Is predator-mediated coexistence possible in unstable systems?

Simple mathematical models are used to study the interaction between two prey species that share common resources and a common predator In contrast to several previous analyses, this one concentrates on systems that may exhibit cyclic or chaotic dynamics due to the predator's saturating functional response. Under very general conditions, sustained fluctuations make coexistence of prey species more difficult than in comparable systems that are stable. In the model analyzed in greatest detail, there: is a limiting similarity in prey vulnerabilities in cycling systems, although such a limit does not exist in similar stable systems. The responses of mean population densities to model parameters often differ qualitatively between stable and unstable systems. In stable systems with two prey species, enrichment always increases the density of the prey that is poorer at resource exploitation and better at predator avoidance, while decreasing the density of the: other prey. In contrast, in some unstable systems, enrichment increases the densities of both prey, and in others it increases the better exploiter at the expense of the better predator avoider. Enrichment increases the amplitude of population cycles; for predators with saturating functional responses, larger cycles tend to favor the mure vulnerable species. The qualitative results of the analysis are robust to many different changes in the form of the model.