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Published on: January 19, 2018
Extinction rates of established spatial populations
Baruch Meerson1, Pavel V Sasorov
1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel.
Summary
Intrinsic noise drives isolated population extinction. We model this using Markov processes and WKB approximation, identifying extinction paths and times, especially predicting optimal refuge size for strong Allee effects.
Area of Science:
- Population dynamics
- Stochastic processes
- Theoretical ecology
Background:
- Intrinsic noise can lead to population extinction.
- The Allee effect describes reduced per capita growth at low population densities.
- Modeling population dynamics requires understanding birth, death, and migration processes.
Purpose of the Study:
- To model and analyze the extinction of isolated populations driven by intrinsic noise.
- To investigate extinction dynamics with and without the Allee effect.
- To determine the most probable extinction paths and mean extinction times.
Main Methods:
- Markov process modeling of population dynamics on discrete lattice sites.
- Wentzel-Kramers-Brillouin (WKB) approximation to the master equation for large populations.
- Analysis of Hamilton's equations to determine extinction paths and times.
Main Results:
- Classified extinction regimes with and without the Allee effect for various refuge types.
- Derived Hamilton's equations encoding most probable extinction paths and mean extinction times.
- For strong Allee effects, predicted an optimal refuge size maximizing extinction time.
Conclusions:
- Intrinsic noise significantly impacts population extinction, particularly with Allee effects.
- The WKB approximation provides a powerful tool for analyzing stochastic population dynamics.
- Understanding refuge dynamics is crucial for predicting and potentially mitigating population extinction.
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