Steinworkth, Bailey, Yuhui Wand, Xing Zhang. 2010. Modeling of a Fish Population and the Effects of Overfishing. Student Project. James Madison University. 22 pp.
Abstract: According to the United Nations, 200 million people depend on fishing as their source of food or livelihood.1 However, current fishing practices threaten the security of marine populations. Dramatic examples such as the collapse of the cod industry in Newfoundland in the early 1990s illustrate that fishing without appropriate limitations can have detrimental effects on fish populations and on the people and economies that depend on them.2 Understanding how populations of marine life can be harvested sustainably is vital to the economies of nations and to the well‐being of millions. We seek to gain insight into how people can use fish as a resource and produce maximum economic benefit while maintaining sustainable marine populations. Using a modified logistic growth model with a limiting equilibrium population and a threshold population, we represented a generalized fish population in order to determine sustainable fishing rates.
We find that 1) increasing the fishing rate will decrease the equilibrium population and increase the threshold population; 2) for a given fish population, there exists some fishing rate that optimizes economic benefit and the growth rate of the fish population; 3) for a given population, there exists a fishing rate at which the threshold and equilibrium populations will be equal; and 4) fishing above will cause the fish population to decline to zero. We apply our findings to a threatened population of fish, the Chinook salmon that spawn in the Lower Skagit River of Puget Sound in Washington State, and issue recommendations for maintaining the security of this population.
Keywords: differential equation, model, fish, population, overfishing, harvest, sustainability, equilibrium
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