Assistant Professor University of Graz Graz, Steiermark, Austria
Global change influences populations and ecosystems in many different ways, including the abundances of interacting species. However, little is known about the effects of changes in abundances on the predictability of systems. Here, we present an approach to examine the influence of stochasticity, linearity and chaos on ecological dynamics and their potential effect on the predictability of predator-prey systems, using a set of Gause's iconic microcosm experiments (Gause, Smaragdova & Witt 1936) as a case study. These experiments with two different predator-prey systems include multiple replicates that differ only in their initial abundances. We reanalyze these using the non-parametric approach (Empirical dynamic modelling) proposed by Sugihara & May (1990) to compare their cross-prediction abilities (i.e. predictions of dynamics in one replicate based on observations in other replicates). These methods allow us to test how prediction ability changes as a function of increasing distance in initial abundances between experimental replicates. Stochasticity, nonlinearity, and chaos all leave distinct signals in the relationship between these two factors, from which we can quantify their relative contributions to overall prediction error.
Our results show that even small changes in abundance hindered our ability to predict population dynamics. In particular, we found rapid divergence in abundance trajectories among many otherwise identical replicates, based only on differences in their initial conditions, which is a strong indicator for nonlinear dynamics and chaos. On net, we estimate that chaos accounted for roughly 20% of the prediction error, whereas non-linear dynamics accounted for roughly 50-75%, depending on the system. One potential driver for this high level of divergence is that spikes in abundance of the yeast Saccharomyces exiguus led to increased sedimentation in microcosms, with corresponding declines in predation, and thus marked changes in observed predator-prey oscillations. Taken together, our results demonstrate that even comparatively simple, well-understood systems can harbor enormous complexity. This suggests that even small changes in species abundance in ecological systems, e.g. from fishing or harvesting pressures, could also lead to highly divergent dynamics. Our findings therefore underline the importance of analyzing ecological dynamics across a wide range of states and stating points. Our results also serve as a template for other studies seeking to quantify the amount of stochasticity, chaos and nonlinearity in ecological timeseries.