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Fishery Bulletin 91(3). 1993 



examined with the most reasonable estimate of A, ± 507 

 for each of the three fish types (see footnote C of Table 2 

 for the type-specific values of A, used in modeling closure 

 effects). An age-at-recruitment to fishery habitat (A, ) value 

 of 1.0 year was assumed for the surgeonfish and jack, 

 and an A, of 0.5 year for the damselfish. 



Results 



General 



Results corroborate several of Polacheck's (1990) major 

 results: SSB/R increased, while Y/R generally decreased, 

 with increasing refuge size (Fig. 1). Even in cases where 

 a closure positively affected yield, Y/R increased little. 

 Y/R often was greater at higher levels of fishing effort 

 (Fig. 1 ) and usually decreased at larger refuge sizes; the 

 rate of decrease was less at higher fundamental transfer 

 rates (Fig. 2, A-C). SSB/R was generally greater for 

 closures of larger size at any particular transfer rate 

 (Figs. 1 and 2). The positive effects of a closure of a given 

 size on SSB/R were greater at lower rates of exploita- 

 tion and diminished at higher transfer rates (Fig. 3). The 

 rate of increase in SSB/R with refuge size was greater 

 at lower transfer rates (Fig. 1, A-C). The progressive 

 gain in SSB /R usually was greater than the progressive 

 loss in Y/R for refuges of increasing size (Fig. 2). 



Another general pattern was the relative importance 

 of the interactive effect of natural and fishing mortal- 

 ity rates, compared to age at recruitment to the fishery. 

 For most combinations of M and F,, B/R was more 

 strongly influenced by these two rates than by age at 

 recruitment (Fig. 4, Table 3). Depending on fish type, 

 B/R values ranged two- to five-fold as M and F r values 

 varied ±507 of their midpoint estimates, but ranged 

 only twofold or less as A, varied ±50% (Table 3). 



By comparison, transfer rates had relatively little 

 effect on SSB/R, compared with the effects of natural 

 and fishing mortality rates. For a median-sized clo- 

 sure of 257, changes in percentage of virgin SSB/R 

 differed <107 within fish type for transfer rates that 

 varied as much as two orders of magnitude (Fig. 3). 



Another generality, not previously made explicit, is 

 that ages at maturity and at first capture can more 

 strongly influence spawning stock than can the pres- 

 ence and size of a refuge. The presence of a refuge will 

 have a relatively weak effect on spawning biomass if 

 the resource begins to be heavily exploited well before 

 sexual maturity. In extreme cases, SSB/R might not 

 be appreciably enhanced by large closures, despite rela- 

 tively low transfer rates. 



Fish types 



Perhaps the most significant, specific result of the 

 simulations was that fish types differed in how ref- 



uge size affected SSB/R levels. Large, apparent gains 

 in percent virgin SSB/R of the damselfish occurred 

 only at the expense of large losses in yield (Figs. 1A, 

 2A, 3A). Nontrivial (>5%) gains in percentage SSB/R 

 of surgeonfish could occur at small (0.1) refuge sizes, 

 although the overall rate of increase in SSB/R would 

 be greater for larger closures (Figs. IB, 3B). For the 

 jack, however, gains in SSB/R of magnitude similar 

 to those of the surgeonfish could be realized with in- 

 creasing refuge size only for large (fl, > 0.3) closures 

 (Figs. 1C, 3C). 



Simulation results appeared to vary among fish 

 types in response to their differing growth rates and 

 natural mortality and exploitation schedules. For ex- 

 ample, in comparing the results for the high-mortal- 

 ity surgeonfish with those for the low-mortality jack, 

 substantive gains in SSB/R of the jack (restricted 

 to large closures) were further restricted to low (F,. < 

 0.4) levels of fishing effort (Fig. 1C). SSB/R dropped 

 below 207 of the virgin stock at F, = 0.3, the fishing 

 effort that was optimal for maximizing Y/R (Fig. 

 1C). For the surgeonfish, appreciable (>10%) gains 

 in SSB/R could occur under heavy (F,. > 1) exploita- 

 tion rates for refuges as small as 10-207 (Fig. 3B), 

 and >207 of virgin SSB/R can be sustained at F < 

 1.15 (Fig. IB). 



The observed differences among fish types in the 

 potential for MFRs to increase SSB/R also were 

 strongly influenced by the ages at sexual maturity and 

 recruitment to the fishery. Ages at first maturity and 

 at first capture were attributes that differed greatly 

 among the three fish types (damselfish: age 1; 

 surgeonfish: age 2; jack: age 4; Table 2). Median B/R 

 (equal to SSB/R for all except the damselfish at A, = 

 0.5 year) varied by 307 for the damselfish, 1007 for 

 surgeonfish, and 357 for the jack among ages at first 

 capture that varied ±507 of their respective midpoints 

 (Table 3). Compared with age at first catch, transfer 

 rates had less effect; SSB/R consistently varied <107 

 for the damselfish (with twofold variation in very low 

 transfer rates; Fig. 3A), for the surgeonfish (with 

 fivefold variation in moderate transfer rates; Fig. 3B), 

 and for the jack (with tenfold variation in rapid trans- 

 fer rates; Fig. 3C). At a reference F, of 1.0 and a me- 

 dian closure size of 257, SSB/R varied from <6 to 

 357 of virgin stock biomass, depending on fish type 

 (Fig. 1,A-C). 



Compensatory transfer rates 



Even small (eighth root of density ratio) compensatory 

 increases in transfer rates could have negated poten- 

 tial increases in SSB/R that might result from the 

 presence of a closure. A larger adjustment with the 

 square root of the density ratio, of course, can have an 



