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The effect of seasonal strength and abruptness on predator-prey dynamics. (English) Zbl 07185526
There is empirical evidence of a sharp reaction of species to the seasonality of the environment; the shape of the forcing signal cannot be ignored as a simple modeling detail without further investigation of its contribution to population dynamics. Authors evaluate the influence of the sharpness of the seasonal transition on the dynamic behavior of the predator-prey community. Taking into account the potential effect of snow properties on the level of predation, a more or less drastic seasonal effect on the rate of detection of predators is modeled. First follows a brief study of the response to sinusoidal stimulation on detection rate, simulating seasonal changes in a predator’s ability to hunt successfully. Then, the combined effect of the seasonal parameter value and the shape (from sinusoidal to rectangular) of the seasonal impact on the rate of detection of predators is studied, and it is checked whether the arising differences between the impact forms of the signal variance are explained. Thus, since the implementation of sharper seasonal shifts leads the community dynamics to bifurcations and chaotic dynamics due to the lower strength of the seasonal forcing, the form of seasonal forcing stands out as a factor contributing to density fluctuations and the type of observed dynamic behavior.
92D25 Population dynamics (general)
92D40 Ecology
34C23 Bifurcation theory for ordinary differential equations
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[1] Barraquand, F.; Louca, S.; Abbott, K. C.; Cobbold, C. A.; Cordoleani, F.; DeAngelis, D. L.; Elderd, B. D.; Fox, J. W.; Greenwood, P.; Hilker, F. M.; others, Moving forward in circles: challenges and opportunities in modelling population cycles, Ecol. Lett., 20, 8, 1074-1092 (2017)
[2] Bibik, Y. V., Investigation of transition to chaos for a Lotka Volterra system with the seasonality factor using the dissipative Henon map, Appl. Math. Sci., 9, 117, 5801-5837 (2015)
[3] Bilodeau, F.; Gauthier, G.; Berteaux, D., Effect of snow cover on the vulnerability of lemmings to mammalian predators in the Canadian Arctic, J. Mammal., 94, 4, 813-819 (2013)
[4] Bjørnstad, O. N.; Falck, W.; Stenseth, N. C., A geographic gradient in small rodent density fluctuations: a statistical modelling approach, Proc. R. Soc. London. Ser. B, 262, 1364, 127-133 (1995)
[5] Copernicus Climate Change Service (C3S), 2017. ERA5: Fifth generation of ECMWF atmospheric reanalyses of the global climate. Copernicus Climate Change Service Climate Data Store (CDS). https://cds.climate.copernicus.eu/cdsapp. accessed 13-December-2019.
[6] Dercole, F.; Rinaldi, S., Dynamical systems and their bifurcations, Adv. Method. Biomed. Signal Process., 291-325 (2011)
[7] Dhooge, A.; Govaerts, W.; Kuznetsov, Y. A., MATCONT: a MATLAB package for numerical bifurcation analysis of ODEs, ACM Trans. Math. Softw. (TOMS), 29, 2, 141-164 (2003)
[8] Doedel, E. J., AUTO: A program for the automatic bifurcation analysis of autonomous systems, Congressus Numerant., 30, 265-284, 25-93 (1981)
[9] ECMWF, Part IV: physical processes, IFS Documentation CY43R1. IFS Documentation CY43R1, IFS Documentation (2016), ECMWF
[10] Fauteux, D.; Gauthier, G.; Berteaux, D., Seasonal demography of a cyclic lemming population in the canadian arctic, J. Anim. Ecol., 84, 5, 1412-1422 (2015)
[11] Gilg, O.; Hanski, I.; Sittler, B., Cyclic dynamics in a simple vertebrate predator-prey community, Science, 302, 5646, 866-868 (2003)
[12] Gragnani, A.; Rinaldi, S., A universal bifurcation diagram for seasonally perturbed predator-prey models, Bull. Math. Biol., 57, 5, 701-712 (1995)
[13] Greenman, J.; Benton, T., Large amplification in stage-structured models: Arnol’d tongues revisited, J. Math. Biol., 48, 6, 647-671 (2004)
[14] Greenman, J.; Kamo, M.; Boots, M., External forcing of ecological and epidemiological systems: a resonance approach, Physica D, 190, 1-2, 136-151 (2004)
[15] Hanski, I.; Turchin, P.; Korpimäki, E.; Henttonen, H., Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos, Nature, 364, 6434, 232 (1993)
[16] Hansson, L.; Henttonen, H., Gradients in density variations of small rodents: the importance of latitude and snow cover., Oecologia, 67, 394-402 (1985)
[17] Inoue, M.; Kamifukumoto, H., Scenarios leading to chaos in a forced Lotka-Volterra model, Progr. Theor. Phys., 71, 5, 930-937 (1984)
[18] Ireland, J. M.; Norman, R.; Greenman, J., The effect of seasonal host birth rates on population dynamics: the importance of resonance, J. Theor. Biol., 231, 2, 229-238 (2004)
[19] King, A.; Schaffer, W. M.; Gordon, C.; Treat, J.; Kot, M., Weakly dissipative predator-prey systems, Bull. Math. Biol., 58, 5, 835-859 (1996)
