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Fishery Bulletin 89(3), 1991 



rockfish (Wyllie Echeverria et al. 1990). 

 Samples were also obtained from a 1980 

 bottom-trawl survey of demersal adult 

 rockfish (Gunderson and Sample 1980), 

 and a 1981 fishery development survey 

 using a midwater trawl (Kato 1981). The 

 cod-end mesh size for these surveys 

 ranged from 0.4 to 1.5 inches, and fish 

 ages 1 and older were vulnerable to the 

 gear. Otoliths were collected from 2238 

 fish from 48 tows at various locations 

 along the northern California-central 

 Oregon coast (Table 1). Sagittal otoliths 

 were removed, cleaned, and either stored 

 dry or in ethanol until they could be 

 examined. 



Following Kimura et al. (1979) and 

 Lenarz (1987), we examined the edges of 

 broken and burnt otoliths collected from all months to 

 determine whether marks formed on an annual basis. 

 We attempted to get at least 100 fish per month (pooled 

 over years); however, sample sizes were less than 100 

 for February, August, September, October, and De- 

 cember (Fig. 1). The broken and burned otoliths were 

 examined without knowledge of sex, length, or date of 

 capture. A dark burned edge was classified as winter 

 growth; otherwise, the edge type was classified as sum- 

 mer growth. A few otoliths that appeared to be from 

 older fish, for which edge type could not be identified 

 clearly, were omitted from the study. Percent fre- 

 quency of summer growth was plotted against month 

 to examine periodicity in the formation of marks. 



We used between- and within-reader comparisons to 

 evaluate the consistency of broken and burnt otolith 

 readings. To evaluate between-reader agreement, two 

 readers independently examined a random subsample 

 of 200 otoliths. To evaluate within-reader agreement, 

 a random subsample of 200 otoliths was read twice, 

 independently, by one reader. To compare ages ob- 

 tained by otolith surface versus broken and burnt 

 otoliths, one reader obtained ages for a random sub- 

 sample of 200 otoliths, first from the surface and then 

 independently from the broken and burnt halves. 



We used the von Bertalanffy growth equation (Ricker 

 1975) to relate length and age: 



L t = L M (1 - e 



(-ka- 



to)) 



where L t 



k 



to 



total length (mm) at age t, 



estimate of average maximum length 



attained, 



growth completion rate, 



theoretical age when fish is length 0. 



JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 



Month 



Figure 1 



Frequency of light-colored edges (rapid growth period) for 

 broken and burnt otoliths from shortbelly rockfish by month. 

 Sample sizes are shown above each bar. 



Parameter estimates were obtained using nonlinear 

 regression analysis (SAS Institute Inc. 1987). Growth 

 equations were fitted separately for males and females 

 and compared using the Extra Sum of Squares Prin- 

 ciple (Draper and Smith 1981, Ratkowsky 1983). 



To calculate potential yield, we estimated natural 

 mortality (M) using several methods: (1) a regression 

 equation relating maximum observed age and total 

 mortality (Z, which equals M in this case) (Hoenig 1983); 

 (2) an exponential model, in which the estimate of Z 

 was based on both maximum observed age and sample 

 size (Hoenig 1983); and a regression equation relating 

 M to water temperature, average maximum length, 



