Ternary network models for disturbed ecosystems

The complex network of interactions between species makes understanding the response of ecosystems to disturbances an enduring challenge. One commonplace way to deal with this complexity is to reduce the description of a species to a binary presence-absence variable. Though convenient, this limits the patterns of behaviours representable within such models. We address these shortcomings by considering discrete population models that expand species descriptions beyond the binary setting. Specifically, we focus on ternary (three-state) models which, alongside presence and absence, additionally permit species to become overabundant. We apply this ternary framework to the robustness analysis of model ecosystems and show that this expanded description permits the modelling of top-down extinction cascades emerging from consumer pressure or mesopredator release. Results therefore differ significantly from those seen in binary models, where such effects are absent. We also illustrate how this method opens up the modelling of ecosystem disturbances outside the scope of binary models, namely those in which species are externally raised to overabundance. Our method therefore has the potential to provide a richer description of ecosystem dynamics and their disturbances, while at the same time preserving the conceptual simplicity of familiar binary approaches.