[20] King, A. A.; Schaffer, W. M., The rainbow bridge: hamiltonian limits and resonance in predator-prey dynamics, J. Math. Biol., 39, 5, 439-469 (1999)
[21] King, A. A.; Schaffer, W. M., The geometry of a population cycle: a mechanistic model of snowshoe hare demography, Ecology, 82, 3, 814-830 (2001)
[22] Korslund, L.; Steen, H., Small rodent winter survival: snow conditions limit access to food resources, J. Anim. Ecol., 75, 1, 156-166 (2006)
[23] Kuang, Y., Nonuniqueness of limit cycles of Gause-type predator-prey systems, Appl. Anal., 29, 3-4, 269-287 (1988)
[24] Kuznetsov, Y. A.; Muratori, S.; Rinaldi, S., Bifurcations and chaos in a periodic predator-prey model, Int. J. Bifurcat. Chaos, 2, 1, 117-128 (1992)
[25] Magnhagen, C., Predation risk as a cost of reproduction, Trend. Ecol. Evolut., 6, 6, 183-186 (1991)
[26] Mott, R.; Vionnet, V.; Grünewald, T., The seasonal snow cover dynamics: review on wind-driven coupling processes., Front. Earth Sci., 6, 197 (2018)
[27] Pau, S.; Wolkovich, E. M.; Cook, B. I.; Davies, T. J.; Kraft, N. J.; Bolmgren, K.; Betancourt, J. L.; Cleland, E. E., Predicting phenology by integrating ecology, evolution and climate science, Glob. Chang. Biol., 17, 12, 3633-3643 (2011)
[28] Penczykowski, R. M.; Connolly, B. M.; Barton, B. T., Winter is changing: trophic interactions under altered snow regimes, Food Webs, 13, 80-91 (2017)
[29] Probst, R.; Nemeschkal, H.; McGrady, M.; Tucakov, M.; Szép, T., Aerial hunting techniques and predation success of Hobbies Falco subbuteo on Sand Martin Riparia riparia at breeding colonies, Ardea, 99, 1, 9-17 (2011)
[30] Reynolds, J. J.H.; Sherratt, J. A.; White, A.; Lambin, X., A comparison of the dynamical impact of seasonal mechanisms in a herbivore-plant defence system, Theor. Ecol., 6, 2, 225-239 (2013)
[31] Rinaldi, S.; Muratori, S., Conditioned chaos in seasonally perturbed predator-prey models, Ecol. Modell., 69, 1-2, 79-97 (1993)
[32] Rinaldi, S.; Muratori, S.; Kuznetsov, Y., Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities, Bull. Math. Biol., 55, 1, 15-35 (1993)
[33] Rosenzweig, M. L.; MacArthur, R. H., Graphical representation and stability conditions of predator-prey interactions, Am. Nat., 97, 895, 209-223 (1963)
[34] Sabin, G. C.; Summers, D., Chaos in a periodically forced predator-prey ecosystem model, Math. Biosci., 113, 1, 91-113 (1993)
[35] Saino, N.; Ambrosini, R.; Rubolini, D.; von Hardenberg, J.; Provenzale, A.; Hüppop, K.; Hüppop, O.; Lehikoinen, A.; Lehikoinen, E.; Rainio, K.; others, Climate warming, ecological mismatch at arrival and population decline in migratory birds, Proc. R. Soc. B, 278, 1707, 835-842 (2010)
[36] Sonerud, G. A., Effect of snow cover on seasonal changes in diet, habitat, and regional distribution of raptors that prey on small mammals in boreal zones of Fennoscandia., Ecography, 9, 33-47 (1986)
[37] Stenseth, N. C.; Shabbar, A.; Chan, K.-S.; Boutin, S.; Rueness, E. K.; Ehrich, D.; Hurrell, J. W.; Lingjærde, O. C.; Jakobsen, K. S., Snow conditions may create an invisible barrier for lynx, Proc. Natl. Acad. Sci., 101, 29, 10632-10634 (2004)
[38] Stollenwerk, N.; Sommer, P. F.; Kooi, B.; Mateus, L.; Ghaffari, P.; Aguiar, M., Hopf and torus bifurcations, torus destruction and chaos in population biology, Ecol. Complex., 30, 91-99 (2017)
[39] Taylor, R. A.; Sherratt, J. A.; White, A., Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator-prey model, J. Math. Biol., 67, 6-7, 1741-1764 (2013)
[40] Taylor, R. A.; White, A.; Sherratt, J. A., How do variations in seasonality affect population cycles?, Proc. R. Soc. B, 280, 1754, 20122714 (2013)
[41] Therrien, J.-F.; Gauthier, G.; Pinaud, D.; Bêty, J., Irruptive movements and breeding dispersal of snowy owls: a specialized predator exploiting a pulsed resource, J. Avian Biol., 45, 6, 536-544 (2014)
[42] Tornberg, R., Prey selection of the goshawk Accipiter gentilis during the breeding season: the role of prey profitability and vulnerability, Ornis Fennica, 74, 1, 15-28 (1997)
[43] Turchin, P., Population Regulation: Old Arguments and a New Synthesis, (Cappuccino, N.; Price, P. W., Population Dynamics: New Approaches and Synthesis (1995), Academic Press: Academic Press New York), 19-39
[44] Turchin, P.; Hanski, I., An empirically based model for latitudinal gradient in vole population dynamics, Am. Nat., 149, 5, 842-874 (1997)
[45] Tyson, R.; Lutscher, F., Seasonally varying predation behavior and climate shifts are predicted to affect predator-prey cycles, Am. Nat., 188, 5, 539-553 (2016)
[46] Vandermeer, J., Seasonal isochronic forcing of Lotka-Volterra equations, Progr. Theor. Phys., 96, 1, 13-28 (1996)
[47] Vandermeer, J.; Stone, L.; Blasius, B., Categories of chaos and fractal basin boundaries in forced predator-prey models, Chaos Soliton. Fractal., 12, 2, 265-276 (2001)
[48] Wiesenfeld, K., Noisy precursors of nonlinear instabilities, J. Stat. Phys., 38, 5-6, 1071-1097 (1985)
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