This activity uses a simple pencil and paper simulation of a predator population and that of its primary prey. Students will discover the inextricable link between the two populations in this surprisingly realistic and involving activity.

• Flat surface, at least two feet square
• Colored tape or masking tape
• 300 one-inch paper squares (snowshoe hares)
• 1 three-inch cardboard square (golden eagle)
• Graph paper
• Population data table (see example of data table below)

Use the tape to delineate a square, two feet on a side, on a table top or other flat surface. The square represents the area inhabited by a population of snowshoe hares. Cut out and decorate with appropriate images, the 300 paper hares and the cardboard eagle (these numbers are for each group conducting the simulation). A paper cutter is an indispensable asset at this stage.

Prepare a data table to record the population tallies by following the example below. Allow for 20 to 25 generations.

1. Begin the simulation by populating the habitat with three hares—spatially dispersed within the square.
2. Toss the cardboard eagle into the square in an effort to capture (i.e., land on any portion of) as many hares as possible. In order to survive and reproduce, the eagle must capture at least three hares when tossed. With the hare population at this stage, eagle survival is virtually impossible. Remove any hares captured and enter the tallies for the first generation.
3. The hare population doubles between generations—multiply "Hares Remaining" by two and enter the resulting number in the "Number of Hares" column for the second generation. If no eagle survived the previous generation another moves into the area. Toss the newly recruited eagle—repeating step 2. Remove any captured hares and enter the new tallies.
4. By generation 5 the eagle should be able to capture three hares when tossed. If successful, the eagle survives until the next generation and also produces offspring (one per each three hares captured). Toss the eagle square once for each eagle.
5. As the population builds it is important to separately tally each eagle’s kills, removing captured hares after each eagle is tossed. Determine eagle survival and reproduction using individual eagle capture numbers. Remember, eagles produce one offspring for each three hares captured. If an eagle captures seven hares, three eagles enter the next generation—the original eagle and two offspring. Individual eagle capture numbers should be tallied on a separate sheet of paper and only totals entered in the table.
6. Between generations 9 and 11, the populations will probably crash back to, or near, zero. If and when this happens be sure to begin subsequent generations with at least three hares. Carry the simulation through 18–20 generations, by which time the cycle will be well on its way to repeating and the next few generations can be (relatively accurately) predicted.

The data are best analyzed graphically. For each animal make a plot of population totals (the first two columns) versus generation number. By plotting the hare population and the eagle population side by side on the same graph, the relationship between the two becomes abundantly clear.

The most evident pattern is the near exponential initial increase in the prey (hare) population followed by a proportional increase in the predator (eagle) population. Students should note the lag time between the two populations. The predator population responds directly to fluctuations in the prey population—recovery follows recovery and crash follows crash.

Students should keep in mind that, as in any simulation (even sophisticated computer models), certain assumptions are made and many variables overlooked. Natural populations are subject to myriad pressures and disturbances such as immigration, emigration, overgrazing, disease, floods, droughts, fires, and extreme cold spells—to name a few. Many of these factors compound each other. Disease spreads more easily as population density increases. Hares intensively competing for food in overpopulated areas will be less able to resist droughts or freezes. The enormous complexity of a relatively simple system is mind-boggling.

If several groups are conducting the simulation, you may wish to introduce other variables. Disease or fire could reduce the hare population at any stage in the cycle. Human activity could impact either population. Ask the students to imagine the outcome if the eagles were to go extinct. Note the well-known impact on deer populations throughout North America—populations no longer regulated by natural predators. Studies have shown that natural predation pressure maintains the overall health and size of prey populations at optimal levels.