Dynamics of a mechanistically derived stoichiometric producer-grazer model

Hao Wang, Yang Kuang, Irakli Loladze

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


One of the simplest predator-prey models that tracks the quantity and the quality of prey is the one proposed by [I. Loladze, Y. Kuang, and J.J. Elser, Stoichiometry in producer-grazer systems: Linking energy flow with element cycling, Bull. Math. Biol. 62 (2000) pp. 1137–1162.] (LKE model). In it, the ratio of two essential chemical elements, carbon to phosphorus, C:P, represents prey quality. However, that model does not explicitly track P neither in the prey nor in the media that supports the prey. Here, we extend the LKE model by mechanistically deriving and accounting for P in both the prey and the media. Bifurcation diagrams and simulations show that our model behaves similarly to the LKE model. However, in the intermediate range of the carrying capacity, especially near the homoclinic bifurcation point for the carrying capacity, quantitative behaviour of our model is different. We analyze positive invariant region and stability of boundary steady states. We show that as the uptake rate of P by producer becomes infinite, LKE models become the limiting case of our model. Furthermore, our model can be readily extended to multiple producers and consumers.

Original languageEnglish (US)
Pages (from-to)286-296
Number of pages11
JournalJournal of biological dynamics
Issue number3
StatePublished - Jul 2008


  • Droop model
  • Logistic equation
  • Phosphorus uptake
  • Producer-grazer model
  • Stoichiometry

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology


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