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Fishery Bulletin 97(3), 1999 



decreased more slowly as fishing mortality increased 

 past the MSY mortality. 



Our analyses of optimal reserve proportions pro- 

 duced several key results. First, reserves produced 

 fisheries enhancements, meaning that the overall 

 catches with a reserve exceeded those without one, 

 whenever the fisheries were overfished (Fig. 31, here 

 defined as fished above the MSY mortality level. 

 When fisheries were overfished, they produced higher 

 yields with a reserve even though the reserve decreased 

 the amount of fishing area. The optimal reserve pro- 

 portion increased with increasing fishing mortality, and 

 heavily exploited fisheries required particularly large 

 reserves to remain productive. The fishery benefit at- 

 tributable to reserves, calculated by subtracting the 

 yield without a reserve ft-om that with an optimally 

 sized reserve, increased with increasing fishing mor- 

 tality up to a near-maximum yield in most cases ( Fig. 

 4). Consequently, a wide span of reserve sizes (up to 

 80% of the management area for some species) pro- 



1,250- 



A Panulirus penicillatus 



1 ,250 - 



B Balisles vetula 



1,500- 



0.2 0.4 0.6 0.8 1 



C Haemulon plumien 



0.2 0.4 0.6 0.8 1 



1 2,000 T 



D Epinephelus guttau 



0.2 0.4 0.6 0.8 1 0.2 0,4 0.6 0,8 1 



Fishing mortality (u) 



Figure 4 



Catch enhancements with the u.se of an optimally proportioned reserve 

 (OPRl. (A) Panulirus penicillatux. Red Sea spiny lobster. (B) Balistes 

 vetula, queen triggerfish. (C) Haemulon plumieri, white grunt. (D) 

 Epinephelus guttatus. red hind. Value.s represent the increase in yield, 

 in kg of catch per year from the whole management area, one could 

 expect if an optimally sized reserve system were established in a man- 

 agement area that lacked reserves initially. 



duced similarly high yields for most species as long as 

 fishing mortalities were chosen accordingly. 



Using this information (Fig. 3), we predicted opti- 

 mal reserve proportions under real-life fishing mor- 

 talities. For queen triggerfish, the fishing mortality 

 estimate of « = 0.45 from Puerto Rico and the Virgin 

 Islands (Aiken, 1983) corresponded to an optimal 

 reserve proportion of approximately s = 0.8. For white 

 grunt, a reported heavy fishing mortality ofu = 0.99 

 from Jamaica (Darcy, 1983) corresponded to an opti- 

 mal reserve proportion of just over s - 0.75. Thus, 

 for these species in these locations, our models pre- 

 dicted that 75-80% of the fishing grounds should be 

 made off-limits to fishing in order to maximize long- 

 term sustainable yields. These numbers may seem 

 unrealistically high, especially since most models 

 predict maximum yields when approximately 50% 

 of the population density at carrying capacity is pro- 

 tected from fishing ( see Clark, 1990, for an overview ). 

 In the case of our models, populations within the 

 reserve did not reach carrying capacity 

 when fishing was heavy outside, and the 

 conditions of peak production corre- 

 sponded to those that protected approxi- 

 mately 50% of the population density at 

 carrying capacity. 



The qualitative conclusions outlined 

 above were consistent across all the spe- 

 cies we examined. However, the model's 

 quantitative predictions of the long-term 

 fishery yields and optimal reserve propor- 

 tion varied from species to species for any 

 given fishing mortality (Fig. 3). The key 

 differences between species were the 

 speeds at which the yield and optimal re- 

 serve proportion changed with increasing 

 fishing mortality ( Fig. 3 ). These differences 

 reflected differences in intrinsic population 

 growth rates (A) — the maximum growth 

 rate of a population with no density-depen- 

 dent constraints or fishing mortality. This 

 summary parameter integrates most of the 

 life history data that we used. It does not 

 include the growth rate of individuals in 

 the population and consequently does not 

 adequately predict yields. However, it is a 

 useful summary of the ability of a popula- 

 tion to sustain harvesting. For example, 

 life history parameters from the literature 

 suggested that the Red Sea spiny lobster 

 had a relatively low A = 1.08, just above 

 the A = 1 necessary for a population to sus- 

 tain itself with no fishing pressure. This 

 species had a low MSY fishing mortality 

 because its slow population growth could 



