Abstract
Marine fisheries are a significant source of protein for many human populations. In some locations, however, destructive fishing practices have negatively impacted the quality of fish habitat and reduced the habitat’s ability to sustain fish stocks. Improving the management of stocks that can be potentially damaged by harvesting requires improved understanding of the spatiotemporal dynamics of the stocks, their habitats, and the behavior of the harvesters. We develop a mathematical model for both a fish stock as well as its habitat quality. Both are modeled using nonlinear, parabolic partial differential equations, and density dependence in the growth rate of the fish stock depends upon habitat quality. The objective is to find the dynamic distribution of harvest effort that maximizes the discounted net present value of the coupled fishery-habitat system. The value derives both from extraction (and sale) of the stock and the provisioning of ecosystem services by the habitat. Optimal harvesting strategies are found numerically. The results suggest that no-take marine reserves can be an important part of the optimal strategy and that their spatiotemporal configuration depends both on the vulnerability of habitat to fishing damage and on the timescale of habitat recovery when fishing ceases.
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Notes
We do not refer to the unfished areas at the habitat boundaries, or, when they occur, unfished areas at the end of the time horizon as “reserves.” In these areas, the marginal rent (PNu − W0 − 2W1h) is negative and no regulation would be required to prevent fishing.
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Acknowledgements
We thank Emily Moberg and Holly Moeller for useful discussions. We have benefited from the breadth of spatial ecology research by Alan Hastings and we are glad to contribute to this special issue.
Funding
This manuscript is based upon the work supported by the National Science Foundation under Grant No. DEB-1558904 (to MGN) and also supported by the National Institute for Mathematical and Biological Synthesis, an Institute supported by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville.
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Kelly, M.R., Neubert, M.G. & Lenhart, S. Marine reserves and optimal dynamic harvesting when fishing damages habitat. Theor Ecol 12, 131–144 (2019). https://doi.org/10.1007/s12080-018-0399-7
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DOI: https://doi.org/10.1007/s12080-018-0399-7