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Extinction in the Lotka-Volterra model
1School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Summary
Oscillating populations, like predator-prey models, face extinction due to random fluctuations. Extinction time follows a power-law, unlike stable models where it
Area of Science:
- Population dynamics
- Theoretical ecology
- Stochastic processes
Background:
- Birth-death processes frequently display oscillatory behavior.
- Marginal stability on the mean-field level is investigated.
- The Lotka-Volterra model serves as a key example.
Purpose of the Study:
- To analyze extinction dynamics in marginally stable oscillating systems.
- To contrast extinction scaling laws between marginally stable and stable models.
Main Methods:
- Investigating mean-field stability of birth-death processes.
- Analyzing fluctuation effects from population discreteness.
- Deriving extinction time scaling laws.
Main Results:
- Fluctuations destabilize marginally stable systems, leading to extinction.
- Extinction time scales as a power-law of population sizes in these systems.
- This contrasts with exponential scaling in mean-field stable models.
Conclusions:
- Population discreteness is crucial for understanding extinction in oscillating systems.
- The power-law extinction scaling provides a new perspective on ecological collapse.
- Distinguishing extinction mechanisms is vital for accurate ecological modeling.
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