In this thesis an age structured model of fish and harvesting of fish are studied. This includes the basic properties as well as the analysis of equilibria and their stability for various recruitment functions. The only nonlinearity of this model lies in the juvenile stage in form of the recruitment function. Recruitment is considered as recruitment into the first year fertile class. The Ricker recruitment function will mostly be used . But we also discuss the Beverton-Holt recruitment and compare its impact. The main result is that monotone recruitment functions lead to a globally stable equilibrium. For Ricker recruitment functions periodic solutions are possible, but this model for cod and herring always leads to stable equilibria. Harvesting occurs in all classes separately with no harvesting in the first class. We describe harvesting in form of harvesting effort, resulting in an increase of mortality. This approach allows to model the interference of natural mortality and fishing mortality. Harvesting cost will be considered as a linear function of effort and the corresponding maxima are determined. This has the advantage to keep the number of parameters low. This makes the model more tractable and easier to apply to other stocks or species of fish. Optimization of the harvest is determined and analyzed. It is based on harvesting intensity and mesh size. We also show that harvesting increases stability of the static model. This model is extended to a discrete optimal control model in order to determine optimal sustainable policies. The solutions are almost of the fastest approach type to the equilibrium type solution. Periodic or pulse solutions do not arise. Near optimal strategies are analyzed and other feasible strategies are also considered. In last part of this thesis the problem of extinction of population is investigated. The effect of various factors as well as natural factors on marine fish populations are studied, which are described by the model in order to get some idea on the size of various factors. Most fishing takes place near the break even intensity. It is defined as the fishing mortality at which cost equals profit. As a further aspect recovery scenarios are studied. Concrete numerical studies for optimal solutions are determined for cod and herring. Care is taken to take into account all possible realistic parameters but also to keep the model tractable for other species.
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:repositorium.ub.uni-osnabrueck.de:urn:nbn:de:gbv:700-2015042813153 |
| Date | 28 April 2015 |
| Creators | Al-Nassir, Sadiq |
| Contributors | Prof. em. Dr. Horst Behncke, Prof. Dr. Horst Malchow, Prof. Dr. Suzanne Lenhart |
| Source Sets | Universität Osnabrück |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, application/zip |
| Rights | Namensnennung-NichtKommerziell-KeineBearbeitung 3.0 Unported, http://creativecommons.org/licenses/by-nc-nd/3.0/ |
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