When very slow is too fast -- collapse of a predator-prey system

Abstract

Critical transitions or regime shifts are sudden and unexpected changes in the state of an ecosystem, that are usually associated with dangerous levels of environmental change. However, recent studies show that critical transitions can also be triggered by dangerous rates of environmental change. In contrast to classical regime shifts, such rate-induced critical transitions do not involve any obvious loss of stability, or a bifurcation, and thus cannot be explained by the linear stability analysis. In this work, we demonstrate that the well-known Rosenzweig-MacArthur predator-prey model can undergo a rate-induced critical transition in response to a continuous decline in the habitat quality, resulting in a collapse of the predator and prey populations. Rather surprisingly, the collapse occurs even if the environmental change is slower than the slowest process in the model. To explain this counterintuitive phenomenon, we combine methods from geometric singular perturbation theory with the concept of a moving equilibrium, and study critical rates of environmental change with dependence on the initial state and the system parameters. Moreover, for a fixed rate of environmental change, we determine the set of initial states that undergo a rate-induced population collapse. Our results suggest that ecosystems may be more sensitive to how fast environmental conditions change than previously assumed. In particular, unexpected critical transitions with dramatic ecological consequences can be triggered by environmental changes that (i) do not exceed any dangerous levels, and (ii) are slower than the natural timescales of the ecosystem. This poses an interesting research question whether regime shifts observed in the natural world are predominantly rate-induced or bifurcation-induced.

References in corpus (2)

• Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system
• Adapting to a Changing Environment: Non-obvious Thresholds in Multi-Scale Systems

Cited by in corpus (14)

• Phase tipping: How cyclic ecosystems respond to contemporary climate
• Mitigating long transient time in deterministic systems by resetting
• Rate-induced tipping and saddle-node bifurcation for a class of quadratic differential equations with nonautonomous asymptotic dynamics
• Rate-Induced Tipping to Metastable Zombie Fires
• Stochastic Resonance in Climate Reddening Increases the Risk of Cyclic Ecosystem Extinction via Phase-tipping
• Most probable transition paths in piecewise-smooth stochastic differential equations
• Non-commutative phase-space Lotka-Volterra dynamics: the quantum analogue
• Recurrent chaotic clustering and slow chaos in adaptive networks
• Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics
• Multimodal distribution of transient time of predator extinction in a three-species food chain
• Dynamical Stability Indicator based on Autoregressive Moving-Average Models: Critical Transitions and the Atlantic Meridional Overturning Circulation
• Quantum prey-predator dynamics: a gaussian ensemble analysis
• Rate-induced biosphere collapse in the Daisyworld model
• Metamorphoses of the flow past an obstacle of a resonantly-driven bistable polariton fluid