Predator—Prey Models of Fisheries

Abstract

In the previous chapter we extended the model of optimal extraction from nonrenewable resources to enable renewal of the resource and then identified optimal harvest from a fish population. In this chapter, we choose an alternative approach to modeling fisheries. Methods of modern marine fisheries management virtually are no different from ancient hunter—gatherer strategies in that the “prey” has to be first spotted, then caught or collected, and hauled to the home port. We therefore use predator—prey models to simulate the interactions between the economic and biological systems.¹ The fish are the prey, and boats of fishermen correspond to the predators.

And it ought to be remembered that there is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things. Because the innovator has for enemies all those who have done well under the old conditions, and luke-warm defenders in those who may do well under the new. This coolness arises partly from fear of the opponents, who have the laws on their side, and partly form the incredulity of men, who do not readily believe in new things until they have had a long experience of them. Thus it happens that whenever those who are hostile have the opportunity to attack they do it like partisans, whilst the others defend lukewarmly.

N. Machiavelli, The Prince, 1513