Marine reserves and optimal dynamic harvesting when fishing damages habitat

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.

Optimal spatial management in a multiuse marine habitat: Balancing fisheries and tourism

“…Note that in the case where tourism activity is prominent, larger no-take optimal areas arise. This is consistent with the findings of Kelly et al (2018) and Viana et al (2017), who found that the size of optimal reserves increases with habitat value. Our results also suggest that accounting for tourism could alleviate overexploitation in especially sensitive habitats, where one could expect a lower intrinsic habitat value for fishing.…”

“…Additionally, habitat value could change with time as different uses can damage the ecosystem and recent studies insist on the importance of stock recovery plans when fishing damages the habitat . In Kelly et al (2018), the authors consider the impact that fishing has on habitat quality over time, but there are several studies pointing that tourism could also damage habitat value (Cowburn et al, 2018;Davis & Tisdell, 1995;Milazzo et al, 2002). In our case that would mean lower tourism profits or even higher u 0 for some cases.…”

Optimal sustainable fishery management of the Black Sea anchovy with food chain modeling framework

“…This cost term is nonlinear in , but the coefficient is taken small enough to have a small effect on numerical calculations. Note the costs in the objective functional have been frequently represented by nonlinear terms in the harvest control (Herrera, Moeller, & Neubert, ; Kelly, Neubert, & Lenhart, ; Moeller & Neubert, ; Neubert & Herrera, ). One possible reason for this quadratic term is the additional cost associated with the interference between vessels and their workers while fishing near the same location (Herrera et al, ).…”

A spatial food chain model for the Black Sea Anchovy, and its optimal fishery

“…Besides, these intervention methods, another way to find management policies is to use optimal control theory together with food chain models to obtain optimal management policies for the natural renewable food resources. In many cases, no-take marine reserve areas are natural results of the optimal control application in fishery management ( [27], [18], [26], and [20]).…”

“…These studies have showed that using spatial and temporal fishery models can offer better strategies for fishery management ( [15,21,18]. The damage to the environment from fishing methods and equipment has also been shown to be important through PDE modeling in [20].…”