I have provided you with a simple simulation, COYOTE. The simulation is inspired by Dewdney 1984, but the animals have been changed to provide a Southwestern feel. I'd like you to experiment with the simulation.
Here are the rules of the simulation. The world consists of a grid of which each square may be occupied by one coyote, one rabbit, or nothing. You may specify the size of the world (the number of rows and columns in the grid, up to 80x22). Time passes in arbitrary units called cronons. For interpretive purposes, you may associate these units with some kind of real-world units like days or weeks. In our model, rabbits don't need to eat and they reproduce asexually with a reproductive period that you set. That is, every x chronons, each rabbit produces an offspring into a random adjacent square. Rabbits die only by being eaten by coyotes. Coyotes must eat rabbits; if they don't eat a rabbit within the starvation period that you specify, they die. Coyotes also reproduce asexually with a reproductive period that you specify. Rabbits move randomly. Each chronon each rabbit moves at random to an adjacent grid square. A coyote occupying a square adjacent to a rabbit will move into the rabbit's square and eat the rabbit. Coyotes not adjacent to rabbits move randomly like rabbits. (A rabbit or coyote moving off the grid ends up in the appropriate spot on the opposite edge.) Finally, you get to specify the initial population of the rabbits and coyotes. On the screen coyotes are represented by large squares, rabbits by dots.
Writeup: Make some qualitative statements about the sets of parameters that yield relatively persistent systems and those in which the ecological system crashes (either all the coyotes die and rabbits fill the world [the simulation stops at the time all the coyotes die] or all the rabbits die and then all the coyotes die). Experiment with different combinations of rabbit and coyote reproductive and starvation times and with different world sizes. You will want to try a range of values for each, perhaps thinking of realistic values for chronons as days. Notice that the world size does matter as does the initial numbers of coyotes and rabbits. Which are the most and least sensitive parameters. Describe the overall behavior of the system for parameter sets that yield systems that survive for a long period of time. Despite its limitations, how does the simulation reasonably model any real-world behavior of which you are aware. This will take a fair amount of experimentation. Finally, contemplate and describe a strategy for more formally assessing the limits of stability (you do not need to actually do it). While your writeup is limited to 3 double-spaced pages. You should write this in a relatively formal tone, discussing the behavior of the model.
You can download coyote from the ASM566 section of my web site, specifically from http://www.public.asu.edu/~kintigh/simulation/coyote.exe. This program will run in a MS-DOS window under Windows. You can start an MS DOS session and type the DOS commands or do it from the Start menu by selecting Start>Run and typing c:\path\coyote.exe where path\ provides the path (if any) to the program file you have saved. Better yet, try a snazzier Windows version of the same program (with sharks substituted for coyotes and fish for rabbits and a square world) available from Kovatch Computing.