Network complexity, stability and growth: Making sense of the multitude of feedbacks
In 1981, Peter Yodzis performed a model disturbance experiment where he randomly permuted pairs of interaction strengths in his theoretically parameterised community networks. Disruption of the biologically "plausible" equilibrium structures led to a dramatic decrease in model stability. More than anything, his results made clear that we have to go beyond the separate interactions, to the feedbacks in the systems, to understand the stability of communities. But how far do we have to go, to explain the stability of complex natural community networks? How many levels of feedback do we have to consider, to capture the stability of a complex n-level system? And does this understanding of the feedbacks tell us anything about key biological properties, about the relation between stability and the functioning of ecosystems, or even about ecosystem change and development? Here we address these questions by using detailed observations on the material flow in two Antarctic ecosystems. We could describe the entire interconnected above- and belowground communities. With this empirical material-flow structure, translated into traditional community matrices of the type that Yodzis used, we analysed the multitude of feedbacks in the systems.
The stability of the observed Antarctic networks could be captured by a metric expressing a relation between the strength of the (positive, destabilising) 3-link and (negative, stabilising) 2-link predator-prey feedback loops in the systems. Our feedback metric compared stability between ecosystems, in a large set of observed food webs. The metric also explained the randomisation effect on stability, in Yodzis-type disturbance experiments. The results suggest that the stronger the predation pressure in a system, the more vulnerable is the food web, and the stronger the self-regulatory feedbacks will have to be to preserve system stability.
We discuss the implications of our approach for ideas on the relation between network stability and network growth, and the opportunities it could offer to link stability across levels of ecological organisation.
Yodzis, P. (1981). The stability of real ecosystems. Nature 289, 674-676.
Neutel, A.M. & Thorne, M.A. (2014). Interaction strengths in balanced carbon cycles and the absence of a relation between ecosystem complexity and stability. Ecol. Lett.17, 651-661.