Journal of Biological Physics

, Volume 39, Issue 3, pp 453–467 | Cite as

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

  • Bapan Ghosh
  • T. K. Kar
Original Paper


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.


Harvesting Combined fishing effort Maximum sustainable total yield (MSTY) Holling-type response function Volterra’s first principle 



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.


  1. 1.
    Legovic, T., Klanjscek, J., Gecek, S.: Maximum sustainable yield and species extinction in ecosystems. Ecol. Model. 221, 1569–1574 (2010)CrossRefGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 3.
    Botsford, L.W., Castilla, J.C., Peterson, C.H.: The management of fisheries and marine ecosystems. Science 277, 509–515 (1997)CrossRefGoogle Scholar
  4. 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. 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)CrossRefGoogle Scholar
  6. 6.
    Legovic, T., Gecek, S.: Impact of maximum sustainable yield on independent populations. Ecol. Model. 221, 2108–2111 (2010)CrossRefGoogle Scholar
  7. 7.
    Legovic, T., Gecek, S.: Impact of maximum sustainable yield on mutualistic communities. Ecol. Model. 230, 63–72 (2012)CrossRefGoogle Scholar
  8. 8.
    Matsuda, H., Katsukawa, T.: Fisheries management based on ecosystem dynamics and feedback control. Fish. Oceanogr. 11, 366–370 (2002)CrossRefGoogle Scholar
  9. 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)CrossRefGoogle Scholar
  10. 10.
    Katsukawa, T.: Numerical investigation of the optimal control rule for decision-making in fisheries management. Fish. Sci. 70, 123–131 (2004)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 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)MathSciNetGoogle Scholar
  13. 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)MathSciNetMATHCrossRefGoogle Scholar
  14. 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)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Pireddu, M., Zanolin, F.: Chaotic dynamics in the Volterra predator–prey model via linked twist maps. Opusc. Math. 28(4), 567–592 (2008)MathSciNetMATHGoogle Scholar
  16. 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)CrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsBengal Engineering and Science UniversityHowrahIndia

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