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Fishery Bulletin 101(2) 



blocks with incomplete time series and mean CPUE in the 

 second quartile were assigned to pseudo-block 2. Blocks 

 with mean CPUE in the third quartile were assigned to 

 pseudo-block 3. Blocks with mean CPUE in the fourth 

 quartile were assigned to pseudo-block 4. 



We fitted a "Poisson" generalized linear model to CPFV 

 logbook data and used it to compute CPUE indices for cow- 

 cod in each pseudo-block and year The model was fitted by 

 quasilikelihood assuming the Poisson distribution for sta- 

 tistical errors (McCullagh and Nelder, 1989). This approach 

 accommodated zeroes in the data (no cowcod in some blocks 

 during some months) and the generally rare and random 

 nature of cowcod catches. Quasilikelihood estimation (Mc- 

 Cullagh and Nelder, 1989) assumes that the variance of 

 CPUE data increases in proportion to the mean (i.e. ct-=(/)jU, 

 not necessarily equal to one) and is appropriate for CPUE 

 data that typically show this pattern (Hilborn and Walters, 

 1992). CPUE was the dependent variable. Independent 

 variables were pseudo-blocks, years, and months, and in- 

 teractions occurred between pseudo-blocks and years. The 

 interaction between psuedo-blocks and years allowed the 

 model to estimate different trends in each psuedo-block. 

 Other interactions were not included because of data and 

 computer limitations. The best Poisson model for cowcod 

 CPUE data was identified by using a step-wise procedure 

 with Mallow's C statistic. 



The CPUE index for the whole stock in each season was 

 computed as the habitat-area-weighted average of CPUE 

 in each pseudo-block. Variance estimates for the Poisson 

 CPUE index were from standard formulas for weighted 

 means and Poisson model estimates of variances. Variance 

 estimates were biased low because the poststratification 

 scheme (pseudo-blocks) was based on block means. 



Population dynamics modeling 



The assessment model for cowcod in the SCB (Butler et al., 

 1999) was a biomass dynamic approach based on Schnute's 

 (1985) delay difference equation implemented in C++ using 

 AD-Model Builder (Otter Software, Ltd."). It estimated 

 "fishable" biomass of cowcod about 40-t- cm PL (roughly age 

 10-I-), fishing mortality, and recruitment to the fishable bio- 

 mass. Fishable biomass is less than total biomass because 

 it includes only the portion of the stock available to the 

 fishery. The assumed natural mortality rate M=0.055/yr 

 was the same for all ages and years. 



The assessment model for cowcod included "virgin" 

 (prior to any fishing), "historical" (1917-50) and "recent" 

 (1951-98) seasons, as well as deterministic projections 

 for the 1999-2009 seasons (Butler et al., 1999). Virgin 

 and historical periods were linked in the model by stock 

 biomass calculations, an assumed level of constant mean 

 recruitment during the historical period, and an assumed 

 low level of fishing mortality (F=0.001/vr) prior to the 1917 

 season. The historical and recent periods were linked by 

 stock biomass calculations and assumptions about mean 

 recruitment during the historical period. Similar to stock 



" Otter Reseach Ltd.. Box 2040, Sidney, British Columbia, V8I- 

 3S3, Canada. 



reduction analysis (Kimura and Tagart, 1982; Kimura et 

 al., 1984; Kimura, 1985), virgin and historical calculations 

 were used to estimate the maximum size of the cowcod 

 stock, and recent data and calculations were used to es- 

 timate trends as the cowcod stock was fished down from 

 maximum size. Only catch data were available for the his- 

 torical period. Both abundance index and catch data were 

 available for the recent period. 



Abundance index data for the recent period used to 

 tune the cowcod assessment model included the Poisson 

 CPUE index from CPFV logbooks, the logistic index from 

 CalCOFI survey data, and proportion of positive tows from 

 LAOCSD bottom trawl tows. Probability of a positive tow 

 in CalCOFI and LAOCSD indices is almost proportional to 

 abundance when positive tows are rare ( Mangel and Smith, 

 1990). At higher levels, the probability of a positive tow is 

 a nonlinear function of larval abundance. Goodness of fit 

 for proportions (CalCOFI and LAOCSD data) assumed bi- 

 nomial measurement errors with adjustments for effective 

 sample size (Appendix). 



LAOCSD bottom trawl data for cowcod were used to 

 track recruitment because the LAOCSD survey takes 

 cowcod about three years old. In tuning the model, we 

 compared recruitment of three-year-old cowcod in 1980 

 as measured by LAOCSD data, for example, with model 

 estimates of recruitment at about age 10 during 1987. 



In modeling, CalCOFI presence-absence data were used 

 as an index of fishable stock abundance (Appendix). Cal- 

 COFI data were not used as an index of recruitment be- 

 cause the link between spawning adults and the presence 

 of larvae is shorter and more direct than the link between 

 presence of larvae and numbers of recruits to the fishable 

 stock at about age 10 yr. The latter would be more variable 

 due to variability in larval, juvenile, and adult survival 

 and growth rates. 



CPFV index data were assumed proportional to abun- 

 dance in the fishable stock and goodness-of-fit was com- 

 puted by assuming lognormal measurement errors. The 

 original logbook data were assumed to follow a Poisson-like 

 distribution in calculation of the index (see "Material and 

 methods" section). However, the index, like a log normally 

 distributed random variable, had no zero values (Butler 

 etal., 1999). 



Yearly catch data were assumed accurate in modeling 

 although cowcod catch data, particularly for early years, 

 were imprecise. Recruitments were assumed to follow a 

 random walk process with relatively small changes from 

 year to year 



Results 



Estimated commercial landings (Table 1 and Fig. 4) were 

 less than 20 t/yr during 1916-44, and ranged from 18 to 

 39 t/yr during 1951-72. Commercial landings increased 

 during the 1970s and early 1980s, peaked during 1984 

 at about 108 I and then declined rapidly to 8 t in 1991. 

 During 1993-97 commercial landings averaged 20 t/yr. 

 Estimated recreational catch peaked in 1973-74 at about 

 228 t (Table 1 and Fig. 4) and declined steadily to only 6 t 



