Crises, noise, and tipping in the Hassell population model

Area of Science:

• Ecology
• Mathematical Biology
• Nonlinear Dynamics

Background:

• Population dynamics are susceptible to noise, potentially leading to abrupt shifts or 'tipping' events.
• The Allee effect, where population growth rate decreases at low densities, can exacerbate tipping phenomena.
• Understanding these transitions is crucial for conservation and ecosystem management.

Purpose of the Study:

• To investigate noise-induced tipping in population systems using a conceptual model.
• To analyze the role of crisis bifurcations in abrupt dynamic changes.
• To identify early warning signals for critical stochastic transitions.

Main Methods:

• Utilized a Hassell-type population model incorporating the Allee effect.
• Employed mathematical analysis of boundary and interior crisis bifurcations.
• Applied stochastic sensitivity function and confidence domains for parametric analysis.
• Investigated noise-induced extinction and transitions from order to chaos.

Main Results:

• Demonstrated the connection between crisis bifurcations and noise-induced tipping.
• Identified specific dynamic changes, including noise-induced extinction and chaos.
• Successfully applied stochastic sensitivity function to detect early warning signals.
• Validated the effectiveness of the proposed approach for critical transition detection.

Conclusions:

• The study provides a robust framework for analyzing noise-induced tipping in ecological models.
• The identified early warning signals can aid in predicting population collapses.
• The methodology offers insights into the complex interplay of noise, Allee effect, and system dynamics.