Stabilizing predator-prey interactions: the impact of supplementary food and anti-predator behavior

Aladeen Al Basheer; Aladeen Al Basheer

doi:10.3934/mbe.2026058

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 6: 1596-1621. doi: 10.3934/mbe.2026058

Previous Article Next Article

Research article

Stabilizing predator-prey interactions: the impact of supplementary food and anti-predator behavior

Aladeen Al Basheer ^,

Department of Basic Sciences, Al Hussein Technical University, King Abdullah Ⅱ St 242, Amman 11831, Jordan

Received: 16 January 2026 Revised: 23 March 2026 Accepted: 20 April 2026 Published: 28 April 2026

This study investigated a modified Holling-Tanner predator-prey model that incorporates supplementary food for predators and anti-predator behavior in prey. The model examined how these ecological mechanisms influence predator-prey dynamics and biological pest control. Local and global stability analyses were performed to determine the conditions that lead to predator persistence and pest eradication. Explicit parametric conditions were derived that guarantee global pest extinction, providing quantitative criteria for effective biological control. Bifurcation analysis revealed the presence of Hopf and saddle-node bifurcations, which identify critical parameter thresholds where the system transitions between stable equilibria, oscillatory dynamics, and collapse of coexistence states. The results showed that anti-predator behavior can stabilize population dynamics and suppress oscillatory behavior that would otherwise occur in the absence of prey defense mechanisms. A reaction-diffusion extension of the model was then considered to investigate spatial effects. Turing instability analysis demonstrated that the interaction between diffusion and anti-predator behavior can generate persistent spatial patterns, offering a mechanistic explanation for patchy predator distributions frequently observed in agricultural ecosystems. The analysis further indicated that the effectiveness of biological control depends on the balance between supplementary food quantity, predation pressure, and the strength of prey defense. Excessive food supplementation may reduce predator pressure on pests and weaken pest suppression. Numerical simulations supported the analytical results and illustrated parameter regimes that lead to system stabilization and successful pest management. The proposed framework provides theoretical guidance for designing predator-based biological control strategies that combine resource provisioning with natural behavioral responses.
- biological control,
- additional food,
- anti-predator,
- stability,
- Turing instability
Citation: Aladeen Al Basheer. Stabilizing predator-prey interactions: the impact of supplementary food and anti-predator behavior[J]. Mathematical Biosciences and Engineering, 2026, 23(6): 1596-1621. doi: 10.3934/mbe.2026058

Related Papers:

Abstract

This study investigated a modified Holling-Tanner predator-prey model that incorporates supplementary food for predators and anti-predator behavior in prey. The model examined how these ecological mechanisms influence predator-prey dynamics and biological pest control. Local and global stability analyses were performed to determine the conditions that lead to predator persistence and pest eradication. Explicit parametric conditions were derived that guarantee global pest extinction, providing quantitative criteria for effective biological control. Bifurcation analysis revealed the presence of Hopf and saddle-node bifurcations, which identify critical parameter thresholds where the system transitions between stable equilibria, oscillatory dynamics, and collapse of coexistence states. The results showed that anti-predator behavior can stabilize population dynamics and suppress oscillatory behavior that would otherwise occur in the absence of prey defense mechanisms. A reaction-diffusion extension of the model was then considered to investigate spatial effects. Turing instability analysis demonstrated that the interaction between diffusion and anti-predator behavior can generate persistent spatial patterns, offering a mechanistic explanation for patchy predator distributions frequently observed in agricultural ecosystems. The analysis further indicated that the effectiveness of biological control depends on the balance between supplementary food quantity, predation pressure, and the strength of prey defense. Excessive food supplementation may reduce predator pressure on pests and weaken pest suppression. Numerical simulations supported the analytical results and illustrated parameter regimes that lead to system stabilization and successful pest management. The proposed framework provides theoretical guidance for designing predator-based biological control strategies that combine resource provisioning with natural behavioral responses.

