FISHERY BULLETIN: VOL. 87, NO. 1 



Table 3.— Estimates of total effort based on commercial and research! catch per unit 

 effort (CPUE) and total commercial landings. Estimates of 1980-82 commercial CPUE 

 (kg/landing) were based on landings by snapper reel vessels (figure 13, Low and Ulricti 

 1983). Researcfi CPUE estimates (kg/tiook) were based on longline sets aboard tfie 

 RV Georgia Bulldog, each estimate is an average of seasonal averages from spring, 

 summer, and fall cruises. Estimates of hooks fished in 1980 and 1981 were based 

 on the commercial CPUE data, using the ratio of trips to hooks fished in 1982. 



rium yield calculations. Our approach for selecting 

 virgin recruitment levels was based on the "tuning" 

 process used in cohort analysis (Mohn 1983; Rivard 

 1983). In that approach, auxiliary information is 

 used to "adjust" or "fine-tune" the estimates itera- 

 tively so that the output from cohort analysis 

 "matches" some series of observations (Rivard 

 1983). The level of agreement between the obser- 

 vations and model predictions can be measured 

 using correlation or regression techniques (Mohn 

 1983). 



We obtained estimates of equilibrium yield by ex- 

 pressing the number of sex-s fish in each age class 

 {N,„,a = 6, . . .,n, where n refers to fish ages 30 

 and older) as a function of the number of age-6 

 female fish (iV^g)- Following Getz (1980), we as- 

 sumed that 



N, 



.1 = [n exp{-Z,^j)]Nfe, 



1 = 6 



6, .... w - 2 



(4) 



JV,„ = [n exp(-Z,,)/(l - exp(-Z,,„)]7V,;6 (5) 



where Z, ^ was the total mortality rate for sex-s, 

 age-j fish. Using Equations (4) and (5), female 

 spawning stock can be redefined as a function of 



N, 



ffi- 



Sf= 2 Af,-.„ w^,, p/.. 



(6) 



n-l 



I 



a = 7 



NffilWffi Pf.6 + 2!^ W/,a Pf.a ^.n^ exp(-Z,j) 



+ Wf, Vfn "n' exv(-ZfJ(\ - exp(-Z,;„)] (7) 



Nf, \(F) 



(8) 



where i^(F) is the bracketed expression in Equation 

 (7) for a specified F. We then substituted (iV/g 'j>(i^)) 

 for Sf and solved Equation (3) for the equilibrium 

 recruitment level as a function of F: 



iV,6 = (0.5 iVelO] W) - S/[0] 

 + A5^[0]/(A \{F)). 



(9) 



The virgin spawning stock S,[0] was calculated 

 from Equations (4) to (6) for the specified level of 

 M and virgin recruitment. We used Equations (4)- 

 (9) to calculate the equilibrium number-at-age vec- 

 tor and associated yield for F& from 0.0 to 0.5. 



Following Francis (1986), we defined the target 

 fishing mortality rate as Fq.i for the constant re- 

 cruitment case and i^^sy for the density-dependent 

 case. F„ 1 was the fishing mortality rate at which 

 the slope of the yield curve was one-tenth the slope 

 of the curve at the origin (Gulland and Boerma 

 1973). Compared to managing for maximum sus- 

 tained yield, the i^o i policy usually results in 

 greater economic efficiency when constant recruit- 

 ment is assumed (Gulland and Boerma 1973; Sissen- 

 wine 1981; Francis 1986). An additional advantage 

 is that a larger spawning stock would be maintained 

 (Sissenwine 1978). The less conservative i^^sy 

 policy was assumed to be appropriate for the more 

 conservative density-dependent case. The recom- 

 mended yields for the constant recruitment and 

 density-dependent cases were the equilibrium yields 

 at FffA and F^^^ respectively. 



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