hal-00656184, version 1

Basic Reproduction Ratio for a Fishery Model in a Patchy Environment.

Pierre Auger ¹, Ali Moussaoui ^a, 2, Gauthier Sallet ^1, 3

Acta Biotheoretica 60, 1-2 (2012) 167-188

• a –  Université Abou Bekr Belkaid Tlemcen
• 1:  Unité de modélisation mathématique et informatique des systèmes complexes (UMMISCO)
• http://www.ummisco.ird.fr
  Institut de recherche pour le développement [IRD] : UR209 – Université Pierre et Marie Curie (UPMC) - Paris VI – Institut de la francophonie pour l'informatique – Université Cadi Ayyad (Marrakech, Maroc) – Université Cheikh Anta Diop (Dakar, Sénégal) – Université Gaston Bergé (Saint-Louis, Sénégal) – Universtié Yaoundé 1 (Cameroun) IRD France Nord - 32 avenue Henri Varagnat - 93143 Bondy cedex France
• 2:  Département de Mathématiques
• http://fs.univ-tlemcen.dz
  Université Abou Bekr Belkaid Tlemcen Algeria
• 3:  MASAIE (INRIA Nancy - Grand Est / LMAM)
• 
  INRIA – Université Paul Verlaine - Metz – CNRS : UMR7122 – Université de Lorraine INRIA Nancy-Grand Est et LMAM UPV-Metz 57045 METZ France

Bibliographic reference

• Type of document: Articles in peer-reviewed journal
• Domain:

  Life Sciences/Ecology, environment/Ecosystems

  Life Sciences/Agricultural sciences/Sciences and technics of fishery

  Mathematics/Dynamical Systems

• Title: Basic Reproduction Ratio for a Fishery Model in a Patchy Environment.
• Abstract: We present a dynamical model of a multi-site fishery. The fish stock is located on a discrete set of fish habitats where it is catched by the fishing fleet. We assume that fishes remain on fishing habitats while the fishing vessels can move at a fast time scale to visit the different fishing sites. We use the existence of two time scales to reduce the dimension of the model : we build an aggregated model considering the habitat fish densities and the total fishing effort. We explore a regulation procedure, which imposes an average residence time in patches. Several equilibria exist, a Fishery Free Equilibria (FFEs) as well as a Sustainable Fishery Equilibria (SFEs). We show that the dynamics depends on a threshold which is similar to a basic reproduction ratio for the fishery. When the basic reproduction ratio is less or equal to 1, one of the FFEs is globally asymptotically stable (GAS), otherwise one of the SFEs is GAS.
• Full text language: English
• Journal title:

  Acta Biotheoretica (Acta Biotheor)
  Publisher	Springer Verlag (Germany)
  ISSN	0001-5342 (eISSN : 1572-8358)

• Publication date: 2012
• Audience: international
• Commercial editor: Springer
• Volume: 60
• Number: 1-2
• Pagination: 167-188
• DOI: 10.1007/s10441-012-9155-3

• hal-00656184, version 1
• http://hal.inria.fr/hal-00656184
• oai:hal.inria.fr:hal-00656184
• From: Abderrahman Iggidr <>
• Submitted on: Tuesday, 3 January 2012 16:52:25
• Updated on: Friday, 14 September 2012 11:42:15