References

[1]	D. Pimentel, Environmental and economic costs of the application of pesticides primarily in the United States, Environ. Dev. Sustain., 7 (2005), 229–252. https://doi.org/10.1007/s10668-005-7314-2 doi: 10.1007/s10668-005-7314-2
[2]	K. Czaja, K. Góralczyk, P. Struciński, A. Hernik, W. Korcz, M. Minorczyk, et al., Biopesticides-towards increased consumer safety in the European Union, Pest Manag. Sci., 71 (2015), 3–6. https://doi.org/10.1002/ps.3829 doi: 10.1002/ps.3829
[3]	C. J. Bampfylde, 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. https://doi.org/10.1007/s11538-006-9158-9 doi: 10.1007/s11538-006-9158-9
[4]	Y. Kang, D. Bai, L. Tapia, H. Bateman, Dynamical effects of biocontrol on the ecosystem: Benefits or harm?, Appl. Math. Modelling, 51 (2017), 361–385. https://doi.org/10.1016/j.apm.2017.07.006 doi: 10.1016/j.apm.2017.07.006
[5]	R. D. Parshad, R. K. Upadhyay, S. Mishra, S. K. Tiwari, S. Sharma, On the explosive instability in a three-species food chain model with modified Holling type IV functional response, Math. Methods Appl. Sci., 40 (2017), 5707–5726. https://doi.org/10.1002/mma.4419 doi: 10.1002/mma.4419
[6]	R. D. Parshad, S. Bhowmick, E. Quansah, A. Basheer, R. K. Upadhyay, Predator interference effects on biological control: The "paradox" of the generalist predator revisited, Commun. Nonlinear Sci. Numer. Simul., 39 (2016), 169–184. https://doi.org/10.1016/j.cnsns.2016.02.021 doi: 10.1016/j.cnsns.2016.02.021
[7]	R. G. V. Driesche, T. S. Bellows, Biological Control, Springer Science and Business Media, 2012.
[8]	E. W. Evans, J. G. Swallow, Numerical responses of natural enemies to artificial honeydew in Utah alfalfa, Environ. Entomol., 22 (1993), 1392–1401. https://doi.org/10.1093/ee/22.6.1392 doi: 10.1093/ee/22.6.1392
[9]	L. A. Canas, R. J. O'Neil, Applications of sugar solutions to maize, and the impact of natural enemies on fall armyworm, Int. J. Pest Manag., 44 (1998), 59–64. https://doi.org/10.1080/096708798228329 doi: 10.1080/096708798228329
[10]	E. W. Evans, D. R. Richards, Managing the dispersal of ladybird beetles (Col.: Coccinellidae): Use of artificial honeydew to manipulate spatial distributions, BioControl, 42 (1997), 93–102. https://doi.org/10.1007/BF02769884 doi: 10.1007/BF02769884
[11]	M. R. Wade, M. P. Zalucki, S. D. Wratten, K. A. Robinson, Conservation biological control of arthropods using artificial food sprays: Current status and future challenges, Biol. Control, 45 (2008), 185–199. https://doi.org/10.1016/j.biocontrol.2007.10.024 doi: 10.1016/j.biocontrol.2007.10.024
[12]	W. E. Snyder, D. H. Wise, Predator interference and the establishment of generalist predator populations for biocontrol, Biol. Control, 15 (1999), 283–292. https://doi.org/10.1006/bcon.1999.0723 doi: 10.1006/bcon.1999.0723
[13]	S. P. Shannon, T. H. Chrzanowski, J. P. Grover, Prey food quality affects flagellate ingestion rates, Microb. Ecol., 53 (2007), 66–73. https://doi.org/10.1007/s00248-006-9140-y doi: 10.1007/s00248-006-9140-y
[14]	G. Saunders, B. Cooke, K. McColl, R. Shine, T. Peacock, Modern approaches for the biological control of vertebrate pests: An Australian perspective, Biol. Control, 52 (2010), 288–295. https://doi.org/10.1016/j.biocontrol.2009.06.014 doi: 10.1016/j.biocontrol.2009.06.014
[15]	A. Tena, A. Pekas, D. Cano, F. L. Wäckers, A. Urbaneja, Sugar provisioning maximizes the biocontrol service of parasitoids, J. Appl. Ecol., 52 (2015), 795–804. https://doi.org/10.1111/1365-2664.12426 doi: 10.1111/1365-2664.12426
[16]	A. Basheer, E. Quansah, S. Bhowmick, R. D. Parshad, Prey cannibalism alters the dynamics of Holling-Tanner-type predator-prey models, Nonlinear Dyn., 85 (2016), 2549–2567. https://doi.org/10.1007/s11071-016-2844-8 doi: 10.1007/s11071-016-2844-8
[17]	A. A. Basheer, R. D. Parshad, E. Quansah, S. Yu, R. K. Upadhyay, Exploring the dynamics of a Holling-Tanner model with cannibalism in both predator and prey population, Int. J. Biomath., 11 (2018), 1850010. https://doi.org/10.1142/S1793524518500109 doi: 10.1142/S1793524518500109
[18]	X. Wang, L. Zanette, X. Zou, Modelling the fear effect in predator-prey interactions, J. Math. Biol., 73 (2016), 1179–1204. https://doi.org/10.1007/s00285-016-0989-1 doi: 10.1007/s00285-016-0989-1
[19]	G. He, F. Chen, Z. Li, L. Chen, Impact of fear on a stage-structured Lotka-Volterra competition model, Qual. Theory Dyn. Syst., 24 (2025), 170. https://doi.org/10.1007/s12346-025-01331-w doi: 10.1007/s12346-025-01331-w
