Examining the influence of prey dynamics on predator-prey interactions. (English) Zbl 07903469
Summary: We develop variations of a discrete-time predator-prey model to examine how intrinsic properties of the prey population may impact overall system dynamics. We focus on two properties of the prey species, namely developmental stage structure and undercompensatory (contest competition) versus overcompensatory (scramble competition) density dependence. Through analysis of these models, we examine how these different prey features affect system stability. Our results show that when prey growth is overcompensatory, the predator may have a stabilizing effect on the system dynamics with increasing predator density reversing the period doubling route to chaos observed with Ricker-type nonlinearities. Moreover, we find that stage structure in the prey does not have a destabilizing effect on the system dynamics unless the prey projection matrix is imprimitive or close to imprimitive, as may occur for semelparous species. In this case, a sufficiently large predator density may stabilize cycles that are otherwise unstable.
MSC:
| 92D25 | Population dynamics (general) |
Keywords:
discrete-time predator-prey models; stability; persistence; stage-structure; overcompensatory and undercompensatory density dependenceReferences:
| [1] | Ackleh, A.S. and Chiquet, R.A., The global dynamics of a discrete juvenile-adult model with continuous and seasonal reproduction, J. Biol. Dyn.3(2-3) (2009), pp. 101-115. · Zbl 1342.92153 |
| [2] | Ackleh, A.S. and De Leenheer, P., Discrete three-stage population model: persistence and global stability results, J. Biol. Dyn.2(4) (2008), pp. 415-427. · Zbl 1315.92057 |
| [3] | Ackleh, A.S., Hossain, M.I., Veprauskas, A., and Zhang, A., Persistence and stability analysis of discrete-time predator-prey models: a study of population and evolutionary dynamics, J. Differ. Equ. Appl.25(11) (2019), pp. 1568-1603. · Zbl 1430.92063 |
| [4] | Ackleh, A.S., Hossain, M.I., Veprauskas, A., and Zhang, A., Long-term dynamics of discrete-time predator-prey models: stability of equilibria, cycles and chaos, J. Differ. Equ. Appl.26(5) (2020), pp. 693-726. · Zbl 1467.92148 |
| [5] | Ackleh, A.S., Hossain, M.I., Veprauskas, A., and Zhang, A., Persistence of a discrete-time predator-prey model with stage-structure in the predator, in Progress on Difference Equations and Discrete Dynamical Systems: 25th ICDEA, London, UK, June 24-28, 2019, 25, Springer, 2020, pp. 145-163. · Zbl 1472.37086 |
| [6] | Ackleh, A.S., Salceanu, P., and Veprauskas, A., A nullcline approach to global stability in discrete-time predator-prey models, J. Differ. Equ. Appl.27(8) (2021), pp. 1120-1133. · Zbl 1475.92120 |
| [7] | Ackleh, A.S. and Veprauskas, A., Frequency-dependent evolution in a predator-prey system, Nat. Resour. Model.34(3) (2021), pp. e12308. |
| [8] | Allen, L.J., An Introduction to Mathematical Biology, Pearson Prentice Hall, Upper Saddle River, NJ, 2007. |
| [9] | Blasius, B., Rudolf, L., Weithoff, G., Gaedke, U., and Fussmann, G.F., Long-term cyclic persistence in an experimental predator-prey system, Nature577(7789) (2020), pp. 226-230. |
| [10] | Caswell, H., Matrix Population Models, Vol. 1, Sinauer, Sunderland, MA, 2000. |
| [11] | Cooke, K.L., Elderkin, R.H., and Huang, W., Predator-prey interactions with delays due to juvenile maturation, SIAM. J. Appl. Math.66(3) (2006), pp. 1050-1079. · Zbl 1090.92047 |
| [12] | Cushing, J. and Stump, S.M., Darwinian dynamics of a juvenile-adult model, Dynamics30(32) (2013), pp. 33. |
| [13] | Cushing, J.M., An Introduction to Structured Population Dynamics, SIAM, Providence, RI, 1998. · Zbl 0939.92026 |
| [14] | Cushing, J.M., Chaos in Ecology: Experimental Nonlinear Dynamics, Vol. 1, Elsevier, San Diego, CA, 2003. |
| [15] | Cushing, J.M. and Henson, S.M., Stable bifurcations in semelparous leslie models, J. Biol. Dyn.6(sup2) (2012), pp. 80-102. · Zbl 1447.92335 |
| [16] | Cushing, J.M. and Yicang, Z., The net reproductive value and stability in matrix population models, Nat. Resour. Model.8(4) (1994), pp. 297-333. |
| [17] | D’Aniello, E. and Elaydi, S., The structure of omega-limit sets of asymptotically non-autonomous discrete dynamical systems, Discrete & Contin. Dyn. Syst.-B25(3) (2020), pp. 903. · Zbl 1436.37023 |
| [18] | Diekmann, O. and Planqué, R., The winner takes it all: how semelparous insects can become periodical, J. Math. Biol.80(1-2) (2020), pp. 283-301. · Zbl 1437.37117 |
| [19] | Fei, L., Chen, X., and Han, B., Bifurcation analysis and hybrid control of a discrete-time predator-prey model, J. Differ. Equ. Appl.27(1) (2021), pp. 102-117. · Zbl 1466.39013 |
