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Undergraduate

**Introduction**

Consider a stock of fish. If there is no harvest, the stock will tend to renew itself with births and deaths: It will arrive at more or less the same level of biomass each year-with variation due to climate and weather variability, and assuming that other variables remain constant, such as food and predation.

The initial growth of such a population is commonly modeled as logistic growth toward an environmental carrying capacity, as in Figure 1.

A fishery is a geographical area where fish breed and are harvested. A contemporary example that we consider is Georges Bank, an area off the coast of Maine. Another example is the area off Newfoundland and Labrador in eastern Canada, which was a fishery for Northern Atlantic cod, until it collapsed in 1992 and was closed [Schijn et al. 2021].

A fishery has multiple competing interests. One is a desire to feed people both today and in the future. At the same time, there is an economic interest for those making a living from fishing. At first glance, the goal would seem to be to harvest the absolute maximum amount available (assuming that we can determine this maximum amount). Such an effort might damage the fishery in terms of reducing future harvests, which depend on uncaught fish reproducing.

We ask: What is the maximum that we could harvest on a sustainable basis? And how challenging is it to do so?

©2022 by COMAP, Inc.

The UMAP Journal 43.1

18 pages

- Differential Equations, Statistics

- Fisheries management, Fishing

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