714 



Fishery Bulletin 92(4), 1994 



1991 fishing seasons in the reduced CalCOFI (Cali- 

 fornia Cooperative Oceanic Fishery Investigation) 

 sampling area surveyed since 1985 (Hewitt, 1988). 

 The HEP index, in contrast, is based on a relatively 

 large grid of CalCOFI sampling stations occupied 

 prior to the 1985 season. As explained below, the EPI 

 makes use of all egg and larva data and is more pre- 

 cise than the modified historical egg production 

 (MHEP) index used for recent seasons by Lo and 

 Methot (1989). Both the HEP and EPI indices of egg 

 production for northern anchovy during the 1979 to 

 1984 fishing seasons were used so that the model 

 could calibrate the HEP and EPI against each other 

 and against DEP spawning biomass estimates. 



The EPI for northern anchovy averages values 

 obtained by using the HEP method and a single equa- 

 tion model (SEM) developed by Lo (1986). We refer 

 to the HEP "method" here to distinguish between the 

 HEP index and calculations for recent seasons based 

 on data from the reduced CalCOFI grid. 



The EPI index was computed as 



/ = W 



1 EPI.y ''SEM, 



l SEM. 



+ **HEP,y *HEP,y> 



(2) 



where the I t are indices of egg production for north- 

 ern anchovy during fishing season y, and the W f are 

 weights. Weights were derived from squared inverse 

 coefficients of variation: 



W 



L_ 



CV, 2 . 



I 



CV HEP.y 



(3) 



where CV s is the coefficient of variation for index s 

 (either SEM or HEP) in fishing season y. Variances 

 for the EPI index were approximated 



VAR(I EPly ) = Wi EMy VAR(l SEM , y ) 

 + W^ EPy VARU HEPy 



J, 



(4) 



where VAR denotes variance. 



The weighted EPI estimates of egg production for 

 northern anchovy were similar to HEP method and 

 SEM estimates but more precise (Table 2). The im- 

 provement in precision is overestimated, however, 

 because covariance between measurement errors in 

 SEM and HEP values in each year were not included 

 in Equation 4. 



Model 



Our model for northern anchovy was based on a for- 

 ward simulation approach (Hilborn and Walters, 

 1992) like that used in the stock synthesis model 

 (Methot, 1989; Methot, 1990) and CAGEAN (Deriso 

 et al., 1985). The model simulated abundance of 

 northern anchovy during the 1963 to 1991 fishing 

 seasons given a set of parameter estimates, data for 

 catches, and ocean temperatures. Parameters were 

 estimated by maximum likelihood calculations that 

 compared observed abundance indices with values 

 predicted by the simulation model. Catch data for 

 northern anchovy and temperature data were as- 

 sumed to be measured without error; abundance in- 

 dices were assumed to include measurement error. 



