Delayed population models with Allee effects and exploitation
Allee effects make populations more vulnerable to extinction, especially under severe harvesting or predation. Using a delay-differential equation modeling the evolution of a single-species population subject to constant effort harvesting, we show that the interplay between harvest strength and Al...
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.83 |
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| author | Eduardo Liz Alfonso Ruiz-Herrera |
| author_facet | Eduardo Liz Alfonso Ruiz-Herrera |
| author_sort | Eduardo Liz |
| collection | DOAJ |
| description | Allee effects make populations more vulnerable to extinction, especially under severe harvesting or predation. Using a delay-differential equation modeling the evolution of a single-species population subject to constant effort harvesting, we show that the interplay between harvest strength and Allee effects leads not only to collapses due to overexploitation; large delays can interact with Allee effects to produce extinction at population densities that would survive for smaller time delays.In case of bistability, our estimations on the basins of attraction of the two coexisting attractors improve some recent results in this direction. Moreover, we show that the persistent attractor can exhibit bubbling: a stable equilibrium loses its stability as harvesting effort increases, giving rise to sustained oscillations, but higher mortality rates stabilize the equilibrium again. |
| format | Article |
| id | doaj-art-10188eb5f4374490a8a95c5d929db2b4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-10188eb5f4374490a8a95c5d929db2b42025-01-24T02:31:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-01121839710.3934/mbe.2015.12.83Delayed population models with Allee effects and exploitationEduardo Liz0Alfonso Ruiz-Herrera1Departamento de Matemática Aplicada II, E.T.S.E. Telecomunicación, Universidade de Vigo, Campus Marcosende, 36310 VigoBolyai Institute, University of Szeged, Aradi vértanúk tere 1., H-6720 SzegedAllee effects make populations more vulnerable to extinction, especially under severe harvesting or predation. Using a delay-differential equation modeling the evolution of a single-species population subject to constant effort harvesting, we show that the interplay between harvest strength and Allee effects leads not only to collapses due to overexploitation; large delays can interact with Allee effects to produce extinction at population densities that would survive for smaller time delays.In case of bistability, our estimations on the basins of attraction of the two coexisting attractors improve some recent results in this direction. Moreover, we show that the persistent attractor can exhibit bubbling: a stable equilibrium loses its stability as harvesting effort increases, giving rise to sustained oscillations, but higher mortality rates stabilize the equilibrium again.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.83bifurcation.bistabilitydifference equationglobal stabilitydelay differential equationallee effectpopulation model |
| spellingShingle | Eduardo Liz Alfonso Ruiz-Herrera Delayed population models with Allee effects and exploitation Mathematical Biosciences and Engineering bifurcation. bistability difference equation global stability delay differential equation allee effect population model |
| title | Delayed population models with Allee effects and exploitation |
| title_full | Delayed population models with Allee effects and exploitation |
| title_fullStr | Delayed population models with Allee effects and exploitation |
| title_full_unstemmed | Delayed population models with Allee effects and exploitation |
| title_short | Delayed population models with Allee effects and exploitation |
| title_sort | delayed population models with allee effects and exploitation |
| topic | bifurcation. bistability difference equation global stability delay differential equation allee effect population model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.83 |
| work_keys_str_mv | AT eduardoliz delayedpopulationmodelswithalleeeffectsandexploitation AT alfonsoruizherrera delayedpopulationmodelswithalleeeffectsandexploitation |