Population Growth Models: Relationship between sustainable fishing and making a profit

Authors

James Sandefur, Georgetown UniversityFollow

Publication Date

11-27-2023

Keywords

compensation, depensation, contest competition, scramble competition, sustainability, revenue, profit, open access

Disciplines

Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

In this paper, we develop differential equations that model the sustainable harvesting of species having different characteristics. Specifically, we assume the species satisfies one of two different types of density dependence. From these equations, we consider maximizing sustainable harvests. We then introduce a cost function for fishing and study how maximizing profit affects the harvesting strategy. We finally introduce the concept of open access which helps explain the collapse of many fish stocks.

The equations studied involve relatively simple rational and exponential functions. We analyze the differential equations using phase-line analysis as well as graphing approximate solutions using Euler's method, which is really a discrete form of the differential equation.

Recommended Citation

Sandefur, James (2024) "Population Growth Models: Relationship between sustainable fishing and making a profit," CODEE Journal: Vol. 17, Article 6.
Available at: https://scholarship.claremont.edu/codee/vol17/iss1/6