Abstract. 
Two problems from population biology will be discussed. First, a
problem from fisheries led to the discovery of chaotic dynamics in the
1950's. This phenomenon was subsequently explained by Sarkovskii, Li and
Yorke, May, and others. There remain similar problems in nonlinear renewal
theory that will be described. Second, an important result in epidemiology
is based on a bifurcation result, called the Kermack-McKendrick Threshold
theorem. This and similar results will be described in the context of
epidemics involving complex age structures.