  We analyst in detail a new approach to the monitoring and forecasting of the
onset of transitions in high dimensional complex systems (see Phys. Rev. Lett .
vol. 113, 264102 (2014)) by application to the Tangled Nature Model of
evolutionary ecology and high dimensional replicator systems with a stochastic
element. A high dimensional stability matrix is derived for the mean field
approximation to the stochastic dynamics. This allows us to determine the
stability spectrum about the observed quasi-stable configurations. From overlap
of the instantaneous configuration vector of the full stochastic system with
the eigenvectors of the unstable directions of the deterministic mean field
approximation we are able to construct a good early-warning indicator of the
transitions occurring intermittently. Inspired by these findings we are able to
suggest an alternative simplified applicable forecasting procedure which only
makes use of observable data streams.
