FISHERY BULLETIN: VOL. 83, NO. 2 



Under series 2, Po and a were estimated based 

 upon q = mtys IPtys (Equations (9B) and (10) ), with 

 tc = tys . The average age of yolk-sac larvae {tys = 

 ^2.5 mm) was 4.7 d. All q's were greater than tys , 

 thus as were all positive. 



The HEP (Po) for both series have the same 

 trend: a gradual increase from the early 1950's to 

 middle 1960's, thereafter fluctuating until 1975 

 when it reached the peak value at 15.32/day per 

 0.05 m^ (series 1) or 19.69/day per 0.05 m^ (series 

 2). From 1978, HEP decreased to the present level 

 of 1.94/day per 0.05 m^ (series 1) and 3.29/day per 

 0.05 m^ (series 2) (Table 3, Fig. 4). The approxi- 

 mate standard error of the estimated HEP (Po) 

 and egg mortality (a) is large for the early years 

 and small for the recent years, possibly because 

 of the poor quality of early egg data, or an insuf- 

 ficiency of the delta method to estimate the 

 variance. 



For the purpose of verification, HEP (Po) from 

 the two series based upon the egg-larval mortality 

 model and the egg production at age estimated 

 from the current EPM (Stauffer and Picquelle 

 footnote 6) were compared for 1980-82 where 

 adequate egg and larval samples were available 

 (Table 4). The Po's from the two series of HEP and 

 the current EPM were not significantly different, 

 nor were the egg mortality rates. However, the 



20 r 



15 



E 



o 

 6 



ffi 



z 



3 



10 



Daily egg production Pq 



'n oi Larval abundance (LCE) La 



1950 



1960 



1970 

 YEAR 



\ -r , -v<>r : 



-^-M 



1980 



Figure 4. — Estimates of historical egg production of the central 

 stock of northern anchovy using the series 2 method (Po ) and the 

 larval abundance (La) of the larval census estimates, 1951-82. 



Table 4. — Daily egg production per 0.05 m^ (Po), egg instan- 

 taneous mortality (a), egg abimdance (mtj) of northern an- 

 chovy, and number of tows in) in CalCOFI regions 4, 5, 7, 8, 9, 

 11, 13, and 14, January-April 1980-82. 



' Picquelle, see text footnote 8. 

 2 Mesh size. 



point estimates of Pq's from the current EPM were 

 lower than those estimated from the two series. 

 The reason for the lower values is unknown at the 

 moment. This could be due to random fluctuation 

 of the statistics. The current EPM estimates of Po 

 were much more precise than those derived from 

 the historical egg-larval mortality model, where- 

 as the precision of egg mortality rate from both 

 methods was similar. 



As to the estimates from the two series of HEP, 

 the point estimates of Pq from series 2 were always 

 higher than those estimated from series 1. Recall 

 that the assumption of series 2 was that the egg 

 through yolk-sac larval stage suffers a constant 

 mortality rate. However, if in fact the yolk-sac 

 larvae suffer a higher mortality rate than eggs, 

 the mortality rate of eggs and larvae when com- 

 bined (series 2) would overestimate egg mortal- 

 ity as well as egg production (Po) (Equation 

 (9B)). 



DISCUSSION 



Historical production (Po) and egg IMR (a) of 

 the central stock of northern anchovy for the first 

 4 mo of the year from 1951 to 1982 were estimated 

 based upon the information of total number of 

 eggs and yolk-sac larvae per 0.05 m^ and the egg- 

 larval mortality model. Two series of Po and a 

 were produced. Series 1 assumed a constant IMR 

 for only the egg stage whereas series 2 assumed a 

 constant IMR for the entire embryonic period. 

 Both series of Po showed the same trend (Table 3, 

 Fig. 4) with a peak in 1975. The high daily egg 



146 



