Ecosystem modelling provides clues to understanding ecological tipping points

Abstract

Ecological thresholds, associated with abrupt changes in the state and organisation of ecosystems, challenge both scientists and managers. Adaptive response to such changes, and planning for their occurrence, requires an understanding of the underlying drivers and system responses as well as appropriate monitoring. In addition to field studies, modelling can advance our ability to anticipate or deal with such major ecosystem shifts. Here, we used an existing multispecies model with smooth continuous functions that were modified to include thresholds representing 3 alternative scenarios of predator responses when prey numbers drop below a critical threshold: (I) no threshold-like response; (II) an abrupt decrease in breeding success by 90%, and (III) an abrupt halving of adult survival. Second, we analysed field observations from 3 independent marine case studies (abalone, starfish, penguins) for evidence of abrupt non-linear responses of predators to changes in abundance of principal prey. Third, we compared the model output with empirical results and tested (using both a statistical method and by fitting multispecies models) the 3 alternative response scenarios. With this approach, we found evidence for nonlinear changes in population parameters (such as survival rate) of predators as prey numbers declined below critical thresholds. As an example of the potential for this approach to inform management, we found that abundances of a range of marine predators become more variable as prey numbers decline, which may be a useful indicator that a system is approaching a tipping point.

Great Barrier Reef recovery through multiple interventions

“…; Plaganyi et al. ; Supporting Information) and applying only stochastic environmental forcing, CoTS outbreaks occurred every 15–20 years (Fig. d), which is also the time between the start of major outbreaks recorded on the GBR since the 1960s (Pratchett et al.…”

“…; Plaganyi et al. ). The mathematical specification of the model and associated parameter values are in Supporting Information.…”

“…; Plaganyi et al. ). Further comparisons with data from the LTMP guided selection of 2 baseline sets of reef connectivity parameters broadly representative of recent conditions (Supporting Information).…”

“…Previous fitting to the LTMP data constrained CoTS mortality and the predation rates of juvenile and adult CoTS on corals only to within specified ranges (Plaganyi et al. ). In these cases, parameters were varied randomly within that range throughout CoCoNet model runs (Supporting Information).…”

Time-dependent saddle–node bifurcation: Breaking time and the point of no return in a non-autonomous model of critical transitions

“…Recently, there has been an intense interest in using a dynamical systems approach to the characterization of a class of phenomenon known as "critical transitions", or "tipping points" [1], in clinical medicine [2,3,4], ecology [5,6], environmental and climate science [7,8], and sociology [9]. In all these problems, complex systems experience a qualitatively large and abrupt change very rapidly.…”