Dependencies Between Competition and Predation---and Their Consequences for Initial Value Sensitivity

Abstract

We commence with a discussion of dependencies between various processes in discrete consumer-resource models. Two basic models are formulated. These models are closely related and differ only in terms of which dependencies are assumed. The models can be regarded as hybrids of the Lotka--Volterra model, the Beverton--Holt model, and the Nicholson--Bailey model.A complete stability analysis of the equilibria is given with the conclusion that the stability properties of these models are closely related to Gause-type predator-prey systems. The numerical part of our analysis brings out remarkable qualitative differences concerning the initial value sensitivity of the oscillations of the two basic models. Initial value sensitivity was measured by Lyapunov exponents and the observed differences cannot be brought to light by a study of limiting cases or by equilibrium analysis. The actual reasons behind these results remain a delicate mathematical question.Properties associated directly with the time series, like...