Harvesting of Age Structured Fish Populations

• Main Author: Mohamed, Mostafa Kamel Saber
• Other Authors: Prof. Dr. Horst Behncke
• Format: Doctoral Thesis
• Language: English
• Published: 2005
• Subjects: Age structured fish populations; nonlinear Leslie matrix model; recruitment functions; harvesting model; 27 - Mathematik; ddc:630
• Online Access: https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2005021812

The aim of this thesis is to define and study harvesting models of fish populations. These models are applied to particular fish species e.g., haddock and cod. The thesis is divided into five chapters: The first chapter is considered as an introductory one. In it, basics of fish biology and the recruitment process are defined. Two simple recruitment models known by the names Ricker and Beverton-Holt are used. In the second chapter the generalized Leslie model or Usher model is introduced. In section 2.2, some matrix theory is presented. For this matrix model, the net reproductive number is defined and studied in section 2.3. It turns out to be more useful than the spectral radius. In section 2.4, this study is extended to nonlinear matrix models. The nonlinearity, however, is defined only by the recruitment process. This allows to determine the equilibrium components. Finally section 2.5, the local stability of nonlinear matrix models is analyzed. Harvesting of such general matrix model is defined in chapter 3. We distinguish three different harvesting models (selective, net and semicontinuous harvesting models). In chapter 4, these harvesting models are then applied to concrete fish populations and analyzed with respect to its various parameters. In chapter 5, the stability is studied again along the lines of the paper of Levin, Goodyear [18]. The key results in this study are: 1) The maximum sustainable yields for selective harvesting and net harvesting are rather close. 2) Semicontinuous harvesting is more realistic harvesting models. 3) From a quantitative point of view, the choice of the recruitment function is important. 4) Harvesting process increases mortality and stability when we used Ricker recruitment model. 5) Stability of populations always holds if we use Beverton-Holt recruitment model.