Abstract The concept of a carrying capacity of an environment for a population has been an effective way of introducing a connection between populations and their environment. This approach has been particularly effective in heuristic Lotka–Volterra models of competition and predation that provide a basis for theoretical considerations of population interactions. However, the concept has proved less useful for interactions such as mutualism. The textbook Lotka–Volterra model of mutualism represents the interaction between two populations at the same trophic level that are each limited by the (negative) carrying capacities of the environment. The model predicts that obligate mutualist populations will either go extinct or become infinite. The classical fail diagram of obligate mutualist population interactions can be remedied by explicitly accounting for resources. The inclusion of explicit connections to the environment through resource representation and accounting for each population shows that the equivalent of the classic fail diagram is actually a sensible solution. A resource-based modelling framework saves the Lotka–Volterra model, allowing the classic population interactions of competition, predation and mutualism to be considered in a single unified framework.