Fixed point sensitivity analysis of interacting structured populations |
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| Affiliation: | 1. Department of Ecology and Evolutionary Biology, University of Michigan, 830 North University, Ann Arbor, MI 48109-1048, United States;2. Department of Biological Physics, Eötvös Loránd University, Pázmány Péter sétány 1A, H-1117, Budapest, Hungary;1. Department of Welding Engineering Technology, College of Industrial Technology, King Mongkut''s University and Technology North Bangkok, Bangkok 10800, Thailand;2. Welding Engineering and Metallurgical Inspection, Science and Technology Institute, King Mongkut''s University and Technology North Bangkok, Bangkok 10800, Thailand;3. Department of Physics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand;4. Department of Materials Science and Engineering, Faculty of Engineering, National University of Singapore, Singapore 117576, Singapore;5. Department of Materials Science, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand;1. Department of Mathematics, College of Science, Bengbu University, 1866 Caoshan Rd., Bengbu 233030, PR China;2. Department of Mathematics, College of Science, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai 201620, PR China;1. Department of Biology, University of North Carolina, Chapel Hill, United States;2. Department of Operations and Decision Technologies, Indiana University, Kelley School of Business, United States;1. Institute of Condensed Matter Physics, Hochschulstraße 6, 64289 Darmstadt, Germany;2. Institute for Biodiversity and Ecosystem Dynamics, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands;1. Department of Physics, University of Gothenburg, SE-412 96 Gothenburg, Sweden;2. Institut für Genetik, Universität zu Köln, 50674 Köln, Germany;3. Department of Zoology, University of Cambridge, CB2 3EJ Cambridge, UK;4. Integrative Systems Biology Lab, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia;5. The Linnaeus Centre for Marine Evolutionary Biology, University of Gothenburg, SE-405 30 Gothenburg, Sweden |
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| Abstract: | Sensitivity analysis of structured populations is a useful tool in population ecology. Historically, methodological development of sensitivity analysis has focused on the sensitivity of eigenvalues in linear matrix models, and on single populations. More recently there have been extensions to the sensitivity of nonlinear models, and to communities of interacting populations. Here we derive a fully general mathematical expression for the sensitivity of equilibrium abundances in communities of interacting structured populations. Our method yields the response of an arbitrary function of the stage class abundances to perturbations of any model parameters. As a demonstration, we apply this sensitivity analysis to a two-species model of ontogenetic niche shift where each species has two stage classes, juveniles and adults. In the context of this model, we demonstrate that our theory is quite robust to violating two of its technical assumptions: the assumption that the community is at a point equilibrium and the assumption of infinitesimally small parameter perturbations. Our results on the sensitivity of a community are also interpreted in a niche theoretical context: we determine how the niche of a structured population is composed of the niches of the individual states, and how the sensitivity of the community depends on niche segregation. |
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| Keywords: | Coexistence Matrix models Robustness |
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