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Keesom, No’am , Trisha Macrae, Anjuli Uhlig, and Richard Wang. 2010. Fishing for Answers: Investigating Sustainable Harvesting Rate. Paper 11 pp.
Abstract: The purpose of this report is to determine and propose a model by which an optimal harvesting frequency can be determined to maintain a steady population of Alaskan salmon. In order to do so, we look at the growth rates of the salmon population as well as death rates due to harvesting and other factors. Some mortality factors, however, are age-dependent (for instance, only adult fish have been found to cannibalize young fish), so we consider the overall Alaskan salmon population as two subpopulations of the adult and juvenile fish [3]. We then find a differential equation to model the population that relates the adult population, the juvenile population, and time t. We consider the periodic nature of harvesting. Every year, fisheries target the adult fish that return to reproduce, for the spawning salmon is the most desirable to human consumers [3]. Because the mating season occurs annually and around the same time, harvesting can be represented by a constant, periodic trigonometric function whose amplitude and frequency represent the harvesting rate limit and the frequency per unit time, respectively [6]. Together, the population model with the oscillatory harvesting component result in a nonlinear differential equation that we solve numerically with Euler’s method of approximation.
Keywords: differential equation, model, logistic, harvesting, canabalism, fisheries, salmon, nonlinear, Euler’s Method
2010-Keesom-EtAl.pdf
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