Intermittent Chaos in Population Dynamics

In modelling single species with discrete, non-overlapping generations, one usually assumes that the density at time t + 1 is a function of the density at time t: Nt + 1 = ƒ(Nt). The dynamical behaviour of this system depends on the parameters in the function ƒ. It commonly changes, as a parameter increases, from a stable equilibrium through a series of bifurcations into stable cycles, to chaotic motion. It is implicit in the assumptions of the model that the population consists of identical individuals. In this paper it is shown that variation within the population can lead to a different route to chaos. Invasion of a mutant phenotype into a resident population can elicit intermittency. This kind of chaotic behaviour consists of regular motion most of the time with short intermittent periods in which the system fluctuates wildly.