FISHERY BULLETIN: VOL. 87, NO. 3, 1989 



1976; Lo 1983). Growth of feeding larvae has 

 been described as a function of season (Methot 

 and Hewitt 1980^). Interannual variations in 

 growth have not been described, and in the ab- 

 sence of additional information, a larval growth 

 model with constant coefficients is used for all 

 years. The set of coefficients encompassed tem- 

 perature effects as well as seasonal effects. The 

 rate of decline of larval production with age 

 represents the mortaUty rate (Hewitt 1981). 



In actual practice, a negative binomial- 

 weighted model (Bissel 1972) has been employed 

 to convert length-specific distributions of larval 

 density to unbiased age-specific distributions of 

 larval production, assuming one set of size-spe- 

 cific extrusion and voidance rates (Zweifel and 

 Smith 1981; Hewitt 1982; Hewitt and Methot 

 1982; Hewitt and Brewer 1983; Picquelle and 

 Hewitt 1983, 1984; Lo 1985). The negative bi- 

 nomial distribution is recommended for describ- 

 ing sample counts of fish eggs and larvae (Smith 

 and Richardson 1977); the distribution is capable 

 of adequately describing patchy spatial distribu- 

 tion patterns. The arithmetic means of these dis- 

 tributions describe the mortality (or production) 

 of larvae with age. 



Although the negative binomial-weighted 

 model produces an estimate of the variance of 

 the mean density at a particular age, each age- 

 specific distribution is unique because of the 

 spatial dispersal of the larvae (Hewitt 1981). The 

 variance of the mean density is underestimated 

 as the extrusion and avoidance are assumed to 

 be constant, and the variance about the mortal- 

 ity curve (hence, the variance of the mortality 

 rate) is not easily determined. In the simulation, 

 random variation of avoidance of the net and 

 extrusion through the meshes of the net were 

 included so that the variance of the mortality 

 rate might best be evaluated. The approach used 

 here is to construct a simulated population, sam- 

 ple it with simulated surveys, and estimate the 

 mortality rate of larvae, using the procedures 

 described above. By conducting many surveys, 

 the accuracy and precision of the estimates of 

 mortality rates may be investigated. 



Potential biases in estimating larval mortality, 

 introduced by assuming no interannual variation 

 in growth, were our main concern and were in- 

 vestigated by simulation. Growth rates were 

 varied when constructing the populations; mor- 



tality rates were subsequently calculated assum- 

 ing a set of growth rates (i.e., no interannual 

 variation). By comparing the calculated mortal- 

 ity rates to a known rate, the magnitude of 

 biases may be investigated. 



METHODS 



A Monte Carlo simulation model (Fig. 1) was 

 employed to address the questions pertaining to 

 the biases and precision of the estimate of larval 

 mortality. A population of anchovy larvae was 

 constructed using observed seasonal and geo- 

 graphic distributions. A known mortaHty rate 

 was imposed on the population and sampling ef- 

 fort was varied over time and space. Known 

 sampling biases were imposed and then adjusted 

 for using the same techniques for calculating 

 larval mortality rate as have been used on real 

 surveys. Several hundred simulated surveys 

 were conducted to assess the accuracy and pre- 

 cision of the estimates of mortahty rates. Sim- 

 ulated larval growth was also varied to deter- 

 mine the sensitivity of the estimates of mortality 

 rates to an assumption of constant larval growth. 

 The details of this simulation are outhned in the 

 following paragraphs. 



Larval Population 



A series of CalCOFI^ ichthyoplankton cruises 

 conducted in 1984 (Fig. 2) was used as a basis for 

 constructing the population of larvae in the 

 ocean. The total abundance of anchovy larvae at 

 each station was adjusted for extrusion of small 

 larvae through the meshes of the net (Fig. 3) and 

 avoidance of the net by large larvae (Fig. 4). The 

 adjusted catches were then stratified by geo- 

 graphic region (Fig. 2), month, and tempera- 

 ture. The negative binomial distribution was fit 

 to the observations (positive tows only) in each 

 region-month-temperature cell owing to the 

 patchiness of larvae and the fact that the mean 

 larval abundance is less than the standard devia- 

 tion in general (Table 1). Samples were ran- 

 domly drawn from these distributions (where 

 the variate was the total number of larvae <9.25 

 mm per station) to conduct a simulated survey. 



'Methot, R. D., Jr., and R. P. Hewitt. 1980. A generalized 

 growth curve for young anchovy larvae: derivation and tabular ex- 

 ample. SWFC Admin. Rep. LJ-80-17, 8 p. 



^California Cooperative Oceanic Fisheries Investigations 

 (CalCOFI) is a consortium of marine institutions engaged in long- 

 term monitoring and study of the pelagic ecology of the California 

 Current. Large-scale ichthyoplankton surveys have been conducted 

 since 1949. See Hewitt 1988, Reid 1988, and Smith and Moser 1988 for 



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