Phase tipping: how cyclic ecosystems respond to contemporary climate

Area of Science:

• Ecology and Mathematical Biology
• Dynamical Systems Theory
• Climate Science

Background:

• Cyclic systems often exhibit tipping points, or critical transitions, under external forcing.
• Predator-prey models with Allee effects are susceptible to extinction, especially under climate variability.
• The influence of the cycle's phase on these transitions has not been previously recognized as a critical factor.

Purpose of the Study:

• To introduce the 'phase of a cycle' as a novel critical factor for tipping points in externally forced cyclic systems.
• To investigate how climate variability can induce phase-dependent tipping to extinction in predator-prey models.
• To develop a general framework for analyzing and predicting phase tipping (P-tipping).

Main Methods:

• Analysis of two paradigmatic predator-prey models incorporating an Allee effect and subjected to time-varying external conditions (climate variability).
• Combination of global dynamics and set theory to explain the observed tipping phenomena.
• Introduction and application of the concept of 'partial basin instability' for attracting limit cycles.

Main Results:

• Identification of a counterintuitive phenomenon termed 'phase tipping' (P-tipping), where extinction occurs only from specific phases of the cycle.
• Demonstration that contemporary climate variability can trigger P-tipping in predator-prey systems.
• Development of partial basin instability as a tool to analyze and identify criteria for P-tipping.

Conclusions:

• The phase of a cycle is a crucial, previously overlooked factor determining tipping points in externally forced cyclic systems.
• Partial basin instability offers a generalizable framework for understanding and predicting phase tipping in various dynamical systems.
• The findings have implications for managing ecosystems and predicting extinctions under fluctuating environmental conditions.