(a) The survival of a species in a consumer resource model depends on the supplied resource levels and the mortality rate (i.e. disturbance intensity). A Zero Net Growth Isocline (ZNGI) may be defined for each species at a given disturbance intensity, delineating the range of resource supply levels where growth can meet or exceed the mortality rate. The ZNGIs intersect the axis at c* values, the minimum concentration needed to support growth of a species on a single resource. The outcome of competition depends on the combination of resources supplied, indicated by a supply point. Resources are consumed until reaching equilibrium along the ZNGI of the species requiring the fewest resources to survive at the specified mortality rate, the winner of the competition. Different supply points can be found that support neither species (gray), a single species (green or purple) or both species (black). Invasion boundaries indicate regions where one species can increase in density in the presence of the other, outlining the region of coexistence (maroon). (b) In a consumer resource simulation with 2-species / 2-resources and Monod growth, the outcome of competition at the given supply point (black) depends on disturbance intensity. Both ZNGIs and invasion boundaries flip as disturbance intensity increases. At intermediate disturbance, invasion boundaries align and the coexistence region collapses, reducing diversity relative to low/high disturbance intensities at the black supply point. (c) Left: Monod consumer resource model for growth of species i with additive non-linear growth on each resource. Right: Shannon diversity of randomly generated 10-species communities, after six days of simulated growth on seven resources at varying dilution rates. For each model, mean diversity was computed for 100 randomly initialized communities, across each mean dilution rate, 50 of which are shown as individual traces.