Abstract In this paper, a general mathematical model is presented to study the effect of two populations on a resource biomass. The interaction between two populations is assumed to be competition, predation, or cooperation. These two populations may depend on the resource biomass partially, wholly, or they may predate on the resource. In each case, criteria for local stability, instability, and global stability are obtained. Numerical simulation is presented to illustrate the theoretical results obtained in each case. It is shown that the depletion of resource biomass is maximum in the case of cooperation and is minimum in the case of competition.