  The spatial rock-paper-scissors ecosystem, where three species interact
cyclically, is a model example of how spatial structure can maintain
biodiversity. We here consider such a system for a broad range of interaction
rates. When one species grows very slowly, this species and its prey dominate
the system by self-organizing into a labyrinthine configuration in which the
third species propagates. The cluster size distributions of the two dominating
species have heavy tails and the configuration is stabilized through a complex,
spatial feedback loop. We introduce a new statistical measure that quantifies
the amount of clustering in the spatial system by comparison with its mean
field approximation. Hereby, we are able to quantitatively explain how the
labyrinthine configuration slows down the dynamics and stabilizes the system.
