FISHERY BULLETIN: VOL. 84, NO. 2 



egg and larval stages. However, predation, the ma- 

 jor cause of mortality in the embryonic period, may 

 be similar for eggs and yolk-sac larvae (Hunter 2 ). 

 If this is true, then the end of the yolk-sac stage is 

 a reasonable separation point for the mortality 

 stanza. 



The conditional survival probability corresponding 

 to IMR in Equation (1) is 



Stf) = e 



— a- at 



t < U x 



(2a) 



and 



S 2 (t) = l — \ u 1 < t< 20 (2b) 



To assess S g (t) for g = 1,2 in Equation (2), anchovy 

 egg and larval data were first divided into K age 

 groups. The mortality curves (Equation (3)) were fit- 

 ted to the sample mean counts (^) and mean age 



E(yd = 



O SJfa xm t { < u x 



0„ SJt£ hit)] m, < t r < 20 



(3) 



where t is the expected number of fish at age t. 

 Using separate equations like Equation (3) is un- 

 satisfactory for some applications because separate 

 mortality curves may produce discontinuities at 

 transitions between mortality stanzas (or life 

 stages). The purpose of this paper is to obtain a 

 regression estimator and a maximum likelihood 

 estimator (MLE) of the IMRs (\{t)). The regression 

 estimator was based upon a single mortality curve 

 for all early life stages of anchovy, and the MLE 

 was based upon a truncated exponential (Equation 

 (2a)) and Pareto (Equation (2b)) likelihood function 

 of time to death (Lo 1985). 



In section on Data, I describe the method of an- 

 chovy egg and larval data collection and standard- 

 ization procedures. The standardization procedures 

 are necessary because the gear and sample sizes 

 used to collect eggs differ from those used to col- 

 lect larvae. In section on Multi-Equation Model, the 

 current estimation procedures for constructing mor- 

 tality functions for different life stages are pre- 

 sented. In these procedures separate mortality func- 

 tions are fitted to the data set for each life stage. 

 In the next two sections, I develop two estimation 

 procedures for the IMRs of different life stages from 

 a single analysis: a single mortality function is con- 



2 J. R. Hunter, Fishery Biologist, Southwest Fisheries Center La 

 Jolla Laboratory, National Marine Fisheries Service, NOAA, P.O. 

 Box 271, La Jolla, CA 92038, pers. commun. July 1983. 



structed which is based on the IMRs of different life 

 stages, and the maximum likelihood estimators of 

 life-stage specific IMRs are described. The MLEs 

 of anchovy eggs and larvae (<20 d) are obtained. The 

 results and the comparisons of various models based 

 on anchovy egg and larval data are given in the last 

 two sections. 



DATA 



The standardized abundance of anchovy eggs and 

 larvae taken in routine biomass surveys was used 

 to elevate different estimation procedures for mor- 

 tality rates (Smith 1972; Parker 1980). The variables 

 used in the standardization procedures were extru- 

 sion through the net, avoidance of the net mouth, 

 and the variation of the water volume filtered per 

 unit depth (Zweifel and Smith 1981). 



The northern anchovy spawning area lies off cen- 

 tral and southern California and Baja California. The 

 sampling area was divided into 23 regions covering 

 17.566 x 10 11 m 2 (Fig. 1). The central anchovy 

 stock is enclosed by 8 regions (4, 5, 7, 8, 9, 11, 13, 

 and 14) with a total of 5.703 x 10 11 m 2 (Duke 3 ). In 

 this paper, I study the mortality of egg and larva 

 of central anchovy stock. Anchovy eggs and larvae 

 are sampled by net tows and each tow is a sampling 

 unit. Every year, m 1 egg tows, vertical tows of 

 0.333 mm mesh with 25 cm diameter mouth open- 

 ing, and m 2 larval tows using an oblique plankton 

 net of 0.505 mm mesh with 60 cm diameter mouth 

 opening are made. Ages were assigned to life stages 

 using stage specific growth curves (Methot and 

 Hewitt 1980 4 ; Lo 1983). The standardized number 

 of larvae in each group was divided by the time that 

 larvae remained at a particular length to yield the 

 sample mean daily larval production per unit area 

 (0.05 m 2 ). A weighted mean per unit area for the 

 entire survey area (8 regions) was calculated: y i = 



2. w r y ir where w r was the weight for region r and 



r 



Z.w r = 1 (Table 1) (Lo 1985) and y ir was the sam- 



r 



pie mean count for i th age group in region r. I con- 

 sidered only larvae smaller than 10 mm (20 d old) 

 because for anchovy larvae larger than 10 mm, the 



3 Duke, S. 1976. CalCOFI station and region specification. 

 Southwest Fish. Cent. Admin. Rep. No. LJ-76-3, 37 p. National 

 Marine Fisheries Service, NOAA, P.O. Box 271, La Jolla, CA 

 92038. 



4 Methot, R. D., and R. P. Hewitt. 1980. A generalized growth 

 curve for young anchovy larvae; derivation and tubular example. 

 Southwest Fish. Cent. Admin. Rep. No. LJ-80-17. National 

 Marine Fisheries Service, NOAA, P.O. Box 271, La Jolla, CA 

 92038. 



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