The last model we will investigate is based on the logistic model. This model, which often goes by the name The Allee Effect, assumes in addition that there is a minimum number of animals present, a, that are needed for the species to continue to give birth. This time, we will give you the differential equation below, and ask you to interpret and justify it. The differential equation for these assumptions is the following:

1. Assuming the population is not going extinct: what should we assume about K and a? Which number should be larger? Explain.

a. What does this model predict about the growth rate if P

b. Find the equilibrium points of this differential equation and classify them. Interpret what your result tells you about the population. That is, why might it make sense biologically for the unstable points to be unstable.

P(t)=(bd)P(1KP)(aP1) P(t)=(bd)P(1KP)(aP1)