Microbial communities often converge to a unique stable steady state, but more complex dynamics are possible.

By a single stable steady-state, we mean that the dynamics converge to a steady-state that is stable to invasion by species that had gone extinct en route. In other words, if a species present initially goes extinct and is absent from the final steady-state, then it can not invade the final community successfully. Thus species presence-absences in the initial community fully determine the outcome. Note that this table only approximately condenses a vast and complex literature; for a more thorough understanding we encourage the interested reader to consult the cited references. We have provided additional details regarding the cited studies in S1 Text Sec.1. Macroscopic organisms are discussed in Ref. [64].