  Ecological systems comprise an astonishing diversity of species that
cooperate or compete with each other forming complex mutual dependencies. The
minimum requirements to maintain a large species diversity on long time scales
are in general unknown. Using lichen communities as an example, we propose a
model for the evolution of mutually excluding organisms that compete for space.
We suggest that chain-like or cyclic invasions involving three or more species
open for creation of spatially separated sub-populations that subsequently can
lead to increased diversity. In contrast to its non-spatial counterpart, our
model predicts robust co-existence of a large number of species, in accordance
with observations on lichen growth. It is demonstrated that large species
diversity can be obtained on evolutionary timescales, provided that
interactions between species have spatial constraints. In particular, a phase
transition to a sustainable state of high diversity is identified.
