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Spread and persistence for integro-difference equations with shifting habitat and strong Allee effect
1Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA. bing.li@louisville.edu.
Journal of Mathematical Biology
|March 1, 2024
Summary
Species persistence in shifting habitats depends on the speed of habitat change relative to the species' spreading speed. A critical patch size is also necessary for survival in finite habitats.
Area of Science:
- Mathematical Biology
- Ecological Dynamics
- Population Modeling
Background:
- Investigates species spatial dynamics in environments with strong Allee effects.
- Considers the challenges posed by shifting habitats for species survival.
Purpose of the Study:
- To analyze species persistence in a shifting semi-infinite habitat connected to a good habitat.
- To determine the conditions for species persistence in a finite shifting habitat patch.
Main Methods:
- Utilizes an integro-difference equation model.
- Employs mathematical analysis to establish spreading speeds and traveling waves.
- Conducts numerical simulations to validate theoretical findings.
Main Results:
- Species persistence is achieved when habitat shift speed is less than the asymptotic spreading speed in a semi-infinite good habitat.
- Species non-persistence occurs if the habitat shift speed exceeds the spreading speed.
- A critical patch size is identified for persistence in finite shifting habitats, dependent on shift speed.
Conclusions:
- Habitat shift speed and spreading speed are critical factors for species persistence.
- The size of hospitable habitat patches plays a crucial role in species survival.
- Theoretical and numerical results highlight the complex interplay between habitat dynamics and species persistence.
Keywords:
Allee effectCritical patch sizeIntegro-difference equationShifting habitatSpreading speedTraveling waveMore Related Videos
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