A simple differential equation system describes the dynamics of a renewable resource coupled by a Cobb-Douglas production function to the capital invested in resource harvesting. This system can model fisheries which operate under open access. Significant resource depletion is shown to follow capital overshoot. We study the influence of biological and economic mechanisms such as the existence of a carrying capacity for the resource, the role of prices and the possibility of a minimum consumption for the labour force on the amplitude of resource depletion. We define a concept of fragility that relates resource depletion to the initial distance of the dynamic variables from equilibrium. An analytic expression of fragility, applicable to differential models of bio-economic systems is derived in this paper. The influence of some institutional interventions is also assessed.
