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Optimal Fisheries Management over Space: An Endangered Predator and Harvestable Prey Model

By Martin D. Smith and Jonathan D. Kaplan

ABSTRACT

This paper analyzes optimal fishery management in the presence of an endangered predator that competes with humans for a commercially viable prey. In the past, natural predators were implicit in the fishery model. We, however, explicitly model the predator-prey relationship given that endangered predators can be found in many fisheries and the importance of allowing these predator populations to expand in conjunction with maximizing rents in the fishery. Because traditional predator controls are not possible when the predator is endangered, we focus on harvest effort controls over the prey's habitat as a means to maintain the predator-prey relationship and sustain the economic viability of the fishery.

The analysis consists of a predator-prey model that allows for density-dependent growth and dispersion as well as spatially specific harvest rates. The management model is based on optimizing fishery rents across several harvesting patches subject to maintaining a growing and expanding predator population. We derive optimal management decisions across the patches with and without the predator constraint and demonstrate the need to consider the predator-prey relationship explicitly.

To illustrate these results, we analyze the contentious California sea otter-urchin system and the related urchin fishery. We simulate the growth and dispersion of the otter population with and without explicit consideration of the predator-prey relationship. Finally, we compare optimal patch-specific harvest levels under the two scenarios.

KEYWORDS: predator-prey, sea otter, sea urchin, spatial modeling, fisheries management


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