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We consider a fishery model with two sites: (1) a marine protected area (MPA) where fishing is prohibited and (2) an area where the fish population is harvested. We assume that fish can migrate from MPA to fishing area at a very fast time scale and fish spatial organisation can change from small to large clusters of school at a fast time scale. The growth of the fish population and the catch are assumed to occur at a slow time scale. The complete model is a system of five ordinary differential equations with three time scales. We take advantage of the time scales using aggregation of variables methods to derive a reduced model governing the total fish density and fishing effort at the slow time scale. We analyze this aggregated model and show that under some conditions, there exists an equilibrium corresponding to a sustainable fishery. Our results suggest that in small pelagic fisheries the yield is maximum for a fish population distributed among both small and large clusters of school.

@article{hieu_effect_2014, title = {Effect of {Small} {Versus} {Large} {Clusters} of {Fish} {School} on the {Yield} of a {Purse}-{Seine} {Small} {Pelagic} {Fishery} {Including} a {Marine} {Protected} {Area}}, volume = {62}, issn = {0001-5342}, doi = {10.1007/s10441-014-9220-1}, abstract = {We consider a fishery model with two sites: (1) a marine protected area (MPA) where fishing is prohibited and (2) an area where the fish population is harvested. We assume that fish can migrate from MPA to fishing area at a very fast time scale and fish spatial organisation can change from small to large clusters of school at a fast time scale. The growth of the fish population and the catch are assumed to occur at a slow time scale. The complete model is a system of five ordinary differential equations with three time scales. We take advantage of the time scales using aggregation of variables methods to derive a reduced model governing the total fish density and fishing effort at the slow time scale. We analyze this aggregated model and show that under some conditions, there exists an equilibrium corresponding to a sustainable fishery. Our results suggest that in small pelagic fisheries the yield is maximum for a fish population distributed among both small and large clusters of school.}, language = {English}, number = {3, SI}, journal = {Acta Biotheoretica}, author = {Hieu, Nguyen Trong and Brochier, Timothee and Tri, Nguyen-Huu and Auger, Pierre and Brehmer, Patrice}, month = sep, year = {2014}, keywords = {ACL, Aggregation of variables, Clusters, E3, Fish school, Marine protected area, Optimal yield, Small pelagic fish, Three level system, WOS}, pages = {339--353} }

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