Stoichiometric Plant-Herbivore Models and Their Interpretation

Yang Kuang; Jef Huisman; James J. Elser; Yang Kuang; Jef Huisman; James J. Elser

doi:10.3934/mbe.2004.1.215

Mathematical Biosciences and Engineering

2004, Volume 1, Issue 2: 215-222. doi: 10.3934/mbe.2004.1.215

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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

Received: 01 May 2004 Accepted: 29 June 2018 Published: 01 July 2004
MSC : 92D25 and 34C60.

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.
- 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[J]. Mathematical Biosciences and Engineering, 2004, 1(2): 215-222. doi: 10.3934/mbe.2004.1.215

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Abstract

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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