  We introduce a toy model of ecosystem assembly for which we are able to map
out all assembly pathways generated by external invasions. The model allows to
display the whole phase space in the form of an assembly graph whose nodes are
communities of species and whose directed links are transitions between them
induced by invasions. We characterize the process as a finite Markov chain and
prove that it exhibits a unique set of recurrent states (the endstate of the
process), which is therefore resistant to invasions. This also shows that the
endstate is independent on the assembly history. The model shares all features
with standard assembly models reported in the literature, with the advantage
that all observables can be computed in an exact manner.
