Before you Begin: Reasoning Through the Model
Consider a natural environment in which predators feed on prey. In any such environment, certain factors determine the populations of both predator and prey. Unlike the first population model you considered, here two populations interact. The population of the predator helps to determine the population of the prey and vice versa.
1. What factors would affect the populations of each group if the other group did not exist? (Review the population worksheet.)
2. How would the population of the prey react to an increase in the population of the predator? How would the population of the prey react to a decrease in the population of the predator?
3. Why would the population of the predator also depend upon the population of the prey?
4. How would the populations affect each other if they were in an unlimited area as opposed to an enclosed area? Would this be an important consideration in modeling the populations? Why?
5. How would a sudden or unexpected drop in the predator population affect the system?
Using the Model: Access the Model at http://www.shodor.org/succeed/models/lynx/
In this model, a lynx population interacts with a hare population. Since lynx hunt hares, the hare population depends on the number of lynx present. And since lynx rely on hares for food, the lynx population depends on how many hares are available to eat. If there are no hares to eat, the lynx will starve.
1. Run the model in simple form with the default options. Observe the graphs. About how many lynx are there initially? How many are there at the end? How many hares are there at the beginning and end? Describe what the graph looks like.
In this model, the birth rates for both populations are in a fraction form. For example, a birth rate of 0.25 means that each member of a population would have 0.25 babies in a given time. Since no one can have 0.25 babies, it makes more sense to express this number as 1 baby per 4 people, or 250 babies per 1000 people. It's all the same.
2. Increase the lynx birth rate to 1. What does this birth rate mean? Describe the resulting graph.
3. Click on "Erase this run" at the bottom of the web page. Run the model again using the default values. Then change the hare birth rate to 0.75. Compare the pairs of graphs that resulted from the two runs. Think of some reasons for the changes you observe.
4. Click on "Erase this run." Change the run time to 100 years. Change the time step to 0.125 if it does not read this now. What trend do you observe in the resulting graphs?
5. Look at the STELLA diagram for the model. What factors affect the number of hare deaths?
6. Does hare density affect the number of lynx deaths? How?
7. Does hare density affect the number of hare deaths? How?
8. What does the "Unexpected Lynx Deaths" mean? What might be a cause of this in the real world?
9. How do these unexpected deaths affect the model? What would happen if there were no unexpected deaths? Try it using the model. What do the resulting graphs look like?
10. Switch to the advanced form of the model. Under "Plotting Options," change the y-minimums of both graphs to zero, and the y-maximums to 60,000. What happens to the graphs? Does the graph of the lynx population mean that the population is more constant? Why or why not?
Follow-Up Questions:
1. Do you think that this model is an accurate simulation of how lynx and hare populations interact? Why or why not?
2. What are some factors you could add to the model to make it more realistic? For instance, consider adding food for the hares to the model (grasshoppers or carrots, for example).
3. Do you think it would be possible to model an entire ecosystem? Why or why not?