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A Gender-Selective Harvesting Strategy: Weak Allee Effects and a Non-hyperbolic Extinction Boundary

A Gender-Selective Harvesting Strategy: Weak Allee Effects and a Non-hyperbolic Extinction Boundary Recently a gender-selective harvesting strategy has been proposed for possible control of aquatic invasive species, wherein females of the invasive species are harvested, whilst stocking the males (abbreviated as FHMS strategy) (Lyu et al. in Nat Resour Model 33(2):e12252, 2020). We consider the FHMS strategy with a weak Allee effect, and show that its extinction boundary need not be hyperbolic. To the best of our knowledge, this is the first example of a non-hyperbolic extinction boundary in two-compartment mating models structured by sex. The model possesses a rich dynamical structure, with several local co-dimension one bifurcations occurring. We also show the occurrence of a global homoclinic bifurcation, which has applicability for large scale strategic bio-control. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

A Gender-Selective Harvesting Strategy: Weak Allee Effects and a Non-hyperbolic Extinction Boundary

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Publisher
Springer Journals
Copyright
Copyright © Prof. Dr. Jan van der Hoeven stichting voor theoretische biologie 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/s10441-023-09462-w
Publisher site
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Abstract

Recently a gender-selective harvesting strategy has been proposed for possible control of aquatic invasive species, wherein females of the invasive species are harvested, whilst stocking the males (abbreviated as FHMS strategy) (Lyu et al. in Nat Resour Model 33(2):e12252, 2020). We consider the FHMS strategy with a weak Allee effect, and show that its extinction boundary need not be hyperbolic. To the best of our knowledge, this is the first example of a non-hyperbolic extinction boundary in two-compartment mating models structured by sex. The model possesses a rich dynamical structure, with several local co-dimension one bifurcations occurring. We also show the occurrence of a global homoclinic bifurcation, which has applicability for large scale strategic bio-control.

Journal

Acta Biotheoretica – Springer Journals

Published: Jun 1, 2023

Keywords: Invasive species; Weak Allee effect; Extinction boundary; Harvesting; Turing instability; 92B05; 92D25; 92D40

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