Bifurcation or state tipping: assessing transition type in a model trophic cascade

Area of Science:

• Ecology
• Mathematical Biology
• Complex Systems

Background:

• Ecosystems exhibit regime shifts, crossing tipping points through different mechanisms.
• State tipping (s-tipping) and bifurcation tipping (b-tipping) are two primary mechanisms.
• Bifurcation tipping generates critical slowing down (CSD), a potential early warning signal, unlike state tipping.

Purpose of the Study:

• To clarify the distinction between state tipping and bifurcation tipping in ecological models.
• To investigate the applicability of critical slowing down (CSD) as an early warning signal for regime shifts.
• To analyze dimension reduction in high-dimensional ecological models for tipping point analysis.

Main Methods:

• Analysis of a prominent trophic cascade model.
• In silico simulations to test critical slowing down (CSD) predictions.
• Application of tipping point analysis to a natural lake ecosystem.

Main Results:

• Demonstrated that distinguishing between s-tipping and b-tipping depends on ecological model formulation.
• Illustrated the process of dimension reduction for complex trophic webs.
• Resolved ambiguity regarding the nature of tipping points in a key ecological model.

Conclusions:

• The distinction between state and parameter-driven tipping points is ecologically dependent, not purely mathematical.
• Accurate identification of tipping point mechanisms is vital for reliable early warning signals.
• This research provides a framework for analyzing tipping points in complex ecological systems.