Predator-Prey ModelA Systems Dynamics Approach

• Predator-prey models are arguably the building blocks of the bio- and ecosystems as biomasses are grown out of their resource masses.

• Species compete, evolve and disperse simply for the purpose of seeking resources to sustain their struggle for their very existence.

• Depending on their specific settings of applications, they can take the forms of resource-consumer, plant-herbivore, parasite-host, tumor cells (virus)-immune system, susceptible-infectious interactions, etc. (Scholarpedia)

Introduction

The System Dynamics Model

AREA

Wol f Rabbit Grass

Elements of the Model

WOLF Model

Wolf Model

Wolf

Birth rate Wolf

(Wolf)

c natality Wolf

Death Rate Wolf

(Wolf)

Death by human

Natural death Wolf

Starvation Wolf

TIME STEP

i Wolf Population

RABBIT Model

Rabbit Model

Rabbits

Birth rate rabbits

(Rabbits)

c natality rabbits

Death rate rabbits

(Rabbits)

actual number of rabbits caught by wolf

Natural death rabbits

Starvation rabbits

TIME STEP

i Rabbits

GRASS Model

Grass Model

Grass

Death rate grassgrass eaten by rabbits

natural death

i Grass

c density grass nom

i Area

Spread rate grass

(Grass)

natality grass

grass untouched

(Grass)

TIME STEP

Wolf, Rabbit, Grass Interaction

As the amount of grass increases, so does the number of rabbits.

When grass is low, rabbit population also becomes low – which means not enough food to support the wolves.

As the secondary predator (the wolves) would dramatically increase in population, and then crash hard when the primary predator (the rabbits) were nearly extinct.

Then, the rabbits would go around eating and reproducing, while the wolves would catch up, after nearly going extinct themselves.

Explanation

The danger is when either population fluctuates so much that population dips down to zero.

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Explanation

The wolves will almost completely cut off the rabbits’ food supply.

Internet Sources• http://www.cs.uwyo.edu/~wspears/courses/CS501

0/frey/rabbits.pdf• http://www.scholarpedia.org/article/Predator-prey_

model