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Mathematical Modeling of the Nile Perch Fishery in Lake Victoria

Kammerer, Johannes

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Abstract

The Lake Victoria ecosystem in East Africa is known to support the world's largest small-scale freshwater fishery. Economically, the most valuable fish in this ecosystem is the Nile perch, whose population plays a vital role for ecosystem stability. The question of the optimal regulatory paradigm for harvesting Nile perch is subject to considerable debate. Theoretical concepts such as 'balanced harvesting' with little size selectivity coexist with a practice of size-based instruments, targeting gear and catch sizes.

This thesis develops, analyzes and simulates a new bio-economic model of the Nile perch fishery that couples a bio-energetic fish population model to an economic model of the fishery, incorporating the size structure of the fish population and gear selectivity.

The existence of a unique, non-negative and regular solution of the model is proven. After validating the model against the empirical population size structure, we show that the current fishery is a steady state solution and that the effort is 2.0% above the optimal effort for fixed fleet selectivity. An alternative fleet selectivity that spares fish below 50cm increases yield, income and stock biomass. The numerical optimization shows that the optimal fleet selectivity spares fish below at least 70cm. Optimizing the fleet selectivity increases yield by 94.6% and income by 151.9%. The dynamic fishers response model shows that boat owners switch to using 6", 7" and 8" gillnets because of the high profitability.

The results indicate significant gains in yield and income from sparing small fish and allow three conclusions to be drawn: First, there is not necessarily a trade-off between harvest and stock biomass, but both can be increased through improved fishing. Second, sparing small fish is not a loss of catch, but exploits the growth potential of fish and increases reproduction and stock biomass. Third, our model suggests that fishing should be selective, focusing on larger fish. This result questions the dominant paradigm of balancing harvest across sizes in proportion to productivity, which implies targeting smaller fish more intensively. The novel size structured bio-economic fishery model therefore challenges the current understanding and suggests new directions for modeling the fishery of Lake Victoria.

Document type: Dissertation
Supervisor: Marciniak-Czochra, Prof. Dr. Anna
Place of Publication: Heidelberg
Date of thesis defense: 18 March 2024
Date Deposited: 25 Mar 2024 13:19
Date: 2024
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Institut für Mathematik
DDC-classification: 500 Natural sciences and mathematics
Uncontrolled Keywords: Mathematical Modeling Nile Perch Fishery Lake Victoria
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