Catch‐to‐stock dependence: The case of small pelagic fishery with bounded harvesting effort

Biologic characteristics of schooling fish species explain why the rates of harvesting in pelagic fisheries are not proportional to the existent stock size and may exhibit no variation between the periods of fish abundance and scarcity. Therefore, the stock‐dependent nonlinearities in catchability must be reflected in the design of flexible fishing policies, which target the sustainable exploitation of this important natural resource. In this study, such nonlinearities are expressed through eventual variability of the “catch‐to‐stock” parameter that measures the sensitivity of an additional catch yield to marginal changes in the fish‐stock level. Using the optimal control modeling framework, we establish that each value of the “catch‐to‐stock” parameter generates a unique steady‐state size of the fish stock and the latter engenders an optimal fishing policy that can be sustained as long as the “catch‐to‐stock” parameter remains unchanged. We also prove the continuous dependence of the steady‐state stock and underlying fishing policy upon the mentioned “catch‐to‐stock” parameter and then focus on the analysis of the equilibrium responses to changes in this parameter induced by external perturbations. Recommendations for Resource ManagersMarginal catches of pelagic fish stocks do not react in a linear way to changes in existing stock level, and the latter is captured in our model by the “catch‐to‐stock” parameter β ∈ ( 0 , 1 ) . Each observable value of β engenders a unique steady‐state stock size that defines an optimal fishing policy, which can be sustained as long as β remains unchanged. The ability of fishery managers to detect variations in the levels of hyperstability expressed by the “catch‐to‐stock” parameter β ∈ ( 0 , 1 ) may help them to anticipate new equilibrium responses in stock evolution and to make timely adjustments in the fishing policy. Plausible estimations of the “catch‐to‐stock” parameter β ∈ ( 0 , 1 ) , as well as detection of its possible alterations, can be carried out within the framework of Management Strategy Evaluation (MSE) approach where different data collected inside and outside the fishery are contrasted via the validation of a relatively simple decision‐making model (presented in this paper) coupled with other “operation models” of higher complexity. If the “catch‐to‐stock” parameter cannot be reasonably assessed ( β → 0 + ), the fishery managers may rely upon the lower bound of stationary stock size, which depends on economic and biological factors (such as the present and future economic values of the exploited fish stock, its marginal productivity, and underlying dynamics of biological growth).