Harvesting of age structured fish populations [Elektronische Ressource] / by Mostafa Kamel Saber Mohamed

HARVESTING OF AGE STRUCTURED FISH POPULATIONS Doctoral Disseration Department of Mathematics and Computer Science University of Osnabrück By Mostafa Kamel Saber Mohamed Osnabrück- Germany January 2005 Supervisor: Prof. Dr. Horst Behncke Mathematics and Computer Science University of Osnabrück ii To my parents, my wife and my children. iii Table of Contents Table of contents iv Acknowledgements vi Synoptic view of the study (Abstract) viii Chapter 1 Mathematical Models for Fishery 1 1.1 Introduction …………………………………………. 1 1.2 The Biology of fish …………………………………. 6 1.3 Specific fish species ……………………………….. 13 1.4 Stock and Recruitment ……………………………... 20 Chapter 2 Models for the population of marine fish 29 2.1 Description of the model ……….…………………. . 29 2.2 Some matrix theory ………………………………… 32 2.3 The net reproductive value …………………………. 34 2.4 Nonlinear matrix models and their equilibria ………. 38 2.