FISHERY BULLETIN: VOL. 84, NO. 2 



(i/i, ti) have to be combined so that y { > y { - for t { 

 < tf. The ratio n { ln can be used in place ofNJN to 

 compute the MLEs. This correction is inappropriate 

 if the reason for y { > y { ; for t { < t? is that in- 

 dividuals were evicted from the sampling area or 

 immigrated into it, as such movements violate the 

 assumption of a stationary population. 



Although %s are sufficient for computing point 

 estimates of the MLE, the total number of deaths 

 between ages t x and t k (N = m(y l - y k ) is required 

 for computation of the ASVAR-COV of the 

 MLEs. N can then be used to determine minimum 

 number of tows (m x ) for the youngest stage 

 through m 1 y l = N for a given precision of the 

 MLE. Although the sample size for eggs may dif- 

 fer from that of larvae, an equal number of sample 

 sizes is assumed to compute the ASVAR-COV. The 

 minimum number of egg tows can be determined 

 by m, = Nly v 



RESULTS 



Both the MEM and the SEM were fitted to the 

 basic data (y i7 t(, 0.17 d < t { < 20 d) collected from 

 1980 to 1983, using NR and LR (Table 1, Fig. 2). 

 The point estimates and their asymptotic standard 



errors are listed in Table 2 and Figure 3. NR and 

 LR produced similar estimates of the IMRs for the 

 MEM. When the SEM was applied to the combined 

 egg and larval data, the WNR was also used to com- 

 pute the IMRs in addition to NR and LR because 

 of the inequality of the variances among life stages. 

 The variance of egg counts was higher than that of 

 larvae because eggs were more patchily distributed 

 than larvae. Because of this, the inverse of the 

 variances of sample means of eggs and larvae was 

 used as the weights for the WNR. The estimates 

 from the WNR were similar to those from LR and 

 the standard errors from both methods were lower 

 than those from NR. 



The WNR estimates of egg IMRs from the SEM 

 were more precise than estimates from the MEM, 

 whereas the most precise estimates of larval IMRs 

 were provided by the MEM using NR. The SEM was 

 more precise than the MEM for eggs but not for the 

 larvae, because the variance of eggs was larger than 

 that of larvae. Thus, when eggs and larvae were 

 combined in an SEM, the variance around the single 

 equation was smaller for the eggs and larger for the 

 larvae. Nevertheless, the SEM produced larval 

 IMRs with reasonable precision when the WNR was 

 used. Therefore, the SEM WNR is suitable for ap- 



UNWEIGHTED SEM 



2.0 r 



1983 



10 15 20 25 5 



AGE IN DAYS 



10 15 20 25 



10 15 20 25 



Figure 2.— Observed daily anchovy egg and larval production/0.05 m z (O = eggs, • = larvae), and the mortality curves from the MEM 

 (two short curves) and the SEM (one single curve) using unweighted and weighted nonlinear regression for 1980-83 field collected data. 



402 



