Advertisement

Stock Dynamics in Stage Structured Multi-agent Fisheries

  • En-Guo Gu
  • Fabio LamantiaEmail author
Chapter

Abstract

The sustainable use of public renewable resources is a crucial issue for the long run survival of mankind.With a rapidly increasing population and a quick economy development, overexploitation of worldwide renewable resources seriously affects their ability to renew themselves and therefore their sustainable use (Food and Agriculture Organization, 2004; Garcia & Grainger, 2005). To complicate the problem further, the modelling of commercial exploitation of renewable resources represents an extremely challenging task, as it always involves nonlinear interaction among many different components (biological, economic, social) as well as uncertainty. In particular the issue of fishery management with chaotic and catastrophic dynamics has been thoroughly discussed in Rosser (2002a). Many researchers have investigated the dynamic of an exploited biomass regarded as a single species (Bischi & Lamantia, 2007; Bischi, Kopel, & Szidarovszky, 2005; Clark, 1990; Fan & Wang, 1998; Gu, 2007). Recently also the evolution of an exploited stage-structured single species has been addressed (see Jing and Ke (2004); Song and Chen (2002); Gao, Chen, and Sun (2005)). This analysis is of particular significance especially for those many species whose individuals have different economic value at different ages. For example, little eels are often called “soft gold,” for their high economic value, so many agents are interested in harvesting only little eels. But the case is exactly the opposite for those species whose immature individuals have negligible conomic value, so that exploiters want to harvest only the mature population and let the immature population grows, so that it can acquire a greater value. Often also public regulators try to direct the harvesting activity toward a target stage, for instance by limiting the use of trawl with too small meshes in order to protect the infant population

Keywords

Bifurcation Diagram Chaotic Attractor Positive Equilibrium Positive Steady State Infant Population 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The authors acknowledge helpful comments of an anonymous referee. The usual disclaimer applies. This Work is Supported by National Natural Science Foundation of China (10871209). The first author is grateful for the support from the key NSF of SCUFN (YZZ06027).

References

  1. Bischi, G. I. & Lamantia, F. (2007) Harvesting dynamics in protected and unprotected areas. Journal of Economic Behavior and Organization,62, 348–370.CrossRefGoogle Scholar
  2. Bischi, G. I., Lamantia, F., & Sbragia, L. (2004) Competition and cooperation in natural resources exploitation: An evolutionary game approach. In C. Carraro & V. Fragnelli (Eds.), Game practice and the environment (pp. 187–211). Edward Elgar Publishing, Cheltenham.Google Scholar
  3. Bischi, G. I., Kopel, M., & Szidarovszky, F. (2005) Expectation-stock dynamics in multi-agent fisheries. Annals of Operations Research,137, 299–329.CrossRefGoogle Scholar
  4. Clark, C. W. (1990) Mathematical bioeconomics: the optimal management of renewable resource. New York, USA: Wiley.Google Scholar
  5. Fan, M. & Wang, K. (1998) Optimal harvesting policy for single population with periodic coefficients. Mathematical Biosciences,l52, 165–177.Google Scholar
  6. Food and Agriculture Organization, The state of world fisheries and aquaculture. Sofia: FAO.Google Scholar
  7. Garcia, S. & Grainger, J. R. (2005) Gloom and doom? The future of marine capture fisheries. Philosophical Transactions of the Royal Society B,360, 21–24.CrossRefGoogle Scholar
  8. Gao, S. & Chen, L. (2005) Dynamic complexities in a single-species discrete population model with stage structure and birth pulses. Chaos, Solitons & Fractals,22, 519–527.CrossRefGoogle Scholar
  9. Gao, S., Chen, L., & Sun, L. (2005) Optimal pulse fishing policy in stage-structured models with birth pulses. Chaos, Solitons & Fractals,25, 1209–1219.CrossRefGoogle Scholar
  10. Gu, E.G. (2007) Global analysis of an ecological populational model with an external interference. Chaos, Solitons & Fractals,32, 224–233.CrossRefGoogle Scholar
  11. Jing, W. and Ke, W., The optimal harvesting problems of a stage-structured population. Applied Mathematics and Computation,148, 235–247.Google Scholar
  12. Hanneson, R. (1995) Sequential fishing: cooperative and non cooperative equilibria. Natural Resource Modeling,9, 51–59.Google Scholar
  13. Mckelvey, R. (1997) Game theoretic insight into the international management of fisheries. Natural Resource Modeling,10, 129–171.Google Scholar
  14. Mesterton-Gibbons, M. (1993) Game-theoretic resource modelling. Natural Resource Modeling,7, 93–147.Google Scholar
  15. Mira, C., Gardini, L., Barugola A., & Cathala, J.C. (1996) Chaotic dynamics in two-dimensional noninvertible maps. Singapore: World ScientificGoogle Scholar
  16. Onozaki, T., Sieg G., & Yokoo, M. (2000) Complex dynamics in a cobweb model with adaptive production adjustment, Journal of Economic Behavior & Organization,41, 101–115.CrossRefGoogle Scholar
  17. Rosser, Jr. J. B. (2002a) Implications for fisheries policy of complex ecologic-economic dynamics. Nonlinear Dynamics, Psychology, and Life Sciences,6(2), 103–120.CrossRefGoogle Scholar
  18. Rosser, Jr. J.B., The development of complex oligopoly dynamics theory. In T. Puu & I. Sushko (Eds.), Oligopoly dynamics: models and tools (pp. 15–29). Berlin: Springer.Google Scholar
  19. Sethi, R. & Somanathan, E. (1996) The evolution of social norms in common property resource use. The American Economic Review,86, 766–788.Google Scholar
  20. Song, X. & Chen, L. (2002) Modelling and analysis of a single-species system with stage structure and harvesting, Mathematical and Computer Modelling,36, 67–82.CrossRefGoogle Scholar
  21. Szidarovszky, F. & Okuguchi, K. (1998) An oligopoly model of commercial fishing. Seoul Journal of Economics,11, 321–330.Google Scholar
  22. Szidarovszky, F. & Okuguchi, K. (2002) A dynamic model of international fishing. Seoul Journal of Economics,13, 4711–476.Google Scholar
  23. Tang, S. Y. & Chen, L. S. (2002) Density-dependent birth rate, birth pulses and their population dynamic consequences. Journal of Mathematical Biology,64, 169–184.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Business SciencesUniversity of CalabriaRendeItaly

Personalised recommendations