Enhancing Population Persistence by a Protection Zone in a Reaction-Diffusion Model with Strong Allee Effect

TL;DR

This paper models how establishing a protection zone can help endangered species persist in a habitat with a strong Allee effect, using reaction-diffusion equations and eigenvalue analysis.

Contribution

It introduces a reaction-diffusion model with a protection zone that combines Allee effect and logistic growth, providing a framework for optimal zone design.

Findings

Conditions for population persistence and extinction are derived.

The dependence of persistence on zone location and size is analyzed.

Guidelines for designing effective protection zones are proposed.

Abstract

Protecting endangered species has been an important issue in ecology. We derive a reaction-diffusion model for a population in a one-dimensional bounded habitat, where the population is subjected to a strong Allee effect in its natural domain but obeys a logistic growth in a protection zone. We establish the conditions for population persistence and extinction via the principal eigenvalue of an associated eigenvalue problem and investigate the dependence of this principal eigenvalue on the location (i.e., the starting point and the length) of the protection zone. The results are used to design the optimal protection zone under different boundary conditions, that is, to suggest the starting point and length of the protection zone with respect to different population growth rate in the protection zone, in order for the population to persist in a long term.