416 



Fishery Bulletin 91 [3), 1993 



Table 1 



Length-weight relations, von Bertalanffy growth function parameters, and 

 natural mortality rates used to simulate spawning stock biomass per recruit 

 and yield per recruit contour surfaces for damselfish (based on Moorean 

 Stegastes nigricans from Galzin, 1987); surgeonfish (length-weight relation: 

 Mnorean Ctenochaetus striatus from Galzin, 1987; VBGF parameters: Sa- 

 moan C. striatus from Ralston and Williams 2 ); and jack (NWHI Caranx 

 ignobilis from Sudekum et al., 1991). M values were estimated after Pauly 

 ( 1980) and Pauly and Ingles ( 1981; see Methods). 



Variable 



Damselfish 



Surgeonfish 



Jack 



Length-weight 



relation 



(Total Length/g) 



L. (Total Length, cm) 



»' (g) 



KtVyear) 



t,Jyear) 



Mil/year) 



W = 0.0195L i 

 17.5 

 128.9 



0.374 

 -0.042 

 1.5 



W = 0.0111L :U " 

 28.2 

 348.6 



0.447 

 -0.760 

 1.0 



W = 0.0072L 298 

 217 

 120,139 



0.111 

 -0.097 

 0.2 



Table 2 



Age-specific parameters used to simulate the standing stock 

 and catch (yield) values for each of the reef fish types described in 

 Table 1. 



'Based on mean weight-at-age estimated from weight-specific VBGF; 

 see Table 1 for sources. 



-Sexual maturity assumed 100'/r complete at age corresponding to 

 the asymptote of the Von Bertalanffy growth function curve; all 

 fish were assumed immature prior to this age. 



'All species were defined as fully recruited to the fishery at the age 

 of 100% sexual maturity, no fish entering the fishery prior to that 

 age: Age-at-first-capture, A, = 1.0, 2.0, and 4.0 years for the dam- 

 selfish, surgeonfish, and jack, respectively. 



line-bounded reef closures will be one- 

 fourth slower than the respective rates for 

 completely nested closures of equal areal 

 extent. ) 



Polacheck's modified Equation 8 was 



T 12 = 3-T, s -(R 1 /R s )-\ 



(1) 



where T v , is the instantaneous emigration 

 rate from closed area 1 to exploited area 

 2; T ls is the emigration rate from a closure 

 of R s standard size; and i?, is the frac- 

 tional closure size evaluated. As in 

 Polacheck (1990), the initial fish densities 

 were assumed homogeneous in both areas, 

 and thus the number of fish initially 

 present in area 1 at time / was defined as 



N,, = R,-N,„ 



(2) 



where N totaU = number of individuals in the co- 

 hort entering areas 1 and 2 at time /. T ls was 

 allowed to vary among fish types, as types surely 

 differ in their fundamental emigration and im- 

 migration rates. Selected values of T u spanned 

 realistic values for each fish type (damselfish: 

 0.001, 0.01, and 0.1; surgeonfish: 0.1, 0.25, and 

 0.5; jack: 0.1, 0.5, and 1.0). T 21 , the rate of immi- 

 gration into area 1 from area 2, given the type- 

 specific value of T|,, was as defined by Polacheck 

 (1990, Equation 6). 



A basic assumption of the model is that fishing 

 does not affect fish distributions by altering habi- 

 tat or by promoting density gradients between 

 areas 1 and 2, i.e., dispersal is random and uni- 

 form throughout both areas and across their 

 boundaries (Polacheck, 1990). This is realistic for 

 fishes like jacks that range widely or that have 

 very large home ranges. However, the assump- 

 tion of uniform dispersal throughout both areas 

 is debatable for fishes with home ranges that are 

 small relative to the size of MFRs, particularly 

 for strongly site-attached, territorial species like 

 damselfishes whose ambits are trivial compared 

 to the area of a reserve. Transfer rates that func- 

 tionally approximate those based on an as- 

 sumption of uniform, random dispersal might be 

 tenable for home-ranging (or even territorial) or- 

 ganisms, if emigration out of MFRs into adjacent 

 fished areas followed a "stepping stone" pattern 

 with minimal time lags. Limited field data at 

 present both support (Walsh, 1984) and counter 

 (Wellington and Victor, 1988) such a model. The 

 key factors here are the magnitude of time lags 

 and the relative sizes of individual home ranges 

 within particular MFRs. 



