Preliminary Exercise Predator Prey Model

This is an island with a simple ecology. There are rabbits that have an infinite supply of food - mostly grass. There is a population of foxes that eat the rabbits. When foxes are well feed, they produce many offspring and the chance of them surviving is better. So the rabbits have a good effect [+] on the foxes but the foxes have a bad effect [-] on the rabbits. With no rabbits the foxes die off in an exponential way, that is the more foxes there are the more die - until the last one dies.

Remember the rabbit's population leads the fox's population : that is as the rabbits population increases there is more food for the foxes and so their population increases. As the rabbit population declines , the foxes have less food and less kits, and the result is a decline in the fox population.

Section One

Run the Predator Prey Simulation

Set the simulation parameters to

• Rabbit Birth Rate = .35
• Fox Death Rate = .7
• Starting Population Rabbits = 500
• Starting Population Foxes = 50
• Interaction Constant = .003
• Maximum Population = 1200
• Number of Years to Graph = 20

Answer the following questions.

1. What is the slope of the rabbit curve initially?___________
2. What is the slope of the fox curve initially? ___________
3. How long does it take to repeat a cycle?___________
4. Find the minimum number of foxes _______________
5. Find the minimum number of rabbits _____________
6. Find the maximum number of foxes _______________
7. Find the maximum number of rabbits______________
8. The quality of life as defined as min. number/Max. number * 100. This is a measure of the stability of the population. Loosing many brothers and sisters would seem to decrease the quality of life.

9. What is the fox quality of life? ____________
10. What is the rabbits quality of life?___________

Section Two

Run the Predator Prey Simulation Again

Set the simulation parameters to

• Rabbit Birth Rate = .6
• Fox Death Rate = .9
• Starting Population Rabbits = 500
• Starting Population Foxes = 50
• Interaction Constant = .005
• Maximum Population = 1000
• Number of Years to Graph = 20

Answer the following questions about using the simulation graph.

1. How long does it take to repeat a cycle?___________
2. Find the minimum number of foxes________________
3. Find the minimum number of rabbits______________
4. Find the Maximum number of Foxes  __________
5. Find the Maximum number of rabbits __________
6. What is the rabbit quality of life?___________
7. What is the fox quality of life? ___________

Slope and the Quality of Life



Introduction

• If a population starts off with a slope or angle inclined to the horizontal [i.e. the angle is not zero], it means that the population is not in equilibrium. A downward starting lope for the foxes means there is too little food for them. A positive starting slope [ see part A & B above] means there is an over supply of rabbits so the foxes are well feed and so the population increases.

• What does a negative starting slope for rabbits mean? [Your answers also will involve the number of foxes.] _________________________________________________________________________ _________________________________________________________________________

• What does a positive slope for the rabbits mean? ____________________________________________ ____________________________________________________________________________________________

• When you look at the starting slope of the rabbit's graph and it is positive, why should you increase the number of foxes to obtain a better quality of life? ______________________________________________________

Run the Predator Prey Simulation Again

Set the simulation parameters to

• Rabbit Birth Rate = .35
• Fox Death Rate = .7
• Starting Population Rabbits = 500
• Starting Population Foxes = 200
• Interaction Constant = .004
• Maximum Population = 1000
• Number of Years to Graph = 20

Find :

1. Max. # rabbits ________________
2. Min. # rabbits ________________
3. Rabbit Quality of Life _______________
4. Max. # foxes ________________
5. Min. # foxes ________________
6. Foxes Quality of Life ________________
7. What does a level starting slope for a population mean? ___________________

General Questions

1. Using Part B and C how does the quality of life for the rabbits relate to the quality of life for the foxes? ________________________________________________________________________

2. What application of this model [admittedly weak] can we make to our steward ship of animal life on the earth? [Note this application should be based on our best interests aside from Christian concerns.] __________________________________________________________________________________ ___________________________________________________________________________________

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Last Modified: Jan 9 ,2002.