Deterministic models have difficulties to take into account
stochasticity during community assembly. As a tool to circumvent this
problem, we present a qualitative discrete-event model, where
consequences of interspecific interactions are described as rules. This
model provides a map of all possible future dynamics for a given system,
which allows to exhaustively describe the possible pathways during an
assembly process. Such a description does not rely on species traits
details and is insensitive to stochastic effects. This allows to show
that subsets of species are sometimes impossible to reach starting from
larger sets of species, and therefore to question the reachability of
community states during the system's dynamics. Applying the model to an
experimental dataset studying the collapse of protist communities, we
obtain a very good theory-experiment agreement. We finally discuss what
the notion of reachability can bring to community assembly.