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Stoichiometric Plant-Herbivore Models and Their Interpretation

1. Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804
2. Aquatic Microbiology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 127, 1018 WS Amsterdam
3. Department of Biology, Arizona State University, Tempe, AZ 85287-1501

The purpose of this note is to mechanistically formulate a mathematically tractable model that specifically deals with the dynamics of plant-herbivore interaction in a closed phosphorous (P) limiting environment. The key to our approach is the employment of the plant cell P quota and the Droop equation for its growth. Our model takes the simple form of a system of two autonomous ordinary differential equations. It can be shown that our model includes the LKE model (Loladze, Kuang and Elser (2000)) as a special case. Our study reveals that the details of ecological stoichiometry models really matter for quantitative predictions of plant-herbivore dynamics, especially at intermediate ranges of the carrying capacity.
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Keywords predator-prey model; stoichiometry; phosphorus uptake.; logistic equation; Droop model

Citation: Yang Kuang, Jef Huisman, James J. Elser. Stoichiometric Plant-Herbivore Models and Their Interpretation. Mathematical Biosciences and Engineering, 2004, 1(2): 215-222. doi: 10.3934/mbe.2004.1.215

 

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