DeMartini Potential of fishery reserves for managing Pacific coral reef fishes 



417 



An R s value of 0.10 was used to represent the "stan- 

 dard-size" closure (Polacheck, 1990). Fishing mortality 

 rates (F,) were input over the range from 0.1 to >3M, 

 with special evaluation of F c = 0.5 M, M, and 2M, based 

 on the best estimate of natural mortality for each fish 

 type. Total fishing effort (F 2 ) was homogeneously re- 

 distributed throughout the exploited area and fixed in 

 magnitude (at a given F c ), regardless of the size of the 

 closed area (Equation 7 in Polacheck, 1990). 



SSB/R and Y/R are used as the primary bases of 

 evaluation. Although measures of biomass are not usu- 

 ally applicable to species like the damselfish that are 

 harvested on a numerical basis (see Ingles and Pauly 

 ( 1984] for examples of consumptive exploitation of small- 

 bodied fishes in artisanal fisheries), these measures were 

 evaluated in the same way to maintain consistency. 



First, the SSB and yield of a cohort were calculated, 

 by using Polacheck's (1990) Equations 2 and 3 for the 

 numerical standing stock and the numerical catch of 

 each cohort comprising that stock: 



n 



I uv M+1 

 (*=1) 



n 



(t=i) 



W M  %mat, tl ), 



W l+l  %mat (+1 ), and 



n 



X (c 2 , ( 

 (t=\) 



W ; ); 



(3) 



(4) 



(5) 



where AT U+1 and N 2M are the numbers of a cohort 

 surviving in the respective area at time (t+1); C 2I 

 is the numerical catch of a cohort in area 2 at time t\ 

 W, and W, +1 represent the mean weights of individual 

 fish of the cohort at times t and {t+1), respectively; 

 and %mat, +1 is the percentage of the cohort that is 

 sexually mature at time (t+1). 



SSB/R and Y/R were then calculated by standard- 

 izing the total spawning biomass and yield, respec- 

 tively, of the cohort over its life span by the total num- 

 ber of recruits potentially (area 1) and directly (area 2) 

 entering the fishery from that cohort (Gabriel et al., 

 1989). SSB/R was evaluated in terms of percentage of 

 the virgin stock biomass possible if fishing was disal- 

 lowed in both areas (Polacheck, 1990); 20% of virgin 

 biomass was considered the threshold for recruitment 

 overfishing (Beddington and Cooke, 1983). 



Two series of simulations were run. One series 

 treated the T 12 and T 21 values as fixed, assuming that, 

 analogous to Polacheck's (1990) analyses for Georges 

 Bank cod, transfer rates would remain constant and 

 independent of relative fish densities in the two areas. 



Additional simulations, using the same initial T u val- 

 ues, were run for selected cases; in these runs, subse- 

 quent values of the transfer rates were treated as a 

 density-dependent function of the changing, relative 

 fish densities in the two areas. Subsequent values of 

 T r2 and T. n were adjusted as follows: 



T 12 , M = T VLI  I {NJNJI (NJN,) h and (6) 



T 2 i, M = T, h , • I (N 2 JN 2 ) / (NJNJ |"; (7) 



where N } is defined in Equation 2 and N 2 is the initial 

 number of the cohort present in area 2; iV u and N 2l 

 are the numbers of fish surviving in the respective 

 area at subsequent age t; and x is the power used to 

 scale the ratio of fish densities. In Equations 6 and 7, 

 the ratio of the numbers offish surviving at time t was 

 further adjusted by the ratio of initial densities in the 

 two areas in order to scale for the propensity to emi- 

 grate at the onset. Two values of .r were evaluated: 

 0.125 (eighth root) and 0.5 (square root). (Note: When 

 x equals 0, the T l2 and T. n are fixed; when .r equals 1.0, 

 these rates are continually readjusted by the changing 

 ratio of relative densities.) Exponents of 0.125 and 0.5 

 were chosen because they bracketed rate changes of 

 reasonable magnitude. In the surgeonfish, for example, 

 an eighth-root adjustment would initially accelerate a 

 median T u of 0.25 by about 20% for a median closure 

 size of 25%, at an F, of 1.0. The corresponding rate 

 increase due to a square-root adjustment would be 60%. 

 Inclusion of a term for the density-dependent ad- 

 justment of transfer rates, as stocks are fished-down 

 in the non-closed area, extends Polacheck's (1990) 

 evaluation. This is perhaps an unnecessary refinement 

 for stocks such as Georges Bank cod for which har- 

 vesting by trawl might reduce habitat quality in the 

 non-closed area (Polacheck, 1990). However, non- 

 destructive (e.g., hook and line) methods of artisanal 

 fisheries on coral reefs do not reduce habitat quality. 

 Furthermore, fishes may emigrate at an accelerated 

 rate from a closure into the surrounding non-closed 

 area where densities continue to decrease (tantamount 

 to improving habitat quality). Compensatory emigra- 

 tion resulting from a density gradient is recognized as 

 potentially important in the siting and design of na- 

 ture reserves (Schonewald-Cox and Bavless, 1986). 



Complementary simulations 



In addition, the effects of varying M and the age-at- 

 first capture (A,) on total biomass per recruit (B/R) 

 were simulated with the conventional Y/R model of 

 Beverton-Holt (Sparre et al, 1989). Fishing mortality 

 was evaluated at 0.5M, M, and 1.5M or 2M. A c was 



