Introduction to the Predator Prey Problem

The predator problem is a simulation that attempts to predict the relationship in populations between a population of foxes and rabbits isolated on an island.

Assumptions :

• Rabbits only die by being eaten by foxes
• Foxes on die from natural causes.
• The interaction between Foxes and Rabbits can be described by a function.

Populations

• For Rabbit Populations if no foxes were present the new rabbit population is calculated from the previous population by the following equation.

P_Rn = P_R(n-1) + B_R *P_R(n-1)

where :

• P_Rn is the new rabbit population after time period n
• P_R(n-1) is the beginning rabbit population at the time period n-1
• B_R is the Birth Rate for Rabbits

(Under these conditions the rabbit population would continually increase.)

• For Fox Populations if no hunters are present the new fox population is calculated from the previous population by the following equation:

P_Fn = P_F(n-1)- D_F*P_F(n-1)

where:

• P_Fn is the new fox population after time period n
• P_F(n-1) is the beginning fox population at the time period n-1
• D_F is the Death Rate for Foxes

(Under these conditions the fox population only will decrease.)

• When foxes can eat rabbits the population equations have another term to describe the interaction.

The population of Rabbits is the same as above with a loss of population due to foxes :

P_Rn = P_R(n-1)+ B_R *P_R(n-1) - A* P_R(n-1)* P_F(n-1)

where :

• A is the interaction constant between the foxes and the rabbits

The population of foxes is increased with the addition of the interaction term :

P_Fn = P_F(n-1) - D_F *P_F(n-1) + A* P_F(n-1)* P_R(n-1)

(Now the population of rabbits is decreased by the foxes with the greater number of foxes causing a greater decrease in the rabbit population. This means that the rabbit population is eventually going to decrease and the resulting fox population will also decease. As a result a cyclic increase and decrease in populations are set up. This is what is observed in the simulation.)

• The Predator Prey Simulation

  • (Be Patient Java may be starting)

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Last Modified: Jan 9,2002.