Ecological Modelling 222 (2011) 1253–1261 Contents lists available at ScienceDirect Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel A management oriented competitive model with two time scales: The case of sardine fishery along the Atlantic coast between Cantin Cape and Blanc Cape Najib Charouki a , Nadia Raïssi b , Pierre Auger c , Rachid Mchich d,∗ , Hmida Atmani a a Institut National de Recherche Halieutique, 2 rue de Tiznit, Casablanca, Morocco b Laboratoire EIMA, Faculté des Sciences, Université Ibn Tofaïl, B.P. 133, Kénitra, Morocco c UMI 209 IRD & UPMC UMMISCO, Centre de Recherche d’Ile de France, 32 avenue Henri Varagnat, 93143, Bondy Cedex, France d Dépt de Gestion, Ecole Nationale de Commerce et de Gestion, B.P. 1255, 90000, Tangier, Morocco article info Article history: Received 4 September 2010 Received in revised form 26 December 2010 Accepted 30 December 2010 Available online 1 February 2011 Keywords: Fishery model Sardina pilchardus Atlantic coast Aggregation of variables Equilibrium points Stability Parameters estimation Fisheries management abstract This work is proposing a dynamic model governing the evolution with respect to time of the sardine (Sardina pilchardus) stock in the Atlantic coast between Cantin Cape and Blanc Cape in the North West Africa, which is harvested by two different fishing fleets. We assume that the sardine stock is distributed on two closed zones and targeted by a composite fleet: The Moroccan purse seiners which can move between the fishing regions and a fleet of deepsea trawlers composed mainly of foreign vessels and operating in the southern zone. The model is a set of 5 Ordinary Differential Equations (ODE) with two components: a stock component which describes the sardine evolutions in its 2 zones of distribution, and a component governing the dynamics of the fishing efforts. By using some aggregation methods, we reduce the system to a set of 4 ODE, and then we study analytically the existence and the asymptotic stability of the equilibrium points. The parameters of the stock dynamics and harvest are then estimated using models fitting techniques based on a set of available data. The conditions leading to sustainable fisheries are then simulated. Interpretations of our results can be used by the authority responsible of fishery management, as general recommendations for a better management of Moroccan fisheries. © 2011 Elsevier B.V. All rights reserved. 1. Introduction The North African Atlantic coast is one of the richest areas of the world in marine resources. Indeed, it is characterized by a large continental shelf which can reach 60 nautical miles in some regions, a geographical situation and an orientation along the dom- inant winds which privilege it to be among the four upwelling ecosystems of the world (Smith, 1984; Wooster et al., 1976). In fact, the upwelling phenomenon activates a rise of cold water by a mechanical process and permits to enrich the habitat of the marine resources by the nutriments and primary production nec- essary for all trophic levels. With more than 70% of small pelagic fish landed, the sardine (Sardina pilchardus) fisheries dominate the fishing activity in the Moroccan Atlantic coast. In addition to the fishing intensity, the sardine dynamic is governed by the vari- ability and seasonality of the upwellings in the region (Belvèze, 1991; Kifani, 1991; Nykjaer and Van Camp, 1994; Roy, 1991; Smith, 1984). The most obvious revelation of this variability is the stock ∗ Corresponding author. Tel.: +212 6 63 03 62 38; fax: +212 5 39 31 34 93. E-mail addresses: charouki@hotmail.com (N. Charouki), n.raissi@lycos.com (N. Raïssi), pierre.auger@bondy.ird.fr (P. Auger), racmchich@yahoo.com (R. Mchich), atmani@inrh.org.ma (H. Atmani). collapse that occurred in 1997, when the biomass decreased from 5660 to 1130 thousand tons, although the catches were maintained at a normal level (Charouki et al., 2004). The complexity of these species requires, thus, a regular follow-up and a rational manage- ment, taking account of its biological, economic and social aspects. The major aim of the manager then is to optimize the activity and to increase its profitability, setting as goal the maintenance of the landings at a level closed to the maximum sustainable activity (FAO, 2001–2007). In this context, this paper presents a contribution to sardine fisheries modelling in the Moroccan Atlantic coast. Modelling is based on knowledge and data available on its dynamics and har- vest. Indices of acoustic biomasses, which are used to describe the natural stock dynamic, were estimated during acoustic sur- veys conducted onboard the Norwegian research vessel “Dr. Fridtjof Nansen” which was operating in the region since 1995–2006 (Cruise reports, 1995–2006). Data related to the harvest are drawn from official statistics on the sardine landings while the commer- cial knowledge is based on the bioeconomic studies carried out on the small pelagic fish in the region (Kamili, 2006; Lamhaidi, 2003). The aim of this study is to present a general and simple model for the sardine fishery along the Moroccan Atlantic coast in two main fishery zones, the central and south zones. We have made the choice to consider a simple global model for which any parame- 0304-3800/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2010.12.022