SimuLab 9: The Deer Program and Population Dynamics

The Deer program (see Java Applet Page, uses the 2-dimensional random walk to model the variations that occur in a deer population. A deer moves randomly on a field, eating the grass wherever it steps. Grass grows back in each eaten square after a certain amount of time. (Time is measured in steps: in one time step, every deer takes one random step.)

Will the deer population grow or decline? A deer dies if it takes a specified number of steps in a row onto squares where the grass has been eaten and has not yet grown back. Every live deer has an offspring after another specified number of steps.

1. Bring up the Deer program. On the left you should see the control window, on the right a green field.


2. After reading the introduction under Describe, create a single deer by clicking the cursor in the middle of the field.


3. Start the program by clicking on Go.


4. Select Show Graph under the Control menu. The top portion of the graph shows the number of deer present in the field; the bottom portion the percentage of grass still alive on the field.


5. If at any time you want to stop the program, press the Pause button.

                        

Q3.42: What happens to the size of your deer population? Does it grow and grow? Does it increase, then decrease? Does it die out?

Q3.43: Suppose you started again with a deer in exactly the same position. Would the population at every step of the second run be exactly the same as the first? Would the final result be the same?

Now you are going to place a dozen deer in the field and let the program run as before. Before doing this, write down your predictions about what will happen:

Will the initial population growth be different for 12 deer than for one deer? Will the final outcome be different for 12 deer than for one deer?

Now start the program as before, but this time click at a dozen different points on the field. Then start the program by clicking outside the field.

Q3.44: What happens to a deer that wanders off, say, the right-hand side of the field?

Q3.45: Q45: Look back at your predictions for 12 deer. Were your predictions correct?

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