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We propose a bio-economic model of a fishery describing the variations of the fish stock, the fishing effort and the price of the resource on the market supposed to depend on supply and demand. The originality of this model comes from taking into account the storage of part of the resource for a certain time before being put up for sale on the market. Taking into account the supposedly fast price dynamics compared to the other mechanisms involved and after integration of the stock equation, the system is reduced to a system of two delayed differential equations. The qualitative analysis of the model is carried out with the search for equilibrium points and the study of their stability. The study shows the existence of a catastrophic equilibrium corresponding to the extinction of the resource and one or two sustainable fishery equilibrium points that can coexist under certain conditions. The model shows that storing part of the resource makes it possible to avoid a catastrophic situation with the extinction of the fish stock and to stabilize the fishery in the long term. The study also shows that the price variation of the resource has a stabilizing effect by avoiding the appearance of periodic solutions associated with a stable limit cycle surrounding a sustainable fishery equilibrium point resulting from a Hopf bifurcation, which is contrary to the case without price variation where this is possible., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

An idealized system of a shared fish stock associated with different exclusive economic zones (EEZ) is modelled. Parameters were estimated for the case of the small pelagic fisheries shared between Southern Morocco, Mauritania and the Senegambia. Two models of fishing effort distribution were explored. The first one considers independent national fisheries in each EEZ, with a cost per unit of fishing effort that depends on local fishery policy. The second one considers the case of a fully cooperative fishery performed by an international fleet freely moving across the borders. Both models are based on a set of six ordinary differential equations describing the time evolution of the fish biomass and the fishing effort. We take advantage of the two time scales to obtain a reduced model governing the total fish biomass of the system and fishing efforts in each zone. At the fast equilibrium, the fish distribution follows the ideal free distribution according to the carrying capacity in each area. Different equilibria can be reached according to management choices. When fishing fleets are independent and national fishery policies are not harmonized, in the general case, competition leads after a few decades to a scenario where only one fishery remains sustainable. In the case of sub-regional agreement acting on the adjustment of cost per unit of fishing effort in each EEZ, we found that a large number of equilibria exists. In this last case the initial distribution of fishing effort strongly impact the optimal equilibrium that can be reached. Lastly, the country with the highest carrying capacity density may get less landings when collaborating with other countries than if it minimises its fishing costs. The second fully cooperative model shows that a single international fishing fleet moving freely in the fishing areas leads to a sustainable equilibrium. Such findings should foster regional fisheries organizations to get potential new ways for neighbouring fish stock management., (Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.)

We investigate a system of two species exploiting a common resource. We consider both abiotic (i.e. with a constant resource supply rate) and biotic (i.e. with resource reproduction and self-limitation) resources. We are interested in the asymmetric competition where a given consumer is the locally superior resource exploiter (LSE) and the other is the locally inferior resource exploiter (LIE). They also interact directly via interference competition in the sense that LIE individuals can use two opposite strategies to compete with LSE individuals: we assume, in the first case, that LIE uses an avoiding strategy, i.e. LIE individuals go to a non-competition patch to avoids competition with LSE individuals, and in the second one, LIE uses an aggressive strategy, i.e. being very aggressive so that LSE individuals have to go to a non-competition patch. We further assume that there is no resource in the non-competition patch so that individuals have to come back to the competition patch for their maintenance, and the migration process acts on a fast time scale in comparison with demography and competition processes. The models show that being aggressive is efficient for LIE's survival and even provoke global extinction of the LSE and this result does not depend on the nature of resource.

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.