  Ecological management problems often involve navigating from an initial to a
desired community state. We ask whether navigation is possible without
brute-force additions and deletions of species, using actions of varying costs:
adding/deleting a small number of individuals of a species, changing the
environment, and waiting. Navigation can yield direct paths (single sequence of
actions) or shortcut paths (multiple sequences of actions with lower cost than
a direct path). We ask (1) when is non-brute-force navigation possible?; (2) do
shortcuts exist and what are their properties?; and (3) what heuristics predict
shortcut existence? Using several empirical datasets, we show that (1)
non-brute-force navigation is only possible between some state pairs, (2)
shortcuts exist between many state pairs; and (3) changes in abundance and
richness are the strongest predictors of shortcut existence, independent of
dataset and algorithm choices. State diagrams thus unveil hidden strategies for
efficiently shifting between states.
