  Predicting the fate of ecologies is a daunting, albeit extremely important,
task. As part of this task one needs to develop an understanding of the
organization, hierarchies, and correlations among the species forming the
ecology. Focusing on complex food networks we present a theoretical method that
allows to achieve this understanding. Starting from the adjacency matrix the
method derives specific matrices that encode the various inter-species
relationships. The full potential of the method is achieved in a spatial
setting where one obtains detailed predictions for the emerging space-time
patterns. For a variety of cases these theoretical predictions are verified
through numerical simulations.
