The (De)Stabilizing effect of juvenile prey cannibalism in a stage-structured model

Eric M. Takyi; Kasey Cooper; Ava Dreher; Caroline McCrorey; Eric M. Takyi; Kasey Cooper; Ava Dreher; Caroline McCrorey

doi:10.3934/mbe.2023158

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3355-3378. doi: 10.3934/mbe.2023158

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The (De)Stabilizing effect of juvenile prey cannibalism in a stage-structured model

1.
Department of Mathematics and Computer Science, Ursinus College, Collegeville, PA 19426, USA
2.
Department of Mathematics and Statistics, Binghamton University, Binghamton, NY 13902, USA
3.
Department of Mathematics, Bellarmine University, Louisville, KY 40205, USA

Received: 28 August 2022 Revised: 04 November 2022 Accepted: 24 November 2022 Published: 05 December 2022

Cannibalism, or intraspecific predation, is the act of an organism consuming another organism of the same species. In predator-prey relationships, there is experimental evidence to support the existence of cannibalism among juvenile prey. In this work, we propose a stage-structured predator-prey system where cannibalism occurs only in the juvenile prey population. We show that cannibalism has both a stabilizing and destabilizing effect depending on the choice of parameters. We perform stability analysis of the system and also show that the system experiences a supercritical Hopf, saddle-node, Bogdanov-Takens and cusp bifurcation. We perform numerical experiments to further support our theoretical findings. We discuss the ecological implications of our results.
- cannibalism,
- stabilization,
- destabilization,
- stage-structured,
- bifurcation
Citation: Eric M. Takyi, Kasey Cooper, Ava Dreher, Caroline McCrorey. The (De)Stabilizing effect of juvenile prey cannibalism in a stage-structured model[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3355-3378. doi: 10.3934/mbe.2023158

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Abstract

Cannibalism, or intraspecific predation, is the act of an organism consuming another organism of the same species. In predator-prey relationships, there is experimental evidence to support the existence of cannibalism among juvenile prey. In this work, we propose a stage-structured predator-prey system where cannibalism occurs only in the juvenile prey population. We show that cannibalism has both a stabilizing and destabilizing effect depending on the choice of parameters. We perform stability analysis of the system and also show that the system experiences a supercritical Hopf, saddle-node, Bogdanov-Takens and cusp bifurcation. We perform numerical experiments to further support our theoretical findings. We discuss the ecological implications of our results.