| [20] | Franklin, D.C., Synchrony and asynchrony: observations and hypotheses for the flowering wave in a long-lived semelparous bamboo, J. Biogeogr.31(5) (2004), pp. 773-786. |
| [21] | Gourley, S.A. and Kuang, Y., A stage structured predator-prey model and its dependence on maturation delay and death rate, J. Math. Biol.49(2) (2004), pp. 188-200. · Zbl 1055.92043 |
| [22] | Holmengen, N. and Seip, K.L., Cycle lengths and phase portrait characteristics as probes for predator-prey interactions: comparing simulations and observed data, Can. J. Zool.87(1) (2009), pp. 20-30. |
| [23] | Huffaker, C.B., Experimental studies on predation: dispersion factors and predator-prey oscillations, Hilgardia27(14) (1958), pp. 343-383. |
| [24] | Kang, Y., Dynamics of a generalized Ricker-Beverton-Holt competition model subject to allee effects, J. Differ. Equ. Appl.22(5) (2016), pp. 687-723. · Zbl 1344.92139 |
| [25] | Kirkland, S., Li, C.K., and Schreiber, S.J., On the evolution of dispersal in patchy landscapes, SIAM. J. Appl. Math.66(4) (2006), pp. 1366-1382. · Zbl 1100.39011 |
| [26] | Kon, R., Nonexistence of synchronous orbits and class coexistence in matrix population models, SIAM. J. Appl. Math.66(2) (2005), pp. 616-626. · Zbl 1096.39009 |
| [27] | Loppnow, G.L. and Venturelli, P.A., Stage-structured simulations suggest that removing young of the year is an effective method for controlling invasive smallmouth bass, Trans. Am. Fish. Soc.143(5) (2014), pp. 1341-1347. |
| [28] | Luckinbill, L.S., Coexistence in laboratory populations of paramecium aurelia and its predator didinium nasutum, Ecology54(6) (1973), pp. 1320-1327. |
| [29] | Marcinko, K. and Kot, M., A comparative analysis of host-parasitoid models with density dependence preceding parasitism, J. Biol. Dyn.14(1) (2020), pp. 479-514. · Zbl 1448.92231 |
| [30] | Meissen, E.P., Invading a structured population: A bifurcation approach, Ph.D. diss., The University of Arizona, 2017. |
| [31] | Miller, T.E. and Rudolf, V.H., Thinking inside the box: community-level consequences of stage-structured populations, Trends. Ecol. Evol. (Amst.)26(9) (2011), pp. 457-466. |
| [32] | Mokni, K., Elaydi, S., Ch-Chaoui, M., and Eladdadi, A., Discrete evolutionary population models: a new approach, J. Biol. Dyn.14(1) (2020), pp. 454-478. · Zbl 1442.92106 |
| [33] | Nyumura, N. and Asami, T., Synchronous and non-synchronous semelparity in sibling species of pulmonates, Zool. Sci.32(4) (2015), pp. 372-377. |
| [34] | de Roos, A., Persson, L., and Thieme, H.R., Emergent allee effects in top predators feeding on structured prey populations, Proc. R. Soc. Lond. Ser. B Biol. Sci.270(1515) (2003), pp. 611-618. |
| [35] | de Roos, A.M., Dynamic population stage structure due to juvenile-adult asymmetry stabilizes complex ecological communities, Proc. Natl. Acad. Sci.118(21) (2021), pp. e2023709. |
| [36] | Rudolf, V. and Lafferty, K.D., Stage structure alters how complexity affects stability of ecological networks, Ecol. Lett.14(1) (2011), pp. 75-79. |
| [37] | Salceanu, P.L. and Smith, H.L., Lyapunov exponents and persistence in discrete dynamical systems, Discrete Contin. Dyn. Syst. Ser. B12(1) (2009), pp. 187-203. · Zbl 1175.34067 |
| [38] | Scharf, F.S., Juanes, F., and Rountree, R.A., Predator size-prey size relationships of marine fish predators: interspecific variation and effects of ontogeny and body size on trophic-niche breadth, Mar. Ecol. Prog. Ser.208 (2000), pp. 229-248. |
| [39] | Sharpe, R.V. and Aviles, L., Prey size and scramble vs. contest competition in a social spider: implications for population dynamics, J. Anim. Ecol.85(5) (2016), pp. 1401-1410. |
| [40] | Stenseth, N.C., Ehrich, D., Rueness, E.K., Lingjærde, O.C., Chan, K.S., Boutin, S., O’Donoghue, M., Robinson, D.A., Viljugrein, H., and Jakobsen, K.S., The effect of climatic forcing on population synchrony and genetic structuring of the Canadian lynx, Proc. Natl. Acad. Sci.101(16) (2004), pp. 6056-6061. |
| [41] | Werner, E.E. and Gilliam, J.F., The ontogenetic niche and species interactions in size-structured populations, Annu. Rev. Ecol. Syst.15(1) (1984), pp. 393-425. |
| [42] | Yakubu, A.A., Two-patch dispersal-linked compensatory-overcompensatory spatially discrete population models, J. Biol. Dyn.1(2) (2007), pp. 157-182. · Zbl 1122.92070 |
| [43] | Zipkin, E.F., Kraft, C.E., Cooch, E.G., and Sullivan, P.J., When can efforts to control nuisance and invasive species backfire?, Ecol. Appl.19(6) (2009), pp. 1585-1595. |
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