This is an example of a systems model, using the arbitrary example of princesses and frogs. In this model, princesses can kiss frogs to turn them into princes and princes can turn sleeping beauties back into princesses, but witches can also turn princesses into sleeping beauties and princes back into frogs.
Each of the groups frogs, princes, sleeping beauties, and princesses interacts with one another as well as witches. Note that, for this model, witches are not a group, but a variable (since they are neither born nor killed). The quantities of each group are graphed on the right.
The only parameter to be set in this model is witch density, which determines nearly all of the other reactions.
There will be a great deal of variation, but the quantities of each class should stabilize over time.