Optimal management in Tilmania: A competitive species assembly constrained by a limiting factor

Resource-based models of species competition predict that when species compete for a limiting resource in a homogeneous habitat, then the equilibrium outcome is a monoculture with the species characterised by the lowest resource requirement outcompeting all the rest. We derive harvesting rules for a habitat that maximise the utility flows generated from consumption activities of the harvested species, and from nonconsumptive activities associated with utility generated from positive species biomass. Under the harvesting rules the maximal desired biodiversity is preserved in the long-run equilibrium assembly. Our harvesting rule at the steady state corresponds to a golden biodiversity rule. The equilibrium assembly is characterised by a 'strong resilience principle' in both deterministic and stochastic environments, indicating that irrespective of the initial state of the assembly, the system tends to the steady state where full biodiversity is preserved.