Population Floors and the Persistence of Chaos in Ecological Models

Chaotic dynamics have been observed in a wide range of population models. Here we describe the effects of perturbing several of these models so as to introduce a non-zero minimum population size. This perturbation generally reduces the likelihood of observing chaos, in both discrete and continuous time models. The extent of this effect depends on whether chaos is generated through period-doubling, quasiperiodicity, or intermittence. Chaos reached via the quasiperiodic route is more robust against the perturbation than period-doubling chaos, whilst the inclusion of a population floor in a model exhibiting intermittent chaos may increase the frequency of population bursts although these become non-chaotic.