Stability of generalized ecological-network models
Stefan Awender, Renate Wackerbauer and Greg A. Breed
Chaos 31, 023106, 2021
The stability of ecological networks of varying topologies and predator–prey relationships is explored by applying the concept of generalized modeling. The effects of omnivory, complexity, enrichment, number of top predators, and predatory response are discussed. The degree of omnivory plays a large role in governing web stability at steady state. Complexity as measured from connectance and network size is not a perfect indicator of stability; large, highly connected webs can be just as stable as smaller, less connected ones. Learning behavior as expressed in Holling’s type III predatory response is stabilizing for food webs and provides exceptions to the paradox of enrichment for some topologies.
Factors that control stability, instability, and reorganization of real and model food webs are little understood. Food webs are described as ecological networks where the vertices represent species and the edges represent predator–prey relationships and encode dynamical equations of biomass. Specific functions and biomass initial conditions are largely unknown but are required for conventional food web models to solve for trajectories. Generalized modeling requires less information and provides a powerful approach for understanding network stability in poorly characterized systems. A series of generalized models are developed to investigate how different factors such as omnivory, network complexity, and types of predator–prey relationships either stabilize or destabilize a food web’s steady state. Consequences of individual factors are not always unique across networks. For example, while adding omnivory to a short food chain with three or four species has a stabilizing effect, omnivory destabilizes steady states in longer food chains.