For each N,M pair above, we explore the space of all possible communities of N strains interacting via M antibiotics.

We numerically solve the associated equations (see Methods, “mixed-inhibition zone model”) describing a well-mixed population, and report N,M pairs for which there exists at least one interaction pattern that displays a stable, internal fixed point. This analysis is performed at two parameter combinations. Common parameters: Different between the two parameter combinations: , or . Parameter-dependence of the fixed points is discussed in the main text.