Mathematical Modeling Interactions Between Human and Fish Populations: A Bio-Economic Approach
Authors:
Jared Duchen, Kimberly VilimasMentor:
Joanna Bieri, Professor of Mathematics, Ph.D, University of Redlands, CAMathematically modeling interactions between fish and fisherman can be a powerful tool in the formulation of optimal management strategies. In our research, we utilized computer simulations in order to model a system of nonlinear recurrence relations which implement population mathematics as well as economic concepts. We then analyzed the system by means of fixed points, Jacobian stability testing, graphical interpretations, and parameter analysis using the Jury test. The main objectives of this piece are to: (i) recreate and verify the traditional pure open access bio-economic model pioneered by Gordon [1954], Scott [1955] and Schaeffer [1957] and (ii) discuss the implications these results have on the fish industry today, including what needs to be improved and updated.