Harvesting technology and catch-to-biomass dependence: The case of small pelagic fish

This note deals with a harvesting model for a single stock fishery. In the case of small pelagic fish it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and on fish stock. Empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way to changes in fishing effort and fish stock levels. This is in contradiction with traditional fishery models where catch-to-input marginal productivities are normally assumed to be constant. While allowing for non linearities in both catch-to-effort and catch-to-stock parameters, this note extends the traditional analysis by focusing on the dependence of the stationary solutions upon the nonlinear catch-to-biomass parameter. Given the emphasis on the case of small pelagic fish, the analysis considers positive but small values for the catch-to-stock parameter.