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Fishery Bulletin 101(2) 



available (McCullagh and Nelder, 1989), and applications 

 have been described (e.g. Smith, 1990; Newman, 1997), but 

 more research and experience are required. 



Zero observations ("zeroes") can be expected to be com- 

 mon in rare-event data and frequently encountered in fish- 

 ery survey data for many species (Lo et al., 1992; Syrjala, 

 2000). They are usually considered a problem in stock as- 

 sessment work because conventional assessment models 

 assume lognormal measurement errors for abundance in- 

 dices and the lognormal distribution does not include the 

 possibility of zero values. However, our experience with 

 CalCOFI and LAOCSD data for cowcod demonstrates the 

 tractability of maximum likelihood estimation using the 

 binomial distribution for proportion positive data with 

 zeroes. Effective sample size calculations can be used with 

 binomial data (e.g. for cowcod) in the same way that Fourni- 

 er and Archibald (1982) and Methot (1990) used effective 

 sample size techniques to gauge the information content of 

 multinomial age- and length-composition data. 



CPFV data 



CPFV logbook data present a bleak time series for cowcod. 

 Because this series was critical to the analysis, it is impor- 

 tant to consider factors other than abundance that may 

 affect CPUE in the CPFV fishery. For example, changes 

 over time in targeting and identification of cowcod in 

 catches would affect reporting and CPUE, but we are not 

 aware of any changes in catch reporting since 1964. 



Trends in CPUE tend to be optimistic (biased towards 

 high biomass in recent years) if fishing effort becomes 

 more effective over time. Changes in angler's gear likely 

 had little effect on catch rates for cowcod because gear used 

 on CPFV vessels has changed little since the early 1960s. 

 Ability of the CPFV fleet to identify, locate, and return to 

 fishing grounds with high catch rates have improved over 

 the last three decades as electronics, including depth find- 

 ers and global positioning systems, became available and 

 were improved. Effort in later years was likely more ef- 

 fective because CPFV operators were better able to locate 

 and return to locations where rockfish and cowcod were 

 abundant. 



Logbook data indicate that recreational fishing effort 

 for rockfish moved from inshore areas (where cowcod are 

 less abundant) to offshore areas during the 1960s to 1980s. 

 Thus, the proportion of total angler hours in the CPFV 

 fishery that could potentially catch cowcod in relatively 

 deep water increased over time as the proportion of anglers 

 fishing offshore and in deep water increased. 



Robustness of area-weighted CPUE index 



The area-weighted CPUE index for cowcod is robust to 

 interannual changes in the spatial distribution of fishing 

 effort among blocks. This is an important point because 

 CPUE computed as the sum of total catch divided by total 

 fishing effort would be biased high, for example, if the 

 amount of relative fishing effort in a stratum with high 

 catch rates increased. Blocks and pseudo-blocks are strata, 

 in statistical terms, that are sampled during each year Our 



area-weighted CPUE index for cowcod is a weighted aver- 

 age of mean CPUE in each stratum during one year The 

 weights used in computing the index are proportional to 

 the amount of potential cowcod habitat in each stratum. 



Thus, the contribution of each stratum to the overall 

 index is proportional to the amount of cowcod habitat in 

 each stratum, not the amount of fishing effort. Increases 

 or decreases in the amount of fishing effort in a stratum 

 with high catch rates will change the precision of the stra- 

 tum mean and the precision of the index as a whole but 

 would not change the expected value of the area weighted 

 index as a whole. In statistical terms, the expected value 

 of the area-weighted CPUE index should be similar to the 

 expected value of mean CPUE computed from anglers 

 distributed randomly across the entire area of potential 

 habitat. Of course, our area-weighted approach does not 

 accommodate interannual changes in the distribution of 

 fishing effort within strata, and movement of fishing effort 

 within strata towards areas of high catch rate would tend 

 to inflate the index as a whole. 



CalCOFI presence-absence data 



CalCOFI data were not used in the assessment model as a 

 recruitment index (see "Materials and methods" section). 

 However, considering the time lag between cowcod larvae 

 and juveniles at about age 3, the qualitative trend in Cal- 

 COFI ichthyoplankton data appears to match the trend in 

 LAOCSD bottom trawl survey data. In particular, CalCOFI 

 and LAOCSD data both suggest that cowcod recruitment 

 is likely to be poor in the coming years. 



Climate change 



Declines in cowcod abundance over the last several decades 

 may have been due to reductions in spawning biomass from 

 fishing or to the environmental regime shift (Lluch-Belda 

 et al., 1989) in the SCB and California current towards 

 warmer water during the late-1970s (Barnes et al., 1992, 

 Moser et al., 2000), or to both factors (Jacobson and Mac- 

 Call, 1995). CalCOFI data show that the probability of 

 occurrence for cowcod larvae in CalCOFI tows declined 

 during the mid- to late-1970s (Fig. 7) and that estimated 

 recruitment to the fishable stock, predictably, declined a 

 decade later (Table 1 and Fig. 11). Catches, recruitment, 

 and abundance for other stocks in the California current 

 changed at about the same time (Beamish, 1995). 



Environmental effects on recruitment estimates during 

 1917-50 are a source of uncertainty in calculating virgin 

 biomass. Historical calculations for cowcod assumed re- 

 cruitment at average levels during 1951-80, which was 

 a relatively cold-water period in the SCB (as measured 

 by sea surface temperatures at Scripps Pier in San Di- 

 ego, California; Barnes et al., 1992). However, sea surface 

 temperatures in the SCB were moderately warm during 

 1917-50 (Barnes et al. 1992). If warm sea surface tempera- 

 tures are correlated with poor cowcod recruitment, then 

 we may have overestimated historical recruitment and 

 virgin biomass, so that the ratio of biomass in 1998 and 

 virgin biomass (6.5'?f ) was underestimated. However, this 



