BIOL / MATH 2350
Homework assignment 3
In class we have discussed the logistic growth model. For continuous time, it has the
differential equation
dn
 n(t ) 
 rc n(t ) 1 

dt
K 

This represents a population growing in one habitat with no immigration or emigration.
Now consider that emigration takes place from this habitat, where successful
reproduction is possible, to a habitat where there is no successful reproduction, but only
death occurs, perhaps at a slow rate. Such a habitat is called a “sink” habitat by
ecologists, while a habitat with successful reproduction is called a “source”.
1. Write a model of a source and a sink habitat, where migration goes from the source to
the sink. Assume that that in the source habitat if there were no migration, population
dynamics would follow the logistic model.
2. Say as much as you can about the dynamics of this model. For example, think about
what happens at equilibrium.