A demonstration of carrying capacity, showing the interaction between species' growth rates,
the carrying capacity of the environment, and environmental degradation due to over population.
Also see the version with predation.
Model details are supplied below.

Source code: CarryingCapacity button radio_button slider

Built with Processing

IBEST
and the Computer Science Department, University of Idaho.
For additional information contact: www2.cs.uidaho.edu/~tsoule

The equation underlying the dynamics is:
Pi+1 = Pi + Pi*R*(1 - Pi/K)
where Pi is the population size in the ith iteration, R is the growth rate of the species, and K is the carrying capacity of the environment.
Note that the growth rate and carrying capacity (and the intitial population size) are all adjustable.
In addition, in this model, if the Resources knob is set to degrade, then the carrying capacity (i.e. the environmental resources) degrade/decline if the population exceeds the carrying capacity. This reflects overgrazing, using up resources, etc.
Setting the Stochasticity slider to a non-zero value introduces a random factor to the growth equation.