Alternative attractors may boost uncertainty and sensitivity in ecological models

Abstract

Numerous ecosystems, ranging from coral reefs, and forests to deserts and lakes have been shown to possess alternative stable states. This phenomenon has obvious important implications for management, as it may imply unexpected collapse of the system and large resistance to restoration efforts. In this paper we show that alternative attractors also have important consequences from the technical modelers’ point of view. Performing a Monte-Carlo uncertainty analysis with an existing individual-based simulation model for macrophyte growth, we found that the uncertainty in the model results may be remarkably high under some conditions. We demonstrate that this high uncertainty is caused by the alternative stable states of the model: if the noise on the parameters exceeds a critical threshold, the model uncertainty can increase steeply, due to switches to the other equilibrium. Such amplification of sensitivity is restricted to certain regions of the parameter space and depends on the initial state of the model. In the vicinity of catastrophical bifurcation points, uncertainty approaches infinity as even tiny parameter changes may cause a switch to the other equilibrium.