  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.
