A stochastic metapopulation model accounting for habitat dynamics

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Metapopulation models are crucial for understanding species persistence.
• Existing models often simplify habitat dynamics and carrying capacity.
• Stochasticity plays a significant role in population fluctuations.

Purpose of the Study:

• To develop a novel stochastic metapopulation model incorporating habitat dynamics and varying carrying capacity.
• To analyze the convergence of this model to a deterministic counterpart.
• To establish approximations for the quasi-stationary distribution.

Main Methods:

• Utilizing Kurtz and Barbour's results for deterministic and diffusion approximations.
• Applying these approximations to a stochastic SIS logistic metapopulation model.
• Comparing the novel model with the standard stochastic SIS logistic model.

Main Results:

• The scaled metapopulation model converges to a previously studied deterministic model.
• A bivariate normal approximation for the quasi-stationary distribution was established.
• Habitat dynamics significantly impact metapopulation modeling outcomes.

Conclusions:

• The developed model provides an effective framework for metapopulation modeling in dynamic landscapes.
• Incorporating habitat variability enhances ecological realism.
• The findings offer insights into population persistence under environmental change.