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Rate-induced tipping in a lake eutrophication model coupled with human activities.
Anji Yang1, Hao Wang2, Sanling Yuan3
1College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China.
Journal of Mathematical Biology
|March 17, 2026
Summary
Human activities impact ecosystems, creating feedback loops. Rapidly increasing conservation costs can unexpectedly worsen lake water quality, highlighting the need to manage cost-increase rates, not just amounts.
Area of Science:
- Environmental Science
- Ecology
- Mathematical Modeling
Background:
- Human activities significantly alter ecosystem states and services, creating complex feedback loops with human behavior.
- Lake eutrophication is a critical environmental issue influenced by human actions and ecological dynamics.
- Understanding these coupled human-environment interactions is vital for effective ecosystem management.
Purpose of the Study:
- To propose and analyze a novel coupled human-environment model integrating human decision-making with lake eutrophication dynamics.
- To investigate the complex dynamical behaviors of the human-environment system, including multistability and oscillations.
- To examine the impact of conservation cost dynamics on ecosystem tipping points.
Main Methods:
- Development of a coupled model using replicator dynamics for human behavior and an ecological subsystem for lake eutrophication.
- Mathematical analysis of the model to identify different dynamical behaviors and steady states.
- Simulation and analysis of rate-induced tipping phenomena under varying conservation cost increase rates.
Main Results:
- The coupled model exhibits rich dynamics, including multistability and sustained periodic oscillations.
- Tristability scenarios reveal that rapid increases in conservation costs can induce rate-induced tipping between ecosystem states.
- A critical threshold exists for the rate of conservation cost increase, influencing the probability of tipping between oligotrophic, intermediate, and eutrophic states.
Conclusions:
- Effective lake deterioration control requires considering the rate of increase in conservation costs, not solely the magnitude.
- Management strategies should account for the dynamic feedback between human behavior and ecosystem response.
- The study provides insights into preventing unintended ecosystem state shifts driven by policy implementation rates.
Keywords:
Coupled human-environment modelCritical transitionEutrophication of lakesRate-induced tippingTipping probabilityMore Related Videos
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