Abstract. — We developed a 

 relatively simple and parsimonious 

 (SMPAR) biomass dynamics model 

 for estimating abundance of north- 

 ern anchovy, Engraulis mordax, off 

 southern California and Baja Cali- 

 fornia, Mexico, during the 1963 to 

 1991 fishing seasons. The SMPAR 

 model was a compromise between 

 simple surplus production and 

 complex age-structured models. It 

 was designed to give more precise 

 biomass estimates for management 

 of northern anchovy for which 

 there are no age-composition data 

 and only noisy abundance index 

 data. We evaluated consistent bias 

 in biomass and recruitment esti- 

 mates, bias in recruitment esti- 

 mates due to log transformation, 

 and retrospective bias. Simple cor- 

 rections based on bootstrap proce- 

 dures were used to remove consis- 

 tent bias and log transformation 

 bias. Retrospective bias was not a 

 significant problem. Results indi- 

 cate that the SMPAR model esti- 

 mates stock biomass more reliably 

 than recruitment because abun- 

 dance indices for northern anchovy 

 contain little information about 

 interannual recruitment variabil- 

 ity. Asymptotic variance estimates 

 calculated by inverting the Hessian 

 matrix averaged 20% smaller than 

 variances calculated by bootstrap- 

 ping. Outliers in abundance data 

 were the biggest source of uncer- 

 tainty in biomass estimates. Simu- 

 lation results indicate that our ap- 

 proach could be useful in a variety 

 of situations. 



A biomass-based assessment 

 model for northern anchovy, 

 Engraulis mordax 



Larry D. Jacobson 

 Nancy C. H. Lo 



Southwest Fisheries Science Center, National Marine Fisheries Service. NOAA 

 RO. Box 271, La Jolla, California 92038 



J. Thomas Barnes 



California Department of Fish and Game 



330 Golden Shore, Suite 50, Long Beach, California 90802 



Manuscript accepted 28 April 1994. 

 Fishery Bulletin 92:711-724. 



Northern anchovy, Engraulis mor- 

 dax, is a small (<18 cm TL), short 

 lived (<8 years) pelagic schooling 

 fish (Baxter, 1967). The central 

 stock of northern anchovy extends 

 from Mexico to central California 

 (lat. 30°-35°N); most of the stock 

 inhabits the Southern California 

 Bight. Spawning occurs all year 

 with a peak between February and 

 April (MacCall and Prager, 1988). 



The central stock of northern an- 

 chovy is among the world's most 

 thoroughly studied fish stocks. Re- 

 liable estimates of northern an- 

 chovy biomass were not available, 

 however, until the daily egg produc- 

 tion method was used to estimate 

 spawning biomass from 1980 to 

 1985 (Lasker, 1985). Estimates of 

 long-term trends in biomass were 

 not available until the stock synthe- 

 sis model for northern anchovy was 

 developed (Methot, 1989). The stock 

 synthesis model was used to man- 

 age northern anchovy until 1992 

 after availability of age-composition 

 data declined. 1 



As data became limited, variance 

 and bias of biomass estimates 2 from 

 the stock synthesis model in- 

 creased. Bias problems included a 

 positive "retrospective" bias in re- 

 cent estimates and a smaller but 

 consistent positive bias in estimates 

 for earlier seasons (Lo et al., 1992). 



Retrospective bias is a newly rec- 

 ognized but common problem in fish 

 stock assessment work (Sinclair et 

 al., 1991) that makes recent biom- 

 ass estimates too large. Consistent 

 bias (usually positive) is a problem 

 of variable severity in biomass esti- 

 mates from most assessment mod- 

 els including the stock synthesis 

 model (Lo et al., 1992; Bence et al., 

 1993), derivatives 3 of CAGEAN (Der- 

 iso et al., 1985), and virtual pop- 

 ulation analysis or VPA(e.g. Lapointe 

 etal., 1989). Consistent bias, unlike 

 retrospective bias, affects all or 

 most of the biomass estimates from 

 a model. 



We hypothesized that problems in 

 the stock synthesis model for north- 



1 Jacobson, L. D., and N. C. H. Lo. 1992. 

 Spawning biomass of the northern anchovy 

 in 1992. U.S. Dep. Commer., NOAA, Natl. 

 Mar. Fish. Serv., Southwest Fish. Sci. 

 Cent., P.O. Box 271, La Jolla, CA 92038. 

 Admin. Rep. LJ-92-24, 71 p. 



2 Jacobson, L. D., and N. C. H. Lo. 1991. 

 Spawning biomass of the northern anchovy 

 in 1991. U.S. Dep. Commer., NOAA, Natl. 

 Mar. Fish. Serv., Southwest Fish. Sci. 

 Cent, P.O. Box 271, La Jolla, CA 92038. 

 Admin. Rep. LJ-91-19, 53 p. 



: ' Deriso, R. 1993. A report on integrated 

 stock assessment of Pacific sardine, Appen- 

 dix 2. In F. J. Hester, Project report on 

 Pacific sardine {Sardinops sagax ) resource 

 research, 1991/1992 phase III. Living Ma- 

 rine Resources Inc., 11855 Sorrento Val- 

 ley Road, Suite A, San Diego, CA 92121. 

 Final Rep. to Calif. Seafood Council, P.O. Box 

 91540, Santa Barbara, CA 93190, 118 p. 



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