Jacobson et al.: A biomass-based assessment model for Engraulis mordax 



719 



SIMPLE MODEL [NO BIAS 

 CORRECTION! 



1962 1964 1966 1966 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 



FISHING SEASON 



Figure 3 



Recruitment estimates for northern anchovy, Engraulis mordax (age-0 fish 

 on 1 July, in thousands of metric tons) for the 1963 to 1991 fishing seasons 

 from the SMPAR model (biomass) and the stock synthesis model (number 

 of recruits) used by Lo and Methot ( 1989). Estimates from the SMPAR model 

 are shown with and without correction for bias. 



models were generally similar (Fig. 2) except where 

 retrospective bias in previous estimates was a prob- 

 lem. Results from SMPAR indicate that high north- 

 ern anchovy biomass in the early 1970's was due to a 

 single large cohort spawned in the 1971 fishing sea- 

 son (age 1 in 1973) rather than to a series of strong 

 recruitments (Figs. 2 and 3). This difference is due 

 to omission of age-composition data and inclusion of 

 SPOTTER data not available to Lo and Methot 

 ( 1989). Unlike SONAR data, SPOTTER data did not 

 increase significantly until the 1973 fishing season 

 (Fig. 1). 



Coefficients of variation for northern anchovy 1+ 

 biomass estimates ranged from 14% to 38% and av- 

 eraged 26% (Table 4). Precision of the biomass esti- 

 mate for the most recent fishing season (29%) was 

 better than that from the original stock synthesis 

 model for northern anchovy (CV=40%, Lo et al., 

 1992). Improvements in data contributed to higher 

 precision, but this result indicates a substantial im- 

 provement as a result of using a simpler, more par- 

 simonious model. 



Recruitment estimates for northern anchovy from 

 the SMPAR model showed less year-to-year varia- 

 tion than those from the stock synthesis model al- 

 though both sets of estimates indicate that northern 

 anchovy recruitment was low during the 1963 to 1968 



fishing seasons and high in the 1972 fishing season 

 (Fig. 3). CVs for arithmetic-scale recruitment esti- 

 mates (11% to 69%, average 41%) from the SMPAR 

 model were about 50% larger on average than CVs 

 for biomass estimates (Table 4). 



The most important conclusion to be drawn in com- 

 paring recruitment estimates from SMPAR with 

 those from the stock synthesis model for northern 

 anchovy is that disparate recruitment estimates (Fig. 

 3) resulted in similar biomass estimates (Fig. 2). This 

 suggests that abundance index data for northern 

 anchovy contain relatively little information about 

 recruitment variability. The SMPAR model probably 

 underestimates recruitment variability for northern 

 anchovy because it uses only abundance data and 

 includes a recruitment constraint that biases recruit- 

 ment estimates towards the mean. 



Comparison of bootstrap and asymptotic 

 variance estimates 



Asymptotic standard errors for parameters obtained 

 by inverting the Hessian matrix were about 19% 

 smaller, on average, than standard deviations ob- 

 tained by bootstrapping. This result indicates that 

 asymptotic variance estimates for parameters in the 

 SMPAR model were too small. 



