HIGHTOWER and GROSSMAN: TILEFISH FISHERY 



rameter A controlled the degree of density-depen- 

 dence. We assumed that recruitment was either con- 

 stant (A = 1.000) or decreasing by 10% when the 

 spawning stock was reduced by 50% (A = 0.889). 

 Few studies have shown a statistically significant 

 relationship between spawning stock and recruit- 

 ment (Hennemuth 1979); nevertheless, recruitment 

 would be expected to decline at high Fs. For that 

 reason, we used the latter assumption to explore the 

 effect of the stock-recruitment relationship on the 

 form of the yield curve. Other investigators have 

 used this approach to obtain conservative estimates 

 of equilibrium yield when information on the stock- 

 recruitment relationship was unavailable (Lenarz 

 and Hightower 1985; Henry 1986; Hightower and 

 Lenarz 1986). 



We simulated the fishery using virgin recruitment 

 levels of 10,000-200,000 6-yr-old fish. This range 

 would result in virgin population sizes of 45,000- 

 2.1 million fish, depending on the assumed level of 

 natural mortality. Assuming that the area inhabi- 

 tated by tilefish off South Carolina and Georgia is 

 about 476 km- (Low et al. 1983), these population 

 sizes correspond to adult densities of 95-4,400 per 

 km-. This appeared to be an adequate range of den- 

 sities, given that estimates of tilefish burrow den- 

 sity in the Hudson and Veatch Canyons off southern 

 New England ranged from 119 to 2,434 per km- in 

 1980 (Grimes et al. 1986). As Low et al. (1983) noted, 

 the 1974-78 catch rates off southern New England 

 (0.49-0.93 kg/hook; Grimes et al. 1980) were sim- 

 ilar to the 1981-82 catch rate in the expanding fish- 

 ery off South Carolina and Georgia (0.86 kg/hook). 



Table 2— Parameter estimates for the sex- and age-struc- 

 tured model of tfie tilefish fishery off South Carolina and 

 Georgia. 



'Harris and Grossman (1985) Lengtti-weight reiationstiip: w = 

 bllji."!'! 



2The estimate of L„ in Harris and Grossman (1985) {895 mm) was 

 incorrect. 



Because tilefish catches were negligible prior to 

 1978, the starting (1978) number-at-age vector at 

 each recruitment level was assumed to be the equi- 

 librium vector obtained at an F of 0. We assumed 

 that our estimates of total landings were much 

 more reliable than our estimates of fishing effort. 

 For that reason, we solved iteratively for the se- 

 quence of fishing mortality rates that would produce 

 the observed 1978-86 catches (Methot in press). For 

 example, we began by solving for the 1978 F that 

 would produce the 1978 catch biomass, and then 

 used that F to project the number-at-age vector re- 

 maining in 1979. [We assumed that the final (1986) 

 F should not exceed 2.0 (an exploitation rate of 

 80-84%), in order to rule out those cases where the 

 1986 harvest was attained by removing essentially 

 all remaining tilefish.] Using this approach to esti- 

 mate F, the observed and simulated catch biomass 

 levels match exactly, although the observed and 

 simulated age distributions may be different. Note 

 that if we had a similar degree of confidence in our 

 estimates of catch and fishing effort, it might be 

 more appropriate to minimize differences between 

 observed levels and model estimates of both catch 

 and effort (see for example, Deriso et al. 1983), 

 rather than forcing the model to reproduce the 

 catches exactly. 



At each virgin recruitment level, we calculated 

 the correlation between the estimated 1978-86 

 Fs and estimates of total effort based on CPUE 

 data. We used two sources of CPUE data: 1) 

 commercial snapper reel CPUE from 1980 to 1982 

 South Carolina vessels (Low and Ulrich 1983); and 

 2) mean longline CPUE from 1982 to 1985 research 

 cruises aboard the RV Georgia Bulldog. Based on 

 commercial snapper reel kg/landing (figure 13 in 

 Low and Ulrich 1983), we estimated that observed 

 annual landings would have required more than 

 22 trips in 1980, 89 in 1981, and 445 in 1982 (Table 

 3). Using research cruise estimates of longline 

 kg/hook, we estimated that observed annual lan- 

 dings would have required 351,000 hooks fished in 

 1982, 1.9 million in 1983, 1.6 million in 1984, and 

 380,000 in 1985 (Table 3). The research catches were 

 made using standard commercial longline gear (Har- 

 ris and Grossman 1985). We also obtained a com- 

 posite 1980-85 effort series using the ratio of hooks 

 fished to trips in 1982 (Table 3), but our results were 

 the same as when only research CPUE data were 

 used. 



At each level of natural mortality, we selected the 

 virgin recruitment level that maximized the corre- 

 lation between estimates oiF and fishing effort. The 

 selected recruitment level was used in the equilib- 



179 