References

[1]	G. A. Polis, The evolution and dynamics of intraspecific predation, Ann. Rev. Ecol. Syst., 12 (1981), 225–251. https://doi.org/10.1146/annurev.es.12.110181.001301 doi: 10.1146/annurev.es.12.110181.001301
[2]	M. L. Crump, Opportunistic cannibalism by amphibian larvae in temporary aquatic environments, Am. Natl., 121 (1983), 281–289. https://doi.org/10.1086/284058 doi: 10.1086/284058
[3]	C. Smith, P. Reay, Cannibalism in teleost fish. Rev. Fish Biol. Fish., 1 (1991), 41–64. https://doi.org/10.1007/BF00042661 doi: 10.1007/BF00042661
[4]	V. Puvanendran, B. J. Laurel, J. A. Brown, Cannibalism of Atlantic cod Gadus morhua larvae and juveniles on first-week larvae, Aquat. Biol., 2 (2008), 113–118. https://doi.org/10.3354/ab00044 doi: 10.3354/ab00044
[5]	C. Ingram, The importance of juvenile cannibalism in the breeding biology of certain birds of prey, Auk, 76 (1959), 218–226. https://doi.org/10.2307/4081778 doi: 10.2307/4081778
[6]	A. E. Pusey, C. Packer, Infanticide in lions: Consequences and counterstrategies, in Infanticide and Parental Care, (eds. Parmigiani and F. S. vom Saal), Harwood Academic Publishers, Chur, Switzerland, (1994), 277–299. https://doi.org/10.1042/bj2990277
[7]	J. Bhattacharyya, S. Pal, The role of space in stage-structured cannibalism with harvesting of an adult predator, Comput. Math. Appl., 66 (2013), 339–355. https://doi.org/10.1016/j.camwa.2013.05.011 doi: 10.1016/j.camwa.2013.05.011
[8]	J. Van Buskirk, Density-dependent cannibalism in larval dragonflies, Ecology, 70 (1989), 1442–1449. https://doi.org/10.2307/1938203 doi: 10.2307/1938203
[9]	J. L. Hayward, L. M. Weldon, S. M. Henson, L. C. Megna, B. G. Payne, A. E. Moncrieff, Egg cannibalism in a gull colony increases with sea surface temperature, Condor, 116 (2014), 62–73. https://doi.org/10.1650/CONDOR-13-016-R1.1 doi: 10.1650/CONDOR-13-016-R1.1
[10]	S. C. Amstrup, I. Stirling, T. S. Smith, C. Perham, G. W. Thiemann, Recent observations of intraspecific predation and cannibalism among polar bears in the southern Beaufort sea, Polar Biol., 29 (2006), 997–1002. https://doi.org/10.1007/s00270-003-0093-y doi: 10.1007/s00270-003-0093-y
[11]	J. M. Cushing, A simple model of cannibalism, Math. Biosci., 107 (1991), 47–71. https://doi.org/10.1016/0025-5564(91)90071-P doi: 10.1016/0025-5564(91)90071-P
[12]	J. M. Cushing, A size-structured model for cannibalism, Theor. Popul. Biol., 42 (1992), 347–361. https://doi.org/10.1016/0040-5809(92)90020-T doi: 10.1016/0040-5809(92)90020-T
[13]	A. Al 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.
[14]	C. Kohlmeier, W. Ebenhöh, The stabilizing role of cannibalism in a predator-prey system, Bull. Math. Biol., 57 (1995), 401–411.
[15]	K. G Magnússon, Destabilizing effect of cannibalism on a structured predator-prey system, Math. Biosci., 155 (1999), 61–75. https://doi.org/10.1016/S0025-5564(98)10051-2 doi: 10.1016/S0025-5564(98)10051-2
[16]	C. Kaewmanee, I. M. Tang, Cannibalism in an age-structured predator-prey system, Ecol. Modell., 167 (2013), 213–220.
[17]	H. Deng, F. Chen, Z. Zhu, Z. Li, Dynamic behaviors of Lotka–Volterra predator–prey model incorporating predator cannibalism, Adv. Differ. Equations, 2019 (2019), 1–17.
[18]	S. Fasani, S. Rinaldi, Remarks on cannibalism and pattern formation in spatially extended prey-predator systems, Nonlinear Dyn., 67 (2012), 2543–2548. https://doi.org/10.1007/s11071-011-0166-4 doi: 10.1007/s11071-011-0166-4
[19]	A. Al Basheer, J. Lyu, A. Giffin, R. D Parshad, The "destabilizing" effect of cannibalism in a spatially explicit three-species age structured predator-prey model, Complexity, 2017 (2017), 3896412. https://doi.org/10.1155/2017/3896412 doi: 10.1155/2017/3896412
[20]	G. Q. Sun, G. Zhang, Z. Jin, L. Li, Predator cannibalism can give rise to regular spatial pattern in a predator–prey system, Nonlinear Dyn., 58 (2009), 75–84. https://doi.org/10.1007/s11071-008-9462-z doi: 10.1007/s11071-008-9462-z
[21]	M. L. Crump, Cannibalism by younger tadpoles: another hazard of metamorphosis, Copeia, 1986 (1986), 1007–1009.
[22]	A. M. Edwards, A. Yool, The role of higher predation in plankton population models, J. Plankton Res., 22 (2000), 1085–1112. https://doi.org/10.1093/plankt/22.6.1085 doi: 10.1093/plankt/22.6.1085
[23]	M. Baurmann, T. Gross, U. Feudel, Instabilities in spatially extended predator–prey systems: Spatio-temporal patterns in the neighborhood of Turing–Hopf bifurcations, J. Theor. Biol., 245 (2007), 220–229.
[24]	S. Rana, A. R. Bhowmick, T. Sardar, Invasive dynamics for a predator–prey system with Allee effect in both populations and a special emphasis on predator mortality, Chaos Interdiscip. J. Nonlinear Sci., 31 (2021), 033150. https://doi.org/10.1063/5.0035566 doi: 10.1063/5.0035566
[25]	M. Pierre, D. Schmitt, Blowup in reaction-diffusion systems with dissipation of mass, SIAM Rev., 42 (2000), 93–106.
[26]	M. Pierre, Global existence in reaction-diffusion systems with control of mass: A survey, Milan J. Math., 78 (2010), 417–455. https://doi.org/10.1007/s00032-010-0133-4 doi: 10.1007/s00032-010-0133-4
[27]	L. Perko, Differential Equations and Dynamical Systems, Springer Science & Business Media, Springer-Verlag, New York, 2013.
[28]	P. A. Naik, Z. Eskandari, H. E. Shahraki, Flip and generalized flip bifurcations of a two-dimensional discrete-time chemical model, Math. Modell. Numer. Simul. Appl., 1 (2021), 95–101. https://doi.org/10.53391/mmnsa.2021.01.009 doi: 10.53391/mmnsa.2021.01.009
[29]	A. Dhooge, W. Govaerts, Y. A. Kuznetsov, H. G. Meijer, B. Sautois, New features of the software matcont for bifurcation analysis of dynamical systems, Math. Comput. Modell. Dyn. Syst., 14 (2008), 147–175.
[30]	B. Buonomo, D. Lacitignola, On the stabilizing effect of cannibalism in stage-structured population models, Math. Biosci. Eng., 3 (2006), 717. https://doi.org/10.3934/mbe.2006.3.717 doi: 10.3934/mbe.2006.3.717
[31]	F. van den Bosch, W. Gabriel, The impact of cannibalism on the population dynamics of cyclopoid copepods, Int.Ver. Theor. Angew. Limnol. Verh., 24 (1991), 2848–2850. https://doi.org/10.1080/03680770.1989.11899180 doi: 10.1080/03680770.1989.11899180
[32]	M. E. Dorcas, J. D. Willson, R. N. Reed, R. W. Snow, M. R. Rochford, M. A. Miller, et al., Severe mammal declines coincide with proliferation of invasive Burmese pythons in Everglades National Park, Proc. Natl. Acad. Sci., 109 (2012), 2418–2422. https://doi.org/10.1073/pnas.1115226109 doi: 10.1073/pnas.1115226109
[33]	P. A. Naik, Z. Eskandari, M. Yavuz, J. Zu, Complex dynamics of a discrete-time Bazykin-Berezovskaya prey-predator model with a strong Allee effect, J. Comput. Appl. Math., 413 (2022), 114401. https://doi.org/10.1016/j.cam.2022.114401 doi: 10.1016/j.cam.2022.114401
[34]	M. Yavuz, N. Sene, Stability analysis and numerical computation of the fractional predator-prey model with the harvesting rate, Fractal Fractional, 4 (2020), 35. https://doi.org/10.3390/fractalfract4030035 doi: 10.3390/fractalfract4030035

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