COMPLEX DYNAMICS IN STOCHASTIC TRITROPHIC MODELS

Stochastic versions of three models of tritrophic interactions among hosts, parasitoids, and hyperparasitoids produced long-term population fluctuations that occurred over a wider range of parameter values in the stochastic models than in the deterministic models, suggesting that long- term population fluctuations are plausible features of natural tritulent systems.

Abstract

We analyzed three models of tritrophic interactions among hosts, parasitoids, and hyperparasitoids. In their deterministic versions, all models can produce dynamics in the form of a torus, in which there are both short-term cycles and long-term cycles of tens or hundreds of generations. To investigate whether similar long-term patterns can occur when there is environmental variability, we produced stochastic versions of the three models. Long-term population fluctuations occurred over a wider range of parameter values in the stochastic models than in the deterministic models. This suggests that long-term population fluctuations are plausible features of natural tritrophic systems. We use this example to argue that characterizing nonlinearities should not be the sole objective when analyzing stochastic population dynamics. The long-term dynamical patterns produced by our stochastic models can be investigated using linear techniques to quantify the patterns of density dependence in the multispecies system. These techniques identify long-term patterns as near-random-walk dynamics occurring concomitantly with short-term quasi-cyclic dynamics in the three-dimensional three-species system. Interpreting stochastic population dynamics in terms of patterns of density dependence makes it possible to identify the potential for long-term population fluctuations in the absence of very long-term data sets.