Here we introduce the case where the resource itself reproduces, occupying Quadrants 3 and 4 simultaneously. We begin with a single resource stock: biomass B. It is necessary to account for its growth rate and for the harvest. Steady states are possible when these two are in balance, Quadrant 3; but the descent into Quadrant 4, “resource mining,” occurs when harvest continuously exceeds growth, leading to extinction: no S, therefore no Q. This would be the analog of resource exhaustion for the sterile resource. It is irreversible.

These resources are local in that they live within a regional ecosystem with finite carrying capacity. The market for the harvest, however, is presumed exogenous, dependent on many things other than this particular resource. The application to fishery management is used throughout to fix ideas.

The base case here uses the logistic function for the growth rate. As the resource (e.g., fish) is fugitive, harvesting requires effort (fishers) as well as fish availablility. The formulation needs to add fishing effort E at a fundamental level. The economic interaction of growth and harvesting is commonly referred to as “bioeconomic.” From a sustainability perspective, there needs to be attention to (a) avoiding the “mining” phenomenon associated with Quadrant 4 extinction; (b) regulating the effort directed at the resource harvesting; and (c) respecting the conditions required for maintenance of the reproducing stock (the ecological carrying capacity).

GROWTH AND HARVESTING

In the case of sterile resources, we have only one consideration: the rate of its exhaustion and the time frame of complete exhaustion.