Sladek Nowlis and Roberts: Fisheries benefits and optimal design of marine reserves 



609 



1,500' 



1,000 



500 



OhoS- 



A Panulirus penicillatus 



,..o -o-o -o- ■■o—<' 



1 



075 



05 



025 



I = 1 .08 

 T»T»t»t«t 



0.2 0,4 06 08 1 



~ 1,500-, 



CO 



C Haemulon plumierl [ 

 o.o--a--ci--a--o--i>o--9 



1.000 



500 



X= 1-16 



1 



0.75 



0.5 



0.25 







0.2 0,4 0.6 0.8 1 



1,500-1 



1 ,000 



500 



B Balistes vetula 



,...o-9 



tc>o--o-;a"-o--D--o--a--o-<T 0.75 

 p" 



- 0.5 



0-fi>°- 



;v= 1 11 



1 



-0.25 

 



Yield without reserve 



ORP 



Yield with ORP 



0.2 0.4 0.6 0.1 



1 



1 2,000 -r 



O 



O 05 

 ^ (0 



3 



0.2 0.4 0.6 0.8 1 



FIsfiing mortality (u) 



Figure 3 



Optimal reserve proportions and corresponding yields. (A) Panulirus penicillatus. Red Sea spiny lob- 

 ster. [B) Balistes vetula, queen triggerfish. (C ) Haemulon ptumieri, white grunt. iTO^ Epinephelusguttatus, 

 red hind. In all graphs, the solid circles and line represent the sustainable yield (kg of catch per year 

 from the whole management area) that occurs in the absence of a reserve, the open circles and dotted 

 line represent the optimal reser\'e proportion (that which produced maximum sustainable yields for 

 each fishing mortality), and the dashed line and squares represent the sustainable yield when the 

 optimal reserve proportion was used. Intrinsic population growth rates (X) determine the robustness of 

 the populations to fishing, high growth rates sustaining heavy fishing and low rates requiring reserves 

 at low fishing mortalities. 



This measure is better than standard deviation alone 

 which would treat a 10-kg fluctuation equally, re- 

 gardless of whether it occurred in a 100 kg or 

 1,000,000 kg per year fishery. We graphed these re- 

 sults with reserve proportion as the independent 

 variate and examined the graphs for trends. 



We performed these analyses on four coral reef fish- 

 ery species for which we obtained relatively complete 

 parameter sets. These included Balistes vetula, queen 

 triggerfish; Epinepheliis gitttatus, red hind; Hae- 

 mulon plumteri, white grunt; and Panulirus penicil- 

 latus, Red Sea spiny lobster (see Table 1 for param- 

 eter estimates). 



Results 



When we ran the models without a reserve (s=0), they 

 produced standard yield-effort curves (Fig. 3). These 



curves are characterized by steep initial gains in long- 

 term sustainable yields with increases in fishing 

 mortality (and thus effort), followed by equally steep 

 declines (Clark, 1990). The curves peaked at the 

 maximum sustainable yield, one of several goals a 

 manager might try to achieve with a fishery (Clark, 

 1990), and we will refer to the corresponding fishing 

 mortality as the MSY mortality for the rest of this 

 paper. Above the MSY mortality, the fishery can be 

 defined as overfished because it is less productive 

 than it would be with less fishing activity. 



When a reserve was present, the yield-mortality 

 curves were still parabolas passing through the ori- 

 gin but spread farther to the right, and the larger 

 the reserve, the more pronounced were these shifts. 

 Consequently, larger reserves required higher fish- 

 ing mortalities to maximize long-term sustainable 

 yields (remember that this mortality only affected 

 fish in fishing areas), whereas the sustainable yields 



