144 



Fishery Bulletin 101(1) 



Wc have shown that weight-specific fecundity was only 

 weakly dependent on age (Fig. 7). If these variables were 

 independent, the age structure of the stock would have no 

 influence on population fecundity; that is, a ton of S-yr-old 

 fish would have the same reproductive output as a ton of 

 20-3T-old fish. Thus, if age and weight-specific fecundity 

 are independent, the natural mortality rate (Ml has no 

 influence on the estimation of biomass, which agrees with 

 the relative insensitivity of the total biomass estimate to 

 estimated natural mortality rate (Table 2, Fig. 14). This a 

 highly desirable characteristic of the assessment methods 

 proposed here. Unlike stock assessments that are predi- 

 cated on measuring the abundance of ichthyoplankton, 

 results from standard age-structured stock assessment 

 models often depend critically on what is almost always 

 an assumed value of M (e.g. Ralston and Pearson^). This 

 can have the effect of reducing an entire stock assessment 

 modeling exercise to guesswork. 



Daily larval production (log^.lA'^gl) is the other estimated 

 parameter that most strongly influences the calculation of 

 biomass, with parameter perturbations of ±1.0 standard 

 error that result in a 16-19% effect on estimated stock 

 biomass (Table 2). This parameter was determined by 

 assuming a constant mortality rate model, which yielded 

 Z = 0.1 1/d. However, we view the selection of a specific 

 mortality model to be of considerable importance and 

 wish to emphasize that other alternatives to the exponen- 

 tial survivorship case are available, including the Pareto 

 model (Lo et al., 1989). Researchers who wish to apply the 

 method that we outline here would be well-advised to ex- 

 amine this particular issue carefully because the estimate 

 of daily larval production (7V„) will depend critically on the 

 mortality model used. 



Another underlying assumption of the lai-val produc- 

 tion method is that over the period represented by the 

 data, the larval production rate and the mortality rate 

 remained constant. Violations of this assumption could 

 cause patterns like those evidenced in Figure 12. How- 

 ever, we conclude that the existing data do not allow us 

 to distinguish between explanations based on correlated 

 estimation errors and those based on time-varying lai-val 

 production rates. Also, the ichthyoplankton survey took 

 place over a 6V2-day period and samples close together 

 in space were also close together in time, which further 

 complicates the issue. Possible future approaches might 

 consist of sampling designs that include spatial and tem- 

 poral replication. 



Another major source of uncertainty in our assessment 

 lies in the expansion of "daily" total biomass to "annual" 

 total biomass. Based upon the long-term mean distribu- 

 tion of spawning activity (Fig. 12), we calculated that 

 the annual biomass was -50 times larger than the daily 

 biomass on 11 February. Use of the long-term mean distri- 



Ral.ston, S., and D. Pearson. 1997. Status of the widow rock- 

 fish stock in 1997. In Status of the Pacific coast groundfish 

 fishery throuRh 1997 and recommended acceptable biological 

 catches for 1998. .Stock assessment and fishery evaluation, 

 appendix, .")'l p. Pacific Fishery Management Council, Port- 

 land, OK 



bution has obvious limitations, however, if the spawning 

 season varies interannually (see Fig. 15). 



Results presented in MacGregor ( 1986) can be used to ex- 

 amine the assumption that spawning seasonality is the same 

 every year He sorted all shortbelly rockfish larvae from all 

 plankton samples that were collected as part of CalCOFI 

 surveys conducted in 1956, 1966, 1969, 1972, and 1975. In 

 each of these years, cruises were conducted in every month 

 and he presented monthly total larval abundances by year 

 in tabular form. His findings showed that, within the region 

 bounded by CalCOFI lines 60-137 (i.e. San Francisco, CA, to 

 Magdalena Bay, Mexico), the mean date of preflexion larval 

 abundance (// ,) encompassed only four days among those 

 five years, which together spanned two decades. Similarly, 

 with the exception of 1972 (an El Nino year) the standard 

 deviation of the preflexion larval distribution (Op) varied by 

 only five days. These results are consistent with other stud- 

 ies that have shown a remarkable consistency in the timing 

 offish reproduction (Gushing, 1969; Anderson, 1984; Peder- 

 sen, 1984; Picquelle and Megrey, 1993; Gillet et al., 1995; 

 but see Hutchings and Myers, 1994). Thus, although mis- 

 specification of the mean time of spawning has the potential 

 to seriously impact the biomass estimate, the observed data 

 suggest that in this application the effect is negligible. 



Perhaps a more important structural assumption we 

 have made is that the spawning season can be represent- 

 ed by a normal distribution. Although Saville ( 1956, 1964) 

 advocated use of the normal distribution for this purpose, 

 we question the generality and accuracy of this symmetric 

 function when used to model spawning seasonality. In the 

 case of shortbelly rockfish, the fit of the five data points to the 

 distribution was reasonably good (dashed line in Fig. 13). 

 Even so, we note that the observed data were monthly 

 means and the April value did not conform well to ex- 

 pectation. Therefore, in future applications of the larval 

 production method we recommend strongly that a well-de- 

 fined year-specific estimate of the seasonal distribution of 

 spawning activity (i.e. the production rate of age-0 larvae) 

 be obtained. In principle these data could be gathered by 

 high-frequency sampling of either the larval or adult por- 

 tions of the stock, and even through monitoring the matu- 

 rity of females in commercial landings. 



It is also true that the entire spatial distribution of early 

 larvae must be surveyed in order for the larval production 

 estimate (A'^q) to represent the complete spawning stock. 

 This concern is not unique to this assessment, however; it 

 is a requirement that must be satisfied whenever egg and 

 larval surveys are used to estimate the absolute biomass 

 of a fish stock. Nonetheless, in this application it is not 

 likely to have been fully met (Fig. 11). Although the pri- 

 mary spawning concentration of shortbelly rockfish along 

 the central California seems to have been largely encom- 

 passed, there is evidence that the offshore extent of very 

 young lai"vae was not fully captured 



Acknowledgments 



Wc would like to thank all the current and fornn'r mem- 

 bers of the (uoundfish Analysis and Physiological Ecol- 



