Macroprediction of Critical Transitions in Adaptive Networks

The collapse of ecosystems, the extinction of species or the breakdown of
company networks, banking networks and political systems usually hinges
on topological properties of the underlying interaction network, such as
the existence of keystone nodes. Knowing just the macroscopic non-
structural information, such as species abundances, company revenues
etc, it seems impossible to make predictions about impending collapses of
these system. We show, however, that such macroscopic predictions are
possible in adaptive networks with catalytic interactions. The appearance
of the most vulnerable autocatalytic structure, a single catalytic cycle, can
be sensed macroscopically by a phenomenon that we dub quantization.
This allows us to accurately estimate the expected time until collapse.