Project #7: Predator Prey Simulation

Goals:

1. Learn to interact and interpret a biological model.
1. What does the birth rate [B] mean for the rabbit population?
2. What does the death rate [D] mean for the fox population?
3. What is the best population of foxes for a given starting population of rabbits?
4. What is the effect on the balance of rabbit and foxes populations by changing the interaction coefficient?
2. See an example of a user friendly program [model].
3. Learn to import a graphics created in a DOS application [program] into a word processor.

   Note importing a graph using a windows word processor is just a matter of pressing <PrintScreen> in the DOS application and the Paste button in the word processor- i.e. very easy!

Goal 1A : Introduction to the Simulation Model

• Run the Predator Prey program using Explorer under Windows (double click on the file name). You should use the C1_PRED.EXE (high resolution) which is on your student disk.
• Run the Paint Shop Pro program.
• Using the C1_Pred program
  1. When the program starts to run is reads a file called MODEL to get the parameters of the model you last used.
  2. Read the opening screen and then an option screen lets you change the model parameters.
  3. Select the parameters desired and press G to show the graph of the model.
  4. Save the graph if it is what you want or change parameters and graph again.
  5. When a graph is displayed that you need to save follow the next procedure.
  6. When you exit the program the last parameters set will be saved in the MODEL file.
  7. The latest versions of the program have a V option to change the screen number for a variety of displays. [Use 12]
• The procedure to save a graph that the program produces is :
  1. When the desired graph is displayed press <PrintScreen>. This will save the DOS screen to the clipboard buffer.
  2. Next switch to the Paint Shop Pro window by clicking on it.
  3. Select the Edit option and then Paste. This will paste the contents of the clipboard into the PSP window.
  4. Since the graph is white text on a black background the colors must be reversed. This is done by Selecting Color from the menu , Grey Scale, Then click on Color again and select Negative image.
  5. Then the file can be saved in a format that can be imported into WordPerfect. (.wpg, .tif .bmp, .gif)
• You may also use the JavaScript version of the simulation.
  (Be Patient Java may be starting)

Goal 1B : Exponential Population Growth

Birth Rate Parameters

• First run the program with A set to zero [A = 0]. This means NO fox rabbit interaction. So the rabbit numbers increase without bounds and the poor, hungry foxes die off.
  
• Now find the value for the birth rate, B = _____________, so that the population doubles in 1 year.

Here's how: Set R = 100
PopMax = 500 and Y=5
now change B until R = 200 after one year.


• What is the number of the rabbits at the end of 2 years ? _______________.
  
• What is their number after 3 years? _____________ Capture this graph for your report.
  
• This is called exponential growth! What is the value of B again? _________.
  Using a scientific calculator, what is the value of the natural log of 2? LN(2) = _________________
  Comment. __________________________________________________________

(The blank lines in this writeup are for your help. You will actually hand in a separate report with all these numerical questions answered as well as complete sentence answers for your comments. Moreover, you will import the required graphs into your report.)

Now find the value of D, the fox death rate, for the fox population to decrease to 50% of its value in one year?

Death Rate Parameters

Now find the value of D, the fox death rate , for the fox population to decrease by 50% each year.

Set F=200 and find the D value that give F=100 after one year.
D= ____________________________

Is this like B ? _________________________




Is this like B?____________________________________________________

Find D for a 50% decrease in 2 years?_______________________________

How does this relate to LOG(2) ____________________________________

Goal 1C : Finding the Best Number of Foxes for a Given Number of Rabbits:

• Run the interactive model program.
  
• Set A = 0.003 and keep it constant.

A is the negative affect of the foxes on the rabbits and also the positive affect of the rabbits on the foxes. (Well fed foxes have more kits that live!)

• Start the Rabbits at 400 and the foxes at 25, PopMax at 1000, B = 0.5, and D = 0.7
  
• Run the model
  
• Next change only the number of foxes at the start to 25, then 50, 100, 150, 200.
  
