Mathematical Modeling of Fish Population Dynamics With Harvesting In Tekeze Dam

Abstract

This study analyzes the mathematical models to determine sustainable harvesting strategies for Tilapia fish population in Tekeze dam, Ethiopia. Even though Tilapia fish farming has been locally commercialized, the use of mathematical models in determining harvesting strategies has not been widely applied in Tekeze dam. Logistic model is appropriate for population growth of fishes when overcrowding, over fishing and competition for resource are taken into consideration. Using a logistic growth models, it formulates and compare three harvesting strategies: constant, periodic and proportional. The carrying capacity of the dam was first estimated at 153312 tonnes using a phosphorus budget model. Analysis reveals a Maximum Sustainable Yield (MSY) of 30662 tonnes per year under constant harvesting, representing a critical threshold beyond which the population collapses. Proportional harvesting demonstrates high sensitivity to fishing effort, with a clear extinction threshold. In contrast, periodic harvesting emerges as the most sustainable and resilient strategy. By incorporating recovery periods, it maintains ecological balance, optimizes long term yield, and presents stock depletion. Numerical simulation confirm the optimal harvesting rate converges to half the intrinsic growth rate(h=r/2) for yield maximization. The findings provide a scientific basis for management, recommending the adoption of regulated periodic closures, effort limits, and community-led monitoring. This work offers a practical, model-driven framework to transform the Tekeze Dam fishery in to a sustainable resources, balancing food security with ecosystem health. These findings can assist fish harvesters neighboring to Tekeze dam, to increase fish supply to meet the demand for Tilapia fish.