American Institute of Mathematical Sciences

Advanced
2004, 1(2): 215-222. doi: 10.3934/mbe.2004.1.215

Stoichiometric Plant-Herbivore Models and Their Interpretation

Yang Kuang 1, , Jef Huisman 2, and  James J. Elser 3,

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, Netherlands
3. 

Department of Biology, Arizona State University, Tempe, AZ 85287-1501, United States

Received  May 2004 Published  July 2004

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.
Keywords: predator-prey model, stoichiometry, phosphorus uptake., logistic equation, Droop model.
Mathematics Subject Classification: 92D25 and 34C6.
Citation: Yang Kuang, Jef Huisman, James J. Elser. Stoichiometric Plant-Herbivore Models and Their Interpretation. Mathematical Biosciences & Engineering, 2004, 1 (2) : 215-222. doi: 10.3934/mbe.2004.1.215
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