Modeling fish population movements: from an individual-based representation to an advection-diffusion equation

Area of Science:

• Ecology
• Mathematical Biology
• Computational Science

Background:

• Modeling fish population dynamics is crucial for fisheries management and ecological understanding.
• Previous models often used heuristic approaches for fish movement, lacking mechanistic underpinnings.

Purpose of the Study:

• To develop and validate a novel partial differential equation (PDE) model for fish population movements.
• To provide a mechanistic link between habitat suitability and fish movement patterns.

Main Methods:

• Formulated an individual-based model (IBM) as a biased random walk with deterministic and stochastic velocity components.
• Derived an advection-diffusion PDE as an approximation to the IBM.
• Simulated both models and compared their outputs using spatial statistics.

Main Results:

• The derived advection and diffusion coefficients showed antagonistic behaviors, reflecting directed vs. searching movements.
• The PDE model demonstrated a strong approximation of the individual-based model's behavior.
• Mechanistic advection and diffusion coefficients were obtained, improving upon heuristic methods.

Conclusions:

• The advection-diffusion PDE model provides a robust and mechanistic approach to modeling fish population movements.
• This PDE model serves as a valuable tool for understanding fish behavior in relation to habitat suitability.