FISHERY BULLETIN: VOL. 84, NO. 2 



0.5 

 0.4 



> 

 ~ 0.3 



o 



S 0.2 - 



en 

 o> 



Ui 



0.1 h 



0.0 

 1979 



0.5 r 



2. 0.4 H 



1980 



x MEM-NR 



• MEM-LR 



o SEM-NR 



A SEM-WNR 



A SEM-LR 



+ MLE 



1981 



1982 



1983 



1983 



^ 3.0 

 oa 



c 2.5 



^ 20 



O 



o 



> 1.5 



r i.o 



o 



« 0.5 



(0 



0.0 



x MEM-NR 



• MEM-LR 



o SEM-NR 



A SEM-WNR 



▲ SEM-LR 



+ MLE 



1980 



1981 



1982 



1983 



1983 



Figure 3.— Estimated anchovy egg mortality (a), larval mortality coefficient (/3), and their standard error (SE) using multi-equation 

 model (MEM), single-equation model (SEM), and maximum likelihood estimator (MLE) for 1980-83. 



specific age needs to be transformed back to the 

 original unit. Direct inverse transformation may 

 bias the estimates. Thus, the LR may not be ap- 

 propriate for biomass estimation or other applica- 

 tions where a transformation back to original units 

 is required. 



In addition to the above regression models, the 

 MLEs of egg and larval IMRs were also computed 

 based on the data set n { = y^\ - y it i = 1, . . .k 

 (Equations (Al) and (A2), Table 1). The ASCOV- 

 VAR for anchovy egg and larval mortality rates re- 

 quires the total number of eggs and larvae that died 

 between ages 4 h and 20 d from the sample (N). It 

 is not possible to obtain N directly from my^ (i.e. 

 N = myx) because eggs and larvae are sampled 

 with different nets and in different regions. Anchovy 

 eggs have a more concentrated and patchy distri- 

 bution than larvae which are less numerous and 

 distributed more uniformly throughout the entire 

 survey area because of the diffusion of larvae after 

 hatching (Hewitt 1982). Zero density of eggs was 

 assumed for the offshore regions where eggs were 



not sampled to compute the weighted average egg 

 production y % = Z. w r y ir . I then divided m^ by 



r 



the proportion of area sampled (q = Z. w r where 



w r 's are summed over the regions where egg tows 

 were taken) to obtain sample daily death N in [t lt 

 t k ). Thus, N = mtfjjq; q ranges from 0.53 to 0.82 

 for 1980-83. Four sets of sample sizes were con- 

 sidered: m = m 1 , 500, 300, m 2 where m x is the ac- 

 tual number of egg tows and m 2 , actual number of 

 larval tows (Table 2). For any given N, one obtains 

 the ASVAR-COV of a and p by dividing a {j by N 

 where a^'s are the elements in matrix A of Equa- 

 tion (12). 



The MLE point estimates a and /?, were between 

 the estimates yielded by the SEM and the MEM in 

 most cases. The precision of the MLE for egg IMR 

 was higher than that of the regression estimates. 

 The standard error of the MLE of the larval IMR 

 was between those of the MEM and SEM regres- 

 sion estimates (Table 2, Fig. 3). 



404 



