Phase tipping: How cyclic ecosystems respond to contemporary climate

TL;DR

This paper introduces the concept of phase tipping in cyclic ecosystems, showing that climate-induced tipping points depend on the cycle phase, with implications for predicting ecosystem responses to environmental changes.

Contribution

It presents the novel concept of phase tipping (P-tipping) and develops a theoretical framework using set theory and basin instability to analyze phase-dependent tipping points.

Findings

Tipping to extinction occurs only from specific cycle phases.

The framework of partial basin instability helps identify phase tipping conditions.

Application to predator-prey models demonstrates climate variability can induce phase-dependent tipping.

Abstract

We identify the phase of a cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how contemporary climate variability induces tipping from a predator-prey cycle to extinction in two paradigmatic predator-prey models with an Allee effect. Our analysis of these examples uncovers a counter-intuitive behaviour, which we call phase tipping or P-tipping, where tipping to extinction occurs only from certain phases of the cycle. To explain this behaviour, we combine global dynamics with set theory and introduce the concept of partial basin instability for attracting limit cycles. This concept provides a general framework to analyse and identify easily testable criteria for the occurrence of phase tipping in externally forced systems, and can be extended to more complicated attractors.