Skip to main content
Log in

Additional Food Supplements as a Tool for Biological Conservation of Biosystems in the Presence of Inhibitory Effect of the Prey

  • Regular Article
  • Published:
Acta Biotheoretica Aims and scope Submit manuscript

Abstract

Provision of additional food supplements for the purpose of biological conservation has been widely researched both theoretically and experimentally. The study of these biosystems is usually done using predator–prey models. In this paper, we consider an additional food provided predator–prey system in the presence of the inhibitory effect of the prey. This model is analyzed in the control parameter space using the control parameters, quality and quantity of additional food. The findings suggest that with appropriate choice of additional food to predators, the biosystem can be controlled and steered to a desirable state. It is also possible to eliminate either of the interacting species. The vital role of the quality and quantity of the additional food in the system dynamics cautions the eco manager on the choice of the additional food for realizing the goal in the biological conservation programme.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Birkhoff G, Rota GC (1989) Ordinary differential equations. John Wiley & Sons, Hoboken

    Google Scholar 

  • Butler GJ et al (1986) Uniformly persistent systems. Proc Am Math Soc 96:425–429

    Article  Google Scholar 

  • Cesari L (1983) Optimization—theory and applications: problems with ordinary differential equations, applications of mathematics series, vol 17. Springer, New York

    Book  Google Scholar 

  • Collings JB (1997) The effects of the functional response on the bifurcation behavior of a mite predator prey interaction model. J Math Biol 36:149–168

    Article  Google Scholar 

  • David S (1995) Hik: does risk of predation influence population dynamics? Evidence from the cyclic decline of Snowshoe Hares. Wildl Res 22:115–129

    Article  Google Scholar 

  • Elkinton Joseph S et al (2004) Effects of alternative prey on predation by small mammals on gypsy moth pupae. Popul Ecol 46:171–178

    Article  Google Scholar 

  • Freedman HI, Wolkowicz GSK (1986) Predator–prey systems with group defence: the paradox of enrichment revisited. Bull Math Biol 48:493–508

    Article  Google Scholar 

  • Glaser O (1983) Wintergattermanagement: Fallstudien in obsersteirischen rotwildgattern. Diploma Thesis. Agricultural University of Vienna

  • Harmon JP (2003) Indirect interactions among a generalist predator and its multiple foods, Ph.D Thesis. University of Minnesota, St. Paul, MN

  • Holt RD (1984) Spatial heterogeneity, indirect interactions, and the coexistence of prey species. Am Nat 124:377–406

    Article  Google Scholar 

  • Huang JC, Xiao DM (2004) Analysis of bifurcations and stability in a predator–prey system with holling type-IV functional response. Acta Math Appl Sin Engl Ser 20:167–178

    Article  Google Scholar 

  • Huang J et al (2014) Bifurcations in a predator–prey system of Leslie type with generalized Holling type III functional response. J Differ Eq 257:1721–1752

    Article  Google Scholar 

  • Kar TK (2012) Bapan Ghosh: sustainability and optimal control of an exploited prey predator system through provision of alternative food to predator. BioSystems 109:220–232

    Article  Google Scholar 

  • Kot M (2001) Elements of mathematical ecology. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Kozak HM et al (1994) Supplemental winter feeding. Rangelands 16:153–156

    Google Scholar 

  • Kozak JM et al (1995) Winter feeding, lactation and calf growth in farmed wapiti. Rangelands 17:116–120

    Google Scholar 

  • Liberzon D (2012) Calculus of variations and optimal control theory: a concise introduction. Princeton University Press, Princeton

    Book  Google Scholar 

  • Putman RP, Staines BW (2004) Supplementary winter feeding of wild red deer Cervus elaphus in Europe and North America: justifications, feeding practice and effectiveness. Mamm Rev 34:285–306

    Article  Google Scholar 

  • Redpath SM et al (2001) Does supplementary feeding reduce predation of red grouse by hen harriers? J Appl Ecol 38:1157–1168

    Article  Google Scholar 

  • Sahoo B, Poria S (2014) Effects of supplying alternative food in a predator–prey model with harvesting. Appl Math Comput 234:150–166

    Google Scholar 

  • Sahoo B, Poria S (2015) Effects of additional food in a delayed predator–prey model. Math Biosci 261:62–73

    Article  Google Scholar 

  • Srinivasu PDN et al (2007) Biological control through provision of additional food to predators: a theoretical study. Theor Popul Biol 72:111–120

    Article  Google Scholar 

  • Srinivasu PDN, Vamsi DKK, Aditya I (2018) Biological conservation of living systems by providing additional food supplements in the presence of inhibitory effect: a theoretical study using predator–prey models. Differ Eq Dyn Syst 26:213–246

    Article  Google Scholar 

  • Zhu H et al (2002) Bifurcation analysis of a predator–prey system with nonmonotonic function response. SIAM J Appl Math 63:636–682

    Article  Google Scholar 

Download references

Acknowledgements

The authors dedicate this paper to the founder chancellor of Sri Sathya Sai Institute of Higher Learning, Bhagawan Sri Sathya Sai Baba. The corresponding author also dedicates this paper to his loving elder brother D. A. C. Prakash who still lives in his heart. The second author acknowledges the partial financial support from SAI-DAMCS fund of SSSIHL for this work. 

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. K. K. Vamsi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vamsi, D.K.K., Kanumoori, D.S.S.M. & Chhetri, B. Additional Food Supplements as a Tool for Biological Conservation of Biosystems in the Presence of Inhibitory Effect of the Prey. Acta Biotheor 68, 321–355 (2020). https://doi.org/10.1007/s10441-019-09371-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10441-019-09371-x

Keywords

Navigation