The influence of Allee effects on optimal harvesting of Nile perch, Nile tilapia, and small pelagic fish in Lake Victoria
| dc.contributor.author | Onekgiu, George | |
| dc.date.accessioned | 2026-01-28T09:41:17Z | |
| dc.date.available | 2026-01-28T09:41:17Z | |
| dc.date.issued | 2025-11-10 | |
| dc.description | A dissertation submitted to the directorate of graduate training, research, and innovations in partial fulfillment of the requirements leading to the award of the degree of master of science in mathematics of Muni University | |
| dc.description.abstract | In this dissertation, models for finding the optimal controls of harvesting Nile perch, Nile tilapia, and small pelagic fish within a food chain formulated with and without the Allee effect were presented. The models were based on reaction-diffusion-advection PDEs subject to Robin boundary conditions. The version without the Allee effect employed logistic growth dynamics, while the one incorporating the Allee effect utilised an Alleetype growth function. The optimality system, comprising the state equations, adjoint equations, and optimality conditions, was derived using the formal Lagrange method. An FBSM based on explicit finite difference schemes was employed to solve the state, adjoint, and control equations in the two models. In the model without the Allee effect, optimal controls that allowed for continuous opti mal harvesting were determined, with higher yields observed toward the end of the period when fish populations had grown. The results also indicated that diffusion and advection coefficients significantly influenced fish distribution and optimal control of harvesting: low diffusion coefficients promoted fish aggregation and higher economic returns, whereas high advection coefficients dispersed fish and reduced returns. In scenarios where the Allee effect was considered, the optimal controls obtained required no harvesting to prevent population collapse when the initial populations were low (below the Allee threshold). At moderate to high initial biomasses of the three fish species (above the Allee threshold), the optimal controls obtained permitted continuous optimal harvesting across the entire domain and throughout the simulation period. This emphasises the pivotal role of the Allee effect in defining population thresholds that ensure an optimal and sustainable harvesting. It is recommended that, without the Allee effect, continuous optimal harvesting that targets areas of high population aggregation to maximise yield and economic returns, should be allowed. With the Allee effect, harvesting should cease when populations are below the threshold to allow recovery, while populations above the threshold can be harvested sustainably at optimal rates. | |
| dc.identifier.citation | Onekgiu, G. (2025). The influence of Allee effects on optimal harvesting of Nile perch, Nile tilapia, and small pelagic fish in Lake Victoria (Unpublished graduate dissertation). Muni University, Arua, Uganda | |
| dc.identifier.uri | https://dir.muni.ac.ug/handle/20.500.12260/908 | |
| dc.language.iso | en | |
| dc.publisher | Muni University | |
| dc.subject | Influence of Allee effects on optimal | |
| dc.subject | harvesting of Nile perch | |
| dc.subject | Nile tilapia | |
| dc.subject | small pelagic fish | |
| dc.subject | Lake Victoria | |
| dc.title | The influence of Allee effects on optimal harvesting of Nile perch, Nile tilapia, and small pelagic fish in Lake Victoria |