Fig. 1: Implementation of antibiotic activity in a CR model.

a Schematic of a well-mixed CR model²⁹ with species-specific death rates \({d}_{i}\). Depicted are cells (colored ovals) from three species competing for two resources (small circles) supplied at rates \({s}_{\mu }\). b The effects of species-specific death rates on coexistence can be determined by reducing the consumption rates \({R}_{i\mu }\) by \({b}_{i}=(d+{d}_{i})/d\). The transformed consumption rates (open circles) have lower enzyme budgets compared to the original consumption rates (filled circles). c When a community of three species competes for three resources, the consumption rates can be visualized on a simplex representing the hyperplane containing the consumption niches of the three species in the space of rescaled consumption rates. In the case shown, the convex hull of the species consumption rate vectors (dashed line and shaded gray) encloses the point representing the normalized resource supply rates (star), hence all species coexist²⁹. d Example in which two possible hyperplanes (dashed lines, i and ii) dictate the conditions for coexistence of three species (colored circles) competing for two resources. The third hyperplane (hashed gray line) does not satisfy the conditions for coexistence. e Along each hyperplane, a pair of species coexists if the normalized resource supply rates \({\hat{s}}_{\mu }\) lie between the rescaled consumption rates (colored triangles) of the species pair (hatched multicolored regions). Otherwise, only the species with \({\hat{R}}_{i\mu }\) closest to \({\hat{s}}_{\mu }\) persists (solid regions). f Species dynamics (bottom) for the community shown in (d) for one case of supply rates (triangle, top).