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

Mohamed Mokeddem

Informations

• Publié par: universitat_osnabruck
• Publié le: 01 janvier 2005
• Nombre de lectures: 58
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

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
2.5 Stability properties for nonlinear Leslie matrix model 42
Chapter 3 Harvesting theory 48

3.1 The semicontinuous description .…………………. . 48
3.2 Discrete harvesting model …………………………….50
3.2.1 Selective harvesting ……………………….50
3.2.2 Harvesting policy ………………………….52
3.2.3 Harvesting with nets ……………………….68
3.3 Semicontinuous harvesting model …………………..73
3.3.1 Selective harvesting ……………………….73
3.3.2 Harvesting with nets …………...………….77


iv

Chapter 4 Numerical Examples and Influence of Parameters on
Harvesting Models 80
4.1 Numerical Examples …………………………………..80
4.2 Influence of parameters ………………………………..98
4.3 Sensitivity of parameters ………………………………106
4.4 Influence of cost in semicontinuous harvesting ……….111
4.5 Conclusion and Results ………………………………..117
Chapter 5 Dynamical Model for fish population and Stability 121
5.1 Description of the model ……………………………...121
5.2 Stability for concrete fish species ……………………...123

References 134





















v

Acknowledgements

I begin this note of acknowledgement by expressing my deepest gratitude
and thanks to my supervisor Prof. Dr. Horst Behncke, Department of
Mathematics and Computer Science, University of Osnabrück, Germany,
for his valuable guidance and encouragement at every stage, which has
enabled me to complete this thesis. I am extremely grateful to him for his
constructive suggestions, invaluable comments, continuous advices and
illuminating points which were greatest help to me while preparing this
thesis. Without his kind supervision, this dissertation would have not
taken its present shape.

I wish to thank the staff members and secretaries of the Department of
Mathematics and Computer Science, University of Osnabrück, for their
continuous helps and assistance.

I pay my humble thanks and regards to the members of the Department of
Mathematics, Faculty of Science, Helwan University, Egypt.

I am very much grateful to the Egyptian Government for financing and
supporting my higher study in Germany.

I owe a great debt of gratitude to my parents and other family members.
Their affection has really been a source of encouragement.






vi



I wish to express my heartfelt gratitude and thanks to my wife, two sons
Ahmed, Mohamed and daughter, without their constant support, cordial
love and encouragement, my study and research would never been
completed. They never complained about my preoccupation with research
and writing.


Osnabrück, Germany Mostafa Kamel Saber Mohamed
2005


























vii
Synoptic view of the study
(Abstract)

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).



viii

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.







ix

Chapter 1

Mathematical Models for fishery



In this chapter we collect some important materials in biology of fish and
harvesting of fish.

§ 1.1 Introduction

More than two thirds of the surface of the earth are covered by oceans or seas. As a
result, fish and other marine products form an important source of food, in
particular protein, for mankind. This role of marine products is still rising, because
land for agriculture has been overexploited to a large extent and no new areas for
agriculture can be found, because of a limitation of water.

Fishing technology has developed from small boats to swimming fishing factories
with sophisticated equipment for detecting, catching and processing fish. This
development was pressured and directed by an ever increasing population with a
high demand for food in particular protein rich food. Thus many areas, in particular
the traditional fishing areas e.g. the Northern sea, the Baltic sea or North Atlantic
are overfished and a number of species of fish are near extinct e.g. herring or
canadian cod. In fact in the fall of 2002 the E U proposed a complete ban on the
fishing of cod because of an almost complete lack of juvenile fish. As a result of
this overfishing the catch has been reduced from 270.000 ton in 1970 to 40.000 in
2000. Similarly Canada closed the cod fishery in the canadian great banks in 1992.
But the cod stocks still do not show any sign of recovery with serious consequences
for the canadian fishing industry. Nations with a large commercial fishing industry
are particularly reluctant to agree on impose limitations for fishing. In many cases,
countries have unilaterally declared fishing zones near their coasts.

1