Advantages and Disadvantages of Rotating Spatial Closures for Managing Fisheries


 Marine reserves are becoming an increasingly important tool in fisheries management. Particularly for species with relatively sedentary adults, the basic approach taken is to permanently close areas to fishing which allows species to recover inside the reserve and export larvae outside the reserve which eventually can be harvested. Two key issues are insuring the movement of larvae outside the reserve to support fisheries and the sociological and economic impact of permanent closures. An alternative approach that deals with these issues is rotating spatial closures which have been implemented for some fisheries. What has been missing is a general analysis of the relative impact of permanent closures versus rotating closures on fisheries yield that could be used to provide general principles to guide management. Using a simplified model with clear assumptions, we show that the approach that provides a higher yield depends on both dispersal and the fraction of the coastline in marine reserves. With high larval retention and small rotational fraction rotating closures are superior and the optimal rate of rotation cannot be too slow or too fast. These results provide quantitative guidelines in cases where decisions must be made in the face of limited data as well as providing a framework for more detailed analyses in cases where more data is available.


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A variety of approaches, including marine reserves [1][2][3][4] , have been used to manage 47 marine fisheries, many of which are coastal fisheries for species with relatively  What has been missing is a general evaluation of the relative merits of spatially 65 dynamic MPAs as compared to permanent closures. We develop a theoretical 66 framework building on earlier work 5 , based on simplifying assumptions, to compare 67 the fishing yield produced from rotational versus permanent marine reserves. The 68 rotational marine reserves are described by rotating an appropriate fraction of the 69 coastline between the marine reserve zone and fishing zone (Fig. 1). The theoretical 70 framework we develop here depends on simplifying assumptions: i) All adults are 71 assumed stationary while larvae are mobile. ii) We assume that all fish outside the 72 marine reserve are harvested. iii) We assume that the larval dispersal rate is 73 deterministic. We recognize that this is unrealistically simple, but this approach allows 74 general conclusions and the effects of more realistic assumptions are easy to deduce.

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Theoretical framework. The model is expressed in terms of a small number of 78 parameters. We define k as the retention fraction (i.e. the total fraction of larvae 79 settling finally inside marine reserves), which includes the fraction of larvae settling 80 immediately in the natal habitat and the fraction of larvae "returning home" 16 after the 81 larvae dispersed. The number of settling larvae produced per year per adult is m, adult 82 survival is a, and a fraction c of the coastline in reserves. The only difference between 83 the two management regimes is that for rotating reserves, a fraction α of the 84 coastline is rotated between reserve areas and fishing areas each year, so α ≤ c. We 85 denote initial adult density inside reserves by NP and NR for permanent and rotational 86 methods, respectively.

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We first focus on the dynamics of initial density Ni for both marine reserves design 89 methods, with the subscripts of i = P for permanent marine reserves and i = R for 90 rotational marine reserves. At the beginning, the adult density inside and outside of 91 the marine reserves are Ni and zero, respectively. The larvae inside marine reserves 92 come from larvae that do not leave and there from returning to their place of origin, respectively (see Table 1  Similarly, the fishing yield produced with permanent marine reserves is: Eq. 3 is subject to the equilibrium condition: We analyze these equations numerically with specific parameters of functional form  Therefore, the two types of yield can be expressed as: In order to compare the yield produced from both methods, a special case is When c = k: To make sure density NR is positive, 1 ± √∆ should be positive. Thus: Substitute these relationships into and , the yield difference − turns out 151 to be: 153 Therefore: For special case when = : Therefore: According to the analytical analysis, the harvesting yield advantage between two

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A simple calculation (see several special cases) shows that maximum sustainable fraction are relatively large (Fig. 2b). The value of yield difference varies from 221 positive to negative and then positive with the increasing of retention fraction, and the 222 intensity of perturbation becomes strong when rotational fraction increases (Fig. 2c).

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The numerical results suggest that which method in marine reserve design leads to 225 higher yield depends on the parameters. The unimodal relationship between yield 226 difference and marine reserve fraction indicates that it is more appropriate to apply 227 rotational method when marine reserve fraction is relatively large (but not too large), 228 while the permanent approach is the best when reserve fraction is relatively small (Fig.   229 2a). A similar unimodal relationship between yield difference and rotational fraction 230 shows that the value of yield difference is always positive when rotational fraction is 231 small and larvae retention fraction is large (Fig. 2b). This indicates the rotational 232 method is the best when rotational fraction is relatively small, while permanent 233 method turns out to be the best when rotational fraction is relatively large (Fig. 2b).

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The effects of retention fraction on yield difference indicate that it is more favorable 235 to use the rotational method when larvae tend to have relatively large retention 236 fraction and the rotational fraction is relatively small (Fig. 2c).      Table 1 The definitions of parameters/variables used in the paper.

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Parameter/variable Definition c The fraction of the coastline in marine reserves. a Adult survival. m The number of settling larvae produced per year per adult. The fraction of the coastline that is rotated between reserve areas and fishing areas each year. k The total fraction of larvae settling finally inside marine reserves. Initial adult density inside marine reserves for permanent methods. Initial adult density inside marine reserves for rotational methods.
The harvesting sustainable yield from marine reserves with permanent methods. The harvesting sustainable yield from marine reserves with rotational methods.  Schematic diagram of rotational marine reserves designing. (a) Implementation order performed in one rotational period. The changing behavior of rotation happens after larvae producing and settling, and the subsequent one is shery harvesting. At the timepoint of shing, four types of habitat occur caused by rotation: part of the marine reserve remains marine reserve; part of the shing areas (not reserve) remains shing areas; part of the marine reserve becomes the shing areas and part of the shing areas becomes marine reserve. (b) Speci c meaning of rotation which happens in space. A rotational proportion α happens between the marine reserve zone and shing areas: a fraction of α inside the marine reserve zone is transformed into shing areas, and, at the same time, the same fraction outside the marine reserve zone is transformed into marine reserve zone.

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