Table of Contents Author Guidelines Submit a Manuscript
Journal of Marine Biology
Volume 2015, Article ID 580520, 8 pages
http://dx.doi.org/10.1155/2015/580520
Research Article

On the Interplay between Cannibalism and Harvest in Stage-Structured Population Models

Harstad University College, Havnegata 5, 9480 Harstad, Norway

Received 23 March 2015; Accepted 3 June 2015

Academic Editor: Garth L. Fletcher

Copyright © 2015 Arild Wikan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. FAO, The State of World Fisheries and Aquaculture, Food and Agriculture Organization, Rome, Italy, 1st edition, 2004.
  2. T. E. E. Oldfield, R. J. Smith, S. R. Harrop, and N. Leader-Williams, “A gap analysis of terrestrial protected areas in England and its implications for conservation policy,” Biological Conservation, vol. 120, no. 3, pp. 303–309, 2004. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Tang and L. Chen, “The effect of seasonal harvesting on stage-structured population models,” Journal of Mathematical Biology, vol. 48, no. 4, pp. 357–374, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. A. Myers, J. A. Hutchings, and N. J. Barrowman, “Why do fish stocks collapse? The example of cod in Atlantic Canada,” Ecological Applications, vol. 7, no. 1, pp. 91–106, 1997. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Wikan, “On reserves, stability and the maximum sustainable yield problem,” Journal of Mathematics and Statistics, vol. 9, no. 4, pp. 325–333, 2013. View at Publisher · View at Google Scholar
  6. M. G. Neubert and M. Kot, “The subcritical collapse of predator populations in discrete-time predator-prey models,” Mathematical Biosciences, vol. 110, no. 1, pp. 45–66, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. B. Bogstad and S. Mehl, “Interactions between Atlantic Cod (Gadus morhua) and its prey species in the Barents Sea,” in Proceedings of the Forage Fishes in Marine Ecosystems (FME '97), Alaska Sea Grant College Program, 1997.
  8. A. Wikan, “From chaos to chaos. An analysis of a discrete age-structured prey-predator model,” Journal of Mathematical Biology, vol. 43, no. 6, pp. 471–500, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. O. Flaaten and E. Mjølhus, “Using reserves to protect fish and wildlife—simplified modeling approaches,” Natural Resource Modeling, vol. 18, no. 2, pp. 157–182, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. M. Cushing, “A simple model of cannibalism,” Mathematical Biosciences, vol. 107, no. 1, pp. 47–71, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. F. Van den Bosch and W. Gabriel, “Cannibalism in an age-structured predator-prey system,” Bulletin of Mathematical Biology, vol. 59, no. 3, pp. 551–567, 1997. View at Publisher · View at Google Scholar · View at Scopus
  12. K. G. Magnússon, “Destabilizing effect of cannibalism on a structured predator-prey system,” Mathematical Biosciences, vol. 155, no. 1, pp. 61–75, 1999. View at Publisher · View at Google Scholar · View at Scopus
  13. A. Wikan and A. Eide, “An analysis of a nonlinear stage-structured cannibalism model with application to the Northeast Arctic cod stock,” Bulletin of Mathematical Biology, vol. 66, no. 6, pp. 1685–1704, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. A. Eide and A. Wikan, “Optimal selection and effort in a fishery on a stock with cannibalistic behaviour the case of the northeast arctic cod fisheries,” Journal of Fisheries and Aquatic Science, vol. 5, no. 6, pp. 454–468, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. A. Hastings and L. W. Botsford, “Equivalence in yield from marine reserves and traditional fisheries management,” Science, vol. 284, no. 5419, pp. 1537–1538, 1999. View at Publisher · View at Google Scholar · View at Scopus
  16. C. W. Armstrong and U. R. Sumaila, “Cannibalism and the optimal sharing of the North-East Atlantic cod stock: a bioeconomic model,” Journal of Bioeconomics, vol. 2, no. 2, pp. 99–115, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. R. Kon, Y. Saito, and Y. Takeuchi, “Permanence of single-species stage-structured models,” Journal of Mathematical Biology, vol. 48, no. 5, pp. 515–528, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer, New York, NY, USA, 1990.
  19. W. Govaerts and R. K. Ghaziani, “Numerical bifurcation analysis of a nonlinear stage structured cannibalism population model,” Journal of Difference Equations and Applications, vol. 12, no. 10, pp. 1069–1085, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. A. Wikan and E. Mjølhus, “Overcompensatory recruitment and generation delay in discrete age-structured population models,” Journal of Mathematical Biology, vol. 35, no. 2, pp. 195–239, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. P. Cull and A. Vogt, “Mathematical analysis of the asymptotic behavior of the Leslie population matrix model,” Bulletin of Mathematical Biology, vol. 35, pp. 645–661, 1973. View at Google Scholar · View at MathSciNet
  22. H. Caswell, Matrix Population Models, Sinauer Associates, Sunderland, Mass, USA, 2nd edition, 2001.
  23. A. Wikan, “Dynamical consequences of harvest in discrete age-structured population models,” Journal of Mathematical Biology, vol. 49, no. 1, pp. 35–55, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet