The Geometry of Irregular Forms: Part 2

Suppose I lived on a country estate on which there lived a predator population of foxes and a prey population of grouse (the example given in Stoppard's Arcadia). On this idealized estate, this is the extent of biological diversity. If the foxes were numerous, they would eat most of the grouse, which would become scarce in the short run. But then the foxes would have nothing to eat, and their numbers would decline. With fewer foxes around, the grouse population would recover. In the case of a marginally stable ecological system, the numbers of foxes and grouse would be cyclical and experience population explosions and crashes. An unstable system would have the foxes eat all the grouse to extinction, followed by their own extinction from starvation. But if the system is stable, the fox and grouse populations would eventually settle to an equilibrium state.

I first learned about this interaction between predator and prey populations when I visited Epcot Center (now just "Epcot") in Orlando at the age of eleven. One of the Future World buildings had an interactive computer exhibit, which was pretty futuristic at a time not far removed from when a Pong game console represented the pinnacle of home computing. The exhibit had a bank of computers each running a simulation of a predator/prey system. It let you enter initial populations, and possibly other parameters such as reproductive rate, and then it would display a graph of how the populations would change over many years. Usually, the graphs would have either an exponential-decay shape or a sine-wave shape. I thought this was very cool.