Dependencies between competition and predation - and their consequences for initial value sensitivity

We commence with a discussion of dependencies between various processes in discrete consumer-resource models. Two basic models are formulated. These m odels are closely related and differ only in terms of which dependencies ar e assumed. The models can be regarded as hybrids of the Lotka-Volterra mode l, the Beverton-Holt model, and the Nicholson-Bailey model. A complete stability analysis of the equilibria is given with the conclusio n that the stability properties of these models are closely related to Gaus e-type predator-prey systems. The numerical part of our analysis brings out remarkable qualitative differ ences concerning the initial value sensitivity of the oscillations of the t wo basic models. Initial value sensitivity was measured by Lyapunov exponen ts and the observed differences cannot be brought to light by a study of li miting cases or by equilibrium analysis. The actual reasons behind these re sults remain a delicate mathematical question. Properties associated directly with the time series, like mean amplitudes a nd dominating periods, did not show the same differences.