Predation

Sheep and Wolves: An Agent-Based Model

The four types of social evolution are cooperation, selfishness, altruism, and spitefulness. A classic example of selfishness is the predator-prey relationship.

In the sheep and wolves model sheep run around eating grass and reproducing. Both of these activities require energy. When a sheep runs out of energy it dies. This could happen if the grass doesn't grow back at a fast enough rate and the sheep has to spend a lot of time running around searching for grass.

But there's another way for a sheep to die. Wolves run around eating sheep and reproducing. These activities also consume energy. When a wolf runs out of energy, it dies.

Note that in this model wolves prey on sheep and sheep prey on grass.

Depending on initial population sizes,

Forgetting about grass for the moment, as the number of sheep increases, the number of wolves increases. As the wolves reduce the number of sheep, wolves start starving, and their population decreases. This allows the sheep population to increase. Therefore, we would expect to see both populations oscillating with the wolves slightly out of phase with the sheep.

Experiment 1: Exponential Growth

Grass off, init-wolves = 0

Experiment 2: Logistic Growth

Grass on, init-wolves = 0

Experiment 3: Predator Prey Oscillation

Grass off, init-wolves > 0

Experiment 4: Oscillation of Grass, Sheep, and Wolves together

System Dynamics: Stocks and Flows

See System Dynamics for an introduction.

Sheep and Wolves: A Stocks and Flows Model

Here's a screen shot:

Compare this smooth plot with the jagged plot in the ABM version of the model. Note that the wolf population is phase shifted slightly to the left of the sheep population.