Skip to main content
SpringerLink
Log in

Maximum sustainable yield and species extinction in a prey–predator system: some new results

  • Original Paper
  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

Though the maximum sustainable yield (MSY) approach has been legally adopted for the management of world fisheries, it does not provide any guarantee against from species extinction in multispecies communities. In the present article, we describe the appropriateness of the MSY policy in a Holling–Tanner prey–predator system with different types of functional responses. It is observed that for both type I and type II functional responses, harvesting of either prey or predator species at the MSY level is a sustainable fishing policy. In the case of combined harvesting, both the species coexist at the maximum sustainable total yield (MSTY) level if the biotic potential of the prey species is greater than a threshold value. Further, increase of the biotic potential beyond the threshold value affects the persistence of the system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Legovic, T., Klanjscek, J., Gecek, S.: Maximum sustainable yield and species extinction in ecosystems. Ecol. Model. 221, 1569–1574 (2010)

    Article  Google Scholar 

  2. Walters, C.J., Christensen, V., Martell, S.J., Kitchell, J.F.: Possible ecosystem impacts of applying MSY policies from single-species assessment. ICES J. Marine Sci. 62, 558–568 (2005)

    Article  Google Scholar 

  3. Botsford, L.W., Castilla, J.C., Peterson, C.H.: The management of fisheries and marine ecosystems. Science 277, 509–515 (1997)

    Article  Google Scholar 

  4. Schaefer, M.B.: Some aspects of the dynamics of populations important to the management of commercial marine fisheries. Bull. Inter-Am. Trop. Tuna Comm. 1, 25–56 (1954)

    Google Scholar 

  5. Kar, T.K., Matsuda, H.: Sustainable management of a fishery with a strong Allee effect. Trend. Appl. Sci. Res. 2(4), 271–283 (2007)

    Article  Google Scholar 

  6. Legovic, T., Gecek, S.: Impact of maximum sustainable yield on independent populations. Ecol. Model. 221, 2108–2111 (2010)

    Article  Google Scholar 

  7. Legovic, T., Gecek, S.: Impact of maximum sustainable yield on mutualistic communities. Ecol. Model. 230, 63–72 (2012)

    Article  Google Scholar 

  8. Matsuda, H., Katsukawa, T.: Fisheries management based on ecosystem dynamics and feedback control. Fish. Oceanogr. 11, 366–370 (2002)

    Article  Google Scholar 

  9. Matsuda, H., Abrams, P.A.: Maximal yields from multispecies fisheries systems: rules for systems with multiple trophic levels. Ecol. Appl. 16, 225–237 (2006)

    Article  Google Scholar 

  10. Katsukawa, T.: Numerical investigation of the optimal control rule for decision-making in fisheries management. Fish. Sci. 70, 123–131 (2004)

    Article  Google Scholar 

  11. Abrams, P.A., Roth, J.D.: The effects of enrichment of three-species food chains with nonlinear functional responses. Ecology 75(4), 1118–1130 (1994)

    Article  Google Scholar 

  12. Zhang, N., Chen, F., Su, Q., Wu, T.: Dynamic behaviors of a harvesting Leslie–Gower predator–prey model. Discret. Dyn. Nat. Soc. 2011, 1–14 (2011)

    MathSciNet  Google Scholar 

  13. Hsu, S.B., Huang, T.W.: Global stability for a class of predator–prey systems. SIAM J. Appl. Math. 55(3), 763–783 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ruan, S., Xiao, D.: Global analysis in a predator–prey system with nonmonotonic functional response. SIAM J. Appl. Math. 61(4), 1445–1472 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pireddu, M., Zanolin, F.: Chaotic dynamics in the Volterra predator–prey model via linked twist maps. Opusc. Math. 28(4), 567–592 (2008)

    MathSciNet  MATH  Google Scholar 

  16. Legovic, T.: Impact of demersal fishery and evidence of the Volterra principle to the extreme in the Adriatic Sea. Ecol. Model. 212, 68–73 (2008)

    Article  Google Scholar 

  17. Takashina, N., Mougi, A., Iwasa, Y.: Paradox of marine protected areas: suppression of fishing may cause species loss. Popul. Ecol. 54, 475–485 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

The research work of Bapan Ghosh is financed by the Council of Scientific and Industrial Research (CSIR), India (File No. 08/003(0077)/2011-EMR-I, dated 23rd March, 2011) and the research work of Dr. T.K. Kar is supported by the University Grants Commission (UGC), India (F. No. 40-239/2011(SR), dated 29th June, 2011). The authors are sincerely grateful to the anonymous referees for their valuable comments and suggestions for the improvement of the manuscript.

Author information

Authors and Affiliations

  1. Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, 711103, India

    Bapan Ghosh & T. K. Kar

Authors
  1. Bapan Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. K. Kar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bapan Ghosh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghosh, B., Kar, T.K. Maximum sustainable yield and species extinction in a prey–predator system: some new results. J Biol Phys 39, 453–467 (2013). https://doi.org/10.1007/s10867-013-9303-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-013-9303-2

Keywords

Search

Navigation