Stage 5: Bonus section: re-visiting the classic predator-prey model.

In this tutorial, I began by sticking faithfully to the mathematical form of the traditional Lotka-Volterra predator-prey model, but I designed the System Dynamics diagram to put more emphasis on biological processes. Thus, I used four flow arrows, representing reproduction and mortality processes for the two populations, even though these were not explicitly mentioned in the original model: all we had were two rate-of-change equations. This reflects my personal attitude to modelling, that it should begin as a conceptual design activity, rather than being driven by mathematical notation.

Nevertheless, there will be times when you come across a model expressed as a set of differential equations, and you feel you have neither the inclination nor ability to re-express it in terms of biological process, represented as separate flows. What can you do?

Well, it’s really pretty straightforward All you have to do is to follow these four simple steps:

  • Create one compartment for each state variable
  • Make a single inflow for each compartment
  • Draw influence arrows from compartments to inflows, as required by the differential equations.
  • Enter each differential equation into the flow for the corresponding state variable

Let’s see this in action:

Step 1
Start a new model.
Step 2
Add two compartments, and re-label them X and Y respectively.
Step 3
Add a single flow into each compartment, and re-label them dXdt and dYdt respectively.
Step 4
Draw influence arrows from both compartments to both flows (i.e. four arrows in total).

Your model diagram should now look like this:

Step 5
Enter the following expressions into the flows:
  • dXdt : 0.5*X - 0.01*X*Y
  • dYdt : 0.01*0.01*X*Y - 0.2*Y
Step 6
Build and run the model!