ones due to local spatial processes [41, 47].…”

“…Theoretical results on the nature and location of these shifts suggest that some generic factors (such as noise and dispersal) [41, 47] could be crucial. Can realistic interventions help preventing green-desert transitions?…”

“…Once a critical state is approached, unstoppable runaway processes are unleashed [38]. Despite much progress has been made in modelling drylands [10, 11, 41] as well as in identifying warning signals [16, 18, 39, 41, 45], feasible strategies to prevent green-desert transitions are currently scarce.…”