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This model explores the relationship between two different models of predator-prey ecosystems: an agent-based model and a aggregate model. Each of the models can be run separately, or docked side-by-side for comparison.
In the agent model, wolves and sheep wander randomly around the landscape, while the wolves look for sheep to prey on. Each step costs the wolves energy, and they must eat sheep in order to replenish their energy - when they run out of energy they die. To allow the population to continue, each wolf or sheep has a fixed probability of reproducing at each time step.
The aggregate model is a System Dynamics model of the relationship between populations our wolves and sheep. It is based on a version of the famous Lotka-Volterra model of interactions between two species in an ecosystem.
Parameters shared between agent and aggregate models: - INITIAL-NUMBER-SHEEP: The initial size of sheep population - INITIAL-NUMBER-WOLVES: The initial size of wolf population - SHEEP-REPRODUCE: The probability of a sheep reproducing at each time step
Parameters for agent model: - SHEEP-MAX-INITIAL-ENERGY: At setup time, sheep are given an energy between 1 and this value - WOLF-GAIN-FROM-FOOD: The amount of energy wolves get for every sheep eaten - WOLF-REPRODUCE: The probability of a wolf reproducing at each time step
Parameters for aggregate model: - WOLVES-DEATH-RATE: The rate at which wolves die. - PREDATION-RATE: The rate at which wolves eat sheep. - PREDATOR-EFFICIENCY: The efficiency of the wolves in extracting energy to reproduce from the prey they eat.
Why do you suppose that some variations of the model might be stable while others are not?
Try adjusting the parameters under various settings. How sensitive is the stability of the model to the particular parameters?
Notice that under stable settings, the populations tend to fluctuate at a predictable pace. Can you find any parameters that will speed this up or slow it down?
There are a number ways to alter the model so that it will be stable with only wolves and sheep (no grass). Some will require new elements to be coded in or existing behaviors to be changed. Can you develop such a version?
Note the use of the System Dynamics Modeler to create the aggregate model.
Look at the Wolf Sheep Predation model for an example of an agent model which can produce a stable model of predator-prey ecosystems.
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Copyright 2005 Uri Wilensky.
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