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Integrable nonlinear reaction-diffusion population models for fisheries

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posted on 2025-03-16, 22:42 authored by Philip BroadbridgePhilip Broadbridge, AJ Hutchinson
Sustainable natural resource management strategies are required to maintain a fishery. One common device is to designate a No-Take Area (NTA) or a less restrictive Marine Protected Area (MPA) within a fishery. In this work, exact time-dependent solutions to 2-D nonlinear reaction-diffusion equations of Fisher type are constructed to model the fish population density of a single species within an NTA. The spillover rate from an NTA, important for harvesters, has previously been calculated without allowing for spatial variation within the NTA. Here, that spatial dependence is incorporated in the calculation. Spatially-dependent and density-dependent diffusivity and birth rates are considered for linear, rectangular and circular geometries, the latter being the most efficient with minimal critical domain area. The effect of the spatial dependence of diffusivity and birth rates, common in fish populations where reproduction and protection are favoured towards the centre, on the minimum size of an exclusion zone that ensures species survival, is studied. It is shown that when any one of these factors is taken into account, the size of the critical domain decreases by a small amount.

History

Publication Date

2022-02-01

Journal

Applied Mathematical Modelling

Volume

102

Pagination

20p. (p. 748-767)

Publisher

Elsevier Inc.

ISSN

0307-904X

Rights Statement

© 2021 The Authors. This manuscript version is made available under the CC-BY-NC-ND 4.0 license: https://creativecommons.org/licenses/by-nc-nd/4.0/

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