International Journal of Nonlinear Analysis and Applications

Mathematical modelling of intraguild predation and its dynamics of resource harvesting

Document Type : Research Paper

Authors

Department of Mathematics, Visva-Bharati, Santiniketan-731 235, West Bengal, India

Abstract

The contemporary theoretical inquest concerns itself with an updated mathematical model involving intraguild (IG) predation in which the IG predator acts as a generalist predator with the inclusion of harvesting in the resource population. Due attention is paid to the positivity and boundedness of the outcomes of the system under consideration. All the conceivable ecologically feasible equilibria are explored for their existence and stability under certain conditions. Special emphasis is put forward on the consequence of harvesting for the present model system. The occurrences of Hopf-bifurcation with respect to harvesting parameters involved in the harvesting effort of the model system are captured. The subsistence of the possible bionomic equilibria is, however, not ruled out from the present pursuit. The optimal harvesting policy is initiated and duly carried out with Pontryagin’s maximum principle. Numerical simulations are performed towards the end to comply with the objectives of the agreement of the numerical outcomes with their analytical counterparts and the applicability of the model is validated thereby.

Keywords

[1] J.D. Murray, Mathematical Biololgy I: An Introduction, Third Edition, Springer-Verlag, 2002.
[2] Y. Kang and L. Wedekin, Dynamics of intraguild predation model with generalist or specialist predator, J. Math. Biol. 67 (2013), 1227–1259.
[3] R.D. Holt and G.A. Polis, A theoritical framework for intraguild predation, Amer. Nat. 149 (1997), 745–764.
[4] J. Brodeur and J.A. Rosenheim, Intraguild interactions in aphid parasitoids, Entomol. Exp. Appl. 97 (2000), 93–108.
[5] C.J. Bampfylde and M.A. Lewis, Biological control through intraguild predation: case studies in pest control, invasive species and range expansion, Bull. Math. Biol. 69 (2007), 1031–1066.
[6] C. Ganguli, T.K. Kar and P.K. Mondal, Optimal harvesting of a prey-predator model with variable carrying capacity, Int. J. Biomath. 10 (2017), 1750069.
[7] GC. Layek, An Introduction to Dynamical Systems and Chaos, Springer, 2015.
[8] S.H. Strogatz, Nonlinear Dynamics and Chaos: with application to Physics, Biology, Chemistry and Engineering, Taylor and Francis, United Kingdom, 1994.
[9] L. Perko, Differential Equations and Dynamical Systems, Third Edition, Springer, 2001.
[10] T.K. Kar, Modelling and analysis of a harvested prey-predator system incorporating a prey refuge, J. Comput. Appl. Math. 185 (2006), 19–33.
[11] P. Amarasekare, Coexistence of intraguild predators and prey in resource-rich environments, Ecology 89 (2008), 2786–2797.
[12] K.S. Chaudhuri, A bioeconomic model of harvesting, a multispecies fishery, Ecol. Model. 32 (1986), 267–279.
[13] F.M. Hilker and H. Malchow, Strange periodic attractor in a prey-predator system with infected prey, Math. Popul. Stud. 13 (2006), 119–134.
[14] C.W. Clark, Mathematical Bioeconomics: The optimal management of renewable resources, Wiley, New York, 1976.
[15] J. Smith, Models in Ecology, Cambridge University Press, Cambridge, 1974.
[16] A.A. Berryman, The origin and evolution of predator-prey theory, Ecology 73 (1992), 1530–1535.
[17] H.C. Wei, Y.Y. Chen, J.T. Lin and S.F. Hwang, The dynamics of an intraguild predation model with prey switching, AIP Conf. Proc. 1978 (2018), 470012.
[18] T.I. Potter, A.C. Greenville and C. Dickman, Assessing the potential for intraguild predation among taxonomically disparate micro-carnivores: marsupials and arthropods, R. Soc. Open Sci. 5 (2018), 171872.
[19] S. Wang, U. Brose and D. Gravel, Intraguild predation enhances biodiversity and functioning in complex food webs, Ecology 100 (2019), e02616.
[20] S. Pirzadfard, N. Zandi-Sohani, F. Sohrabi and A. Rajabpour, Intraguild interactions of a generalist predator, Orius albidipennis, with two Bemisia tabaci parasitoids, Int. J. Trop. Insect. Sci. 40 (2020), 259–265.
[21] R. Han, B. Dai and Y. Chen, Pattern formation in a diffusive intraguild predation model with nonlocal interaction effects, AIP Adv. 9 (2019) 035046.
[22] K. Sarkar, N. Ali and L.N. Guin, Dynamical complexity in a tritrophic food chain model with prey harvesting, Discontinuity, Nonlinearity, Complexity 10 (2021), 705–722.
[23] HL. Smith, Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems, Amer. Math. Soc. Providence, Rhode Island, 2008.
[24] L.N. Guin and P.K. Mandal, Spatiotemporal dynamics of reaction-diffusion models of interacting populations, Appl. Math. Model. 38 (2014), 4417–4427.
[25] L.N. Guin, Existence of spatial patterns in a predator-prey model with self- and cross-diffusion, Appl. Math. Comput. 226 (2014), 320–335.
[26] L.N. Guin, S. Djilali and S. Chakravarty, Cross-diffusion-driven instability in an interacting species model with prey refuge, Chaos Solit. Fractals 153 (2021), 111501.
[27] R. Han, L.N. Guin and S. Acharya, Complex dynamics in a reaction-cross-diffusion model with refuge depending on predator-prey encounters, Eur. Phys. J. Plus 137 (2022), 1–27.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 837-861
  • Receive Date: 27 January 2022
  • Revise Date: 30 March 2022
  • Accept Date: 12 April 2022