[20]	K. Put, T. Bollens, F. L. Wäckers, A. Pekas, Type and spatial distribution of food supplements impact population development and dispersal of the omnivore predator Macrolophus pygmaeus (Rambur) (Hemiptera: Miridae), Biol. Control, 63 (2012), 172–180. https://doi.org/10.1016/j.biocontrol.2012.06.011 doi: 10.1016/j.biocontrol.2012.06.011
[21]	P. Turchin, Complex Population Dynamics: A Theoretical/Empirical Synthesis, Princeton University Press, 2003.
[22]	P. D. N. Srinivasu, B. S. R. V. Prasad, M. Venkatesulu, Biological control through provision of additional food to predators: A theoretical study, Theor. Popul. Biol., 72 (2007), 111–120. https://doi.org/10.1016/j.tpb.2007.03.011 doi: 10.1016/j.tpb.2007.03.011
[23]	P. D. N. Srinivasu, B. S. R. V. Prasad, Time optimal control of an additional food provided predator-prey system with applications to pest management and biological conservation, J. Math. Biol., 60 (2010), 591–613. https://doi.org/10.1007/s00285-009-0279-2 doi: 10.1007/s00285-009-0279-2
[24]	P. D. N. Srinivasu, B. S. R. V. Prasad, Role of quantity of additional food to predators as a control in predator-prey systems with relevance to pest management and biological conservation, Bull. Math. Biol., 73 (2011), 2249–2276. https://doi.org/10.1007/s11538-010-9601-9 doi: 10.1007/s11538-010-9601-9
[25]	H. M. Ulfa, A. Suryanto, I. Darti, Dynamics of Leslie-Gower predator-prey model with additional food for predators, Int. J. Pure Appl. Math., 115 (2017), 751–765. https://doi.org/10.12732/ijpam.v115i2.1 doi: 10.12732/ijpam.v115i2.1
[26]	R. D. Parshad, S. Wickramsooriya, S. Bailey, A remark on biological control through provision of additional food to predators: A theoretical study, Theor. Popul. Biol., 132 (2020), 60–68. https://doi.org/10.1016/j.tpb.2019.11.010 doi: 10.1016/j.tpb.2019.11.010
[27]	A. Basheer, E. Quansah, R. D. Parshad, The effect of additional food in Holling Tanner type models, Int. J. Dyn. Control, 7 (2019), 1195–1212. https://doi.org/10.1007/s40435-019-00580-3 doi: 10.1007/s40435-019-00580-3
[28]	Y. Choh, J. Takabayashi, M. W. Sabelis, A. Janssen, Witnessing predation can affect strength of counterattack in phytoseiids with ontogenetic predator-prey role reversal, Anim. Behav., 93 (2014), 9–13. https://doi.org/10.1016/j.anbehav.2014.04.008 doi: 10.1016/j.anbehav.2014.04.008
[29]	S. L. Lima, Nonlethal effects in the ecology of predator-prey interactions, Bioscience, 48 (1998), 25–34. https://doi.org/10.2307/1313225 doi: 10.2307/1313225
[30]	J. K. Ford, R. R. Reeves, Fight or flight: Antipredator strategies of baleen whales, Mamm. Rev., 38 (2008), 50–86. https://doi.org/10.1111/j.1365-2907.2008.00118.x doi: 10.1111/j.1365-2907.2008.00118.x
[31]	B. Tang, Y. Xiao, Bifurcation analysis of a predator-prey model with anti-predator behaviour, Chaos Solitons Fractals, 70 (2015), 58–68. https://doi.org/10.1016/j.chaos.2014.11.008 doi: 10.1016/j.chaos.2014.11.008
[32]	A. R. Ives, A. P. Dobson, Antipredator behavior and the population dynamics of simple predator-prey systems, Am. Nat., 130 (1987), 431–447. https://doi.org/10.1086/284719 doi: 10.1086/284719
[33]	K. D. Prasad, B. S. R. V. Prasad, Qualitative analysis of additional food provided predator-prey system with anti-predator behaviour in prey, Nonlinear Dyn., 96 (2019), 1765–1793. https://doi.org/10.1007/s11071-019-04883-0 doi: 10.1007/s11071-019-04883-0
[34]	F. Chen, On a nonlinear nonautonomous predator-prey model with diffusion and distributed delay, J. Comput. Appl. Math., 180 (2005), 33–49. https://doi.org/10.1016/j.cam.2004.10.001 doi: 10.1016/j.cam.2004.10.001
[35]	S. H. Strogatz, Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering, CRC Press, 2018.
[36]	W. M. Liu, Criterion of hopf bifurcations without using eigenvalues, J. Math. Anal. Appl., 182 (1994), 250–256. https://doi.org/10.1006/jmaa.1994.1079 doi: 10.1006/jmaa.1994.1079
[37]	M. Haque, Ratio-dependent predator-prey models of interacting populations, Bull. Math. Biol., 71 (2009), 430–452. https://doi.org/10.1007/s11538-008-9368-4 doi: 10.1007/s11538-008-9368-4
[38]	L. Perko, Differential Equations and Dynamical Systems, Springer, 2013.
[39]	K. A. J. White, C. A. Gilligan, Spatial heterogeneity in three species, plant-parasite-hyperparasite systems, Phil. Trans. R. Soc. Lond. B, 353 (1998), 543–557. https://doi.org/10.1098/rstb.1998.0226 doi: 10.1098/rstb.1998.0226

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)