Optimum Harvesting with Marine Reserves

Abstract

The optimum harvest fishery is modeled as a perpetual annuity investment with a sudden and total stock collapse governed by a Poisson process in a linearly homogeneous harvest production model. The traditional economic harvesting models, which use harvest effort as the only control variable to maximize seasonal harvest profit, are extended to include reserve size as a second control variable to maximize total fishery value (present and future potential harvest profits). As insurance against the risk of a stock collapse at the expense of lower seasonal harvest profits, the optimal size of a marine reserve can achieve the most common management objectives of lowering harvest output, increasing the sustained stock, and decreasing the catch rate. As a management tool, an optimal size reserve can also make fishery management errors more tolerable and less costly. A stylized fishery is included to give a quantitative demonstration.

Notes

¹ An open-access harvest regime, in contrast to optimum harvesting, typically results in extremely high levels of fishing effort and totally dissipates economic value or rent (harvest profit). Therefore, it is often argued that a marine reserve for both the biological objective of conserving fish stock and the economic objective of maximizing the fishery value is destined to be ineffective without some form of restraint on effort and catch output. Thus, a marine reserve is a necessary but not sufficient condition for economically efficient optimum harvesting. Allison et al. (1998) also regard a marine reserve as necessary but not sufficient for marine conservation, albeit for different reasons: highly variable water mass movements, inadequate population replenishment, threat of chemical contaminations, etc.

² There are other arguments suggesting that marine reserves will, in fact, promote stock increase in addition to preventing sudden decline. In practice, the effectiveness of a marine reserve in preventing collapse also depends on the design of the reserve. For example, if larval distribution and recruitment are more localized (low transfer rate between reserve and nonreserve areas), many small reserves will be preferred to one large one of the same total size. Furthermore, the shapes and locations of the actual reserves can also be very important.

³ The biological world also employs a number of measures to prevent species collapse or extinction: multiple episodes of reproduction (iteroparity), dispersal of progeny, delayed germination of seeds, and metapopulation structures increasing the chances of species survival in spite of local extinctions (Seger and Brockmann 1987; Pulliam 1988; Yoshimura and Clark 1993).

⁴ A marine reserve by itself can also be considered a simple form of diversification strategy: exploit part of the fishery resource while protecting the remainder (Lauck et al. 1998:75).

⁵ Strictly speaking, a “marine reserve” is an area in which some consumptive utilization is allowed, but protection is afforded to most species. If the reserve is an area set aside for the protection of a specific individual exploited species, then it is normally named a “fishery reserve.” The heaviest protection is provided by a “marine sanctuary” where no extractive exploitation of any marine resources is allowed. Finally, a “marine park” is a protected area that includes any combination of the above (Hockey and Branch 1997:371).

⁶ Most noneconomic studies on marine reserves hold constant the harvest effort. For example, Holland and Brazee (1996) assume that the overall level of fishing effort is a fixed parameter so that effort displaced from the reserve is applied to the portion of the fishery that remains open. The authors then simulate the impacts of a range of effort levels on the optimal reserve size and the present value of the fishery. In our analysis, fishing effort outside the reserve area is the control variable chosen to maximize harvest profit.

⁷ Holland and Brazee (1996) note that although a marine reserve may reduce the probability of a stock collapse, it is in general not the best strategy to produce the most economically efficient use of the resource. Walters and Pearse (1995) even argue that marine reserves can interfere with economic efficiency of the fishery. Although the latter argument is contentious, I suggest that a reserve is indeed only the necessary but not sufficient condition for maximizing fishery value (achieving economic efficiency). It needs to be supported by optimum harvesting to do so.

⁸ The current literature, to the best of my knowledge, has not attempted to model directly the stochastic nature of commercial harvest profitability and the effects of a marine reserve on it. The closest is the study by Lauck et al. (1998). It imposes a beta distribution on catch and examines how likely the fishery will retain a certain percentage of the stock carrying capacity a number of years after establishment of a marine reserve.

⁹ This is in contrast to the risk premium used by Clark (1998). He describes it as short-run economic costs imposed by the marine reserve, including reduced availability of fish and increased costs of harvesting.

¹⁰ There are strategies other than marine reserve that tackle the problem of risk in this sense. Most of these target the effort or catch level. For example, F _0.1, which is the level of fishing mortality F at which the slope of the yield-per-recruit curve equals 0.1 times the slope at F = 0, is more conservative than the maximum sustained yield criterion (equation 3). Although F _0.1 is commonly adopted to allow for some degree of error (Lauck et al. 1998:73), its application has not produced much historical success because F _0.1 generally has not been achieved.

¹¹ There are a host of other nonfishery or noneconomic performance measures for marine reserves, including regional representation; biogeographical conservation; habitat diversity; vulnerable/fragile habitats protection; representation of vulnerable species; protection of vulnerable life history stages; restoration to pristine and natural condition; preservation of natural or international features of importance; support of exploited species; supply of stocks to adjacent areas; an area large enough to fulfil designated objectives; an area lying adjacent to a terrestrial conserved area; effective management and adequate policing; esthetic appeal; accessibility to people; satisfaction of education, recreational, research, and tourism needs; and preservation of historical, archaeological, and geological features and cultural activities (Hockey and Branch 1997).