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Harvesting and Dynamics in Some One-Dimensional Population Models

  • Eduardo LizEmail author
  • Frank M. Hilker
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 102)

Abstract

We review some dynamical effects induced by constant effort harvesting in single-species discrete-time population models. We choose three different forms for the density-dependent recruitment function, which include the overcompensatory Ricker map for semelparous species; a modified Ricker model allowing for adult survivorship; and a model with both strong Allee effect and overcompensation which results from incorporating mate limitation in the Ricker model. We show that these simple models exhibit some interesting (and sometimes unexpected) phenomena such as the hydra effect; bubbling; sudden collapses; and essential extinction. We underline the importance of two often underestimated issues that turn out to be crucial for management: census timing and intervention time.

Keywords

Constant Effort Harvesting Strong Allee Effect Ricker Model Hydra Effect Census Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

E. Liz was partially supported by the Spanish Government and FEDER, grant MTM2010–14837. He acknowledges the support and nice hospitality received from the Organizing Committee of the 19th International Conference on Difference Equations & Applications, particularly to Dr. Ziyad AlSharawi. F. M. Hilker acknowledges a Santander research travel grant that facilitated his visit to Universidad de Vigo to collaborate with the first author.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada IIUniversidad de VigoVigoSpain
  2. 2.Centre for Mathematical Biology, Department of Mathematical SciencesUniversity of BathBathUK
  3. 3.Institute of Environmental Systems Research, School of Mathematics/Computer ScienceOsnabrück UniversityOsnabrückGermany

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