• What happens to the maximum number of rabbits? ______________
  
• Does it change by a big or small percent? __________________
  
• Record the maximum number of rabbits for each starting number of foxes:

Estimate the value of the MAXIMUM NUMBER OF RABBITS for each value of F.
25________, 50________, 100________, 150________, and 200__________

Estimate the value of the MINIMUM NUMBER OF RABBITS for each value of F
Min number of Rabbits :
25________, 50________, 100________, 150________, and 200__________

• Now compute the quality of rabbit life for each starting value of the foxes.(Quality rabbit = 100*Min/Max number of rabbits)

  Compute the RABBIT QUALITY OF LIFE (Min/Max*100):

  25________, 50________, 100________, 150________, and 200__________

  What starting number of foxes maximizes the rabbit quality of life (A=.003) ? ___________

Goal 1D : A Different Interconnection Parameter:

• Let the interaction parameter A = .005. Keep the B = .5 and D=.7 constant.
  
• Now Repeat the simulations in part 1C to find the best starting number of foxes for a maximum rabbit quality of life.

  Foxes	25	50	100	150	200
  Rabbit Max
  Rabbit Min
  Rabbit Quality of Life

• What starting number of foxes maximizes the rabbit quality of life (A=.005)? ___________

• Capture the graph of the best quality of life for your report.

Goal 1E : Another interaction parameter

• Next set the interaction parameter A = .007. Keep the B = .5 and D=.7 constant.
  
• Now Repeat the simulations in part 1C to find the best starting number of foxes for a maximum rabbit quality of life.

  Foxes	25	50	100	150	200
  Rabbit Max
  Rabbit Min
  Rabbit Quality of Life

• What starting number of foxes maximizes the rabbit quality of life (A=.007)? ___________

• Capture the graph of the best quality of life for your report.

Goal 2 : How does the best number of foxes change as you change the interaction coefficient?

• First Summarize the results of the previous experiments in the following table :

  Trial	A (Interaction Const)	Starting Foxes for Best Quality of Life
  1
  2
  3

• How does this number of foxes for A = .007 compare to the number of foxes for A = .005, and A=.003? _______________________________________________________

• Explain the reason why less interaction (lower A) has the effect it does on the starting number of foxes.

Extra Credit :

• This procedure does not give the exact value of the best starting number of foxes.
• If you try numbers between your 2 best values, you can come close to finding the best number.
• For example, if 25 and 50 give the best quality of life, the exact value could be 35.
• For extra credit find the "exact" number for A = .003,by using a trial and error method. Check for a level slope to lead you to the best quality of life. (See Previous Project)

Goal 3: Another Conclusion : Is the Model Linear?

• Keep everything the same [except PopMax] as the last graph captured above, except double the number of rabbits, foxes, and PopMax.
  
• Run the graph and capture it.
• Is the graph the same as the graph with half the number of animals?___________ Explain

• Mr. Barrett believes that doubling the number of rabbits causes a seeming greater A or interaction parameter. Do you agree? why _________________

• This would mean that the model is run on an island with limited land area where greater numbers mean increased contact between the species.
  Comment __________________________________________________

• What starting number of foxes maximizes the rabbit quality of life? _________

  (Quality of life may be considered less brother and sisters eaten in a given period.) This is trial and error work and may take quite a few trials.

• Capture the graph of the highest quality of life for your report.
  

• How is the fox quality of life related to the rabbit quality of life?__________________

Goal 4 : Report

• Your report must be done in WordPerfect or Word.
• You will need to import at least three graphs into your report.
• Write your report like a research paper.
  • Include the purpose of your experiment.

  • A description of your model including the assumptions.

  • The design of your experiment.

  • The data, tables, and graphs that you have found.

  • Conclusions that you can make from the results.

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This page is Copyright 1998 by J. Barry DeRoos. All Rights Reserved.
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Last Modified: Jan , 2002.