Critical patch size reduction by heterogeneous diffusion
M A F Dos Santos1, V Dornelas1,2, E H Colombo3,4
1Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900, Rio de Janeiro, RJ, Brazil.
Physical Review. E
|November 20, 2020
Summary
Heterogeneous diffusion in a habitat patch can reduce the minimum area needed for species survival. This finding holds true across various diffusion profiles, offering crucial insights for conservation biology and population dynamics.
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Population survival is influenced by spatial factors and landscape heterogeneity.
- Species survival depends on population growth exceeding losses from individuals leaving suitable habitats.
Purpose of the Study:
- To investigate the effect of space-dependent diffusion on the minimal patch size required for population survival.
- To compare survival dynamics under heterogeneous versus homogeneous diffusion coefficients.
Main Methods:
- Analytical investigation of single-species dynamics within a patch.
- Application of the Stratonovich framework for diffusion processes.
- Exploration of Itô and Hänggi-Klimontovich interpretations.
Main Results:
- Heterogeneous diffusion significantly reduces the minimal patch size for population survival compared to homogeneous diffusion with the same average diffusivity.
- This reduction effect is robust across different diffusion coefficient profiles.
- The Itô interpretation can lead to the opposite effect, while Hänggi-Klimontovich reinforces the reduction.
Conclusions:
- Space-dependent diffusion is a critical factor in determining population survival thresholds.
- Conservation strategies may benefit from considering landscape heterogeneity's impact on habitat patch size requirements.
- The mathematical framework used (Stratonovich vs. Itô) critically influences the interpretation of diffusion effects on population dynamics.
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