Predator-Prey Model

1. Predator-Prey Model A Systems Dynamics Approach

2. Introduction • 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)

3. The System Dynamics Model

4. Elements of the Model Grass Rabbit Wolf AREA

5. WOLF Model

6. Wolf Model

7. RABBIT Model

8. Rabbit Model

9. GRASS Model

10. Grass Model (Grass) Death rate grass grass eaten by rabbits natural death TIME STEP c density grass nom Grass i Grass i Area (Grass) grass untouched Spread rate grass natality grass

11. Wolf, Rabbit, Grass Interaction

12. Explanation • 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.

13. Explanation • The danger is when either population fluctuates so much that population dips down to zero. • The wolves will almost completely cut off the rabbits’ food supply. Grass Rabbit Wolf AREA

14. Internet Sources • http://www.cs.uwyo.edu/~wspears/courses/CS5010/frey/rabbits.pdf • http://www.scholarpedia.org/article/Predator-prey_model