Trophic structure and dynamical complexity in simple ecological models |
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| Affiliation: | 1. Department of Biology, Laurentian University, Ramsey Lake Road, Sudbury, Ontario, Canada P3E 2C6;2. Department of Environmental Biology, University of Guelph, Guelph, Ontario, Canada N1G 2W1;3. Department of Applied Mathematics, Indian School of Mines University, Dhanbad, Jharkhand 826004, India;4. Department of Applied Mathematics, HMR Institute of Technology and Management, GT Karnal Road, Delhi 110 036, India;1. Water Problems Institute, Russian Academy of Sciences, 3 Gubkina Str., Moscow 119333, Russian Federation;2. Max Planck Institute for Terrestrial Microbiology, Karl-von-Frisch-Strasse 10, 35043 Marburg, Germany;1. State Key Laboratory of Mycology, Institute of Microbiology, Chinese Academy of Sciences, No. 3, 1st Beichen West Road, Chaoyang District, Beijing, 100101, China;2. Westerdijk Fungal Biodiversity Institute, Uppsalalaan 8, 3584, CT, Utrecht, the Netherlands;3. State Key Laboratory of Microbial Resources, Institute of Microbiology, Chinese Academy of Sciences, Beijing, China;1. Faculty of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400045, PR China;2. Key Laboratory of the Three Gorges Reservoir’s Eco-Environments, Ministry of Education, Chongqing University, Chongqing 400045, PR China;1. Dipartimento di Matematica “F. Casorati”, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy;2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany;3. Dipartimento di Matematica “F. Enriques”, Università di Milano, Via Saldini 50, 20133 Milano, Italy;4. Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany |
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| Abstract: | We study the dynamical complexity of five non-linear deterministic predator–prey model systems. These simple systems were selected to represent a diversity of trophic structures and ecological interactions in the real world while still preserving reasonable tractability. We find that these systems can dramatically change attractor types, and the switching among different attractors is dependent on system parameters. While dynamical complexity depends on the nature (e.g., inter-specific competition versus predation) and degree (e.g., number of interacting components) of trophic structure present in the system, these systems all evolve principally on intrinsically noisy limit cycles. Our results support the common observation of cycling and rare observation of chaos in natural populations. Our study also allows us to speculate on the functional role of specialist versus generalist predators in food web modeling. |
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