Tri-Trophic Model

This model contains three trophic levels (e.g. a plant, R, an herbivore,N, and a carnivore, P). Compare with book Figures 11.1 and 11.2 and Box 11.1. The model implemented on this page has only linear (Type I) functional responses (similar to the Chase et al 2000 model in box 11.1 but unlike the Oksanan et al. (1981) model. Also this model has only exponential growth with no logistic density dependence. Therefore some of the isoclines cannot curve as in the Oksanen model (Figure 11.1). Parameters include:

The supply rate, S, and death rate, c_R for the resource
conversion efficiency f_N, attack rate, a_N and death rate, c_N for the herbivore
conversion efficiency f_P, attack rate, a_P and death rate, c_P for the predator

In this model the predator can be made to go extinct, but when not extinct, the preadtor and resource increase or decrease together, while the herbivore population size is independent.

To run the model set the initial abundances in the top, orange box, and then click the "Start Dynamics Button". The isocline graph can be rotated by clicking and dragging on it.

\begin{gather*} \frac{dR}{dt} = S- a_N N R - c_R R\\ \frac{dN}{dt} = f_N a_N N R-a_P P N - c_N N \\ \frac{dP}{dt} = f_P a_P N P -c_P P \end{gather*}