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Reviews in Fish Biology and Fisheries

, Volume 19, Issue 3, pp 313–327 | Cite as

On the stock estimation for some fishery systems

  • A. Guiro
  • A. Iggidr
  • D. Ngom
  • H. Touré
Research Paper

Abstract

In this work we address the stock estimation problem for two fishery models. We show that a tool from nonlinear control theory called “observer” can be helpful to deal with the resource stock estimation in the field of renewable resource management. It is often difficult or expensive to measure all the state variables characterising the evolution of a given population system, therefore the question arises whether from the observation of certain indicators of the considered system, the whole state of the population system can be recovered or at least estimated. The goal of this paper is to show how some techniques of control theory can be applied for the approximate estimation of the unmeasurable state variables using only the observed data together with the dynamical model describing the evolution of the system. More precisely we shall consider two fishery models and we shall show how to built for each model an auxiliary dynamical system (the observer) that uses the available data (the total of caught fish) and which produces a dynamical estimation \(\hat x(t)\) of the unmeasurable stock state x(t). Moreover the convergence speed of \(\hat x(t)\) towards x(t) can be chosen.

Keywords

Fishery models Stage-structured population models Estimation Harvested fish population Observers 

Notes

Acknowledgments

We thank the anonymous referees for their valuable comments and suggestions that have helped us to improve the presentation of this article.

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Laboratoire d’Analyse Mathématique des Equations (LAME), Faculté des Sciences et TechniquesUniversité de OuagadougouOuagadougouBurkina Faso
  2. 2.INRIA Nancy – Grand Est and University Paul Verlaine-MetzMetz Cedex 01France
  3. 3.Laboratoire d’Analyse Numérique et d’Informatique (LANI), UFR de Sciences Appliquées et de TechnologieUniversité Gaston BergerSaint-LouisSenegal

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