How to model marine reserves ?

Patrice Loisel (1) , Pierre Cartigny (1, 2)

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

The safeguarding of resources is one of the principal subjects of halieutics studies. Among the solutions proposed to avert the disappearance of species, the setting in place of no take reserves is often mentioned. Most work on this subject, theoretical as well as applied, was undertaken in recent years. In this paper, we seek to compare two different models presented in existing literature by highlighting their underlying assumptions. Both models were derived from what is often referred to as the "model of Schaefer-Clark'' (reference to the work of the last author on Mathematical Bioeconomics : Clark [7]). We show that various variations of this model lead to properties that can be very different.

Mots clés: Dynamical system; Calculus of variation; Infinite horizon; Marine reserve; Bioeconomic model

Domaines: Optimisation et contrôle [math.OC]

Patrice Loisel, Pierre Cartigny. How to model marine reserves ?. Nonlinear Analysis: Real World Applications, 2009, 10 (3), pp.1784-1796. ⟨10.1016/j.nonrwa.2008.02.023⟩. ⟨hal-00793648⟩