Early warning signs in social-ecological networks
  Social ecological systems are often difficult to investigate and manage because of their inherent complexity1. Small variations in external drivers can lead to abrupt changes associated with instabilities and bifurcations in the underlying dynamics2-4. Anticipating critical transitions and divergence from the present state of the system is particularly crucial to the prevention or mitigation of the effects of unwanted and irreversible changes5-10. Recent research in ecology has focused on leading indicators of regime shift in ecosystems characterized by one state variable5,7,11,12. The case of systems with several mutually interacting components, however, has remained poorly investigated13, while the connection between network stability and research on indicators for loss of resilience has been elusive14. Here we develop a theoretical framework to analyze early warning signs of instability and regime shift in social ecological networks. We provide analytical expressions for a set of precursors of instability in social ecological systems with additive noise for a variety of network structures. In particular, we show that the covariance matrix of the dynamics can effectively anticipate the emergence of instability. We also compare signals of early warning based on the dynamics of suitably selected nodes, to indicators based on the integrated behavior of the whole network. We find that the performances of these indicators are affected by the network structure and the type of interaction among nodes. These results provide new advances in multidimensional early warning analysis and offer a framework to evaluate the resilience of social ecological networks. 
Samir Suweis and Paolo D'Odorico
q-bio.PE