Theories based on competition for resources predict a monotonic negative relationship between population density and individual biomass in plant populations. They do not consider the role of facilitative interactions, which are known to be important in high stress environments. Using an individual-based ‘zone-of-influence’ model, we investigated the hypothesis that the balance between facilitative and competitive interactions determines biomass–density relationships. We tested model predictions with a field experiment on the clonal grass Elymus nutans in an alpine meadow. In the model, the relationship between mean individual biomass and density shifted from monotonic to humped as abiotic stress increased. The model results were supported by the field experiment, in which the greatest individual and population biomass were found at intermediate densities in a high-stress alpine habitat. Our results show that facilitation can affect biomass–density relationships.