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Reaction-Diffusion for Fish Populations with Realistic Mobility

journal contribution
posted on 2025-04-01, 00:32 authored by Philip BroadbridgePhilip Broadbridge
Nonlinear reaction-diffusion equations, with Fisher logistic growth and constant diffusion coefficient, have been used in fisheries research to estimate sustainable harvesting rates and critical domain sizes of no-take areas. However, constant diffusivity in a population density corresponds to standard Brownian motion of individuals, with a normal distribution for displacement over a fixed time interval. For available good data sets on mobile fish populations, the distribution is certainly not normal. The data can be fitted with a long-tailed stable Lévy distribution that results from diffusion by fractional Laplacian. Exact multidimensional solutions are developed here for realistic Fisher-Kolmogorov-Petrovski-Piscounov models with diffusion by fractional Laplacian. These can also account for a delay in the reaction term. It is then shown how to modify critical domain sizes of protected areas with Dirichlet and Robin boundary conditions for populations.

Funding

The author gratefully acknowledges support from the Australian Research Council for the project DP220101680.

History

Publication Date

2024-12-01

Journal

International Journal of Mathematics for Industry

Volume

16

Issue

1

Article Number

2450025

Pagination

11p.

Publisher

World Scientific

ISSN

2661-3352

Rights Statement

© The Author(s) 2024 This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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