270 



Fishery Bulletin 101(2) 



i4r 



12 - 



Q. 0.08 - 



S 006 - 



^— Data 



Ivlodel Fits 



004 



002 



1950 



1960 



1970 



JOOCXXOOOO^'-LOOOSOO-' 



1980 1990 2000 



Year 



Figure 7 



Probability of positive tows (at least one cowcod larvae, an index of larval 

 presence used to track spawning biomass) in California Cooperative Oce- 

 anic Fishery Investigation (CalCOFI) ichthyoplankton surveys. "Data" are 

 from the logistic model for larval presence. "Model fits" are predicted values 

 from the stock assessment model fitted to the data. 



Effective sample sizes (Appendix) based on goodness of 

 fit in preliminary assessment model runs were less than 

 actual sample sizes. This discrepancy often occurs when 

 binomial or multinomial proportions are used to track 

 biological characteristics offish stocks (e.g. age composi- 

 tion of catches) and sample size is large (Fournier and Ar- 

 chibald, 1982). Geometric mean effective sample sizes for 

 cowcod were about 75 bongo net tows per year for CalCOFI 

 index data and about 50 bottom trawl tows per year for 

 LAOCSD index data. The number of actual CalCOFI tows 

 during 1987-98 was about one-third of the number during 

 1951-86 because sampling intensity was reduced begin- 

 ning in 1987 (Hewitt, 1988). For simplicity and to avoid 

 [)lacing too much emphasis in fitting our assessment mo- 

 del to LAOCSD and noisy ('al(X)Fl indices, goodness-of-fit 



calculations in subsequent assessment model runs as- 

 sumed sample sizes of 75 tows per year for CalCOFI data 

 during 1951-86, 25 tows per year for CalCOFI data during 

 the 1987-98 seasons, and 50 tows per year for LAOCSD 

 index data. Use of smaller effective sample size values in 

 model calculations helped us avoid placing too much weight 

 on the noisy CalCOFI data when fitting our model. 



Population dynamics modeling 



Like the abundance data, preliminary model runs indicated 

 that cowcod biomass declined during the 1951-98 seasons 

 and that recruitment declined after the 1980 season. 

 Catches were relatively low during the historical period 

 prior to 1951, particularly during earlier years. Therefore, 

 biomass was likely high prior to the 1951 season due to 

 good recruitment and low catches. Based on these consid- 



