Delayed population models with Allee effects and exploitation

Mathematical Biosciences and Engineering : MBE
Eduardo Liz, Alfonso Ruiz-Herrera

Abstract

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.

References

Apr 24, 2001·Journal of Mathematical Biology·S J Schreiber
Sep 19, 2002·Proceedings of the National Academy of Sciences of the United States of America·André M De Roos, Lennart Persson
Oct 17, 2002·Journal of Theoretical Biology·David S Boukal, Ludek Berec
Sep 2, 2003·Theoretical Population Biology·Sebastian J Schreiber
May 10, 2011·Mathematical Biosciences·Abdul-Aziz YakubuMary-Lou Zeeman
Dec 14, 2011·Journal of Mathematical Biology·Stefan A H Geritz, Eva Kisdi
Jul 1, 2010·Journal of Biological Dynamics·Saber N Elaydi, Robert J Sacker
Dec 24, 2013·Mathematical Biosciences·Begoña CidEduardo Liz

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Citations

Dec 3, 2017·Chaos·Gábor Kiss, Gergely Röst
Apr 24, 2017·Journal of Mathematical Biology·Pablo G BarrientosAlfonso Ruiz-Herrera
Apr 4, 2018·Bulletin of Mathematical Biology·Irina Bashkirtseva, Lev Ryashko

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