LO: MORTALITY RATES OF NORTHERN ANCHOVY 



DISCUSSION 



All the estimates of instantaneous mortality rates 

 (IMR) discussed in this paper were computed from 

 age (stage) frequency data. To ensure the unbiased- 

 ness of the estimates, three assumptions have to be 

 met: a stationary population, reliable growth curves, 

 and accurate samplers. Any violation of these 

 assumptions will cause biases in the mortality 

 estimates. Nets usually do not retain fish of all sizes 

 because some small fish extrude through the net and 

 some large fish avoid the net. Thus the estimates 

 of size-specific retention rates are essential correc- 

 tion factors for the catch. If fish migrate at a signifi- 

 cant rate, either the migration rate should be 

 estimated or the sampling area should be expanded 

 to eliminate migration problems, for migration 

 violates the assumption of a stationary population 

 and thus biases the mortality. Because growth 

 curves are normally used to assign age to stage of 

 eggs and larvae, biased growth curves would lead 

 to inaccurate age assignments which definitely 

 would bias the mortality estimates. 



Although modeling the mortality rates of the early 

 life stages of anchovy is the focus of this paper, I 

 have shown that the SEM (Fig. 2) can be applied 

 to any continuous process whose parameters are life- 

 stage specific and generally estimated separately. 

 For example, many allometric relations such as the 

 growth curves may have different instantaneous 

 growth rates for different life stages. A single con- 

 tinuous growth curve for the whole life cycle is possi- 

 ble using the SEM which allows greater latitude of 

 modeling life-stage-specific growth rates than 

 modeling the instantaneous growth rate for the 

 whole life cycle as proposed by Schnute (1981). How- 

 ever, the SEM does require knowledge of the forms 

 of instantaneous rates and the endpoint of each mor- 

 tality stanza (or life stage). 



In this study, the determination of a cutoff point 

 between life stages was based upon examination of 

 the empirical data and biological implications. It is 

 conceivable to include the cutoff point (%) as one 

 of the parameters in both SEM and MLE (Matthews 

 and Farewell 1982). The cutoff point can then be 

 estimated directly through the models. Matthews 

 and Farewell considered the exponential mortality 

 curve with one cutoff point and obtained MLE of 

 the cutoff point (change point). For anchovy egg and 

 larvae, the cuttoff point for the eggs and larvae up 

 to 20 d old was easily determined from the IMR and 

 age data (Lo 1985). Estimation of the cutoff point 

 through SEM or MLE would be laborious and any 

 improvement may be minimal. However, the 



estimates through the models would eliminate the 

 problem of whether u x should be hatching time or 

 the age of yolk-sac larvae. 



Comparison of these two regression models with 

 the MLEs based on anchovy egg and larval data in- 

 dicated that the point estimates of the IMRs were 

 similar. The SEM using WNR provided the most 

 precise egg IMR which was nearly the same as the 

 MLE. The MEM, using NR, provided the most 

 precise estimates of larval IMR's. The regression 

 estimators of the IMR's are easier to compute than 

 the MLEs, yet they require larger sample sizes than 

 the MLEs. If money is not a constraint, the SEM 

 is preferred to the MLE. Otherwise, the MLE 

 should be used. Based upon 1980 anchovy egg and 

 larval data, 300 tows for eggs and larvae each (a 

 total of 600 tows) could guarantee MLEs of a and 

 (i with cv = 0.10. The current sampling design (egg 

 tows ~ 1,000) seems to use an excessive number of 

 egg tows for the MLEs of egg and larval IMRs. If 

 the larval IMR is the only parameter to be 

 estimated, the MEM is recommended. 



ACKNOWLEDGMENTS 



I thank J. Hunter of Southwest Fisheries Center, 

 National Marine Fisheries Service, and C. J. Park 

 of San Diego State University for valuable discus- 

 sions through the writing of the manuscript, the 

 referee for constructive comments, and Mary Ragan 

 and Larraine Prescott for typing the manuscript. 



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