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Area of Science:

  • Earth System Science
  • Ecological Dynamics
  • Climate Modeling

Background:

  • Rate-induced tipping describes abrupt system shifts due to rapid forcing changes.
  • The Daisyworld model illustrates emergent temperature regulation by life.
  • Understanding tipping points is crucial for Earth system science.

Purpose of the Study:

  • To analyze rate-induced tipping in the classic Daisyworld model.
  • To investigate the impact of rapid insolation changes on Daisyworld's ecosystem.
  • To explore the conditions under which life in Daisyworld may go extinct.

Main Methods:

  • Mathematical analysis of the Daisyworld model under changing insolation.
  • Investigation of the system's dynamics relative to the stable manifold of a saddle point.
  • Simulation of transient forcing scenarios exceeding critical rates.

Main Results:

  • Demonstrated rate-induced tipping in the Daisyworld model.
  • Showed that rapid insolation increases can cause ecosystem collapse (extinction).
  • Confirmed that extinction can occur even if the final state is survivable.

Conclusions:

  • Rate-induced tipping is a potential mechanism for ecosystem collapse in simple models.
  • The findings suggest that rapid environmental change can be catastrophic.
  • This study provides evidence for the prevalence of rate-induced tipping in diverse systems.