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WA-TOR A Predator-Prey Simulation This program is an implementation of the Wa-Tor world simulation described by A. K. Dewdney in his "Computer Recre- ations" column in the Scientific American, December, 1984, pp. 14-22. For a more complete discussion, you should see that article. Essentially, it simulates the behavior of a simple system of two species, predators ("sharks") and their prey ("fish"). According to Dewdney, the simulation was originally imple- mented by David Wiseman on a VAX, using an "ocean" of 80-by-23 points. Dewdney's own version for a PC used five arrays to keep track of the positions and properties of the sharks and fish in a "humbler, 32-by-14 ocean," and he reports it to be "rather slow." Late in the article, Dewdney suggested that it might be made to run faster if it were built on linked lists instead of arrays. Wanting an exercise in the use of pointers and lists in Turbo Pascal, that is how I made it. It uses a 50-by-25 ocean, and writes directly to the screen for speed. What it Does There are three parts to the program. 1. Some introductory information appears, and you are then asked to specify certain parameters. Here they are (with my suggestions for values to use in the first run): - Fish breeding time (try 2) - Shark breeding time (try 7) - Shark starvation time --how long they can hold out between meals (try 3) - Initial number of fish (try 500) - Initial number of sharks (try 100) - Do you want a record kept (answer Y) The simulation then begins. You see the fish (dots) and the sharks (exclamation points) move and breed. (A newborn shark is a bright apostrophe and stays that way until after it catches a fish.) And you get various statistics along the sides of the display. The display will run indefinitely. You stop it by pressing any key, after which it will complete its current cycle and Wa-Tor: a Predator-Prey Simulation Page 2 stop. At this point, you get a choice. You can quit or, if you've asked that a record be kept, you can choose one of the following: 2. If you have the color/graphics board, you can ask for a graph of the first 320 cycles (they are called "Chronons," which is the time unit on Wa-Tor). The graph will appear on the screen without text. If you want it printed on paper (and have a suitable printer), press P. If you don't want the graph printed out, press anything else. 3. Even if you aren't equipped for graphs, you can get a table of the statistics, chronon by chronon. At your choice, you can have it printed out or page through it on the screen. What You Need to Work it: To run the program, put the files WA-TOR.COM and WA-TOR.000 on a disk in the default drive and enter WA-TOR from the DOS prompt. To get the best out of WA-TOR, you need a color/graphics board (though a green monitor is sufficient --that's what I have, so there's no color in the program). It looks fine on a text monitor with the monochrome display board, but, of course, you can't get it to show you a graph. If you want the graphs printed out, you must run the DOS 2 GRAPHICS command before you start WA-TOR. The printed graph is got by a Print-Screen (don't do it from the keyboard --the pro- gram does it better), so you can't get the printed graph unless you are equipped for screen graphics. The GRAPHICS command will set up an IBM or Epson graphics printer to do it. I'm sure there are other graphics programs that work on other printers, but I can't help you about that. Since the program works by printing to the screen memory directly, it may not work on all PC clones. I can report that it runs fine on a Compaq, both under IBM DOS 2.10 and under Compaq's version of MS-DOS 1.10. One trick: to keep its records, WA-TOR makes a file called WA-TOR.DAT on the default disk. If you want to keep the files for reference, rename them before you make another run keeping records. To print one out, you must rename it back to WA-TOR.DAT and run WA-TOR >>without<< keeping records. You can hurry past the simulation display by just hitting <ENTER> for all the pa- rameters and answering N to "Keep a record?" It will then offer you the usual print-out options, and it will make its graph and table from whatever is in WA-TOR.DAT on the default disk. Wa-Tor: a Predator-Prey Simulation Page 3 Comments & Suggestions: Essentially, the "ocean" is a rectangular grid. Each crea- ture can move in only four directions, one step each chronon. The fish aren't very interesting, they move simply at random into unoccupied adjoining places. When they breed, they simply divide. (Everything on Wa-Tor is parthenogenic). If there's no empty place for them, they neither move nor breed. I've put a few tricks into the sharks, however. They have just enough in- telligence to catch a fish if one adjoins. Otherwise, they move at random, unless completely surrounded by other sharks. They breed by calving. The calf emerges alongside its mother (pro- vided there's an empty place for it). It's fully fed, but the mother is not, and has paid a certain price for breeding in that she has lost a chance to feed, because she cannot move and catch a fish in that chronon. The calf stays in its immature condition and does not start its breeding cycle until it catches a fish. You can see this because they change to the mature (exclamation point) form in the next chronon. The interesting thing is to vary the parameters and see what difference it makes. I've hardly explored the possibilities, but I can see a couple of tendencies. Initially, both sharks and fish are distributed randomly in the ocean, and they have ran- domly assigned stages in their breeding cycles and (for the sharks) randomly assigned degrees of hunger. Generally, there's a big explosion and then a severe crash in the shark population when you start, because the sharks are distributed more or less evenly among the fish. After the first recovery, the sharks are likely to be unevenly placed, and you begin to get local explo- sions and crashes, so the swings in the totals are liable to be smaller, though that depends on the parameters. One curious development: the tougher the sharks, the worse the crashes. The parameters I've suggested above usually give a fairly severe initial crash, but then the swings damp out. If you let the sharks go four or five chronons between meals, they seem much more likely to fish out the whole ocean and become extinct. So, it seems that weaker sharks are fitter to survive, but how could a species evolve that way? Naturally, the stronger the fish --the more frequently they breed, the more sharks they will support. I did some runs with the fish breeding every chronon, sharks breeding every ten and lasting three chronons between meals, with the result that the shark population oscillated gently between about 140 and 300. I've included the source code in WA-TOR.PAS. If you have a Pascal compiler you might try to vary other properties of the Wa-Tor: a Predator-Prey Simulation Page 4 sharks. Dewdney suggests several possibilities. One might also try adding a second predator. Duplicate my shark list with another, giving them a distinct symbol in the Procedure Markit case structure, and allow the user to assign different proper- ties. Then, see how they compete. Or, you might take the in- telligence out of a predator (make them move just like the fish), and see what happens under various combinations of breeding and starving times.