Pearson et al.: Age. growth, and potential yield of Sebastes jordani 



407 



Natural mortality 



Using Hoenig's (1983) regression equation, we esti- 

 mated that M = 0.212 for males and 0.203 for females. 

 We obtained higher estimates using Hoenig's (1983) 

 exponential model (males 0.378, females 0.374) and 

 Pauley's (1980) regression equation (males 0.356, 

 females 0.437). Our sample sizes used in Hoenig's 

 exponential model may have been overestimates (rela- 

 tive to true simple random samples from the popula- 

 tion) because of the within-tow correlation. The effec- 

 tive sample size would probably be between 48 (the 

 number of tows) and the number aged per sex (males 

 959, females 1279). Given the uncertainty of the above 

 estimates, we assume that 0.20-0.35 is a reasonable 

 range for M until a catch-curve estimate can be made. 

 Catch-curve estimates for other Sebastes spp. from 

 British Columbia waters were lower, ranging from 0.03 

 to 0.10 with a range of maximum observed ages from 

 32 to 77 years (Leaman 1986). Based on a catch-curve 

 analysis, Lenarz and High tower (1985) estimated that 

 M for widow rockfish S. entomelas off Washington- 

 Oregon-California ranged from 0.15 to 0.20. Lenarz 

 (1984) reported that the maximum observed age for 

 Washington-Oregon-California widow rockfish was 

 about 45 years. 



Potential yield 



The historical estimate of maximum sustainable yield 

 (MSY), 44,250 t, was based on the relationship MSY 

 = 0.5MB (Gulland 1971), where B was an estimate 

 of virgin biomass (PFMC 1982). The MSY estimate was 

 based on an assumed M of 0.275 and the 1977 survey 

 estimate of Ascension Canyon to Farallon Islands area 

 biomass (295,000 t) (E. Nunnely, NMFS Alaska Fish. 

 Sci. Cent., Seattle, WA 98115-0070, pers. commun., 

 Jan. 1989). 



Our revised estimates of MSY were obtained from 

 a more conservative model (0.3MB ) that Gulland pro- 

 posed because the former equation was thought to 

 overestimate MSY (Gulland 1983). We used M = 

 0.20-0.35 and the average of the 1977 and 1980 Ascen- 

 sion Canyon to Farallon Island area biomass estimates 

 (223,850 1). The revised estimates of MSY (13,431- 

 23,504 1) should be viewed as highly preliminary, given 

 that the 1977 and 1980 biomass estimates had con- 

 fidence intervals in excess of 50% and were not sig- 

 nificantly different. 



The above estimates of MSY were based on the 

 assumption that the fishing mortality rate (F) that pro- 

 duces MSY would be about equal to M. An alternative 

 approach for obtaining a recommended F would be to 

 determine the fishing mortality rate that reduced 

 spawning biomass per recruit to 35% of the unfished 



Fishing mortality rate 



Figure 5 



Female spawning biomass per recruit versus fishing mortal- 

 ity rate (F) at two levels of natural mortality (M) and four ages 

 at recruitment. Horizontal lines represent spawning biomass 

 per recruit equal to 35% of the level at F = 0; vertical lines 

 represent the associated F (F 35% ). F 35% exceeds 1.0 for 

 M = 0.35 and recruitment age of 4 years. 



level (F 35% ). That criterion is being used to manage 

 most of the stocks in the Washington-Oregon-California 

 groundfish fishery (PFMC 1990). Following Ricker's 

 (1975) yield-per-recruit analysis, we calculated spawn- 

 ing biomass per recruit assuming M = 0.20 or 0.35 and 

 linearly increasing maturity. Wyllie Echeverria (1987) 

 reported that 50% of female shortbelly rockfish were 

 sexually mature at age 2 and 100% at age 4. Those 

 estimates were based on whole otolith ages; however, 

 we found relatively good agreement between whole and 

 broken-and-burnt otolith ages through age 4 (Fig. 3). 

 The estimates of F 35% were similar to M if recruit- 

 ment occurred at about age 2 (Fig. 5). Because short- 

 belly rockfish mature at a young age, estimates of 

 F 35% increased considerably if recruitment was 

 delayed. These results suggest that assuming F = M 

 when calculating potential yield should provide protec- 

 tion for the spawning stock. 



Our estimates of MSY for the Ascension Canyon to 

 Farallon Island area are greater than the current 

 (coastwide) acceptable biological catch (13,000t) estab- 

 lished to permit development of a fishery (PFMC 1989); 



