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. 2016 Dec;64(4):479-493.
doi: 10.1007/s10441-016-9299-7. Epub 2016 Oct 26.

Interactions Between the Cross-Shore Structure of Small Pelagic Fish Population, Offshore Industrial Fisheries and Near Shore Artisanal Fisheries: A Mathematical Approach

Rachid Mchich  1 , Timothée Brochier  2   3 , Pierre Auger  2 , Patrice Brehmer  3
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Interactions Between the Cross-Shore Structure of Small Pelagic Fish Population, Offshore Industrial Fisheries and Near Shore Artisanal Fisheries: A Mathematical Approach

Rachid Mchich et al. Acta Biotheor. 2016 Dec.

Abstract

This work presents a mathematical model describing the interactions between the cross-shore structure of small pelagic fish population an their exploitation by coastal and offshore fisheries. The complete model is a system of seven ODE's governing three stocks of small pelagic fish population moving and growing between three zones. Two types of fishing fleets are inter-acting with the fish population, industrial boats, constrained to offshore area, and artisanal boats, operating from the shore. Two time scales were considered and we use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model, which is a four dimension one. The analysis of the aggregated model is performed. We discuss the possible equilibriums and their meaning in terms of fishery management. An interesting equilibrium state can be obtained for which we can expect coexistence and a stable equilibrium state between fish stocks and fishing efforts. Some identification parameters are also given in the discussion part of the model.

Keywords: Aggregation of variables; Fishery model; Industrial and artisanal fisheries; National policy management; Parameters identification measures.

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